Changes in the Rate of Sea Level Rise

 

Guest Post by Willis Eschenbach

There’s been some discussion of the rate of sea level rise lately, so I thought I’d take a look at some underlying data.

I started with a 2016 paper by the modern master of failed serial doomcasting, James Hansen. It has the frightening title of Ice melt, sea level rise and superstorms: evidence from paleoclimate data, climate modeling, and modern observations that 2°C global warming could be dangerous… yikes! Be very afraid!

In Figure 29 of that paper, Hansen claims to show that sea level rise has been accelerating, from 0.6 mm/year from 1900 to 1930, to 1.4 mm/year from 1930 to 1992, and 2.6 mm/year from 1993 to 2015.

hansen global sea level change.png

Now, as is far too common with this charming fellow, James Hansen is playing fast and loose with the facts. First, he’s taken the data of Church and White from 1900 to 1992 and multiplied it by 0.78. This has the effect of flattening the record and thus reducing the prior sea level trends … which of course makes it seem like there is more acceleration than might actually exist.

Next, he has cherry-picked the Church and White (C&W) data shown in blue. The C&W data actually goes from 1860 to 2009, and Hansen and his merry band have chopped off both the early and the late part of the data.

Finally, post-1992 he has spliced the satellite data (with a trend which differs from Hansen’s specially flattened tide gauge data) on to the end of the tide gauge data. They are measuring different things, and thus cannot be directly compared. This is the reason for the “knuckle” in Hansen’s Figure 29 at the year 1993.

In any case, as those who know me are aware, I prefer to go to the original data. I don’t believe anyone until I’ve run the numbers myself … and this is another example of why I do that. As my beloved grandmother used to say, “You can believe half of what you read, a quarter of what you hear … and an eighth of what you say” … and Hansen’s claims seemed unbelievable.

In this instance I went to the Church & White (2011) paper cited by Hansen above, entitled Sea-Level Rise from the Late 19th to the Early 21st Century.  (I guess C&W didn’t get the memo about how scientific papers now require terrifying titles.) I digitized the C&W Figure 5 and analyzed it. This is their Figure 5:

church and white 2011 fig 5.png

(Notice that because this data has not been subjected to the special Hansen flattening, the trends of the tide gauge and the satellite altimeter data are similar … but I digress.)

In particular, I wanted to look at the trends. Since Hansen had used a 31-year trend from 1900-1930, I looked at the same length trends. Here are all of the trailing 31-year trends, indexed by the final year of each trend, including of course the 1900-1930 trend referenced by Hansen et al.

thirty one year trends in sea level.png

I’m sure you can see the problem with making any general statements about whether or not there is any acceleration in the rate of sea level rise during the last hundred years or so …

You can also see why Hansen cherry-picked the 1900-1930 trend as his data to try to show acceleration … because if he’d used 1930-1960 instead, there wouldn’t be any acceleration to show.

Here’s my conclusion in all of this. Until we can say why the rate of sea level rise:

• decelerated from the start of the C&W record until 1930

• accelerated rapidly until 1960

• decelerated for the next ten years

• stayed about the same from 1970 to 2000

• and then started accelerating again,

… until that time, I say that making just about any statement about sea level acceleration is premature. However, one thing is clear:

There is no simple relationship between CO2 levels and the rate of sea level rise …


My best to all on a lovely spring day. Fog in the morning, sun in the afternoon, and now a foggy night. When the fog rolls in like this in the evening, on nights like tonight it sometimes traps the sound of the foghorn on the Bodega Bay breakwater six miles (ten km.) away, and carries that mournful wail up the hill to draw my mind away, away to the eternal sea …

w.

As Always: When you comment, please quote the exact words you are discussing so that we can all understand your exact subject. Misunderstandings are the bane of the intarwebs—please avoid them by being crystal clear about the topic of your comment.

Data: The digitized C&W data is below:

Year Sea Level (mm)

1860 -189.26

1861 -188

1862 -181.91

1863 -190.25

1864 -183.17

1865 -195.65

1866 -173.16

1867 -165.84

1868 -165.97

1869 -178.11

1870 -185.01

1871 -188.48

1872 -176.14

1873 -183.09

1874 -186.54

1875 -194.25

1876 -173.47

1877 -157.7

1878 -142.53

1879 -160.14

1880 -156.5

1881 -151.98

1882 -167.18

1883 -163.06

1884 -142.54

1885 -143.86

1886 -145.98

1887 -150.93

1888 -149.59

1889 -148.08

1890 -146.2

1891 -147.32

1892 -144.44

1893 -140.21

1894 -148.15

1895 -138.29

1896 -144.3

1897 -140.22

1898 -130.42

1899 -123.61

1900 -128.64

1901 -128.78

1902 -124.68

1903 -117.49

1904 -125.51

1905 -131.25

1906 -124.66

1907 -126.68

1908 -128.87

1909 -125.03

1910 -125.02

1911 -116.97

1912 -119.44

1913 -118

1914 -111.49

1915 -103.77

1916 -105.22

1917 -109.45

1918 -111.33

1919 -110.29

1920 -108.7

1921 -106.76

1922 -107.55

1923 -106.2

1924 -113.18

1925 -111.98

1926 -105.11

1927 -105.62

1928 -109.52

1929 -108.45

1930 -105.16

1931 -105.19

1932 -100.24

1933 -95.73

1934 -99.6

1935 -95.54

1936 -97.99

1937 -93.5

1938 -90.97

1939 -85.54

1940 -90.15

1941 -78.75

1942 -78.74

1943 -78.26

1944 -84.11

1945 -82.05

1946 -75.11

1947 -71.97

1948 -66.46

1949 -67.77

1950 -65.8

1951 -56.29

1952 -58.63

1953 -54.39

1954 -56.98

1955 -55.69

1956 -60.77

1957 -47.21

1958 -46.93

1959 -46.46

1960 -44.06

1961 -37.11

1962 -40.57

1963 -42.94

1964 -50.72

1965 -39.43

1966 -44.65

1967 -43.95

1968 -43.36

1969 -36.39

1970 -38.3

1971 -33.01

1972 -24.35

1973 -29.12

1974 -18.55

1975 -19.64

1976 -20.5

1977 -22.17

1978 -16.03

1979 -20.79

1980 -15.65

1981 -3.64

1982 -7.17

1983 -0.27

1984 -0.67

1985 -10.31

1986 -10.55

1987 -9.99

1988 -6.51

1989 -1.08

1990 0.43

1991 2.78

1992 6.46

1993 2.45

1994 4.85

1995 8.76

1996 12.28

1997 22.09

1998 15.39

1999 20.05

2000 21.88

2001 26.62

2002 26.53

2003 34.82

2004 34.47

2005 34.04

2006 35

2007 37.88

2008 44.69

2009 52.43

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185 thoughts on “Changes in the Rate of Sea Level Rise

  1. Wouldn’t you expect to see a little acceleration of SLR coming out of the Little Ice Age? I would also blame to a lesser degree all the ground water pumped out for irrigation would have a slight impact as well.

    • The oceans are huge (and I mean HUGE) heat-sinks. Even with alleged significant atmospheric warming, it will take a LONG time to impact the oceans.

      • Oh, I thought I had read that the oceans had been impacted significantly in more than one way when massive amounts of cold water were released due to the failure of ice dams.

      • My thoughts too Javert and that is why the accelerations and decelerations in the rate of sea level rise suggest either no dependency on CO2, which has been rising steadily, or a general lack of accuracy or reliability of the data.

      • …and yet, one rain storm in one small part of Australia lower sea level……..bullcrap

      • Causal relationships between systems with masses 300x different usually run from the more massive to the less. I would imagine CO2 is less than a rounding error for the oceans, except perhaps on millennial scales or larger.

      • “…it will take a LONG time to impact the oceans.”
        Apparently it takes 800 years.

    • There was a dramatic acceleration at the end of the Little Ice Age, pretty well as you’d expect. Up to about 1850 there was little or no sea level rise that may have lasted several centuries. But at about 1850 (the end of the LIA) the modern sea level rise started at 1 or 2 mm/year. Since 1850 the rate has been remarkably constant.
      It’s a perfect hockey stick – except that the blade started in 1850! Correct me if I’m wrong, but I don’t think SUV’s or mass air travel had really taken off in 1850.
      Chris

    • There is no simple relationship between CO2 levels and the rate of sea level rise …
      =======
      The is a better correlation between sea level rise and me peeing in the ocean than there is to sea level rise and CO2.

    • Sea level has been rising not since the end of the LIA, but since its depths during the Maunder Minimum, c. AD 1695.

    • “Wouldn’t you expect to see a little acceleration of SLR coming out of the Little Ice Age?”
      Since sea level rise is a artifact of temp….I would expect to see it flatten out because temps have been flat

  2. Virtually all tide gauges – worldwide – show linear trends and inconsequential (de)acceleration; take your pick, affected by local tectonics. In places that are tectonically inert, moving neither up nor down, Sea-Level is rising between 1mm and 1.4mm per year. Slipshavn (Nyborg) Denmark is a good example. All the rest (& Hansen et al is among them) is pandered drivel, by people wallowing in grants, and accepting prizes from unknown foundations and governments desperate to raise revenue. Sad, very sad!!!

    • Hansen’s Figure 29 is a bad joke and I’m thankfully glad that Willis zeroed in on it!!!

    • Yes tomwys1, its a sick sad world. The water levels at Fort Denison in Sydney show similar and no acceleration. I am living in hope that Tim Flannery walks out onto the road in front of my car one day. .

    • Second to Jmac (and everyone else). Hard to believe Hansen expected to be taken seriously. Oh wait, this was just political agitprop…..

  3. The entire notion that picking one variable (CO2) out of the 50 odd variables to make it chief culprit and trying to make it fit the hypothesis is pseudoscience. Manipulating data to make it fit with some hypothesis is NOT science, it is fraud.
    The persistent fraud will discredit science across the board.

  4. Depuis des millions d’années il y a des milliards de km³ d’eaux douces (venus des pluies, des fleuves & des rivières) qui se sont déversés dans les mers & océans… SANS QU’ELLES OU ILS NE MONTENT !!! Çà alors ! Tout simplement parce que l’eau s’infiltre continuellement dans les planchers océaniques et maritimes vers le magma où cette soupe toxique (les poissons chient dans la mer !) y est chauffée/bouillie et remonte donc (comme dans une cafetière électrique) vers les sources (chaudes ou froides suivant l’altitude) et vers les nappes phréatique qu’elle remplit.
    For millions of years there are billions of km³ of fresh water that are poured into the seas & oceans … WITHOUT WHERE THEY DO NOT UP !!! That’s it! Quite simply because the water is continuously infiltrating the ocean and sea floors towards the magma where this poisonous soup (the fish shit in the sea!) It is heated / boiled and goes back up (as in a coffee maker) to the sources (hot or cold depending on the altitude) and the groundwater that it fills.

  5. Hansen has his fingerprints on a lot of what’s wrong with climate science. He was the first to misapply Bode’s feedback analysis to the climate, is largely responsible for the fake legitimacy of homogenization and has produced numerous predictions of scenarios that failed to materialize and none that did. Given this guys history of buffoonery, why would anyone take anything he says seriously?

    • the great climate prophet’s time is coming. When we hit the minimum this September his prediction that the Arctic would be ice free in the summer will be falsified. Then in a few more years when all of the West Side Hwy remains above SL he will be shown to be wrong again. Has he made any other predictions for which he can be held accountable during our life times?

    • Because, and I say this much more in sadness than in anger, the public
      1) never really grasps the details of the claims to fully grasp that they failed to materialize, and
      2) has a collective attention span of about 30 seconds, so is off to the next sex scandal, etc., on the MSM narrative, and
      3) Climate Change (TM) constantly evolves to ensure its non-falsifiability.
      Just as politicians have an advantage from name recognition (“all publicity is good publicity”), Hansen is a “world-renowned climate scientist”. I believe that’s his official title in the stylebook isn’t it?

    • Could you be a little more specific about “first to misapply Bode’s feedback analysis to the climate”?
      I’m no Hansen fan, and I don’t for a moment believe the climate system exhibits much net positive feedback. Apart from the improbably high feedback parameters, though, I’ve yet to see anyone explain how “Bode’s” feedback analysis is wrong as applied to the climate system.
      In other words, you don’t mean there’s something wrong with \Delta T_\mathrm{eq}=\dfrac{\lambda_0}{1-\lambda_0f}\Delta F_{\mathrm{ind}}, do you?

      • sailboarder:
        You may well be right about its being applied incorrectly. However, I’d caution against relying on Lord Monckton as authority for that proposition.
        In a recent series of posts on this site he completely misconstrued the equation he represented as based on Bode’s chapter 3. And he seemed to confuse what in some circles are known as “small-signal” quantities with the “large-signal” quantities they imply.
        Although he’s been going on about feedback for years, he still flubs the most-basic concepts. So at least on that topic you’re better off looking elsewhere.

      • Joe,
        There are 2 preconditions for applying Bode’s LINEAR feedback analysis set out in the first 2 paragraphs of his book. This book is still the definitive reference on electronic feedback amplifiers, despite being written nearly a century ago. This book was the only feedback related reference in either Hansen’s or Schlesinger’s papers on climate system feedback. These papers comprised the primary theoretical justification for a sensitivity high enough to establish the IPCC and UNFCCC.
        The first missing precondition is strict linearity between the input and output and there’s absolutely no physics that supports a linear relationship between W/m^2 and degrees K as the input and output of a linear system. The units of lambda0 are K per W/m^2 and f is W/m^2 per degree K, where these units themselves are meaningless as are the Cn constants quantifying the many ‘feedback’ terms. Another consequence of linearity is that the absolute and incremental gains (sensitivity) must be the same and the incremental application of climate feedback applied to sensitivity estimations is itself non sequitur.
        Second is the requirement for an implicit, internal source of Joules to power the gain. This can’t be the forcing input (the Sun) since this is already accounted for as the ‘signal’ input to the system. It would be like plugging a signal source into both the source input and the power cord of an audio amplifier.
        A Bode feedback amplifier measures the sum of the input and feedback to determine how much output to deliver from its implicit power supply. In the climate system, the source of the output Joules are the input Joules (not an implicit power supply) and this COE constraint has been ignored because Bode ignores it owing to his 2 preconditions.
        The equation you cited is pure garbage and has absolutely no correspondence to anything having to do with the climate. There’s so much wrong with how Hansen and then Schlesinger applied feedback analysis to the climate, it would be amusing that anyone actually bought this garbage if the consequences of the IPCC’s oppressive agenda based on this weren’t so dire.
        https://wattsupwiththat.com/2016/09/07/how-climate-feedback-is-fubar/

      • Joe,
        Regarding Monkton’s feedback analysis, he’s basically correct. The flaws in his analysis are mostly due to him trying to use language and terms that are consistent with how consensus climate science applies them, rather than how Bode applies them.
        Regarding the difference between small signal and large signal, there’s no difference in a linear amplifier, as the gain is constant and independent of the input. When the signal gets so large that the output starts to clip, the amplifier is no longer operating in its linear range and Bode’s analysis no longer applies.
        The only distinction to be made is between the small signal or AC gain and the DC gain setting the operating point, where the DC gain can be different from the AC gain. For example, adding a resistor to the emitter leg of a transistor amplifier sets and stabilizes the DC gain with negative feedback, but adding a bypass capacitor across it that has a low impedance at the operating frequencies and the AC gain at those frequencies will be much higher as the negative feedback gets reduced. This distinction doesn’t apply to the climate system, as again, it depends on an internal source of Joules to power the gain.

      • co2isnotevil:
        Thanks for your input. But I’m having trouble getting my mind around your reasoning.
        I do recognize that the circuits Bode had in mind employed power supplies not reflected in the math, but to me that means the math can be applied to something that doesn’t have a power supply. And those circuits were vacuum-tube circuits, whose relationships of, e.g., plate current to grid-to-cathode voltage were highly non-linear. So he was obviously linearizing if he made a linearity assumption. And that’s presumably what Hansen did.
        Let’s remind ourselves of what linearization involves. An output T_\mathrm{eq} is a not-necessarily linear function g of an intermediate quantity F_\mathrm{tot}. F_\mathrm{tot} in turn is the sum of (1) the (output-independent) input F_\mathrm{ind} and (2) feedback F_\mathrm{dep} that’s a not-necessarily linear function f of the output T_\mathrm{eq}.
        T_\mathrm{eq}=g(F_{\mathrm{tot}})=g(F_{\mathrm{ind}}+F_{\mathrm{dep}})=g[F_{\mathrm{ind}}+f(T_\mathrm{eq})].
        Note that no power supplies were employed in building that equation.
        In these contexts it is the temperature-independent portion F_{\mathrm{ind}} of g‘s argument that is normally thought of as the system’s input. But the g and f functions aren’t usually so obliging as to permit us analytically to obtain from that general large-signal equation T_\mathrm{eq}=g[F_{\mathrm{ind}}+f(T_\mathrm{eq})] a closed-form relationship between the input and the output. That is, we can’t in general find a function h analytically such that T_\mathrm{eq}=h(F_{\mathrm{ind}}). Even when specific instances of those functions do admit of analytic solution, moreover, the resultant h is not usually linear.
        But linear math would make analysis easier, so analysts often “linearize” the system by concentrating on small changes from a known equilibrium state to other (in this context, equilibrium) states. In the equilibrium context we’re dealing with here, linearization involves differentiating the foregoing large-signal equation to obtain:
        dT=g'\left[F_{\mathrm{ind}}+f(T_\mathrm{eq})\right]\cdot\left[dF_{\mathrm{ind}}+f'(T_\mathrm{eq})dT\right],
        where g' and f' are the first derivatives of g and f. The derivatives are then evaluated at some known equilibrium state (F_0,T_0), where F_0 may include a temperature-independent constituent F_{\mathrm{ind}\,0} such that F_0=F_{\mathrm{ind}\,0}+f(T_0). If we additionally replace the infinitesimal differentials with finite differences, we obtain the following approximation:
        \Delta T_\mathrm{eq}\approx g'(F_0)\cdot\left[\Delta F_{\mathrm{ind}}+f'(T_0)\Delta T_\mathrm{eq}\right].
        After making the substitutions \lambda_0= g'(F_0) and k= f'(T_0) and converting approximation to equality, the response perturbation \Delta T_\mathrm{eq} can be isolated to obtain the form I described above:
        \Delta T_\mathrm{eq}=\dfrac{\lambda_0}{1-\lambda_0k}\Delta F_{\mathrm{ind}}.
        (Here we use k instead of f because we’ve used f already, for the feedback function rather than the feedback coefficient.)
        If you’ve followed that derivation you’ll see that nothing in it was based on an external power supply. And, yes, the equation is linear, but it’s the linearization of a non-linear equation.
        So I don’t see how power supplies or nonlinearity make the equation invalid, so long as the forcing and temperature increments are not large.

      • Joe,
        The non linearity of a vacuum tube (or transistor for that matter) is irrelevant to Bode’s analysis because a DC bias moves the device into the linear portion of its transfer curve. The non linearity is only present in a small region where the device is just starting to conduct. Once a sufficient current is flowing through the device, the response of its output to the input signal becomes linear until the output runs out of power supply and it starts to clip. Bode’s analysis assumes strictly linear systems, not linear approximations of non linear relationships, besides, the assumption of approximate linearity between W/m^2 and degrees K is far from valid over the range of temperatures found on the planet.
        A misunderstanding arises by conflating the DC operating point with the steady state average gain of the system in order to establish a false distinction between the absolute gain and the incremental gain. BTW, gain is the proper term, not sensitivity, which per Bode has a completely different meaning. Also, per Bode, gain is dimensionless and the dimensionless small signal gain required to amplify the 240 W/m^2 of incident solar energy into the 385 W/m^2 of surface emissions at its average temperature is about 1.6. This is not the DC gain, but the average small signal gain which is the same as the incremental small signal gain where each W/m^2 of input results in 1.6 W/m^2 of surface output. There is no DC gain or DC bias because there is no DC power supply. The 240 W/m^2 of input is the small signal input to a passive (i.e. no internal source of energy) climate system.
        What this means is that the incremental gain applied to the next W/m^2 is also 1.6 which means that the next W/m^2 increases surface emissions by 1.6 W/m^2, corresponding to a temperature increase from about 287K to 287.3K which is far from the 0.4-1.2 C claimed to arise from 1 W/m^2 of incremental solar input and corresponds to an effect from the 3.7 W/m^2 of EQUIVALENT forcing said to arise by doubling CO2 concentrations of about 1.1C.
        The idea that the next W/m^2 can increase surface emissions by 4.3 W/m^2 corresponding to the nominal 0.8C increase claimed is absurd beyond reason. Based on how Bode’s analysis was applied, the only possible source to replenish the additional 3.3 W/m^2 of surface emissions is the implicit, internal source of Joules that’s not actually present in the system. The reason of course is that COE dictates that all Joules contribute equally to the work producing a result. In fact, Joules are the units of work and Watts are just a rate of Joules, which integrated over time becomes work.
        Linearizing the system is the correct thing to do, but the proper linearization is between forcing and surface emissions, which is already quite linear, and not between forcing and the surface temperature. Note that degrees K and W/m^2 interchangeably represent the same thing via the SB LAW, the only difference is the units. This is the fundamental error that’s making climate science so hard to get right. The problem with linearizing the relationship between W/m^2 and temperature is that this infers a constant derivative (i.e. gain/sensitivity). Since the relationship actually goes as T^4, the derivative goes as 1/T^3, thus the incremental gain where the output is expressed as a temperature is far from being a constant.
        Forcing and surface emissions have the same units (W/m^2). Feedback must also have the same units as the input. The feedback fraction is defined as the dimensionless fraction of the output added back to the input and can be between -1 and 1, thus when the output has the same units as the input, the feedback term also has the proper units and can be summed with the input. The bottom line is that you can’t add degrees K to W/m^2 and the Cn constants that convert one to the other have no physical justification and again are only claimed to be ‘approximately linear’.
        Why go through all this effort of coercing a linear relationship between degrees K and W/m^2 when a nearly perfect linear relationship already exists between W/m^2 of forcing and the equivalent W/m^2 of surface emissions? The are only 2 possible reasons. One is incompetence and the other is to confuse and deceive.

      • Joe,
        Let me try to explain this from another angle.
        Analyzing passive circuits of inductors, capacitors, transformers and resistors in terms of how they behave in the time domain requires solving complex sets of simultaneous differential equations. If instead, we apply the Laplace transform to convert between the time domain and the frequency domain, the analysis is simplified to the linear application of Ohms Law on resistance that has both real and imaginary parts. Afterwards, we can apply the Laplace transform in reverse to produce time domain results.
        The SB Law is the bidirectional transformation function that converts between the non linear domain of degrees K and the linear domain of energy. In fact, the T^4 component of the SB LAW is responsible for most of the stated non linearity!
        The correct way to analyse the climate is to convert temperatures into W/m^2 using the SB LAW, perform linear calculations on W/m^2 and convert the resulting W/m^2 into a temperature using SB in reverse. To calculate a delta T, do this before and after the delta F and subtract the resulting T’s from each other.
        The reason consensus climate science rejects this (or more precisely fails to consider it), is because it produces an unambiguous answer that’s not the answer they need, hence all the obfuscation from excess complexity, adding the wiggle room necessary to accommodate what the laws of physics can not.

      • co2isnotevil:

        The correct way to analyse the climate is to convert temperatures into W/m^2 using the SB LAW, perform linear calculations on W/m^2 and convert the resulting W/m^2 into a temperature using SB in reverse.

        I think I agree with that as an abstract proposition, but I don’t see why you think they’re not doing it. In contrast, you seem to think Lord Monkton’s right, and he adds temperatures where he should be adding forcings. There seems to be a disconnect.

      • co2isnotevil:

        Regarding Monkton’s feedback analysis, he’s basically correct.

        Actually, he got it wildly wrong, as you can see if you work through what in his fourth post he introduced as the “standard, mainstream” equation that is “universal in all dynamical systems except climate”:
        T_{\mathrm{eq}}=\dfrac{\mu T_{\mathrm{ref}}}{1-\mu\beta}.
        In form, this equation can indeed be found in Bode, Network Analysis and Feedback Amplifier Design. But Lord Monckton completely misconstrued it.
        The problem is that he switched the T_{\mathrm{ref}} symbol’s meaning when he introduced the “standard, normal” equation. He had previously used T_{\mathrm{ref}} to represent the sum T_{\mathrm{ref}\,0}+\Delta T_{\mathrm{ref}} of a constant reference portion and a variable portion: a variable. (See, for instance, his first post’s paragraph beginning with “The error.”) In his proposed equation, though, he used it to represent only the constant, reference-value portion T_{\mathrm{ref}\,0}. So the equation’s form makes it seem that the system input is a constant. Meanwhile, he represented the actual input’s variable component \Delta T_{\mathrm{ref}} in a highly unorthodox fashion. Specifically, he represented it in a variation of the gain parameter \mu: \mu=1-\Delta T_{\mathrm{ref}}/ T_{\mathrm{ref}}.
        Instead of causing the output to increase by increasing the input, that is, he did so by increasing the gain. He compounded the unconventional parameter dependence by making the feedback coefficient \beta depend on \mu and, worse, on the output T_{\mathrm{eq}}: \beta=1/\mu+T_{\mathrm{eq}}/ T_{\mathrm{ref}} .
        The overall result is that for every positive value of \beta there’s an input value \Delta T_\mathrm{ref} for which the output T_\mathrm{eq} blows up. That’s not linear, and it’s not what Bode intended.
        I’m afraid I didn’t find in your responses a compelling argument for the proposition that the equation I asked about is “pure garbage.” To me your argument seems based on misunderstanding the greenhouse effect—and, for that matter, Bode’s technological milieu. (Although there are some vacuum-tube operating regimes that are less nonlinear than others, for example, the whole reason for negative feedback is to combat those devices’ nonlinearities.)
        Nonetheless, I thank you for taking the time to respond.

      • Joe, Let me put it into simpler terms. Without an external power supply you can only get an output equal to the input. If you try to assume feedback will increase the output when there is no external power, where does the increased power come from? Continue down that road and you will invent perpetual motion as you are creating energy from nowhere!

      • Joe,
        ” … but I don’t see why you think they’re not doing it. In contrast, you seem to think Lord Monkton’s right,”
        Consensus climate science is not doing this because if they did, they would get a sensitivity less then the lower limit claimed in IPCC reports and the debate would have ended decades ago.
        The IPCC calculates the sensitivity to doubling CO2 as the 3.7 W/m^2 of EQUIVALENT forcing that arises by doubling CO2 times the sensitivity factor, which they cite, without foundation, as 0.8C +/- 0.4C per W/m^2 (3.7*0.8 = 3C). They then curve fit arbitrary values of lambda0 and f so that deltaT/deltaF is the 0.8C they need it to be. They really need to choose arbitrary values of lambda0 and f such that deltaT/deltaF is the 0.3C that fits the skeptics estimates of the ECS. This still won’t make the equation correct, as the upper limit on the actual sensitivity is highly temperature dependent and given by 1/(4eoT^3), where e is the ratio between the average planet emissions and average surface emissions, o is the SB constant and T is the average surface temperature in degrees K. The lower limit is given by the same equation, except with e=1.
        The problem with the derivation of the equation you cited is assuming the relationship between T and P is linear is to assume that dT/dP is constant, and it’s not. This ends up decoupling the magnitude of dT/dP from the constraints of T^4/P allowing dT/dP to be arbitrarily high. After all, 0.8C per W/m^2 of forcing sounds plausible enough, while 4.3 W/m^2 of incremental surface emissions per W/m^2 of forcing is an obvious violation of COE, even as both represent the same thing. Feedback then becomes the only possible source replenishing the additional 3.3 W/m^2 of emissions and any system where the feedback exceeds the forcing is unconditionally unstable. Relative to the climate, the T^4/P constraint is about 1.6 W/m^2 of surface emissions per W/m^2 of forcing, or about 600mw of ‘feedback’ per W/m^2 of forcing.
        Climate science doesn’t understand that the exponent in T^4 is immutable from first principles and no feedback or anything else can change this, moreover; it’s the non linearity consequential to this exponent that they try fudge away, when there’s a far easier way.
        My point still stands. Why make gross assumptions and invent a bunch of complexity to linearize something intrinsically non linear, when a simple transformation makes the relevant relationships trivially linear?
        Regarding Monkton’s analysis, conceptually, he’s right, but there are errors in his analysis. As I mentioned, these seem to be the result of attempting to be consistent with the bad assumptions and subverted terminology used by consensus climate science. For example, the terms forcing, feedback and sensitivity are all defined in Bode’s book, but as applied to the climate, they have retained the same meaning while being subverted to represent something so different that the original meanings are no longer relevant. More specifically, the mu term in Bode is also referred to as the open loop gain, is a dimensionless constant and is why Monkton went with the form of a ratio of temperatures, as ratios are the only way to arrive at dimensionless values and he was stuck with using temperatures as the inputs and outputs, rather than power densities which are already intrinsically linearly related to each other. Additionally, the beta term is the fraction of the output returned as feedback and is also a dimensionless constant and has the same issues. What he did was to shoehorn the climate feedback model into the Bode model in a way more consistent with Bode, and as you noticed, it didn’t make much sense and if once you understand Bode, it makes even less sense the way it has been framed by the consensus climate science.

      • Jim Gorman:

        Without an external power supply you can only get an output equal to the input.

        Wrong.
        A transformer, for example, needs no external power source for its output voltage to exceed its input voltage.
        A voltage-doubler circuit requires no external power source for its output voltage to exceed its input voltage.
        More to the point, in our equations the input is forcing and the output is temperature. How great a temperature is greater than how much forcing?
        The power source is the sun. The temperature is a measure of how much of that energy from the sun has accumulated before the power out to space equals the power out to the sun.
        Knowing what the inputs and outputs are would make your opinion on whether one can exceed the other more informed.

      • Jim Gorman:

        Without an external power supply you can only get an output equal to the input. If you try to assume feedback will increase the output when there is no external power, where does the increased power come from?

        Joe Born responded:

        Wrong.
        A transformer, for example, needs no external power source for its output voltage to exceed its input voltage.

        No Joe. You’re wrong. Jim asked “where does the increased power come from?” There is no increase in power with a transformer. Double the voltage and you half the current. Nor is there an increase in power with a voltage doubler.
        The Bode feedback model requires a amplifier. Amplifiers by definition are an active element that requires an external power source.
        3.2 Elementary Theory of Feedback Circuits

        In its simplest form, a feedback amplifier can be regarded as a combination of an ordinary amplifier, or u circuit, and a passive network, or B circuit, by means of which a portion of the output of the u circuit can be returned to its input.

        The Bode model simply doesn’t apply to the “climate feedback” which has no additional energy sources. A proper model for the “climate feedback” can only contain passive elements. Use of the Bode model is grossly inappropriate.

      • Greg,
        Yes, you’re exactly correct. You seem to understand Bode and are similarly amused at how anyone can think a transformer is an active amplifier per Bode. You’ll probably also get why this passive network of the climate makes the most sense.
        Model the atmosphere as a transmission line between the surface and space that’s well matched to free space at TOA, but mismatched at the boundary with the surface. The source of the ‘feedback’ power is surface emissions reflected back to the surface by the impedance mismatch.

      • co2isnotevil,
        I was going to respond a couple of times today but you kept beating me to it. Damn you!
        A transmission line model makes a lot of sense. Never considered that angle. I would add thermal capacitance for the energy that is absorbed by the surface. Having adequate data to construct a model is another story.
        What I don’t get is how anybody (with at least high school physics) could not see the “climate feedback” model as 100% passive. Calling it “feedback” … I just don’t know what to say. Words have meaning. Obfuscation of the technical meaning of the word is just so wrong.

      • Greg F
        You are confusing the mathematics with the application. Bode applied the mathematics to an amplifier, which is indeed an active-element. Hansen applied the mathematics to the earth, which indeed is a passive element. But the math requires no active element.
        What carbon dioxide does is increase the atmosphere’s optical depth, which increases the average altitude of the radiators that space receives earth-sourced radiation from, which, lapse rate being what it is, increases the difference between the surface temperature and the effective radiation temperature. For a given surface temperature, that is, it reduces the effective radiation temperature and thus causes an imbalance between the incoming radiation, which hasn’t changed, and the outgoing radiation, which has fallen.
        If we ignore lapse-rate changes, then the surface temperature has to increase by the necessary emission-altitude temperature increase. (This means that the change in surface radiation exceeds the forcing change, a fact that seems to bother co2isnotevil). Finally, the resultant surface-temperature increase causes more water vapor, and, according to Hansen’s hypothesis (which I question), that causes more forcing. That additional, temperature-dependent forcing is what’s referred to as feedback, since the output quantity, temperature, is causing a change in the input quantity, forcing.
        Note that all of this happens without any external power source: on average, the power into the system equals the power out of the system, with the exception that the earth may occasionally change its temperature by temporarily emitting more or less energy than it absorbs.
        If you can’t explain why the feedback equation doesn’t describe this, then your argument for its being “pure garbage” is not compelling.

      • You are confusing the mathematics with the application. Bode applied the mathematics to an amplifier, which is indeed an active-element. Hansen applied the mathematics to the earth, which indeed is a passive element.

        You are still wrong. Bode applied the mathematics to a system that is composed of an active (μ) and passive (β) element. Hansen incorrectly applied the mathematics where there is no active element.

        But the math requires no active element.

        It most certainly does require an active element.

      • Greg F

        It most certainly does require an active element.

        Ah, yes, the “Yes, it is, too” argument. Very effective.
        Serious discussion, please. I’m not interested in a high-school debate. If you want to participate in an adult conversation, please identify what in the equation that requires an active element. Yes, Bode used \mu to characterize his active element, but there’s no reason why it can’t be used to characterize a passive one.
        Here, let me help:
        For the sake of simplicity, let’s say T_\mathrm{eq}=g(F_\mathrm{tot})=(T/\sigma)^{1/4}\rightarrow F_\mathrm{tot}=g^{-1}(T_\mathrm{eq})=\sigma T^4. (The actual function is more complicated, but I’m suggesting an easy function for discussion purposes.) That gives surface temperature as a function of the total forcing that caused it. (Again, that’s not precisely correct, but it doesn’t matter for present purposes.) All passive. No outside power sources involved.
        The total forcing F_\mathrm{tot} is the sum of temperature-independent forcing F_\mathrm{ind}, which is caused by things like human-generated CO2, and temperature-dependent forcing F_\mathrm{dep}=f(T_\mathrm{eq}), which is caused by, e.g. water vapor: T_\mathrm{eq}=g(F_\mathrm{ind}) Presumably f, like g, is highly nonlinear. If we adopt \mu=g'(F_0) and \beta=f'(T_0), we get:
        T_\mathrm{eq}=T_0+\Delta T_\mathrm{eq}=T_0+\mu(\Delta F_\mathrm{ind}+\beta\Delta T_\mathrm{eq}),
        or
        \Delta T_\mathrm{eq}=\dfrac{\mu}{1-\mu\beta}\Delta F_\mathrm{ind}.
        Same equation as Bode’s, but no active elements involved.
        There, I’ve laid it all out there for you. All you have to do is identify where it’s wrong and give a logical reason for your belief. That’s how adult discussions work.

      • Joe,
        “But the math requires no active element.”
        You have identified the feedback fubar. In fact, Bode’s math does require an active element. The active element is implied by the mu term which is why you don’t perceive it and why Hansen missed it. This is stated in the first paragraph of Bode’s book where he specified his simplifying assumptions. Mu is the open loop gain (gain with no feedback) and you can’t have any open loop gain if there’s no IMPLICIT power supply. Mu is transconductance which is a dimensionless ratio that represents the amplification of a small voltage into a high impedance on the input into a relatively larger current change on the output driving a lower impedance. If you don’t recognize this as implicit power gain, then you definitely don’t understand the math of feedback systems.
        Feedback systems can be tricky and there’s no hope of understanding how to analyze them until you thoroughly understand the implications of the simplifying assumptions. This is what led Hansen and all who followed him astray. Amateurs should not apply analysis they don’t understand.
        You also seem to be missing the distinction between voltage gain and power gain. While Bode’s math is quantifying voltage gain, it only works when power gain is implied. The reason is impedance. In Bode’s basic analysis, the input impedance is assumed to be infinite while the output impedance is assumed to be zero. The implication of this is that the input forcing plus feedback is measured by the input of an amplifier to determine how much power to deliver to the output from its implicit supply. The input impedance of the climate system is zero and the input plus forcing is consumed to produce the output power. The later is not covered by Bode’s math and requires an additional COE constraint that has never been applied to the climate system.
        Here’s how power gain works relative to impedance. If the input impedance is 1K ohms and the output load is 100 ohms, even a voltage gain of unity has a power gain of 10.

      • Yes, Bode used \mu to characterize his active element, but there’s no reason why it can’t be used to characterize a passive one.

        co2isnotevil has made a more than adequate response. As he stated μ is the open loop gain. A passive component cannot have gain. Gain requires additional energy. Why is that so hard to understand?

      • Joe,
        I mis-stated transconductance and mu. Mu is a dimensionless ratio of voltage gain calculated from the transconductance (which has units of 1/ohms) and the output impedance of the active element.
        Transconductance is the change in output current divided by the change in input voltage. As long as the output impedance is less then the input impedance, which is always the case for vacuum tubes, the potential power gain is greater than 1.
        Note that if no load is present on the output of the amplifier, there is no power gain and there is no current drawn from the implicit power supply (except for bias currents). Maximum power gain occurs when the load impedance the amplifier is driving is equal to the output impedance of the amplifier.
        BTW, Bode does talk about how to adjust the model for finite input and output impedances, but this comes much later in his book and was clearly not accounted for by Hansen who stuck with the idealized model and its many assumptions.

      • Joe,
        Getting back to the adult conversation, there are several errors in the derivation you presented.
        First is the assumption that GHG ‘forcing’ is on an equal footing with solar forcing, while only the incoming solar energy conforms to Bode’s definition of forcing. This is the result of the IPCC’s ambiguous definition and usage of forcing. When they say that doubling CO2 results in 3.7 W/m^2 of ‘forcing’ what they actually mean is that doubling CO2 is EQUIVALENT to increasing the solar forcing by 3.7 W/m^2 while keeping CO2 concentrations constant.
        The ambiguity in the definition of forcing arises from its quantification as a delta flux up/down at TOT/TOA. This assumes that an instantaneous W/m^2 more post albedo solar energy from the SUN has the same influence as an instantaneous 1 W/m^2 decrease in the size of the transparent window (i.e. increased GHG concentrations). The problem is that in the steady state, all of the incremental solar forcing affects the surface temperature, while only about 1/2 of the incremental atmospheric absorption does the same, as the other half of this absorbed energy eventually exits into space rather than being returned to the surface. This brings up another failure in pedantic climate science where it’s generally assumed that all of the energy absorbed by the atmosphere eventually ends up being returned back to the surface as ‘feedback’.
        The other error is a failure to account for COE relative to feedback power. Since the presumed gain element has an input impedance close to zero, feedback power is consumed by the input of the gain block and is no longer available as output power until it passes through the gain block once more. Your analysis counts this power twice, once as feedback power ultimately passing through the gain block to affect the temperature and again as directly contributing to replacing emissions consequential to the output temperature. Because of the malformed gain block whose input is forcing and whose output is temperature, you fail to notice that you must account for COE between the input and output. COE between the input and output doesn’t apply to a Bode linear amplifier, again owing to the implicit power supply that provides all the output Joules required. Only COE between the output power and the implicit power supply actually matters.

      • co2isnotevil:
        I’m afraid you’re making a lot of assertions with no reasoning to back them up. Just saying that a separate power supplied is implied by \mu doesn’t make it so. Just saying that transconductance is dimensionless doesn’t stop it from being expressed in siemens.
        Gain is nothing more than the ratio of output to input. It’s math. It isn’t exclusive to amplifiers. An amplifier’s input impedance is usually high, but it doesn’t have to be; people who know this stuff tell me that the input impedances of the common-base bipolar-transistor amplifiers used in some radio-frequency circuits aren’t particularly high. And an amplifier without a load may exhibit high voltage gain even though the power in exceeds the power out.
        Gain doesn’t imply a power supply. Many antennas have plenty of gain with no power supply.
        And “the input impedance of the climate system is zero and the input plus forcing is consumed to produce the output power” sounds to me like gobbledygook. In the first place, you haven’t said what quantities you think are analogous to the voltage and current whose ratio is impedance. Secondly, forcing isn’t something that’s “consumed.”
        I appreciate your efforts, but you’ve fallen far short of demonstrating that the equation I asked about is “pure garbage.”

      • Joe,
        “Just saying that a separate power supplied is implied by \mu doesn’t make it so. ”
        I’m not saying this, but Bode did and as far as I’m concerned, Bode is the definitive reference for the math describing linear feedback amplifiers. Also, I corrected my mis-statement about the dimensionality of the transconductance, which has units of 1/ohms. The dimensionless gain, mu, is the transconductance times the output impedance. And yes, mu must be dimensionless per Bode, as this is the ratio of the output change divided by the input change, where both are expressed in the same units. The only one who took liberties with assumptions without backing them up was Hansen, Schlesinger and those who echo the broken feedback analysis. Just because Hansen claims something definitely doesn’t make it true.
        The ‘power gain’ of an antenna is just a convenience for analysis as the power exiting the antenna is not increased. Instead, it’s focused on a smaller region, thus the energy density increases in some places, decreases in others and the total power remains the same.
        Relative to the climate, amplifying 240 W/m^2 of incident solar energy into 390 W/m^2 of surface emissions requires power gain if you want to model this as a feedback amplifier. The point being that power gain by the climate system is impossible without an implicit power supply that’s not the same as the forcing input. This being said, a Bode linear feedback amplifier is not an adequate model for the climate system. A passive transmission line between the surface and space (the ‘gain’ block) is a far better model. Alternatively, this can be quantified in the Z^-1 domain (discrete time) and the ‘feedback’ can be modelled as a delay element between surface emissions absorbed by the atmosphere and its return back to the surface and another between absorbed surface emissions and the fraction of them that ultimately leaves the planet.
        Apparently, the COE argument went over your head, so let me try once more. You calculate feedback power in W/m^2 as some dimensionally scaled version of the output (surface) temperature. This means that the feedback power is already contributing to the output temperature, but since it’s also being consumed by the gain block to produce the output power, this power is no longer available to contribute to the output temperature upon which the feedback power is predicated. In effect, you are counting this power twice, once as it contributes to T that the feedback is based on and again as the feedback passes through the gain block contributing further to the emissions corresponding to an increased T.
        If you can’t grasp how the input power is consumed by the climate feedback modelto produce the output power, then where is the output power coming from?

      • people who know this stuff tell me that the input impedances of the common-base bipolar-transistor amplifiers used in some radio-frequency circuits aren’t particularly high.

        They are by design due to transmission line effects. For RF they are typically 50 or 75 ohms. Network cables have a characteristic impedance of 110 ohms and network cards are all terminated with 110 ohms.

        Many antennas have plenty of gain with no power supply.

        The total radiated power doesn’t change. The “gain” is merely a function of the directivity of the antenna relative to a reference antenna. The reference antenna is usually an ideal isotropic antenna (radiates in all directions equally). Cut the radiation pattern to a half sphere and relative to the ideal isotropic antenna you would have a 3 dB gain.

      • The input impedance of a common base amplifier is low because the input current is superimposed on the output current. Common base amplifiers do not amplify current, but do amplify voltage and this produces power gain. Common emitter amplifiers amplify both voltage and current. Emitter followers amplify current, but not voltage. Since power is voltage times current, all configurations exhibit power gain.
        Even common emitter RF amplifiers have a low input impedance, but this is the consequence of some kind of transformer on the input. If a transformer has a 10:1 winding ratio, it will present a 100:1 impedance transformation. This is because a transformer multiplies voltage by the same factor it divides current, such that the voltage times the power is the same on the primary and secondary. Since impedance is voltage divided by current, increasing the voltage by N and decreasing the current by N increases the secondary impedance to N^2 times the primary impedance.

      • Oops, a small editing error.
        “voltage times the power” was originally “voltage times current” that I changed to power and didn’t delete all of the earlier phrase.

      • co2isnotevil:

        I’m not saying this, but Bode did and as far as I’m concerned, Bode is the definitive reference for the math describing linear feedback amplifiers. . . . The dimensionless gain, mu, is the transconductance times the output impedance. And yes, mu must be dimensionless per Bode, as this is the ratio of the output change divided by the input change, where both are expressed in the same units. The only one who took liberties with assumptions without backing them up was Hansen, Schlesinger and those who echo the broken feedback analysis.

        I’m afraid our background differences are getting in the way here. I’m a retired lawyer, not a scientist, so I had to deal with a wide range of fact situations over the course of my professional life. Perhaps that has made me take a broader, more-conceptual view of the relevant disciplines. Among my clients feedback was used in electronic circuits, sure, but it was used it for other things as well. And in my experience people in those fields didn’t slavishly follow Bode’s nomenclature. On page 20 of his Control Systems Theory, for example, Olle Elgerd used gain for a quantity whose dimensions are newtons per radian. I’m sure the term has also been used for all manner of other dimensioned quantities.

        If you can’t grasp how the input power is consumed by the climate feedback model to produce the output power, then where is the output power coming from?

        Who said anything about output power? In the equation we’re dealing with the output is temperature, not power. Temperature is roughly a measure of how much energy has been received over time without being re-emitted. You seem to be going by how well Hansen’s system matches Bode’s, while I’m interested in whether the equation fits.
        It’s like the level of water that has entered a bathtub without leaving through a loosely plugged drain. If you increase the inflow, there’s a temporary imbalance between the inflow and the outflow through the drain, but the resultant water-level increase causes the rate outflow to increase to reach a new equilibrium at the higher water level. If the resultant water-pressure increase pushes the plug in further, outflow decreases from what it was, so the water level increases still more: the outflow change is added to the inflow change.
        If we knew enough about the bathtub system we could write an equation for the equilibrium relationship between the equilibrium water level and inflow that would take into account the effect that water-level has on the loosely plugged drain, the equation you’d have would be of the same one we’ve been dealing with. Inflow is the input, water level is the output, and gain is expressed in meters per liter per second.
        Feedback outflow would be calculated from the output water level. If in your view this means that the outflow “is already contributing to the output” water level “but since it’s also being consumed by the gain block to produce the output power, this power is no longer available to contribute to the output” water level “upon which the feedback power is predicated,” then your view of feedback is fundamentally different from mine, and I am pessimistic about the prospects for convergence here.
        But, again, thanks for the discussion.

      • Joe,
        “In the equation we’re dealing with the output is temperature, not power.”
        And this is the fundamental reason for why consensus climate science is so screwed up. By focusing on temperature, rather than power, they conveniently ignore COE between the forcing and the temperature, thus the change in T is unconstrained by the energy requirements of the increased emissions consequential to that change. This is how they can arm wave a 0.8C increase in T that increases emissions by 4.3 W/m^2 and yet is the result of only 1 W/m^2 of new input to the system.
        Where to you think the extra 3.3 W/m^2 of surface input in excess of the forcing is coming from in order to replace the energy that’s being emitted away consequential to the presumed increase in temperature?
        You can’t decouple the temperature of a body from its emitted power where the emitted power is proportional to T^4. They are interchangeable metrics that represent the same exact state of a body and you can’t have one without the other. Since energy can’t be created or destroyed and all Joules are equivalent, the climate system must be linear in the energy domain, that is if one more Joule arrives, 1 one more must leave, or if each W/m^2 of forcing results in 1.6 W/m^2 of surface emissions, the next one must too and in no possible Universe can it be as large as the 4.3 W/m^2 required in order to be consistent with the climate sensitivity factor claimed by the IPCC. Note that the extra 0.6 W/m^2 of actual Earth ‘feedback’ is not new power as the consensus formulation allows, but power emitted by the surface in the recent past, delayed by GHG’s and clouds in the atmosphere and subsequently returned to the surface. Note as well that 0.6 W/m^2 is less than the forcing of 1 W/m^2, thus the system is unconditionally stable, as it most certainly is, otherwise, we wouldn’t even be here to worry about it.
        The fundamental problem is that the language framing climate science is broken and we can’t correct the science until we fix the language so the errors can actually be expressed. One of the biggest mistakes was to express sensitivity as a change in temperature due to a change in forcing, rather than as a change in emissions due to a change in forcing, where the deltaT is calculated by subtracting the SB equivalent temperatures of those emissions before and after the change in forcing. As best as I can tell, it was Schlesinger who formalized this as the sensitivity metric when he attempted to ‘fix’ the many mistakes in Hansen’s feedback paper. He actually added more errors and made it far more convoluted.

      • “then your view of feedback is fundamentally different from mine”
        Not necessarily. Your view and my view is also Bode’s view of how a feedback amplifier works. The problem is that how a feedback amplifier works is irrelevant to how the climate system responds to change, thus Bode’s math can’t be legitimately used to model the climate. His view of feedback and gain (incorrectly referred to as a sensitivity) is based on 2 simplifying assumptions. One is strict linearity and the other is the existence of an implicit and infinite source of Joules to power the gain. While these assumptions are embodied by the climate feedback model, they have absolutely no correspondence to how the actual climate system responds to change.
        The assumption of approximation of linearity does not conform to strict linearity. Solar power is the only true forcing input to the climate system and can not also be the implicit, infinite source of Joules powering Bode’s ideal gain block. An implicit power supply does not mean connecting the power supply input to the forcing input, it means a power supply that’s independent of the forcing.
        CO2 ‘forcing’ isn’t real. Changing CO2 concentrations changes the system, not the stimulus (forcing). Changes to the system are said to be EQUIVALENT to changes in forcing keeping the system constant. What is called CO2 ‘forcing’ is not forcing at all, but represents how much new forcing would be required to have the same effect as a change to system arising from a change in CO2 concentrations.
        BTW, your tub model of feedback doesn’t hold water.because once more, there’s no active gain, although it’s a better model of how the climate operates …

      • Co2 and Greg F ==>. You have done an excellent job of explaining. Are you guys EE’s. That’s my background. The suggestion of using transmission line theory will be important somewhere down the line. It answers my questions about delays and no extra energy being required.
        GREAT JOB!

      • Jim,
        Yes, I’m an EE (Cornell ’78). My first exposure to feedback amplifiers when I was about 11 years old and received a 5-tube radio kit for my birthday. The output stage was a 2-tube feedback amplifier (actually 3 active elements, since the 12ax7 is a dual triode) and it came complete with a theory of operation which I kept reading until I understood it.
        It’s interesting how most EE’s grasp the ‘feedback fubar’ intuitively, while many climate scientists are clueless.
        Schlesinger doesn’t, although he claims to have some kind of EE background and has asserted to me that he’s the worlds leading expert on climate system feedback. After our exchanges, it seemed to me that he was either a failing EE student or was perpetrating a masterful deception.

      • Co2 ==> BSEE University of Kansas (1972), had my General Class ham radio license at 12. Made money in high school repairing tractor fender radios. The first ones were tubes and shook themselves apart!

      • co2isnotevil:

        By focusing on temperature, rather than power, they conveniently ignore COE between the forcing and the temperature, thus the change in T is unconstrained by the energy requirements of the increased emissions consequential to that change. This is how they can arm wave a 0.8C increase in T that increases emissions by 4.3 W/m^2 and yet is the result of only 1 W/m^2 of new input to the system.

        In addition to looking at feedback differently, we lawyers also look at conservation of energy differently from the way you engineers do.
        A lawyer proposes the following scenario. A 2-electron-volt photon enters a cavity. It bounces around inside the cavity, hitting the cavity’s 1 m^2 bottom wall five times before leaving the cavity through an aperture 20 nanoseconds later. The lawyer would say energy has been conserved: 2 electron-volts entered, 2 electron-volts left, and none remains.
        But that’s the lawyer; he only knows about energy
        The engineer, on the other hand, also knows about power and temperature. So he would instead count how many times a photon had hit the bottom wall’s area in 20 nanoseconds and accuse that shyster of “arm-waving” whatever temperature half an electron-volt per nanosecond per square meter translates to “and yet is the result of only” a tenth of an electron-volt per nanosecond per square meter of input to the system.
        As I say, our backgrounds make us look at things differently. I’m okay with that.

      • Joe Born ==> An engineer would ask at what ev level is that photon leaving. You assume the same as when it came in. Does a cue ball hit another ball with the same energy it started with after bouncing off the rail five times? In order for that to happen you must make several assumptions, like the walls are pure, ideal reflectors.

      • Jim Gorman:
        <blockquote An engineer would ask at what ev level is that photon leaving. You assume the same as when it came in. Does a cue ball hit another ball with the same energy it started with after bouncing off the rail five times? In order for that to happen you must make several assumptions, like the walls are pure, ideal reflectors.
        Thank you for a perfect example of the engineer’s focusing on irrelevant details at the expense of the relevant concept.
        For the tediously literal-minded:
        Commenter co2isnotevil thinks it violates conservation of energy for a forcing of 1 W/m^2 to cause a surface-temperature increase worth, say, 1.4 W/m^2. That is, it makes no sense to him that it would take 1.4 W/m^2 worth of surface-temperature increase to redress a top-of-the-atmosphere imbalance of only 1 W/m^2.
        What I’m pointing out is that the surface 1.4 W/m^2 includes an increase in the amount of radiation circulating between the surface and the atmosphere, i.e., in the amount of energy retained on earth. That’s what’s analogous to the photon bouncing off the (yes, of course they’re ideally reflecting) walls.
        It’s irrelevant that, e.g., the photons emitted by the atmosphere to the surface aren’t the same photons that the surface emitted to the atmosphere (or, incidentally, that there are actually more—but lower-energy—photons emitted to space than are received without reflection from the sun). Disputants like co2isnotevil and Christopher Monckton regularly raise irrelevancies like that. Maybe they do so because they don’t recognize the irrelevance, or maybe they do it to frighten the natives.
        In any event, what’s important is that in comparing power from space with power from the surface co2isnotevil is multiple-counting at the surface; you can’t infer from that difference that energy is being created. The relevant comparison is power from space with power to space. And the equation we’re discussing deals with conditions that prevail when those quantities are equal.
        That said, I suppose I should admit to being provocative in drawing the lawyer/engineer distinction. I’ve known engineers in my time whose intellects were incandescent, while my brothers at the bar often embarrass me vicariously. Still, in writing the statement I quoted above an engineer was making a mere debating point, not a relevant argument, and that’s something engineers accuse us lawyers of doing.

      • Joe,
        A physicist on the other hand would consider that the energy of a photon is quantized, so either the photon leaves the box or it’s energy was absorbed by a wall, heating it. You can’t divide the energy of a photon into pieces unless that photon was absorbed by matter and then re-emitted in a combination of lower energy absorption/emissions bands. You should think about the consequences of this relative to ‘thermalization’.
        “co2isnotevil thinks it violates conservation of energy for a forcing of 1 W/m^2 to cause a surface-temperature increase worth, say, 1.4 W/m^2. ”
        No, this is not even close to what I think, although it would be true for the Moon or a planet without an atmosphere. What I’ve said is that each W/m^2 of solar forcing results in 1.6 W/m^2 of surface emissions. This is not a COE violation because the retained and reflected energy is limited to the forcing, which sets an absolute upper limit on the emissions sensitivity as 2 W/m^2 of surface emissions per W/m^2 of forcing, i.e. the 100% positive feedback case.
        My point is that the 4.3 W/m^2 of emissions that the IPCC claims results from each W/m^2 of forcing is a violation of COE and that this violation arose because the internal, infinite power supply magically (implicitly) added this power to output of the model, yet the climate system has no implicit, internal, infinite power supply powering the increase from 1 W/m^2 up to 1.6 W/m^2, Instead, the 600 extra milliwatts of ‘feedback’ is the energy of prior surface emissions that was absorbed by GHG’s or clouds and then re-emitted back to the surface at a later time. This is why ‘feedback’ is limited to an additional 1 W/m^2.
        The only way to avoid this is if the open loop gain was greater than 1, however; this doesn’t work in the degenerate case with no atmosphere where the surface would still be warmer than the power from the Sun can support.
        BTW, assuming unit open loop gain was a ‘mistake’ in Hansen’s feedback paper that was ‘corrected’ by Schlesinger by changing the output of the model from W/m^2, which surprisingly, Hansen had correct, to degrees K and then providing the illusion of non unit open loop gain by obfuscating the Stefan-Boltzmann Law that converts between power and temperature as the open loop gain. After a few weeks of back and forth with Schlesinger about a decade ago, I brought this up at which point he got angry and didn’t want to communicate with me any more.

      • Joe,
        I thought it might be helpful to explain why the feedback power is limited to the forcing, because this is not the case with the Bode model owing to the implicit power supply.
        Consider a gain block with an open loop gain of 1. 1 W/m^2 goes into it and 1 W/m^2 leaves. For a Bode linear feedback amplifier, 100% positive feedback would be unstable, even with unit open loop gain. 1 W/m^2 is fed back, making the input 2 W/m^2. Now 2 W/m^2 comes out, all is fed back and 3 W/m^2 goes in and so on and so forth. This is the so called ‘runaway’ condition. Per Bode’s simplifying assumptions, the additional energy coming out of the gain block originates from the implicit and infinite power supply. The reason the gain block doesn’t consume the input and feedback power is because it has an infinite input impedance and the input consumes no power itself.
        What they want you to believe is that the feedback model is a theoretical abstraction of incremental behavior. But, what’s really being modelling from a physical perspective is not incremental and is identifiable, thus removing this level of abstraction. however; this level of abstraction is required to provide the wiggle room to support a sensitivity as high as they need it to be. When the abstraction is constrained by what it’s modelling, the wiggle room disappears.
        The physical correspondences are that the output of the model is the average state of the surface which is comprised of 2 components, its average temperature and its average emissions, immutably related to each other through the Stefan-Boltzmann Law. The model also has a single input, which is solar forcing, while the combination of unit open loop gain and feedback is modelling the atmosphere which adds additional complexity by modulating the fraction of surface power leaving the planet as well as the fraction of solar power arriving at the surface.
        The power leaving the gain block can be either feedback power or output power, but not both, because there’s no implicit power supply within what they’re modelling, instead, the output power of the gain block can only originate from its input, moreover; feedback to the surface originates from the atmosphere and only half of what enters the atmosphere can be fed back to the surface, since the remaining half ultimately exits into space.
        If 100% of the surface emissions were absorbed by the atmosphere, half of this would be returned to the surface as feedback and the remaining half would be emitted out into space. This sets the maximum amount of feedback power to half of the surface emissions which is what it would be 100% of the surface emissions were absorbed. Whether this is 50% or 100% feedback really doesn’t matter as this is the maximum possible that it can be. In any event, this sets the maximum ratio between surface emissions and the incident energy to 2 which sets the maximum feedback to half of 2 which is equal to the 1 of forcing input. Linearity in the power domain means that this applies to all average Joules equally, including the next one. The current ratio is 1.6 as I have pointed out before.
        If all of the surface emissions were absorbed and we needed to replace 240 W/m^2 of incident energy, all must come from the atmosphere, thus the atmosphere must be absorbing 480 W/m^2, so that half can be emitted into space, corresponding to a surface temperature of 303K which is the absolute highest AVERAGE temperature for the planet, given the amount of incident solar energy. Of course, for the atmosphere to be absorbing that much, it would need to be 100% covered by dense clouds which would reflect away a lot more power significantly reducing the 240 W/m^2 of post albedo incident power. This is as bad as a runaway condition can get (BTW, the surface temperature of Venus has a different origin).
        If none of the surface emissions were absorbed (the zero feedback case) then surface emissions would be 240 W/m^2 corresponding to a temperature of 255K. However; the albedo would also be reduced increasing the total incident solar energy, increasing the temperature. If we consider the albedo to be that of the Moon, which is made from the same stuff, the average surface temperature would be about 271K. The consensus considers the zero feedback case, or reference, 255K, rather than 271K it should be.

      • co2isnotevil:

        A physicist on the other hand would consider that the energy of a photon is quantized, so either the photon leaves the box or it’s energy was absorbed by a wall, heating it. You can’t divide the energy of a photon into pieces unless that photon was absorbed by matter and then re-emitted in a combination of lower energy absorption/emissions bands. You should think about the consequences of this relative to ‘thermalization’.

        Okay, so you don’t know enough physics for that to be a good analogy. (Frankly, despite my surname I don’t know much quantum optics myself, but I’m pretty sure the photons reflected from a mirror are identical to the incident ones, and any absorption occurs only to the extent that the mirror isn’t, as we assume, ideal. That is, most photons are in essence reflected, while, in the case of a non-ideal mirror, a few photons randomly chosen in accordance with the laws of quantum mechanics are absorbed) So let’s drop that analogy.
        I seem not to have taken your meaning last time, but your response appears to share much of the same misapprehension:

        [T]he retained and reflected energy is limited to the forcing, which sets an absolute upper limit on the emissions sensitivity as 2 W/m^2 of surface emissions per W/m^2 of forcing, i.e. the 100% positive feedback case. . . .
        [T]he climate system has no implicit, internal, infinite power supply powering the increase from 1 W/m^2 up to 1.6 W/m^2, Instead, the 600 extra milliwatts of ‘feedback’ is the energy of prior surface emissions that was absorbed by GHG’s or clouds and then re-emitted back to the surface at a later time. This is why ‘feedback’ is limited to an additional 1 W/m^2.

        I’m afraid that reflects too profound a misunderstanding of a couple relevant disciplines for this exercise to be worth continuing further. For the benefit of any lurkers, though, I’ll review the issue.
        Let’s not forget that the question before the house is whether \Delta T_\mathrm{eq}=\lambda_0(\Delta F_\mathrm{ind}+k\Delta T_\mathrm{eq}) is the right equation to use for approximating climate response. Instead of talking about what Bode said or whether gain implies a separate power supply, let’s look at the equation in operation. For purposes of explanation, we’ll describe it as happening in discrete steps, although in reality it’s a continuous process.
        Step 1: The CO2 concentration so increases that the resultant emission-altitude increase reduces top-of-the-altitude temperature by 0.33 K and the resultant emissions by \Delta F_\mathrm{ind}=1\,\mathrm{W/m}^2. Note that this involves no increased power input. The same amount of power comes in from the sun, but it has a harder time getting out. The value \Delta T_{\mathrm{eq}\,0} of the temperature change before the resultant radiation imbalance has had any effect is zero.
        Step 2: The resultant radiation imbalance warms the surface until its temperature has increased by \Delta T_{\mathrm{eq}\,1}=\lambda_0(\Delta F_\mathrm{ind}+k\Delta T_{\mathrm{eq}\,0})=0.33\,\mathrm{Km}^2/\mathrm{W}\cdot(1\,\mathrm{W/m}^2+2\,\mathrm{W/m}^2\mathrm{K}\cdot 0\,\mathrm{K}) = 0.33 K, i.e., by the amount needed to raise the new emission altitude’s temperature back to what the previous emission altitude’s was. Again, no internal power supply has been used; the surface temperature increased because more of what was always coming in from the sun gets backed up before it goes out. Once that previous emission temperature has been restored there would be no imbalance if nothing further happened.
        Step 3: But the increased temperature makes water-vapor concentration increase enough that the emission-temperature decrease caused by the resultant emission-altitude increase reduces emission to space by an additional \Delta F_{\mathrm{dep}\,1}=k\Delta T_{\mathrm{eq}\,1}=(2\,\mathrm{W/m}^2\mathrm{K})(0.33\,\mathrm{K})=0.67\,\mathrm{W/m}^2. No internal power source is involved. Evaporation energy came from the sun.
        Now, I do not believe that \lambda_0k, i.e., the gain experienced in thus traversing the “loop,” is in reality the 0.67 value we’re using. But that’s not the issue here. The issue is whether we’re using the right equation, and we are. This would be the way to estimate the response if that k value were indeed the approximate derivative of the feedback, i.e., of temperature-dependent forcing, as a function of temperature.
        Step 4: The resultant radiation imbalance warms the surface until its temperature has increased by another \Delta T_{\mathrm{eq}\,2}=\lambda_0\Delta F_{\mathrm{dep}\,1} = 0.22 K. Again, no internal power supply was needed.
        Step 5: Again, the increased temperature makes water-vapor concentration increase. And, again, no internal power source is involved. Evaporation energy came from the sun. The emission-temperature decrease caused by the resultant emission-altitude increase reduces emission to space by an additional \Delta F_{\mathrm{dep}\,2}=k\Delta T_{\mathrm{eq}\,2}=0.44\,\mathrm{W/m}^2. That raises the total forcing \Delta F_\mathrm{tot} to \Delta F_\mathrm{ind}+\Delta F_{\mathrm{dep}\,1}+\Delta F_{\mathrm{dep}\,2}=2.11\,\mathrm{W/m}^2.
        The preceding sequence so continues as to cause \Delta F_\mathrm{tot} to approach 3\,\mathrm{W/m}^2, all without the aid of any internal, infinite power supply.
        The explanation gave by co2isnotevil makes no sense to me, so I’ll probably misrepresent it again. But he seems to think that the difference between a forcing and the resultant additional surface emission is feedback: that somehow a value equal to forcing is emitted from the surface, and a percentage equal to the loop gain returns to the surface from the surface. As we saw above, though, the additional power from the surface appeared before, say, the water vapor responded, i.e., before feedback.
        In any event I’ve already wasted too much time on this, this I’ll leave it at that.

      • Joe writes

        Step 4: The resultant radiation imbalance warms the surface until its temperature has increased by another \Delta T_{\mathrm{eq}\,2}=\lambda_0\Delta F_{\mathrm{dep}\,1} = 0.22 K.

        All standard AGW theory. However the warming effect originates from the TOA because its fundamentally an accumulation of energy but the water vapor feedback doesn’t impact the TOA imbalance directly because its concentrated at the surface. Its not at all obvious that more GHG at the surface impacts the imbalance.

      • Joe,
        “Let’s not forget that the question before the house is whether \Delta T_\mathrm{eq}=\lambda_0(\Delta F_\mathrm{ind}+k\Delta T_\mathrm{eq}) is the right equation to use for approximating climate response.”
        This is about as valid as \Delta T_\mathrm{eq}=k\Delta F. Neither are valid because the ‘constants’ are temperature dependent and non linearly dependent as well. Solving, you end up with a \Delta T on the left and linearized temperature dependent coefficients on the right.
        To see why this is broken, consider the function a = b^4. At b == 2, we can linearly approximate it as a = 8b, but this curve fitted approximation only works for b == 2 and has absolutely no predictive power for other values of b. Now, to take this a step further, approximate the sensitivity of b to changes in a as the derivative of b with respect to a. The actual ‘sensitivity’ becomes 1/4b^3, which at b=2 becomes 1/32 while the ‘sensitivity’ of the approximation is 1/8 and independent of b.
        Replace a with F, b with T and throw in a few scaling coefficients and this is the smoke and mirrors used to approximate their insanely high sensitivity while maintaining sufficient confusion. This was combined with their misappropriation of Bode as the theoretical justification for a sensitivity as high as the IPCC needed to justify their formation.
        The problem is that it T is implicitly approximated to be linear to F which makes the dT/dF (sensitivity) meaningless with respect to the actual relationship between T and F.

  6. Hawaii lava is filling up the oceannnnnnnnnnnnnnnnnnnnnn
    On Tue, May 22, 2018 at 9:33 PM, Watts Up With That? wrote:
    > Willis Eschenbach posted: “Guest Post by Willis Eschenbach There’s been > some discussion of the rate of sea level rise lately, so I thought I’d take > a look at some underlying data. I started with a 2016 paper by the modern > master of failed serial doomcasting, James Hansen. It has th” >

    • It’s worse. Hawaii lava lost to the sea is reducing the size of Hawaii so its GONNA SINK

      • Actually, there’s other evidence — the presence of a small amount of basalt above the water at French Frigate Shoal about 1000km NW of Honolulu — that suggests the rate of subsidence probably slows as the Hawaiian hot spot moves further South and East away from the volcanoes. So maybe the higher parts of the Island of Hawaii will be around for 10,000,000 or even 20,000,000 years. But it almost certainly is going to sink.eventually.

      • It’s not subsidence that sinks these seamounts, it’s erosion (denudation) of the basalt because it is quite unstable subaerially exposed. The rate of denudation is fast at first when the magma chamber empties and no longer provides a force against gravity, and then it slows to the rate you see on the eastern islands.

      • RWTurner,
        Basalt is quite resistant to erosion, chemical or physical. Basaltic ocean sea mounts sink eventually (without continuous volcanism) because they are built on relatively thin oceanic crust and mantle, which cannot support them.

  7. The final sentence of the (way, way too long) Hansen 2016 abstract says, “We discuss observations and modeling studies needed to re- fute or clarify these assertions.”
    (My bold).
    They threw everything from accelerating SLR, melting poles, slowing AMOC, to children dropping dead in the streets into this 2016 paper in a quest for study money. Obviously they were expecting Hilly to win. (Okay maybe not children dropping dead, but close)
    Conclusion: carnival barking rentseeking at work.

  8. The decision to multiply the rate by 0.78 wasn’t arbitrary, it was taken (according to the graph’s caption) from Hay et al. 2015. That paper (If I have the right one) states:

    Several previous analyses of tide gauge records–employing different methods to accommodate the spatial sparsity and temporal incompleteness of the data and to constrain the geometry of long-term sea-level change–have concluded that GMSL rose over the twentieth century at a mean rate of 1.6 to 1.9 millimetres per year. Efforts to account for this rate by summing estimates of individual contributions from glacier and ice-sheet mass loss, ocean thermal expansion, and changes in land water storage fall significantly short in the period before 1990. The failure to close the budget of GMSL during this period has led to suggestions that several contributions may have been systematically underestimated. [bold mine] Probabilistic reanalysis of twentieth-century sea-level rise

    If I can paraphrase what they’re saying: “We can’t explain the data so we changed the data.”

    That, Madame, is intellectual baby-talk, …

    Christopher Monckton of Brenchley did a wonderful WUWT story about logical errors as applied to climate change. I’m not sure which particular logical error Hay et al. committed (perhaps a form of argument from ignorance) but it is surely not logical to change the data simply because you can’t explain why the data shows what it does.
    Hansen didn’t pull the 0.78 multiplier out of the air but when one looks at where it came from it’s still bunk.
    What things could Hay et al. have ignored in their attempt to close the GMSL budget? How about sediment? How about the volcanoes beneath the Ross Ice Sheet?
    “We couldn’t explain the data so we changed it.” Dear God in Heaven!

    • Or maybe their theory was just wrong ? If they seriously thought their data was wrong, why didn’t they go back and collect good data? No reputable scientist would change good data to match a bad theory.

      • Would any “reputable scientist” stand for his host sneaking in and disabling the AC and opening the windows in the Chamber where he/she are going to present on what has been historically the hottest day of the year in Washington, DC to try and make a point without informing those present what had been done?

      • No, no, you’re confused. They changed bad data into good “data” that fits their preordained double-plus-good law of nature.
        It would be so much less effort just to write a computer program to spit out reams of “data”, instead of risking measurement error and all the labor of collecting and compiling. Oh wait, they already did that. GCMs. But they have rigorously checked the models with …
        the output from more models.

    • Figure 29. Estimated sea level change (mm) since 1900. Data through 1992 are the tide-gauge record of Church and White (2011) with the change rate multiplied by 0.78, so as to yield a mean 1901–1990 change rate of 1.2 mm year−1
      (Hay et al., 2015). The two estimates for the satellite era (1993–2015) are from Nerem et al. (2010, updated at http://sealevel.colorado.edu) and Watson et al. (2015)

      So, they used Hay et al. for their trend, forced Church and White on top of that, and then grafted with measurements (or should I say estimates) done with a totally different method. Did I get it right?
      I think it is a misrepresentation of data. The accuracy of Church and White is used with the trend of Hay et al. I’m not saying that it looks childish, because I’m not a qualified world-known iconic climate scientist, but I do raise eye-brows. But the whole thing is very complicated so not many are able to say how terrible that kind of graph really is.
      In my opinion, Hansen does these graphs not for science, but for alarmists to use in blogs, newspapers and the worst, eventually in Wikipedia, where they appear as ‘sourced’ and from a ‘trusted journal’.

  9. Willis,
    “I digitized the C&W Figure 5 and analyzed it. “
    CSIRO has a rather complete zipfile of C&W data here. The file that corresponds to the numbers you listed is CSIRO_Recons_gmsl_yr_2011.txt, though it starts in 1880. Your numbers look pretty good.

      • Er, no, not much difference between 1920-30 and the later trend.
        Funny how that chart looks nothing like Mr Eschenbach’s.

      • To AC Osborn’s “Funny how that chart looks nothing like Mr Eschenbach’s”.
        Try narrowing the “width” (/ adjusting the X-axis) of your viewing window …
        paulski0 plotted the 2015 UPDATE to C&W 2011 (data to 2013), Willis digitised and plotted the ORIGINAL data (to 2009, published in 2011).
        Checking the differences (2015 update – 2011 original), there is a CONSTANT -1.6mm offset from 1880 to 1989, followed by variable but ALMOST always negative values from 1990 to 2001 (the exception is 1994, with a delta of +1.1mm).
        From 2000 the deltas are :
        2000 : -2.1
        2001 : -1.1
        2002 : 2.3
        2003 : 2.5
        2004 : 2.7
        2005 : 3.2
        2006 : 6
        2007 : 4.4
        2008 : 3.2
        2009 : 2.5
        “Funny” how it’s the most recent data that needs the most “adjustments” …

      • A C Osborn,
        The most recent trend (1983-2013) is about 35% higher than the highest in the 1920s/30s. If you consider that not much difference, there’s not much point in whatever scale you’re using. And again, that difference has only increased beyond 2013.
        I’m using the actual official published data as per the link. By suggesting an important discrepancy you can only be implying there’s something wrong with Willis’ chart, since his is a digitization. There are some visual differences obviously – Willis’ chart is more squashed, horizontally and vertically (to emphasise how strange your notion is of it showing “not much difference”, recent trends are waaaay above the top of Willis’ y-axis). My x-axis dates refer to start of trend rather than end of trend. And the official published data goes back to 1880 rather than 1860. But, as Nick Stokes says above, Willis’ digitization looks fine.
        There are some small differences in the more recent trends due to increased availability of tide gauge data for the 2015 update, so the final data point in Willis’ graph (for 1979-2009) has a trend of 2.3mm/yr in the official update.

      • AC,
        That is rate of rise plot, not a plot of sea level. The current 30 year trailing rate is the highest in the record.

      • Mark BLR,
        “Funny” how it’s the most recent data that needs the most “adjustments”
        Nothing to do with adjustments. It’s due to an increase in tide gauge data availability (and therefore, presumably, accuracy). Look at the uncertainty estimate in the original data for 2009, compare with 2009 uncertainty in the update. Substantially reduced. This is because of new data coming in providing better coverage.

      • Nothing to do with adjustments. It’s due to an increase in tide gauge data availability (and therefore, presumably, accuracy). Look at the uncertainty estimate in the original data for 2009, compare with 2009 uncertainty in the update. Substantially reduced. This is because of new data coming in providing better coverage.

        All this boils down to, more than what the actual measurements are, but do we trust that the people in don’t have confirmation bias affecting them?
        Like
        “look, these station data show a lot of rise, are they included?”
        “look, these station data show a drop lately, I guess that must be because of the earthquake/Moon/Evil spirits made the data bad. Let’s exclude it to make sure it doesn’t contaminate good data”
        Basically, that should not happen. In practice, I have no means to make sure it does not happen.
        Given that satellite data have been said to be much higher than tide gauge, motivation to find low-biasing tide gauges has been high.

      • paulski0 writes

        Clear acceleration beyond previous rates.

        It also shows about 40 years of decreasing acceleration, and considerable acceleration at a time when CO2 isn’t claimed to be the major driver of climate.
        Both those features need to be adequately explained before you can make claims about recent rates of acceleration.

      • Now let’s see the error bars!!! People are hiding the truth. Literally by hiding things from view.
        Do you think that Church and White do not have the confidence intervals to go with that graph?
        Of course they will have computed them. So why are they not on the graph?
        Could it be that they don’t want us to see the massive flaw that lies at the heart of basing global policy on short term estimations of sea level rise rate. The estimate for short term trends is completely swamped by the huge statistical uncertainty.
        see here: http://www.realclimate.org/index.php/archives/2011/07/is-sea-level-rise-accelerating/

      • Paulski and Nick Stokes, thanks for the links. It appears that they have “adjusted” only the recent data. As Mark BLR pointed out,

        From 2000 the deltas are :
        2000 : -2.1
        2001 : -1.1
        2002 : 2.3
        2003 : 2.5
        2004 : 2.7
        2005 : 3.2
        2006 : 6
        2007 : 4.4
        2008 : 3.2
        2009 : 2.5

        I can understand adjustments if say unknown data from earlier days were discovered … but why is the change only in the recent data? Not saying it is wrong, just saying it is suspicious.
        Next, you say:

        Clear acceleration beyond previous rates.

        I fear you are mistaking increasing sea levels with an increase in acceleration. Acceleration is the SLOPE of the data in your (or my) graph … and the recent slope is little different from the 1930-1960 slope.
        Finally, I say again:

        Here’s my conclusion in all of this. Until we can say why the rate of sea level rise:
        • decelerated from the start of the C&W record until 1930
        • accelerated rapidly until 1960
        • decelerated for the next ten years
        • stayed about the same from 1970 to 2000
        • and then started accelerating again,
        … until that time, I say that making just about any statement about sea level acceleration is premature. However, one thing is clear:
        There is no simple relationship between CO2 levels and the rate of sea level rise …

        Best regards,
        w.

      • paulski0,
        What was being discussed is whether or not there has been recent “acceleration” in sea level rise. What you have presented is essentially the upward ‘velocity’ over time. The slope of the curve represents the acceleration over time. The slope of the velocity during the 1920s is comparable to the recent slope. That is, the accelerations are comparable. Osborn is correct in pointing out that the accelerations are comparable. Currently, the ‘velocity’ of upward movement is high, but the rate of change of velocity is not unprecedented. But, inasmuch as we have seen decelerations in the last century, I don’t think that we should get too excited about the recent trends.

      • ” It appears that they have “adjusted” only the recent data.”
        There’s been no recent temp increase…..if anything the recent data should show sea level rise slowing…or even stopped if it’s an artifact of temp like they claim….it had to be adjusted to show it rising
        …and no, I do not trust a single one of them….Trump is a threat to the entire swamp

      • Those graphs of avg SLR rate vs. year are basically graphs of the first derivative of sea-level, after high-frequency variations are filtered out. That means acceleration of SLR is appears as a “rising” trend in the graph, and deceleration of SLR appears as a falling trend in the graph.
        That makes the variations look more significant than they really are. The difference between 1 mm/yr SLR rate and 2 mm/yr SLR rate is just four inches of sea-level per century, which is too little for a person to notice in his own lifetime, without very careful measurements.
        Additionally, those graphs are almost invariably created using measurements from mixes of locations which vary over time. That means that the variations in rate of SLR might have more to do with variations in where it is measured than with real changes in trend.
        A plain graph of sea-level vs. date is a lot simpler:
        Quick ref:
        http://sealevel.info/acceleration_primer_big_green_text.png
        Details:
        http://sealevel.info/acceleration_primer.html

    • Willis,
      I fear you are mistaking increasing sea levels with an increase in acceleration. Acceleration is the SLOPE of the data in your (or my) graph … and the recent slope is little different from the 1930-1960 slope.
      Then you aren’t talking about acceleration in the same sense as is typically the case in mainstream science. What you’re talking about is really variability in rate, which to a large extent is a consequence of natural forced and unforced climate variability. What’s meant by SLR acceleration is a sustained increase in rate, due to sustained imbalances in TOA flux, glaciers and ice sheets.
      There is no simple relationship between CO2 levels and the rate of sea level rise
      In terms of the variability in SLR rate over the 20th Century, that’s a straw man. No-one has said there should be. See Dangendorf et al. 2017 for a representation of what modeling including the expected effects of CO2 (and other known factors) produces (blue curves).
      The simple relationship is the fact that the rate at present is much high than (has accelerated from) the rate of the 19th Century and the 20th Century, and will keep increasing.

      • Oops, missed the right thread. Also, ‘sustained imbalances in TOA flux, glaciers and ice sheets’ should really say ‘increasing imbalances in TOA flux, glaciers and ice sheets’.

      • paulski0 writes

        due to sustained imbalances in TOA flux, glaciers and ice sheets.

        Why would you expect a sustained imbalance to cause acceleration? From an energy perspective a sustained imbalance causes the energy to be retained in the ocean for melting and thermal expansion at the same rate over time. To accelerate, you need an increasing imbalance.

      • paulski0 went on to correct himself

        ‘increasing imbalances in TOA flux, glaciers and ice sheets’.

        And this is far from a given. It could go either way. There is no reason to suspect SLR will accelerate.

  10. Thank you, Willis, for going back to the original data and for showing us to what happened with that data. An important and impressing analysis.
    But I have got one question. I was confused about the third graphic, the thick blue line that shows the Trailing Trend. I suppose ‘Trailing Trend’ is the same as ‘Moving Average’. I ever learned to show the moving average for a period in the year in the middle (!) of the period, so the average for 1960 to 1990 is shown in the graphic for the year 1975. Instead I see you using ‘Year of End of Trailing Trend’ which shows the trend for the last year of the data. But now, as I see it, all averages for every 31 year period are shown 15.5 year to the right in the graphic. Which is confusing for me.
    If ‘Trailing Trend’ is the same as ‘Moving Average’ I would be pleased to get a graphic with the moving averages put 15.5 years to the left: in the middle of the 31 year period. That enables me to read the average for a period in the middle of that period. Which is conform reality.

    • Thanks, Wim. The problem with doing it your way is that it is non-causal, that is to say, it includes events that happen AFTER the date we assign them to …
      For example, we can determine the trend for the past 31 years ending today,1988-2018.
      But we can’t determine the trend from fifteen years prior to fifteen years from now, 2003-2033.
      That’s why I posted it as a trailing trend.
      Finally, posting it as a trailing trend makes it perfectly clear why Hansen used the period 1900-1930 …
      Best regards,
      w.
      PS—There are both a centered moving average and a trailing moving average …

      • Hi Willis, thanks for the quick reply.
        In my old fashioned geography education I was obliged to show the moving average for the middle year of the period. I never learned about trailing moving averages.
        Using a paint program I changed the years at the bottom of the graphic (putting them around 15 years to the right which places the moving average in the middle of the period) with an interesting result. (I don’t know how to post the graphic in a way it shows up in the comments, it is a .png format)
        It shows that the sea level trends if averaged over 31 year periods, rise faster from around 1926 to around 1950 and restart their rise in the beginning of the nineties. Conform what we should expect when we look at ‘raw’ temperature data.
        Of course the most interesting of all numbers stays the same: an average sea level rise over the whole period
        of one and a half century which is around 1.5 mm per year. Nothing to be worried about.

      • Wim, I learned the same thing for “the” moving average in school myself. Then I got out into the REAL world – financial services, in my case.
        You want to know what the trend is NOW – not at some time in the past (15.5 years in this case).
        Now, it is just possible (although I think it unlikely) that there is an ~15 year lag between an increase in temperature and an increase in the acceleration of sea level rise. Of course, the main problem is that there is no real correlation between CO2 and temperature – except with a very long lag period.

  11. Willis, i think your grandmother said it all. As (the tv) fonzie once wrote on the bathroom wall, bull makes the world go round

  12. In Fig 5 is the satellite figures corrected by removing the “Global Isostatic Adjustment” by 0.4 mm/yr, which is supposed to compensate for a hypothetical increase in the volume of the ocean basins?
    This must be done to be able to compare with non-satellite data.

  13. Here is a plot of my favorite data point whenever ”acceleration” is discussed.
    http://www.psmsl.org/data/obtaining/rlr.monthly.plots/70_high.png
    It is from Kungsholmsfort in southern Sweden. This is an old coastal fort built on solid Precambrian bedrock of the Baltic Shield, one of the most stable and tectonically quiet areas on Earth. The only complication is the isostatic rebound from the last glaciation 12,000 years ago which is very nearly linear. By a coincidence the tide gauge at Kungsholmsfort was situated (when built in 1886) almost exactly on the line where sea-level rise and isostatic rebound are similar at about 1.8 millimeter per year. As you can see from the diagram it is still on that line.

  14. One would think that values of houses in areas close to the sea would take a tumble — but no. I see that a property in Sandbanks, Dorset (in the UK) is asking 7 — 8 Million £ making it the highest priced area after London.
    Houses are at the top of the beach.

    • Yep it’s the same for Miami which is a poster child for SLR for alarmists and thus the press. No effect on the prices at all despite years of SLR hype.

      • If I were building a house near a south Florida beach I would build the first floor slab about four meters above ground level (the area under this slab would be used as a garage and boat storage space), make it two stories high, use cement blocks for the outer walls, put removable stainless steel bars outside the windows, use a well anchored Spanish tile roof, install a small 2KW generator in an elevated platform on the ground floor, and a 200W solar panel covered with bullet proof glass on the roof. That house ought to last at least 60-70 years.

      • Was it not one Albert Gore who after cashing in his ill-gotten gains from An Inconvenient Truth, spent some $4M on sea-front property, after telling everyone how fast sea-levels were going to rise?

    • That might just mean that those who have a lot of money and like the beach just aren’t interested in following the CAGW “debate”. In fact if I got lucky and came into enough money to buy a $10,000,000 beachside palace my give a $hit factor in CAGW would probably disappear

    • John Moore
      One would expect SLR to impact the River Thames where the houses of parliament are ‘precariously’ perched. It would therefore seem logical that, when the opportunity arose to ‘jump ship’ and abandon the the place before it’s swamped, it would be taken.
      Instead, they are spending billions refurbishing the place.

      • Yep and Boston completed the most expensive public works project up to that time digging tunnels for freeways called “The Big Dig”.

      • The “Big Dig” is already under water. It was designed that way.
        Expensive as hell, but it goes right *under* Boston harbor.
        At ~11 inches/century that Boston has, SLR will not impact the Big Dig until about the year 4520.

      • Yes, it’s below SL and if SL rises until it reaches the entrances to the tunnels it will be done for. And that was the point! If SL is supposed to rise as they have said it will, it would have been foolish to build it.

  15. A problem with that Church & White data is that the mix of locations which they use when computing their “average” varies over time. Since different locations experience different sea-level trends, that can lead to apparent accelerations and decelerations which are actually just artifacts of the changing mix of stations.
    I prefer to look at long, high-quality, sea-level measurement records for individual locations. Here are “thumbnails” of graphed, seasonally-adjusted, mean sea-level from over 150 GLOSS-LTT tide stations:
    http://sealevel.info/154_thumbnails.png
    To view larger versions, click here and then click on the individual thumbnail graphs:
    http://www.sealevel.info/MSL_NOAA2010_thumbs.html
    The most obvious thing about those graphs is that all the long, high-quality, continuous or near-continuous measurement records are remarkably linear.
    Some locations saw a very slight acceleration in rate sometime between 1850 and 1930, which increased the rate of sea-level rise by at most +1½ mm/yr. (It is most evident at Brest, France.) But when CO2 level rose above 310 ppmv, sea-level rise acceleration ceased.
    Obviously the sea-level trends vary from one location to another. In a few places sea-level is rising quickly (mostly because of land subsidence). In some places sea-level is falling (where the land rising faster than the ocean). But in most places sea-level is rising very, very slowly; the average is only about 1½ mm/year, or 6″ per century. (That number is so small that it is hardly significant, since it is often dwarfed by natural processes like sedimentation and erosion.)
    The trends vary a lot, but there’s one thing that every long, high-quality, sea-level measurement record has in common: the lack of any significant “acceleration” (increase in rate) within the last ≈90 years. The sea-level trends are about the same now, with CO2 above 400 ppmv, as nine decades ago, when CO2 was under 310 ppmv.
    Since precise measurements began, CO2 level has risen every year for 59 consecutive years (315🠆407 ppmv), yet those CO2 increases caused no detectable increase in rate of sea-level rise. That is ironclad proof that CO2 emissions from fossil fuels, and rising CO2 levels, don’t significantly affect sea-level.
    Here are four graphs of sea-level rise juxtaposed with CO2 level. The top two graphs are of particularly high-quality measurement records from tectonically stable locations on opposite sides of the world, with typical trends (sea-level is rising about 1½ mm/year = 6 inches per century). The bottom two graphs are atypical: they show sea-level trends at the two locations where Nobel Prize Committees meet; sea-level is falling at both of those locations, due to “post-glacial rebound” (i.e., the land is rising). The sea-level trends are obviously very different, but they have one thing in common: just like at everywhere else, there’s been no acceleration in sea-level rise in more than nine decades:
    http://sealevel.info/Wismar_Honolulu_Oslo_Stockholm_vs_CO2_annot1.png
    You can look up sea-level trends for other locations here:
    http://www.sealevel.info/data.psp

    • daveburton
      Thanks for this very complete look at global tide data. I reviewed the NOAA data early last year and it was obvious that sea level change is a local issue and is disconnected from atmospheric CO2 concentrations. Sea level change ranged from -5.79 ft/100 yr (Alaska) to +5.31 ft/100 yr (Louisiana). Nowhere did I observe a change in slope of sea level rise as is shown in 1930 and 1992 in Figure 29 above. In Steward, Alaska, sea level is gradually decreasing (post-glacial rebound) except for one day in 1964 when it rose 3 ft as a result of the Good Friday earthquake.

      • Agreed, Farmer Ch E retired.
        I agree that there are serious problems with these composite sea-level trend graphs from the alarmist community.
        For instance, for many years climate realists have been pointing out that the claimed 1.7 to 1.8 mm/year “average” rate of global mean sea-level rise from teams like Church & White must be too high, because most measurement sites show lower rates. For example:
        http://www.john-daly.com/ges/msl-rept.htm
        More recently, I calculated an average sea-level trend of under 1½ mm/year from the best tide gauge records. I think nearly everyone who studies sea-level realized that those 1.7 to 1.8 mm/yr numbers must be too high, but, as in the story of the Emperor’s new clothes, the “team players” wouldn’t say it aloud.
        It is not widely noted that the team players had been fudging their numbers for years, to report higher trends. There are a lot of games that can be played when computing “global mean sea-level rise” from large numbers of tide gauges. Church & White like to use very large numbers of short-record gauges, compute empirical orthogonal functions to fit them, and adjust them in a variety of ways. It enables them to find “global sea level rise” trends which are quite different from simple averages of the rates at tectonically stable locations.
        Here’s a quote from the most famous sea-level paper of all, Church & White (2006), A 20th Century Acceleration in Global Sea-Level Rise:

        “An additional spatially uniform field is included in the reconstruction to represent changes in GMSL. Omitting this field results in a much smaller rate of GMSL rise…”

        The added “additional spatially uniform field” was obviously a fudge factor, to increase the reported rate of sea-level rise. But I wondered: why did they say “spatially?”
        Surely, I thought, since they were reporting measured acceleration trends, the “additional field” must at least have been temporally uniform. So why did they use the word “spatially?” What other sort of non-uniformity could there be, besides spatial and temporal?
        I emailed Drs. Church & White and asked them why they used the adjective “spatially.” Was the “additional field” temporally uniform, I asked?
        I’ve never learned what that “field” was, but to my amazement Dr. Church replied that it was not temporally uniform.
        In 2009 they posted on their web site a new set of averaged sea-level data, from a different set of tide gauges. But they published no paper about it, and I wondered why not. So I duplicated their 2006 paper’s analysis, using their new data, and not only did it, too, show slight deceleration after 1925, all the 20th century acceleration had gone away, too. Even for the full 20th century their data showed a slight (statistically insignificant) deceleration.
        My guess is that the reason they wrote no paper about it was that the title would have had to have been something like this:
        Church and White (2009), Never mind: no 20th century acceleration in global sea-level rise, after all.
        Finally, in 2015, an “insider,” Carling Hay, published a paper saying, right out loud, that the emperor had no clothes, and the claimed GMSL rates were too high. Suddenly the “accepted” rate of 20th century sea-level rise became 1.4 mm/year instead of 1.7 or 1.8 mm/year.
        But that left the other team players with a dilemma: what to do with all that data they’d been using? Hansen’s solution was simply to scale the old Church & White data by 0.78, to match the new received wisdom.
        BTW, Tony Heller memorably called the splicing together of tide gauge data with satellite altimetry to create the appearance of acceleration the “IPCC sea level Nature trick,” when the IPCC did it in AR4.
        I think that was, perhaps, a little bit unfair. (Willis & I corresponded about this, and he thinks I’m letting them off too easy.) But at least Hansen and the IPCC did not hide what they did in their spliced-together sea-level graphs. Hansen even used contrasting colors in his graph, to make it clear what he did. They just don’t seem to realize it’s wrong.
        In contrast, Jones, Mann, Bradley, Hughes, Briffa & Osborn, in their infamous WMO Report cover “hockey stick” temperature graph, used the same colors for the proxy data and the spliced-on real temperatures, and even rounded the splice points, to hide the splicing. Phil Jones and his pals clearly knew what they did was wrong, because they tried to hide it.
        So, what Hansen (and the IPCC) did with their spliced sea-level graphs was merely scientific malpractice. What Jones, Mann et al did with paleo-temperature data was similar, but added intentional deception to the sin, making it much worse.
        .
        I agree, also, that the area around Seward, AK is the only place I know which really did see disastrously high sea-level rise… once.
        https://www.sealevel.info/MSL_graph.php?id=seward&boxcar=1&boxwidth=3&c_date=1964/2-2019/12
        http://sealevel.info/9455090_Seward_problem_solved_67pct.png

    • I’ll take the 3.3mm and raise it to 5.58. Based on the rest of the coast this looks like an anomaly. https://tidesandcurrents.noaa.gov/sltrends/sltrends_station.shtml?id=8774770
      Which is based on this station https://tidesandcurrents.noaa.gov/stationhome.html?id=8774770
      With this — “The bench marks are near the Yacht Basin. The tide gauge is on the southern-most pier in the Yacht Basin.” There has been construction work on this basin in recent years and construction companies look at such data to justify projects.
      Winds at this location are important for sea level, also runoff, which may explain flat line during 50s drought. Which leads to the question of quality control with bench marks. On the Louisiana coast, almost floating in places, buildings have to been very careful with substrate. Piling depths are dependent on weight, especially important when you are talking about mm.

    • Exactly.
      Thank you for posting real data!
      So many continuous tide gauge measurements show no acceleration.
      How can the sea level rise accelerate and not affect these sites?
      For this to happen it must be either all these sites started to raise in a (synchronised) accelerated way, or the sea is making a huge blob somewhere 🙂

  16. Thanks Willis.
    The IPCC said exactly the same in AR5:
    It is very likely that the mean rate of global averaged sea level rise was 1.7 [1.5 to 1.9] mm/yr between 1901 and 2010 and 3.2 [2.8 to 3.6] mm/yr between 1993 and 2010. Tide gauge and satellite altimeter data are consistent regarding the higher rate during the latter period. It is likely that similarly high rates occurred between 1920 and 1950.,/b>
    http://ar5-syr.ipcc.ch/topic_observedchanges.php#node11
    We should also remember that the satellite figures are inflated by a GIA adjustment of 0.3mm/yr. While this may be valid as far as “ocean volume” is concerned, it is clearly not relevant for “sea levels” (The argument being that ocean floors have been sinking since the Ice Age)
    As such, it should not be used when comapring satellite data with tidal gauge data (which measures sea levels at the coast)

    • Both satellite and tide gauge data are adjusted upward by ~0.3 mm per year in most studies, including Church and White.

    • I do not think so. I looked at Boston tide gauge data.
      What I saw was a 74.4 year wave form tied directly to the orbit of the moon.
      Specifically, the moon’s apsidal precession, periodicity (8.0 years), and nodal precession, periodicity (18.6 years).
      You would expect that these variations will be different in different locations.
      For example, some areas get two high tides and two low tides per day. Some areas get only one. Some get one large high tide and one small high tide per day.
      So it is with the various lunar precessions on longer time frames.

    • I think the AMO and PDO influence is small at most locations. (It certainly isn’t as obvious as the shorter-cycle ENSO influence.)
      However, quite a few authors claim to have detected evidence of such an influence:
      Schlesinger, M. & Ramankutty, N. (1994), An oscillation in the global climate system of period 65-70 years. Nature, Vol. 367, pp. 723-726 (24 February 1994), doi:10.1038/367723a0
      Douglas, B. (1995). Global sea level change: Determination and interpretation. Reviews of Geophysics 33(S1): doi:10.1029/95RG00355. issn: 8755-1209.
      Douglas B (1997). Global Sea Rise: a Redetermination, Surveys in Geophysics, Vol. 18, No. 2-3 (1997), 279-292, doi:10.1023/A:1006544227856.
      Excerpt: “It is well established that sea level trends obtained from tide gauge records shorter than about 50-60 years are corrupted by interdecadal sea level variation…”
      Klyashtorin, L., and Lyubushin, A. (2007), Cyclic Climate Changes and Fish Productivity, VNIRO Publishing, 2007. 224 p. ISBN 978-5-85382-339-6.
      Excerpt (p.8): “At the background of the secular linear trend, Global dT undergoes longperiod, up to 60-year long, fluctuations… Global dT detrending allows detection of 2.5 cycles of approximately 60-year Global dT fluctuations.”
      Jevrejeva, S., J. C. Moore, A. Grinsted, and P. L. Woodworth (2008), Recent global sea level acceleration started over 200 years ago? Geophys. Res. Lett., 35, L08715, doi:10.1029/2008GL033611.
      Excerpt (p. 3): “The multi-decadal variability in global sea level for the past 300 years shows the same pattern as previously found in the climate system [Delworth and Mann, 2000], including a 60 – 70 years variability in sea surface temperature (SST) and sea level pressure (SLP).Similar 60-year cycles exist in early instrumental European records of air temperature (1761 – 1980) and longer paleoproxies from different locations around the world [Shabalova and Weber, 1998, 1999], suggesting a global pattern of 60-year variability. A global pattern of 60-year variability is supported by comparison of the GSL and North East Atlantic variability…”
      Frolov, I., et al (2010), Climate Change in Eurasian Arctic Shelf Seas: Centennial Ice Cover Observations. Springer Science & Business Media, 2010. ISBN: 354085875X, 9783540858751. (The abstract notes an evident 60 year cycle, and Section 2.4 discusses it.)
      In most individual tide gauge records there’s no obvious AMO influence, but Murmansk looks like a possible exception:
      http://sealevel.info/AMO_vs_murmansk_7.png

  17. What sea-level rate graphs show is the 60-year oceanic-related climate periodicity and a small constant acceleration due to post-LIA warming that is unrelated to CO₂ forcing.
    https://i.imgur.com/kI3WANh.png
    Your last graph shows the same.
    This is the same 60-year oscillation you defended doesn’t exist.
    https://wattsupwiththat.com/2014/04/25/the-elusive-60-year-sea-level-cycle/
    I guess you just found it in the data. Congratulations. Better late than never.

    • Given the third graphic by Willis and graphic b of Javier:
      The cyclical tendency in sea level rise seems to reflect a cyclical tendency of heat uptake by the oceans.
      The atmosphere reacts on higher sea surface temperatures by showing a rise in temperature. As demonstrated by Ole Humlum, atmospheric temperatures follow sea surface temperatures with a delay of a couple of months.
      The Cloud Hypothesis of Roy Spencer comes into mind: less clouds, more heat uptake by the oceans and warmer oceans are warming the atmosphere. All quite logic. A cyclical sea level rise could be seen as a proof for this hypothesis.
      If warming happens this way, the next question is: what causes clouds to behave in a cyclic manner?

    • Javier
      Just like the AMO a 62 year cycle is present. It seems to be in a lot of places. I used Willis’ data at the bottom of his post and analyzed it. I was quite surprised at what I found. I have looked at other sea rise data sets but I have never found one that had something close to a 1000 year cycle of something close to the 208 year cycle. I do have both in my analysis of the H4 data. The fit is simply outstanding.
      https://1drv.ms/u/s!AkPliAI0REKhgZhsLcxMQ1u1fHxjTQ
      The projection is shocking.
      https://1drv.ms/u/s!AkPliAI0REKhgZhufrmr26bsbpcHGA
      Here is how some of the waves fit into the projection.
      https://1drv.ms/u/s!AkPliAI0REKhgZhtPJs_LwrMSPlRlQ
      BTW, I did not check yet to see where the 874 year cycle peaks but I would not be surprised if it came close to 2135 you once identified.
      The interesting part does not end there. I now have four datasets showing a nice drop in values before 2020.
      Is that coincidence?
      Here are the AMO data and its projection.
      https://1drv.ms/u/s!AkPliAI0REKhgZhv7XILqEiNx6fW3Q
      https://1drv.ms/u/s!AkPliAI0REKhgZhwuS0iX3jUSr9l6Q
      That step change shocked me.
      Here is the PDO. Instead of a 62 year cycle it shows an 82 year cycle. There is no step change like the AMO but we do have a nice drop in temperature before 2020 coming.
      https://1drv.ms/u/s!AkPliAI0REKhgZhpTDctmQeAOHNCPQ
      https://1drv.ms/u/s!AkPliAI0REKhgZhr_P-InTa4jNSCfA
      I am going to be completely honest here. I am not sure what to make out of all this yet. I do have four datasets that are indicating a measurable drop in temperature before 2020. I am open to your suggestions.

      • Hi Charles,
        Very interesting set of graphs. And even more interesting to see what it happens over the next three years. However, I do not think that sea level is going to start dropping significantly. It has been going up for quite a long time and didn’t decrease during the long Gleissberg solar minimum of ~ 1900. Even if the rate goes to zero or slightly negative during a couple of decades that should not cause a significant drop in sea levels. One possibility is that the cycles are modulated by longer cycles. The 210-year de Vries solar cycle is strongly modulated by the 2500-year Bray solar cycle, so it only has a significant effect at ± 500 years of a Bray low.
        Also I’ve read a couple of reports about a possible strong La Niña in the 2019-2020 time frame. That could produce some cooling and affect oceanic indexes. Other than that I find fascinating that AMO, solar, sea level rate, LOD and other indexes are synchronizing on a cooling phase at about the same time. It is unlikely to be by chance. Without the very strong El Niño of 2015-16 we could have been seeing signs of a moderate cooling already.

        • Javier
          Thanks for taking the time to respond. I too am dubious of the change in predicted sea level rise but as you pointed out. But the fact that I have a number of datasets indicating a shift that seems nearly synchronized may the most significant discovery here.
          On your mention of the Bray cycle, I have found it in my analysis of some of the longer proxy records but introducing it here with such a short time record is questionable. All of the cycles that I used in the sea level rise were found from the OFT. I made no manual additions.
          BTW, I do analyze all four Nino regions and in my latest analysis of Nino region 3.4 it indicates a modest El Nino early in 2019. I am a little bothered by the fact that the last update of the daily record for all four regions was dated 04/06/2018. Normally, I look for these around the end or beginning of the month and here it past mid-May. I hope they are not being delayed because they are playing games with the data again. I just checked a few moments ago and there is sill no update.

  18. Thanks Willis for doing some proper ‘peer review’ that was obviously lacking before your keen eye!
    I’m an interested CAGW (now intangibly described as ‘Climate Change’ [nobody likes change!]) observer, often denigrated as a ‘denier’ for denying ‘irrefutable facts’ I never seem to be presented with… I think in the climate world, ‘facts’ are synonymous with ‘made up numbers based on opinions’.
    Keep up the good work!
    Adrian

  19. The graph provided by James Hansen is a pure case of climate fraud. How anyone can get away with publishig a graph showing an inflexion point of increased SLR from around 1990 that is not supported by a single tide global gauge, is indeed a great mystery.

  20. AGW Cultists like to defy the laws of physics. Any time this comes up and I show Tide & Current’s graphs showing no acceleration, they claim those are individual locations, but GLOBALLY there is acceleration. So let me see if I have this correctly. 1000 individual cars are moving at a constant speed on the highway, but collectively they are all accelerating in speed. Got it.

  21. Hansen made a Faustian pact with the politicians controlling the purse strings at the moment he connived in arranging the over heating of the meeting room in Washington in which he made his first pitch to them on CAGW.
    Since then, the politest thing that can be said about his activist ‘science’ is that It is prone to confirmation bias.

  22. Nonsensical to use data that claims to be “global sea level” to the nearest 100th of a millimeter (as in “1860 -189.26”) — even last years sea level can not be calculated to anything near that degree of accuracy or precision. Thus the whole exercise is just “sea level taxonomy” — fooling around with numbers and calculations — none of which adds to our knowledge or understanding of the real world.
    Not Willis’ fault — he is just playing their game — and a game is all it is.

    • In relation to “the game”. 1) Just how do tidal gauges measure “sea level”? It seems that if the land is rising or falling (either above or below the water level), then all they measure is some relationship of water level to land, not necessarily “real sea level” above the center of the earth. 2) If they are only measuring a relative level at any location, how do you combine them and say “this is the global sea level”? Measuring different things with different instruments is just not amenable to averaging and obtaining a true answer. 3) We have hundreds of years of paintings and photos that should have unique physical characteristics (buildings, rocks, sea port heights, etc.) at various locations throughout the world to see how relative levels have changed over time. Am I the only one who wonders why a forensic database of the changes has not been established in order to check these so-called “scientific” projections against?

      • Paintings and photos are practically useless since they will only tell you what the state of the tide was at the time. Even in areas where there is no tide sea level varies 3-4 feet depending on wind and air pressure. Only by taking continuous measurements and averaging them over months or years is it possible to measure the true (relative) sea-level. And even then it takes decades before a trend is visible.

      • I don’t think that is totally true. I am not talking about absolutely accurate measurements. But a painting from hundreds of years ago or a more recent photo can give relative differences. If a rock that has been visible for hundreds of years is now submerged one could make a conjecture about the reason. Likewise a building right at the oceans edge is now yards away, should generate some questions.

  23. James Hansen does seem to be trying to be the Harold Camping of climate predictions.

  24. When you have Ellison, a converted Muslim, being elected Senator in 2006, just prior to Obama being elected, , one gets the idea that the stage was being set for further action.
    When Sovereignty is lost, there is no where for Law Abiding citizens to turn to for redress, as they no longer have elected leaders, only Appointed ones..Re: California.. Here, We are being governed by Environmental and Social NGOs, who have fought up all the Elected Officials, along with the Unions. An UnHoly alliance if there ever was one.
    How are you? It would be fun to get together for a lunch or a talk. Love to all, Clark >

  25. I have a graph showing the sea level rise in Sweden.
    Between 1995 and 2016 the slope is 3 mm/year (20 Years)
    There are 3 more periods showing this rate of rise:
    1896-1926 (30 Years)
    1960-1988 (28 Years)
    1975-2005 (30 Years)
    The average slope is 1,85 mm/year.
    Yet the SMHI(gov) are confident to say -We see an acceleration to 3 mm/year due to global warming.
    https://www.smhi.se/polopoly_fs/1.133603.1523542160!/image/Havsniv%C3%A5h%C3%B6jning.png_gen/derivatives/Original_1256px/image/Havsniv%C3%A5h%C3%B6jning.png

  26. Beautifully accurate analysis, Willis. Today’s Wall St Journal has letters in response to Fred Singer’s previous article on CO2 and sea level rise – including one from Michael Mann. I’ve quoted your article in rebuttal, accurately I hope. Hope your analysis will sway some taken in by Hansen’s ilk.

  27. Just an out-of-curiosity question: how much is it possible to determine whether some of the sea level rise data is due to coastal subsidence as opposed to just a rise in sea level? I’m thinking about this because in parallel, there was concern about lake level lowering in the Great Lakes region some years ago, and it was apparently determined in that case that land adjacent to the Great Lakes was still rebounding from about 10,000 years of glacier pressure on top of that land. This meant the lake levels were not lowering, they were staying the same while the land was actually rising slowly. Is is possible the converse is true with ocean levels? Another example of course is the Tohoku earthquake next to Japan. Coastal land levels sunk about 3m after that quake. How much is the data affected by events like earthquakes in general?
    Willis, your thoughts are welcome.

    • Nowadays it is possible by locating a sensitive GPS receiver nearby. This will measure the height of the ground in geocentric coordinates. However it takes a number of years to get good data.
      Normally lake levels are not affected by glacial rebound, since both the land around and under the lake and the lake water rebound together. However if the lakes are very large the rebound will be greater at the northern end (which deglaciated later) and you get a phenomenon kalled “sjööverstjälpning” in Swedish,which translates as “lake overtipping”, i e the water in the lake will tip over towards the southern end where the relative water level will rise while it sinks in the north. I would guess that this effect should be quite noticeable e. g. in Lake Michigan.

  28. Thanks to everyone for a very interesting discussion and to Willis for starting it off. What I did not see was the way in which Willis was able to detect or determine where the data from Hansen was derived from different data sets, adjusted, and then patched together? I love the forensic work, but was it listed in their Materials and Methods, or did you just figure it out by deduction?
    A high school science student would get an F for combining data in this way. My brother in law is a high school science teacher, and believes strongly in AGW, and yet as I remind him, he would never allow one of his students to change their data to fit their hypothesis. I just cannot understand how rational educated adults accept this stuff as scientific or authoritative. He also cannot countenance the idea a scientist would act in any way unethically to advance their career. Yet he believes that every business person is a greedy schmuck.
    I look forward to future neuroscience experiments that determine how and why our world views are so rigidly fixed at some early period such that facts become irrelevant. And what kind of psychic shock is needed to alter those thought patterns, as sometimes (but rarely) occurs. I wonder if studies on psychedelic drugs would convert any of these AGW believers in the same way as they can treat opioid addicts?

    • Cold in Wisconsin May 23, 2018 at 9:31 am

      Thanks to everyone for a very interesting discussion and to Willis for starting it off. What I did not see was the way in which Willis was able to detect or determine where the data from Hansen was derived from different data sets, adjusted, and then patched together?

      Thanks, Cold. It’s all listed in the caption under his Figure 29, shown in the head post.
      w.

  29. In Eschenbach’s Figure 5, there does seem to be a “knee” (inflection point?) in the curve at around 1930, but little acceleration (or deceleration) since then. If we use -105.16 mm in 1930 and +52.43 mm in 2009, then the average rate of sea level rise (per Eschenbach) would be (52.43 + 105.16) / (2009 – 1930) = 1.99 mm/year, or about 7.85 inches per century.
    Raise your hand if you think it’s possible to build an 8-inch high seawall around your coastal city in the next 100 years!
    I’m also wondering–how did Church & White (or those whose data they quoted) measure sea level to the nearest hundredth of a millimeter as far back as 1860, when the tide normally rises and falls twice a day by over a full meter in some places? Shouldn’t the data be rounded to the nearest full millimeter to account for imprecision of the measurements?

    • Willis said that he digitized the chart, so it’s the precision of his program only.
      Did you know that the maximum height of tide in the Bay of Fundy (Nova Scotia) is 16 meters?
      sorry, 16,000.00 mm

    • Tidal gauges are just that. They measure the tides. When you subtract the tides, what is left is sea-level change. Most of this is due to weather. Over a sufficiently long time this will average out.

    • Also if you look at fig 5 you will see that the uncertainty is much larger in the early part of the diagram when there were fewer stations.
      And don’t underestimate nineteenth century instrument makers. Here is a swedish tidal gauge from 1886:
      https://upload.wikimedia.org/wikipedia/commons/f/f9/Mareograph.jpg
      Sea level is measured continuously by a float and mechanically transferred to a pencil which draws a curve on a paper roll driven by the clock while a second pencil, driven by the same clock, marks each full hour.

  30. Hypothesis:
    The change in trend since the LIA is all manmade.
    1) Improved irrigation and hydro power plants (like the Boulder dam) became prevalent at the start of the 20th century. This slowed the loss of water from the land to the sea and allowed vegetation to tie up more moisture. The sea level rise slowed.
    2) Nuclear tests after WW2 caused small areas of the sea to hold far more thermal energy than before. Ths caused some thermal expansion but also allowed local warm water pockets to survive long enough to circulate round the world. This increased Arctic ice loss. The sea levekl rise spikes.
    3) Early 1960s, Khruschev and JFK ban nuclear tests. The change in trend disappears. The rest of the graph is just measurement noise.

  31. Nice article Willis! One small clarification. Hansen attributes the multiplying the Church and White data by .78 to Hay, et al 2015. In this paper the Church and White data is adjusted in order to close the sea level rise budget from various inputs (heat expansion, ice melt, and land water storage changes, etc.). So there may be some rationale existing for the adjustments since these factors are presumably are being considered in more recent papers. However, it should bring attention to adjustments in general as years ago surface temperature record trends were adjusted down in part because of low levels of recorded sea level change not to speak of tossing some early Argo data on ocean warming trends due to sea level change. Having those adjustments then lead to adjusting sea level change downwards because of a lower warming trend speaks to creeping bias in the whole program.

    • Changing actual data to conform with theory is an extremely dubious practice. Nobody knows what the ice melt in Antarctica was in 1901 for example (or in 1950 for that matter). If you have sea-level measurements that don’t fit your modelled sea-level budget, I submit that there is probably something wrong with your budget. And how likely is it that tide gauges all over the world were consistently wrong by a constant 22% over a 90-year period? And apparently this problem then disappeared just as satellite measurements started.

  32. Church paper itself states:
    The linear trend from 1900 to 2009 is 1.7 ± 0.2 mm year−1 and from 1961 to 2009 is 1.9 ± 0.4 mm year−1. Note the error estimates.

  33. Willis, pardon my ignorance, but I don’t understand your digitized C&W data. What does it mean to say that sea level in 1860 is 189.26 mm? Or that in 1960 it was 40.06 mm? Surely sea levels were higher in 1960 than 1860. So maybe the numbers refer to annual sea level rise–but obviously they don’t, otherwise Al Gore’s 20 foot wall of water would have washed over us long ago.

    • Marlo, the only stupid questions on my planet are the ones you don’t ask. Those always come back to bite you in the differential housing … you’ve simply missed the minus (-) sign. In 1860 it was -189.26 mm. All of these numbers are anomalies around a specified zero point.
      Best to you,
      w.

  34. Willis,
    Is there some reason why one would not just run a standard F-test to see if the addition of a quadratic term in the expression for sea level would be significant?

  35. Having been interested in this topic since John Daly’s time, I am perplexed as to why the papers of the expert, Nils-Axel Mörner are completely ignored? The paper: “Glacial Isostasy: Regional—Not Global” has a detailed account of the Fennoscandian region’s glacial rebound and the Netherland’s sinking with the location of the ‘hinge.’ [http://dx.doi.org/10.4236/ijg.2015.66045]
    Other of his papers also discuss the problems of tide gauge and satellite data. The above paper has references to many of his papers. If not located, ask him for a copy.
    Church & White made a curious/odd selection of tide gauge sites leading to questionable conclusions, especially when they tack on the satellite data, which in turn supposedly relates to a ‘spheroidal surface,’ not necessarily the ocean surface. My guess is that the “additional spatially uniform field” mentioned above, is to make the satellite data ‘match’ the greater-than-a-global average rise of about 1.4 mm/yr, of the USA coastal data (around 3 mm/yr) due to slight sinking of the USA part of the continent as the Canadian part rises. Was this to be parochially correct?
    Church & White conveniently ignored their “home” long-term tide gauge, Fort Denison in Sydney Harbour with a rate of rise <1 mm/yr.
    As to short-term changes in rate of sea level rise, when ocean basins are subject to cyclical lunar tide changes, atmospheric pressure changes, prevailing wind flow and storm surges it is not surprising that such fluctuations are seen. Thermal expansion is a doubtful factor as changes in continental shelf gauges are no different to those on stable islands surrounded by deep ocean.

    • prcgoard May 24, 2018 at 10:49 pm

      Having been interested in this topic since John Daly’s time, I am perplexed as to why the papers of the expert, Nils-Axel Mörner are completely ignored?

      I ignore him because he claims over and over that the sea level is not rising anywhere on the globe … which contradicts the tide gauges everywhere.
      I also ignore him because he claims he is able to determine historical sea level rises in Fiji from the cuts made by waves in the tropical islands. Having lived in Fiji, I know that is simply not possible at the level of precision and accuracy that he is claiming.
      I’ve met him, he’s a charming guy, but he truly doesn’t understand sea level.
      There’s a discussion of his other … well … eccentric claims here … read’m and weep.
      w.

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