Who’s Afraid of Sea-Level Acceleration?

by Joe Born

This is kind of a coda to Willis Eschenbach’s recent post about sea-level rise. In that post Mr. Eschenbach argued against confidence in the recently observed accelerations’ reality. His post was characteristically compelling. But there’s a sense in which the question of whether apparent acceleration is real seems secondary to whether the acceleration means much if it actually is real.

How would our resultant conclusions differ if we were certain that Mr. Eschenbach’s skepticism is misplaced? Suppose we knew that the published oceans-average values are precisely accurate and that all tide-gauge locations exhibit them uniformly. Would we then base our expectation of future rise on the observed acceleration? I’m no scientist, but I don’t think we would. Or at least we shouldn’t if we’re serious people. Acceleration is too fickle an indicator.

To place that claim into context, let’s briefly set acceleration aside and look at the trends of which accelerations are the first derivatives. The plots below show that, if we accept the PSMSL data as accurate, the 50-year trend has been increasing for about ten years. Before that it had decreased for a quarter of a century from a mid-century peak of nearly 3 mm/year.

clip_image001[1]

Those observations are reasonably helpful. They tell us that the latest 50-year trend is in the lower portion of a range that’s prevailed for over a century, a range that would suggest an increase through the end of this century of between 4 and 10 inches.

Of course, we don’t know that the trend will remain in that range. Maybe we’d get a better sense of whether it will, though, if we shortened the intervals our projections are based on? That way the trend would be less insensitive to the most-recent data.

But here’s the problem. The data tell us it’s a mistake to start making projections based on shorter trend lengths. As the plot below shows, projections of the 2010 level based on past intervals’ trends can err wildly. Note how often the error exceeds the entire differences between the 2010 value and the past interval’s values themselves. The worst projections are the ones based on shorter intervals; those based on 25- and 50-year intervals tend to be better.

clip_image002[1]

I hasten to add that the plot shows only extreme projections; other intervals’ trends project values that are almost exactly correct. But that’s just because the projections vary so widely that they’re bound to be right sometime.

Not only do the trends vary widely but, particularly for the shorter intervals, they also reverse frequently. And that brings us back to accelerations; it tells us that accelerations—the trends’ first derivatives—tend not only to be large but also to be followed by decelerations. The following plots show this.
clip_image003[1]

Those plots also show that accelerations as high as recent ones are not uncommon. So there’s no reason to believe that the current acceleration, real or not, is cause for alarm. It is not unprecedented. And, if the past is prologue, it will be followed by deceleration. To assume the opposite is to ignore the existing record.

In short, basing projections on current acceleration has little to recommend it. But let’s try it anyway:

clip_image004[1]

Obviously, basing projections of today’s level on accelerations would have been worse than basing them on trends. Basing projections of the future on accelerations would be a triumph of hope over experience. So how can scientists profess alarm at signs of acceleration?

Now permit me a digression. In The Death of Expertise: The Campaign against Established Knowledge and Why it Matters, Thomas Nichols decries the public’s failure to trust experts. Dr. Nichols admits that experts sometimes get it wrong, but he argues that this doesn’t justify my or some other layman’s basing rejection of an expert-proffered proposition on half an hour’s Googling.

In my own areas of expertise I, too, have experienced frustration at seeing laymen reject facts there’s really little room to doubt. Yet as a layman I’ve seen too many instances in which experts have lacked candor about which propositions fall into that category. In a world in which climate scientists base catastrophic projections on as fickle an indicator as sea-level acceleration, it’s questionable that as laymen we err more in skepticism than in credulity.

That’s why, for example, laymen like me often reject experts’ “social cost of carbon” estimates in favor of back-of-the-envelope calculations. In my case I’ve estimated that over this century CO2 fertilization would yield over a quarter million dollars in increased grain production alone per acre of land lost to a 3 mm/year sea-level rise. So to me increased carbon-dioxide concentration doesn’t seem like such a bad thing.

It’s not lost on us laymen that this type of analysis is highly simplistic, that it ignores the myriad facts the experts took into account. We’d like to have better alternatives. But, given scientist arguments like the acceleration one, our default position is to go with our guts unless the scientist can make a pretty compelling case for his reliability. True, this approach is non-intellectual. But under the circumstances I think it’s realistic.

End of digression.

Mr. Eschenbach did a good job of showing how shallow the evidence is for sea-level acceleration. But let’s not lose sight of how little meaning acceleration has in the first place. Or of who relies on it anyway.

Advertisements

115 thoughts on “Who’s Afraid of Sea-Level Acceleration?

  1. Trying to reduce reality to a single number is an exercise in persuasion, usually. It does not usually describe the phenomena well. In this case, it is also an example of the cut-off-graph game in fancy trickery.

    • Of course, we don’t know that the trend will remain in that range.

      Yes, the whole concept of “trends”, that are so central much of climate pseudo-science, is the idea that “if this trend continues, then …. OMG etc”, when there is no reason to suggest that a particular “trend” or acceleration ( a trend of the trend ) will continue. However, this seems to be taken as a given, established fact: that as soon as you can fit a “trend” in Excel, it becomes a valid means extrapolating future change.

      the 50-year trend has been increasing for about ten years.

      Taking a 50 average is supposed to remove shorter term variation, so why would you look at 10 year wiggles in 50y averages. They are at best the noise that got through a badly conceived filter may even be total artefacts of the frequency inversions you get with running averages.

      If we need to remove the confusing visual noise then we use a properly construct low-pass filter an we see that yes, was a recent “acceleration” but that it was indistinguishable for earlier ups and downs.

      • There has been a steady underlying rate of change since 1860 and there is no visible evidence of an AGW driven “acceleration” since 1960 when IPCC says GHE became significant.

      • Here is the same data with an extra derivative to show sea level acceleration.

        Clearly nothing since 1960 that is out of the range of earlier changes. If anything that period has been rather subdued.

      • I won’t argue whether applying a Gaussian or other filter would have been a better choice for coming up with an acceleration measure; frankly, I’m agnostic about that. And, anyway, the question should be, What measure of acceleration did the doomsters use? I really don’t know, but it seems they tend to use short-term ones.

        As to the precise measure I used myself, please see my other response on the matter.

      • What measure of acceleration did the doomsters use?

        Doomsters rely upon linear regression to compute a “trend” and start talking about “acceleration” when its slope increases. Never mind that the calculated intercept with the present time has the frequency response of a very crude band-pass filter which, unlike backward first differences of data, lags the original data in phase,

        Regression is simply not a legitimate tool of time-series analysis. It is, however, an elementary statistical technique that virtually everyone is familiar with. That’s what gives this wholly unscientific notion of acceleration the aura of legitimacy.

      • Clearly nothing since 1960 that is out of the range of earlier changes.

        Little is clear about the PRESENT state of acceleration in that graph, because the end-loss due to the lengthy gaussian filter produces NO smoothed values beyond the 1990s.

    • Don’t you need to know what the sea level is before you can actually determine whether it has risen or fallen? To me this is analogous to believing that the Earth actually has a mean surface temperature. It is all complete nonsense.

    • As the GLOBAL long term tide guages, after adjustment for known land rise or sinking, only show 1.49 mm per year SL rise, and ZERO acceleration, then any and ALL short term trend in satellite data is meaningless drivel.

    • No, because if they did then hardly anything in this ‘field’ would get published. LPU’s (least publishable units) are the order of the day, preferably with “PEER Reviewed” boxes ticked but no actual content review. Its a bit like snack foods at the supermarket, miimum actual content let alone health information on the packet, maximum marketing exposure “NEW”, “HEALTHY”, “WITH EXTRA WHOOPEEE”.

      This is ‘science communication’ at its lowest form.

  2. I’ve just discovered this very useful graph of 95% confidence intervals for linear trends over varying trend lengths. I hunted for this graph using a general Google search.
    But, the version that I found happened to have been posted on this blog, back in 2013, by a certain Willis Eschenbach.

  3. Guest Blogger

    Who’s our guest, Sr. Moderator?

    Reply: Sorry, behind in editing after I requested his/her/ze/zhir/it/zu/’s name. Updated now.~ctm

  4. 12,000 years ago at the end of the last glaciation sea level was about 120 meters lower than it is today. That is a convenient number because that works out to an average increase of about 1 meter (40″) per century. Somehow Mother Gaia endured, so until we start seeing a projected rise of at least this scale I’m not going to lose any sleep.

      • I’ll accept your dates but the point holds. Earth survived and in fact thrived while experiencing sea level rise on the order of 1 meter per century. If you seriously fear this, get out front and buy next century’s oceanfront property for bargain prices today.

      • Mike Nelson/ristvan, the part of geology called Sequence Stratigraphy, discovered and formalized by geologists/geophysicists of Exxon in the mid-70’s, and now utilized by all oil exploration groups, shows sea level variations more-or-less 150 meters lower and 50 meters higher than current. Accelerations, rate-of-changes, etc, are difficult to quantify but no reason, based on the general theory, to think they are different than current. These cycles are produced by very larger forces. Cow farts and SUV emissions are not large forces. Mike, don’t lose any sleep, and ristvan, don’t worry about a few millennia, everything is normal.

    • Waterfront real estate was reportedly substantially cheaper in 9983BCE than it is today. The economic impact of an (unlikely) one meter sea level rise would be substantial. But mostly, you’re right. There look to be far greater threats to life as we know it than sea level rise.

  5. not even wrong.

    lets recap the argument.
    basic physics and climate models predict that in a warming world the sea level rise will begin to accelerate.

    the observations have yet to show that conclusively.

    its not that hard.

    of course if you argue against strawmen youll never get anywhere

    • “basic physics and climate models predict that in a warming world the sea level rise will begin to accelerate.”

      Well, that depends on how you define “a warming world”. It’s cooler now than it was in the 1930’s, so are we in a warming world, or a cooling world right now?

    • Steven Mosher July 25, 2017 at 4:39 pm

      not even wrong.

      lets recap the argument.
      basic physics and climate models predict that in a warming world the sea level rise will begin to accelerate.

      the observations have yet to show that conclusively.

      its not that hard.

      Huh? That makes no sense at all.

      First, YOU HAVE NOT SAID WHAT IT IS THAT YOU THINK IS “NOT EVEN WRONG”. You seem to think that we are mind readers. I have no clue what you are babbling about.

      Next, what you say other than that is true as far as I know … but it doesn’t disagree anywhere with anything that Joe wrote in the head post.

      Steven, this drive-by cryptic posting style is slowly destroying your reputation. Perhaps you think it is cute or that it shows your brilliance. It is nothing of the sort. It just makes you look like an arrogant jerk.

      I post this for a simple reason—at those rare times when you deign to explain whatever it is you are saying, your ideas are often provocative, insightful, and interesting.

      Call me crazy, but I’d like to see that Steven more often …

      w.

      • Mosh is referring to the Pauli anecdote.

        Hullo, Willis.

        Hey, Mosh.

        My fellow data mud-wrestlers.

        Shout-out to Willis. I’ve seen a very interesting process as a bunch of insignificantly different sub-samples wind up with a hugely significant totality. I begin to wonder if a lot of those double-sigmas are merely dodging the sample-size inconvenience.

        (To Mosh. Patience. Just a bit more (unearned) patience …)

      • @Evan

        You say that Mosh is referring to the Pauli anecdote. Mind reading is always a tricky thing. Perhaps soften “is” to “might be”.

        [REPLY – Yet a working knowledge of moshspeak serves to reduce the margin of error significantly in the calculation. Double-Sigma, Out. ~ Evan]

      • People, listen to Mr. Mosher. Following his statement, there is no observable acceleration. Logically, that means the globe is not warming. No?

        The 21st Century has not warmed appreciably.

      • I don’t know which particular double sigmas are being talked about however …

        When you talk about double sigmas you are almost certainly talking about the upper case Greek letter sigma, Σ. It’s the sign that means you add a bunch of things. One common use is to calculate averages. You sum all the data and divide by the number of samples. Sigma gives you a simple way of writing that. link

        So … double sigma could mean that you’re taking the average of averages. We’ve dealt with that before. WUWT It can lead to profound error.

    • Your comment -> Not even relevant.

      “basic physics and climate models predict that in a warming world the sea level rise will begin to accelerate.”

      No one is disputing this.

      “the observations have yet to show that conclusively.”

      Yet, the media and some scientists are saying that it IS conclusive. See any recent news article about sea level.

      But, this is not even what the above article is about. It is not about whether or not it is accelerating, it is about what acceleration could imply.

    • Oh Mossshhher the once Great and Powerful, have a little lie down and then try to write something intelligible which conveys your actual meaning, if you have one.

      BTW: you don’t happen to own a dozen or more cats do you?

      • One does not own cats.
        Either they are being imprisoned, or they have, so far, decided to hang out with you for a while longer.

    • Mosh:

      basic physics and climate models predict that in a warming world the sea level rise will begin to accelerate.
      the observations have yet to show that conclusively.

      Wrong. Observations do not yet show that AT ALL. For them to show that, even inconclusively, would require a recent rate of change greater than all earlier rates of change. That is very clearly not the case. There was a greater rate of change around 1950. The largest acceleration BY FAR happened around 1860 and nothing like it has happened since.

      The claim that “the observations have yet to show that conclusively” carries the implied claim that they do do show it but not conclusively. That claim is “not even wrong”.

      • This is what the acceleration looks like:

        Clearly there is nothing in recent acceleration which suggests the slightest impact of AGW, GHE etc.

      • Church is a Kiwi alarmist. His recent 4mm/y rise is even higher than the GAIA “corrected” satellite data which produces a sea level which hovers phantom-like above the waves. Ends justifies the means pseudo-science.

      • Note that he conveniently removes the earlier period of negative trend and thus avoids showing the main feature of the dataset: the significant acceleration from negative to positive change.

      • Afonzarelli – My take on church & white –
        Deceptive –
        Misleading –
        Other adjectives –

        A significant part of church White’s SLR rise is due to the switch in method of measurement of SLR. Around 1993, there was a switch to satelite vs tide gauges.
        Church White also shows a significant increase in the rate of acceleration – Like duh – when the tide gauges show 1.8mm to 2.mm per year with a rate of doubling every 150 years, then switch to satelites which show 3.2-3.3mm per with a rate of double every 150 or so years, there appears to be a significant increase in the rate SLR. Yet when you compare apples to apples and oranges to oranges, there is barely any change in the rate.

        Deceptive and misleading are two good terms for Church White

      • If global geostationary tide guages show ZERO acceleration in the miserly rate of rise, then what the satellite’s show is meaningless drivel, 100% irrelevant to how we live.

    • Climate models that are tuned to show that.

      Or are your climate models somehow doing more than their programming?

    • Which begs the question, Mosher: How long do we have to wait until the observations show it conclusively?

    • As always, Mosh gets even the basic science wrong.
      If the rate of warming is constant, than the rate of SLR will also be constant. (once accounting for the many lags in the system)
      If the temperature is constant, the rate of SLR will slow until it stops.
      Since some of the lags in the system are hundreds to thousands of years long, arguing about what has happened over the last 50 years is an exercise in delusion.

      • MarkW,
        I’m with you on this. I was going to ask Mosher for a citation or demonstration for his statement, but there have been enough push backs that I’ll ignore his unsubstantiated claim.

  6. The other useful illustration is shown here. The two sigma range for calculations of SLR acceleration mushroom rapidly as we approach starting dates as late as 1970.
    The result becomes less and less meaningful. Such that the section following 1970 is seemingly never shown.
    I however would like to amuse myself by viewing the crazy post-1970 portion of this graph.
    Does anybody have a copy?

  7. In most any real world data set, a higher order polynomial will yield a better fit than the standard linear fit. This is simply due to adding a degree of freedom to the fit model. The question now becomes “is the fit significantly better”.

    This is one of the Classic Problems in analytical chemistry.
    If the higher order term is not significant, then you are said to have overfit the data. At this point, it is relatively easy to show that the overfit model will give worse predicted values than the simpler model. (A standard exercise in chemistry statistics.) And this goes double, when you are extrapolating past the end of your data set.

    Willis showed, in a very emphatic way, that the acceleration term is *not* significant, so the regression fits (or models, if you will) which use an acceleration term are indeed overfit.
    So, in short, all those model predictions are just plain No Good.

    • I believe that in a well defined data set, a higher order polynomial will always fit the data better than a lower order polynomial. But, if you have no theory to determine the mathematical basis for the equation used, that does not translate into improved predictive ability. In fact willy-nilly high order polynomial curve fitting will almost always reduce the predictive ability.

    • TonyL,
      Indeed! An observation that I have made is that in fitting polynomials to real world data, the polynomial will often wildly deviate at the ends from the general pattern, and do so in such an extreme manner that it would appear to be a physically unrealizable situation. Extrapolation should always be taken with reservation.

  8. [Basing] projections on current acceleration has little to recommend it.

    Amen! End of services. Time to get back to mundane realities.

  9. http://www.nationalgeographic.com/magazine/2013/09/rising-seas-ice-melt-new-shoreline-maps/#/01-ice-melt-north-america.jpg.
    Looks like a minor problem for the US other than the east and south coasts. Not many folks in Alaska and Hawaii. No biggie the way I see it. Florida is soemwhat disconcerting. They have plenty of time to move. Next glaciation and all that land comes back anyway. The bottom line is that it’s happened before and will happen again. It’s the time frame that’s confusing folks.

    • My prediction:

      Greenland will melt entirely.
      Florida and parts of Georgia will disappear under shallow water.
      No one will miss them.

      Florida will become a rich fishing ground.

      Greenland will have a temperate climate and millions of people will live there.

    • It’s hard to take someone as a grownup…when they show their ignorance and post something like this…makes everything they say look childish….and discredits it all

      “Miami is already spending about half a billion dollars to deal with the flooding they’re already getting from sea level rise. Another foot will bring yet more damage”

      ….absolute ignorance about why Miami floods at King tides and always has
      and at this rate, it will be another 120 years to get to that “another foot”

      …and it’s Miami Beach…not Miami

    • “Demolished” by Tamino?
      Read Roy Spencer from July 21: “Study : Sea level rise revised downward.”
      Ah! Another debate in the settled science!

      • It seems we have dualing graphs here. (kind of difficult to “demolish” an argument with a cherry pick)…

      • I got the underlying data from the same source as your second graph, but it computed trends (or otherwise filtered) over four-, not fifty-year intervals, as I did.

        I can’t explain your first graph.

        My experience suggested that popular-audience sites are relatively less welcoming of proposed posts if they contain much math, so I emphasized intuitive appeal over mathematical rigor in writing the head post. But I’ll take this opportunity to dispel an ambiguity that the resultant rather-impressionistic approach may have left.

        If the least-squares quadratic fit to the data y(t) in the \Delta t-wide interval -\Delta t/2<t-t_{mid}<\Delta t/2 is given by \hat{y}(t)=\beta_0+\beta_1t+\beta_2t^2, the acceleration measure I assigned to the interval's midpoint t_{mid} is 2\beta_2. A reader might understandably have instead supposed my measure to be based on the least-squares linear fit \alpha_0+\alpha_1t. That is, one might have thought I computed acceleration as the rate \frac{d\alpha_1}{dt_{mid}} at which the t coefficient \alpha_1 varies with interval midpoint t_{mid}.

        I have no reason that I can rigorously defend for rejecting the latter measure. But that measure has much more high-frequency content, i.e., a lot more jitter, than the measure I chose. And, since the point of my post is how fickle acceleration is, choosing the higher-jitter measure might have opened me to accusations of over-egging the pudding.

        However that may be, the two measures are similar in that the measure I used bears a rough resemblance to the higher-jitter measure’s short-term average, whose magnitude range is about the same as the chosen measure’s.

        Of course, there are any number of filters one could have used instead. In general, though, the shorter the interval, the more fickle the indicator.

      • “I can’t explain your first graph.”

        The top graph is courtesy of tamino (from the 2nd link provided by RS). Here’s the rahmstorf graph (which middleton says is also based on C&W derived from PSMSL data) courtesy of real climate:

        It would be nice to know what the difference is (in the “sausage making”) between jevrejeva and church&white…

      • BTW, Joe, my dig was at “Really Skepical”, not you. i was just undermining his “demolished this post” claim with a comparison of graphs. (i think RS would do well to learn how to spell “Really Skeptical” first before grandstanding with a shallow argument… ☺)

      • scarletmacaw

        I don’t know where Tamino got his Boston graph RS, but NOAA’s shows no acceleration

        Tamino states up front that he’s using PMSL data for Boston and also links to the NOAA Boston data that you linked to. They are virtually identical. Therefore, using the same technique, i.e. converting to annual or a 12-month smooth, then fitting a modified lowess smooth or continuous piecewise-linear model, will produce the same result in the NOAA Boston data as it does in the PMSL Boston data – a period of acceleration up to the early 1950s followed by a slight deceleration, then renewed acceleration starting around the early 1990s.

        Using the same technique on your Mayport Florida data above also shows the same thing. This is not to say that the renewed acceleration is anything unusual, or something to be overly concerned about; but he’s not “lying” about it, as anyone can see by downloading the data from NOAA and calculating it themselves (fitting a 3rd order polynomial trend to the smoothed data does a similar thing)..

      • DWR, the tide guages show no acceleration period, end of story, as we live on the land where tide guages exist. We do not live on satelites. The satelite data always varies with drift, new satelites which give a different reading then the ones they replace and satelites do mot have a 50 year history.

      • David A

        DWR, the tide guages show no acceleration period, end of story, as we live on the land where tide guages exist. We do not live on satelites.

        Both the PMSL and NOAA data referred to are based on tide gauges, not satellites.

      • True, but for very limited area. Global long term tide guages ajusted for known land movement show no acceleration and a rise of 1.49 mm per year.

    • Because grown-ups say things like “it’s for the grown ups”.

      It’s one of those unconscious irony things.

    • ReallySkepical,

      And you think that it is “grown up” behavior to toss in an insult that implies that you are somehow superior to those you are insulting? It strikes me as the behavior of someone who is insecure and needs to bolster his self image. It certainly doesn’t do much to encourage a rational exchange.

  10. Good read. Let’s not lose sight of the principle that public policy should err on the side of caution. Meaning it stays out much more than it gets in

    • troe,
      All other things being equal, erring on the side of caution is pragmatic. However, all other things are rarely equal. The whole problem is that we usually don’t have the luxury of being able to afford to err on the side of caution. As an example: Earth has had numerous asteroid impacts throughout its history. To err on the side of caution would be to implement an Apollo-like program to deflect or destroy any asteroids that might potentially impact Earth. However, it would be a tremendously expensive, multi-year program that would almost certainly be opposed by those who would prefer to see that money spent on short-term social programs. Therefore, because of finite resources, it will be difficult to impossible to get agreement to spend money on caution.

  11. Regarding the comments about the public’s failure to trust experts, it’s not really about a matter of trust. It’s about a matter of freedom. Having an expert on hand to help you with something is great. But having an expert’s opinions taken by the government and translated into government policy that coerces behavior is something that should be treated as skeptically as the climate change argument. This leads right into the disaffection of so many Americans with perceived elites who think they know best how everyone should lead their lives. Plus we have many examples that lend themselves to a confirmation bias that many experts don’t know much beyond how to market themselves.

  12. @ Joe Born
    “In my case I’ve estimated that over this century CO2 fertilization would yield over a quarter million dollars in increased grain production alone per acre of land lost to a 3 mm/year sea-level rise.”

    Do you happen to have a link to your inference behind that conclusion?

    • I was just giving the grain-production estimate as an example of the type of half-baked, back-of-the-envelope estimate to which we laymen will resort when we see the “experts” rely on something as non-predictive as sea level acceleration.

      Of course it’s a half-baked estimate. It’s highly dependent on assumptions. There are lots of things I didn’t take into account. And, truth be told, I have no real idea of what global-average waterfront property goes for. If you want to know how I arrived at it, though, it went something like this:

      RCP45File = paste(RCPFolder, "RCP45_MIDYR_CONC.DAT", sep = "");
      RCP45 = read.table(RCP45File, header=TRUE, skip=38);
      RCP45.ts = ts(RCP45$CO2, start = 1765, freq = 1)
      hectares.per.square.kilometer <- 100
      acres.per.hectare <- 2.47105
      acres.per.square.kilometer <- acres.per.hectare * hectares.per.square.kilometer
      
      default.land.price <- 25e6
      
      dummy <- function(land.price = default.land.price, #  Dollars per square kilometer
                        crop.base = 2534e6, # Initial annual cereal-grain production in metric tons
                        sea.level.rise.rate = 0.003,  # Rate of sea-level rise, m/yr
                        crop.price = 400,  #  Dollars per metric ton
                        land.area.loss.rate = 369000,  # km^2 of land lost per meter sea-level rise
                        start.year = 2017, # first year
                        end.year = 2100, # last year
                        concentration = RCP60.ts,
                        crop.sensitivity.to.CO2 = 0.367/300, # Fraction of base concentration added per additional ppm
                        discount.rate = 0.03){
        t <- seq(start.year, end.year)
        discount <- (1 + discount.rate) ^ (start.year - t)
        concentration <- window(concentration, start = start.year, end = end.year)
        additional.crops <- crop.base * crop.sensitivity.to.CO2 * 
          (concentration - concentration[1])  # Additional cereal-grain production caused by CO2 increase
        additional.crop.value <- crop.price * cumsum(additional.crops)
        discounted.additional.crop.value <- crop.price * 
          cumsum(additional.crops * discount)
        sea.level <- (t - start.year) *sea.level.rise.rate  #  Sea-level difference from present
        delta.A <- land.area.loss.rate * sea.level
        land.value <- land.price * delta.A
        discounted.land.value <- cumsum(c(0, diff(land.value)) * discount)
        title <- paste("$", crop.price, "/tonne, $",
                       round(land.price / acres.per.square.kilometer / 1e3, 1), 
          "k / acre, ", 1000 * sea.level.rise.rate, " mm/yr",  sep = "")
        plot(t, additional.crop.value / 1e12, type = "l", xlab = "Year", ylab = "Value (Dollars)", 
             main = "Crop Increase vs. Land Loss", sub = title)
        lines(t, land.value / 1e12, lty = 2, lwd = 2, col = 2)
        legend("topleft", legend = c("Additional Cereal Production", "Lost Land Value"),
               lty = c(1, 2), col = c(1,2), title = "Not Discounted", bty = "n")
        title <- paste(title, ", ", 100 * discount.rate, "% discount rate", sep = "")
        plot(t, discounted.additional.crop.value / 1e12, type = "l",
             xlab = "Year", ylab = "Value (Trillions of Dollars)", 
             main = "Crop Increase vs. Land Loss", sub = title)
        legend("topleft", legend = c("Additional Cereal Production", "Lost Land Value"),
               lty = c(1, 2), col = c(1,2), title = "Discounted", bty = "n")
        lines(t, discounted.land.value / 1e12, lty = 2, lwd = 2, col = 2)
        n <- 1 + end.year - start.year
        c(discounted.additional.crop.value[n], discounted.land.value[n])
      }
      comparison <- dummy(concentration = RCP45.ts)
      breakeven.land.price <- default.land.price * comparison[1] / comparison[2]
      dummy(land.price=breakeven.land.price, concentration = RCP45.ts)
      breakeven.land.price / acres.per.square.kilometer
      # 270043.6
      
      #  That is, under the RCP 4.5 scenario, if grain price is $400/tonne and future 
      #  flows are discounted at 3%, then the present value of increased production 
      #  equals the present value of land lost in response to 3 mm/yr of sea-level
      #  rise if that land costs $270,043.60/acre.
      

      (If you want to run this yourself, you need to replace “RCP45File” with the location into which you’ve stored the RCP 4.5 scenario from the IPCC.)

      Obviously, your mileage may differ.

      • Thanks, I should have mentioned that I was just interested in the inference and the figures you used, I realized that a lot of assumptions would have to be baked in. :)

  13. Who is afraid of accelerating the sea level?
    Nobody except the climatic alarmists, the misguided scientists, the false prophets of the Holy Church Warming up, some politicians, the media.

  14. Essentially what was proven is that time and sea level are independent variables, and as such, any linear or parabolic, or any other trends with time have no predictive meaning. This is equivalent to making a trend fit on commodity futures prices to predict future prices. It does not work for commodities as time does not determine commodity prices. Similarly, sea level is not based on time either, and also has no predictive meaning. This author has discovered Statistics 101, and nothing else. Trends only work predictively for dependent variables, so the graph must be, for example, CO2 versus sea level with a significant correlation coefficient, say over 0.7.

    • Setting aside the fact that I hadn’t claimed to have written the Twenty-First Century equivalent to Gödel’s proof, you do realize you’re arguing my point, right? Namely, acceleration’s predictive value is scant.

      As to correlation between CO2 concentration and sea level, you’ll find it’s sensitive to which time period you calculate the correlation from. Pick the right time period, and you’ll find a negative correlation.

      I’m not saying that CO2 concentration doesn’t ultimately have any effect on sea level. I’m merely saying that scientists are being disingenuous when they use acceleration to frighten the natives.

      • The paleo record is clear. For hundreds of thousands of years, when CO2 levels are low the oceans start rising and when they are high the oceans start falling.

    • DK,
      Considerably over 0.7 as that only explains less than half of the variance in the dependent variable.

  15. ” In my case I’ve estimated that over this century CO2 fertilization would yield over a quarter million dollars in increased grain production alone per acre of land lost to a 3 mm/year sea-level rise. So to me increased carbon-dioxide concentration doesn’t seem like such a bad thing.

    Does your analysis include predicted changes in precipitation for different regions?

  16. One issue with sea level rise, accelerating or not, is that as it increases the area of the surface increases.

    As a very rough analogy we could think of the oceans as an inverted cone. As the water level inside the cone increases, the surface area increases. This means that if ‘X’ amount of added water causes the level to increase 1 inch, then adding another amount equal to ‘X’ will NOT cause the level to increase another 1 inch because the 1 inch at the new higher level represents a larger volume.

    Is this effect accounted for in the predictions of sea level rise?

    • ddpalmer–I brought that point up in a recent comment to Willis’ article. He (correctly) pointed out that for small sea level rise it really isn’t a significant effect, but would only start to count when you are talking about tens of meters of rise. I agreed, and pointed out that the alarmists are continually showing those illustrations of NYC under 150 feet of water; that a simple Google search yields abundant predictions (again, in the woefully ignorant, illiterate and apathetic media) of 100+ foot sea level rises by 2100. I have not seen (nor tried to create) a model that accounts for this. Of course, there are secondary effects to consider (which start reaching imho into the we-have-no-idea land of assumptions) such as increased melt of exposed-to-the-coast ice sheets, addition of earthen materials into the water via erosion, and so on. The picture gets really cloudy with assumptions/projections. IMHO the long term tide gauges in places w/o isostatic rebound or subsidence are the best indicators (not satellites), and these appear to show no threatening acceleration. Locally in northern California, the press predicts 100 feet of SLR by 2100; but the tide gauges at SF and Alameda (if they continue their linear trends w/o change–and as we all know, anything *can* change, in any direction) will only show less than 7 inches rise by 2100. The NPS has a display at Alcatraz pitching the rising seas flooding everything story–at what point will they acknowledge reality and take it down?

    • ddpalmer,

      To be more precise, the topography of the inundated shorelines will control how much land is flooded for any given rise in sea level, and the subsurface topography will also control how much the oceans rise for a given volume increase. Imagine if you have a tall, thin cylinder containing 1 liter of water and a wide pan with 1 liter. Adding 1 milliliter of water to each will result in a very different increase in the height of the water in the containers.

      This explains why Mosher’s claim that “basic physics and climate models predict that in a warming world the sea level rise will begin to accelerate.” is naïve. To be able to make that generalized claim, one needs to take into account the shape of the current ocean basins and the topography of the world shorelines. Even if the volume of the oceans accelerates with warming (which I’m not convinced is valid), it is conceivable that the topography of the shorelines could nullify sea level acceleration. In any case, Mosher does not demonstrate that acceleration is inevitable in the real world. His claim might be valid for a flat world where the oceans are constrained to rectangular basins.

  17. Who’s Afraid of Sea-Level Acceleration?

    Ultimately, nobody [nobody sensible], because we adapt faster than the sea level changes. Current new buildings will be obsolete and be demolished before the sea level rises enough to threaten them with a few extra inches. The next generation will either be built further uphill, or on stilts.

    Of course much major damage will often come during exceptionally high tides coupled with storms, but that is already the case today. Nothing will change. It is not difficult for insurance companies to factor such slow changes into their actuarial calculations.

  18. Any trend that changes when you change the end points is not a true trend.

    The problem is that every trend line added to a graph is a form of curve fitting. And while it may perfectly predict the past, the very annoying thing about the curve is that it has zero skill when predicting the future. Almost always a better prediction is to be had simply by predicting tomorrow will be pretty much like today.

  19. So, Mr. Born, argues, very reasonably in my view, that a noisy and uncertain time series, becomes more noisy and uncertain when differentiated once, and becomes increasingly noisy and uncertain with another differentiation.

    However, Mr. Mosher counters that such a view is so foolish as to be not even wrong, with the “basic physics” that somewhat more water poured into a glass causes the observed water surface to rise.

    Surely this is one of the foremost science sites.

    • Sirely K kilty understands that short term trends in very large oceans which experience lags on the melennial scale, are meaningless.

      This is profoundly true when tide guages, direct observations where people live, shoe ZERO acceleration.

      • Shoe enough David. Nuthin’ in my post is at odds with what you say. And stop callin’ me sirely.

      • Lol, sorry for the typos. Small keys, fat fingers, and a tired mind led me to think you were supporting Mosher`s irrelevant truisms.

  20. Joe asks: Who’s Afraid of Sea-Level Acceleration?

    I am. 5K of warming at the end of the last ice age produced 120 m of SLR. Today’s situation is very different, but SL is very sensitive to global temperature in the long run.

    SLR data from individual tide gauges is so noisy and autocorrelated that it takes about 50 years to produce a rate with a useful (narrow) 95% confidence interval. Then one needs two 50-year periods to answer the question of whether SLR is accelerating at that location. Useless.

    If we combine the records from a hundred or so tide gauges, we will have a stronger signal. Unfortunately, they are all contaminated with different amounts of local vertical land motion (VLM). We have invested everything in satellite altimetry and haven’t invested anything in getting accurate GPS measurements of VLM at the locations that will be DAMAGED by SLR. And after two decades, the rate of SLR from satellite altimetry for 1993-2000 was reduced by well over 50% when a systematic error was discovered. (For the full period, SLR is down to 2.4 mm/yr from 3.2 mm/yr, so the correction must have been huge.) We also need to know about local SLR because melting from Greenland produces much less SLR in the North Atlantic than melting in Antarctica.

    Unfortunately, your work doesn’t include any confidence intervals. I suspect that if you did calculate confidence intervals (including corrections for autocorrelation) and put the results in a table (instead of your graph with many trend lines), your readers would recognize that all of the short trends had meaninglessly-wide confidence intervals. And if it takes 20 or 40 years to measure a useful rate of average SLR, then we have no useful idea of whether SLR is accelerating.

    We are in the dark about acceleration in SLR I’m afraid of the dark!

    I can shed some light on the subject. Current SLR is about 1 inch/decade (or 2.5 mm/yr if you want to be more scientific and less tangible about it). Acceleration of 1 inch/decade/decade (0.25 mm/yr/yr) will produce about 1 m of SLR by the end of the century. (2″ in the 2020’s, up to 9″ in the 2090s, totally 44 inches by the end of the century. Nice round numbers even I can understand and remember.)

    So, I’d be thrilled if you, Willis, or someone could show with confidence intervals that acceleration of SLR is much less that 1 inch/decade/decade.

    • Current SLR is about 1 inch/decade (or 2.5 mm/yr if you want to be more scientific and less tangible about it). Acceleration of 1 inch/decade/decade (0.25 mm/yr/yr) will produce about 1 m of SLR by the end of the century. (2″ in the 2020’s, up to 9″ in the 2090s, totally 44 inches by the end of the century. Nice round numbers even I can understand and remember.)

      The rough guess that we are experiencing an acceleration 0.25 mm/yr/yr presumes that the current SLR started from zero quite recently. That is far from the case! Fairly steady SLR has been observed for at least a century. Furthermore there is considerable evidence for multidecadal cycles of acceleration and deceleration. Thus the presumption that any currently experienced acceleration will persist unabated through the remainder of this century is hazardous at best.

      These are far more significant aspects of the problem than any lack of formal confidence intervals for acceleration. Great worry is simply unwarranted by the evidence.

      • 1sky1: Confidence intervals take into account multi-decadal changes in SLR. If you use only one or two decades of data, the confidence interval for acceleration is huge. If you use longer periods, multi-decadal variability widens the confidence interval. So I think formal confidence intervals help interpret the meaning of the data we have and reduce the possibility of being fooled by confirmation bias.

        When would we have expected an acceleration in SLR to have started? Global WARMING mediated by rising GHG’s didn’t become significant until the second half of the 20th century according to the IPCC or until about 1975 (0.17 K/decade since) according to my biases. So if we allow a few decades for heat to diffuse into the deep ocean (and cause thermal expansion) or lubricate and speed up ice flow in Greenland and Antarctica, maybe we should be looking for acceleration beginning in the 1990s (the satellite altimetry era though I don’t trust their data analysis). The fundamental problem is that it takes a long time to determine an accurate RATE of SLR and even longer to detect a change in that rate – ACCELERATION. There is at least one publication (I can’t easily locate) that discusses how long a detection period would be required for both tide gauge and satellite altimetry

        My amateur attempts to quantify the confidence interval around current acceleration includes zero and don’t reach as high as 1 inch/decade/decade (or 0.25 mm/yr/yr). In the past, I confidently stated there was no danger of reaching +1 m in 2100 – we aren’t experiencing anything like 1 inch/decade/decade today! Unfortunately, we don’t know what is happening today: We know about past decadeS when a modest amount of acceleration probably occurred, but which we can’t accurately quantify. If an acceleration rate of 1 inch/decade/decade first was reached in 2025, how long would it take before measurements unambiguously informed us what was happening? It could take another two decades. Fortunately, we would have many decades to prepare for the coming “innundation” (half a foot a decade and more), but probably can’t mitigate the problem by reduction of CO2 emissions once the problem is clear.

      • Confidence intervals take into account multi-decadal changes in SLR.

        That’s what they SHOULD do, But, because they are usually computed on the bald assumption that the underlying process is “red noise”–which has no truly cyclical components–they fail to account for quasi-cyclical multidecadal oscillations.

        In any event, the detection of acceleration in SLR is not particularly demanding. It certainly doesn’t take two decades when smoothed ROC methods, rather than regressional slopes, are properly employed. (There’s no good reason to cascade the smoothing, as Greg does, in computing estimates.) Nevertheless, the significance of any acceleration or deceleration is highly uncertain. That’s why responsible oceanographers who note the current increase in SLR to ~3mm/yr usually include the caveat that we simply don’t know whether such rates (let alone accelerations) will persist in the near future. Alarmists, of course, want you to worry unduly about it

    • Frank, very nice comment. (an antagonistic point of view without being antagonistic — BTW, use a night light, it works for me… ☺)

      Keep in mind that it took 10,000 years for sea levels to rise 120 meters. That’s only about a meter per century. So if we don’t see runaway global warming, we sure aren’t going to see even those kinds of numbers. (plus, recall that in the depths of an ice age there’s a whole lot more ice on land) So this sea level thing, as with all other “alarmism”, is eventually going to result in yet another collective yawn from all of society. (sea levels rising as “see” levels fall)…

      • Afonzarelli: Joe Born was trying hard to inform us. I appreciated that and tried to explain why I was looking for a more sophisticated analysis. I’ve tried and it was a pain for the satellite data. The tide gauge data appears far more complicated.

        I’ve though about the 1 m/century for 12 millennium a lot. That was driven by +0.5 K/millennium for 10 millennia. We’ve just experience 1 K in a single century (not all of which was forced by GHGs). Lukewarmers will find it hard to avoid another 1 K in the next century. The rate of SLR experienced as the last ice age ended isn’t a very good models for our future.

    • I hope you can stay tuned, because I will be otherwise occupied for a couple of days.

      But I’ll take a moment to note that I didn’t compute confidence intervals explicitly. At first blush, though, it seems to me that your comment about short intervals’ confidence intervals largely supports the point of my post, although I’m open to being convinced otherwise.

      There’s another issue your comment suggests, though, that I didn’t investigate, and I suspect I won’t be able to whip the answer out in the couple of minutes I have now.

      So, if you can hang tight, I’ll get back to you.

    • Frank:

      Now returning to your comment, I see it really makes only the unremarkable observation that the acceleration data don’t enable you to rule out much of any projection. I don’t disagree. That is, you can’t use the record’s accelerations to rule out doomsday scenarios, just as it’s irresponsible for scientists to use them to frighten the natives.

      Consequently, I don’t think you “shed some light” when you assumed an acceleration to make a projection. Since you insisted on doing it, though, you might have tied it a little more closely to the data. For example, the end of the century is 82.5 years from now, so you might have based it on 82.5-year intervals in the record. In the PSMSL record I used for the head post, the latest 82.5-year trend is 2.016 mm/year, which is about in the middle of a fairly tight 82.5-year-trend range that’s prevailed for the last forty years (before which trends were lower). This would imply a rise of 6.5 inches by 2100.

      The range of 82.5-year-interval accelerations exhibited by that 1807-2010 record is [ 0.034, 0.091] mm/yr^2. Tacking that onto the latest trend projects a rise of between two and nineteen inches. But remember that we started with a trend value produced by a linear projection. If we do a complete quadratic projection from the most-recent 82.5-year interval, we actually get a sea-level reduction of 2.3 inches, not a rise: on that time scale the rise has been decelerating.

      I agree with you, though, that, in light of how heavily autocorrelated the data are, the ranges in our short record don’t mean much. (I didn’t attempt the autocorrelation-adjusted confidence intervals, but my guess is that doing so would smear the projection range out over several feet.)

      So, no, we can’t use those data to rule out high sea-level rise. Nor can we use them to rule out the possibility that making full use of our fossil-fuel resources could prevent tens of millions of premature deaths from malnutrition and respiratory ailments.

  21. Very long term sea level is a decaying exponential. If anything, an AGW component plus other anthropogenic components such as soot, are likely bringing us to the ultimate asymptote more quickly. I seriously doubt that anthropogenic components are going to change the nature of that asymptote. That asymptote is likely more strongly correlated with underlying constraints which control the series of glacials and interglacials.

  22. When talking of sea level rise you fail to acknowledge that the land masses are merely floating on a liquid mantle. The land masses are moving greater distances annually than any perceived change of water level against said land mass. Your tide measurements are not a significant indicator of ocean temperature or the temperature of the planet. Cloud cover has more affect on earth surface temps than CO2 ppm.

    • I also “fail to acknowledge” that the pope is Catholic.

      In the head post the question before the house is whether climate scientists would be justified in basing predictions of catastrophic sea-level rise on available measures of sea-level acceleration even if “the published oceans-average values [were] precisely accurate and that all tide-gauge locations [exhibited] them uniformly.” That question is separate and distinct from what causes sea-level rise in the first place and whether there may be some other, more-justified reason for concern.

  23. ” In a world in which climate scientists base catastrophic projections on as fickle an indicator as sea-level acceleration, it’s _questionable_ that as laymen we err more in skepticism than in credulity.”

    I find this confusing. Did you mean to say “not surprising” instead of “questionable”?

    • I suppose I could have made that clearer.

      By “err on the side of skepticism” I meant making errors more often by being skeptical than by being credulous, as Dr. Nichols says we laymen do. I think that’s a questionable proposition.

Comments are closed.