Sea Water Level, Fresh Water Tilted

Guest Post by Willis Eschenbach

Among the recent efforts to explain away the effects of the ongoing “pause” in temperature rise, there’s an interesting paper by Dr. Anny Cazenave et al entitled “The Rate of Sea Level Rise”, hereinafter Cazenave14. Unfortunately it is paywalled, but the Supplementary Information is quite complete and is available here. I will reproduce the parts of interest.

In Cazenave2014, they note that in parallel with the pause in global warming, the rate of global mean sea level (GMSL) rise has also been slowing. Although they get somewhat different numbers, this is apparent in the results of all five of the groups processing the satellite sea level data, as shown in the upper panel “a” of Figure 1 below

cazenave figure 2Figure 1. ORIGINAL CAPTION: GMSL rate over five-year-long moving windows. a, Temporal evolution of the GMSL rate computed over five-year-long moving windows shifted by one year (start date: 1994). b, Temporal evolution of the corrected GMSL rate (nominal case) computed over five-year-long moving windows shifted by one year (start date: 1994). GMSL data from each of the five processing groups are shown.

Well, we can’t have the rate of sea level rise slowing, doesn’t fit the desired message. So they decided to subtract out the inter-annual variations in the two components that make up the sea level—the mass component and the “steric” component. The bottom panel shows what they ended up with after they calculated the inter-annual variations, and subtracted that from each of the five sea level processing groups.

So before I go any further … let me pose you a puzzle I’ll answer later. What was it about Figure 1 that encouraged me to look further into their work?

Before I get to that, let me explain in a bit more detail what they did. See the Supplemental Information for further details. They started by taking the average sea level as shown by the five groups. Then they detrended that. Next they used a variety of observations and models to estimate the two components that make up the variations in sea level rise.

The mass component, as you might guess, is the net amount of water either added to or subtracted from the ocean by the vagaries of the hydrological cycle—ice melting and freezing, rainfall patterns shifting from ocean to land, and the like. The steric (density) component of sea level, on the other hand, is the change in sea level due to the changes in the density of the ocean as the temperature and salinity changes. The sum of the changes in these two components gives us the changes in the total sea level.

Next, they subtracted the sum of the mass and steric components from the average of the five groups’ results. This gave them the “correction” that they then applied to each of the five groups’ sea level estimates. They describe the process in the caption to their graphic below:

cazenave figure S3Figure 2. This is Figure S3 from the Supplemental Information. ORIGINAL CAPTION: Figure S3: Black curve: mean detrended GMSL time series (average of the five satellite altimetry data sets) from January 1994 to December 2011, and associated uncertainty (in grey; based on the dispersion of each time series around the mean). Light blue curve: interannual mass component based on the ISBA/TRIP hydrological model for land water storage plus atmospheric water vapour component over January 1994 to December 2002 and GRACE CSR RL05 ocean mass for January 2003 to December 2011 (hybrid case 1). The red curve is the sum of the interannual mass plus thermosteric components. This is the signal removed to the original GMSL time series. Vertical bars represent the uncertainty of the monthly mass estimate (of 1.5 mm22, 30, S1, S3; light blue bar) and of the monthly total contribution (mass plus thermosteric component) (of 2.2 mm, ref. 22, 30, 28, 29, S1, S3; red bar). Units : mm.

So what are they actually calculating when they subtract the red line from the black line? This is where things started to go wrong. The blue line is said to be the detrended mass fluctuation including inter-annual storage on land as well as in water vapor. The black line is said to be the detrended average of the GMSL The red line is the blue line plus the “steric” change from thermal expansion. Here are the difficulties I see, in increasing order of importance. However, any of the following difficulties are sufficient in and of themselves to falsify their results.

• UNCERTAINTY

I digitized the above graphic so I could see what their correction actually looks like. Figure 3 shows that result in blue, including the 95% confidence interval on the correction.

cazenave %22correction%22Figure 3. The correction applied in Cazenave14 to the GMSL data from the five processing groups (blue)

The “correction” that they are applying to each of the five datasets is only statistically different from zero for 10% of the datapoints. This means that 90% of their “correction” is not distinguishable from random noise.

• TREND

In theory they are looking at just inter-annual variations. To get these, they describe the processing. The black curve in Figure 2 is described as the “mean detrended GMSL time series” (emphasis mine). They describe the blue curve in Figure 2 by saying (emphasis mine):

As we focus on the interannual variability, the mass time series were detrended.

And the red curve in Figure 2 is the mass and steric component combined. I can’t find anywhere that they have said that they detrended the steric component.

The problem is that in Figure 2, none of the three curves (black:GMSL, blue:mass, red:mass + steric) are detrended, although all of them are close. The black curve trends up and the other two trend down.

The black GMSL curve still has a slight trend, about +0.02 mm/yr. The blue steric curve goes the other way, about -0.6 mm/yr. The red curve exaggerates that a bit, to take the total trend of the two to -0.07 mm yr. And that means that the “correction”, the difference between the red curve showing the mass + steric components and the black GMSL curve, that correction does indeed have a trend as well, which is the sum of the two, or about a tenth of a mm per year.

Like I said, I can’t figure out what’s going on in this one. They talk about using the detrended values for determining the inter-annual differences to remove from the data … but if they did that, then the correction couldn’t have a trend. And according to their graphs, nothing is fully detrended, and the correction most definitely has a trend.

• LOGIC

The paper includes the following description regarding the source of the information on the mass balance:

To estimate the mass component due to global land water storage change, we use the Interaction Soil Biosphere Atmosphere (ISBA)/Total Runoff Integrating Pathways (TRIP) global hydrological model developed at MétéoFrance22. The ISBA land surface scheme calculates time variations of surface energy and water budgets in three soil layers. The soil water content varies with surface infiltration, soil evaporation, plant transpiration and deep drainage. ISBA is coupled with the TRIP module that converts daily runo simulated by ISBA into river discharge on a global river channel network of 1 resolution. In its most recent version, ISBA/TRIP uses, as meteorological forcing, data at 0.5 resolution from the ERA Interim reanalysis of the European Centre for Medium-Range Weather Forecast (www.ecmwf.int/products/data/d/finder/parameter). Land water storage outputs from ISBA/TRIP are given at monthly intervals from January 1950 to December 2011 on a 1 grid (see ref. 22 for details). The atmospheric water vapour contribution has been estimated from the ERA Interim reanalysis.

OK, fair enough, so they are using the historical reanalysis results to model how much water was being stored each month on the land and even in the air as well.

Now, suppose that their model of the mass balance were perfect. Suppose further that the sea level data were perfect, and that their model of the steric component were perfect. In that case … wouldn’t the “correction” be zero? I mean, the “correction” is nothing but the difference between the modeled sea level and the measured sea level. If the models were perfect the correction would be zero at all times.

Which brings up two difficulties:

1. We have no assurance that the difference between the models and the observations is due to anything but model error, and

2. If the models are accurate, just where is the water coming from and going to? The “correction” that gets us from the modeled to the observed values has to represent a huge amount of water coming and going … but from and to where? Presumably the El Nino effects are included in their model, so what water is moving around?

The authors explain it as follows:

Recent studies have shown that the short-term fluctuations in the altimetry-based GMSL are mainly due to variations in global land water storage (mostly in the tropics), with a tendency for land water deficit (and temporary increase of the GMSL) during El Niño events and the opposite during La Niña. This directly results from rainfall excess over tropical oceans (mostly the Pacific Ocean) and rainfall deficit over land (mostly the tropics) during an El Niño event. The opposite situation prevails during La Niña. The succession of La Niña episodes during recent years has led to temporary negative anomalies of several millimetres in the GMSL, possibly causing the apparent reduction of the GMSL rate of the past decade. This reduction has motivated the present study.

But … but if that’s the case then why isn’t this variation in rainfall being picked up by the whiz-bang “Interaction Soil Biosphere Atmosphere (ISBA)/Total Runoff Integrating Pathways (TRIP) global hydrological model”? I mean, the model is driven by actual rainfall observations, including all the data of the actual El Nino events.

And assuming that such a large and widespread effect isn’t being picked up by the model, in that case why would we assume that the model is valid?

The only way that we can make their logic work is IF the hydrologic model is perfectly accurate except it somehow manages to totally ignore the atmospheric changes resulting from El Nino … but the model is fed with observational data, so how would it know what to ignore?

• OVERALL EFFECT

At the end of the day, what have they done? Well, they’ve measured the difference between the models and the average of the observations from the five processing groups.

Then they have applied that difference between the two to the individual results from the five processing groups.

In other words, they subtracted the data from the models … and then they added that amount to the data. Lets do the math …

Data + “Correction” = Data + (Models – Data) = Models

How is that different from simply declaring that the models are correct, the data is wrong, and moving on?

CONCLUSIONS

1. Even if the models are accurate and the corrections are real, the size doesn’t rise above the noise.

2. Despite a claim that they used detrended data for their calculations for their corrections, their graphic display of that data shows that all three datasets (GMSL, mass component, and mass + steric components) contain trends.

3. We have no assurance that “correction”, which is nothing more than the difference between observations and models, is anything more than model error.

4. The net effect of their procedure is to transform observational results into modeled results. Remember that when you apply their “correction” to the average mean sea level, you get the red line showing the modeled results. So applying that same correction to the five individual datasets that make up the average mean sea level is … well … the word that comes to mind is meaningless. They’ve used a very roundabout way to get there, but at the end they are merely asserting is that the models are right and the data is wrong …

Regards to all,

w.

PS—As is customary, let me ask anyone who disagrees with me or someone else to quote the exact words that you disagree with in your reply. That way, we can all be clear about what you object to.

PPS—I asked up top what was the oddity about the graphs in Figure 1 that made me look deeper? Well, in their paper they say that the same correction was applied to the data of each of the processing groups. Unless I’m mistaken (always possible), this should result in a linear transformation of each month’s worth of data. In other words, the adjustment for each month for all datasets was the same, whether it was +0.1 or -1.2 or whatever. It was added equally to that particular month in the datasets from all five groups.

Now, there’s an oddity about that kind of transformation, of adding or subtracting some amount from each month. It can’t uncross lines on the graph if they start out crossed, and vice versa. If they start out uncrossed, their kind of “correction” can’t cross them.

With that in mind, here’s Figure 1 again:

cazenave figure 2Figure 1 redux …

I still haven’t figured out how they did that one, so any assistance would be gratefully accepted.

DATA AND CODE: Done in Excel, it’s here.

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JP Miller
March 29, 2014 6:41 pm

And we’re given this from the International New York Times:
http://www.nytimes.com/2014/03/29/world/asia/facing-rising-seas-bangladesh-confronts-the-consequences-of-climate-change.html?ref=world&_r=0
Has the world gone insane?
This global warming thing is the equivalent of the Salem Witch Trials, only more people are being killed as a result (e.g., winter deaths in GB due to expensive power caused by….).

bushbunny
March 29, 2014 6:57 pm

Deep sea heat? Well there is a bit of proof that deep sea vents do throw out hotter water, and the life around them exists on chemosynthesis, rather than photosynthesis. Anyway that is restricted to around volcanic vents and trenches. But the volume of the cold water soon cools it down.

ossqss
March 29, 2014 6:59 pm

I have often wondered what a persistent high pressure system does to sea levels when over the water for an extended period of time.
Just a thought.
Nice read Willis!

March 29, 2014 7:10 pm

” Global averages for sea levels are as nonsensical as global averages for land temperature”
both averages make perfect sense.

March 29, 2014 9:21 pm

Wills
Another factor that I don’t see mentioned is how much water is bound up in plants? Since, according to several studies, the planet has greened by 30% due to carbon fertilization since the 1960’s, that would imply greater water storage in the floral system.

March 29, 2014 9:21 pm

The question of the contribution of erosion and tectonics to SLR could use a philosophical perspective. One consideration: how much water is rained down on the earth from space? How much space dust? Both are surely trivial, but space dust is not only trivial but irrelevant, since it should be spread evenly over the planet, raising ocean and land evenly. Space water, on the other hand, would only raise sea level.
Ignoring ice and thermal expansion, that is, considering only depth and elevation distribution, it should at least be noted that the continents have always floated on the mantle, and while subduction of the continents does occur, it is reasonable to assume that they resurface at an approximately equivalent rate. Likewise the same plate tectonics that alter the width and depth of ocean basins simultaneously build mountain ranges, and the same sedimentation that builds the continental shelves results in uplift of the plateaus and river basins from which the sediment is removed.
In other words there is little reason to believe that over the long run geological processes make much difference in SLR, let alone over decades. The earth has never been flat, mountains are always growing, and gravity and erosion limit their height.
The separate question as to SLR serving as a thermometer is complicated by a few factors that need mentioning. For one thing, it takes about two orders of magnitude more energy to raise SL through expansion than through melting land ice, so that the relative contribution of each must be known before we can calibrate. Also, since thermal expansion of seawater varies by temperature, pressure, and salinity–significantly–we have to know at what depth and temperature the expansion is taking place before we can calculate energy input from steric SLR. Obviously with ARGO it’s easier to calculate in the other direction.
Through the Pleistocene there has been obvious correlation between SLR and T, but it is not a case of cause and effect with T as cause. Rather the reverse is closer to the truth, since SLR is a function of ice volume, and T is a function of albedo, or ice area. Therefore T/SLR corresponds to ice area/ice volume, on a Pleistocene secular scale. –AGF

Dave Wendt
March 29, 2014 10:01 pm

Willis Eschenbach says:
March 29, 2014 at 7:24 pm
A couple of papers along these lines
http://onlinelibrary.wiley.com/doi/10.1029/2007GL030862/abstract
Gyre-scale atmospheric pressure variations and their relation to 19th and 20th century sea level rise
Laury Miller1 andBruce C. Douglas2
http://www.ocean-sci.net/6/185/2010/os-6-185-2010.pdf
The gyre-scale circulation of the North Atlantic and sea level at
Brest
P. L. Woodworth1 , N. Pouvreau2, and G. Woppelmann ¨

tonyb
Editor
March 30, 2014 12:03 am

mosh said in reply to me
” Global averages for sea levels are as nonsensical as global averages for land temperature”
He said ‘both averages make perfect sense.”
In that case it should be very easy for you to explain them.
They make as much sense as the average for global economic growth which ignores that some areas remain in recession whilst others are powering ahead. You will set economic policy according to what is happening in your own country/region not what is happening elsewhere
Surely it is more useful to look at what is actually happening in the real world rather than at some averaged one which doesn’t exist?
But look forward to your detailed article. A good title would be ‘One size does fit all.’
tonyb

Gamecock
March 30, 2014 8:59 am

Willis Eschenbach says:
March 29, 2014 at 7:10 pm
The question is not whether the ocean basin size varies. Everyone knows it varies. The question is, does it vary enough to make a difference?
=======================
I have never, ever heard anyone mention variability of the ocean basin. All discussions of sea level are about water only.
Does it vary enough to make a difference? We simply don’t know.

Steve Keohane
March 30, 2014 9:32 am

rgbatduke says:March 29, 2014 at 9:57 am
Thank you for your expansion of my thought. Although TonyB responded to your query of ancient harbor’s sea level, he didn’t point to his sites post http://climatereason.com/Articles/
Third article down, entitled ‘A Look at Historic Sea Levels’, by Tony Brown, with links.

March 30, 2014 9:53 am

Gamecock says:
March 30, 2014 at 8:59 am
I have never, ever heard anyone mention variability of the ocean basin. All discussions of sea level are about water only.
===============================================================
Three years ago UofC adjusted SLR 10% upwards for GIA, which is vertical change in ocean basin. Where were you?
http://wattsupwiththat.com/2011/05/05/new-sea-level-page-from-university-of-colorado-now-up/
–AGF

Tonyb
March 30, 2014 12:30 pm

Willis
Of course averages are useful in some cases.
I was particularly concerned with the worth of global averages for something as local as sea temperatures, and land temperatures and sea levels. By averaging we are missing out on useful nuances whereby for example not all the world is warming and not all the sea in its various basins is rising, indeed in some areas sea level is falling whilst in others it is rising much faster than ‘average,’
Tonyb

March 30, 2014 7:00 pm

Willis, if you want to explore bounds on thermal gain using steric expansion, I recommend this reference: http://publishing.cdlib.org/ucpressebooks/view?docId=kt167nb66r&chunk.id=d3_4_ch03&toc.id=ch03&toc.depth=1&brand=eschol&anchor.id=tab009#X. I also checked my numbers against Levitus et al [GRL 2012].
Levitus et al [GRL 2012] estimate the 55 year trend of ocean thermal gain (1955-2010) to be 0.4W/m2 over the entire ocean volume, which is much less than 1.5W/m2, but theoretically could have increased in the last 16 years of flat lower tropospheric temperatures. They correspondingly estimate less of a thermosteric component of sea level rise, at 0.54mm/y which means that my back-of-the-envelope upper bound of 2mm/y sea level per 1 – 2 W/m2 heat storage (1-2mm/W/m2) agrees with Levitus et al’s number of 0.54mm/y/0.4W/m2 (1.35mm/W/m2).
Since implicit in Levitus is 1.35mm of sea level rise per W/m2 of ocean-stored global forcing, and the IPCC estimates net anthropogenic forcing to be 1.5W/m2. That comes out to just about exactly 2mm/y of sea level rise if it all goes into the ocean. If the current rate is 3mm/y, that leaves only 1mm/y for the natural post LIA rise plus all the anthropogenically melted glaciers.

March 30, 2014 7:24 pm

Willis writes “Consider for example the grade-point-average (GPA) for a student. How is that not useful in measuring how well a student is learning?”
I think you missed the point. Consider for example the grade-point-average (GPA) for all students. How is that useful in measuring how well a student is learning?
I’ve subtly rewrittewn your statement so you can see his point.

March 30, 2014 11:34 pm

Willis writes “Recall that his comment to which I was responding was in reference to sea level measurements:”
Because you ignored his argument.which was “You will set economic policy according to what is happening in your own country/region not what is happening elsewhere. Surely it is more useful to look at what is actually happening in the real world rather than at some averaged one which doesn’t exist?”
I dont think you understood. His point was about the importance of local effects not whether there was any use for a global average at all. Your example specifically didn’t address what I would consider his main point.

March 31, 2014 3:36 am

Willies writes “If you’re going to be a jerkwagon, at least be consistent.”
Thanks for the abuse Willis.
Willis writes “Now his explanation (as you point out) was that averages are nonsensical because some areas are going up and some areas are going down … do you really believe that?”
I dont know about “going down” but certainly its very well known that sea level rise differs regionally and so it makes sense for local authorities to be looking at their regional changes when considering policy rather than focussing on the global average. He made that point and its a fair one.
You ignored it entirely and instead focussed on your own interest area. Fine. I expect nothing less from you actually.

March 31, 2014 4:58 am

Willis writes “Tim, re-read the thread. Things were going quite nicely until you accused me of malfeasance, saying that I deliberately was ignoring what someone was saying. ”
Good idea.
Tim writes “I think you missed the point.”
Well there’s a hateful comment telling you you were ignoring something. That was bound to start an abusive argument from you. And it did.
And then you wrote _rant_ including calls of omniscience and ESP regarding my “understanding” of what you ignored. Well what you ignored was what you didn’t reply to…otherwise, yes ESP would have to be involved. Followed by “I have no clue what you are getting at. Likely my mistake, my lack of understanding, but I’m just not getting it. Far too roundabout for me.”
And you wonder why I said I thought you didn’t understand?
I do love your rants though. This… “You might get away with that kind of bs with your friends, but I can guarantee that when you try it on me, it will blow up in your face every time.” …is gold.

James at 48
March 31, 2014 11:54 am

The long tail of the Great Melt would be expected to go asymptotic to a 0 slope. And at some point it will go negative as the Continental Ice builds back up at the end of the Interglacial.