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



Figure 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:



Figure 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.

Figure 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:

Figure 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.