Sea level as a global thermometer

With 70% of the earth covered by sea water, it looks a lot like the fluid in a thermometer. There is some water added by melting, land based ice, but there are credible reports that the bulk change occurs from temperature. This is my investigation of that hypothesis.

Straight-line Average versus Gaussian Average

A straight-line average, summing the data values and dividing by the count, has the effect of suppressing peaks and valleys in the data. It deadens detection of external forcing functions.

In contrast, a Gaussian average weights the data values depending upon how far they are away from the central point. This preserves the peaks and valleys while giving a valid average around each point. So here are two examples.

NOAA Satellite Sea Level Measurements Using 1-year Gaussian Filter

The year boundary starts on March 20, 1991, the Spring equinox. The yearly gridlines are 365.25 days per year:

So we see the change in sea level that follows the annual cycle. What surprised me was the sea level increase in the Northern hemisphere summer. The Southern hemisphere has a lot more sea water that should be cooler in the Northern summer and reduce the overall sea level. This asymmetry of Northern and Southern hemisphere can be mapped using GISS data.

Here is the land area as a function of latitude with the South Pole on the left:

Now these have not been adjusted for albedo and solar heat capture. But we only see this forcing function because of the Gaussian weighted average.

Although all straight-line averages suppress latent signals, excel trend-lines have another, latent defect:

Using the same sea level data, I plotted a straight-line average centered about the straight-line date. Then I added an excel generated trend line for the same number of data points, 36 for one year, only to reveal the trend line lags the central date. Not many people are aware of this latent defect as it only shows up when dealing with larger, statistically valid, sample sets (quiz: What is 32?)

Berkeley Temperature Using Gaussian Weighted Average

So this is what we see with the Berkeley, land-based, temperature record using a year-long, Gaussian average:

Again, the data is too noisy to measure an average. We know of at least three forcing functions: solar radiance, particulates (pollution and volcanoes), and El Nino/La Nina. But these temperature records are also impacted by the annual, seasonal cycle and sea/land ratios during the year. Regardless, can use a calculus trick of straight-line plot the peaks as one line and valleys as another:

• minimums ~ 0.0128 C/year 78 years for next 1 C
  • 1999.25 0.3 C
  • 2011.75 0.46 C
• maximums ~ 0.0082 C/year 122 years for next 1 C
  • 1998 0.65 C
  • 2010.0 0.75 C

Compared To First Chart

So this is the quick chart published last month using excel, running averages:

• minimums 0.0127 C/yr 79 years to next 1 C
  • 1996.5 .19 C
  • 2012.25 .39 C
• maximums 0.0127 C/yr 79 years to next 1 C
  • 1998.5 0.68 C
  • 2010.3 0.83 C

Expected, the local peaks and valleys shifted in time. Since the spreadsheet calculated values are known to be accurate, I trust the Gaussian versions over the Excel, trend line version. Also, the slope of the line connecting local minimums appears to give the same rate of temperature increase. But the connected, local maximums line in the Gaussian chart shows a slower rate of increase.

Gaussian Temperature and Sea Level



I'm looking forward to measuring the annual cycle signal and removing it from the sea level record. Then seeing if I can find some surface metrics to model what is going on.

Bob Wilson

Sea level source: CU Sea Level Research Group | University of Colorado
Temperature source: Berkeley Earth

 

Well I had some time to work on this:

It turns out the sea rise pause in 2010-2012 appears to be the result of the Iceland volcano that shutdown airspace over Europe that year. The eruption hit right at the spring equinox and lasted to the middle of July spreading an ash cloud over about 1/3d of the Northern hemisphere. So there was a pause in sea level rise that appeared to clear up by 2012-2013.

Now the anti-cyclic sea level pattern, rising in the Northern summer and lowering during the Southern 'summer' may be due to something mentioned in Denial 101x. Apparently low clouds have a cooling effect, counter to the water vapor greenhouse gas effect. In contrast, high thin clouds demonstrate a greenhouse effect. I don't know the details but now I'm beginning to suspect the counter-cyclic might be a feature of water:

• When exposed to solar heating, water inhibits temperature rise by evaporation. The solar heat is converted to water vapor which soon forms clouds to inhibit further solar heating.
• In contrast, solar heating of land does not exhibit the phase change but actually warms the surface and the air. This air can then move over nearby oceans and Northern glaciers to melt and warm the ice and water.

It may be possible to map the land area by latitude and reflected light radiance. Use this to make a land-heating model of the earth's latitudes. Then using geometry and the orbital inclination to model the land-based heating by subtracting the Solar radiance spectrum. If the counter-cyclical variation matches the predicted solar heating, we'll have a way to factor out this forcing function.

When a predictive forcing function can be removed from the data, it often reveals the second and sometimes parts of the third forcing function. For example, when dealing with an intermittent problem, solving the primary often means a less frequently occurring, intermittent problem will become visible. The disciplined diagnostician knows to not back-out the fix for the first but focus on the next bad boy.

BTW, the 1997-1998 burst is interesting because that is the year many climate deniers choose to assert the false claim that temperatures have 'paused.' If there are several, independent forcing functions, sometimes they can combine to make a unique, random, peak event. I look forward to mapping the forcing functions and if they have a period, identify.

Bob Wilson

 

I believe this is the reference about clouds:
http://ipcc.ch/pdf/assessment-report/ar5/wg1/WG1AR5_Chapter07_FINAL.pdf
(pp. 8 has the graphical synopsis)

Now I haven't printed this one to read but it is important for my understanding of why the sea level appears to drop when the Southern oceans are exposed more directly to the sun and rise in the Northern 'summer.' Something about the reduced, Southern land mass is having an effect.

Here is the lecture:

Bob Wilson

 

I had an equipment failure at home that knocked out my Internet access. But in the meanwhile, I continued looking at the data:

Here I took out the linear increase in sea level, ~3.26 mm/year, by selecting the same day of the year at the beginning and end of the series and dividing by the time. This was ONLY to remove the slope that made detection of artifacts harder and should not be taken as 'this is the sea level rise.':

• The Icelandic volcano is very evident, March 20, 2010 with effects felt during the Northern 'summer.'
• There was also a temperature spike in 1997-1998 that many have attributed to El Nino. But some of the reports still have me wondering. Still, it all but killed the 1998 cooling phase from the Southern 'summer.'

In this chart, I plotted over a year, the annual sea levels with vertical grid lines of ~1 month each:

• Magnitude of the Northern 'summer' sea level rise is larger than the Southern 'summer' sea level decline
• Icelandic volcano effect is easy to spot
• El Nino effect is not so easily seen in the plots

I suspect what is happening is in the Northern 'summer', the sea and land ice melt significantly reduces the albedo, leading to the sea level rise with higher temperature. In contrast, the Southern 'summer' shines of a highly reflective, Antarctica. Even though there is more sea water exposed to the sun's heat, the South pole may be giving some relief but not enough to compensate for the Northern 'summer' heat gain. But this suggests a rapid tipping point in the future.

If Antarctic land is more exposed in the 'summer' and there are losses of sea ice cover because of ice shelf collapse, the Southern oceans could see a significant warming and sea level rise from temperature alone. Raise the sea level a bit and more shelf collapse and land ice melt, it could be pretty ugly.

Something else that happens when the sea level rises, the earth's moment of inertia changes. Like a figure skater who extends their arms to slow their rotation, the earth's days can get longer. This is an area of active investigation by others but I took a quick look:

• The Norther 'summer' can be clearly seen BUT the results are opposite of a sea level increase. The earth appears to speed-up or I've misunderstood Length Of Day (LOD).
• The Sourthern 'summer' shows a distinct slow down.

These are opposite the effect expected from just a sea level change. So I'll need to do some more reading to understand these forcing functions.

Bob Wilson

 

Wished I'd thought of that!

The first set of data had the 'leap seconds' and it nearly drove me mad. Apparently there have been some non-linear judgement calls about 'leap seconds.' I could not use that data.

What I did was use an European source that showed the LOD as a smooth function over the satellite era. Other than being counter to my expectations (snow fall/melt may solve that problem,) it is data I can deal with.

"Leap Seconds" are really an artifact needed for those who don't understand time (and I AM a Dr. Who fan!)

There are some modeling challenges in dealing with the sea vs land issues of the Northern and Southern hemisphere. I don't think I know the answers nor really all the questions. Just I know there is something there to find out.

Bob Wilson

 

Occasionally I come across a puzzle and this one is:

• Why does the Northern Summer 'heat' and the Southern Summer 'cool'?

There are probably more precise terms and I'm open to suggestions. In the meanwhile, here is the evidence:

• Mar 20 - for each vertical gridline
• Slowing of the earth rotation, LOD, means something expanded, sea level?
• Both are Gaussian filtered:
  • Sea level is Gaussian over a 1 year period
  • Length Of Day is Gaussian over 36 day periods (one year takes more work)
• Both show evidence of two climate anomalies:
  • 1997-98 El Nino
  • 2010-11 Iceland volcano

The only other independent variable is the relative, land area by latitude:

• Antarctica is on the left and Arctic on the right

The next steps:

1. Geometry - the solar radiance as a function latitude for the years 1991-2015
2. Argo - the sea temperature as a function of latitude for the years 1991-2015
3. Albedo - reflection of polar orbiting satellites as a function of latitude for the years 1991-2015

I also am curious about the thermal dynamics of what happens in sea level under different conditions:

• direct solar by offset steps corresponding to the latitudes, 90 degrees to 0

Look at Northern and Southern CO{2} concentrations.

SUMMARY

The data says something is going on different between the Northern and Southern hemispheres each year. Amazing because every one recognizes there are 'regional' climates. But the biggest regions are the Northern and Southern hemispheres. Which reminds me of the old joke, there are two kinds of people in the world: those who break problems into two parts, and; those who don't.

Bob Wilson

 

You were in the right area:

I found a paper "Seasonal Global Water Mass Budget and Mean Sea Level Variations", J.L. Chen, C.R. Wilson, D.P. Chambers, R.S. Nerem, B.D. Tapley, Geophysical Research Letters, Vol. 25, No. 19, pages 3555-3558, October 1, 1998:

Abstract. Analysis of TOPEX/Poseidon satellite altimeter data indicates that the global mean sea level variation has a clear seasonal signal with an amplitude of about 2 to 3 mm, along with a long term drift. This seasonal variation is associated with mass redistribution within the global hydrological cycle plus steric thermal contributions. We investigate seasonal variations of water vapor in the atmosphere and water storage on land using both assimilated atmospheric models and climatological data, and to estimate the corresponding global mean sea level changes. The predicted seasonal global mean sea level changes are then compared with the seasonal variabilities observed by TOPEX/Poseidon altimetry data, after the latter are corrected for the steric effect using a simplified thermal model derived from the NOAA World Ocean Atlas 1994. The good agreement in both amplitude and phase indicates that the T/P altimeter may provide key information for the global water mass budget by placing observational constraints on the mass budget variations predicted by global atmospheric and hydrological models.​

The good news is this appears to be the annual signal I'm seeing in the data. However there may be a problem with El Nino vs Icelandic volcano. I'm seeing opposite signs which makes sense in my case. However, J.L. Chen sees El Nino in his paper "Contributions of ice sheet and mountain glacier melt to recent sea level rise." What this means is I need to understand more about El Nino hydro-cycle events vs. volcanic cooling.

I am still interested in the "seasional adjusted" sea level values report at:
CU Sea Level Research Group | University of Colorado

I'll send them a note and ask if we can get more details about their "seasonal signals." This may be where I'll find the temperature.

Bob Wilson

 

Partially correct and my original thought:

Snow and ice above 35 degrees (*) accumulates on land during the Northern winter and this lowers the sea level and speeds up the earth. During the Northern summer it mostly melts and flows down to the sea. There it displaces water towards the equator and raises sea level:

• Land water flowing down-hill reduces the moment of inertia and spins the earth faster, a little bit
• Sea water displaced toward the equator increases the moment of inertia and slows the earth spin, a lot

In effect the seasonal variation of sea level is a measure of water exchange on either side of 35 degrees. Only the Northern hemisphere has the land mass to hold the water in snow/ice above sea level until the summer melt. This also means there is information hidden in the seasonal change:

Next to do the same with the LOD data and see what happened between the two over the different years. The greatest dip happened during the Icelandic volcano 2010-2011 but we also have the 1997-98 El Nino in these data.

Bob Wilson

* - I need to independently confirm this latitude. Getting the same results by different approaches gives more confidence. It also allows us to made a geophysical model for quantitative numbers.

 

Interesting data:

• Sea level shows a somewhat linear, upward trend
  • 1997-98 El Nino shows a spike in sea level and brief leveling of LOD
  • 2010 Iceland volcano shows a sea level dip, perhaps a cool summer, less ice melt. LOD shows a local speed-up, snow/ice not melting and moving South
• Length of Day
  • For first half, the earth spin is increasing, getting smaller, huh?
  • From 2003 on, earth rotation slight slowing consistent with less polar and mountain snow and ice

Some of this period overlaps GRACE.

SPECULATIONS

From 1993-2003, the latitudes above 35N and below 35S accumulated water, snow and ice. Meanwhile, the oceans continued to accumulate water. The deficit suggests 35N to 35S lost water, a drought.

From 2003-2014, the latitudes above 35N and below 35S lost water, snow and ice. Meanwhile, the oceans continued to accumulate water. This suggests 35N to 35 may be seeing some drought relief.

Given the scattered land masses, it is possible some of the earth's wobble may be induced by land hydrology. I'm thinking Greenland would be an area of interest.

Bob Wilson

 

Interesting, I had sent some e-mails on Friday seeking additional information about what I'm seeing in the data. One response was a link to this open paper:
"The Sea Level Budget Since 2003: INference on the Deep Ocean Heat Content"

Now this paper does not directly address the temperature vs. sea level that I am looking at as much as looking at:

Abstract This study provides an overview of the various components of the global mean
sea level evolution over two time spans: (1) 2005–2012 (corresponding to the full
deployment of the Argo program) and (2) 2003–2012. Using a sea level budget approach,
we compare altimetry-based global mean sea level, global ocean mass from GRACE space
gravimetry and steric sea level from Argo and other in situ measurements. One goal of this
study is to investigate whether it is possible to constrain the deep ocean contribution to the
global mean sea level rise over the last decade. This question is particularly relevant,
considering the current debate about the ‘hiatus,’ i.e., the observed recent pause of the
global mean air and sea surface temperature evolution while the planet is still in thermal
imbalance. We consider a total of 16 different data sets. Differences are noticed between
data sets related to each variable (sea level, ocean mass and steric sea level), mostly due to
data processing issues. Therefore, we perform the analysis using averages of the available
data sets. . .

I like this paper because it points me to 16 sources of data. I had found GRACE data this weekend and planned to look for Argo. Now I have a paper with pointers directly to these sources. But I have a real problem with "averages" because it suppresses the peaks and valleys in the data.

BTW, this is a January 28, 2015 paper so I'm rapidly reaching the limits. Still the paper is pretty definitive about using El Nino and La Nina effects to explain the water/snow/ice migration over time. There was no mention of the Icelandic volcano which makes me wonder "Why?"

Bob Wilson

 

You open up the data and find a surprise:

• 3 or 9 month phase offset between LOD minimum and SL maximum

The pattern is in the data but I don't know why. When debugging, I'm an inductive thinker who starts with the data and moves towards hypothesis and theory. So I have to test both 3 and 9 month offsets.

Bob Wilson

 

Thanks! Understanding La Nina vs volcanism, this is an interesting subject . . . especially since the El Nino appears to be already well defined.

I'm using Length Of Day to indicate how much the earth rotation changes due land-based snow/ice/water melt back into the oceans. One paper by Chen has already identified melt as a metric in the earth moment of inertia. But the total inventory of water does not change. Rather, we're expecting:

• snow/ice/water stored on land above 35 degrees - this should reduce the earth moment of inertia and result in faster rotation.
• snow/ice/water flows into the ocean - this should increase the sea level and as it migrates to between 35N and 35S, increase the moment of inertia and slow the earth.
• Northern hemisphere is accumulating the bulk of seasonal, land based snow/ice/water - due to the different land masses between the northern and southern hemisphere, the effect should be most pronounce between the Spring and Fall equinox.
  
• migration between northern, seasonal melt to below 35N should have a lag - the water does not arrive instantly across the whole oceans

Yes, I agree one has to be careful with letting a chart lead one astray. But there appears to be a strong seasonal signal in the LOD and sea level suggesting a coupled mechanism that Chen's earlier paper said is there.

Bob Wilson

 

Thanks, I read both the article and abstract. Both of them are addressing global effects. In my case, I'm expecting a strong regional effect under the ash footprint. Also, both of them suggest the negative sign which is what we see in the data. It suggests the La Nina and volcanism may have combined to generate the distinct loss in sea level in 2010-2011.

I did take a quick peak at sea ice historical records but could find no signature. What I need to do is see if Cryosat and possible GRACE have detailed data about the Northern Eurasian area under the ash footprint that we can compare to the earlier and later years.

Bob Wilson