'splain' My Detrending

There are a lot of sophisticated methods to manipulate time series to determine trends and remove trends for data series. I ain't all that sophisticated, some I am starting with baby steps. As the oceans temperature changes, the sea level should change somewhat. There are other factors involved in sea level change, but I wanted to see how well the UAH atmopsheric temperature data followed the sea level changes recorded by satellite altimetry. I downloaded the data for the NCDC site, but right now I can't find the exact link. Anywho, there is a much higher slope in the sea level change than in the mid troposphere temperature over the oceans as determined by the UAH MSU data. To better compare, I removed the slope in the seal level data, or simple removed the greater trend.

The first step was to remove the trend. In the above chart, the downloaded data is in blue. There are 665 data point, so I divided the rise by 665 and shifted each point by increasing the number of steps subtracted from the start. Nothing major, just removed the slope until the mean equaled the linear regression of the series.

After the series was detrended, I shifted the series and divided by common factor to get the series mean to equal the x-axis zero. This results in a scaled anomaly with not definite value. It is just scaled to provide a reasonable comparison of the detrended mean sea level orange and the UAH mid-troposphere oceans in blue which is in degrees C anomaly.

Since the Mean sea level data is recorded more often than the monthly UAH, I used a running mean of 5 mean sea level points to better compare the two without, hopefully, over smoothing the data. This post is just to briefly describe the detrending, if something really nifty turns up, I may get a little more detailed.

So it is off a Touch, So What?

With billions of dollars invested and trillions at risk, how accurate should the climate data be? That question will cause many to proclaim I am a merchant of doubt. I don't make a living selling doubt but I do have a pretty good inventory. The chart above compares the gold standard surface station temperature data for the Southern Hemisphere with the state of the art satellite telemetry data for the same region. The University of Alabama, Huntsville data compiled by Dr. Roy Spencer is a bit controversial. Another group, Remote Sensing Systems (RSS) also has a satellite temperature product that is comparable. The UAH currently has a slightly higher trend over the period than the RSS group's. Doubters can make their own comparison. The trends in the above plot are 0.0107 degrees per year for the GISS surface station data and 0.0019 for the UAH data. So in one hundred years, if nothing changes, the Southern Hemisphere would be 100*0.0107=1.07 degrees warmer or 100*0.0019=0.19 degrees warmer. Now this is just the land mass temperatures for the bottom half of the planet which has more water than it does land mass. Most of us live in the Northern Hemisphere where we KNOW it is warmer.

Let's see, 100*0.0637=6.37, so if nothing changes, according to NASA GISS Northern Hemisphere land only surface temperatures it will be 6.37 degrees C warmer in 100 years. Pretty alarming huh? 100*0.092=0.92degrees C warmer in one hundred years based on the high dollar satellite data. The two sets disagree. They significantly disagree. That is not that unusual, what they are attempting to do is pretty damn hard, averaging the surface temperature of the whole planet by less than adequate means. So what's a guy to do? This guy compares something that is known to be happening to both. There are pretty good measurements of CO2 concentration from the Mauna Loa Observatory, increasing CO2 does have a radiant impact and that impact will have a relationship with temperature that is a natural log curve fit. Where on that curve is a question and that means that the magnitude of the impact is in question, but it will fit a natural log curve fairly well. You can prove that to yourself with some ink, and aquarium and your eyeballs if properly calibrated, a light meter is not. Start with clear water, add a half of drop of black ink at a time and measure the change in the light passing through the tank. The change will roughly match a natural log curve. Just for fun, use a rectangular tank and measure the light change from front to back and from side to side also. If you look up at the night sky, that is side to side, if you look up from a very high mountain top up, that is front to back. More on that later. Right now, here is my check.

The blue squiggly line in the middle of that plot is the estimate forcing due to CO2 increase since 1979 and it is compared to the global land only UAH satellite data. 100*0.0082=0.82 degrees C if nothing changes with the CO2 and 100*0.0080=.80 if nothing changes for the land temperature data. That is fairly good agreement. Note that the satellite data is all middle troposphere data. The data that should be warmer than the surface. Think about the aquarium for a second. Now assuming that nothing changes is not all that bright. Things do and will change but it is nice to have a somewhat reliable baseline to determine how much and what changed. Without getting into a graph, here is a quick check for the GISS data. The GISS data says the Southern Hemisphere is warming. The Antarctic sea ice is at record levels for the satellite era, which is about the only data we have on Antarctic sea ice. Would Antarctic sea ice be growing and at record levels if the Antarctic were warming? That Arctic sea ice is declining in summer. Is it declining in winter? There has been some decline in winter Arctic sea ice, but not a huge amount. Summer ice has either set or come close to setting a minimum record in 2007. This gives us a little logical check of GISS. Yes there has been warming in the Northern Hemisphere and it is unlikely there has been significant warming in the Southern Hemisphere. One thing is certain, there is definitely more seasonal change in the area and perhaps volume of sea ice globally since the start of the satellite era. Now a neat fun fact. Sea ice growth, drives the deep ocean currents. When salt water freezes, it losses some of the salt content so the actual ice formed is fresher than the water that formed it. That salt is lost to the unfroze water where it increases the density of that water which sinks deeper than the less dense water surrounding it. The more sea ice formed, the greater the volume of sinking, more dense, water. This water would be very close to the freezing point of fresh water, 0 C or 32 F. The deep oceans are not frozen, so the denser water settles into a thermal layer of approximately the same density beneath the surface. This sinking water must force some less dense water toward the surface. This creates a deep ocean current, falling cold dense water and rising less dense water. If the rate of sea ice production increases, the rate of the deep water cold current increases. That water is always at the same temperature as it is set by the freezing point of the water salinity. Now the harder part. With more rapid ice melt, the surface water would be fresher than normal, unless winds and currents mix the fresher melt water with the more saline ocean water. In the Antarctic, there is no indication of summer melt increase but evidence of increased winter formation, so there has been an increase in flow into the deep ocean current. In the Arctic, it really depends on which way and how strong the wind blows. So GISS gets a no go in the Antarctic and Southern Hemisphere and a grudging maybe in the Northern Hemisphere. So should we spend trillions of dollars because of a grudging maybe? I don't think so. There is still quite a bit of work to be done before we can predict climate.

What the Flux!

hat is a busy chart comparing the Mauna Loa CO2 concentration change estimated forcing to the University of Alabama (UAH) Microwave Sounding Unit (MSU) middle tropospheric temperature data. The light blue line burried in the noise is the calculated forcing of CO2 based on the formula 5.35ln(Cf/co) were Co is 280 Parts Per Million PPM. Cf is the monthly average from the Mauna Loa observatory CO2 measurements. Since the UAH data is in anomalies, I converted the CO2 forcing estimate to Anomalies by subtracting the average of the period of the satellite data series.

Low and behold, the CO2 forcing is nearly a perfect fit of the UAH land temperature data series. Both the global and the ocean series are below the land series.

This chart is just the land data and the estimated CO2 forcing. Pretty close match. If you extend the regressions out to the year 2100, it is about 0.8 C greater than the start in 1979. Now here is a little bit of a shocker, CO2 is causing most of that warming. But why is it only a good match over land?

The average surface temperature of the Earth is often listed as 288K degrees with a outgoing energy flux of 390Wm-2. Average temperature, average flux right? The average temperature of the oceans, 70% of the global surface is about 294K degrees and the average temperature of the land area is about 273K degrees. The energy flux at 294K degrees is about 423.6Wm-2 and the flux at 273.15 is about 315.6Wm-2. .7*294+.3*273.15=287.7 and .7*423.6+.3*315.6=391.2 the temperature is a touch lower and the flux a touch higher. Small errors right?

If you add 3.7Wm-2 of forcing to a 273.13K surface it would increase to 273.9K. Add 3.7Wm-2 of forcing to a surface at 294K and it would increase the temperature to 294.6K, only 80% of the increase. If you estimate the increase in forcing based on an average of temperatures instead of an average of fluxes, you get a slightly high bias in your estimate. Then if you apply the slightly high estimate to an average of temperatures you would get a slightly low response. This is exactly what appears to have happened to the climate change projections.

This does not explain all of the discrepancies, but since the oceans appear to also have a negative water vapor feedback, it should explain a large percentage of the error.