Guest Post by Willis Eschenbach
I’ve been mulling over a comment made by Steven Mosher. I don’t have the exact quote, so he’s welcome to correct any errors. As I understood it, he said that much of the variation in temperatures around the planet can be explained by a combination of elevation and latitude. He described this as a “temperature field”, because at any given latitude and elevation it has a corresponding estimated temperature value.
Intrigued by this idea, I decided to use the CERES dataset. However, rather than using latitude, I decided to take a look at how well a combination of the sunlight and the elevation can predict the average temperature. Let’s start with the average surface temperature. It’s shown below in Figure 1.
Figure 1. Average surface temperature according to the CERES dataset, on a 1°x1° gridcell basis.
To estimate the temperature, what I did was to make a simple linear function of solar energy and elevation (see end notes for details). This gave me the following estimate of gridcell temperatures.
Figure 2. Estimated surface temperature based on elevation and sunlight. R^2 = 0.94, p-value less than 2e-16. See end notes for calculation.
Now, that’s a pretty good facsimile of the actual temperatures shown in Figure 1. Indeed, the “R-squared” (R^2) of the temperature field and the observations is 0.95, meaning that the temperature field explains 95% of the variation in the observed temperature.
That’s not the interesting part, however. The fun questions are, where is the temperature NOT as expected, and why? Where is the greatest departure from the estimated temperature, and why is it there? To investigate those, I next looked at the difference between observations and the estimated temperature field. Figures 3 and 4 show two views of the observations minus the temperature field.
Figure 3. Observed temperatures minus the estimated temperature field, centered on Greenwich. Gray line shows the boundary between positive and negative values. Positive values (yellow to red) mean that the observations are warmer than expected.
I found this most fascinating, as it shows the great oceanic heat transport systems that move the energy from the tropics, where there is an excess, to the poles where it is radiated to space. I was surprised to see that the warmest location compared to expectations is the area above Scandinavia. This has to be a result of the Gulf Stream current which is also quite visible along the edge of the East Coast of North America.
I note that as we’d expect, the deserts and arid areas of the world like the Sahara, the Namib, and the Australian deserts are warmer than would be otherwise expected.
You can see another view showing the overall results of the El Nino/La Nina heat pump below in Figure 4. This is the same data as in Figure 3, but centered on the Pacific.
Figure 4. Observed temperatures minus the estimated temperature field, centered on the International Dateline. Gray line shows the boundary between positive and negative values. Positive values mean that the observations are warmer than expected.
Here we can see the area off of Peru that runs cool because the El Nino/La Nina pump pushes warm surface water across the Pacific. This exposes underlying cooler waters. When the warm water hits the Asia/Indonesia/Australia landmasses, the warm water splits north and south and moves polewards. As with the area above Scandinavia, the heat seems to pile up at the polar extremities of the heat transport system. In the case of the Pacific, the northern branch ends up in the Gulf of Alaska. The southern branch ends up where it is blocked by the shallow narrows between the Antarctic Peninsula and the tip of South America.
In any case, that’s what I learned from my wanderings. The beauty of climate is that there are always more puzzles to be solved and oddities to be pondered. For example, why are the western parts of the northern hemisphere continents warmer than the eastern parts?
My best to each of you,
w.
As I’ve Mentioned: If you disagree with someone, please quote the exact words you disagree with so we can all understand your objections.
The Math: I used the form:
Estimated Temperature = a * sunlight + b * elevation + c * sunlight * elevation + m
where a, b, c, and m are fitted constants. The results were as follows:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -4.052e+01 7.122e-02 -568.9 <2e-16 ***
sunvec 1.675e-01 2.033e-04 823.8 <2e-16 ***
elvec -1.918e-02 7.723e-05 -248.4 <2e-16 ***
sunvec:elvec 4.354e-05 2.485e-07 175.2 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2557 on 64796 degrees of freedom
Multiple R-squared: 0.9479, Adjusted R-squared: 0.9479
F-statistic: 3.933e+05 on 3 and 64796 DF, p-value: < 2.2e-16
where “sunvec” is average gridcell solar energy in W/m2, and elvec is the average gridcell elevation in meters.
Willis,
Very interesting.
Two thoughts occurred to me:
1. I glanced at the eastern US, and was a bit surprised to see how cool that region is. I realize how much more important the sun is than manufacturing, but I thought industrial production would register. The other region of the world with industrial production is China, and that is equally cool.
2. As you noted, the warm areas in the difference map highlight ocean transport, such as the Gulf Stream. How difficult would it be to built a second order model, which includes ocean transport of heat, then do the same process to look at the difference, and see what else might be a driver?
Phil
Sunshine is about 1 kW/m^2, Industrial energy is very point source intense, but averaged over even just one degree cell in near nothing. Typical office loads are about 10 W/m^2 then you get to diffuse that over the surrounding empty spaces,,, then diffuse that ovrr the 90%+ non urban around it…
Thanks for the data
Willis,
1) It might make sense to do oceans and land separately. 70% of your model is areas where altitude = 0m, which would heavily weight the analysis toward the areas at sea level. Further, nearly 100% of the 0m data is water, so that is a confounding factor here.
2) Where did you get the ‘sunvec’ values and what exactly is it measuring? Is it …
a) insolation at the top of atmosphere,
b) insolation reaching the surface (subtracting the amount absorbed by the atmosphere & reflected by clouds), or
c) the actual amount absorbed by the surface (additionally factoring in albedo)?
Each would give a rather different result. (a vs b are shown in this graphic: http://en.wikipedia.org/wiki/File:Insolation.png)
3) There seems to be some interesting correlations with global cloud cover (no surprise) (http://wegc203116.uni-graz.at/meted/satmet/microwave_topics/overview/media/graphics/cloud_amount.jpg).
Actually, I just looked more closely at Figure 2 and it is pretty clear you simply used the top-of-atmosphere insolation. So using actual surface insolation might give a better estimate.
One interesting note. The relatively cloudless Sahara as warm, but the relatively cloudy patch north of Scandinavia is also warm. There are some other patterns for which I can also come up with some plausible explanations, but I think I will leave it to others to ponder these for a bit.
W.,
Can you describe your formula and explain the reasoning? Some of us don’t speak R and I don’t see why you chose an elevation x sunshine term. Was it just to get another configuration parameter or something more interesting?
The elevation*sunshine term is necessary because the lapse rate varies with the temperature, being greater in cold areas. And because I can’t use temperature as a variable, I substituted incoming sunshine to serve as a proxy. This seemed to work quite well, bringing estimated mountain temperature to within close tolerances.
The final equation, as I mentioned in the end notes, is
Estimated Temperature = a * sunlight + b * elevation + c * sunlight * elevation + m
where a, b, c, and m are fitted constants.
w.
“The elevation*sunshine term is necessary because the lapse rate varies with the temperature, being greater in cold areas. And because I can’t use temperature as a variable, I substituted incoming sunshine to serve as a proxy. ‘
SLICK.
“And because I can’t use temperature as a variable, I substituted incoming sunshine to serve as a proxy. This seemed to work quite well, ”
Something bothered me, took me a bit to figure it out, you’ve just replicated the BEST field, CERES Web page says they adjust temp, to better match measurements, and if they all do some sort of the same thing, you’re just matching that field with a small residual.
While that might give a good estimate, I’m not sure it’s right. For instance, my daily temp is set by the jet stream, and can swing 20F from one day to the next. 40 years ago summers were driven by Canadian air,20 years ago it was driven by Gulf of Mexico tropical air. Just a difference in area,cold explain all of the warming, ignoring the large swings in minimum temp due to the topic here, where the warm water is and what’s down wind.
micro6500 May 15, 2015 at 10:21 pm Edit
As I understand it, the “BEST field” uses latitude and elevation to create their estimate. Instead of latitude I used solar energy, a totally different variable. So I fail to see how I’ve “just replicated the BEST field” as you claim.
While all of that is indeed true, the reality is that greater than 90% of the variation in temperature is explained by a simple linear regression.
w.
“As I understand it, the “BEST field” uses latitude and elevation to create their estimate. Instead of latitude I used solar energy, a totally different variable. So I fail to see how I’ve “just replicated the BEST field” as you claim”
They both end up being a function of surface curvature, as that’s what drives the ratio of incoming energy as it applies to temperature.
“While all of that is indeed true, the reality is that greater than 90% of the variation in temperature is explained by a simple linear regression.”
That 10% is way, way bigger than the forcing from Co2, it could be all of the increase in temp as defined by series like BEST. they’d never know because they don’t mind infilling with unmeasured values.
Just a change in the amount of sampling of the areas defined by the path of the jet stream, could be larger that Co2’s impact. And just look at the field in the Arctic, and how over estimated that is due to the small number of stations and their proximity to water.
I want to add, I do think that there’s value in this line of thinking, I’ve been working on adding the solar forcing for each surface stations latitude and looking at the response of temp, I just don’t think it tells you anything about the weather field 1,000km away when it isn’t measured.
Micro we don’t infill with unknown values.
We take known values.. Lat and elevation. We take a known relationship between those and temperature and we PREDICT the values for temperature at unsampled locations. Then we test the prediction.
Steven Mosher
Thankyou for your information. I write to ask for a clarification. You say
If the locations are “unsampled” then how can you “test the prediction” of a value that is not known?
Richard
Stephen, we’ve discussed this before, yes you do out of band testing, yes you think this confirms your predictions, I on the other hand fell that since I can regularly see a multi degree difference between the airport station 30 miles away verses stations a few miles from my home, it seems unlikely to have high fidelity, let alone how you can predict whether the jet stream is north or south of us if the nearest station was 100 miles away, let alone 1000km away.
Especially when BEST shows a warming trend, that I’m still skeptical actually exists.
Although this is interesting I don’t see the significance of it. You have taken an observation of a dynamic system and subtracted the static “presumed” baseline. You are simply left with the underlying patterns of the dynamic system highlighted. What else would you expect?
um I don’t, may be to see the underlying patterns of the dynamic system highlighted.
Kirkc May 15, 2015 at 6:15 am
Thanks, Kirk. That’s what I would expect. The surprising part is that you see no value in discovering the unknown details of the dynamic system.
w.
But all the underlying information being revealed is previously known phenomenon. “The desert regions are warmer than non-desert regions.” I guess this could be considered a gem of a discovery and we should never have expected that kind of thing to show up in the raw satellite data…. But I guess that is your point . It’s in there if you can coax it out.
Willis, I always enjoy your insight, hard work and the passion you reveal in your articles. I may even be one of your biggest fans – I’m just wondering what is the most provocative thing to grab from this bit of work? Some mountain regions don’t meet the “average” factors you have assumed to apply to all mountain systems. Why is that? A valid question..but the answer is why would you assume that elevation is constant for temperature? Or average? As others have pointed out there is a huge variable here. Perhaps the gradient of the slope ( 1x1grid to grid deviation) should be factored into your elevation equation?… And then both the anomaly and question will become moot. Adiabatic maybe….no idea. It’s a slippery slope.
Best regards,
Kirk
Kirkc May 15, 2015 at 6:09 pm
Absolutely not. If you think so, then please show me the equivalent of Figure 4 from some other source. The way that the heat is moving across the Pacific and pooling in the Gulf of Alaska, for example, is previously unknown to me.
And if you claim that it is NOT previously unknown to you, then please provide the Figure that you think predates mine.
It’s easy to denigrate, Kirk. But until you provide something other than just your word, I fear you haven’t demonstrated anything.
Regards,
w.
Willis, when I compare visually figures 1 and 2 and then look at figures 3 and 4; I don’t get the same result. Is the color intensity of figure 1 set higher than figure 2?
Thanks, John. The color intensity is the same. But since Figs 3/4 are the difference between the estimate and the reality, it is dominated by smaller values, with large and small values being the outliers.
w.
Yep. Been sayin it and sayin it. But pictures are better than words. I wish I had your acumen for letting data speak instead of words.
Or said differently, a picture is worth a thousand words.
Thanks Willis
This is just common knowledge which is of course the latitude position of the continents, the percentage of land versus oceans, the arrangements of oceans versus land, the average elevation of the land, and the variation of the elevation of the land all play a big role in what kinds of climate the earth may have in response to various forces being applied to it.
This is a big part of the reason why given forces applied to the climate give a different result.
And how much more can be explained by the fact that valleys will effect the heat gain/loss and/or provide protection from trade winds. For example look at the daily temperature difference between Barbers Point and Kaneohe, HI all summer long.
This can be captured by using a high fidelity DEM that gives you areas for cold air drainage and wind sheltering,
BUT the data requirements are huge
the effect of valleys on temperature can be estimated by using a TWI or topographical wetness index.
The index is built from a DEM. It basically shows you where water can “pool” and can be used to account
for areas that have cold air drainage or temperature inversions
http://worldgrids.org/doku.php?id=wiki:twisre3
Interesting that your elevec is -1.9 K /100 meters.. Suggests that there are multiple sets of coeffcients that minimise the residuals.
yes , you have to cross elevation and latitude,
shows either no clouds up north or data is contaminated with Cowtan and Way models. Clouds rather than currents to explain anomalies
CERES temperature product is a cloud free product.
You’ll find that Cowtan and Way validate against many Sat products. With the recent update to AIRS
it looks even better
Steven Mosher May 15, 2015 at 12:37 pm
Not true as far as I know. Do you have a citation? Thanks.
w.
Willis it should be if you are using their surface temp product.
Steven Mosher May 16, 2015 at 7:37 am
Thanks for the clarification, Mosh. Not sure which “surface temp product” you’re referring to. I’m using the CERES Surface EBAF (Energy Balanced And Flled) product. They have two datasets for upwelling surface radiation, named surf_lw_up_all and surf_lw_up_clr. The latter is clear-sky, the former is all-sky. I have converted their dataset surf_lw_up_all dataset to temperature using Stefan-Boltzmann, as I described in my post The CERES Calculated Surface Datasets.
As a result, it is not a “cloud free product”, because I am using the all-sky dataset.
Regards,
w.
My scribbles on a napkin, indicate a much higher percentage of solar insolation per square meter in the tropics and sub tropics than your results mostly based on the angle of incidence. The Tropics and sub tropics get over 80% of the solar insolation.
In other words your baseline is already biased by the atmospheric heat pumps. But your diagrams do partially show the oceanic heat pump because it isn’t evenly distributed like the atmospheric heat pump.
This is why Willis is a treasure
His curiosity is peaked by all comers.
He lets the data take him where ever it leads.
He loves when he is surprised by something.
He always leaves the conclusions to others.
He looks at things from as many angles as he can.
He is never satisfied that he has the right answer.
He enjoys being challenged and corrected when someone finds and error because it just gives him something new to play with.
If only everyone would come at issues like Willis does, the world be a better place.
This temperature field test is really cool. R^2 of 0.95 is extremely high, I would never have expected that.
Interesting how areas with lush life, like rainforests, are cooler than expected (while having more CO2 according to satellites) while areas of the least amount of life like mountains and deserts are warmer. It may be interesting to take this temperature field model and look at how it interacts with the CO2 spacial mapping.
since we got .93 with two variables Im not the least bit surprised.
I hate average temperatures. They do far more to obscure than they do to illuminate.
?dl=0
?dl=0
Here are links to two images. This is of August 23, 1966 from the Nimbus High Resolution Infrared Radiometer data. This is a measure of temperature by measuring infrared energy at 3.5-4.1 microns. This does much more to sustain what Mosher is talking about.
One of the images is centered on the Indian ocean and exceptionally clearly shows the cooler temperatures of the Himalayas as well as the cold cloud tops of the 1966 Monsoon season. You can clearly see the temperature differentials between land and oceans as well as other altitude and latitude dependencies. You also see in the second image, centered on the pacific, the cold cloud tops and the latitude based temperature differences.
This is data that my company processed and turned into KML files for the National Snow and Ice Data Center from the Nimbus II HRIR raw data.
The CERES average data looks like crap in comparison.
Willis Great work.
No errors but just a clarification and an explanation of the significance of what you show.
“I’ve been mulling over a comment made by Steven Mosher. I don’t have the exact quote, so he’s welcome to correct any errors. As I understood it, he said that much of the variation in temperatures around the planet can be explained by a combination of elevation and latitude. He described this as a “temperature field”, because at any given latitude and elevation it has a corresponding estimated temperature value.”
Let’s start with the clarification. In the Berkeley Earth approach we decompose the temperature into two components: A deterministic component and a residual.
We say
T = C+W
Where T is the temperature at a location
and where C is the climate at a location
and where W is the weather at a location.
The climate of a location is defined as a function of latitude an elevation. If you know the latitude and elevation and season, you know the monthly average temperature to about 1.6C. In other words the climate at that location is determined by its physical properties. What’s left over when you subtract this climate field from the temperature is the weather. The weather is that portion of the temperature that is not determined by the physical properties of the location.
One interesting thing that falls out of this is the notion that climate change is in the weather field.
( note that some people dont get this
http://www.hi-izuru.org/wp_blog/2015/04/a-follow-up/)
Let’s take a little time to understand the regression and this different conception of climate. Willis and I both like Geiger’s book climate near the ground. In that book Gieger discusses how the physical properties near the ground determine the temperature. So when we discuss the climate we are talking about this definition of climate. The next thing to notice is that willis adds some variables to his regression. That’s good work.
In the Berkeley system we only use latitude and elevation and we get an R^2 of .93. It’s pretty clear to anyone who has studied temperature that there are other physical properties left of out our regression:
a) distance to coast.
b) albedo
c) land class ( crops, trees, urban, bare soil)
d) local geometry : land aspect, slope, propensity for cold air drainage
e) insolation
And folks can add more variables. These additional variables fall into a couple classes: those that can change
and those that dont change. So land class ( say urban/rural) can change over time, while some of the geometry variables ( like slope ) may not change. And these additional variables have effects at different spatial scales. To the extent that we leave these variables out of our regression they will end up ( as residual) in the weather field. And changes in these variables can be mis attributed to changes in weather.. and thus mis indentified as climate change. The other challenge one has with these other variables is we have no historical record. So I might be able to add albedo to a regression for todays temperature, but I cant do that for 1850, unless I assume that albedo didnt change. The last challenge is that some variables like the DEM variables you could use for slope, aspect and cold air drainage areas require pretty big machines to process.
There is a trade off then in adding variables to the regression. Work continues most of it painfully slow.
And now to the larger points. there are couple of mistaken notions that people have about sampling and interpolation (infilling) that Willis’ approach iluminates. Because there is a relationship between temperature and the variables he uses, your sampling requirements drop dramatically. I guess he could take a subsample
and get the ~same coefficients. So when people argue that we dont have enough stations, they don’t really understand how much of the temperature is actually determined by the location. because so much of the temperature is determined, you dont need a large sample. You only need a sample that is representative, one that has good latitude and good elevation coverage. Willis could probably show this by doing some subsamples. The coefficients wont be exactly the same and residuals and errors will grow, but you’ll get the point about not needing that many samples to reconstruct the field.
The last point bears on interpolation. people get bent out of shape when folks infill. The complaint is
“there is no data there” But there IS data there. the regressors are there. So if I have no temperature data at
lat 60- 70, lon 180- 150, I can estimate it using the regression. I do have data for that region, I have the regressors. So when we infill we are not making up temperature data. we are predicting temperature at unmeasured locations using information ( about lat and elevation) from measured locations. This prediction can be tested. The prediction works.
summary: minor clarification. lat and elevation determine the climate field. the residual is the weather.
big point: sampling requirements are less than people generally think and “infilling” is not
“making up” data. It is using known data, and known physical relationships to predict data
at unmeasured locations.
Mosher
“big point: sampling requirements are less than people generally think and “infilling” is not
“making up” data. It is using known data, and known physical relationships to predict data
at unmeasured locations.”
If that is the case then why not just predict all of the data points?
Of course if this did work the models would work too.
Bob Boder,
There is a very basic rule about regressions that scientists learn early on: Regression, when thoughtfully applied, can give very good results when interpolating, but extrapolating a regression quickly gets you in big trouble. Infilling is interpolating; predicting the future is extrapolating.
Give me accurate global average temperatures for 2020 and 2030, and I will do a decent job of predicting the average global temperature in 2025.
Mike M.
Take last year 2014 and 10,000 BC you give me a decent average for 3993 BC. You don’t have any accurate information about the areas Steve is talking about you only have info on areas he thinks are similar. and your “decent” is plus or minus what? Funny thing about predicted data it only good if its right.
Steve can’t accurately predict the temperatures out side his doors 10 or 20 days from now be he is sure that his predicted data is accurate because he thinks he knows all of the controlling conditions in an un-sampled area, again if he can do this he should be able predict the temperature any where. what is great about Willis is he will let the data provide the information, Steve creates the data and see what he already expected.
“If that is the case then why not just predict all of the data points?
we can. the regression produces continous fields.
In our google earth version we did this at a 1km resolution.
The best DEM is 30 meters, so we could do every 30 meters. Probably take a year to run
“Bob Boder,
There is a very basic rule about regressions that scientists learn early on: Regression, when thoughtfully applied, can give very good results when interpolating, but extrapolating a regression quickly gets you in big trouble. Infilling is interpolating; predicting the future is extrapolating.
Give me accurate global average temperatures for 2020 and 2030, and I will do a decent job of predicting the average global temperature in 2025.”
Yup.
Some of the artifacts we find are at very high altitude. For example predicting the temp in in the Andes
and the himalyian mountains
Mosher
““If that is the case then why not just predict all of the data points?
we can. the regression produces continous fields.
In our google earth version we did this at a 1km resolution.”
I’ll bet it was dead nuts on and exactly what you expected. No matter how arrogantly you state a SWAG it is still a SWAG.
“I’ll bet it was dead nuts on and exactly what you expected. No matter how arrogantly you state a SWAG it is still a SWAG.”
no predictions always differ from observations. its called the error of prediction.
Mosher
Berlin and Ottawa. same basic altitude. which is warmer on average in March, which is further North?
Bonus question pick a point in the pacific ocean with no land for a 1000 miles at the latitude half way between the 2 and predict the average temperature in march and then test against measured data.
Mosher
“no predictions always differ from observations. its called the error of prediction.”
Sometimes yes and sometimes it just means your predications are wrong.
bob, predictions are ALWAYS WRONG. the question is “how wrong”
That depends on your use case and purpose.
Mosher
“bob, predictions are ALWAYS WRONG. the question is “how wrong”
That depends on your use case and purpose”
You are an unmovable rock, someday even you will have to move a little. I just hope you find it enlightening and not maddening.
Until then I will still read everything you post because you are least never boring.
Bob Boder:
You raise fundamental points whose import is scarcely grasped by would-be climatologists, whose analytic framework does not go beyond simple linear regression. Even there, they mistakenly think that very high computed correlation of prevailing ABSOLUTE temperature levels with ex ante spatial expectations provides any reliable basis for “predicting” the all-important spatio-temporal deviations around those expected, let alone actual, levels. In fact, were they to regress those deviations against the “physically constant climate” expectations, they would find totally insignificant correlation. And if they were to employ genuine time-series analysis methods, they would discover that actual temperature time-series are quite highly area-specific, with regression relationships providing quite useless “predictions” not only for future times, but for the “interpolated” past as well.
That is the most interesting response I’ve read. Thanks..
Mosher;
I am assuming you not what SWAG is?
Sorry know not “not”
yes. However, we make a prediction which is testable.
Willis can also do this, by decimating his data
It will be an awesome prediction.
Steven Mosher, you have written a good set of comments here, of which I’ll select one for special mention:
Some of the artifacts we find are at very high altitude. For example predicting the temp in in the Andes
and the himalyian mountains
Interesting, and a well-chosen example.
the other artifacts are in antarctica.
where it looks like seasonal adabatic winds cause us to assume empirical breaks where there are none.
there is another interesting case where we fail, but I think zeke is going to write that up as paper.
in short a very unique and documented land class change that has been mis interpreted as climate change because we dont include land class in the regression.
Mountainous regions are very hard to get correct because the local terrain ( like north facing and south facing, or terrain aspect) can be every important.
These regression errors essentially put climate factors into the residual where it is mis interpreted. It can also mess up homogenization.
It would seem that a long time average should give and average of=0. Does it?
Take a look at the global average shown in the headings of Figures 3/4.
w.
Thanks for the great explanation. Too bad the politics around CO2 emissions are so charged, if they weren’t more people might see how efforts like those help advance the field…
I does not work when trying to figure out why the climate changes over spans of hundreds or even thousands of years..
Mosher
That was a very interesting explanation and seems reasonable in all ways.
So, is the only reason that climate models so greatly overestimate future temperatures, even on short timescales, traceable to their overestimation of the heating value of CO2 and feedbacks?
If I were modelling climate I would right smartly reduce the assumptions about CO2 until I got a match with known temperatures.
Every model is different. Who knows.
Willis,
“For example, why are the western parts of the northern hemisphere continents warmer than the eastern parts?”
In the residual plots (actual – expected) the same is true for western Eurasia vs.eastern Eurasia. Also, it looks like the oceans are generally cooler than expected and the land warmer. My guess is this: Over the ocean evaporation exceeds precipitation and overland the opposite is true. So there is a net transfer of latent heat from the ocean to the land. The effect on the land is strongest in the areas just downwind of the oceans. In the mid-latitudes, that is the west coast.
To an engineer’s eye, Figure 3 resembles a map of the Great Deserts and Rainforests of the World. Is there a relaitve humidity factor at work here?
Hmmmm… fascinating. I don’t think you counted albedo as a variable. This might boost your R^2. It would also be interesting to see if the seasons are all similar, or similar to annual, or do they change throughout the year.
He could use GLASS albedo dataset,
Using the albedo values in the CERES dataset, I find the following. First, using just latitude and elevation. I used
estimated temperature = a * cos(latitude) + b * elevation * c * elevation * latitude + intercept.
With those I get:
Adding albedo to the mix gives a slight improvement:
Using net sun [solar * (1-albedo)] in place of albedo gives little change
Regards,
w.
The temperature model seems to overestimate in areas with high relative humidity and underestimate in areas of low relative humidity. Estimating heat index instead of absolute temperature might find an even closer approximation with reality.
The only desert in your difference calculations that does not conform to expected desert temperature levels is the Atacama in Peru. But, the Atacama is the highest desert and its daily temperatures range from around 0-25 degrees C. And there there is that cold Antarctic current running up the west coast of South America.
For AC and others.
The easiest way for me to wrap my head around this, was this little page
http://www-das.uwyo.edu/~geerts/cwx/notes/chap16/geo_clim.html
“It has long been assumed that climate is largely controlled by location or geography. In the sixth century BC, the Greek philosopher Pythagoras recognised the sphericity of the Earth and the dominance of latitude in explaining climate variation (Sanderson 1999). Two centuries later Aristotle expanded on Pythagoras’s foundation and introduced five climate zones, ranging from tropical to northern frigid. It is not coincidental that in the early 20th century German scientist Koeppen also used 5 climate zones in his classification, identified with the letters A-E.
Koeppen’s classification was developed at a time when it was widely believed, especially in the German scientific arena, that climate, and therefore geography determined flora and fauna, even the physical and behavioural traits of human societies. Obviously such determinism has its limitations, but it highlights the widespread and longstanding belief that location determines climate. More recent work by Geiger (1960) indicates that even the microclimate is largely controlled by the local ‘geographical’ conditions, such as orography and coastlines.
Given this control one could hypothesise that one can infer the place where given climatic data were obtained. In other words, can we work out the one or more locations where a station may be, even approximately, if we are given its climatic record? This is the key question addressed herein.”
Little???? But then everything is big to me, and this was eye candy to me.
There is another dimension to Koppen’s zones, ie. time, they change over time, so your latt/elev is time dependent, not location.
http://i59.tinypic.com/141k56r.jpg
Willis, the warm ocean near Norway is well known as the continuation of the Gulf Stream. If you google the term “Arctic Mediterranean”, you will see discussion of this area.
Thanks, Steve. I knew the Gulf Stream ended up there. I didn’t realize just how much warmer it is than we’d expect from first principles.
Regards,
w.
Willis,
Why would the Norwegian Current surprise a sailor such as yourself? It and the Irminger are well known branches of the North Atlantic Current.
It’s why the Allies could send Lend Lease aid to the USSR via Murmansk.
The short-term average CERES data confirm in considerable detail what has
been known by professional climatologists for well-nigh a century: the
global field is very highly correlated with estimates based on latitude and
elevation alone. That much should be expected from first principles.
But such a basic relationship of the global temperature field is not the
matter of essential interest. It is the dynamic spatio-temporal variations
over much longer time-scales that occupy professional attention.
Real-world temperature variations are by no means simply the sum of static
“climate” and “weather” terms. The essence of bona fide climatology lies
in determining the ACTUAL temperature field, which departs significantly
from expectations virtually everywhere and whose short-term time-averages
vary significantly from decade to decade. Little light is shed here upon those
crucial variations.
1sky1: Great comment. The CERES data set a stage. In a world without the bother of mobile water and winds, they would write the story. But in the real world, things like oceanic currents (swishing along the most incredible material – H20 – that God (or Nature, your choice) – ever invented) start moving that static picture into a tapestry that is both fascinating and changeable. Other things, for example Hadley cells, bringing down dry, and by their descent warming, air brings out other variations that probably change year to year. The system within the constraints of the current disposition of continents and seas, varies with time. Add in a few other potential natural variations, and one gets hot this year, cold the next. So, Mosher et al. have discovered the grand scheme of the earth’s climate. They cannot however, predict next year’s T at a given spot and time within about 10 degrees F, much less that a hundred years from now. If you don’t like the weather, wait a day. If you don’t like the climate, wait a few (ten, hundred?) thousand years. We have a fair handle on our climates. Its just its extremes that make us edgy. And CO2? – plants LOVES IT; otherwise, the more the better.
///… I note that as we’d expect, the deserts and arid areas of the world like the Sahara, the Namib, and the Australian deserts are warmer than would be otherwise expected. ..///
Not unexpected at all, Right ?
///… Having lost most of its water vapor to condensation and rain in the upward branch of the circulation, the descending air is dry. Low relative humidities are produced as the air is adiabatically warmed due to compression as it descends into a region of higher pressure. The subtropics are relatively free of the convection, or thunderstorms, that are common in the equatorial belt of rising motion. Many of the world’s deserts are located in these subtropical latitudes. …/// http://en.wikipedia.org/wiki/Hadley_cell . . .