It looks like you're new here. If you want to get involved, click one of these buttons!
Hi, I haven't been reading Azimuth for the past couple of months just because I've been very overworked, but I've been keeping up my life as someone interested and trying to improve humanity's interaction with the environment. One of the things I've been looking at over the last couple of weeks is the Berkeley Earth Surface Temperature dataset, and trying to figure out how one might formulate some statistical measure one could use to determine if "climate change" is present in the data. Obviously one thing that often happens is that this is done via plugging the data in to climate models, but that involves an extra level of variables that need to be fitted (which is fine if one has expertise in actual climate models). Before I post some of my thoughts, I wonder if anyone else has any thoughts about how one might try to draw conclusions about climate change from this data?
Comments
From a pure time series perspective, you can apply econometrics-type tests for non-stationarity, such as a unit root test. But often people want to get at attribution, not just detection: is the change due to humans? For that, you need to compare to radiative forcing data. People tend to do multiple regression of temperature on forcings and various climatic indicators such as ENSO index, although there are also econometrics approaches like Granger causality. Personally, I don't really trust the econometrics approaches; regression is better, but I think you're better off building a simple climate model, like an energy balance model, and doing parameter estimation with that. It still will be more physically realistic than a regression.
From a pure time series perspective, you can apply econometrics-type tests for non-stationarity, such as a [unit root test](http://en.wikipedia.org/wiki/Unit_root_test). But often people want to get at attribution, not just detection: is the change due to humans? For that, you need to compare to radiative forcing data. People tend to do multiple regression of temperature on forcings and various climatic indicators such as ENSO index, although there are also econometrics approaches like [Granger causality](http://en.wikipedia.org/wiki/Granger_causality). Personally, I don't really trust the econometrics approaches; regression is better, but I think you're better off building a simple climate model, like an energy balance model, and doing parameter estimation with that. It still will be more physically realistic than a regression.Thanks for the pointers Nathan: I'll do some reading up on those. And your point about building a climate model being the best way to get at good conclusions is well taken.
This is basically me just thinking outloud about what a researcher would do if he doesn't think he has a meaningful grasp of the underlying physics (which is not to imply thinking that no-one has a grasp on the physics). Obviously temperature records are a spatial and a temporal patchwork which need joint analysis for any reasonable estimates. Intuitively one would like to marginalise over variables like weather, but to take into account that weather must be similar in nearby areas.
Looking at the wikipedia entry for Berkeley Earth has a link to one of their papers which discusses their procedure for estimating the average. This seems a reasonable way of doing things, but it's not clearly the "one true" way to do things, so I'm just idly thinking about stuff an amateur might toy with.
Thanks for the pointers Nathan: I'll do some reading up on those. And your point about building a climate model being the best way to get at good conclusions is well taken. This is basically me just thinking outloud about what a researcher would do if he doesn't think he has a meaningful grasp of the underlying physics (which is not to imply thinking that no-one has a grasp on the physics). Obviously temperature records are a spatial and a temporal patchwork which need joint analysis for any reasonable estimates. Intuitively one would like to marginalise over variables like weather, but to take into account that weather must be similar in nearby areas. Looking at the wikipedia entry for [Berkeley Earth](http://en.wikipedia.org/wiki/Berkeley_Earth) has a link to one of their papers which discusses their procedure for estimating the average. This seems a reasonable way of doing things, but it's not clearly the "one true" way to do things, so I'm just idly thinking about stuff an amateur might toy with.So the BEST papers are assuming that the earth has at each instant in time a "mean temperature" $\theta(t)$ which is affected by a purely spatial additive term $C(x)$ (loosely "climate") and a spatially and temporally varying term $W(x,t)$ (loosely "weather") to give the measure temperature $T(x,t)$:
$T(x,t) = \theta(t) + C(x) + W(x,t)$
with some additional cross-site constraints on the C and W terms. (They do say in passing in the paper that some effects which would conventionally be regarded as climate are included in their weather term). Is that reasonable in terms of physics? (Clearly there is an average global temperature at any time, the question is whether the temperatures all over the globe are accurately modelled by additive modifications which are unchanging.)
So the BEST papers are assuming that the earth has at each instant in time a "mean temperature" $\theta(t)$ which is affected by a purely spatial additive term $C(x)$ (loosely "climate") and a spatially and temporally varying term $W(x,t)$ (loosely "weather") to give the measure temperature $T(x,t)$: $T(x,t) = \theta(t) + C(x) + W(x,t)$ with some additional cross-site constraints on the C and W terms. (They do say in passing in the paper that some effects which would conventionally be regarded as climate are included in their weather term). Is that reasonable in terms of physics? (Clearly there is an average global temperature at any time, the question is whether the temperatures all over the globe are accurately modelled by additive modifications which are unchanging.)I guess $C(x)$ gives the base climatology (pre-industrial or whatever), but $W(x,t)$ must contain a lot of the climate change signal. I think a minimal assumption for a "climate" term would have some time dependence, such as a separable product $C(x) \theta(t)$, with temperatures treated as anomalies. This is known as "pattern scaling". Maybe that's all built into $W$.
It's reasonable to assume that the spatial pattern of the climatology is additive with the mean if you define that to be some baseline climate state, and not too bad to assume that the "weather" is also additive. (If you get a little more sophisticated and propagate additive weather noise through linear dynamics, you'll get an additive term with autocorrelation.) This will break down eventually as you force the system more strongly and nonlinearities become more apparent, but is probably ok for the instrumental record. But you do need something that can capture regional climate change effects like polar amplification (such as a pattern scaling approach), which change the spatial climatology (e.g. by decreasing meridional gradients). It also needs to encode some of the spacetime correlations adequately (I don't know what covariance model they're using).
I guess $C(x)$ gives the base climatology (pre-industrial or whatever), but $W(x,t)$ must contain a lot of the climate change signal. I think a minimal assumption for a "climate" term would have some time dependence, such as a separable product $C(x) \theta(t)$, with temperatures treated as anomalies. This is known as "pattern scaling". Maybe that's all built into $W$. It's reasonable to assume that the spatial pattern of the climatology is additive with the mean if you define that to be some baseline climate state, and not too bad to assume that the "weather" is also additive. (If you get a little more sophisticated and propagate additive weather noise through linear dynamics, you'll get an additive term with autocorrelation.) This will break down eventually as you force the system more strongly and nonlinearities become more apparent, but is probably ok for the instrumental record. But you do need something that can capture regional climate change effects like polar amplification (such as a pattern scaling approach), which change the spatial climatology (e.g. by decreasing meridional gradients). It also needs to encode some of the spacetime correlations adequately (I don't know what covariance model they're using).David wrote:
I am not sure but by what you write it seems you assume that the underlying temperature data has been received via measurements in contrast to received via simulation? I don't know for which data set exactly you are heading for on that page, but at least for some temperature data IT SEEMS it has been explicitly outlined that THE UNDERLYING TEMPERATURES ARE NOT FROM MEASUREMENTS. That is for example the: README of the gridded data says:
In any case one could of course still try to "formulate statistical measure one could use to determine if “climate change” is present in the data" even if the data may not be based on real measurements. Actually it could be fun for you to test your statistical indicators also for other simulations like for example as in climate change games like in this, but I don't know how available the temperature data is for this game.
David wrote: >One of the things I’ve been looking at over the last couple of weeks is the Berkeley Earth Surface Temperature dataset, and trying to figure out how one might formulate some statistical measure one could use to determine if “climate change” is present in the data. Obviously one thing that often happens is that this is done via plugging the data in to climate models, but that involves an extra level of variables that need to be fitted (which is fine if one has expertise in actual climate models). I am not sure but by what you write it seems you assume that the underlying temperature data has been received via measurements in contrast to received via simulation? I don't know for which data set exactly you are heading for on that page, but at least for some temperature data IT SEEMS it has been explicitly outlined that THE UNDERLYING TEMPERATURES ARE NOT FROM MEASUREMENTS. That is for example the: <a href="http://berkeleyearth.lbl.gov/auto/Global/Gridded/Gridded_README.txt">README of the gridded data</a> says: >This file describes the format used by the Berkeley Earth Surface Temperature project for gridded data fields. These fields contain reconstructed monthly temperature anomaly values generated by the Berkeley Earth project based on our method of climate analysis. In any case one could of course still try to "formulate statistical measure one could use to determine if “climate change” is present in the data" even if the data may not be based on real measurements. Actually it could be fun for you to test your statistical indicators also for other simulations like for example as in climate change games like in <a href="http://www.bbc.co.uk/sn/hottopics/climatechange/climate_challenge/">this</a>, but I don't know how available the temperature data is for this game.Hi Nad,
my understanding is that there are various sets of data files: one set describe all the "raw sets of temperature measurements" the BE team could find, which includes some duplicated data sets (due to different aggregations of datasets done in the past and found by BE including the same sets of observations), a set where they've done removal of duplicate or completely spurious sets of observations and then various results of their reconstructions like the one you mention. (I think the "generated" word is there just because this is a file of gridded data whereas temperature stations are in non-uniform locations, so they've first "solved" for the temperature field (and anomaly) at those locations, then "generated" values on a uniform grid by interpolation.) At the moment I'm experimenting with that middle set that has been processed in an attempt to remove "gross record-keeping issues" but none of the detailed statistical techniques to remove other confounding factors. In general, from what I've read given the things they're assuming the BE team seem to have done a good job of analysis. However, it's seems to me that while the assumptions BE are making seem reasonable they're not obviously the best set of assumptions to be making.
Incidentally, testing statistical methodologies against a simulation is a good idea: it's one of the methods BE mentioned they used to validate their statistical approach. The one drawback is that you tend to generate simulation data that matches your statistical model.
Hi Nad, my understanding is that there are various sets of data files: one set describe all the "raw sets of temperature measurements" the BE team could find, which includes some duplicated data sets (due to different aggregations of datasets done in the past and found by BE including the same sets of observations), a set where they've done removal of duplicate or completely spurious sets of observations and then various results of their reconstructions like the one you mention. (I think the "generated" word is there just because this is a file of gridded data whereas temperature stations are in non-uniform locations, so they've first "solved" for the temperature field (and anomaly) at those locations, then "generated" values on a uniform grid by interpolation.) At the moment I'm experimenting with that middle set that has been processed in an attempt to remove "gross record-keeping issues" but none of the detailed statistical techniques to remove other confounding factors. In general, from what I've read given the things they're assuming the BE team seem to have done a good job of analysis. However, it's seems to me that while the assumptions BE are making seem reasonable they're not obviously the best set of assumptions to be making. Incidentally, testing statistical methodologies against a simulation is a good idea: it's one of the methods BE mentioned they used to validate their statistical approach. The one drawback is that you tend to generate simulation data that matches your statistical model.Hi Nathan, thanks for that info. From my understanding of the paper their analysis is only doing simple things in their models of $C(x)$ and $W(x,t)$, primarily
The spatial average of $C(x)$ is 0.
For each fixed value of the other variable, the spatial averages and temporal averages of $W(x,t)$ are 0.
There are constraints on how quickly $C(x)$ and $W(x,t)$ can vary based between nearby observation stations, based partly upon the degree of correlation between observations and upon spatial difference and an estimate of station reliability.
So I think they're doing some basic stuff, but not the kind of deeper structure in the model that you're talking about.
Hi Nathan, thanks for that info. From my understanding of the paper their analysis is only doing simple things in their models of $C(x)$ and $W(x,t)$, primarily 1. The spatial average of $C(x)$ is 0. 2. For each fixed value of the other variable, the spatial averages and temporal averages of $W(x,t)$ are 0. 3. There are constraints on how quickly $C(x)$ and $W(x,t)$ can vary based between nearby observation stations, based partly upon the degree of correlation between observations and upon spatial difference and an estimate of station reliability. So I think they're doing some basic stuff, but not the kind of deeper structure in the model that you're talking about.David wrote:
Where did you find that phrase about measurements? On the data page I found:
a report may not need to be based on a measurement and on the about data set page it is written:
In short I found no explicit statement that real measurements (and no description how these were performed) were used and as said for the gridded data they mention that they use a
David wrote: >my understanding is that there are various sets of data files: one set describe all the “raw sets of temperature measurements” the BE team could find Where did you find that phrase about measurements? On the <a href="http://berkeleyearth.org/data">data page</a> I found: >Source data consists of the raw temperature reports that form the foundation of our averaging system. a report may not need to be based on a measurement and on the <a hef="http://berkeleyearth.org/about-data-set">about data set</a> page it is written: >Best value series: "Best value" time series were formed by averaging across multiple records when they existed at the same site. In addition, flagged values were dropped and previously manipulated GHCN-M and Hadley Centre data was ignored in favor of other data sources when possible. These series are expected to be the primary records for most future studies, but the fully-flagged and multi-valued records will also be preserved and made available for more detailed analyses. In short I found no explicit statement that real measurements (and no description how these were performed) were used and as said for the gridded data they mention that they use a >reconstructed monthly temperature anomalyI think I had already mentioned this here, but I think this should be repeated: I find it scary that there are not more measurements for such critical climate issues. Like for the methane measurements it seems Ed Dlugokencky is the only person in the world who conducted measurements since the eighties. That is traveling with earth feels currently a bit like going in an airplane with a balloon, which may give some indication about speed, outside airpressure etc. but not with real instruments.
I think I had already mentioned this here, but I think this should be repeated: I find it scary that there are not more measurements for such critical climate issues. Like for the methane measurements it seems Ed Dlugokencky is the only person in the world who conducted measurements since the eighties. That is traveling with earth feels currently a bit like going in an airplane with a balloon, which may give some indication about speed, outside airpressure etc. but not with real instruments.I'm still getting my head around the terminology, but there are three kinds of things
Temperature "measurements" taken at a given site (modulo issues about multiple records, etc). I had thought that these were pretty much just measurements but some processing may have been done to them. These are the actual temperature and hence, in BE's model, contain both climate and weather effects. This is an "input".
A statistically-estimated/model-fitted/reconstructed absolute global temperature at that point at a given time along with similar values for climate and weather over all the observation stations, where they believe they've decoupled the original measurements into global temperature and effects of climate and weather. This is an output.
A gridded temperature anomaly, that is, values for what their model says the difference of the absolute temperature from "the global average" at regularly spaced locations where there may not have been an observation station. This is an output obtained by further interpolation of the output 2.
At various points they say they don't like 3, but because it's what all mainstream climate modellers produce they have to produce it to compare their results to others. They say that in terms of understanding what's going on in the world 2 is better. I had thought that all preprocessing before step 1 was doing was that, since they're not actually seeking out individual weather station reports but just big-ish collections that various people have already done, they' were just trying to throw out actual duplicates of reports from the same station. However, it seems like something additional has been done to the reports, which is a bit troubling when so unspecific.
I can't immediately find a sentence which says they are looking at historical recordings of temperature at weather stations. The closest I can find is this from the paragraph at the top of this page :
Source data consists of the raw temperature reports that form the foundation of our averaging system. Source observations are provided as originally reported and will contain many quality control and redundancy issues. Intermediate data is constructed from the source data by merging redundant records, identifying a variety of quality control problems, and creating monthly averages from daily reports when necessary.
I'm still getting my head around the terminology, but there are three kinds of things 1. Temperature "measurements" taken at a given site (modulo issues about multiple records, etc). I had thought that these were pretty much just measurements but some processing may have been done to them. These are the actual temperature and hence, in BE's model, contain both climate and weather effects. This is an "input". 2. A statistically-estimated/model-fitted/reconstructed absolute global temperature at that point at a given time along with similar values for climate and weather over all the observation stations, where they believe they've decoupled the original measurements into global temperature and effects of climate and weather. This is an output. 3. A gridded temperature anomaly, that is, values for what their model says the difference of the absolute temperature from "the global average" at regularly spaced locations where there may not have been an observation station. This is an output obtained by further interpolation of the output 2. At various points they say they don't like 3, but because it's what all mainstream climate modellers produce they have to produce it to compare their results to others. They say that in terms of understanding what's going on in the world 2 is better. I had thought that all preprocessing before step 1 was doing was that, since they're not actually seeking out individual weather station reports but just big-ish collections that various people have already done, they' were just trying to throw out actual duplicates of reports from the same station. However, it seems like something additional has been done to the reports, which is a bit troubling when so unspecific. I can't immediately find a sentence which says they are looking at historical recordings of temperature at weather stations. The closest I can find is this from the paragraph at the top of [this page](http://berkeleyearth.org/data) : Source data consists of the raw temperature reports that form the foundation of our averaging system. Source observations are provided as originally reported and will contain many quality control and redundancy issues. Intermediate data is constructed from the source data by merging redundant records, identifying a variety of quality control problems, and creating monthly averages from daily reports when necessary.David wrote:
As said above they wrote:
Sofar I know these two centres are THE centers for collecting global temperature measurements. I haven't heard of that the data at GHCN-M and Hadley centre was manipulated but if this was so then this would of course be troublesome. Do you know on which incident this assertion is based? Was there a cyber attack? Don't they have still unmanipulated copies at the centres? If not then one should may be ask publicly wether people hold still some old unmanipulated files, like I have a copy of the Hadley temperature anomalies from march this year.
So I guess IF this should be real measured data what they use then either the Berkeley earth people picked up the data from local weather stations and archives themselves or there are other centers, which we do not know about like I could imagine that central intelligence services of some countries might have collected that data as well, since well this is of course vital information for the survival of each country. So maybe Berkeley earth people have special access to classified temperature data that might explain their cautious wording.
David wrote: >I can’t immediately find a sentence which says they are looking at historical recordings of temperature at weather stations. As said above they wrote: >GHCN-M and Hadley Centre data was ignored in favor of other data sources when possible Sofar I know these two centres are THE centers for collecting global temperature measurements. I haven't heard of that the data at GHCN-M and Hadley centre was manipulated but if this was so then this would of course be troublesome. Do you know on which incident this assertion is based? Was there a cyber attack? Don't they have still unmanipulated copies at the centres? If not then one should may be ask publicly wether people hold still some old unmanipulated files, like I have a copy of the Hadley temperature anomalies from march this year. So I guess IF this should be real measured data what they use then either the Berkeley earth people picked up the data from local weather stations and archives themselves or there are other centers, which we do not know about like I could imagine that central intelligence services of some countries might have collected that data as well, since well this is of course vital information for the survival of each country. So maybe Berkeley earth people have special access to classified temperature data that might explain their cautious wording.