Comments on: Example of Simple Linear Regression – global warming trends http://landshape.org/enm/example-of-simple-linear-regression/ The power of numeracy Mon, 15 Mar 2010 09:48:22 -0500 http://wordpress.org/?v=2.8.6 hourly 1 By: Franko http://landshape.org/enm/example-of-simple-linear-regression/comment-page-1/#comment-168471 Franko Fri, 08 Aug 2008 08:54:24 +0000 http://landshape.org/enm/example-of-simple-linear-regression/#comment-168471 Perhaps, do ARIMA, with various number of coefficients. Plot the residual errors. Frequency domain also. Starting since records kept. Predict a few steps ahead. Perhaps, do ARIMA, with various number of coefficients. Plot the residual errors. Frequency domain also. Starting since records kept. Predict a few steps ahead.

]]> By: Niche Modeling » Rahmstorf 7 Finale http://landshape.org/enm/example-of-simple-linear-regression/comment-page-1/#comment-116730 Niche Modeling » Rahmstorf 7 Finale Wed, 23 Apr 2008 08:04:54 +0000 http://landshape.org/enm/example-of-simple-linear-regression/#comment-116730 [...] This paper claimed to show that: The data available for the period since 1990 raise concerns that the climate system, in particular sea level, may be responding more quickly to climate change than our current generation of models indicates. By way of recap, this paper figured prominently in the Interim Report of the Garnaut Review where it is clearly used as a source of mainstream scientific opinion: “Developments in mainstream scientific opinion on the relationship between emissions, accumulations and climate outcomes, and the Review’s own work on future business-as-usual global emissions, suggest that the world is moving towards high risks of dangerous climate change more rapidly than has generally been understood.” Interest in the current weather has been growing since people have been observing either sharp declines in temperatures since last year, or relative stability in temperatures over about the last 10 years and wondering how these fit into the picture of global warming. I did some posts putting it into context showing last years temperature drop was not unusual here, that a particular 10 year period has been flat here, and that a number of climate indicators are showing decadal stability here. The Blackboard has been spear-heading rigorous statistical methods for checking IPCC projections and finding post 2001 TAR consistently falsified by climate trends. Contradicting these findings was the paper by Rahmstorf et al 2007, published in Science, by seven of the leading members of the IPCC scientific team. So, I started to audit this paper to see if this paper does in fact provide a more reliable perspective on the issue of whether climate is changing faster or slower than expected. A number of bloggers ‘raised concerns’ about the vague description of the methodology, and argued at Niche Modeling and The Blackboard that there were important sources of uncertainty unaccounted for. Other blogs picked up the issue including Peter Gallagher and Mark Lawson. Stefan Rahmstorf and I exchanged comments at RealClimate.org and here. His main defense was that the end point uncertainty would only affect the last 5 points of the smoothed trend line with an 11 point embedding. Here the global temperatures were smoothed using a complex method called Singular Spectrum Analysis (SSA). I gave examples of SSA and other methods where the end point uncertainty affected virtually ALL points in the smoothed trend line, and particularly more than 5 end points. Stefan clearly had little idea of how SSA worked. His final message, without an argument, was: [Response: If you really think you’d come to a different conclusion with a different analysis method, I suggest you submit it to a journal, like we did. I am unconvinced, though. -stefan] So much for the recap. Keep in mind that the purpose of a scientific exchange like this is to clarify the points of agreement and disagreement and attempt to arrive at a resolution on the validity of the claims. Note the problem I raised is not the only obvious problem either, but just one I worked on. This is not meant to be a personal process. I am grateful for someone to point out errors in my work and would try to understand them, as I would rather not be blowing smoke unintentionally. This example highlights the power of numbers to resolve an issue. Stefan can have his opinion, and I have opinions too, but the thing I love is the power of numbers to arbitrate and discriminate, and ultimately eliminate the unjustified ones. Also I was wanting to address the Garnaut Review, as I feel that they are abrogating a duty of diligence by not paying more critical attention to papers such as these. Here was an opportunity to give a specific example of a paper with flaws so obvious that it SHOULD have been dismissed by anyone with statistical training, or background knowledge. So thank you readers for your patience with this process. I have put a submission into the Garnaut Review supported by documentation from the web sites involved. Here is a good example of the use of blogs. As the time for comments has closed, I could not submit a critique to Science. It is also better to have a through and open discussion of the issues at hand anyway, before rushing to publication of critical comments, so both can gain a deeper understanding of the finer points. It is unfortunate that Stefan cut the discussion off, but to his credit he was responsive to the actual concerns in the replies he did make. [...] [...] This paper claimed to show that: The data available for the period since 1990 raise concerns that the climate system, in particular sea level, may be responding more quickly to climate change than our current generation of models indicates. By way of recap, this paper figured prominently in the Interim Report of the Garnaut Review where it is clearly used as a source of mainstream scientific opinion: “Developments in mainstream scientific opinion on the relationship between emissions, accumulations and climate outcomes, and the Review’s own work on future business-as-usual global emissions, suggest that the world is moving towards high risks of dangerous climate change more rapidly than has generally been understood.” Interest in the current weather has been growing since people have been observing either sharp declines in temperatures since last year, or relative stability in temperatures over about the last 10 years and wondering how these fit into the picture of global warming. I did some posts putting it into context showing last years temperature drop was not unusual here, that a particular 10 year period has been flat here, and that a number of climate indicators are showing decadal stability here. The Blackboard has been spear-heading rigorous statistical methods for checking IPCC projections and finding post 2001 TAR consistently falsified by climate trends. Contradicting these findings was the paper by Rahmstorf et al 2007, published in Science, by seven of the leading members of the IPCC scientific team. So, I started to audit this paper to see if this paper does in fact provide a more reliable perspective on the issue of whether climate is changing faster or slower than expected. A number of bloggers ‘raised concerns’ about the vague description of the methodology, and argued at Niche Modeling and The Blackboard that there were important sources of uncertainty unaccounted for. Other blogs picked up the issue including Peter Gallagher and Mark Lawson. Stefan Rahmstorf and I exchanged comments at RealClimate.org and here. His main defense was that the end point uncertainty would only affect the last 5 points of the smoothed trend line with an 11 point embedding. Here the global temperatures were smoothed using a complex method called Singular Spectrum Analysis (SSA). I gave examples of SSA and other methods where the end point uncertainty affected virtually ALL points in the smoothed trend line, and particularly more than 5 end points. Stefan clearly had little idea of how SSA worked. His final message, without an argument, was: [Response: If you really think you’d come to a different conclusion with a different analysis method, I suggest you submit it to a journal, like we did. I am unconvinced, though. -stefan] So much for the recap. Keep in mind that the purpose of a scientific exchange like this is to clarify the points of agreement and disagreement and attempt to arrive at a resolution on the validity of the claims. Note the problem I raised is not the only obvious problem either, but just one I worked on. This is not meant to be a personal process. I am grateful for someone to point out errors in my work and would try to understand them, as I would rather not be blowing smoke unintentionally. This example highlights the power of numbers to resolve an issue. Stefan can have his opinion, and I have opinions too, but the thing I love is the power of numbers to arbitrate and discriminate, and ultimately eliminate the unjustified ones. Also I was wanting to address the Garnaut Review, as I feel that they are abrogating a duty of diligence by not paying more critical attention to papers such as these. Here was an opportunity to give a specific example of a paper with flaws so obvious that it SHOULD have been dismissed by anyone with statistical training, or background knowledge. So thank you readers for your patience with this process. I have put a submission into the Garnaut Review supported by documentation from the web sites involved. Here is a good example of the use of blogs. As the time for comments has closed, I could not submit a critique to Science. It is also better to have a through and open discussion of the issues at hand anyway, before rushing to publication of critical comments, so both can gain a deeper understanding of the finer points. It is unfortunate that Stefan cut the discussion off, but to his credit he was responsive to the actual concerns in the replies he did make. [...]

]]> By: Niche Modeling » Recent Climate Observations Compared to Predictions by Rahmstorf et.al. - a review http://landshape.org/enm/example-of-simple-linear-regression/comment-page-1/#comment-103569 Niche Modeling » Recent Climate Observations Compared to Predictions by Rahmstorf et.al. - a review Tue, 01 Apr 2008 19:11:59 +0000 http://landshape.org/enm/example-of-simple-linear-regression/#comment-103569 [...] The method used is non-linear fitting of a trend to temperatures. The conclusion is from a marked increase in the trend in recent years beyond IPCC decadal projections. However, there appear to be many statistical black holes. Lucia has been trying to verify the provenance of the IPCC projections as they are not described explicitly in paper, with no success. The method is described only as a nonlinear trend line computed with an embedding period of 11 years and a minimum roughness condition at the end with a reference to Moore et.al. “New Tools for Analyzing Time Series Relationships and Trends“. The non-linear method appears to be singular spectrum analysis (SSA). This method decomposes a time series into orthogonal components, such a a periodic, linear trend and random noise parts. Rahmstorf et.al. also mentions a non-SSA ‘minimum roughness condition applied at the end’ without further elaboration. Any ad-hoc techniques appled to the end of the series should raise a red flag, as the part of the series of interest is the recent temperatures at the end. Digging into Moore et.al. we find the ‘minimum roughness condition’ consists of ‘padding the series so the local trend is preserved’. The reference to the padding the data is none other than Mann 2004, “On smoothing potentially non-stationary climate time series“!. Figures. Mann has been outed for various dubious extrapolation activities at ClimateAudit here). Second, the unique adjustment was not disclosed in the MBH98 footnotes. Worse, the start date of this series was actually misrepresented in the original supplementary information, which listed the series as starting at the “adjusted” start date rather than the true start date. We only noticed the extrapolation when we compared the Mann version to original data. We noted this in MM 2003, but were not then fully aware of the impact. Amazing what you find with a bit of digging. It seems like the ‘minimum roughness condition’ is simply a fancy name for the extrapolation of the trend of the last few data points in the series. In that case, the conclusions of the paper — that observed trends surpass the IPCC projections — are based on only a few end points, raising the specter of ‘cherry-picking’. Another opportunity for cherry picking is in the selection of the 11 year embedding interval in the SSA. No justification is provided in Rahmstorf for the choice. Although Moore et.al. does provide the helpful suggestion: A wise choice of embedding dimension can be made with a priori insight or perhaps more commonly found by simply playing with the data. Wise choice or parameter tuning? Not having assess to SSA, as I can’t find it among the R packages at CRAN, I examined the degree that conclusions of Rahmsdorf et.al. might be cherry-picked by looking at how trends vary with length of series. Below is the plot the HadCRU temperature trend for increasing intervals starting from the present, starting with three years (2004, 2005, 2006), then four years (2003, 2004, 2005, 2006) and so on. Below is the code (which I am not proud of but shows you can program R in proceedural style when you want to). Figure: Above is the plot the HadCRU temperature trend for increasing intervals starting from the present, starting with three years (2004, 2005, 2006), then four years (2003, 2004, 2005, 2006) and so on. The plot shows clear peaks with a trend of +0.37C per decade at 16 years trend length (1990-2006) and declines to the long term trend of around +0.1C for longer intervals. The elevated trends reported in the paper and shown on the figure are clearly a reflection of local trends in this period. However, there are no significance tests quoted for the trend!. Unlike other examinations of IPCC projections here and here, no attempt has been made to determine if the trends are due to climate variability. As reported, trends are declining, as expected if the increase was simply a random fluctuation. There are multiple potential problems with Rahmsdorf et.al.: [...] [...] The method used is non-linear fitting of a trend to temperatures. The conclusion is from a marked increase in the trend in recent years beyond IPCC decadal projections. However, there appear to be many statistical black holes. Lucia has been trying to verify the provenance of the IPCC projections as they are not described explicitly in paper, with no success. The method is described only as a nonlinear trend line computed with an embedding period of 11 years and a minimum roughness condition at the end with a reference to Moore et.al. “New Tools for Analyzing Time Series Relationships and Trends“. The non-linear method appears to be singular spectrum analysis (SSA). This method decomposes a time series into orthogonal components, such a a periodic, linear trend and random noise parts. Rahmstorf et.al. also mentions a non-SSA ‘minimum roughness condition applied at the end’ without further elaboration. Any ad-hoc techniques appled to the end of the series should raise a red flag, as the part of the series of interest is the recent temperatures at the end. Digging into Moore et.al. we find the ‘minimum roughness condition’ consists of ‘padding the series so the local trend is preserved’. The reference to the padding the data is none other than Mann 2004, “On smoothing potentially non-stationary climate time series“!. Figures. Mann has been outed for various dubious extrapolation activities at ClimateAudit here). Second, the unique adjustment was not disclosed in the MBH98 footnotes. Worse, the start date of this series was actually misrepresented in the original supplementary information, which listed the series as starting at the “adjusted” start date rather than the true start date. We only noticed the extrapolation when we compared the Mann version to original data. We noted this in MM 2003, but were not then fully aware of the impact. Amazing what you find with a bit of digging. It seems like the ‘minimum roughness condition’ is simply a fancy name for the extrapolation of the trend of the last few data points in the series. In that case, the conclusions of the paper — that observed trends surpass the IPCC projections — are based on only a few end points, raising the specter of ‘cherry-picking’. Another opportunity for cherry picking is in the selection of the 11 year embedding interval in the SSA. No justification is provided in Rahmstorf for the choice. Although Moore et.al. does provide the helpful suggestion: A wise choice of embedding dimension can be made with a priori insight or perhaps more commonly found by simply playing with the data. Wise choice or parameter tuning? Not having assess to SSA, as I can’t find it among the R packages at CRAN, I examined the degree that conclusions of Rahmsdorf et.al. might be cherry-picked by looking at how trends vary with length of series. Below is the plot the HadCRU temperature trend for increasing intervals starting from the present, starting with three years (2004, 2005, 2006), then four years (2003, 2004, 2005, 2006) and so on. Below is the code (which I am not proud of but shows you can program R in proceedural style when you want to). Figure: Above is the plot the HadCRU temperature trend for increasing intervals starting from the present, starting with three years (2004, 2005, 2006), then four years (2003, 2004, 2005, 2006) and so on. The plot shows clear peaks with a trend of +0.37C per decade at 16 years trend length (1990-2006) and declines to the long term trend of around +0.1C for longer intervals. The elevated trends reported in the paper and shown on the figure are clearly a reflection of local trends in this period. However, there are no significance tests quoted for the trend!. Unlike other examinations of IPCC projections here and here, no attempt has been made to determine if the trends are due to climate variability. As reported, trends are declining, as expected if the increase was simply a random fluctuation. There are multiple potential problems with Rahmsdorf et.al.: [...]

]]> By: Niche Modeling » Programming in R — statistics http://landshape.org/enm/example-of-simple-linear-regression/comment-page-1/#comment-101385 Niche Modeling » Programming in R — statistics Wed, 26 Mar 2008 21:35:01 +0000 http://landshape.org/enm/example-of-simple-linear-regression/#comment-101385 [...] The large drop in temperatures in the last 12 months here a decline in temperatures in the last 7 years reported here, decline in the last 10 years here, and now, indications of atmospheric stability back to 1995, or 13 years. Simple regression modeling and validation have teased out components of atmospheric stability, and shown difference between northern hemisphere tropospheric temperatures and the rest of the atmosphere that are seemingly unrelated. CO2 however is globally distributed gas influencing temperatures at all levels of the atmosphere. These results are at variance with presentations of long term trends of globally averaged temperatures. Global warming is not ‘taking a breather‘. The recent warming is not global, but better described as northern hemisphere warming. If the pattern doesn’t fit, you should acquit (CO2 that is). Below is the statistics R code used here: [...] [...] The large drop in temperatures in the last 12 months here a decline in temperatures in the last 7 years reported here, decline in the last 10 years here, and now, indications of atmospheric stability back to 1995, or 13 years. Simple regression modeling and validation have teased out components of atmospheric stability, and shown difference between northern hemisphere tropospheric temperatures and the rest of the atmosphere that are seemingly unrelated. CO2 however is globally distributed gas influencing temperatures at all levels of the atmosphere. These results are at variance with presentations of long term trends of globally averaged temperatures. Global warming is not ‘taking a breather‘. The recent warming is not global, but better described as northern hemisphere warming. If the pattern doesn’t fit, you should acquit (CO2 that is). Below is the statistics R code used here: [...]

]]> By: admin http://landshape.org/enm/example-of-simple-linear-regression/comment-page-1/#comment-99186 admin Fri, 14 Mar 2008 20:32:12 +0000 http://landshape.org/enm/example-of-simple-linear-regression/#comment-99186 Lucia, Yes. Jim Hansen predicts a rapid return to higher temperatures in his recent newsletter on his personal website here. http://www.columbia.edu/~jeh1/ There is no 'royal road to science'. You try to avoid gross errors. Lets see if this short time frame prediction (months?) is correct or not (like his prediction of severe El Nino). Lucia, Yes. Jim Hansen predicts a rapid return to higher temperatures in his recent newsletter on his personal website here. http://www.columbia.edu/~jeh1/ There is no ‘royal road to science’. You try to avoid gross errors. Lets see if this short time frame prediction (months?) is correct or not (like his prediction of severe El Nino).

]]> By: lucia http://landshape.org/enm/example-of-simple-linear-regression/comment-page-1/#comment-99183 lucia Fri, 14 Mar 2008 20:00:48 +0000 http://landshape.org/enm/example-of-simple-linear-regression/#comment-99183 David, On the one hand, someone might accuse me of confusing weather and climate. However, all that happens with shorter data sets is that the uncertainty in estimates of any metric describing climate increases. I am also willing to admit here are difficulties in short records in and of themselves. There may be very long trends in climate -- including multidecadal ones like the PDO. The existence of these cuts against both your analysis and mine to some extent. But, it also cuts against using data from 1975-- we should include several full complete PDO cycles to average out that effect. The most recent half cycle seems to have lasted 30 years, right? Do we need 120 years to fully describe the baseline climate uninfluenced by GHG's? This isn't an easy issue. That said, in principle, the climatologist in the IPCC considered the possibility of any switch in PDO and incorporated its effect into <i>their</i> uncertainty intervals for trends. What's interesting is that, currently, it's rather difficult to find any reasonable criterion for selecting a "start" point that permits the IPCC projections to <i>survive</i>. The only thing that can bring those in line with the data is for temperatures to rise, and pronto. David,
On the one hand, someone might accuse me of confusing weather and climate. However, all that happens with shorter data sets is that the uncertainty in estimates of any metric describing climate increases.

I am also willing to admit here are difficulties in short records in and of themselves. There may be very long trends in climate — including multidecadal ones like the PDO. The existence of these cuts against both your analysis and mine to some extent. But, it also cuts against using data from 1975– we should include several full complete PDO cycles to average out that effect. The most recent half cycle seems to have lasted 30 years, right? Do we need 120 years to fully describe the baseline climate uninfluenced by GHG’s?

This isn’t an easy issue.

That said, in principle, the climatologist in the IPCC considered the possibility of any switch in PDO and incorporated its effect into their uncertainty intervals for trends.

What’s interesting is that, currently, it’s rather difficult to find any reasonable criterion for selecting a “start” point that permits the IPCC projections to survive. The only thing that can bring those in line with the data is for temperatures to rise, and pronto.

]]> By: Raniers or Maraschino? Accusations of Cherry Picking and Climate Change. | The Blackboard http://landshape.org/enm/example-of-simple-linear-regression/comment-page-1/#comment-99170 Raniers or Maraschino? Accusations of Cherry Picking and Climate Change. | The Blackboard Fri, 14 Mar 2008 18:07:00 +0000 http://landshape.org/enm/example-of-simple-linear-regression/#comment-99170 [...] In the first place, those who have examine recent trends are always compelled to select the most recent year as their endpoint: these include David Stockwell, Basil, and me. [...] [...] In the first place, those who have examine recent trends are always compelled to select the most recent year as their endpoint: these include David Stockwell, Basil, and me. [...]

]]> By: admin http://landshape.org/enm/example-of-simple-linear-regression/comment-page-1/#comment-98793 admin Wed, 12 Mar 2008 19:02:28 +0000 http://landshape.org/enm/example-of-simple-linear-regression/#comment-98793 Lucia, you have raised a valid issue, but here is why I don't think it matters. 1. Are you saying IPCC didn't project a rising temperature trend prior to 2001? By including years they already examined makes a test even easier to pass. Despite seeing some of the data the predictions have failed. There is no need to set a harder test for them. They even fail the easier one. 2. If we are to choose between a shorter and a longer interval we should choose the longer one, as we are talking about 'climate', the long term average of weather. So if its the 10 year stable trend extends to 15, 20 etc that is still important. You are opening yourself to more criticism of confusing weather and climate by choosing a shorter trend. 3. What is gained by choosing 2001? The IPCC would gain the independence of the test, if they were the ones doing the test of their projections. But they are not doing the test. Your choice has an educational value, in illustrating how one might carry out a well structured test, and I am guessing this is part of the motivation for it. Lucia, you have raised a valid issue, but here is why I don’t think it matters.

1. Are you saying IPCC didn’t project a rising temperature trend prior to 2001? By including years they already examined makes a test even easier to pass. Despite seeing some of the data the predictions have failed. There is no need to set a harder test for them. They even fail the easier one.

2. If we are to choose between a shorter and a longer interval we should choose the longer one, as we are talking about ‘climate’, the long term average of weather. So if its the 10 year stable trend extends to 15, 20 etc that is still important. You are opening yourself to more criticism of confusing weather and climate by choosing a shorter trend.

3. What is gained by choosing 2001? The IPCC would gain the independence of the test, if they were the ones doing the test of their projections. But they are not doing the test. Your choice has an educational value, in illustrating how one might carry out a well structured test, and I am guessing this is part of the motivation for it.

]]> By: lucia http://landshape.org/enm/example-of-simple-linear-regression/comment-page-1/#comment-98767 lucia Wed, 12 Mar 2008 16:35:56 +0000 http://landshape.org/enm/example-of-simple-linear-regression/#comment-98767 Hi David, I don't mean to suggest 10 years is cherry picking <i>per se</i>. But, since my goal is to apply a hypothesis to the IPCC projections, 10 years is cherry picking <i>in this instance</i>. I think it's best to pick a start date based on when they made their projections. Their projections are for 2001- on. So saying the post 2001 projections don't match earlier trends doesn't mean much. The IPCC's own projections indicate that the trend is supposed to increase in time. So, in a sense, the trend was <i>supposed</i> to be less than 2C/century before 2001. Otherwise, of course we can gain insight looking at 10 year trends, bearing in mind that we must be cautious about what it means for one particular trend to fall below some statistical threshold. (But I think you already know this, and I doubt we disagree. Hi David,

I don’t mean to suggest 10 years is cherry picking per se. But, since my goal is to apply a hypothesis to the IPCC projections, 10 years is cherry picking in this instance. I think it’s best to pick a start date based on when they made their projections. Their projections are for 2001- on. So saying the post 2001 projections don’t match earlier trends doesn’t mean much. The IPCC’s own projections indicate that the trend is supposed to increase in time. So, in a sense, the trend was supposed to be less than 2C/century before 2001.

Otherwise, of course we can gain insight looking at 10 year trends, bearing in mind that we must be cautious about what it means for one particular trend to fall below some statistical threshold. (But I think you already know this, and I doubt we disagree.

]]> By: Niche Modeling » Greenhouse effect in semi-transparent planetary atmospheres by Miskolczi - a review http://landshape.org/enm/example-of-simple-linear-regression/comment-page-1/#comment-98722 Niche Modeling » Greenhouse effect in semi-transparent planetary atmospheres by Miskolczi - a review Wed, 12 Mar 2008 10:23:51 +0000 http://landshape.org/enm/example-of-simple-linear-regression/#comment-98722 [...] While there is a lot of mathematics, they are mostly fairly simple balance [...] [...] While there is a lot of mathematics, they are mostly fairly simple balance [...]

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