Guest Post by Willis Eschenbach
The Inter-Tropical Convergence Zone from space
A while ago I started studying the question of the amplification of the tropical tropospheric temperature with respect to the surface. After months of research bore fruit, I started writing a paper. My intention was to have it published in a peer-reviewed journal. I finished the writing about a week ago.
During that time, I also wrote and published The Temperature Hypothesis here on WUWT. This got me to thinking about science, and about how we establish scientific facts. In climate science, the peer review process is badly broken. Among other problems, it is often an “old boy” system where very poor work is waved through. In common with other sciences, turnaround of ideas in journals takes weeks. Under pressure to publish, journals often do only the most cursory examination of the papers.
Upon reflection, I have decided to try a different way to examine the truth content of my paper. This is to invite all of the authors whose work I discuss, and other interested scientists of all stripes, to comment on the paper and on whether they can find any flaws in it. To facilitate the process I have provided all of the code and data that I used to do the analysis.
To make this process work will require cooperation. First, I ask for science and science only. No discussions of motives. No ad homs. No generalizations to larger spheres. No asides. No disrespect, we can be gentlemen and gentlewomen. No comments on politics, CO2, or AGW, no snowball earth. This thread has one purpose only, to establish whether my ideas stand: to either attack and destroy the ideas I put forth in the paper below, or to provide evidence and data to support the ideas I put forth below.
People think science is a cooperative endeavor. It is not. It is a war of ideas. An idea is put out, and scientists gather round to attack it and disprove it. Sometimes, other scientists may support and defend it. The more fierce the attack, the better … because if it can withstand the strongest attack, it is more likely true. When your worst scientific enemies and greatest disbelievers can’t show that you are wrong, your ideas are taken as scientific fact. (Until your ideas in turn are perhaps overthrown). Science is a blood sport, but all of the attack and parry is historically done in private. I propose to bring it out in public, and I offer my contribution below as the first victim.
Second, I will insist on a friendly, appreciative attitude towards the contributions of others. We are interested in working together to advance our primitive knowledge of how the climate works. We are doing that by trying to tear my ideas down, to disprove them, to find errors in them. To make this work we must do this with respect for the people involved and the ideas they put forwards. You don’t have to smash the guy to smash the idea, in fact it reduces your odds.
Third, no anonymous posting, please. If you are think your ideas are scientifically valid, please put your name on them.
With that in mind, I’d like to invite any and all of the following authors whose work I discuss below, to comment on and/or tear to shreds this study.
J. S. Boyle, J. R. Christy, W. D. Collins, K. W. Dixon, D. H. Douglass, C. Doutriaux, M. Free, Q. Fu, P. J. Gleckler, L. Haimberger, J. E. Hansen, G. S. Jones, P. D. Jones, T. R. Karl, S. A. Klein, J. R. Lanzante, C. Mears, G. A. Meehl, D. Nychka, B. D. Pearson, V Ramaswamy, R. Ruedy, G. Russell, B. D. Santer, G. A. Schmidt, D. J. Seidel, S. C. Sherwood, S. F. Singer, S. Solomon, K. E. Taylor, P. W. Thorne, M. F. Wehner, F. J. Wentz, and T. M. L. Wigley
(Man, all those 34 scientists on that side … and on this side … me. I’d better attack quick, while I have them outnumbered … )
I also invite anyone who has evidence, logic, theory, or data to disprove or to support my analysis to please contribute to the thread. Because at the end of this process, where I have exposed my ideas and the data and code to the attacks of anyone and everyone who can find flaws with them, I will have my own answer. If no one is able to disprove or find flaws in my analysis, I will consider it to be established science until someone can do so. Whether you consider it established science is up to you. However, it is certainly a more rigorous process than peer-review, and anyone who disagrees has had an opportunity to do so.
I see something in this nature, a web-based process, as the future of science. We need a place where scientific ideas can be brought up, discussed and debated by experts from all over the world, and either shot down or provisionally accepted in real time. Consider this an early experiment in that regard.
Three months to comment on a Journal paper is so 20th century. I’m amazed that the journals haven’t done something akin to this on the web, with various restrictions on reviewers and participants. Nothing sells journals like blood, and scientific blood is no different from any other.
So without further ado, here is my paper. Tear it apart or back it up, enjoy, ask questions, that’s science.
My best to everyone.
w.
A New Amplification Metric
ABSTRACT: A new method is proposed for exploring the amplification of the tropical tropospheric temperature with respect to the surface. The method looks at the change in amplification with the length of the record. The method is used to reveal the similarities and differences between the HadAT2 balloon, UAH MSU satellite, RSS MSU satellite, RATPAC balloon, AMSU satellite, NCEP Reanalysis, and five climate model datasets In general, the observational datasets (HadAT2, RATPAC, and satellite datasets) agree with each other. The climate model and reanalysis datasets disagree with the observations. They also disagree with each other, with no two being alike.
Background
“Amplification” is the term used for the general observation that in the tropics, the tropospheric temperatures at altitude tend to vary more than the surface temperature. If the surface temperature goes up by a degree, the tropical temperature aloft often goes up by more than a degree. If surface and tropospheric temperatures were to vary by exactly the same amount, the amplification would be 1.0. If the troposphere varies more than the surface, the amplification will be greater than one, and vice versa.
There are only a limited number of observational datasets of tropospheric temperatures. These include the HadAT2 and RATPAC weather balloon datasets, and two versions of the Microwave Sounding Unit (MSU) satellite data. At present the satellite record is about thirty years long, and the two balloon datasets are about 50 years in length.
Recently there has been much discussion of the the Santer et al. 2005, Douglass et al. 2007, and the Santer et al. 2008 papers on tropical tropospheric amplification. The issue involved is posed by Santer et al. 2005 in their abstract:
The month-to-month variability of tropical temperatures is larger in the troposphere than at the Earth’s surface. This amplification behavior is similar in a range of observations and climate model simulations, and is consistent with basic theory. On multi-decadal timescales, tropospheric amplification of surface warming is a robust feature of model simulations, but occurs in only one observational dataset [the RSS dataset]. Other observations show weak or even negative amplification. These results suggest that either different physical mechanisms control amplification processes on monthly and decadal timescales, and models fail to capture such behavior, or (more plausibly) that residual errors in several observational datasets used here affect their representation of long-term trends.
Metrics of Amplification
Santer 2005 utilizes two different metrics of amplification, viz:
We examine two different amplification metrics: RS(z), the ratio between the temporal standard deviations of monthly-mean tropospheric and TS anomalies, and Rβ(z), the ratio between the multi-decadal trends in these quantities.
Neither of these metrics, however, measures the amount of the amplification at altitude which is related to the surface variations. Ratios of standard deviations merely measure the size of the swings. They cannot indicate whether one is an amplified version of the other. The same is true of trend ratios. All they can show is the size of the difference, not whether the surface and atmosphere are actually correlated.
In order to measure whether one dataset is an amplified version of another, the simplest measure is the slope of the ordinary least squares regression line. This measures how much one temperature varies in relation to another.
Despite a variety of searches, I was unable to find published studies showing that the “amplification behavior is similar in a range of observations and climate model simulations” as Santer et al. 2005 states. To investigate whether the tropical amplification is “robust” at various timescales, I decided to calculate the tropical and global amplification (average slope of the regression line) at all time scales between three months and thirty years or more for a variety of temperature datasets. I started with the UAH and the RSS versions of the satellite record. Next I looked at the HadAT2 balloon (radiosonde) dataset. The results are shown in Figure 1.
To measure the amplification, for every time interval (e.g. 5 months) I calculated the amplification of all contiguous 5-month periods in the entire dataset. In other words, I exhaustively sub-sampled the full record for all possible contiguous 5-month periods. I took the average of the results for each time period. Details of the method are given in the Supplementary Online Material (SOM) Sections 2 & 3 below.
I plotted the results as a curve which shows the average amplification for each of the various time periods from three months to thirty years (the length of the MSU datasets). This shows the “temporal evolution” of amplification, how it changes as we look at longer and longer timescales. I show the results at a variety of pressure levels in Figure 1. In general, at all pressure levels, short term (3 – 48 month) amplifications are much smaller than longer term amplifications.
Figure 1. Change of amplification with length of observation. Left column is amplification in the tropics (20N/S), and the right column is global amplification. T2 and TMT are middle troposphere measurements. T2LT and TLT are lower troposphere. Starting date is January 1979. Shortest period shown is amplification over three months. Effective weighted altitudes (from the RSS weighting curves) are about 450 hPa for the lower altitude TLT (~ 6.5 km) and 350 hPa (~ 8 km) for the higher altitude TMT.
Tropical Observations 1979-2008
Figure 1(a). UAH and RSS satellite data. This was the first analysis done. It confirmed the sensitivity of this temporal evolution method, as it shows a clear difference between the two versions (RSS and MSU) of the MSU satellite data. Both of the datasets (UAH and RSS) are quite close in the first half of the record. They diverge in the second half.
The higher and lower altitude amplifications are very similar in both the RSS and the UAH versions. The oddity in Fig 1(a) is that I had expected the amplification at higher altitude (T2 and TMT) to be larger than at the lower altitude (T2LT and TLT) amplification. Instead, the higher altitude record had lower amplification. This suggests a strong stratospheric influence on the T2 and TMT datasets. Because of this, I have used only the lower altitude T2LT (UAH) and TLT (RSS) datasets in the remainder of this analysis.
Figure 1(b). HadAT2 radiosonde data. (Note the difference in vertical scale.) Despite the widely discussed data problems with the radiosonde data, this shows a clear picture of amplification increasing with altitude to 200 hPa, and decreasing above that. It confirms the existence of the tropical tropospheric “hot spot”, where the amplification is large. It conforms with the result expected from theoretical consideration of the effect of lapse rate. It also shows remarkable internal consistency. The amplification increases steadily with altitude up to 200 hPa, and decreases steadily with altitude above that. Note that the 1998 El Nino is visible as a “bump” in the records at about month 240. It is also visible in the satellite record, in Fig. 1(a).
Figure 1(c). HadAT2, overlaid with MSU satellite data. Same vertical scale as (a). The satellite and balloon data all agree in the first half of the record. In the latter half, the fit is much better for the UAH satellite data analysis than the corresponding RSS analysis. Note that the amplification of the UAH version is a good fit with the 500 hPa level of the HadAT2 data. This agrees with the theoretical effective weighted altitude of the T2LT measurement.
Global Observations 1979-2008
Figure 1(d). Global UAH and RSS satellite data. Note difference in vertical scale. There is little amplification at the global level.
Again, the UAH and RSS records are similar in the short term but not the long term.
Figure 1(e). Global HadAT2 radiosonde data. Note difference in vertical scale. Here we see that the amplification is clearly a tropical phenomenon. We do not see significant amplification at any level.
Figure 1(f). Global HadAT2, overlaid with MSU satellite data. Same vertical scale as (d). Once again, the satellite and balloon data all agree in the first half of the record. In the latter half, again the UAH analysis generally agrees with the observations. And again, the RSS version is a clear outlier.
Both in the tropics and globally, amplification of the levels above 850 hPa start low. After that they show a slow increase. The greatest amplification occurs at 8-10 years. After that, they all (except RSS) show a gradual decrease up to the 30 years end of the record.
Having seen the agreement between the UAH T2LT and the HadAT2 datasets, I next compared the tropical RATPAC data with the HadAT2 data. The RATPAC data is annual and quarterly. I averaged the HadAT2 data annually and quarterly to match. They are shown in Fig. 2. Note that these are fifty-year datasets, a much longer timespan than Fig. 1.
Figure 2. RATPAC and HadAT2 Tropical Amplification, 3 years to 50 years. Left column is annual data. Right column is quarterly data.
There is very close agreement between the HadAT2 and the RATPAC datasets. The annual version shows a number of levels of pressure altitude. The quarterly version averages the troposphere down into two levels, one from 850-300 hPh, and one from 300-100 hPa. Both annual and quarterly RATPAC versions agree well with HadAT2.
Before going further, let me draw some conclusions about tropical amplification from Figs. 1 & 2.
1. Three of the four observational datasets (HadAT2, RATPAC, and UAH MSU) are in surprisingly close agreement. The fourth, the RSS MSU dataset, is a clear outlier. The very close correspondence between HadAT2 and RATPAC at all levels gives increased confidence that the observations are dependable. This is reinforced by the good agreement in Figs. 1(c) and 1(f) between the UAH MSU and the HadAT2 500 hPa level amplifications, both in the tropics and globally.
2. Figure 1(c) clearly shows the theoretically predicted “tropical hot spot”. It is most pronounced at 200 hPa at about 8-10 years. At its peak the 200 hPa level has an amplification of about 2. However, this gradually decays over time to a long-term (fifty year) amplification of about 1.5.
3. The lowest level, 850 hPa, has a short-term amplification of just under 1. It gradually increases over time to an amplification of about 1. It varies very little with the length of observations. RATPAC and HadAT2 are in excellent agreement regarding the amplification at the 850 hPa level.
4. The amplification of the next two levels (700 and 500 hPa) are quite similar. The higher level (500 hPa) has slightly greater amplification than the lower. Again, both datasets (RATPAC and HadAT2) agree very closely. This is supported by the UAH MSU satellite data, which agrees with the 500 hPa level of both the other datasets.
5. The amplification of the 300 and 200 hPa levels are also quite similar. The amplification of the higher level (200 hPa) exceeds that of the next lower level in the early part of the record. However, the 200 hPa amplification decreases over time more than that of the lower level (300 hPa). This accelerated long-term decay in amplification is also seen in the 150 and 100 hPa levels.
6. Between 700 and 200 hPa, amplification rises to a peak at around 8-10 years, and declines after that.
Observations and Models
Because it is the most detailed of the observational records, I will take the HadAT2 as a comparison standard. Fig. 3(a) shows the full length (50 year) HadAT2 record. Figures 3(b) to (e) show the outputs from five climate models. These models were selected at random. They are simply the first five models I found to investigate.
In Fig. 3(a) the decline in the observed amplification at the 200 hPa level seen in the shorter 30 year record in Fig. 1(c) continues unabated to the end of the 50 year record. The 200 hPa amplification crosses over the 300 hPa level and keeps declining. The models in Fig. 3(b-f), however, show something completely different.
Figure 3. Three month to fifty year amplification for HadAT2 and for the output of various computer models.
The model results shown in Figs 3(b) to (e) were quite unexpected. It was not a surprise that the models disagreed with observations. It was a surprise that the model results varied so widely among themselves. The atmospheric amplification at the various pressure levels are very different in each of the models
In the observations, the greatest amplification is at 200 hPa at around eight to ten years. Only one of the models, the GISSE-R, Fig. 3(d), reproduces that slow buildup of amplification. Unfortunately, the model amplification continues to increase from there on to the end of the record, the opposite of the observations.
The observed amplification at all levels except 850 hPa peaks at 8-10 years and then decreases over time. This again is opposite to the models. Amplification in all levels above 850 hPa of all of the models either stay level, or they increase over time.
In the observations, amplification increases steadily with altitude from 850 hPa to 200 hPa. Not a single model showed that result. All of the models examined showed one or more inversions, instead of the expected steady increase in amplification with altitude shown in the observations.
The 850 hPa observations start slightly below 1, and gradually increase to 1. Only one model, BCCR (c), correctly reproduced this lowest level.
Variability of Observations and Models
To investigate the natural variability in the amplification of both observations and models, I looked at thirty-year subsets of the various 50-year datasets. Figure 4 shows the amplification of thirty-year subsets of the datasets and model output. This shows how much variability there is in thirty year records. I show subsets taken at 32 month intervals, with the earliest ones at the back of the stack.
Once again, there are some conclusions that can be drawn from first looking at the observations, which are shown in Fig 4 (a).
1. The relationship between the various layers is maintained in all of the subsets. The lowest level (850 hPa) is always at the bottom. It is invariably below (smaller amplification than) the rest of the levels up to 200 hPa. The 700/500 hPa pair are always very close, with the higher almost always having the greater amplification. The 200 hPa level is above the 300 hPa level for all of the early part of the record. This order, with amplification steadily increasing with altitude up to 200 hPa, holds true for every one of the thirty-year subsets of the observations.
2. The 700 hPa amplification is never less than the 850 hPa amplification. As one goes lower, so does the other. They cross only at the short end of the time scale.
3. At all but the 850 hPa level, amplification peaks at somewhere around 8-10 years, and subsequently generally declines from that peak.
4. The amplification at 200 hPa is much larger than at 300 hPa at short (decade) timescales, but decreases faster than the 300 hPa amplification.
5. There is a surprising amount of variation in these thirty-year overlapping subsets. This implies that the satellite record is still too short to provide more than a snapshot of the variation in amplification.
Figure 4. Evolution of amplification in thirty year subsets of fifty-year datasets. The interval between subsets is 32 months. Fig. 4(a) is observations (HadAT2). The rest are model hindcasts.
The most obvious difference between the models and the observations is that most of the models have much less variability than the observations.
The next apparent difference is that the amplification in the models trend level or upwards with time, while the observed amplifications generally trend downwards.
Next, the pairings of levels are different. The only model which has the same pairings as the observations (700/500 and 300/200 hPa) is the HadCM3 model. And even in that model, both pairs are reversed from the observations. The other models have 700 hPa paired with (and often below) the 850 hPa level.
There is a final oddity in the model results. The short term (say four year) amplification at 200 hPa is very different in the various models. But at thirty years the models converge to a range of around 1.5 to 1.9 or so. This has led to a mistaken idea that the models reveal a “robust” long term amplification.
DISCUSSION
Having examined the changes in amplification over time for both observations and models, let us return to re-examine, one by one, the issues involved as stated at the beginning:
The month-to-month variability of tropical temperatures is larger in the troposphere than at the Earth’s surface.
This is clearly true. There is an obvious tropical “hot spot” of high amplification in the upper troposphere. It peaks at a pressure altitude of 200 hPa at about 8-10 years.
This amplification behavior is similar in a range of observations and climate model simulations, and is consistent with basic theory.
This amplification behavior is in fact similar in a range of observations. However, it is very dissimilar in a range of climate model simulations. While the observations are consistent with basic theory (amplification increasing with altitude up to 200 hPa), the climate models are inconsistent with that basic theory (higher levels often have lower amplitude than lower levels).
On multi-decadal timescales, tropospheric amplification of surface warming is a robust feature of model simulations, but occurs in only one observational dataset [the RSS dataset].
There are no “robust” features of amplification in the model simulations. They have very little in common. They are all very different from each other.
Multi-decadal amplification decreases gradually over the 50-year observational record. Three of the observation datasets (UAH, RATPAC, and HadAT2) all agree with each other in this regard. The RSS dataset is the outlier among the observations, staying level over time. This RSS behavior is similar to several of the models, which also stay level over time. One possible explanation of the RSS difference is that I understand it uses computer climate modeling to inform a portion of its analysis of the underlying MSU data.
Other observations show weak or even negative amplification.
None of the tropical observational datasets above 850 hPa show “negative amplification” (amplification less than 1) at timescales longer than a few years. On the other hand, all of the observational datasets show negative amplification at short timescales, as do all of the models.
These results suggest that either different physical mechanisms control amplification processes on monthly and decadal timescales, and models fail to capture such behavior, or (more plausibly) that residual errors in several observational datasets used here affect their representation of long-term trends.
The problem is not that the observations fail to capture the long term trends. It is that every model disagrees with every other model, as well as disagreeing with the observations.
It appears that different physical mechanisms do indeed control the amplification at different timescales. The models match the observations in part of this, in that amplification starts out low and then rises to a peak over a period of years. In most of the models examined to date, however, this happens on a much shorter time scale (months to a few years) compared with observations (8-10 years).
However, the models seem to be missing a longer-term mechanism which leads to long-term decrease in amplification. I suspect that the problem is related to the steady racheting up of the model temperature by CO2, which increases the longer term amplification and leads to upward trends. Whatever the cause may be, however, that behaviour is not seen in the observations, which decrease over time.
Conclusions
1. Temporal evolution of amplification appears to be a sensitive metric of the state of the atmosphere. It shows similar variations in the various balloon and satellite datasets with the exception of the RSS MSU satellite temperature dataset.
2. The wide difference between the individual models was unexpected. It was also surprising that none of them show steadily increasing amplification with altitude up to 200 hPa, as basic theory suggests and observations confirm Instead, levels are often flipped, with higher levels (below 200 hPa) having less amplification than lower levels.
3. From this, it appears that we have posed the wrong question regarding the comparison of models and data. The question is not why the observations do not show amplification at long timescales. The real question is why model amplification is different, both from observations and from other models, at almost all timescales.
4. Even in scientific disciplines which are well understood, taking the position when models disagree with observations that “more plausibly” the observations are incorrect is adventurous. In climate science, on the other hand, it is downright risky. We do not know enough about either the climate or the models to make that claim.
5. Observationally, amplification varies even at “climate length” time scales. The thirty year subsets of the observations showed large changes over time. Climate is ponderous and never at rest. Clearly there are amplification cycles and/or variations at play with long timescales.
6. While at first blush this analysis only applies to temperatures in the tropical troposphere, it would not be surprising to find this same kind of amplification behavior (different amplification at different timescales) in other natural phenomena. The concept of amplification, for example, is used in “adjusting” temperature records based on nearby stations. However, if the relationship (amplification) between the stations varies based on the time span of the observations, this method could likely be improved upon.
Additional Information
The Supplementary Online Material contains an analysis of amplification in the AMSU satellite dataset and the NCEP Reanalysis dataset. It also contains the data, the data sources, notes on the mathematical methods used, and the R function and R program used to do the analyses and to create the graphics used in this paper.
References
Douglass DH, Christy JR, Pearson BD, Singer SF. 2007. A comparison of tropical temperature trends with model predictions. International Journal of Climatology 27: Doi:10.1002/joc.1651.
Santer BD, et al. 2005. Amplification of surface temperature trends and variability in the tropical atmosphere. Science 309: 1551–1556.
Santer BD et al. 2008. Consistency of modelled and observed temperature trends in the tropical troposphere. Int. J. Climatol. 28: 1703–1722
SUPPLEMENTARY ONLINE MATERIAL
SOM Section 1. Further investigations.
AMSU dataset
A separate dataset from a single AMSU (Advanced Microwave Sounding Unit) on the NOAA-15 satellite is maintained at <http://discover.itsc.uah.edu/amsutemps/>. Although the dataset is short, it has the advantage of not having any splices in the record. The amplification of that dataset is shown in Fig. S2.
Figure S-1 Short-term Global Amplification of AMSU satellite data, MSU data, and HadAT2 data . The dataset is only ten years long.
Figure S-1(a). AMSU satellite data. This is a curious dataset. The 400 hPa level is a clear and dubious outlier. The distinctive “duck’s head facing right” shape of the second half of the 900 and 600 hPa levels is similar, while that of the 400 hPa level is quite different. It is very doubtful that one level would be that different from the levels above and below it. This was a strong indication of some unknown error with the 400 hPa data that is affecting the longer term amplification.
Figure S-1(b). Adjusted and unadjusted AMSU satellite data. To attempt to correct this error, I added a simple linear trend to the 400 hPa level. I did not adjust it until the amplification was right. Instead, I adjusted it until its long-term trend ended up proportionally between the long-term trends of the layers above and below. This gave the adjusted version (light green) of the amplification.
Figure S-1(c). Adjusted AMSU satellite data. After the adjustment of the 400 hPa trend, the amplifications fit together well. Curiously, despite being adjusted by a linear trend, the shape of the latter half of the 400 hPa level has changed. Now it has the “duck’s head facing right” shape of the 600 and 900 hPa levels. This unexpected change supports the idea that there is indeed an error in the trend of the 400 hPa data.
Figure S-1(d). Interpolated AMSU satellite data. Unfortunately, the referenced levels in the two datasets are at different pressure altitudes than HadAT2. To compare the AMSU to HadAT2, we need to interpolate. Fortunately, the HadAT2 dataset range (850 to 200) fits neatly inside the AMSU range (900 to 150). This, along with the similar and close nature of the signals at various levels, allows for linear interpolation to give the equivalent AMSU amplification at the HadAT2 levels. The interpolated version is shown.
Figure S-1(e). HadAT2 and RSS/UAH satellite data. The global observational data over this short period (ten years) is scattered. Also, the HadAT2 data has a more jagged and variable shape. We may be seeing the effects of the paucity of the observations. In the short-term (this is ten years and less) the RSS and UAH amplification records are quite similar. As before, both are close to the 500 hPa HadAT2 amplification.
Figure S-1(f). AMSU and HadAT2 data. Close, but not a good match. The 200, 700, and 850 hPa levels match, but 300 and 500 hPa are quite different. Overall, the satellite data seems more reliable. The AMSU data shows a gradual change in amplification with altitude. The HadAT2 data is bunched and sometimes inverted.
My conclusions from the AMSU dataset are:
1. It contains an error, which appears to be a linear trend error, in the 400 hPa level.
2. Other than that, it is the most internally coherent of the observational datasets.
3. It points up the weakness of using short (one decade) subsets of the HadAT2 dataset.
NCEP REANALYSIS
One of the attempts to provide a spatially and temporally complete global dataset despite having limited observational data is the NCEP reanalysis dataset. Figure S-2 compares the temporal evolution of amplification of HadAT2 and NCEP Reanalysis output
Figure S-2 Evolution of amplification of HadAt2 and NCAR. Left column is amplification from 3 months to 50 years, right column is amplification of 30 year subsets of the 50 year datasets. The interval between the individual realizations in the right column is 32 months.
The NCEP reanalysis data in Fig. S-2 (b) shows a fascinating pattern. The three middle levels (700,500, and 300 hPa) are close to the HadAT2 observations. The 300 hPa levels agree extremely well. And while the 700 and 500 hPa levels are flipped in NCEP, still they are in the right location and are very close to the observed values.
But at the same time, the amplification of the lowest and highest levels are way off the rails. The 850 hPa amplification starts at 1, and just keeps rising. And the 200 hPa amplification starts out reasonably, but then takes a big jump with a peak around thirty years. That seems doubtful.
The observation that there are problems at the lowest and highest levels is reinforced by the analysis of the variation of thirty year subsets in the right column of Fig. S-2. These show the 200 hPa amplification varying wildly over all of the different 30 year datasets. In one of the thirty year subsets the 200 hPa amplification dips down to almost touch the highest 850 hPa line. There is clearly something wrong with the NCEP output at the 200 hPa level.
In addition, in the full NCEP record shown in Fig. S2(b) and all of the 30 year subsets shown in Fig. S2(d), the lowest level (850 hPa) increases steadily over time. After about 20 years it has more amplification than either of the 700 and 500 hPa levels. This behavior is not seen in either the observations or any of the models.
Conclusions from the NCEP reanalysis
1. The 700, 500, and 300 hPa level of the NCEP reanalysis are accurate. The 850 and 200 hPa levels suffer from large problems of unknown origin.
2. Use of the NCEP reanalysis in other work seems inadvisable until the 850 and 200 hPa amplification problems are resolved.
SOM Section 2. Data Sources
KNMI was the source for much of the data. It has a wide range of monthly data and model results that you can subset in various ways. Start at http://climexpknmi.nl/selectfield_co2.cgi?someone@somewhere . It contains both Hadley and UAH data, as well as a few model atmospheric results. My thanks to Geert for his excellent site.
Surface data for all observational datasets is from the CruTEM dataset at http://climexp.knmi.nl/data/icrutem3_hadsst2_0-360E_-20-20N_n.dat
UAH data is at http://www.nsstc.uah.edu/data/msu/t2lt/uahncdc.lt
RSS data is at http://www.remss.com/data/msu/monthly_time_series/
HadAT2 balloon data is at http://hadobs.metoffice.com/hadat/hadat2/hadat2_monthly_tropical.txt
CGCM3.1 model atmospheric data is at http://sparc.seos.uvic.ca/data/cgcm3/cgcm3.shtml in the form of a large (250Mb) NC file.
Data for all other models is from the “ta” and “tas” datasets from the WCRP CMIP3 multi-model database at <https://esg.llnl.gov:8443/home/publicHomePage.do>
In particular, the datafiles used were:
GISSE-R: ta_A1.GISS1.20C3M.run1.nc, and tas_A1.GISS1.20C3M.run1.nc
HadCME: ta_A1_1950_Jan_to_1999_Dec.HadCM3.20c3m.run1.nc, and tas_A1.HadCM3.20c3m.run1.nc
BCCR: ta_A1_2.bccr_bcm2.0.nc, and tas_A1_2.bccr_bcm2.0.nc
INCM3: ta_A1.inmcm3.nc, and tas_A1.inmcm3.nc
As all of these are very large (1/4 to 1/2 a gigabyte) files, I have not included them in the online data. Instead, I have extracted the data of interest and saved this much smaller file with the rest of the online data.
SOM Section 3. Notes on the Function and Code.
The main function that does the calculations and created the graphics is called “amp”.
The input variables to the function, along with their default values are as follows:
datablock=NA : the input data for the function. The function requires the data to be in matrix form. By default the date is in the first column, the surface data in the second column, and the atmospheric data in any remaining columns. If the data is arranged in this way, no other variables are required The function can be called as amp(somedata), as all other variables have defaults.
sourcecols=2 : if the surface data is in some column other than #2, specify the column here
datacols=c(3:ncol(datablock)) : this is the default position for the atmospheric data, from column three onwards.
startrow=1 : if you wish to use some start row other than 1, specify it here.
endrow=nrow(datablock) : if you wish to use some end row other than the last datablock row, specify it here.
newplot=TRUE : boolean, “TRUE” indicates that the data will be plotted on a new blank chart
colors=NA : by default, the function gives a rainbow of colors. Specify other colors here as necessary.
plotb=-2 : the value at the bottom of the plot
plott=2 : the value at the top of the plot
periods_per_year=12 : twelve for monthly data, four for quarterly data, one for annual data
plottitle=”Temporal Evolution of Amplification” : the value of the plot title
plotsub=”Various Data” : the value of the plot subtitle
plotxlab=”Time Interval (months)” : label for the x values
plotylab=”Amplification” : label for the y values
linewidth=1 : width of the plot lines
linetype=”solid” : type of plot lines
drawlegend=TRUE : boolean, whether to draw a legend for the plot
SOM Section 4. Notes on the Method.
An example will serve to demonstrate the method used in the “app” function. The function calculates the amplification column by column. Suppose we want to calculation the amplification for the following dataset, where “x” is surface temperature, “y” is say T200, and each row is one month:
x y
1 4
4 7
3 9
Taking the “x” value, I create the following 3X3 square matrix, with each succeeding column offset vertically by one row. This probably has some kind of special matrix name I don’t know, and an easy way to calculate it. I do it by brute force in the function:
1 4 3
4 3 NA
3 NA NA
I do the same for the “y” value:
4 7 9
7 9 NA
9 NA NA
I also create same kind of 3X3 matrix for x times y, and for x squared.
Then I take the cumulative sums of the columns of the four matrices. These are used in the standard least squares trend formula to give a fifth square matrix:
slope of regression line = (N*sum(xy) – sum(x)*sum(y)) / (N*sum(x^2) – sum(x)^2)
I then average the rows to give me the average amplification at each timescale
This method exhaustively samples to find all contiguous sub-samples of each given length. This means that there will be extensive overlap (samples will not be independent). However, despite the lack of independence, using all available samples improves the accuracy of the method. This can be appreciated by considering a fifty year dataset. There are a number of thirty year contiguous subsets of a fifty year dataset, but if you restrict your analysis to non-overlapping subsets, you only can pick one of them … which way will give the best estimate of the true 30-year amplification?
SOM Section 5. Of Averages and Medians.
The distribution of the short-term amplifications is far from normal. In fact, it is not particularly normal at any scale. This is because the amplification is calculated as the slope of a line, and any slope is the result of a division. When the divisor approaches zero, very large numbers can result. This makes averages (means) inaccurate, particularly at the shorter time scales.
One alternative is the median. The problem with the median is that it is not a continuous function. This limits its accuracy, particularly in small samples. It also makes for a very ugly stair-step kind of graph.
Frustrated by this, I devised a continuous Gaussian mean function which outperforms the mean for some varieties of datasets, and outperforms the median on other datasets. It is usually in between the mean and median in value. In all datasets I tested, it equals or outperforms either the mean or the median.
To create this Gaussian mean I reasoned as follows. Suppose I have three numbers picked at random from some unknown stable distribution, let’s say they are 1,2, and 17. What is my best guess as to the actual underlying true center of the distribution?
Since we don’t know the true distribution, the best guess as to its shape has to be a normal distribution. With such a distribution, if we know the standard deviation, we can iteratively calculate the mean.
To do so, we start by calculating the standard deviation, and picking a number for the estimated mean, say 5. If that is the mean, the numbers (1,2,17) when measured in standard deviation units is (-0.6, -0.5, 1.2). Each of those standard deviations has an associated probability. I figured that the sum of these individual probabilities is proportional to the probability that the mean actually is 5.
I then iteratively adjust the estimated mean to maximize the total probability (the sum of the three individual probabilities. It turns out that the gaussian mean of (1, 2, 17) calculated by my method is 3.8. This compares with an average for the three numbers of 6.7, and a median of 2.
In general there is very little difference between my gaussian mean, the arithmetic mean, and the median. However, it is much better behaved than the mean in non-normal datasets. And unlike the median, it is a continuous function, which gives greater accuracy.
All three options are included in the amp() function, with two of them remarked out, so you can see the effects of each one. The only noticeable difference is that the mean is not very accurate at short time scales, and the gaussian mean and the mean are not discontinuous like the median.
Interesting approach Willis (note it’s not Anthony), it maybe better if you had posted on realclimate as well to get a wider audience. I don’t know for sure, but I suspect you’ll only get responses where you’ve FUBARed because the Team tend not to get into debate on the science as they don’t seem to feel they have a very strong case? I don’t know why but they don’t, and to be sure if I’d achieved my goal of persuading the politicos of GW I’d hardly jeopardise it by entering into open debate with those that disagreed with me. Betcha Nature and Science won’t publish your efforts.
Good luck though.
The long term surface temperature record appears to show a linear increase with a roughly 60 year oscillation superimposed on top of it. This combined with an extended lag in the tropospheric temperatures could be producing the declining amplification shown in figure 3(a). Look for example at a plot of stock prices with trailing 30, 50 and 200 day moving averages. The longer period averages of an oscillating plot will have a smaller amplitude.
If the climate models you used for comparison do not reproduce the oscillation of the surface temperatures they would not show the decline in amplification over the longer time periods.
It would be interesting to see a plot of the individual amplifications (for example the 30 year) over time to see if it varies over time in sync with the long period surface temperature variation.
The author appears too defensive. He would be wise to try to incorporate the suggestions. There is a reason for scientific style and structure. This is not the place to go into detail about scientific writing but this reviewer has published in a scientific journal and has taken graduate course work in scientific writing.
If the end goal of this paper is to stand shoulder to shoulder with papers that have made it into snail mail journals, the author is advised to swallow the bullet and use the same style and structure. It is important to note that the author presumably comes to the table with less credentials than the scientists listed. If this paper under consideration is to get into the ring, let alone the viewing stand, with the referenced scientific papers in the review section, this paper must wear similar attire. As it stands, it is a difficult paper to read and suffers from lack of a clear path to the conclusion, ergo the need for standard structure.
This reviewer would also second another comment made above. A paper that reviews opposing literature (which is a good thing to do but very difficult to pull off) must do so with standard courtesy. Be careful what is written and how it is written in the literature review section. Try to use dry, neutral language. Authors of opposing ideas must agree to disagree without being disagreeable (IE, don’t use that word).
One more thing, this reviewer must be aging. This new style of referring to oneself in a scientific paper with first person singular pronouns doesn’t sit well with this reviewer. It is easier to read a scientific paper with the emphasis on what the researcher DID. No what the RESEARCHER did. Even when reviewing a paper, the reviewer usually refers to him or herself with the phrase, “This examiner…” or “This reviewer…”
Get the idea?
My mistake, Mr. Watts. Good luck to Willis Eschenbach; a brave individual. :0)
Pamela Gray:
Well written.
I am an avocational, amateur climate scientist. As a regular consumer at this site, I am aware of the first line of defense against research that refutes AGW. Those who dare to oppose are slimed with labels such as “non-scientist”, “not a climate scientist”, “professional opponent funded by big oil”, or other forms of personal attack. The AGWers simply refuse to engage on the merits of the issues.
With that in mind, I Goggled Willis and discovered that he is an amateur. I ponder this and realized that Einstein was also an amateur Go for it, Willis. You are in great company.
Pamela,
Your comments on style are well considered and will need to be taken into account if the author decides to publish this in a more traditional medium.
Willis,
This is an interesting experiment in open-source science. As it breaks a mold, you will get criticisms for not adhering to standard form. If you truly care less for personal credit than for advancement of knowledge, let them pass without reply. Good ideas eventually will be adopted as Wegener and Milankovich have proven.
Those taking note of the unusual circumstances of a request for comments on this not yet submitted paper have valid points . This excercise in simulated peer review need not be constrained by so many pedantic restrictions. It is so realclimatelike. The criticisms or support are either scientifically valid, or they are not, regardless of the author’ s identity. Snip this and lose this interested and up to now appreciative reader.
REPLY: Willis made this request, he’s headed into night now where he’s at, so it may be a few hours before we hear back from him. However, there’s a reply from him further up in comments that addresses your issue.- Anthony
Willis,
One small suggestion. People who have not read Santer, et al (2005 or 2008), and who do not have easy access to these papers, would benefit from a more detailed summary/description of those papers and their methodology so that your contrasting results would be more meaningful.
REPLY: Willis made this request, he’s headed into night now where he’s at, so it may be a few hours before we hear back from him. However, there’s a reply from him further up in comments that addresses your issue.- Anthony
Thank you. You are a gentleman and a scholar. I did not see Willis’s response. It should have not been necessary. His undoubtedly sincere and strenuous effort will stand or fall on it’s own. I do commend him for graciously conceding his error.
Since this does not have to be a formal review but a comment on the paper, although Pamela’s 2nd comments are very valid I would suggest the following:
1) Remove 75% of the content and aim of this paper. In this I mean concentrate predominantly on defining a metric for amplification and dealing with autocorrelation. Show what happens when taking a difference between surface to troposphere trends for various time periods. Is the persistance signal minimised and autocorrelation of trends better accounted for. Show that it is possible to define a better metric by calculating a previous metric and comparing.
2) Show all errors/uncertainties for the trends. This is especially important with reference to point 1. If the metric has less uncertainty than the ratios then introduce some examples for application and comment. If the mathematics of the metric are robust enough leave further detailed analysis of data sets for a different paper.
3) Always use passive voice, “The author notes that ” or don’t mention the author at all.
4) Lastly, make sure your uncertainties and errors have influence over the remit of your conclusions. This is not a typo. Be brutally honest about your analysis and its pros and cons. Also do not make statements that cannot be referenced or that appear general i.e. “Climate is ponderous and never at rest” , which is also why cutting a lot of information out and just concentrating on the metric and rationale of defining it is better
It’s an interesting analysis and a good start. Once the autocorrelation issues are better appraised then it could be very useful.
Look people, there are standard forms for many things. Examples: Recipes. Math proofs. Fables. Table of Contents. Indexes. Citations. There really is a reason for these forms. The message is clearer if standard form is used. Can you imagine trying to find a page number of an index item if instead of a simple word and page numbers you get a rambling paragraph? It would certainly be a fresh way of doing things, but not very useful.
Willis you’d be well advised to listen to Pamela Gray.
Pamela Gray (15:03:26) : is essentially what you would get back from whatever journal you submitted your work to! They would reject your paper on style and it would be returned without any comments of the substance.
Save yourself a step if you are truly serious about trying to get this published.
Best of luck (even if I don’t agree with your conclusions!)
Ben
There needs to be physical basis/explanation to carry on the analysis beyond the timelines of the forces at work here. 600 months is 50 years.
The tropospheric amplification needs to have boundaries around the timelines which can be logically tied to the physical warming effects provided by surface temperatures. These are the timelines I consider relevant.
18 hours – the greenhouse effect operates at the speed of light modulated by atmospheric, land and ocean molecules ability to store up the energy represented by photons from the Sun. The energy represented by a photon from the Sun only spends 18 hours in the Earth system on average before it escapes to space. Other than the timelines noted below, all the amplification in the troposphere from surface temperatures occurs within that 18 hours – over 90% of the total amplification effect will be felt within this time period.
35 days – surface temperatures on land peak about 35 days after the solstices. Land molecules can store up a few tens of a Watt/metre^2 of energy from the Sun each day for 35 days – after that the energy starts to leak off and is lost to space – with a delay of 18 hours before the troposphere starts to feel this effect again.
80 days – ocean surface temperatures peak about 80 days after the solstice. Like the land surface temperatures lag behind the Sun’s energy by 35 days throughout the year, the ocean surface lags behind the Sun by about 80 days throughout the year. The troposphere feels this effect about 18 hours later than the 80 day lag again.
Several years – the upper ocean down to several hundred metres lags behind surface temperatures by several years. The troposphere in the long-term could therefore lag behind the surface for several years (probably at a very minimal level) as the upper ocean absorbs some of the energy.
1500 years – the deep ocean takes up to 1,000 years to catch up to surface temperatures. In the interval, the deep ocean may be absorbing energy from the surface that would available to amplify the troposphere. Ice sheets could be slowly absorbing energy and ice-sheet melt and vegetation changes can affect the Earth’s albedo and, thus, on the same 1500 year timeline, affect the troposphere amplication factor.
So, generally I think much shorter timelines need to be incorporated and any timeline longer than several years can be left for future generations to examine.
Willis,
An interesting article. Here are a few comments that I have on it:
(1) You have tried very hard here to push the models until they break…I.e., to find a more sensitive metric that can probe in more detail exactly what the data and models show, and that is great. However, I would suggest that you do the same in regards to the experimental data. Hence, I would recommend looking at, say, the RAOBCORE re-analysis (despite the claims that some may make that it has some bias…After all, there are lots of concerns about the general biases in the radiosonde data set that RAOBCORE is trying to correct). And, you could look how sensitive your result (particularly concerning whether the amplification trend with time interval is up or down at the longer times) is to the overall trend in the data set in order to understand how sensitive things are to possible artifacts in the data set that affect that the overall multidecadal trends without having much effect on the shorter-term variability, since it is the longer term secular trends that are most subject to artifacts in the observational data sets.
(2) I think that your conclusions are in general overstated based on the results that you show. Where you see the glass half-empty, I see it half-full. I.e., you seemed to consider it some sort of significant problem that you can find any disagreement between the models and the data. In fact, I would be shocked if you couldn’t, particularly given how hard you are trying to develop a metric to test things as diligently as possible. Honestly, when I look at Figs. 3 and 4, I say, “Wow…The models are doing pretty well at getting the most of the basic features correct. Are there discrepancies? Sure…and it would be interesting to further probe these and understand what problems with the models or the data they could be due to. But, the take-away message is that there are many basic features that are quite robust across the data and the models and then also some notable differences in the details.” In essence, I think you are creating a strawman that is “The models are perfect” and then demolishing it by showing that they are not perfect. (Although the extent to which the discrepancy is due to imperfections of the models and the extent to which they are due to limitations or problems with the data are unclear. However, I am willing to imagine that at least some of it is due to imperfection of the models). I think your presentation would seem more balanced if you had more emphasis of the points where the models and observational data do agree rather than only the points where they differ.
(3) You comment on Santer et al.’s statement that “Other observations show weak or even negative amplification”. However, I know that their statement of negative amplification in particular applied to the UAH data that was available at the time, which was just before a major fix was applied to that data that I am pretty sure changed the amplification (at least as they defined it) from negative to positive. So, it isn’t really fair to say this statement by Santer is wrong since it is based on the UAH data that has been corrected between the time they made that statement and the time you have done your analysis. [See here for UAH’s record of the corrections to their data: http://vortex.nsstc.uah.edu/data/msu/t2lt/readme.17Apr2009 I think that the correction that I am referring to is the one from 7 Aug 2005. (Note the statement “This artifact contributed an error term in certain types of diurnal cycles, most noteably in the tropics.”)]
(4) Just to point you in this direction in case you missed it, Arthur Smith posted some stuff on his blog on the tropical tropospheric amplification issue using your metric as a jumping-off point here: http://arthur.shumwaysmith.com/life/content/hot_spot_redux_analysis_of_tropical_tropospheric_amplification I have to admit that I haven’t read that in a long time and even then not that carefully, but I thought you might want to have a look at it to see where it agrees and disagrees with your analysis.
(5) I agree with some of Pamela’s stylistic points but I disagree with her on always using the passive voice…I think that is somewhat “old school” thinking these days and the scientific community has begun to catch up with the rest of the world in rejecting the need to use the passive voice so exclusively. In particular, I have noticed that overuse of the passive voice sometimes even makes it difficult to determine when the author is referring to work that he/she has done versus when the reference is to the work of others. Having written almost all of my papers with co-authors, I am not sure what the guidelines are for using “I” vs “we” though. I kind of think that “we” sounds better, but I know that Physical Review once had a prohibition against the use of “we” for a single-author paper that led an author to once add his dog as a co-author so that he could keep the “we”!
Brian– I think some answer to your questions may be found at the Christy link in the post just before yours.
I will not comment on the science of the paper as it is far outside my specialty but I have two suggestions. In the Observations and Models section first paragraph you mention choosing models at random, you clarify this in the next sentence but I suggest just leaving the sentence out or use different wording. Random sort-of implies you looked at a bunch and picked 5 from a hat or some such thing. My second suggestion is to evaluate the scales and symbology on the graphs. The third set of graphs with constant Y axis were much easier to compare. Sometimes doing this makes thing more difficult to read and a lager vertical magnification helps, but I would at least look into it. Also using only color to separate lines on a plot makes it tough for the color blind out there also the few print technical journals that I read do not incorporate color, although on-line versions often do.
I would also try and incorporate Pamela’s suggestions on style.
Dear Joel,
Gawd. I’m old school. Listen here sonny boy. I can run circles around you without even having any overies! Gawd damned whipper snapper. That said, your comments are quite good.
Willis,
A couple more comments:
(6) You say “The oddity in Fig 1(a) is that I had expected the amplification at higher altitude (T2 and TMT) to be larger than at the lower altitude (T2LT and TLT) amplification. Instead, the higher altitude record had lower amplification. This suggests a strong stratospheric influence on the T2 and TMT datasets.” I think this is a fairly well-known issue so I think it is not really such an oddity and it is a good place to make reference to some previous literature (the lack of such references being a general weakness of this paper that others have already pointed out).
(7) You say
However, if one looks at the context in which Santer et al. made that claim, it seems to be in arguing that they believe that the tropospheric tropical amplification as seen in the models and not so much in the data at multidecadal timescales really is there. And, strangely enough, it seems to me that your analysis seems to confirm this basic fact…In fact, you seem to find that the amplification is there in the data (perhaps a little weaker at the multidecadal timescales than on average in the models although it depends on which model you compare to). So, you seem to chide Santer et al. for their hubris at the same time as you confirm their basic point that the amplification is really there at the multidecadal timescales. One thing that confuses me a bit though is why you seem to see it in the data sets whereas they don’t…I.e., how does your analysis of the data (in the 30-year limit) differ from theirs (besides the fact that you used the corrected UAH data set)? Is it the difference between the length of the data set that you used vs what they used (since they didn’t have 30 years yet); Or, is there some other difference in the definition of the amplifications or what?
Wally, your comment on “random selection” is close to the central issue of Willis’ method. There are several vitally important parameters regarding “random selection” that researchers should be well-school in. It would be wise to study these when doing any kind of small subject pseudo-random selection. Decisions regarding choice of statistic analysis depends on subject number and “kind” of randomness.
Regarding my own research, because my study subjects served as their own control, I needed to find subjects who had clear ABR’s with clicks (white noise clicks) in order to find frequency specific responses to pips. That meant that I had to perform 1000’s of data collection runs in order for the f to be acceptable for such a small subject number (6). And back then, I hand entered the data using punch cards. Sonny.
Pamela is right and gives good advice. So does Michael Corbett.
It is worth taking the time to polish good work into concise professional presentation and it makes it much easier and more rewarding to read and review.
An important part of any paper is identifying what remains uncertain to anticipate any criticism. Be the first to find your own weaknesses.
Willis,
Do not be discouraged by format/form comments. Although it is true that if you do not submit your income taxes on the appropriate format they will not be accepted by authorities, it is not true that a scientific paper in a format different from institutionalized science can be rejected by authority. This is simply because there are no authorities in science . . . no appeal to authority fallacies in the final outcome.
Go for it. I will read you paper in more detail as my schedule permits.
Regards,
John
OK, first things first. Got home, haven’t even read the thread.
The data, the function, and the R code used to generate all the graphics is located at:
http://homepage.mac.com/williseschenbach/.Public/Amplification.zip
There are PDF and Word DOC copies of the original post, “A New Amplification Metric” (about 2 mb each) at
http://homepage.mac.com/williseschenbach/.Public/Tropical_Amplification.pdf
and
http://homepage.mac.com/williseschenbach/.Public/Tropical_Amplification.doc
My apologies for not posting this with the original paper, life gets away from you sometimes.
Anthony, if you’d be kind enough to to post these links at the foot of the original paper, it would be much appreciated.
Onwards,
w.
Willis,
I may be way off base but I do not see what you did shows what you claim. Amplification is an integral value of running present temperature ratios. If the data record or model calculated temporal resolution is not adequate, assumptions have to be made and supported on what happens between points. You can average the amplification over different length time periods, but each amplification point in the average still has to be the very short time period ratio, and stretching out the time between points is not physically meaningful. As one comment stated, the physics of all the processes that probably affect the temperatures occur on a short time basis except for deep sea effects. Based on the above comments, the values for all periods of about 3 months are well less than 1 and thus there is no amplification greater than 1. If you look at 3 month records restarting at all times along the record and average them over the total time, you still get less than 1. Please reply.