Beckers and Rixen 2003 – Another Infilling Approach

Beckers and Rixen 2003 url is an interesting read in two respects:
1) they present a non-RegEM infilling approach. The method appears to be exactly the same as one that I (independently) implemented and illustrated about a month ago – what I termed “truncated PC”. This was actually the very first thing that I did in climate science, as I used this sort of method in 2003 to try to calculate temperature PCs when there was missing data, in that case applying notes from Sam Roweis.

2) their key example is infilling of missing AVHRR data for the Adriatic Sea.

Beckers and Rixen infilling proceeds as follows. They do a trial infill of missing data with monthly means from the available data. They then do a PC decomposition of the trial matrix. They retain k PCs and eignevectors and expand these to obtain an estimate of the full matrix. In the next iteration, they infill with the estimates of the missing data. The process converges quite quickly and stops when the matrices are close enough together. RegEM operates line-by-line with a huge expansion of the number of operations. I find it hard to understand what advantages line-by-line RegEM truncated TTLS has over truncated PC. There’s nothing in Schneider that deals with this specifically.

For reference, I noticed that there are now a number of canned packages in R for imputing missing values and a website devoted to this issue, which provides many references, including Schneider 2001, though not the Mannian corpus.

The Beckers and Rixen example of Adriatic data is shown below – and, in this case, there is quite a bit of cloud data to be infilled. I presume that something similar had to be done in the Antarctic by Comiso.

Comiso appears to have done a series of Antarctic cloud masking exercises, with substantial changes from version to version and with Steig et al 2009 being the most recent version (assuming that Comiso did it). The Antarctic infilling seems to be a bit more complicated than the Adriatic because it seems that cloud temperatures can be higher than surface temperatures, adding a substantial layer of complexity to the problem of deconvolving cloud and surface measurements.

Beckers and Rixen, J Clim 2003 url
Kondrashov and Ghil url

43 Comments

  1. Posted Mar 28, 2009 at 1:15 PM | Permalink

    Dear Steve, are the fixed points of RegEm and “truncated PCs” really different from one another? I didn’t quite understand whether the technical issue you mentioned is important for obtaining realistic reconstructions of the physics, or whether they’re just important for getting a fast algorithm to do something.

    I suppose that RegEm is used because the rule is intuitively simple, avoids complicated terms like PCs, and works pretty universally. It may surely be a slower algorithm to obtain something, in which case faster algorithms are better in practice. But if your point was that the non-RegEm method is more “true” than RegEm, I am still waiting for some rational argument to support this point.

    Clouds are bitches, and while their effect is likely to be dominated by “overall cooling” in our latitudes, they can do a lot of other things in Antarctica. ;-)

  2. Nicholas
    Posted Mar 28, 2009 at 6:16 PM | Permalink

    It would be interesting to manually compare the output of the two algorithms on the same piece of data requiring infilling and see which seems to have a more sensible result. It would also be interesting to see if there are cases where either or both methods create a result which is obviously not going to match the likely values of the missing data and if so how frequently it occurs. I guess this can be determined by taking a set of complete data, breaking it up into chunks, randomly removing portions of each chunk, then doing the infilling and compare it to the original. If repeated often enough it should be possible to quantify the uncertainties introduced by these algorithms for sets of data with known properties/distributions/etc. That would be a useful exercise I think.

  3. Nicholas
    Posted Mar 28, 2009 at 6:20 PM | Permalink

    For example, what if you took each chunk of the satellite data which is being infilled in this case that has no clouds, generate a random “cloud” which obscures some portion of the data, run the infilling, then subtract the original and calculate an RMS error value which is introduced by the infilling algorithm. Repeat this on thousands of squares and average the RMS values. Now you have a way to quantify the error which is being introduced when infilling the chunks which actually have cloud cover.

  4. Posted Mar 28, 2009 at 10:37 PM | Permalink

    Steve’s first application of his truncated PC algorithm converged to the same result as the truncated total least squares version of RegEM. I think this is expected because of the nature of the math. The only difference between the methods is how fast they converge and how unusual they are.

    I have to add, I’m no expert. My only background with this is a half dozen papers, the internet and some single stepping through matlab code.

    • Steve McIntyre
      Posted Mar 28, 2009 at 11:14 PM | Permalink

      Re: Jeff Id (#4), I asked Tapio Schneider about this:

      > On the basis that RegEM TTLS with regpar=k converged to a rank 3
      > recon, I did some experiments with truncated SVD recons retaining 3
      > PCs and using the expansion of U_3 S_3 V_3^T to infill iteratively for
      > regpar=3 as in your regem.m method. This yielded results that were
      > extremely close to the RegEM TTLS recon (closer than I could get to the reported Steig values, for
      > example.) Going this route resulted in a huge increase in efficiency.

      Yes, you can do that. This has been done for some time, for example, by Everson and Sirovich (J. Opt. Soc. Am. A, 12, 1657–1664, 1995); Ghil and Kondrashov (2006) use a very similar algorithm. We typically do that to get good initial estimates for a more accurate regularized EM computation. What you are missing if you do this is the contribution of the imputation error to the covariance matrix estimate. Taking the imputation error into account (which you must for the algorithm to converge toward the maximum likelihood estimate for normal data in the full-rank case) makes the resulting matrix computations more difficult because it is more difficult to operate only on a factor of a covariance matrix estimate (Cholesky factor, or data matrix). I am working with some colleagues on more efficient methods.

      > I’ve been trying to think of an operational reason to prefer RegEM
      > TTLS to a EM-truncated PC method and can’t really think of any. Can
      > you shed any light on this?

      I am not sure what you mean. If by a truncated PC method you mean using principal component regressions (TSVD) in a regularized EM algorithm, this of course is fine (and is close to TTLS, without taking the error in the available values into account). But you will have to take the imputation error variances into account to get unbiased variance estimates in the full-rank case (e.g., see the book by Little and Rubin, “Statistical Analysis with Missing Data.”) In the rank-deficient case, you will get biased variance estimates in any case (the bias-variance tradeoff), but they will be even more severely biased if you do not take the imputation error into account.

      He attached a lecture note defining singular value decomposition, which seemed a little snotty, particularly given that the question as posed showed reasonable comprehension of the issues; the notes made no mention of any of the above points and were unhelpful. I had this correspondence prior to being aware of Beckers-Rixen and perhaps he didn’t quite get the point that I was asking.

      I don’t understand from this why he believes RegEM TTLs to be “more accurate”. Perhaps I’ll try again with him.

      • Geoff Sherrington
        Posted Mar 29, 2009 at 4:34 AM | Permalink

        Re: Steve McIntyre (#5),

        Maybe you are tired and serious and need some relief.

        (e.g., see the book by Little and Rubin, “Statistical Analysis with Missing Data.”)

        Is it possible that the information you seek is in the data missing from the statistical analysis book of Little & Rubin?

        • Steve McIntyre
          Posted Mar 29, 2009 at 8:14 AM | Permalink

          Re: Geoff Sherrington (#6),
          :) Nice.

          PS. I already checked and the book is missing from the library.

      • Posted Mar 29, 2009 at 8:15 AM | Permalink

        Re: Steve McIntyre (#5),

        But you will have to take the imputation error variances into account to get unbiased variance estimates in the full-rank case (e.g., see the book by Little and Rubin, “Statistical Analysis with Missing Data.”) In the rank-deficient case, you will get biased variance estimates in any case (the bias-variance tradeoff), but they will be even more severely biased if you do not take the imputation error into account.

        Since the algorithm is converging to a minimum it seems to me that the purpose of a better estimate would be faster convergence or convergence of an array that wouldn’t otherwise converge. In this case from your work it seems that was not the case. I’ve forgotten, have you put your code for this on the ftp?

  5. DJ
    Posted Mar 29, 2009 at 11:44 AM | Permalink

    FYI, I found this Web page on “What to do with missing/incomplete information”. Hope it helps!

    http://www.faqs.org/faqs/ai-faq/neural-nets/part7/section-3.html

  6. Jeff C.
    Posted Mar 29, 2009 at 12:38 PM | Permalink

    I hope this isn’t too far OT, as it relates to the amount of infilling required rather than the method. Steve, if you think this belongs somewhere else, please move it.

    I have been reviewing the cloud cover percentages from the UWisc data set. These values can be extracted from the UWisc data set using Steve’s script in the UWisc thread. Change “surft” to “cldtype” to retrieve the cloud type parameter. For the monthly datasets, cloudtype is a value from 0 to 99 that gives the per-cent of time a cell was considered cloud covered during the given month.

    I have all the individual values, but calculated some monthly means to give a quick read on how often the continent is cloud covered. I was surprised by the high frequency, but also found some other interesting items that make me question the effectiveness of the cloud detection and masking process.

    Here are plots of the continental monthly means (average of all 5509 cells) for the 0200/1400 average, the 0200 alone, and the 1400 alone. I have added the time periods of the various spacecrafts to the plots.

    There seems to be a clear step at the transitions from one spacecraft to another. In the 0200 set, there is a downward trend over time of the cloud percentage over the life of each spacecraft. This isn’t readily apparent in the 1400 set.

    The 1400 set has a clear seasonal pattern, that isn’t as clear in the 0200 set. This may be caused by problems with cloud detection at night as the optical channels aren’t much help in the dark. This may explain some of the seasonal difference in the 1400 set.

    The continental cloud covered percentage exceeds 80% fairly often. It makes me wonder how high-quality temperature values can be extracted from these periods with so much of the continental temperature measurements cloud contaminated.

    Here is an average over time for each of the continental cells. This is over the entire UWisc record of 1982 to 2004. White is 50%, blue is less than 50%. More than half of the continent is cloud covered 50% or more of the time.

    As you might expect from the average over time plots, the continental plot looks considerably different during each of the different spacecraft durations. NOAA-16 is particularly striking as it looks completely different from the others.

    It bears a strong resemblance to Dr. Comiso’s trend plot shown in the SI. It might be a coincidence; I need to dig into this more. I’m going to write Dr. Key at UWisc to see if he can help answer some of the questions.

    I’m happy to forward the code and data files if anyone wants to look into this more.

    • Steve McIntyre
      Posted Mar 29, 2009 at 5:00 PM | Permalink

      Re: Jeff C. (#10),

      That’s pretty amazing. I’ll email Christy and see if he’ll comment.

      • Jeff C.
        Posted Mar 29, 2009 at 6:22 PM | Permalink

        Re: Steve McIntyre (#12), These are from Dr. Key’s CASPR dataset apparently using one of its built-in cloud masking modes. Perhaps calibrations for the different spacecraft weren’t applied thus causing the steps (not sure if that would explain the drop over time though). Dr. Comiso’s processing may include something that accounts for this, that wasn’t done to this dataset. Even so, the plots certainly make me wonder what is going on.

        I did some spot checking of the raw data files to make sure they agreed and everything checked out. I did find that that the values in the data do contain some “100”s despite the data description at the UW website claiming they range from 0 to 99. At first I thought the 100’s might be a flag for missing data, but if you look at them in a spatially, they make sense. They are surrounded by values in the 90’s.

        Re: curious (#11), I really have not thought about this a whole lot and am not sure what to make of it. There are a number of cloud parameters that can be extracted from the dataset that might help answer this question. Unfortunately, we only have access to the monthly data and I think you need daily data to track patterns and flow.

    • Kenneth Fritsch
      Posted Mar 31, 2009 at 10:06 AM | Permalink

      Re: Jeff C. (#10),

      Jeff C, I admire your analytical tenacity and insights (and that of others here at CA whom have put forth major efforts – and without the benefits of a retired person’s schedule and demands).

      In an ideal world what you have revealed in your post would be considered by the author’s using the data and answered with a reply that would acknowledge it is as a revelation that needs further explanation and, in the meantime, adds to the uncertainty of the results, or by offering an explanation of how the authors took its effects into consideration in reporting their results.

      Your recent review posted on this subject at CA makes comprehension of this post just that much easier for this layperson.

      • Steve McIntyre
        Posted Mar 31, 2009 at 10:28 AM | Permalink

        Re: Kenneth Fritsch (#18), There’s a further good post on this topic at Jeff Id’s blog.

  7. curious
    Posted Mar 29, 2009 at 4:17 PM | Permalink

    Jeff C 10 above – thanks for this post. The discontinuity from satellite to satellite looks huge.

    Do you or others have any thoughts/comments on how these patterns of cloud cover relate to the actual wind pattern and cloud formation across the Antarctic? If I’ve picked up correctly from other posts one thoery is that wind arrives vertically downward approx. at the South Pole and then all runs pretty much radially northward. If this is the case would it be reasonable to suggest cloud cover is likely to be low over the pole with formation taking place towards the coastal areas?

    http://www.antarcticconnection.com/antarctic/weather/clouds.shtml

    There is a 1968 paper which looks good on this but I haven’t found a free access version:

    “The pattern of surface wind flow in Antarctica”
    Journal Pure and Applied Geophysics, KB Mather.

    http://www.springerlink.com/content/r2k2078548721167/

    The abstract refers to use of data from 34 Antarctic stations, both coastal and inland. Any thoughts or other references (inc. more recent) gratefully received.

    • Phil
      Posted Mar 29, 2009 at 11:57 PM | Permalink

      Re: curious (#11), Town, Walden, Warren 2006 has some info on wind speed and direction on page 12 of this pdf. On page 13, the authors also make some interesting comments about Comiso 2000 regarding his cloud masking algorithm and near-surface air temperature estimates. It is not clear to me whether in Steig 2009 Comiso has overcome the above referenced comments.

  8. Posted Mar 30, 2009 at 11:36 AM | Permalink

    I forgot about this comment from methods.

    Using RegEM with TTLS provides more robust results for climate field reconstruction than the ridge-regression method originally suggested in ref. 11 for data infilling problems, when there are large differences in data availability between the calibration and reconstruction intervals.

    I think it gives exactly the same results? I wonder what I’m missing.

  9. Geoff Sherrington
    Posted Mar 31, 2009 at 2:37 AM | Permalink

    This map was produced from the NOAA satellite series.

    See the text at http://terraweb.wr.usgs.gov/projects/Antarctica/AVHRR.html

    The satellite images used in the mosaic were acquired by the Advanced Very High Resolution Radiometer (AVHRR) sensors on the National Oceanic and Atmospheric Administration (NOAA) satellites; the images used in the mosaic were collected during the period 1980 to 1994. Although the AVHRR scans a 2400 km-wide swath and can image nearly half of the continent of Antarctica on a single orbit, 63 sections of 38 scenes were needed to compile the nearly cloud-free digital mosaic.

    Note the large number of images needed to make the cloud-free scene, in accord with above comments about Antarctic cloud.

    The AVHRR channel 1 in particular was used to discriminate cloud from surface (wheter surface is solid or driven snow I do not know). This Channel shows prima facie evidence of drift with time. Now, when the various images were being selected to make the cloud free map, the temperatures on the ground would not have stayed conveniently constant. They too would be “drifting” to use the word that way.

    There was a signal:noise ratio of about 9 when all went well on this channel on NOAA 9, so there was another error source here.

    Then, we are referred to Beckers & Rixen, whose paper abstract is

    The paper presents a new self-consistent method to infer missing data from oceanographic data series and to
    extract the relevant empirical orthogonal functions. As a by-product, the new method allows for the detection
    of the number of statistically significant EOFs by a cross-validation procedure for a complete or incomplete
    dataset, as well as the noise level and interpolation error. Since the proposed filling and analysis method does
    not need a priori information about the error covariance structure, the method is self-consistent and parameter
    free.

    We have seen that there are error sources, yet B&R say they need no a priori information about error covariance structure. They then go to a mathematical method of elegant guessing, with seemingly little idea that one cannot make a silk purse from a pig’s ear.

    It is entirely possible that the pre-existing error magnitudes completely swamp or adversely affect their elegant guesswork.

    Why, we do not even know if cloud top temperatures are always colder or always warmer than the ice surface below (or 2 bob each way) so hoe can cloud free reconstructions of time-dependent temperature and sensor responses be validy guessed? And that for decision making of world importance.

  10. Geoff Sherrington
    Posted Mar 31, 2009 at 2:41 AM | Permalink

    I forgot to add that the NOAA satellites were mainly tasked to detect pre-emptive nuclear strikes from the USSR in the cold war era and the great bulk of the data were gathered from the Arctic, not the Antarctic. Have a dig in the literature to see the data memory devices used on these early satellites and the number of hours they could store data before rolling over to transmit to large satellite dishes on the ground. Magnetic wire loops and the like. It was really rudimentary technology compared to what could well be in the minds of many people today.

  11. Jeff C.
    Posted Mar 31, 2009 at 3:36 PM | Permalink

    Here is a link to The Air Vent post Steve mentioned. http://noconsensus.wordpress.com/2009/03/31/measuring-the-clouds/ . It looks like some of the discontinuities in the plots in #10 above may be from this parameter not having a diurnal drift correction applied. This seems rather odd as the data isn’t very useful without the correction. I’ve sent an email to the U of Wisconsin asking for clarification.

    At the Air Vent post I look at the another parameter, “cmask”. This data does seem to have the drift correction applied but still has some strange quirks. One interesting note is that the areas of the heaviest cloud cover seem to coincide with the portions of Antarctica with the most warming.

    • Geoff Sherrington
      Posted Apr 1, 2009 at 2:09 AM | Permalink

      Re: Jeff C. (#20),

      If there is indeed a true correlation of red areas with clouds, then it serves as a vehicle to introduce a term like “Postmodernist” which I newly call “Postexperimentalist”. With this technique, an assumption is made (e.g. “The rest of the world has the hots from GHG so the Antarctic must also). Then there is some data mining to gather figures that might of might not be relevant, with externalities controlled or not, free enough of noise or not — we do not know because the majority of the effort is post experiment.

      This majority of effort uses numerous mathematical and statistical techniques until one seems to yield a pattern, whether the error bounds are carried through properly or not. Then the pattern is published, sometimes with the introduction of new words and variations and acronyms that the author hopes will forever be attributed to his/her name, the “Elvis the Pelvis” syndrome.

      The physics, the chemistry, the limitations, the findings of papers to the contrary, tend to be downplayed. The important part of Postexperimentalism is the subsequent number crunching. The calibrations and errors of prior experiments get nil, poor or passing mention.

      This is not the way that good science has been done. I see no reason why it should now be acceptable — what fundamentals have changed? As one guess, the risk of reverse causation has been increased because less effort has gone into seminal actual experiments and calibrations and attempts to falsify at the foundation level.

      Postexperimentalism is not to be confused with mathematical, statistical and remeasured value auditing as is done here. To the contrary, the audit assumes a much greater importance in the overall scheme, especially when kept open-minded and free of the preconception that started a Postexperimental publication.

      So endeth the sermon. I feel better now.

    • Posted Apr 1, 2009 at 8:25 AM | Permalink

      Re: Jeff C. (#20),

      One interesting note is that the areas of the heaviest cloud cover seem to coincide with the portions of Antarctica with the most warming

      Since there is a strong temperature inversion over the Antarctic ice sheets, clouds there are significantly warmer than the surface so wouldn’t you expect that? You can’t think of clouds there in the same way as in the rest of the world because their bases are usually at the top of the inversion layer and so they occur in a warmer, moist layer over a cold, dry surface layer.

      • DeWitt Payne
        Posted Apr 1, 2009 at 2:53 PM | Permalink

        Re: Phil. (#22),

        Since there is a strong temperature inversion over the Antarctic ice sheets…

        That would be true in the winter when there is no sun visible. Is it also true in the summer? I thought that was a major problem with identifying clouds, because they are warmer than the surface in the winter and colder in the summer.

      • Jeff C.
        Posted Apr 1, 2009 at 3:13 PM | Permalink

        Re: Phil. (#22),

        Since there is a strong temperature inversion over the Antarctic ice sheets, clouds there are significantly warmer than the surface so wouldn’t you expect that?

        I understand what you are saying, but I think this means these areas are warmer, but not necessarily warming. Unless, of course, there is an increase in cloud cover over time. I’m going to look at that next.

        The thing that bothers me is that the areas of warming have cloud cover as much as 80% of the time. Due to the cloud masking methodology, trends are being calculated using only 20% of the temperature measurements. There is an inherent assumption that the trend on the surface is the same when cloud cover is present but we don’t know that. We also don’t know how the cloud-masked days are handled. Are they merely thrown out with monthly averages calculated using only 6 days (20% of the month)? Or is an infilling algorithm used?

        There does seem to be a relationship between data sparseness (i.e. frequently cloud masked areas) and areas with warming trends. It may be spurious, but it warrants further investigation.

  12. Layman Lurker
    Posted Apr 2, 2009 at 12:44 PM | Permalink

    #24 Jeff C.

    “…I think this means these areas are warmer, but not necessarily warming.”

    This is the crux of the matter. It seems obvious from your work that there are persistent cloud patterns in Antarctica. These persistent patterns coincide with identified areas of warming. Since these areas are not cloud free this means that a large part of warming (likely) comes from cloud mask infilling. What were these infilled values based on? How much is known about the effect on temp of the various combinations and permuations of cloud type, seasons, geography, oceans, etc.

    Having said that, the trend conincidence may be explainable if the areas of persistent cloud and temp inversions were an amplifying factor. However I have not seen anything to document such an effect.

    • Jeff C.
      Posted Apr 3, 2009 at 9:56 AM | Permalink

      Re: Layman Lurker (#25), Cloud cover is so common, on the order of 50 to 75% of the total daily cells are thrown out as cloud masked. Some locations are close to 80%. Do they infill the missing dates or simply calculate an average with the days remaining? Either option can cause problems.

      The UWisc dataset shows an abrupt change in cloud patterns with the introduction of NOAA-16 in January 2001. This after 19 years of cloud patterns showing virtually no change year after year from 1982 to 2000. I’ve exchanged emails with those responsible for the UWisc dataset and they acknowledged that the NOAA-16 data has problems, and they have not resolved all the issues. They were very candid about the shortcomings.

      To my knowledge, Dr. Comiso has not described how he addressed the NOAA-16 data problems. I have seen enough tidbits of info to indicate that the Comiso data set does have some discrepancies during this period.

      • Posted Apr 3, 2009 at 9:59 AM | Permalink

        Re: Jeff C. (#26),

        Have you considered emailing Comiso?

        • Jeff C.
          Posted Apr 3, 2009 at 11:05 AM | Permalink

          Re: Jeff Id (#27), I emailed him previously about something else and he did not reply. I was using my personal email account and that might have something to do with it. If someone with an *.edu address emailed him it might get more notice.

          Re: Layman Lurker (#28), Good question, I wish I had the answer. Dr. Comiso is much better than others in explaining his methods, but there are still large gaps.

          We know that Cosimo has mentioned the comparison of masked and unmasked temps using surface station data and referred to seasonal averages, but this seems too simplistic if such a large part of the reconstruction depends on these values.

          Can you point me to where he went over this? I have most of his papers and don’t remember seeing this.

        • Posted Apr 3, 2009 at 1:50 PM | Permalink

          Re: Jeff C. (#29),

          Maybe he thinks you’re me.

        • Jeff C.
          Posted Apr 3, 2009 at 3:22 PM | Permalink

          Re: Jeff Id (#31),

          Maybe he thinks you’re me.

          Could be, but why would he snub the president of his own fan club? My reference as “the widely-respected NASA physicist” seems like rather faint praise compared to your description of him as the Antarctic Jedi.

          http://noconsensus.wordpress.com/2009/03/28/comisos-data/

          Re: Layman Lurker (#30), Thanks for the reference, I had forgotton about this part. Regarding your suggestion, that is exactly the comparison I’m working on now. Should have something within the next day or two.

  13. Layman Lurker
    Posted Apr 3, 2009 at 10:36 AM | Permalink

    #26 Jeff C.

    You know this stuff a lot better than I do, however if there is greater warming in the areas with cloud, how can there be a difference between cloud and no-cloud temps if there is no infilling based on assumed physical properties? We know that Cosimo has mentioned the comparison of masked and unmasked temps using surface station data and refered to seasonal averages, but this seems too simplistic if such a large part of the reconstruction depends on these values. The dynamics of cloud microphysics, elevation, geography, and seasonality will invariably have dramatic implications for how such values should be calculated.

    And that doesn’t even touch on the measurement / insturmental questions.

  14. Layman Lurker
    Posted Apr 3, 2009 at 11:53 AM | Permalink

    #29 Jeff C.:

    From J. Cosimo, “Variability and Trends in Antarctic Surface Temperatures from In Situ and Satellite Infrared Measurements”
    JOC, May 2000:

    http://ams.allenpress.com/perlserv/?request=get-document&doi=10.1175%2F1520-0442(2000)013%3C1674%3AVATIAS%3E2.0.CO%3B2

    The monthly averages derived from the infrared data are not true monthly averages since they are just averages of surface values during cloud-free conditions. The magnitude of the associated error has been studied by taking the differences between the true monthly averages, using station data, and the monthly averages of cloud-free data (as identified by the AVHRR cloud mask) from the same stations. The results show that the cloud-free only monthly average is colder than the true monthly average by about 0.3°C with a standard deviation of about 0.6°C during summer and 0.5°C with a standard deviation of 1.5°C during the winter.

    This quote is the last paragraph of section 3.

    If you do not get a response from Cosimo, then it might be interesting to look at the differences between NSIDC AVHRR and Steig AVHRR in grids corresponding with surface stations. Hopefully, it would show where and when cloud masking was applied, and what the values were. Looking at these grids in aggregate may be interesting as well. For example, it may tell you if there was a forced calibration of cloud masked grids back to monthly surface station means. Comiso almost seems to imply this in the quote above.

    • Kenneth Fritsch
      Posted Apr 4, 2009 at 12:02 PM | Permalink

      Re: Layman Lurker (#30),

      The results show that the cloud-free only monthly average is colder than the true monthly average by about 0.3°C with a standard deviation of about 0.6°C during summer and 0.5°C with a standard deviation of 1.5°C during the winter.

      You probably are going to obtain more information by doing the station by station differences. The information provided from Cosimo above is not sufficient, for example, to determine a standard error – without some big assumptions.

  15. Ryan O
    Posted Apr 4, 2009 at 3:13 AM | Permalink

    Guys,
    .
    Finally got internet working in the Netherlands . . .
    .
    Re: Jeff C. (#10),
    .
    The big difference between the cloud masking for NOAA-16 and previous satellites is that the AVHRR instrument for NOAA-16 has a split Channel 3. They added a 1.6 micron receiver for better discrimination between snow and cloud albedo:
    .

    .
    In the CASPR algorithm, all previous satellites had to use a combination of different channels to do the cloud masking. One of the steps involves measuring albedo, which requires use of Channels 1 and 2. Channels 1 and 2 degrade fairly quickly over the life of the satellite. That is the reason for the behavior shown in the UWisc data here: (#10) .
    .
    I seriously doubt that Comiso uses the CASPR method because it depends on input from Channels 1 and 2. He probably does some slick differencing/ratioing between Channels 3-5 and then supplements with time-averaged composites of Ch. 1 and 2 to help determine seasonal surface condition (snow, ice, water, etc.).
    .
    AFA the strong coastal warming band, I think that’s coincidence. I’m still slogging through a pseudo-calibration of the Comiso cloudmasked data, and I think the coastal warming band feature in the SI is a result of how he calibrated, not how he masked. Hopefully soon I will have a post on that.
    .
    BTW, a good reference for CASPR is here: http://nsidc.org/data/docs/daac/nsidc0066_avhrr_5km/CASPRrefman.pdf
    .
    It’s interesting reading. The amount of processing that is required to make the AVHRR data work at all is impressive. I think it’s even more impressive how well Comiso is able to do it. One of the Jeffs called him an Antarctic Jedi at the Air Vent, and I think it’s a deserved moniker.

  16. Ryan O
    Posted Apr 4, 2009 at 3:19 AM | Permalink

    BTW . . . NOAA-16’s problems are NOT cloud-masking related. NOAA-16’s AVHRR instrument with the split Channel 3 is much much much better at allowing cloud masking than previous AVHRR instruments. The “change” in cloud patterns doesn’t indicate a problem with NOAA-16; it simply shows how poor the CASPR algorithm works on Version 1/2 data.
    .
    NOAA-16’s problems are with the scan motor, which leads to intermittent misidentification of geographical location during a scan.
    .
    So NOAA-16 gets +1 point for better masking . . . but -1 point for a crappy scan motor. :)

  17. Beckers Jean-Marie
    Posted Jun 19, 2009 at 2:58 AM | Permalink

    Hi everyone,

    I just came across your discussions on our paper

    http://hdl.handle.net/2268/4291

    and would like to take the opportunity to respond to some of your questions/comments.

    Our method always assumes that clouds are correctly masked (so whether clouds are colder or warmer is a question for the groups that provide the masks). Systematic errors here will always affect the reconstruction and probably lead to cold bias for cold clouds incorrectly masked. To help the user, we are currently testing a posteriori quality control for each pixel and firsts results are promising in the sense that undetected haze and cloud edges are automatically flagged and can be masked for a second filling iteration.

    Whether our method is more “true” than the RegEM approach cannot be proven in general but can be tested in each case, for example setting aside some data under artificial clouds and then calculating the reconstruction errors for both methods there (as suggested by Nicholas). Hopefully both methods provide similar results, otherwise it means that there are not enough data constraints available to fill in clouds. In fact this artificial cloud approach is used in our method to optimise the number of PC to retain and provides also a global error estimate for the reconstruction.

    For the regions with almost permanent cloud coverage, our method will never provide a reasonable reconstruction, because there is no a priori spatial covariance function defined. Hence the method has to derive the spatial covariance from the data themselves, which is not possible if there are insufficient data in one location. This is why we apply a “land” mask also in points with a too large cloud coverage in time. In other words, the filling can only be done in places where there is sufficiently statistical evidence that allows to infer values there knowing observations in other locations and other moments.

    Since the 2003 paper we added a fundamental tool to the reconstruction itself, the associated error field. There interesting point here is that, as expected, under clouds the errors are larger than elsewhere, but depending on the PC structures, some locations are better constrained than others for the filling.

    Specially the error fields are of importance when dealing with the computation of spatial averages for detecting trends, as the imputation error influences the mean values and the standard error on the mean.
    See for example our discussion in http://www.ocean-sci.net/2/183/2006/os-2-183-2006.html which seems important for the case you discuss here; ie detecting weak temporal trends in spatial averages, themselves depending on errors in the interpolation. The most critical part here is that errors might be spatially correlated which has a strong influence on the error on the spatial average and hence the confidence you can have on the trends.

    For further understanding and reading on our method, from the original 2003 version it was later optimised for efficient use of Arpack library

    http://hdl.handle.net/2268/4296

    and later extended with error estimates

    http://www.ocean-sci.net/2/183/2006/os-2-183-2006.pdf

    and multivariate approaches

    http://hdl.handle.net/2268/9485

    The code itself and documentation is available

    http://ocgmod2.marine.usf.edu/DINEOF-welcome.html

    http://ocgmod2.marine.usf.edu/mediawiki/index.php/DINEOF-_User_guide

    Also do not hesitate to contact us for the questions and possibly a comparison with other methods.

    • Ryan O
      Posted Jun 22, 2009 at 5:47 PM | Permalink

      Re: Beckers Jean-Marie (#36), Thanks for the additional references. I may have a script and a description for you at some point if you have time to comment. The method is similar, but not exactly the same.

      • Jean-Marie Beckers
        Posted Jun 23, 2009 at 1:57 AM | Permalink

        Re: Ryan O (#37),
        Good to see that the discussion is still open. We would be happy to have at some moment your comments on comparisons with RegEM, specially on “difficult cases”.
        Do not hesitate to contact us if you have questions, suggestions, test cases for comparisons etc.

    • Posted Jun 22, 2009 at 7:23 PM | Permalink

      Re: Beckers Jean-Marie (#36),

      My thanks as well. It’s fantastic to have the authors of these papers stop by from time to time. From some of the work done on CA, I think the result from your method will be quite almost the same as RegEM on most datasets with substantially less computing time.

  18. Steve McIntyre
    Posted Jun 23, 2009 at 6:00 AM | Permalink

    Jean-Marie, I probably won’t be able to chip in on this for a week or so, but will do so. As I mentioned in the thread, at first blush, the E-M approach that you used seems more logical than RegEM. I corresponded briefly with Tapio Schneider about the reason for his much more long-winded algorithm and got what I regarded as an arm-waving answer.

  19. Ryan O
    Posted Jun 23, 2009 at 10:09 PM | Permalink

    If Jeff C is still running around looking at stuff, I just realized something. The % cloud cover graphs he posted here are almost exactly proportional to the apparent offsets between the satellites.

  20. Ryan O
    Posted Jul 6, 2009 at 12:45 PM | Permalink

    Jeff Id was kind enough to post an evaluation of the differences between RegEM TTLS, the standard truncated SVD a la Steve McI and Beckers/Rixen, the iterative TSVD method, and the eigenvector weighting method.

    http://noconsensus.wordpress.com/2009/07/06/tav-to-realclimate-you-can't-get-there-from-here/

    Iterative and eigenvector weighting show substantial improvements in stability and accurately imputing withheld data.

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