NOAA decadal scale rainfall trends found to be 'wildly wrong'


Guest post by Craig Loehle, Ph.D.

I have good news and bad news. The good news is that USA rainfall is, according to NOAA, rising at 6.5 inches per century. The bad news is that this number is wildly wrong. I also have some observations about temperature

Data from on March 20. Graphs from on March 20.

First the good news. In Figure 1, we have the precipitation trend according to NOAA.


Figure 1. Precipitation trends for lower 48 US state region according to NOAA.

I am not happy that they don’t give the time period for the trend value, nor confidence intervals, but the problem is worse than that. Precipitation is rising for every month and for the year is rising at 0.65 inches per decade. This is 6.5 inches per century. Since the mean annual value for the region is 29.14 inches according to the data link page, this is a 26% rise over the period since 1895 (length of data record here). Wow! This is exciting! Good for farmers and gardeners! Except no one has ever noticed or mentioned this rise. Have you heard about it? Aren’t we supposedly getting more drought? Contradictions make me itchy, so I downloaded the underlying data from on March 20 (Fig. 2).


Figure 2. Annual total mean precipitation (anomalies vs 1901-2000 mean) for lower 48 USA. This graph matches the one from the website.

The linear trend for the period is 1.6 inches per century (c.i. 0.5 to 2.8in) or 5.5% per century, not 6.5 inches. If you pick the period 1976 to 2012, as people like to do, you get an even lower trend of 0.58 inches per century. Picking 1976 to 2005, as some have done and as NOAA appears to have done according to the NOAA email below, is even worse, at 0.35 inches per century which is 18 times lower than the bar chart. Also note that 2012 (remember? We were all going to die?) was not particularly dry compared to many previous years, at least in terms of total precipitation.

In order to check my work, I emailed NOAA to ask about the discrepancy. I quickly got the following reply:

Hi Dr. Loehle,

There are several major factors which lead to the differences. The most important are:

  • According to the notes, the Climate Prediction Center bar graph depicts the trend from 1976-2005, while the data from NCDC (“Climate at a Glance”) is for the entire period of record (1895-2012). I do not know when the bar graph was created or if it was updated. The enveloping web pages were created on Jan 5, 2005.
  • NCDC’s underlying dataset is an area-weighted aggregate of underlying climate division data derived from stations. I believe (but do not know) that CPC uses a “reanalysis” dataset as their underlying data. I do not know whether their national value is constructed from climate division data or is a gridded representation.
  • NCDC uses a simple linear regression to determine trend, while CPC uses a “best fit” approach. I do not know the specifics of the “best fit” approach but the CPC notes explicitly note it is different than the linear trend.

NOAA staff

Clearly the NOAA staff member who replied (name withheld to protect the innocent) is trying his best to answer and is not responsible for creating either the 2005 maps and bar charts or the methods used, so please do not pick on him. Following the links back, including the Livezey and Smith 1999 reference (available at free), I do not see how even a more sophisticated “fitting” algorithm could get a trend of 6.5 inches/century out of this data unless it simply took the very low 1976 value (-3.52in) and the very high 2004 value (3.74in) and somehow let the fancy trend be governed by them, with perhaps some sort of polynomial or spline fitting, which IMO is unjustified for such short period of data as 1976 to 2005. In any case, we can consider this a prediction as of 2005 which has turned out to be false, since extrapolating from the 2005 prediction through 2012 we find 0.58 inches/century for 1976 to 2012, not 6.5. So the forecast tested 7 years later is off by a factor of 10. If the difference is due to different data being used, then either: the data used for the trends is wrong since they are so different, or the trend data is right, the underlying data needs to be made public, and the public needs to hear about the good news of rapidly increasing precipitation.

Next, I downloaded the maps of regional trends from


Figure 3. National map of annual mean precipitation trends by region. Trends (apparently) from 1976 to 2005.

This figure looks consistent with the 6.5 inches per century rate from the bar chart, but not from the underlying data, with most of the country medium green or darker. So this map is wrong too. Notice the blue regions which are asserted to be gaining rainfall at the rate of 15 inches (or more) per century. Really? Do they have any idea how much 15 inches of rain is? It is equivalent to a hurricane landfall direct hit. 6.5 inches of rain would most assuredly be noticed in the dry western states. We can also ask why they have not updated this map since 2005 if it is truly based on data up through 2005 (and is not merely a failure to update the legends). That was more than 7 years ago. If the regional trends for 1976 through 2005 are correctly reflected in this data (which I can’t test but doubt) this says that the regional data is not adequate to making a forecast. Note that this map also does not show the recent drought in the Southwest so it clearly is not based on very recent (say past 5 yr) data.

For comparison, I found the EPA precipitation map (their fig 3 from and supposedly based on the NOAA data).


This is a 110 year change map (note: gray is zero change), and they give 5.9% increase per 100 years for the country as a whole (including Alaska and Hawaii), which is very close to what I got above from the underlying NOAA data for the lower 48. This map is more sensible and has fewer extreme values. I am not saying the details are right, of course.

For completeness I also looked at the temperature data from the same sites.


Figure 4. Annual temperature trends (Deg F).

The annual trend is 0.4 F per decade or 4 degrees per century. There is no statement about the time period used and no confidence intervals on the results. This is disconcerting. However, if we plot the data from their site, we get the following (Fig. 5):


Figure 5. Temperatures (mean annual, deg F) since 1895 for lower 48 states. Matches graph from the NOAA website.

The linear trend (ignoring autocorrelation) is 1.3 deg F/century (c.i. 0.87 to 1.73), which closely matches the global rise over this period. The very high 2012 value seems unlikely and the post 1998 trend to 2011 would have been negative without it. The value of 4 deg F in the bar chart clearly depends on cherry picking recent decades. If we use 1976 to 2012 the slope is 5.6 (c.i. 3.1 to 8.1) deg F/century. If we use 1976 to 2005 to match the figure legends for the maps, we get 6.4 (c.i. 3.2 to 9.6) deg F/century. So I fail to see a way to get 4 deg F warming trend from their own data. Perhaps they have not updated the maps and bar charts since the new versions of GHCN and so on that recently came out but the data dump is updated. The 4 degree (or 6 degree) trend is so out of line with the 118 years long trend of only 1.3 deg F/century, and is matched by a warming period in the early part of the century and interrupted by cooling periods, that only the assumption that the system has radically changed could allow this number to be accepted at face value. What about the map?


Figure 6. National map of temperature trends (deg F).

This map is broadly consistent with the high rate of rise figures from the recent data. If the legend is correct, we might again wonder why this has not been updated in 7 plus years. We can also note the rate of rise in the southwest of over 10 degrees per century. Surely these would be uninhabitable by now since they were already hot. I wonder about how the sparseness of thermometers in the West and their sensitivity to placement might influence these results. The neutral trend or even cooling in the South is notable and is more prominent in other maps I have seen but cannot locate right now.

The data, trends, and maps of NOAA are used without question by EPA, other government agencies and in summary reports on climate change, as well as in countless research studies and student reports. A simple script should be able to update these maps more often than since 2005. This degree of error is not exactly comforting. The precipitation trend plot and map is simply impossible to believe and does not match the underlying data provided by NOAA. So something is very wrong there. These maps and trend estimates are crucial to discussions of future impacts on agriculture, forestry, and ecosystems and contradict claims of impending droughts (either with or without the errors). The extreme values for precipitation and warming trends in certain regions surely would suggest that reexamination of the data or methods is warranted. Bar charts of trend for a national database site should really point to specific documentation of methods and data, and include confidence limits. Even the general public knows what a confidence interval is, since they see them on opinion polls and voting projections ad nauseum.

Note: all my analyses and data are turnkey in Mathematica notebooks and are available to anyone requesting them: craigloehl at ncasi dot org.


56 thoughts on “NOAA decadal scale rainfall trends found to be 'wildly wrong'

  1. A simple random sample of mine showed we are cooling, for at least the past 12 years (= one solar cycle)
    Most seem to agree with my dataset
    Furthermore, my data set on maxima shows we will be cooling for some time to come.
    this will cause a shift in cloud formation and condensation causing some places to get much cooler whilst other countries might get some GH benefit- even though they will see less sun…
    an example is Alaska (getting much cooler) and Washington DC (getting warmer)
    So, paradoxically, current global cooling is causing a few places at lower latitude to get a bit warmer (although they will see less sun) and wetter.

  2. The reason for such fallacious results is very simple: garbage in equals garbage out.
    Not only are data like the 4 degrees F per century unreliable, ALL of the data is unreliable because they are generally based on non-replicated, non-random samples with sample size equal to ONE. Variance and error are effectively infinite and therefore the data is essentially anecdotal. Sad, really.
    All discussions of historical climate data need to start with these facts understood…

  3. I’m reminded of the NOAA mission statement from just a few years ago. I can’t remember the exact wording, but it essentially said: “NOAA knows all there is to know about everything on land, on the sea, and in the air.” They’ve toned down the hype a little, since, but the mindset may still be there.

  4. Maybe I don’t understand the issue, but in Figure 1, shouldn’t the yearly trend just be the average of the monthly trends?

  5. Very nice work, Craig. I like the examination of the suspect dataset versus various other options.
    I’d like to get a copy of the Mathematica notebooks. I think Mathematica is great, I use it and can make it do things, but there’s a whole lot I don’t know.

  6. It looks like the Year calculation in the first graph was done by summing up all the three-month rates and dividing by 3. The three-month rates are already rates (hence the clever axis label) so this is an utterly inappropriate calculation. Assuming there is underlying validity in the method, the yearly rate should just be the mean of the 12 three-month rates. This appears to be the way the yearly temp rate was calculated in the fifth graph (temp trend).
    Divide 0.65 per decade by 4 and you get .16 inch per decade of increased precip. No clue if it relates to reality but it is at least consistent with the data portrayed in the first graph. As shown is just loopy, a very sloppy calculation.

  7. And to be picking nits, the Y axis label in the first graph should be “Rate (inches per decade)”, or maybe “Change (inches)”. Just poor chartsmanship.

  8. : annual rainfall is the sum of monthly values, not the mean.
    chugiaktinkerer : the “rate” axis in figure 1 is rate of change by running 3-month windows and then the “year” figure is what I focus on. However, you might be right that that is the silly method they used to get 0.65.

  9. Dr. Loehle,
    I went to the NOAA site you linked ( and generated a plot and trend for 1976 – 2005. I’ll link screen caps once I get them stashed somewhere. Anyway, the decadal rate of increased calculated by that NOAA web page is +0.35″ per decade. As you mentioned it is extremely sensitive to start and end years.
    Decadal trends reported by NOAA are as follows:
    1975 – 2004 +0.24″
    1976 – 2005 +0.35″
    1977 – 2006 -0.00″

  10. chugiaktinkerer: the timeseries page seems more or less correct, the problem is with the bar chart and map not matching actual data.

  11. Dr. Loehle,
    Yep, I just wanted to point out that NOAA’s own calculation using NOAA’s own data yields a number that is within the realm of reason but very much pointless, given its sensitivity to endpoints.
    As promised, here’s some screen caps from the NOAA page ar :

  12. chugiaktinkerer says:
    March 22, 2013 at 12:45 pm
    “It looks like the Year calculation in the first graph was done by summing up all the three-month rates and dividing by 3. The three-month rates are already rates (hence the clever axis label) so this is an utterly inappropriate calculation. Assuming there is underlying validity in the method, the yearly rate should just be the mean of the 12 three-month rates. This appears to be the way the yearly temp rate was calculated in the fifth graph (temp trend).”
    You’re right, but now I wait for Tamino’s post that debunks you and defends the silly graph.

  13. Excellent work Dr. Koehler. We can all expect the climate fear praganda news media will be quoting the erroneous NOAA increasing rainfall and temperature rates as “proof” that man made catastrophic climate change is clearly upon us. Why bother actually examining and analyzing the faulty data allegedly supporting these ridiculous NOAA claims.

  14. Craig Loehle says:
    March 22, 2013 at 1:00 pm : annual rainfall is the sum of monthly values, not the mean.

    Dr. Loehle, that’s not what the first graph appears to chart. It’s about the changes. I don’t see how you can sum the rates of change. If the rate of change in every month year-over-year was 0.1 in/yr, then the average per year would still be 0.1 in/yr, wouldn’t it? Since it’s Friday at the end of a very long week for me, you’ll need to use small words if I’m to understand ;-).

  15. Hawkins: the graph shows rate of change by period. The rate of change in inches for the year is the sum of the rates of change in inches for each month. Imagine if each month had one more inch of rain than usual, the year would have 12 more inches of rain. The graph shows overlapping 3 month periods, perhaps to smooth out noise so you can’t just add them up. Yes, it is friday evening…

  16. By the way, I wondered just what the 30-year trend looks like over the entire record. I imported data into LibreOffice and calculated 31-year regression slope for 1910 to 1997. A plot is shown below.
    I am acquainting myself with Photobucket and fiddled with album settings. If the images I linked in the prior comment don’t show, you may need to inset the NOAA_Precip album name into the path.

  17. Dr. Loehle,
    You have provided a remarkably valuable service to NOAA and to all departments of government that use NOAA products, especially the EPA. No doubt they are cutting a check as your reward. Given this example, they need to hire you to police all their products.

  18. Are we *sure* that science doesn’t mean “making crap up to drive an agenda?” Because if it does, then this is all fine.

  19. Merovign, I think you have it nailed when it comes to “communicating climate science”.

  20. Theo: yes, waiting for the check…waiting…
    Merovign: I favor the innumeracy theory…

  21. Charles Gerard Nelson says: “God warned Noaa about a great Flood…as I recall.”
    And his children “looked upon Noaa’s nakedness,” as I recall.

  22. Maxwell Smart strikes again: Missed it by THAT MUCH, Chief!
    Thanks for the excellent analyses, Dr. Loehle!

  23. Yes! And compare the precipitation change maps with the US Drought Monitor Map:
    I have lived and worked in south eastern SC for 40 years. I can personally attest that the drought monitor map for southern SC (Colleton, Beaufort, & Jasper counties) is complete and utter crap! It shows these counties to range from abnormally dry to moderate drought. Bullshit! This has been an exceptionally wet winter for us. Water tables are at an all time high. and streams, swamps, and ponds are overflowing. It is raining as I write this, with a 60% chance of rain for tomorrow and a 70% chance of rain for Sunday.
    When a government agency can’t even do something as simple and basic as provide accurate rainfall data, what can they be relied upon to do correctly?

  24. There is a very disturbing trend emerging in all of climate alarmist science.
    So many instances are now coming to light where supposedly professionally run, major publicly funded climate and weather science data and analysis centres are being exposed as quite deliberately exaggerating quite minor weather and climate related trends into grossly alarmist claims usually illustrated by lurid and inflated and highly inaccurate graphs,
    Thanks to the endeavors of the skeptics and the all pervading capabilities of the internet the claimed extent and size of those inflated trends as promoted by the climate analysis centres are now being revealed as having little or no basis in fact or science.
    In the fields of integrity and honesty and scientific ethics global warming science is no longer on it’s knees.
    It is now well and truly down in the gutter

  25. Craig Loehle says:
    March 22, 2013 at 4:19 pm
    Merovign: I favor the innumeracy theory…
    That might work if we were discussing poll workers or some such. NOAA employees cannot use innumeracy as an excuse..

  26. The stench of scientific effluvium now issuing from the bowels of NASA and NOAA makes one wonder why any scientist worthy of the label would want to tarnish his reputation by working for such bastions of politicized science.

  27. ROM says:
    March 22, 2013 at 5:01 pm
    You are right. And that is the problem facing this iteration of the genus Homo. Plain and simple.

  28. Louis Hooffstetter says:
    March 22, 2013 at 4:55 pm

    … When a government agency can’t even do something as simple and basic as provide accurate rainfall data, what can they be relied upon to do correctly?

    Jack energy prices through the roof?

  29. Is anyone satisfied that “your life” is being steered in one way or another by policy from bad, lazy, or ideologically driven analysis?
    Just sayin,,,,,,,, should not be happening!
    It appears that science needs legislated and governmentalized.
    I offer you Cyprus! Pay attention this weekend……….

  30. john parspns says:
    March 22, 2013 at 4:57 pm
    “So what happened to the last sticky thread. Not so sticky afterall (sic)? JP

    We are sorry your meds got lost in the mail. New shipment soon. Hang on.

  31. I have never in my peer-reviewed paper given credit to anything NOAA.
    For good reason !

  32. I have been looking at rainfall data and studies of trends lately. It started at work and went home as a bit of a hobby. Most studies that I have seen are of long term (100 year plus) trends. But when I look at the hundred year trend of stations in areas I deal with, They have trends of about 5 to 6 inches per century, but confidence intervals of 1 inch to 10 inches, and R^2 less than 2%. This seems to me to be statistically significant, but meaningless. The assumption of a long-term linear trend is masking something more meaningful.

  33. Such trends in precipitation obviously haven’t been sustained for a century, but might be associated with the warming. Wentz in the journal science (2007) argued that the observations showed precipitation increased in proportion to the humidity, while the models were correlated in representing less than half the increase associated with the warming.
    An accelerated water cycle would be a negative feedback to the warming and might contribute to a Climate sensitivity of less than 1 degree C. An acceleration of the water cycle and the failure of the models to represent it was recently confirmed:
    There never was good evidence for the drought fear mongering.

  34. These damn “trends” they are so keen on doing are meaningless in the presence of long term warming and cooling periods. The result so heavily dependant on how you (cherry-)pick the start and end points.
    For a major climate monitoring service to be producing this kind of sub-highschool kind of graph without even stating what period the data refers to is clearly, totally unacceptable.
    Worse they do not even seem to be able to state what period of data was used when asked.
    Thanks to Craig Loehle for pointing a light at this totally unscientific presentation by NOAA.
    And they are wailing about the budget cuts affecting funding?

  35. Craigh L. ” We can also ask why they have not updated this map since 2005 if it is truly based on data up through 2005″
    We can also ask why, when the data is stated to run from 1931, they chose to show “trends” from 1976 only. Blatent cherry picking if ever there was.
    They are implicitly recognising the presence of the strong natural variation and chosing the rising part to derive the trends. Yet more trough-to-peak “trends”.
    Even worse that it does not even seem to be reproducable from their data.

  36. From the “notes” link: “Using an approximation based on the results of Livezey and Smith (1999), a best-fit method was used for each climate region and time period, to determine a flat baseline value for the years prior to the mid-1970’s, and the linear increase or decrease with time from that baseline value through the ensuing years (up to 2005). It is this best-fit rate of change per unit time since the mid-1970’s that is described in these products as the “trend” (expressed in units per decade) for a given region and time of year.”
    It’s very unclear but it seems like they are using 1931-76 to get a “baseline” value (of something) then work out the linear change for each year since 1976. This would give a negative “trend” in years around 1976 and positive later.
    As far as I can tell from this vague description they then look at the difference between the negative starting and positive ending values for their “best fit”.
    ” this best-fit rate of change per unit time ” err, rate of change per unit time, that would be an acceleration.
    “expressed in units per decade” , so the units of measurement are “units per decade”.?
    Who ever wrote this either does not understand what they are doing or is very bad at expressing something in clear scientific terms. I get the impression of someone trying to use all the right words to sound scientific while not really knowing what they mean.
    Like an arts graduate in media studies attempting science “communication”. Just my impression.

  37. I can attest rainfall has increased in the local area — at least back to where it was ~1900.
    Nearby Cumberland, MD averaged ~40″/year in 1900. That dropped significantly to ~35″ during the ’30s thru 1970. It then gradually increased to ~40″ in the last few decades. My raingauge avg here for the last 10 yrs is ~42″/yr. What’s interesting is that 1880’s ~1920 was a cool/wet period, the ’30s-’40s was a warm/dry period, the ’50s -70 was a cool/dry period, and since then has been a warm/wet period. Natural cycles….

  38. In “Crowdsourcing the WUWT “Extreme Weather” Reference Page:
    I provided links plus data for Southern California precipitation from 1769 to 2000. My comment is at:
    A linear regression of the data shows slope indistinguishable from zero. I extended the data set through the 2011-2012 water year and the regression slope is still essentially zero. Admittedly this is only one precipitation record for one area, but given NOAA touting its rainfall as applicable for the entire USA using only one century of data, one precipitation record with more than two centuries of data that fails to match NOAA’s statement should be sufficient to cast doubt on NOAA’s claim.

  39. I think you guys are still not really getting it.
    Before they started with the carbon dioxide nonsense, people looked at the planets to explain weather cycles, rightly or wrongly.
    see here
    to quote from the above paper:
    “A Weather Cycle as observed in the Nile Flood cycle, Max rain followed by Min rain, appears discernible with
    maximums at 1750, 1860, 1950 and minimums at 1670, 1800, 1900 and a minimum at 1990 predicted.
    The range in meters between a plentiful flood and a drought flood seems minor in the numbers but real in consequence….
    end quote
    According to my table for maxima,
    I calculate the date where the sun decided to take a nap, as being around 1995.
    and not 1990 as William Arnold predicted.
    This is looking at energy-in. I think earth reached its maximum output (means) a few years later, around 1998.
    Anyway, look again at my best sine wave plot for my data
    now see:
    1900 minimum flooding – end of the warming
    1950 maximum flooding – end of cooling
    1995 minimum flooding – end of warming.
    predicted 2035-2040 – maximum flooding – end of cooling.
    Do you see the pertinent correlation with my a-c wave for maximum temps?
    This being true and verifiable, it follows that in a cooling period, such as now, higher altitudes will get cooler and get less precipitation whilst at lower altitudes they might get some more clouds and rain and it may even get a bit warmer (but not that much) –
    there is just that small shift of cloud bands southwards in the NH and northwards in the SH.
    now try to correlate your precipitation results with this curve?
    (i am not going to do it)

  40. When I read the “notes” link I tried to understand exactly what they meant be the term “best fit”. I thought that “best fit” was usually (by default or convention) taken to mean a least squares fit – minimisation of the sum of squares of the y-axis differences between the fitted line and the data points. This procedure is very widely understood and the arithmetic/algebra that lies behind it is relatively simple for a straight line . However, this implies that it is also necessary to know what model is being fitted to the data. If the chosen model is a straight line the usual term is simple linear regression, but other models could be equally plausible. In a single dimension the model might be a quadratic. It would still be linear regression but with a curve (a parabola) as the underlying model. If more than one predictor variable is involved the usual term is “multiple linear regression”. If the model is non-linear in the parameters only then is it known as non-linear regression. In all these cases “best fit” is normally used to describe the equation that minimises the sum of squared distances from the model to the data. Of course it is not the only way to define “best fit”, and others are appropriate in certain circumstances You could decide to minimise the sum of linear distances of observations from the model but then the arithemetic/algebra becomes much more burdensome, and you would also need to explain your choice of technique.
    So what are these guys doing? It was not at all obvious to me. This is all a bit pedantic I suppose, but I’d still like to know.

  41. Craig: It’s interesting to take the next step and convert changes in precipitation into changes in latent heat flux. If one starts with the standard KT global (not US) energy balance diagram, we have 80 W/m2 of latent heat convected away from the earth’s surface (roughly 1 m of precipitation per year). At first glance, a 4% increase in precipitation appears to be equivalent to the radiative forcing for 2X CO2 (3.5 W/m2). However, radiative forcing is calculated at the tropopause and evaporation occurs at the surface. For 2X CO2, the net decrease in upward radiation at the SURFACE is about 0.8 W/m2 – which is equivalent to a 1% increase in precipitation. Small changes in precipitation involve changes in energy flux which are comparable to forcings by GHGs.
    Climate models and satellite observations both indicate that the total amount of water in the atmosphere will increase at a rate of 7% per kelvin of surface warming. However, the climate models predict that global precipitation will increase at a much slower rate of 1 to 3% per kelvin. A recent analysis of satellite observations does not support this prediction of a muted response of precipitation to global warming. Rather, the observations suggest that precipitation and total atmospheric water have increased at about the same rate over the past two decades.

  42. kirkmyers says:
    The stench of scientific effluvium now issuing from the bowels of NASA and NOAA makes one wonder why any scientist worthy of the label would want to tarnish his reputation by working for such bastions of politicized science.
    Maybe that’s the problem. With most (all) people who are competent (numerate, able to notice when a model is at odds with reality, etc) having left some time ago.
    I can’t see that an environment where political dogma and faith is important whilst “skeptic” is a dirty word would attract and keep people who want to do good science.

  43. 3-27-2013 12:25 am As a Professor Emeritus at a US University having taught and published statistical/econometric analysis, I was greatly impressed by the excellent scientific and critical analysis in an area I have only very skeptical views about. I saw the terms: confidence interval, linear regression, autocorrelation, linear trend, and the least precise “best fit” used. Wonderful ! The thoroughness of the analysis and the factual digging and presentations were marvelous to behold. Too bad our US media couldn’t use such rigorous and critical analysis ! Like NOAA, the EPA, and “progressives”, they rely on “beliefs that can’t be shaken by factual analysis – even so for University Professors who are self-designated experts. I can sum up by saying:
    Очен Хорошо Долтор Лоеле und vielen dank für Ihre bewundernswert Analyse !
    Es macht mir Freude !

Comments are closed.