(2021/06/05發表於個人臉書)
1955年7月29日，John von Neumann寫了一份四頁的文件，標題是 “Dynamics of the General Circulation”，他提出用電腦模式研究大氣環流的初步構想，這份文件Harry Wexler有稍微編修一下。當時，電腦氣象模式才剛起步，還處於實驗跟探索階段，才剛開始做一到兩天的數值天氣預報。John von Neumann在這樣的背景下，就提出用氣象模式來研究大氣長期的環流特徵，是個很大膽的想法，後來也證明他的遠見。而且，在這份文件中， John von Neuman提出氣象模式可能面臨的挑戰，像季節預報，水氣和雲的處理等，現在依然是尚未解決的問題，再次顯示他的遠見。
這篇文章想筆記一下John von Neumann的這份文件，主要參考資料是Washington and Kasahara (2011), The evolution and future research goals for general circulation models, The Development of Atmospheric Circulation Models, Cambridge University Press，是一本書裡頭的一個章節。John von Neumann的這份文件原稿是GFDL提供，可惜網路上我只有在Google書評裡找到全文，Google書評的連結放在文末。
在筆記John von Neumann這份文件前，我想先簡單介紹一下John von Neumann和Harry Wexler這兩個人。
John von Neumann (1903-1957) 是生於匈牙利的美籍數學家，科學上的成就驚人。在他對數值天氣預報感興趣之前，他在數學上提出許多重要理論 (如 von Neumann algebras )，在經濟學上提出博弈理論 (game theory)，為量子力學建立嚴謹的數學基礎 (Dirac–von Neumann axioms)，參與曼哈頓計劃，還奠定了電腦的邏輯結構設計 (First Draft of a Report on the EDVAC)。John von Neumann對電腦感興趣，也不意外的他會對數值天氣預報感興趣。
Harry Wexler (1911-1962) 是二十世紀最有影響力的氣象學家之一，他推動許多氣象觀測科技，像用飛機觀測颱風，雷達，氣象衛星，數值模式等。他是第一位搭乘飛機穿過颶風收集資料的科學家 (於1944年)，他是1957/58國際地球物理年美國在南極探索計畫的首席科學家，他推動了世界第一個氣象衛星 TIROS-1 (1960年升空)，他參與建立夏威夷的Mauna Loa Observatory，他積極推動全球氣象觀測及資料交換的World Weather Watch計畫。為了表彰他的貢獻，南極有座高山以他命名 (Mount Wexler)，月球上的一個隕石坑也以他命名 (Wexler crater)。
回到John von Neumann的這份文件。
John von Neumann這份文件的一開始，總結了一下從1947幾年下來的氣象數值模式研究成果。雖然這個模式做了很多簡化，比方說沒有水氣和降水，基本上忽略地形和輻射，只有涵蓋北半球部分區域等，但是模式的一到兩天預報結果仍是相當驚艷，大部分時候還比傳統主觀預報還要準。
因為數值模式在短期預報的初步成果，John von Neumann認為可以把數值模式拿來研究大氣長期的環流特徵，他的理由是如果把模式拿來做無限期的預報，某種程度上就是在看大氣長期的特徵，也就是大氣環流了。
“The logical next step after this is to pass to longer range forecasts and, more generally speaking, to a determination of the ordinary circulation pattern may be viewed as forecast over an infinite period of time, since it predicts what atmospheric conditions will generally prevail when they have become, due to [the lapse] of very long time [intervals, causally] and statistically independent of whatever initial conditions may have existed.”
(“[]”裡頭的字是Harry Wexler的編修)
(“[]”裡頭的字是Harry Wexler的編修)
模式從一兩天的天氣預報一下跳到長期的預報，這跳躍似乎有點大，為什麼不先試著延長到一個月到三個月的預報，即季節尺度的預報呢？John von Neumann認為，長期預報反而比季節尺度預報簡單，因為長期預報只會由幾個因素主宰，而季節預報需要考慮各種不同的因素，更加複雜。先研究長期預報，而其研究成果可能用來研究季節預報，所以長期預報的研究順位應該擺在季節預報之前。
“There is reason to believe that the above mentioned ‘infinite’ forecast, i.e., deriving the general circulation, is less difficult than intermediate length forecast, say, to 30 or 90 days. This is just a reflection of the fact that extreme cases are usually easier to treat than intermediate ones, since in extreme cases only a part [of] factors plays a role, [dominating] all others, while in intermediate cases, all factors become of comparable importance.”
“In view of the above, it seems logical to investigate now the ‘infinite’ forecast, i.e., the general circulation. It is hoped that this will subsequently lead to a better understanding of the factors involved in the ‘intermediate’ forecasts, (compared above). Thus, the ‘intermediate’ forecasts should enter into the program at a somewhat later stage”
“In view of the above, it seems logical to investigate now the ‘infinite’ forecast, i.e., the general circulation. It is hoped that this will subsequently lead to a better understanding of the factors involved in the ‘intermediate’ forecasts, (compared above). Thus, the ‘intermediate’ forecasts should enter into the program at a somewhat later stage”
在文件尾聲，John von Neumann提出了一個兩年計畫來進行大氣環流研究以及模式改進，他列了一些模式依序應該繼續改進的方向，
“In the second year, the obvious physical improvements should be gradually introduced into the treatment. As such, one would consider in order of increasing difficulty the introduction of the following factors:
a) Purely [cinematic] effects of geography and topography
b) [A]cquisting of humidity in the atmosphere by evaporation. It also requires the introduction of, presently reasonably well understood, semi-[empirical] rules regarding the dependen[ce] of the rate of evaporation on [the] local atmospheric and oceanic temperatures, atmospheric stability, and wind velocity.
c) Some, as yet, necessarily very imperfect [empirical] rules about the [delay-] relationship of over-saturation, cloud formation, and precipitation. Also, some [empirical] rules about the decrease of solar irradiation by clouds.
d) The very difficult problem of the effects of atmospheric humidity on the solar irradiation of the earth.
I repeat that (d) is [an] extremely difficult problem, which will probably only be reached at the end of the two year period, and on which progress will only be made at still later stages, and then only in combination with a great deal of experimental work.
(c) is, in principle, even more difficult, but in this case, acceptable prati[cal] approximations can probably be made. (a) is quite simple; (b), while not very simple, is nevertheless based on things that we understand reasonably well at present.”
a) Purely [cinematic] effects of geography and topography
b) [A]cquisting of humidity in the atmosphere by evaporation. It also requires the introduction of, presently reasonably well understood, semi-[empirical] rules regarding the dependen[ce] of the rate of evaporation on [the] local atmospheric and oceanic temperatures, atmospheric stability, and wind velocity.
c) Some, as yet, necessarily very imperfect [empirical] rules about the [delay-] relationship of over-saturation, cloud formation, and precipitation. Also, some [empirical] rules about the decrease of solar irradiation by clouds.
d) The very difficult problem of the effects of atmospheric humidity on the solar irradiation of the earth.
I repeat that (d) is [an] extremely difficult problem, which will probably only be reached at the end of the two year period, and on which progress will only be made at still later stages, and then only in combination with a great deal of experimental work.
(c) is, in principle, even more difficult, but in this case, acceptable prati[cal] approximations can probably be made. (a) is quite simple; (b), while not very simple, is nevertheless based on things that we understand reasonably well at present.”
John von Neumann提的這些東西，(b)和(c)基本上是物理參數法的概念，而(d)可說是cloud feedback，都是現在的大氣科學家們仍在奮戰的課題，這也再次顯示John von Neumann的精準眼光和遠見。
最後做個總結。
John von Neumann這份1955年寫的文件，我想可以視為氣象模式的預言書。當時氣象模式還在起步的階段，才剛開始做一兩天的數值天氣預報以及初始的大氣環流研究，John von Neumann就已經看出氣象模式在天氣預報，氣候研究，以及季節預報的潛力，還指出模式可能遇到的挑戰，非常的有遠見，令人佩服。
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參考資料
Washington and Kasahara (2011), The evolution and future goals of general circulation models, the Development of Atmospheric Circulation Models, Cambridge University Press
(Google book review) https://books.google.com/books?id=HTM0xMthjSQC&pg=PA18&lpg=PA18&dq=%22dynamics+of+the+general+circulation%22+von+neumann&source=bl&ots=1kV3WKTv7q&sig=ACfU3U3R8qXzpum-M_zmFIJptd-QCsPnmA&hl=en&sa=X&ved=2ahUKEwivhP3pmYHxAhVsS98KHbiUCRQQ6AEwB3oECAYQAw#v=onepage&q=%22dynamics%20of%20the%20general%20circulation%22%20von%20neumann&f=false
John von Neumann - Britannica
https://www.britannica.com/biography/John-von-Neumann/World-War-II
Harry Wexler - Encyclopedia
https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/wexler-harry
Harry Wexler - the European Space Agency
http://www.esa.int/About_Us/ESA_history/Harry_Wexler_Father_of_weather_satellites