地球科學 1922

以數值過程預報天氣

劉易斯·弗萊·理查森

用大氣的方程，一步一步地把天氣算到未來。

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In depth · the introduction

1922 年，一位貴格會數學家算出了如何只憑物理定律與算術來預報天氣——而他得到的答案，錯得離譜，卻也錯得發人深省。

把這個想法拆開看

天氣不是魔法，而是空氣在守物理。只要你知道此刻每一處空氣的氣壓、溫度、濕度與運動，物理方程就能告訴你：在接下來的幾分鐘裡，這些量各自會怎樣變化。把這筆帳算出來，向前邁幾分鐘，再重複——你便算出了未來。

理查森的飛躍，是把這件事照字面去做。他在地圖上鋪了一張網格，一格一格地，用手把方程往前磨。沒有諺語，沒有「朝霞不出門」——只有數字，把大氣推向未來。你見過的每一份天氣預報，都是這樣運作的。

它從哪裡來

劉易斯·弗萊·理查森是一位貴格會信徒、和平主義者。第一次世界大戰期間，他在西線當救護車司機。在一次次傷員之間的間隙，他用手算他的天氣帳——一次跨越德國上空、僅六小時的預報，花掉了他將近兩年。手稿曾在一次撤退的混亂中遺失，幾個月後，在一堆煤底下被翻了出來。

當他終於算完，答案是一派胡言：他的計算說，地面氣壓會跳升一個自然界從未見過的幅度。他還是把這次失敗，原原本本地，於 1922 年發表了出來——他深信方法是對的，縱然這一次嘗試不是。

它為何重要

他是對的。這次預報之所以失敗，只因為起始的測量數據有極輕微的不平衡——而非想法有誤，這層微妙之處，幾十年後才被理清。方法本身，正是今天每一個國家氣象局在超級電腦上所執行的東西。理查森不過是想徒手去做它，卻早了八十年。

一個類比

把天空想成一部電影，一格一格地向前放。每一格，都是整個大氣——網格裡每一格的氣壓與風。物理定律，就是那條由當前格畫出下一格的規則。理查森用一支鉛筆和一把計算尺去畫這些畫面；今天，一臺電腦每秒畫上幾百萬格。麻煩在於：哪怕你的第一格只是稍稍偏了一點，誤差也會隨著每一格的推進而長大——這正是把他絆倒的東西。

它處在何處

「從物理定律出發做預報」這個夢，屬於威廉·皮耶克尼斯，1904 年；理查森把它變成了一份真正的菜譜。它在 1950 年成真：第一批電子電腦之一的 ENIAC——在約翰·馮·諾伊曼與朱爾·查尼的指引下——算出了第一次成功的數值預報，這一回，把曾經毀掉理查森那次嘗試的快速擾動濾掉了。同一條血脈，一路延伸到愛德華·洛倫茲：他 1963 年發現的混沌（也在本館中），揭示了為什麼縱使是理查森那臺機器的完美版本，也只能看到一兩週之後。

The original document

Original source text

Lewis F. Richardson · Cambridge University Press · 1922 · xii + 236 pp.

The aim

the scheme is complicated because the atmosphere is complicated.

Richardson sets out to forecast the weather by numerically integrating the governing differential equations of the atmosphere. He divides the air into a horizontal lattice of cells and several vertical layers, tabulates pressure, temperature, density, water content and the two horizontal winds, and replaces the equations' space- and time-derivatives with finite differences so the future can be computed by arithmetic alone.

The trial forecast

He demonstrates the method on a single example: a six-hour forecast of the change in surface pressure and wind over central Europe for 20 May 1910, using Vilhelm Bjerknes' observational data. Much of the hand computation was done in France, where Richardson served as a wartime ambulance driver; the manuscript was once lost in the retreat at the Battle of Champagne and recovered months later under a heap of coal.

[ … ]

The forecast-factory — a fantasy

After so much hard reasoning, may one play with a fantasy?

Richardson imagines a vast theatre-like hall, its walls painted as a map of the globe, filled with tens of thousands of human “computers,” each solving the equations for one patch of the world, coordinated from a pulpit at the centre.

In this respect he is like the conductor of an orchestra in which the instruments are slide-rules and calculating machines.

But instead of waving a baton he turns a beam of rosy light upon any region that is running ahead of the rest, and a beam of blue light upon those who are behindhand.

He estimates the staff required: a roughly 200-km grid gives about 3,200 columns over the globe, some 2,000 of them active at once, about 32 computers to a column — some 64,000 people working in concert merely to keep pace with the weather as it happens.

The dream

Perhaps some day in the dim future it will be possible to advance the computations faster than the weather advances and at a cost less than the saving to mankind due to the information gained. But that is a dream.

Cambridge · 1922