地球科学 1922

以数值过程预报天气

刘易斯·弗莱·理查森

用大气的方程，一步一步地把天气算到未来。

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In depth · the introduction

1922 年，一位贵格会数学家算出了如何只凭物理定律与算术来预报天气——而他得到的答案，错得离谱，却也错得发人深省。

把这个想法拆开看

天气不是魔法，而是空气在守物理。只要你知道此刻每一处空气的气压、温度、湿度与运动，物理方程就能告诉你：在接下来的几分钟里，这些量各自会怎样变化。把这笔账算出来，向前迈几分钟，再重复——你便算出了未来。

理查森的飞跃，是把这件事照字面去做。他在地图上铺了一张网格，一格一格地，用手把方程往前磨。没有谚语，没有「朝霞不出门」——只有数字，把大气推向未来。你见过的每一份天气预报，都是这样运作的。

它从哪里来

刘易斯·弗莱·理查森是一位贵格会信徒、和平主义者。第一次世界大战期间，他在西线当救护车司机。在一次次伤员之间的间隙，他用手算他的天气账——一次跨越德国上空、仅六小时的预报，花掉了他将近两年。手稿曾在一次撤退的混乱中遗失，几个月后，在一堆煤底下被翻了出来。

当他终于算完，答案是一派胡言：他的计算说，地面气压会跳升一个自然界从未见过的幅度。他还是把这次失败，原原本本地，于 1922 年发表了出来——他深信方法是对的，纵然这一次尝试不是。

它为何重要

他是对的。这次预报之所以失败，只因为起始的测量数据有极轻微的不平衡——而非想法有误，这层微妙之处，几十年后才被理清。方法本身，正是今天每一个国家气象局在超级计算机上所运行的东西。理查森不过是想徒手去做它，却早了八十年。

一个类比

把天空想成一部电影，一帧一帧地向前放。每一帧，都是整个大气——网格里每一格的气压与风。物理定律，就是那条由当前帧画出下一帧的规则。理查森用一支铅笔和一把计算尺去画这些帧；今天，一台计算机每秒画上几百万帧。麻烦在于：哪怕你的第一帧只是稍稍偏了一点，误差也会随着每一帧的推进而长大——这正是把他绊倒的东西。

它处在何处

「从物理定律出发做预报」这个梦，属于威廉·皮耶克尼斯，1904 年；理查森把它变成了一份真正的菜谱。它在 1950 年成真：第一批电子计算机之一的 ENIAC——在约翰·冯·诺伊曼与朱尔·查尼的指引下——算出了第一次成功的数值预报，这一回，把曾经毁掉理查森那次尝试的快速扰动滤掉了。同一条血脉，一路延伸到爱德华·洛伦茨：他 1963 年发现的混沌（也在本馆中），揭示了为什么纵使是理查森那台机器的完美版本，也只能看到一两周之后。

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