Lesson 11 Historical Background of Numerical Prediction

课程 11 数值预报的历史背景

Dynamic meteorology provides the theoretical basis and methodology for modern weather forecasting. Stated simply, the objective of dynamical forecasting is to predict the future state of the atmospheric circulation from knowledge of its present state by use of numerical approximations to the dynamical equations. To fulfill this objective requires observations of the initial state of the field variables, a closed set of prediction equations relating the field variables, and a method of integrating the equations in time to obtain the future distribution of the field variables.

动力气象学为现代天气预报提供了理论基础和方法论。简单来说，动力预测的目标是利用动力方程的数值近似，从已知大气流通的当前状态预测其未来状态。为实现这一目标，需要观察场变量的初始状态、一套封闭的预报方程以关联场变量，以及一种随时间积分方程的方法，以获得场变量的未来分布。

Numerical prediction is a highly specialized field, which is continually evolving. Operational forecast centers utilize complex prediction models that require the largest available supercomputers for their solution. It is difficult to provide more than a superficial introduction to such models in an introductory text. Fortunately, however, many aspects of numerical prediction can be illustrated using a simple model, such as the barotropic vorticity equation. In fact, this equation was the basis of the earliest operational numerical prediction models.

数值预报是一个高度专业化的领域，正在不断发展。气象预报中心利用复杂的预报模型，这些模型需要最大的超级计算机来进行求解。在入门文本中，很难对这些模型提供超过肤浅的介绍。然而，幸运的是，数值预报的许多方面可以通过简单模型来说明，例如条带涡度方程。实际上，这个方程是最早的操作性数值预报模型的基础。

The British scientist L. F. Richardson made the first attempt to predict the weather numerically. His book, Weather Prediction by Numerical Process, published in 1922, is the classic treatise in this field. In this work Richardson showed how the differential equations governing atmospheric motions could be written approximately as a set of algebraic difference equations for values of the tendencies of various field variables at a finite number of points in space. Given the observed values of the field variables at these grid points, the tendencies could be calculated numerically by solving the algebraic difference equations. By extrapolating the computed tendencies ahead a small increment in time an estimate of the fields at a short time in the future could be obtained. These new values of the field variables could then be used to re-compute the tendencies. The new tendencies could then be used to extrapolate further ahead in time, etc. Even for short-range forecasting over a small area of the earth, this procedure requires an enormous number of arithmetic operations. Richardson did not foresee the development of high speed digital computers. He estimated that a work force of 64,000 people would be required just to keep up with the weather on a global basis.

英国科学家 L.F.理查森首次尝试用数值方法预测天气。他于 1922 年出版的《数值过程的天气预测》一书是该领域的经典著作。在这部作品中，理查森展示了如何将控制大气运动的微分方程近似地写成一组代数差分方程，以表示空间中有限数量点上各种场变量趋势的值。在给定这些网格点处的场变量观测值的情况下，通过求解代数差分方程，可以用数值方法计算出趋势。通过将计算出的趋势向前推算一个很小的时间增量，可以得到短时间后场的估计值。这些新的场变量值可以再次用于重新计算趋势，新的趋势随后可用于进一步的时间推算，依此类推。即使是对地球上小范围的短期预测，这一过程也需要大量的算术运算。理查森未能预见高速数字计算机的发展。他估计，单单要在全球范围内维持天气观测，就需要一支由 64,000 人组成的工作队伍。

Despite the tedious labor involved, Richardson worked out one example forecast for surface pressure tendencies at two grid points. Unfortunately, the results were very poor. Predicted pressure changes were an order of magnitude larger than those observed. At the time this failure was thought to be due primarily to the poor initial data available, especially the absence of upper air soundings. However, it is now known that there were other, even more serious, problems with Richardson’s scheme.

尽管涉及繁琐的劳动，理查森还是为两个网格点计算了一个表面气压趋势的示例预测。不幸的是，结果非常糟糕。预测的气压变化比观测到的变化大了一个数量级。当时，人们认为这种失败主要是由于可用的初始数据较差，尤其是缺乏高空探测。然而，现在知道理查森的方案还有其他更严重的问题。

After Richardson’s failure to obtain a reasonable forecast, numerical prediction was not again attempted for many years. Finally, after World War II interest in numerical prediction revived due partly to the vast expansion of the meteorological observation network, which provided much improved initial data, but even more importantly to the development of digital computers which made the enormous volume of arithmetic operations required in a numerical forecast feasible. At the same time it was realized that Richardson’s scheme was not the simplest possible scheme for numerical prediction. Richardson’s equations governed not only the slow-moving meteorologically important motions, but also included high-speed sound and gravity waves as solutions. These high-speed sound and gravity waves are in nature very weak in amplitude. However, for reasons that will be explained later, if Richardson had carried his numerical calculation beyond the initial time step, these oscillations would have amplified spuriously, thereby introducing so much "noise" in the solution that the meteorologically relevant disturbances would have been obscured.

在理查森未能获得合理的预报之后，数值预报很多年没有再被尝试。最终，在第二次世界大战之后，数值预报的兴趣复苏了，这部分是由于气象观测网络的大规模扩展提供了更为改进的初始数据，但更重要的是数字计算机的发展使得数值预报所需的巨大算术运算量成为可能。同时，人们意识到理查森的方案不是数值预报可能的最简单的方案。理查森的方程不仅控制了缓慢移动的对气象非常重要的运动，还包括高速的声波和重力波作为解。这些高速的声波和重力波在自然界中幅度非常弱。然而，出于随后将要解释的原因，如果理查森继续他的数值计算超过初始时间步，这些振荡会假性地放大，从而在解中引入大量的"噪音"，以至于气象相关的扰动会被掩盖。

The American meteorologist J. G. Charney showed in 1948 how the dynamical equations could be simplified by systematic introduction of the geostrophic and hydrostatic assumptions so that the sound and gravity oscillations were filtered out. The equations that resulted from Charney’ filtering approximations were essentially those of the quasi-geostrophic model. Thus, Charney’s approach utilized the conservative properties of potential vorticity. A special case of this model, the so-called equivalent barotropic model, was used in 1950 to make the first numerical forecast.

美国气象学家 J.G.查尔尼在 1948 年展示了如何通过系统地引入地转和静水假设来简化动力学方程，从而滤除声波和重力振荡。查尔尼过滤近似所得到的方程基本上是准地转模型的方程。因此，查尔尼的方法利用了潜在涡度的保守性质。这个模型的一个特例，即所谓的等效条带模型，于 1950 年被用于进行第一次数值预报。

This model provided forecasts of the geopotential near 500 hPa. Thus, it did not forecast "weather" in the usual sense. It could, however, be used by forecasters as an aid in predicting the local weather associated with large-scale circulations. Later multilevel versions of the quasi-geostrophic model provided explicit predictions of the surface pressure and temperature distributions, but the accuracy of such predictions was limited owing to the approximations inherent in the quasi-geostrophic model.

该模型提供了接近 500 hPa 的地势势能预测。因此，它并没有以通常意义上的"天气"进行预测。然而，预报员可以将其作为预测与大规模环流相关的地方天气的辅助工具。后来的准地转模型的多层版本提供了对地面压力和温度分布的明确预测，但由于准地转模型固有的近似性，这些预测的准确性受到限制。

With the development of vastly more powerful computers and more sophisticated modeling techniques, numerical forecasting has now returned to models that are quite similar to Richardson’s formulation and are potentially far more accurate than quasi-geostrophic models. Nevertheless, it is still worth considering the simplest filtered model, the barotropic vorticity equation, to illustrate some of the technical aspects of numerical prediction in a simple context.

随着功能更强大的计算机和更复杂的建模技术的发展，数值预报现在已经回归到与理查森的公式非常相似的模型，这些模型可能比准地转模型更准确。然而，在一个简单的背景下，考虑最简单的过滤模型，即正压涡度方程，来说明数值预报的一些技术方面，仍然是值得的。