集成预报

  集成预报是进行具有随机特性的天气预报工具。对日益不可或缺的确定性天气预报而言,集成预报既是另一选择,也是一种补充。集成预报通过随机描绘数值天气预报中的误差来模拟其最可能的演变。这些不可避免的误差可能来自大气的初始状态,方程的近似,或陆气、海气界面建模时普遍接受的不确定性。

1. 集成预报的意义和原理

  人们可基于观测使用模型(例如,数值天气预报模型,NWP)(参见天气预报介绍)来模拟一个真实的系统的演变(这里指的是大气)。由此可产生对未来天气可能的最佳估计,即确定性预报。随后便利用最佳数据来进行一次预报。众所周知,在实践中由于缺少初始数据、观测有误差,以及在数值模拟过程中所做的近似,这种预报往往是不准确的。此外,由于大气的混沌特性,天气预报的误差会放大,这就是蝴蝶效应,即:数据或模型中的一个微小误差会在几小时或几天后使预报完全偏离。其实,天气预报必须要比常规方法更好,更便宜才是实用的,比如可直接用季节均值进行天气预报。通常,我们将可以做出有用预报的时间尺度称为可预报水平。目前阵雨天气的平均值是几分钟,暴风雨是几小时,低压或气旋是几天,寒潮或热浪是几周,厄尔尼诺等热带气候异常则为几个月。

  这个预报水平,或预报质量是随时空变化的。因此,我们需要准确知道人们对预报的各个方面的置信度:这时会产生一系列可能的结果,这就是概率预报的目标。由于计算所有可能的备选方案会非常昂贵,因此,解决这个问题的近似方法是用一些经随机扰动的数值预报来代替确定性预报的计算,这就是集成预报。集成预报与确定性预报同样是实时的。如果我们有 n 个预报(称为成员),它们对给定气象参数 x 的所有预报(例如,给定时间和地点的风速)由 n 个值组成,考虑到运行预报时可用的数据,这些值在数学上构成了一个离散样本x的概率密度[1]。本文第3节中提到,集成预报不仅产生参数概率,而且还产生在物理上清晰的全方位时空天气图像。因此,它是一个非常丰富的信息资源,如何正确使用这些信息本身就是一种挑战。

  洛伦兹普及了气象学中可预报水平的概念[2],他对蝴蝶效应图像相关的混沌过程的阐释给公众留下了深刻的印象。托特和卡内尔[3]使用美国气象模型进行了首次实时业务集成预报。从那时起,集成预报技术无论是预报本身,还是在数据同化方面都得到了完善,并应用于所有主要的气象服务中(洛伊特贝歇尔和帕尔默[4])。同时,它也被推广到诸如:工业、金融、水文等部门的季节预报中[5](见季节预测)。

环境百科全书-集成预报-风暴锋过境期间降雨预报
图1. 2016年8月4日风暴锋过境期间都市区的总体降雨预报。12个成员均显示该国中部的降雨量,它们之间的差异反映了预报精确分布的不确定性。

  从业务预报的角度来看,进行全面预报时,需要通过随机扰动其输入数据和软件计算本身来执行一个数值预报软件n。这些扰动应该合理地反映所有这些数据(例如观测误差)和计算的不确定性(已知建模不佳的气象过程,例如海洋表面流动)的分布,从而使我们能模拟模型中所有误差的可能演变及其对预报结果的影响。受较大误差或混沌放大扰动影响的参数,将比在受扰动后预报保持稳定的参数的结果更分散:由此,集成预报的离散度为我们提供了数值模型模拟天气现象可预报性的信息(图 1)。

2. 天气预报会如何受到扰动?

  在实践中,由于我们对误差来源的认识非常有限,只有数值预报系统的一些关键方面受到扰动。目前而言,扰动主要涉及如下方面:

  • 预报的初始状态。其目的是表征分析过程中主要与观测误差和数据同化算法的缺陷有关的不确定性。最简单的方法是在确定性分析中加入数值噪声[6],例如高斯噪声,其空间相关性和振幅应与过去的统计分析一致。这种噪声也可以由最近的分析或预报之间的差异的线性组合来构建(LAF 方法:滞后平均预报)。一种常见的方法是在分析中添加优化的扰动,从而使扰动在集成预报时尽快放大,以保证整个过程能模拟当天主要来自混沌的影响。另一种更严格同时也更昂贵的方法是计算整个同化过程的数据集合(参见气象资料同化):这就是集成同化方法,或集成卡尔曼滤波方法
  • 预报模型的方程。这是有关建模错误的问题。可通过将若干版本的大气数值模型混合到集成预报中来(多模型法),或通过改变某些最佳值不明的关键参数(多参数法),或通过向已知的可疑代码的某些部分注入随机扰动(随机物理法)来实现。困难在于,按定义多数建模错误是未知的,因为它们可能来自于未知的气象过程,从而缺乏模拟它们的信息。目前已经专门研究了一些误差来源,例如:由于数值模型分辨率有限,因此不能分辨现实世界中的物理尺度。这个问题可以在集成预报中使用虚拟能源进行模拟(随机能量反向散射法)。
  • 界面条件。大气和陆面之间的相互作用是预报误差的一个重要来源。这通常是由于在天气预报中,我们不清楚如何正确表表征物理参数的变化,因而使用人为确定值来表示。因此,有必要以一种特定的方式来表示它们的不确定性,扰动的方式需要与我们对其不确定性的了解相一致。其中,最重要的是土壤、植被、冰雪、海洋的特性,这些特性决定了热流、湿度和湍流的计算。在最精细的集成预报中,界面本身就是一个完整的数值模型,从而可对与大气耦合的系统进行预报。在季节预报时尤为如此。
  • 大尺度的耦合。这只适用于具有有限域的数值模型。他们的预报对与之耦合的全球天气模型中的误差很敏感,而这对于预报快速传播的大规模大气波动的演变至关重要。有限区域集成预报必须与真实反映大规模大气演变不确定性的全球集成预报相结合。

3. 从集成预报到应用

  集成预报会产生丰富且往往难以理解的信息。从数学的观点来看,集成预报产生了不同大气演变的可能情景。由于大气状态演变的空间维度(数十亿自由度)远大于集成预报(几十个成员),后者只提供了可能演变的概貌。集成预报的解读方法很多,主要有以下几种:

  • 训练有素的预报员可通过主观分析集成预报数据(参见预报员的作用)来估计不同预报情景发生的可能性。一般来说,在用户要求解释预报时,预报员会查看由所有近期模型输出(集成或确定性)组成的超级集成。现代预报员可以获得大量来自不同的天气中心、不同的模型或在不同的时间计算的可能性较高的情景,预报员总是以概率推定的方式进行或者命名实际的集成预报。大多数预报员宁愿使用多数模型和成员支持的共识情景;过于非典型的预报通常不被采纳,因为不太可能在公告中提及。然而,如果某些预报表明有发生风险事件的可能,那么该预报则有助于在必要时发出预警。考虑到事件的潜在严重性,可以冒着误报的风险予以发布。在估计天气事件的强度、时间和地点的不确定性时可使用集成预报。所以,集成预报比仅使用确定性预报更可靠,但这也需要预报员付出更多的努力[7]
环境百科全书-集成预报-城市温度预报的时间函数图
图2. 39小时城市温度预报的时间函数图,有12个成员(每个成员一条曲线)。该集成表明,在接下来的24小时内,预报是非常准确的,误差幅度小于1度。但随后它变得非常不确定,同时还有50%的结冰风险(因为6个成员低于0℃)。
  • 出于与上述相同的原因,基于集成的自动预报比仅基于确定性预报的自动预报更有效(即更准确)。事实上,这些集成提供了丰富的信息,使得我们可以综合处理预报。此类处理通常模仿人类在预报方面的专业工作。例如,模型中气象参数在网格点上的预报值分布是该参数的概率分布;在每个点上的数值与成员总数一样多(见图2)。这些值可以通过统计处理来进行修正,以弥补数值模型中的系统缺陷,如:预报值中的偏差,或预报中的置信度过高(与最近的预报中发现的误差相比,该集成的离散度太小)。可以向用户提供的集成预报通常是最可能的中值。然而,如果我们可以为他们提供集成计算的概率分布,效果会更好。比如,即使用户收到的风暴误报数是漏报数的三倍,如果他得到了集成概率大于25%风暴的预警,他实际感觉的误报率会比中值预报或确定性预报要低得多(不管是有意还是无意,大部分普通公众的感受都是如此)。在要求误报率远低于50%的应用场景中,全面的预报对天气预报的改进程度最大。这种预报方法类似于在有经济风险时金融家为使经济损失最小化所进行的计算。由于数值预报处理适用于不同的用户,集成预报便可将此方法应用于具体的天气问题。
  • 整体预报的耦合。用天气变量的概率来概括集成预报的情景,往往会导致信息的丢失;在某些应用中,最好将预期成员的数值输出直接耦合到该应用程序特定的复杂计算中。对气象变量空间分布敏感的应用尤其如此:洪水预报与流域尺度的综合降雨分布相关,商用飞机航线与每架飞机通过该航线的时间有关,电网管理又与风能和光伏发电以及家庭供暖情况有关。在这些情况下,由应用模型管理者将天气集成预报转换为自己关心的参数的集成预报,那么这种预报可能会受非气象因素的影响。该工作方法主要针对专业用户,他们本身必须是使用数值天气预报和概率计算方面的专家。

4. 集成预报的价值

  如果天气预报说有50%的降雨概率,但实际上并没有下雨,那么该预报是好是坏?我们无法通过一个孤例回答这个问题:概率预报本质上没有好坏之分。为了评估其质量,有必要对预报历史进行统计,这可能会给偶发现象的研究带来一些问题。如上所述,集成预报的使用取决于用户,特别是用户对误报的容忍度。以前一节的例子为例,关注概率25%风暴的用户(如野餐活动组织方)与追寻80%风暴概率的用户(如龙卷风“猎户”)对预报系统性能的认识会完全不同。这两个因素(需要长时间的统计数据和用户的多样性)说明了为什么集成预报的质量需要用相当复杂的数学工具进行衡量。通过简化,我们可以从与集成预报中提炼出度量质量的3个主要指标:

  • 可靠性:指针对有后续观测的预报,其预报概率与观察数据统计之间的一致性。可靠性的基本度量——离散度与误差间的关系是(a)集成离散度变化和(b)预报误差幅度变化之间的相关性:在一个可靠的系统中,最分散的预报往往是最差的,所以这种相关性愈高愈好。我们还可以观察以下,当预报给定某概率值时,观测到的预报误差是否与该概率一致。例如:在预报降雨概率为50%的一系列案例中,能否在50%的案例中观察到降雨。测量可靠性可以帮助我们发现整个预报系统的缺陷。然而,这并不能保证所预报结果可用。可靠性测量也无法得出从一种情景到另一中情景时预报的变化程度有多大,而我们恰恰需要这一数据来在不同情景下传达信息。
  • 统计分辨率,也称为锐度或分辨率,是一种诊断类型,它衡量的是预报概率与气候学有多大差异(即集成是否有“冒险”),它们的平均精度是多少。最常用的工具是ROC图(相对业务预报特性),它衡量所有预期概率水平的预报成功率(即,取大量用户预期成功率的平均值)。ROC对于评估集成预报系统(参见预报员的作用)的内在特性非常有用(见图3)。
环境百科全书-集成预报-ROC图
图3. 该ROC图显示“大于50km/h阵风”的误报率和检出率。确定性预报模型误报率为10%,检出率为70%(红点)。集成预报可提供多种概率(蓝色曲线)结果,成功率可调:例如,中位数(接近红色点的蓝点)与确定性预报模型具有相同的性能。如果我们使用整体检出概率最高的情况(最高色点),可得出90%的检出率和25%的误报率,这对于十分重视检出结果的用户来说是十分重要的(例如,可使自己避免一场意外强风造成的损失)。
  • 决策价值(由于历史原因也称为经济价值)衡量的是预报系统对特定类型用户的价值,他们的天气敏感性通常借助两个变量进行参数化建模:(a)对他们来说较为敏感的天气参数的阈值,(b)他们为超出上述阈值的误报和漏报而付出的相对成本。在这个框架下,集成预报的价值,特别是它们对确定性预报[8]的贡献可以被十分严格地量化。使用这种方法需要专门与用户进行交流,以正确地模拟他们对天气的敏感性。

  任何预报系统都必须克服的第四个障碍是用户对信息的理解。虽然目前的集成预报远非完美,但它们在很多用途中都具有极高的决策价值。遗憾的是,它们经常被用户方误解,用户往往愿意使用不成熟但易于理解的预报工具。集成预报目前面临的最大挑战是如何实现集成所产生的信息的自动化处理,从而使集成预报成为一种既智能又精确的预报工具。

 


参考资料及说明

封面图片:2016年8月4日法国的降雨预报。

[1] 概率密度是一个函数,它在数学上描述了一个参数可能取值的范围。

[2] Lorentz, E. N. 1963: Deterministic nonperiodic flow. Journal of Atmospheric Sciences. 20 : 130-141.

[3] Toth, Z., and E. Kalnay, 1993: Ensemble forecasting at NMC: The generation of perturbations. Bull. Bitter. Meteor. Soc., 74, 2317-2330.

[4] Leutbecher, M., and T. N. Palmer, 2008: Ensemble forecasting. J. Comp. Phys. , 227, 3515-3539.

[5] Hagedorn, R., F. J. Doblas-Reyes, and T. N. Palmer, 2005: The rationale behind the success of multi-model ensembles in seasonal forecasting–I. Basic concept. Tellus, 57A, 219-233.

[6] 噪声的相关性衡量其在某一点的值与其在相邻点的值之间的关系。

[7] Novak, David R., David R. Bright, Michael J. Brennan, 2008: Operational Forecaster Uncertainty Needs and Future Roles. Wea. Forecasting, 23, 1069-1084. doi: http://dx.doi.org/10.1175/2008WAF2222142.1

[8] 气候学是指过去观察到的天气情况的统计分布。


环境百科全书由环境和能源百科全书协会出版 (www.a3e.fr),该协会与格勒诺布尔阿尔卑斯大学和格勒诺布尔INP有合同关系,并由法国科学院赞助。

引用这篇文章: BOUTTIER François (2024年3月12日), 集成预报, 环境百科全书,咨询于 2024年11月6日 [在线ISSN 2555-0950]网址: https://www.encyclopedie-environnement.org/zh/air-zh/overall-forecast/.

环境百科全书中的文章是根据知识共享BY-NC-SA许可条款提供的,该许可授权复制的条件是:引用来源,不作商业使用,共享相同的初始条件,并且在每次重复使用或分发时复制知识共享BY-NC-SA许可声明。

The ensemble forecasting

Ensemble forecasting is the tool used to make probabilistic weather forecasts. It is both an alternative and a complement to deterministic weather forecasting that has become essential. It consists of simulating by random drawing the errors made when calculating a numerical weather forecast to arrive at the most probable evolution. These unavoidable errors may result from inaccuracies in the values used to characterize the initial state of the atmosphere, or from approximations made in the equations, or from accepted uncertainties in modelling conditions at the land/air or sea/air interfaces.

1. Interest and principle of ensemble forecasting

Based on observations, a model (for example, a numerical weather prediction model, NWP) (see Introduction to Weather Forecasting) can be used to simulate the evolution of a real system (here, the atmosphere). This produces the best possible estimate of the future, called a deterministic forecast: the best data are then used to make a single forecast. Everyone can see that in practice, this forecast is often imprecise, due to the lack of initial observations, their errors, and the approximations made during the numerical simulation. In addition, weather forecast errors frequently increase due to the chaotic nature of the atmosphere: it is the butterfly effect, whereby a small error in the data or model can make the forecast completely wrong a few hours or a few days later. For a forecast to be useful, it must be better than a trivial forecast, less costly to obtain, for example a weather report that would simply state seasonal normals as a forecast. The time scale beyond which we generally do not know how to make a useful forecast is called the predictability horizon. This horizon is currently, on average, a few minutes for a shower, a few hours for a storm, a few days for a depression or cyclone, a few weeks for a cold or heat wave, a few months for a tropical climate anomaly such as El Niño.

This horizon, and more generally the quality of the forecasts, are highly variable in space and time. It is therefore interesting to know precisely how much confidence one can have in each of the aspects of a forecast: this is the objective of probabilistic forecasting, where a range of possible forecasts is produced. Since it would be numerically very expensive to calculate all possible alternatives, the problem is approximated by replacing the calculation of a deterministic forecast with that of a few randomly disturbed numerical forecasts: this is the ensemble forecast. These forecasts are made in real time, as would a deterministic forecast. If we have n forecasts (called members), all their forecasts for a given meteorological parameter x (for example, the wind speed at a given point at a given time) are made up of n values, which mathematically constitute a discrete sample of the probability density [1] of x, taking into account the data available at the time the forecast was run. Section 3 shows that ensemble forecasting produces not only parameter probabilities, but also a full range of meteorological scenarios, physically coherent in space and time. It is therefore a very rich source of information, the proper use of which is a challenge in its own right.

The notion of predictability horizon has been popularized in meteorology by Lorentz [2], whose explanation of the chaotic processes involved by the image of the butterfly effect has left its mark on the general public. The first real-time operational ensemble forecasts are due to Toth and Kalnay [3], using the American meteorological model. Since then, ensemble prediction technology has been perfected and applied in all major weather services (Leutbecher and Palmer [4]), both for the prediction itself and for data assimilation. It has also spread to other sectors, such as numerical simulation for industry, finance, hydrology, seasonal forecasting [5] (see The Seasonal Forecast), etc.

Encyclopedie environnement - prevision ensemble - Prevision ensemble des pluies 4 aout 2016 - forecast storm 2016
Figure 1. Overall rainfall forecast for the metropolitan area during the passage of a storm front on August 4, 2016. The 12 members all indicate the rainfall in the centre of the country, with differences that reflect uncertainty about their precise distribution.

From an operational point of view, making an overall forecast consists in executing a numerical prediction software n times, disturbing by random numbers its input data as well as the calculations of the software itself. These disturbances should ideally reflect the distribution of our uncertainties over all these data (e.g. observational errors) and calculations (e.g. meteorological processes that are known to be poorly modelled, such as ocean surface flows). This makes it possible to simulate different possible evolutions of all these errors within the forecast model and their impacts on the predicted parameters. Parameters affected by large errors, or by a chaotic amplification of disturbances, will have more scattered forecasts than parameters whose prediction remains stable despite disturbances: the dispersion of ensemble forecasts thus provides us with information on the predictability of phenomena simulated by the numerical model (Figure 1).

2. How to disrupt a weather forecast?

In practice, only some key aspects of numerical prediction systems are disrupted because our knowledge of the sources of errors is very limited. In the current state of the art, the disturbances concern:

  • The initial state of the forecast. The aim is to represent the uncertainties of the analysis process, mainly related to observation errors and defects in data assimilation algorithms. The simplest technique consists in adding to the deterministic analysis a numerical noise [6], for example Gaussian, with spatial correlations and amplitudes faithful to the statistics carried out on past analyses. This noise can also be constructed by linear combinations of differences between recent analyses or forecasts (LAF method: lagged averaged forecasting). A common method is to add optimized disturbances to the analyses in order to amplify as quickly as possible during the ensemble forecast. This ensures that the whole will simulate the effect of the main sources of chaos of the day. A more rigorous, but also more expensive, method is to calculate sets of the complete data assimilation process (see Assimilation of meteorological data): these are the ensemble assimilation methods, or the ensemble Kalman filter methods.
  • The equations of the forecast model. It is about representing modeling errors. This can be done by mixing several versions of the numerical model of the atmosphere (the multimodel method) into the ensemble prediction, or by varying certain key parameters whose optimal value is poorly known (multiparameter method), or by injecting random disturbances into certain parts of the code that are known to be suspect (stochastic physics method). The difficulty is that most modelling errors are by definition unknown, since they come from meteorological processes that may be unknown; there is therefore a lack of information to simulate them. Some sources of errors have been particularly studied, such as the presence in the real world of unresolved physical scales due to the limited resolution of the numerical model; they can be simulated by using fictitious energy sources in ensemble forecasts (stochastic energy backscatter method).
  • Surface conditions. The interaction between atmosphere and surfaces is a major source of forecast errors. This is often due to the representation of physical parameters by artificially fixed values during weather forecasting, because we do not know how to correctly represent their variability. It is therefore necessary to represent their uncertainties in a specific way, by disturbing them in a way that is consistent with what we know about their uncertainty. This concerns in priority the characteristics of the soil, vegetation, snow, oceanic properties determining the calculation of temperature flows, humidity and turbulence. In the most sophisticated assemblies, the surfaces themselves are complete numerical models from which predictions of systems coupled with the atmosphere can be made. This is particularly the case in seasonal forecasting.
  • Large-scale couplings. This only applies to digital models with a limited domain. Their predictions are sensitive to errors in the global weather model to which they are coupled, which is crucial to predict the evolution of large, rapidly propagating atmospheric waves. The limited area ensemble forecasts must be coupled with global ensemble forecasts that realistically represent the uncertainties of large-scale atmospheric evolution.

3. From ensemble forecasting to applications

The ensemble forecast produces rich and often difficult to understand information. From a mathematical point of view, an ensemble forecast produces different possible scenarios of atmospheric evolution. Since the dimension of the space in which the atmospheric state evolves (several billion degrees of freedom) is much larger than that of the ensemble forecast (a few dozen members), the latter only provides an overview of possible evolutions. There are different methods of interpreting ensemble forecasts, the main ones being as follows.

  • The subjective examination of ensemble forecasts allows a trained forecaster (see The Role of the Forecaster) to estimate the likelihood of different possible forecast scenarios. In general, he/she will look at a super ensemble of forecasts consisting of all recent model outputs (set or deterministic) available at the time he/she is asked to interpret the forecast. Modern forecasters have access to a large number of very likely forecasts, from different weather centres, different models, or calculated at different times: they always reason probabilistically, whether they use or name real ensemble forecasts. Most forecasters prefer the consensus scenario, i.e. the one supported by the majority of models and members; forecasts that are too atypical are then rejected as too unlikely to merit mention in the bulletins. However, if some forecasts indicate the possibility of a hazardous event occurring, this can help to issue a weather warning, if necessary by taking the risk of issuing a false alarm, given the potential severity of the event. Ensemble forecasts can be useful in estimating uncertainty about the intensity, location or timing of weather events, and this allows them to be predicted with greater confidence than if only deterministic forecasts were available, knowing that this requires a specific effort on the part of the forecaster [7].
Encyclopedie environnement - prevision d'ensemble - Previsions des temperatures sur une ville en fonction du temps
Figure 2. 39-hour forecast of temperatures over a city as a function of time, with a set of 12 members (one curve per member). Here the set indicates that the forecast is quite accurate over the next 24 hours, with a margin of error of less than 1 degree, but then it becomes very uncertain, with 50% risk of freezing (since 6 members are below 0C).
  • The production of automated forecasts is more efficient (i.e. more accurate) if it is based on sets than on deterministic forecasts alone, for the same reasons as above. Indeed, the sets provide rich information, which makes it possible to process forecasts in a sophisticated way. These treatments often mimic the work of human expertise in forecasting. For example, the distribution of predicted values of a meteorological parameter at a grid point in the model is an estimate of the probability distribution of that parameter; at each point there are as many values as there are members overall (see Figure 2). These values can be corrected by statistical processing to compensate for systematic defects in the numerical model, such as biases in the forecast values, or too much confidence in the forecast (represented by too little dispersion of the set compared to errors found in recent forecasts). Users can be provided with the median value predicted by the set, which is usually a very likely value. But we can do better, by using the range of probabilities calculated by the ensemble; for example, a user who accepts 3 times more false storm alerts than no detection (which is, consciously or unconsciously, the case for most users in the general public) will perceive far fewer forecast failures if he is warned of the risk of a storm from the probabilities of a ensemble greater than 25%, than if he were given the median forecast, or that of a deterministic model. It is in applications where the false alarm rate tolerated is very different from 50% that the overall forecast provides the greatest improvement in weather forecasting. This way of using forecasts is similar to the calculations of a financier who seeks to minimize his losses according to the hazards of the economic context: the ensemble forecast applies this approach to concrete weather problems, thanks to a numerical forecast processing adapted to the needs of various types of users.
  • Coupling of the overall forecasts. Summarizing the scenarios of an ensemble forecast by probabilities of weather variables often results in a loss of information; in some applications, it is better to directly couple the numerical outputs of the expected members to the complex calculations specific to that application. This is particularly true for applications that are sensitive to the spatial distribution of meteorological variables: flood forecasting depends on integrated rainfall at the watershed scale, routing of commercial aircraft depends on the time encountered along the trajectories of each aircraft, electricity grid management depends on the mapping of wind and photovoltaic production and domestic heating, etc. In these cases, it is up to the application model manager to transform the weather ensemble forecast into an ensemble forecast for his own parameters of interest, which can be influenced by non-meteorological factors. This working method is primarily aimed at professional users, as they must themselves be experts in the use of numerical weather forecasts and probability calculations.

4. What is an ensemble forecast worth?

If rain was forecast with a probability of 50% and it does not rain, was the forecast good or bad? On an isolated case, it is impossible to answer: a probabilistic forecast is never intrinsically good or bad. To assess its quality, it is necessary to carry out statistics on a forecasting history, which can be problematic for the study of rare phenomena. As mentioned above, the very use of an ensemble forecast depends on the user, in particular on his tolerance for false alarms. To take the example of the previous section, a user interested in storm probability forecasts of 25% (adapted for example to the organization of a picnic) will have a very different perception of the performance of a forecasting system than a user who is looking for probabilities of 80% (such as a tornado hunter). These two factors (need for long statistics, and diversity of users) explain why the quality measurements of ensemble forecasts are made with rather complex mathematical tools. By simplifying, we can distinguish 3 main categories of quality measures from forecasts that are relevant for ensemble forecasts:

  • Reliability is the consistency between predicted probabilities and observed statistics when comparing forecasts with observations a posteriori. A basic measure of reliability, the dispersion/error relationship, is the correlation between (a) changes in the dispersion of a set, and (b) changes in the amplitude of forecast errors: in a reliable system, the most dispersed forecasts are on average the worst, so this correlation should be as high as possible. We can also look at whether, when a given probability value is predicted, the forecast errors found are consistent with that probability. Example: on an ensemble of cases where rain has been forecast with a 50% probability, rain must be observed in 50% of these cases. Reliability measurements can detect some shortcomings in overall forecast systems, but unfortunately they do not guarantee that the forecasts produced are useful: they do not measure the extent to which forecasts vary from one situation to another, which is necessary to communicate information adapted to each situation.
  • Statistical resolution, also called sharpness or resolution, is a type of diagnosis that measures how substantially different the predicted probabilities are from climatology (i.e. whether the ensemble is “taking risks”) and then what their average accuracy is. The most common tool is the ROC (receiver or relative operating characteristic) diagram, which measures the success rates of forecasts for all expected probability levels (i.e., on average over a wide range of possible users). The ROC is very useful for assessing the intrinsic performance of an ensemble forecasting system (The role of the forecaster) (see Figure 3).
Encyclopedie environnement - prevision ensemble - Diagramme ROC
Figure 3. ROC diagram indicating the false alarm and detection rates of the phenomenon “gusts are greater than 50km/h”. A deterministic model produced 10% false alarms and 70% detections (red dot). An ensemble forecast provides several levels of probability (blue curve), with adjustable success rates: for example, the median (blue point close to the red point) has the same performance as the deterministic model. If we use the lowest probabilities of the whole (highest blue point), we obtain 90% of detections in exchange for 25% of false alarms, which is interesting for a user who gives a lot of importance to detections (for example to protect himself from the damage that could be caused by a strong wind badly predicted).
  • Decision value (also called economic value for historical reasons) measures the value of a forecasting system for a specific type of user, whose weather sensitivity is often modelled by (a) the threshold value of a weather parameter to which he or she is sensitive, and (b) the relative cost he or she attributes to false alarms and non-detections of this threshold exceedance. It is within this framework that the value of ensemble forecasts can be most rigorously quantified, and in particular what they contribute in relation to deterministic forecasts [8]. This approach requires a specific work of dialogue with the user to correctly model his weather-sensitivity.

A fourth obstacle that any forecasting system must overcome is the understanding of information by users. Although the current ensemble forecasts are far from perfect, they contain a very high decision value for many uses. Unfortunately, they often suffer from misunderstanding on the part of users, who often prefer more rudimentary but easy-to-understand forecasting tools. The greatest current challenge in ensemble forecasting will be the development of automated processing of the information produced by ensembles, in order to present it in a form that is both intelligible and as accurate as possible.

 


References and notes

Cover image. Rainfall forecast over France on August 4, 2016 using the ensemble forecast.

[1] Probability density is a function that mathematically describes the range of possible values that a parameter can take.

[2] Lorentz, E. N. 1963: Deterministic nonperiodic flow. Journal of Atmospheric Sciences. 20 : 130-141.

[3] Toth, Z., and E. Kalnay, 1993: Ensemble forecasting at NMC: The generation of perturbations. Bull. Bitter. Meteor. Soc., 74, 2317-2330.

[4] Leutbecher, M., and T. N. Palmer, 2008: Ensemble forecasting. J. Comp. Phys. , 227, 3515-3539.

[5] Hagedorn, R., F. J. Doblas-Reyes, and T. N. Palmer, 2005: The rationale behind the success of multi-model ensembles in seasonal forecasting–I. Basic concept. Tellus, 57A, 219-233.

[6] Correlations of a noise measure the relationship between its value at one point, and its values at neighbouring points.

[7] Novak, David R., David R. Bright, Michael J. Brennan, 2008: Operational Forecaster Uncertainty Needs and Future Roles. Wea. Forecasting, 23, 1069-1084. doi: http://dx.doi.org/10.1175/2008WAF2222142.1

[8] Climatology refers to the statistical distribution of weather situations observed in the past.


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引用这篇文章: BOUTTIER François (2024年3月6日), The ensemble forecasting, 环境百科全书,咨询于 2024年11月6日 [在线ISSN 2555-0950]网址: https://www.encyclopedie-environnement.org/en/air-en/overall-forecast/.

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