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CHAPTER 3

第三章

VERIFICATION APPROACH

验证方法

The proposed approach for verification of ensemble streamflow predictions involves selecting discrete events. The probabilistic forecast for an event – a forecast variable is less than or equal to a threshold – is obtained from the probability distribution forecast. The corresponding continuous observation is also converted into a discrete number: 1 indicates that the event occurred, 0 means that the event did not occur. The verification dataset for the event consists of the pairs of probabilistic forecasts and discrete observations. Using the verification datasets derived for discrete events, forecast quality of the probability distribution forecast can be assessed over the range of possible outcomes.

提出的集合流量预报检验方法涉及选择离散事件。从概率分布天气预报可以获得一个事件的概率预报——预报变量小于或等于一个阈值。相应的连续观测也被转换成一个离散的数字:1表示事件发生，0表示事件没有发生。该事件的验证数据集由成对的概率预测和离散观测组成。利用为离散事件派生的验证数据集，可以在可能的结果范围内进行评估概率分布天气预报的预报质量。

In this chapter, a distributions-oriented (DO) approach for forecast verifica- tion is described. The DO approach is extended to case of continuous probabilistic forecasts with parametric and nonparametric techniques to estimate the joint distri- bution of forecasts and observations. Secondly, the technical methods are described in detail. Then, DO measures and other common measures for forecast verification are discussed. The technical methods in the extended DO approach will be assessed in the next chapter.

本章描述了一种面向分布的预测验证方法。将DO方法推广到具有参数和非参数技术的连续概率预测中，以估计预测和观测的联合分布。其次，详细介绍了各种技术方法。然后，讨论了DO措施和其他常用的预报验证措施。扩展DO方法中的技术方法将在下一章进行评估。

Introduction

3.1引言

Verification procedures can be classified into two categories (Murphy, 1997): a measures-oriented (MO) approach and a distributions-oriented (DO) approach. The MO approach is traditionally used in the verification process. Literally, this approach emphasizes calculating quantitative measures of only one or two aspects of forecasting quality such as bias, accuracy, or skill, and then makes conclusions based on these measures. In most cases, the mean squared error (hereafter re- ferred to as MSE), and the correlation coefficient (CC) are used as the accuracy measure. However, CC is shown to be a measure of potential skill by Murphy et al. (1989). Although many verification measures had been developed, until the 1980rsquo;s the investigation of the relationships between measures, examination of their relative strengths and weaknesses, or general concepts about verification itself had not been studied extensively (Murphy and Winkler, 1987). For example, Barnston (1992) showed the nonlinear, one-to-one relationship between CC and RMSE for standardized forecasts and observations, and the significant variation of the mean correspondence between CC and Heidke score with the number of equally likely Heidke categories. Murphy (1995) concluded that the coefficient of determination is superior to the CC as the measure of linear association, and both of them are not proper as the measure of skill.

验证过程可以分为两类(Murphy，1997):面向度量(measures-oriented，MO)方法和面向分布(distribution-oriented，DO)方法。传统的验证过程采用MO方法。从字面上看，这种方法强调只计算预测质量的一个或两个方面的定量度量，如偏差、准确性或技能，然后根据这些度量得出结论。在大多数情况下，采用均方误差(以下简称均方误差)和相关系数(CC)作为精度度量。然而，Murphy等人(1989)证明，CC是一种潜在技能的衡量标准。虽然制定了许多核查措施，但直到1980年代，对措施之间关系的调查、对措施的相对长处和弱点的审查或关于核查本身的一般概念没有得到广泛的研究(墨菲和温克勒，1987)。例如，Barnston(1992)展示了标准化预测和观测的CC和RMSE之间的非线性、一对一的关系，以及CC和Heidke得分的平均对应值随海德克类别数的增加而显著变化。Murphy(1995)的结论是，决定系数作为线性关联的度量优于CC，但两者都不适合作为技能的度量。

The DO approach was developed in the 1980rsquo;s. Since then, the DO approach has played an important role, especially in the verification of meteorological fore- casts. For instance, the diagnostic verification of Climate Prediction Center Long- Lead Outlooks has been done with this approach (Wilks 2000). The forecasts made by human forecasters and guidance products from numerical weather prediction models were investigated (Brooks and Doswell, 1996). Also, the verification of the forecasts produced based on the Ensemble Prediction System (EPS) has been done (e.g., Hamill and colucci 1997, and Hou et al. 1998). The DO approach involves the use of the joint distribution of forecasts and observations, from which all the measures of forecast quality are derived systematically. The reason why the DO ap- proach is preferable is that it gives insights on forecast quality from various aspects and allows the user to identify the situations in which forecast performance may be weak or strong, something the MO approach fails to do (Brooks and Doswell III, 1996).

DO方法是在80年代发展起来的。从那时起，DO方法就发挥了重要作用，特别是在气象预报的验证方面。例如，气候预报中心长期前瞻的诊断性验证就是用这种方法进行的(Wilks2000)。研究了人工预报员的预报和数值天气预报模型的指导产品(Brooks and Doswell, 1996)。此外，还对基于集合预报系统(EPS)产生的预报进行了验证(例如，Hamill和colucci1997，和Hou等人1998)。DO方法是利用预报和观测值的联合分布，从中系统地推导出所有预报质量的衡量标准。DO分析之所以可取，是因为它从各个方面提供了对预报质量的见解，并允许用户识别预报性能可能较弱或较强的情况，而MO方法未能做到这一点(Brooks和DoswellIII，1996年)。

The major difficulty in applying this approach to verification stems from the estimation of the joint distribution. Two fundamental characteristics of the verifi- cation problem are complexity and dimensionality, which are quantitatively defined by Murphy (1991). Complexity is defined by the number of factorizations (C_F ), number of basic factors in each factorization (C_BF ), or total number of basic factors (C_{T BF} ). For example, in Absolute Verification (AV), where one kind of observation and one forecasting system are examined, the joint distribution can be factorized into one conditional and one marginal distribution. Thus, C_F = 2, C_BF = 2, and C_{T BF} = 4. On the other hand, the general definition of dimensionality D is that D is the number of degrees of freedom in order to estimate the joint distribution of forecasts and observations. In the case where a forecasting s

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