Estimating reliability and resolution of probability forecasts through decomposition of the empirical score

Proper scoring rules provide a useful means to evaluate probabilistic forecasts. Independent from scoring rules, it has been argued that reliability and resolution are desirable forecast attributes. The mathematical expectation value of the score allows for a decomposition into reliability and resolution related terms, demonstrating a relationship between scoring rules and reliability/resolution. A similar decomposition holds for the empirical (i.e. sample average) score over an archive of forecast–observation pairs. This empirical decomposition though provides a too optimistic estimate of the potential score (i.e. the optimum score which could be obtained through recalibration), showing that a forecast assessment based solely on the empirical resolution and reliability terms will be misleading. The differences between the theoretical and empirical decomposition are investigated, and specific recommendations are given how to obtain better estimators of reliability and resolution in the case of the Brier and Ignorance scoring rule.     

Verification of ceiling and visibility forecasts using the ranked probability score

Abstract

A terminal forecast verification scheme employing the ranked probability score (rps) has been developed. The forecast is interpreted in terms of probabilities of six operationally significant ceiling and visibility classes using probability interpretations of the terms vrbl, ocnl, RSK, etc. Comparison with the rps of climatological and persistence forecasts permits the assessment of forecast skill.

To illustrate the technique, five months of forecasts for Winnipeg International Airport have been examined. The subjective forecast shows skill over climatology for the first five hours of the forecast period. A persistence forecast shows skill over climatology for three hours into the period and is a little superior to the subjective forecast in the first hour.     

Long-range weather forecasts through numerical and empirical methods

There has been much improvement in numerical weather prediction since L.F. Richardson (1922, Weather Prediction by Numerical Process, Cambridge University Press, Cambridge, p. 236) wrote his famous book. NWP has primarily been successful in improving day-by-day forecasts starting from an observed detailed Initial Condition (IC) out to about a week. The purpose of this paper is to discuss first the state of the art in long-range NWP by presenting results of a new large numerical experiment (named DERF90; from Dynamical Extended Range Forecasting in 1990 out to 90 days) conducted at the National Meteorological Center (NMC) during the summer and autumn of 1990 (Section 2). One hundred and twenty eight 90-day global forecasts were made from successive daily initial conditions (IC), thus giving us ample opportunity to assess skill of forecasts at lead times beyond 1 week.We then move on to define the notion of a limit of predictability (LOP), and following a procedure by Lorenz (1982), give a numerical estimate of the LOP using the DERF90 data set. We then produce a list of reasons, as to why this estimate (LOP = 18 days) should not be taken too literally. In particular, we argue that the LOP varies as a function of the flow itself, and it would be (much) larger if we had, as we will ultimately, a coupled ocean-atmosphere model for making long-lead forecasts. Last, but not least, we present results of empirical forecasts that point to modest but significant skill well beyond the traditional LOP (a few weeks).A specific recent example of empirical forecasting is discussed. Through Canonical Correlation Analysis (CCA), experimental forecasts are being made for the United States surface temperatures at lead times of several seasons. While modest, the skill is significant in that it defies the existence or a 3-week LOP, and so demonstrates the potential for model improvements.     

多种空间检验方法在不同分辨率模式降水预报评估中的应用

利用单一的客观评估方法并不能有效揭示预报误差来源。利用逐小时5 km格点融合降水产品,本研究使用了多种客观评估方法综合评估了南京大学2016年夏季汛期试验4 km与12 km WRF模式。整体上,两种分辨率都能成功地预报主雨带,4 km WRF在午后对流及复杂地形预报上更优。比较了各类客观评估方法,邻域法显示4 km WRF预报准确性更高,但对于强降水(≥13 mm·(6 h)^-1),两种模式预报的空间误差都较大。尺度分离法显示,对于小尺度系统,4 km WRF能较好再现对流但存在较大位置误差,而12 km WRF则漏报。MODE法(Method for Object-based Diagnostic Evaluation)显示4 km WRF在对象强度预报上更接近观测,但强度和范围偏大,导致华南偏强,而范围偏小造成江淮偏弱,12 km WRF低估主要是漏报。不同评估方法能清晰展示4 km WRF和12 km WRF预报误差的差异,为后续模式改进提供了重要参考。     

全国248站中—大雨以上降水概率MOS预报及其因子设计

本文给出了全国中—大雨以上降水概率MOS预报的制作方法、样本过滤条件、预报因子的设计与推导、预报值后处理以及检验与误差原因分析。还论述了MOS预报中采用σ面上的数值预报产品作因子、两维二次插值和预报值变量因子的作用与求取方法。     

Scenary forecasts of air temperature variations for the regions of the Russian Federation up to 2030 using the empirical stochastic climate models

It is demonstrated that the results of the climate modeling cannot be directly used to forecast the regional climate changes on the territory of the Russian Federation for one-three decades due to the strong influence of the natural long-period climatic variability associated with the processes in the ocean-atmosphere system in the North Atlantic. A model is proposed of the temperature variations in the regions of the Russian Federation including the variations of the global temperature and North Atlantic Oscillation (NAO) index. An empirical dynamic-stochastic model with external radiation impacts is used for the global temperature. Different scenarios of concentration variations of the radiation-active atmospheric components and NAO are considered. It is demonstrated that depending on the accepted hypothesis concerning the type of the expected NAO variations (natural fluctuations or the result of anthropogenic impacts) and on the scenario of concentration variations of the sulfate aerosols and methane, the average annual temperature variations on the territory of the Russian Federation between 2007 and 2030 may amount from 0.81 to 1.90°C. The estimates of temperature variations for the main physiographic regions of the Russian Federation are obtained.     

Development of the specialized automatic meteorological observational network based on the cell phone towers and aimed to enhance feasibility and reliability of the dangerous weather phenomena forecasts

In this paper, requirements to the meteorological observational network density and accuracy of measurement of meteorological variables, which are necessary to enhance the effectiveness and lead time of the dangerous weather phenomena forecasts, are considered. An effective technically and economically feasible way of development of the specialized automatic meteorological network based on the existing and consistently developing cell phone network is proposed.     

Quantitative precipitation forecasts: a statistical adaptation of model outputs through an analogues sorting approach

Medium-term quantitative precipitation forecasts (QPFs) up to several days ahead are required to issue early flood warnings and to allow optimum operation of hydraulic structures or reservoirs. This paper describes an approach which can be seen as an adaptation of deterministic meteorological model outputs. It involves searching for a sample of past situations similar to the current one from a long meteorological archive. The analogy is considered in terms of general circulation patterns over a window covering western Europe. For this restricted sample of days similar to the day at hand, the corresponding sample of observed daily precipitation is extracted for each catchment. The rainfall to be observed during the current day is assumed to follow the same distribution, known from this empirical sample. This provides a probabilistic forecast expressed, for example, by a central quantile and a confidence range. This paper describes the many choices underlying the optimisation of this approach: choice of predictor variables to characterise a meteorological situation, choice of similarity criterion between two situations, criterion for performance evaluation between two versions of the algorithm, etc. This method was calibrated over about 50 catchments located in France, Italy and Spain, using a meteorological and hydrological archive running from 1953 to 1996. Comparisons carried out over a validation sample (1995–1996) with three poor-man methods prove the interest of this approach, in a perfect prognosis context. In real-time operation, the use of forecast instead of observed predictor variables, essentially geopotential fields, produces only a minor decrease in performance. The use of the single-valued central quantile supplemented by the confidence interval provided a QPF that has proved effective and informative on the potential for extreme values.     

山东省近50年来降水事件变化特征

基于1951—2017年淮河流域及其周边68个气象站的年暴雨日数和年最大日降水量数据,采用经验模态分解方法分析暴雨频率和强度的平均趋势和周期,采用Copulas函数分析暴雨的综合危险度及重现期,探讨淮河流域暴雨危险度的时空变化特征。结果表明：(1) 流域暴雨频次呈现先降后升趋势,转折点在1980年左右;暴雨强度则一直呈显著的线性上升趋势。暴雨频率和强度的主周期均为准2 a。(2) 全流域90 % 以上的暴雨频次在3 d及以内,且暴雨强度小于100 mm。暴雨频率和强度超过该阈值后,增加显著变缓。暴雨重现期值随两单指标值的增加而增大,且增大速率逐步变快。(3) 暴雨频次和强度的平均变化趋势的高值在空间格局上基本一致,且两指标升降趋势的面积比相当。(4) 流域暴雨危险度联合概率的均值和最小值空间格局基本一致,最大值分布则比较分散。流域西北部的部分区域虽然暴雨频次和强度呈现下降趋势,但联合概率估计的暴雨危险度均值和最小值却很高。

     

基于EMD和BP算法的降水数据插补

为解决气温观测记录缺测的问题,选择反距离权重插值（Inverse Distance Weighted,IDW）、普通克里金插值（Ordinary Kriging,OK）和多元线性回归（Multiple Linear Regression,MLR）三种方法,以湖北省2020年为例,对全省逐日平均气温（T）、最高气温（T_max）和最低气温（T_min）进行空间插补,并采用平均绝对误差（Mean Absolute Error,MAE）对3种方法的插补结果进行检验。结果表明：用MLR插补得到的T_max、T_min、T的MAE最小,分别为0.41℃、0.31℃和0.20℃,其中T的插补误差在1℃以内的站点比例高达100%;相比IDW和OK,MLR插补结果的MAE空间分布均匀,其不仅随海拔高度变化较小,随季节变化也相对较小。单站试验结果表明,当用于MLR模型的样本数量越多、时间离散度越大时,MLR对气温的插补效果越好。总体上,对日气温缺测数据的插补效果,MLR最优,IDW次之,OK最差;对于建立气象站点长时间连续气温数据集而言,MLR更适合解决区域自动气象站日气温数据缺测问题。

     

基于小波长短期记忆网络的风电功率超短期概率预测

随着大规模的风电并网,风电所具有的间歇性与随机性对电力系统的稳定性产生了很大的影响,风电功率预测成为当前解决该问题重要的方式之一.本文利用长短期记忆（LSTM）网络良好的时序记忆特性,将小波分解技术与LSTM深度网络结合,提出基于小波长短期记忆网络的风电功率超短期概率预测模型.首先通过小波分解技术将原始时间序列进行平稳化处理,再建立各子序列样本的LSTM网络预测模型,借助最大似然估计法估计预测误差的高斯分布函数,最终实现对未来4 h时刻的风电功率概率区间预测.最后,采用中国东北某风电场数据对所提方法进行算例分析,结果表明,将小波分解与深度学习方法结合可以较好地提高预测的精度,提高概率预测的区间可靠性.     

Sensitivity of medium-range weather forecasts to the use of reference atmosphere

In this paper, the authors develop the earlier work of Chen Jiabin et al. (1986). In order to reduce spectral truncation errors, the reference atmosphere has been introduced in ECMWF model, and the spectrally-represented variables, temperature, geopotential height and orography, are replaced by their deviations from the reference atmos-phere. Two modified semi- implicit schemes have been proposed to alleviate the computational instability due to the introduction of reference atmosphere. Concerning the deviation of surface geopotential height from reference atmos-phere, an exact computational formulation has been used instead of the approximate one in the earlier work. To re-duce aliasing errors in the computations of the deviation of the surface geopotential height, a spectral fit has been used slightly to modify the original Gaussian grid-point values of orography.A series of experiments has been performed in order to assess the impact of the reference atmosphere on ECMWF medium- range forecasts at the resolution T21, T42 and T63, The results we have obtained reveal that the reference atmosphere introduced in ECMWF spectral model is generally beneficial to the mean statistical scores of 1000-200 hPa height 10-day forecasts over the globe. In the Southern Hemisphere, it is a clear improvement for T21, T42 and T63 throughout the 10-day forecast period, In the Northern Hemisphere, the impact of the reference atmos-phere on anomaly correlation is positive for resolution T21, a very slightly damaging at T42 and almost neutral at T63 in the range of day 1 to day 4. Beyond the day 4 there is a clear improvement at all resolutions.     

A Method for Estimating the Cost of CO2 Mitigation through Afforestation

The Kyoto Protocol allows Annex I countries to use afforestation (theconversion of non-forest landto forest) to meet emissions reduction targets. We present a new method forestimating the cost of CO₂mitigation through afforestation based on econometric models of land use. Landuse models are developed from dataon observed land allocation decisions and quantify the relationship betweenthe share of land in forest and the netreturns to forestry, among other land use determinants. The econometricapproach measures the actual responsesby landowners to observed changes in net returns, in contrast to earlierstudies in which landowner responses aredictated by the researcher. Models are estimated for Maine, South Carolina,and Wisconsin. The estimated modelsare used to simulate subsidies for afforestation, which imply increases inforest area and net reductions inatmospheric CO₂ concentrations. Average cost measures – totalsubsidies divided by total carbon sequestered –are derived for afforestation programs with and without timber harvesting. Theuse of econometric land use modelsin integrated assessments of climate change is explored. We model the effectson land use patterns and the costsof CO₂ mitigation of changes in the net returns to agricultureinduced by climate change.     

Erratum to: Climate change projections over three metropolitan regions in Southeast Brazil using the non-hydrostatic Eta regional climate model at 5-km resolution

Theoretical and Applied Climatology -     

500毫巴月平均环流长期预报的十年试验结果

一、引言 月平均环流预报是目前长期预报的重要组成部分。但是长期数值预报目前投入日常业务使用尚有困难,另一方面建立模式也需要丰富的实际经验。因此尝试用统计方法做月平均环流预报也是很有意义的。这不仅可以作为长期天气预报的重要依据,也有利于认识大气环流长期变化的过程与规律,为长期数值预报积累经验。 我们曾在1972年提出一个500毫巴月平均环流形势的统计预报方案。这个方案是先计算纬圈谐波系数,再用平稳随机过程的自回归模式做系数的预报。但是在应用过程