Statistical performances of various deterministic and stochastic models for rainfall series disaggregation

This paper compares the performance of seven disaggregation models, based on various approaches and/or concepts, for the generation of 10-min time step rainfall series from hourly rainfall series. The so-called constant disaggregation model and a linear model based on the external temporal pattern of rainfall are first considered. The other models are stochastic: the first ones are based on a given probability density function applying for the 10-min rainfall amounts of the hour to disaggregate. This probability density function is either uniform or derived from the external temporal pattern of rainfall. The other stochastic models are scaling models using canonical or microcanonical multiplicative random cascades. The comparison of the models is based on their ability to reproduce some important statistical characteristics of the observed time series: variance, skewness coefficient, wet/dry properties of 10-min rainfall amounts; rainfall amounts quantiles for different return periods; autocorrelation of 10-min rainfall amounts. A continuous hydrological simulation is next applied to produce for each generated rainfall series a continuous discharge series used afterwards for a retention design. The ability of the different disaggregation models to produce rainfall time series resulting in the same retention design than the one obtained with the observed rainfall series is finally analysed. Deterministic models as well as simpler stochastic models have rather bad performances when compared to the others. Because it is non-conservative, the model based on a microcanonical random cascade performs also very poorly. It significantly overestimates all studied statistics. Models based on microcanonical random cascades achieve the best performance. They perform reasonably well for the reproduction of rainfall statistics and almost perfectly for the reproduction of runoff and storage design variables. Results finally highlight the interest of including in the disaggregation scheme information related to the external temporal pattern of rainfall.     

Comparison of two hourly to 5-min rainfall disaggregators

A disaggregation method used by the UK water industry to disaggregate simulated hourly data to the 5-min time-scale is examined using data from Heathrow (London). This analysis shows the shortcomings of this algorithm, both in reproducing the temporal structure of rainfall depths and generating extreme events. An alternative method is proposed, based upon a random cascade with a log-Poisson generator. This is a parsimonious model requiring only two parameters per season. It is shown to provide a clear improvement upon the existing disaggregator, both in terms of temporal structure and extreme behaviour. It could thus be a powerful tool for urban hydrology which requires data at fine time-scale for design purposes and simulation studies. The utility of such a tool depends upon its potential for operational use, i.e., for implementation without any fine-scale data. The model's performance is found to be maintained when hourly rainfall time series are the only available data.     

Random cascade driven rainfall disaggregation for urban hydrology: An evaluation of six models and a new generator

Six variations of multiplicative random cascade models for generating fine-resolution (i.e., 5-minute interval) rainfall time series were evaluated for rainfall in Wroclaw, Poland. Of these variations, one included a new beta-normal generator for a microcanonical cascade. This newly proposed model successfully reproduces the statistical behavior of local 5-minute rainfalls, in terms of intermittency as well as variability. In contrast, both the canonical cascade models with either constant or time-scaled parameters and a microcanonical cascade model with a beta generator substantially underestimate 5-minute maximum rainfall intensities. The canonical models also fail to properly reproduce the intermittency of the rainfall process across a range of timescales. New observations are also made concerning the histograms of the breakdown coefficients (BDC). The tendency of the BDC histograms to have values exactly equal to 0.5 is identified and explained by the quality of pluviograph records. Moreover, the hierarchical evolution of BDC histograms from beta-like for long time steps to beta-normal histograms for short time steps is observed for the first time. The potential advantage is shown of synthetic high resolution rainfall time series generated by the revised microcanonical model for use in hydrology, especially hydrodynamic modelling of urban drainage networks.     

Improving the accuracy of tipping-bucket rain records using disaggregation techniques

We present a methodology able to infer the influence of rainfall measurement errors on the reliability of extreme rainfall statistics. We especially focus on systematic mechanical errors affecting the most popular rain intensity measurement instrument, namely the tipping-bucket rain-gauge (TBR). Such uncertainty strongly depends on the measured rainfall intensity (RI) with systematic underestimation of high RIs, leading to a biased estimation of extreme rain rates statistics. Furthermore, since intense rain-rates are usually recorded over short intervals in time, any possible correction strongly depends on the time resolution of the recorded data sets. We propose a simple procedure for the correction of low resolution data series after disaggregation at a suitable scale, so that the assessment of the influence of systematic errors on rainfall statistics become possible. The disaggregation procedure is applied to a 40-year long rain-depth dataset recorded at hourly resolution by using the IRP (Iterated Random Pulse) algorithm. A set of extreme statistics, commonly used in urban hydrology practice, have been extracted from simulated data and compared with the ones obtained after direct correction of a 12-year high resolution (1 min) RI series. In particular, the depth–duration–frequency curves derived from the original and corrected data sets have been compared in order to quantify the impact of non-corrected rain intensity measurements on design rainfall and the related statistical parameters. Preliminary results suggest that the IRP model, due to its skill in reproducing extreme rainfall intensities at fine resolution in time, is well suited in supporting rainfall intensity correction techniques.     

Misspecification of extreme rainfall population statistics and frequency inference due to measurement bias and variability

Statistical analysis of rainfall extremes is mostly based on the assumption of error-free data, despite common knowledge about the widespread incidence of precipitation measurement bias and variability. The objective of this study is primarily to investigate the impact of measurement bias and variability in statistical classification and quantile estimates of rainfall extremes. A theoretical framework is presented for the analysis of moment coefficients and probability distributions for rainfall extremes corrupted by measurement bias and variability. Furthermore, methods are outlined for practical statistical analysis of error-corrupted rainfall extremes, based on maximum likelihood. Frequency inference and testing for the presence of measurement variability are the main topics. Modelling of data series is undertaken in order to exemplify the statistical assessment and the real-life impact of measurement error.It is shown that: (a) unaccounted measurement error may potentially cause a considerable degree of misspecification about the conventional moment and L-moment coefficients of variation, and the conventional moments of skewness and kurtosis; (b) the presence of measurement variability alone can cause significant and nonlinear quantile bias which further strongly increases with the additional presence of measurement bias; and (c) maximum likelihood estimation provides a general and efficient tool for assessing measurement error in extreme rainfall frequency analysis.     

使用遗传算法优化雷达测量降水Z-R关系

将遗传算法应用到雷达测量降水的Z-R关系参数优化问题中,通过引入改进的误差函数加入总降水量误差控制,对1998年6月28日~7月2日阜阳地区的两次降水过程进行了参数优化试验,并和常规的最小二乘法、最优化方法及M-P参数法进行了对比,试验结果表明:新方法在总降水量估测方面具有更高的准确性和更好的动态适应性。     

利用对地闪的观测估算对流性天气中的降水

地闪与对流性天气中的降水量之间存在着较好的相关性,本文利用1997年6～8月间在陇东地区以平凉雷电与雹暴实验站为中心对对流性天气过程进行地闪与降水的观测,解决以下三个问题：(1)单个地闪所对应的对流性天气中的降水量;(2)相对于地闪发生位置的对流性降水空间分布;(3)相对于地闪发生时刻的对流性降水时间分布,实现了利用地闪资料更加精确地估算对流性天气中的降水量。     

Rainfall regionalization on the basis of the precipitation convective features using a raingauge network and weather radar observations

The main objective of the present paper is to show a methodology for undertaking rainfall regionalization of a region taking into account the convective features of the precipitation, and useful for establishing homogeneous zones for improving the alert system. This methodology has been applied to a hydrographic region located in northeast Spain, with an area of 16000 km² and characterized by a highly contrasted topography. Information provided by meteorological radar and 5-min precipitation data for 126 automatic raingauges has been used for the period 1996–2002. The previous analysis done on the basis of the 1927–1981 rainfall rate series for the Jardí raingauge, located in Barcelona, has also been considered. To that end, the first step was to draw up a proposal for classification of the pluviometric episodes. Recourse was had for this purpose to definition of the β parameter, related with the greater or lesser convective character of the event and calculated on the basis of the rainfall intensity at the surface (Llasat, 2001) and, when data are available, on the basis of radar reflectivity. Results show that the threshold of 35 mm/h to characterize convective episodes from raingauge data can be corroborated from the radar point of view when convective precipitation is identified using 2-D algorithms with a reflectivity threshold of 43 dBZ. Once the soundness of the β parameter had been corroborated, it was applied to more than 2900 precipitation episodes recorded in the region, in order to discriminate the features of the different subregions and their time and space distribution throughout the entire series of the samples. Using this definition, 92% of the precipitation events recorded in this region, with accumulated rainfall above 35 mm, are classified as convective ones, representing 95% of the precipitation amount. Application of the β parameter combined with monthly rainfall data allows differentiation of 8 regions with different convective precipitation features.     

Scaling of tropical rainfall as observed by TRMM precipitation radar

We used a three-year (1998–2000) dataset of TRMM Precipitation Radar observations to investigate the scaling properties of spatial rainfall fields. This dataset allows consideration of spatial scales ranging from about 4.3 km to 138 km and short temporal scales corresponding to the sensor overpasses. The focus is on the marginal spatial moment scaling, which allows estimation of the scaling parameters from a single scene of data. Here we present a global perspective of the scaling properties of tropical rainfall in terms of its spatial variability, atmospheric forcing, predictability, and applicability. Our results reveal the following: 1) the scaling parameters exhibit strong variability associated with land/ocean contrast and mean precipitation at the synoptic scale; 2) there exists a one-to-one relationship between the scaling parameters and the large-scale spatial average rain rate of a universal functional form; 3) the majority of the scenes are consistent with the hypothesis of scale invariance at the moment orders of 0 and 2; 4) relatively there are more scale-invariant rain scenes over land than over ocean; and 5) for the scenes that are non-scale-invariant, deviation from scale-invariance mainly arises from the increasingly intermittent behavior of rainfall as spatial scale decreases. These results have important implications for the development and calibration of downscaling procedures designed to reproduce rainfall properties at different spatial scales and lead to a better understanding of the nature of tropical rainfall at various spatial resolutions.     

中国1 min降雨量极值的统计研究

由于中国降水阵性很强,短历时降水极值就是世界极值,已有的估计1 min降雨量极值的气候学模型可能不适合用于中国。在分析大量水文气象资料的基础上,提出了时间风险率确定条件下降雨量极值随降水历时变化的幂律模型,找到了用业务自记资料估计1 min降雨量极值的方法。进一步建立了3类气候学模型。与国外已有模型相比,不仅更适合中国降水气候特征,具有较高精确度,且可反映地区、季节和年际变化,为有关设备的设计和应用提供更多信息。     

利用多普勒雷达定量估测降水试验

利用南昌多普勒雷达体扫资料和抚州市气象台站自记雨量资料,建立了定量估测降水方程,在抚河流域的不同区域进行了定量估测降水对比试验,据此给出了有利人工增雨作业的多普勒雷达产品判据。结果表明,综合利用多仰角基本反射率、回波顶高和垂直积分含水量进行定量估测降水,效果明显好于单独利用单仰角基本反射率估测定量降水。在降水量≤3 mm时,综合定量估测降水值、常规定量估测降水值与实测降水值比较吻合;在降水量>3 mm、特别是出现较大降水(>5 mm)时,与常规定量估测降水值相比,综合定量估测降水值更接近实测降水值。     

兰州市暴雨强度公式拟合方法研究

本文基于兰州市国家基本气象站1960~2014年降雨资料,通过直接拟合、耿贝尔分布、皮尔逊-Ⅲ型分布研究兰州市暴雨强度公式。选用芝加哥雨型来研究兰州市雨峰系数,结合暴雨强度公式确定短历时暴雨雨型。结果表明:(1)皮尔逊-Ⅲ型分布要优于耿贝尔分布和直接拟合,其调整后的兰州市暴雨公式中1年雨力参数A1为5.532mm/min,重现期调整参数c为3.198,降雨历时偏移参数b为14.92min,n为0.942,平均绝对均方差为0.036mm/min;(2)皮尔逊-Ⅲ分布能够满足不同的降雨历时以及更久的重现期。降雨历时小于90min或者重现期大于20年的暴雨模拟精确度更高,重现期在2~20a的暴雨平均绝对均方差最小为0.03mm/min。      

华南暖季极端降水与气温的对应关系

利用华南地区1966—2005年5—10月台站小时降水和日降水以及气温观测资料,分析了极端降水与气温的对应关系。结果表明,气温低于25℃时,日极端降水强度与小时极端降水强度均随气温升高而升高,且越极端的降水出现向两倍Clausius-Clapeyron (CC)变率转换的气温越低;气温高于25℃时,日极端降水强度和小时极端降水强度出现不同程度的下降,其中前者下降更为显著。考察降水持续时长发现,气温高于25℃时,华南地区小时极端降水随气温的下降主要由短持续性降水所贡献;气温高于28℃时几乎无长持续性降水发生。     

Seasonal variability of rainfall extremes

Monthly rainfall extremes have been analyzed for three stations in Southern Ontario. The double exponential probability distribution was fitted to the extreme values for each month considered, each duration selected, and sets of annual extremes. A station‐year approach yielded monthly and annual extreme value distributions for the lumped region of Southern Ontario. The analysis has revealed a pronounced seasonal pattern in the rainfall extremes – the amount of rain expected with a selected probability of occurrence during the summer being considerably greater than the rainfall that might be expected to be exceeded at the same probability level during the spring or fall. The extent of the seasonal variability was found also to vary with duration. The implications of the variability are seen to be significant for the estimation of the magnitude and frequency of floods.     

Assessing future climatic changes of rainfall extremes at small spatio-temporal scales

Climate change is expected to influence the occurrence and magnitude of rainfall extremes and hence the flood risks in cities. Major impacts of an increased pluvial flood risk are expected to occur at hourly and sub-hourly resolutions. This makes convective storms the dominant rainfall type in relation to urban flooding. The present study focuses on high-resolution regional climate model (RCM) skill in simulating sub-daily rainfall extremes. Temporal and spatial characteristics of output from three different RCM simulations with 25 km resolution are compared to point rainfall extremes estimated from observed data. The applied RCM data sets represent two different models and two different types of forcing. Temporal changes in observed extreme point rainfall are partly reproduced by the RCM RACMO when forced by ERA40 re-analysis data. Two ECHAM forced simulations show similar increases in the occurrence of rainfall extremes of over a 150-year period, but significantly different changes in the magnitudes. The physical processes behind convective rainfall extremes generate a distinctive spatial inter-site correlation structure for extreme events. All analysed RCM rainfall extremes, however, show a clear deviation from this correlation structure for sub-daily rainfalls, partly because RCM output represents areal rainfall intensities and partly due to well-known inadequacies in the convective parameterization of RCMs. The results highlight the problem urban designers are facing when using RCM output. The paper takes the first step towards a methodology by which RCM performance and other downscaling methods can be assessed in relation to the simulation of short-duration rainfall extremes.     

多部雷达联合估算淮河流域降水

以淮河流域内6部CINRAD雷达基数据资料以及高密度自动雨量站观测资料为源,在应用多种方法进行降水估算和校准,并采用主成分集成方法进行集成应用的基础上,采用"先估算降水再拼图"和"重叠区域选取最大值"的方法来进行整个流域的降水估算结果拼图,从而实现了整个淮河流域的降水估算。从2007年7月初降水过程应用结果来看,经过校准以后估算误差在45%以下,并且能够反映出缺少地面雨量观测站的区域的降水分布,是一种切实可行的淮河流域降水估算的方法。     

Conditional concentration statistics for surface plumes in the atmospheric boundary layer

A set of concentration time series from ground-level plumes in the atmosphere has been used to generate conditionally sampled (zeros ignored) plume concentration statistics. These have been compared and contrasted with corresponding unconditionally sampled statistics. It is found that conditional statistics are much less sensitive to the location of the receptor (relative to the mean plume) and to averaging time. Indeed, most of the variation apparent in unconditionally sampled statistics (both explained and unexplained) resides in the intermittency, the fraction of non-zero readings.The data are used to test three commonly used models for the concentration frequency distribution. At the simplest level of modelling, it is assumed that conditional statistics are invariant; then the data are best represented by a clipped-normal distribution. However, an exponential distribution is only slightly conservative and has the advantage of simplicity. A log-normal distribution is clearly not supported by the data. With this simple approach the intermittency remains unspecified and this is a serious deficiency.More advanced modelling must account for the residual variation in conditional statistics, which implies a relationship between these statistics and the intermittency. Although there is evidence for such a relationship in the data, it is not adequately represented by any of the distribution models considered.     

Accuracy evaluation of ClimGen weather generator and daily to hourly disaggregation methods in tropical conditions

Daily and sub-daily weather data are often required for hydrological and environmental modeling. Various weather generator programs have been used to generate synthetic climate data where observed climate data are limited. In this study, a weather data generator, ClimGen, was evaluated for generating information on daily precipitation, temperature, and wind speed at four tropical watersheds located in Hawai??i, USA. We also evaluated different daily to sub-daily weather data disaggregation methods for precipitation, air temperature, dew point temperature, and wind speed at M??kaha watershed. The hydrologic significance values of the different disaggregation methods were evaluated using Distributed Hydrology Soil Vegetation Model. MuDRain and diurnal method performed well over uniform distribution in disaggregating daily precipitation. However, the diurnal method is more consistent if accurate estimates of hourly precipitation intensities are desired. All of the air temperature disaggregation methods performed reasonably well, but goodness-of-fit statistics were slightly better for sine curve model with 2?h lag. Cosine model performed better than random model in disaggregating daily wind speed. The largest differences in annual water balance were related to wind speed followed by precipitation and dew point temperature. Simulated hourly streamflow, evapotranspiration, and groundwater recharge were less sensitive to the method of disaggregating daily air temperature. ClimGen performed well in generating the minimum and maximum temperature and wind speed. However, for precipitation, it clearly underestimated the number of extreme rainfall events with an intensity of >100 mm/day in all four locations. ClimGen was unable to replicate the distribution of observed precipitation at three locations (Honolulu, Kahului, and Hilo). ClimGen was able to reproduce the distributions of observed minimum temperature at Kahului and wind speed at Kahului and Hilo. Although the weather data generation and disaggregation methods were concentrated in a few Hawaiian watersheds, the results presented can be used to similar mountainous location settings, as well as any specific locations aimed at furthering the site-specific performance evaluation of these tested models.     

Modeling distribution of temporal sampling errors in area-time-averaged rainfall estimates

In this paper, the authors examine models of probability distributions for sampling error in rainfall estimates obtained from discrete satellite sampling in time based on 5 years of 15-min radar rainfall data in the central United States. The sampling errors considered include all combinations of 3, 6, 12, or 24 h sampling of rainfall over 32, 64, 128, 256, or 512 km square domains, and 1, 5, or 30 day rainfall accumulations. Results of this study reveal that the sampling error distribution depends strongly on the rain rate; hence the conditional distribution of sampling error is more informative than its marginal distribution. The distribution of sampling error conditional on rain rate is strongly affected by the sampling interval. At sampling intervals of 3 or 6 h, the logistic distribution appears to fit the conditional sampling error quite well, while the shifted-gamma, shifted-weibull, shifted-lognormal, and normal distributions fit poorly. At sampling intervals of 12 or 24 h, the shifted-gamma, shifted-weibull, or shifted-lognormal distribution fit the conditional sampling error better than the logistics or normal distribution. These results are vital to understanding the accuracy of satellite rainfall products, for performing validation assessment of these products, and for analyzing the effects of rainfall-related errors in hydrological models.     

The extreme value distribution of 5-min rainfall data at Belgrade

Summary For practical applications both the parent distribution of rainfall intensities and the distribution of their annual maxima are of interest. The relationship between these two distributions cannot be obtained from classical extreme value theory because of seasonal variation and serial correlation in the data. Mathematical results for the distribution of maxima in m-dependent sequences are presented to illustrate the effect of local dependence on the extreme value distribution. The average number of exceedances in a cluster is an important parameter in the relationship between the parent and the extreme value distribution. For 5-min rainfall data from Belgrade, quantiles of the annual maxima are overestimated by about 10 mm h^–1 if the effect of serial correlation is ignored. This bias can easily be removed by taking the local clustering of large rainfall intensities in a rainy spell into account.With 4 Figures