Preservation of rainfall properties in stochastic disaggregation by a simple random cascade model

We analyse properties of a simple discrete multiplicative random cascade model for rainfall disaggregation in urban hydrology. Two types of cascade models (canonical and microcanonical) are applied to the stochastic fine graining of rainfall observations into high resolution data. In particular, we analyse the disaggregation of 1280-min into 10-min data for a 20-year record period (Zurich raingauge, 1979–1998). Differences between the models and parameter estimation techniques are explored on simulated data with a special focus on three important properties of observed rainfall: distribution, intermittency, and extremes. The canonical models are overall better at preserving the distribution of rainfall at the 10-min scale. It is demonstrated that the growth of intermittency across scales is preserved well with all studied models. The ability of the models to reproduce rainfall extremes is a fundamental requirement in disaggregation. The studied models preserved annual rainfall maxima satisfactorily for short durations; however, the performance deteriorated for longer durations. The canonical models performed substantially better in capturing the variability in rainfall. The results are encouraging considering the parsimonious nature of the models and simple parameter estimation.     

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.     

Rainfall generator with spatial and temporal characteristics

The aim of this paper is to present a rainfall generator which takes both spatial and temporal characteristics into account. The statistical model behind the generator is based on long-time experience with statistical analyses of empirical rainfall data and represents, therefore, a genuine theoretical point for simulating series of precipitation values. The sites of the recording gauges and the actual time (day, month, year etc.) enter a statistical model as systematic components for the prediction of expected rainfall in a two-way analysis of variance design. Beyond these systematic components, spatial correlations among the observations are still present in nature, a feature which is modelled also by the rainfall generator.     

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.     

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。     

2004年主汛期各数值预报模式定量降水预报评估

随着数值预报技术的飞速发展, 模式定量降水预报已成为天气预报业务工作中的主要参考依据。本文对目前在国家气象中心应用的3个业务运行模式T213L31, HLAFS0.25, 华北中尺度模式MM5和德国模式及日本模式的降水预报产品进行了季节空间分布、区域时间序列演变及统计检验, 试图从空间、时间及统计方面对降水预报产品的预报性能进行综合评估。检验结果表明:目前的数值预报模式对短期时效内定量降水预报均具有一定的空间预报能力, 但强降水中心位置有一定的偏差; 从时间序列演变检验来看, 模式对区域强降水过程的发展趋势具有较强的预报能力, 但降水量预报与实况有一定的差距; 从累加统计评分检验结果来看, 模式短期时效的预报性能差别不大, 全球模式在小中雨预报方面有一定优势, 其中日本模式的综合预报性能最好, 大雨以上量级的预报则是国内的模式有一定的优势, 其中华北中尺度MM5模式, T213L31模式各有所长, 但均存在预报量和预报区偏大问题。     

基于南海夏季风季节内振荡的降水延伸预报试验

利用代表南海夏季风季节内振荡特征的850 hPa纬向风EOF分解的前两个主成分,定义南海夏季风季节内振荡指数,并利用美国国家环境预测中心第2代气候预报系统 (NCEP Climate Forecast System Version 2, NCEP/CFSv2) 提供的1982—2009年逐日回算预报场计算了南海夏季风季节内振荡指数的预报值,用于我国南方地区持续性强降水的预报试验。试验结果表明:利用南海夏季风季节内振荡实时监测指数与模式直接预报降水量相结合的统计动力延伸预报方法,能够有效提高季节内降水分量的预报效果。同时,该方法能够避免末端数据损失,修正了对模式预报降水直接进行带通滤波而导致的负相关现象,并起到消除模式系统误差的作用。     

Wavelet-based combination approach for modeling sub-divisional rainfall in India

Agriculture in India is highly sensitive to climatic variations particularly to rainfall and temperature; therefore, any change in rainfall and temperature will influence crop yields. An understanding of the spatial and temporal distribution and changing patterns in climatic variables is important for planning and management of natural resources. Time series analysis of climate data can be a very valuable tool to investigate its variability pattern and, maybe, even to predict short- and long-term changes in the series. In this study, the sub-divisional rainfall data of India during the period 1871 to 2016 has been investigated. One of the widely used powerful nonparametric techniques namely wavelet analysis was used to decompose and de-noise the series into time–frequency component in order to study the local as well as global variation over different scales and time epochs. On the decomposed series, autoregressive integrated moving average (ARIMA) and artificial neural network (ANN) models were applied and by means of inverse wavelet transform, the prediction of rainfall for different sub-divisions was obtained. To this end, empirical comparison was carried out toward forecast performance of the approaches namely Wavelet-ANN, Wavelet-ARIMA, and ARIMA. It is reported that Wavelet-ANN and Wavelet-ARIMA approach outperforms the usual ARIMA model for forecasting of rainfall for the data under consideration.     

Intermittency of turbulence within open canopies

Eddy covariance data have been analyzed to examine intermittency and clustering properties of turbulence within open canopies. Intermittency consists of two aspects: one is related to amplitude variation and the other to clustering. Using the telegraph approximation (TA), the clustering properties have been separated from amplitude effects. Intermittency of canopy turbulence has been explored via clustering exponent, probability density distribution of inter-pulse period of TA, intermittency exponent and structure kurtosis. Intermittency and clustering properties of turbulence within open canopies show similar features to those within dense canopy but some differences are also noted. Unlike within a dense canopy, temperature does not show larger clustering than velocity, which seems to be due to a different thermal structure of the sub-canopy and larger vertical scale of canopy eddy within open canopies. Within the crown region, the inter-pulse probability distribution of TA does not show the ‘double regime’ which was observed within the crown of a dense canopy, indicating less influence of near-field source on canopy turbulence within open canopies. For TA series of the flow variables, intermittency exponent is higher for temperature than for two velocity components within open canopies, which are opposite within a dense canopy. When comparing intermittency for flow variables and their TA series, it is shown that amplitude variation mitigates intermittency for both velocity components and temperature although amplitude variations play a much larger role in velocity intermittency than in temperature counterpart. Kurtosis analysis demonstrates that structure kurtosis is higher at large scales in stable conditions than in unstable conditions, indicating the existence of global intermittency due to stable stratification. The intermittency features of canopy turbulence within open canopies have been discussed in comparison with those within a dense canopy.     

An empirical model of decadal ENSO variability

This paper assesses potential predictability of decadal variations in the El Ni?o/Southern Oscillation (ENSO) characteristics by constructing and performing simulations using an empirical nonlinear stochastic model of an ENSO index. The model employs decomposition of global sea-surface temperature (SST) anomalies into the modes that maximize the ratio of interdecadal-to-subdecadal SST variance to define low-frequency predictors called the canonical variates (CVs). When the whole available SST time series is so processed, the leading canonical variate (CV-1) is found to be well correlated with the area-averaged SST time series which exhibits a non-uniform warming trend, while the next two (CV-2 and CV-3) describe secular variability arguably associated with a combination of Atlantic Multidecadal Oscillation (AMO) and Pacific Decadal Oscillation (PDO) signals. The corresponding ENSO model that uses either all three (CVs 1–3) or only AMO/PDO-related (CVs 2 and 3) predictors captures well the observed autocorrelation function, probability density function, seasonal dependence of ENSO, and, most importantly, the observed interdecadal modulation of ENSO variance. The latter modulation, and its dependence on CVs, is shown to be inconsistent with the null hypothesis of random decadal ENSO variations simulated by multivariate linear inverse models. Cross-validated hindcasts of ENSO variance suggest a potential useful skill at decadal lead times. These findings thus argue that decadal modulations of ENSO variability may be predictable subject to our ability to forecast AMO/PDO-type climate modes; the latter forecasts may need to be based on simulations of dynamical models, rather than on a purely statistical scheme as in the present paper.     

Characterization of Coherent structures in the Atmospheric Surface Layer

The ramplike coherent structures, observed in the temporal series of temperature and humidity in the atmospheric surface layer, are analyzed using the intermittency function and the wavelet transforms, with Haar, D4 and Mexican Hat functions as mother wavelets, in order to find the most efficient conditional sampling technique. It was found that the intermittency function and the wavelet transform, using Mexican Hat as mother wavelet, are the only ones that sample structures that fulfill the ramplike coherent structures definition of a slow rise followed by a sudden drop in the temporal series. The conditionally averaged structures detected by both techniques were similar for temperature, humidity, and vertical velocity at heights of 3, 5, and 9.4 m. Significant discrepancies were found among the conditional averaged structures detected by both techniques for zonal and meridional components of the wind at 11.5 m. Considering both techniques, it was observed that the averagedcoherent-structure duration ranged from 23.7 ± 0.5 s to 37.8 ± 3.0 s. Furthermore, the averaged number of events per 20-minute period ranged from 20.0 ± 1.0 to 28.5 ± 1.1, and the averaged intermittency factor from 45.0 ± 0.4% to 59.1 ± 1.3%. It was also observed that the averaged duration of the ramplike coherent structures increases with height, while their intensity, number, and intermittency factor decrease. Despite the good matching obtained for temperature and humidity, the coherent-structure properties did not show the expected variation with wind speed, stability parameter, and friction velocity. The Kolmogorov–Smirnov test indicated that the intermittent function and the wavelet transform did not detect coherent structures belonging to the same population.     

Selection of regional historical rainfall time series as input to urban drainage simulations at ungauged locations

It has become established practice during the past 20 years to use high-resolution historical rainfall time series as input to hydrological model packages for detailed simulation of urban drainage systems. However, sufficiently long rain series are rarely available from the exact catchment in question and simulations are hence often based on available rain series from other locations. Extreme rainfall properties of importance to the performance of urban storm drainage systems vary significantly even in regions with only minor physiographic differences. Part of this variation can be explained by regional variations of the mean annual rainfall and the remaining statistical residue can be interpreted as statistical uncertainty.In Denmark, more than 75 high-resolution rain gauges are installed across a total area of 43,000 m. About 40 gauges had sufficiently long records to be included in a comprehensive national investigation where newly developed statistical regionalisation procedures were used to model the regional variation of extreme rainfalls. On this basis, a spreadsheet model was made available for estimation of extreme design rainfalls and the associated uncertainty at any location in the country. Statistics were furthermore computed to classify historical rainfall time series according to the developed regional model, and this makes it possible to assess the uncertainty related with using different historical rain series for simulations at ungauged locations.This research indicates that use of historical point rainfall data at ungauged locations introduces a significant uncertainty that is largely overlooked in today's practice. The engineering recommendation is to select historical rain series based on an evaluation of the local physiographic characteristics (e.g., the mean annual rainfall) and a (pre-defined) desired safety level of the simulations.     

基于BCC_CSM模式的中国东部夏季降水预测检验及订正

基于国家气候中心第二代季节预测模式的历史回报试验数据,检验了模式对我国东部夏季降水的预测能力,探讨了预测误差形成的可能原因,并应用降尺度方法提高了模式的降水预测技巧。分析表明:（1）模式能在一定程度上把握我国东部夏季降水时空变率的两个主要模态（偶极子型模态和全区一致型模态）,但是不同超前时间的预测在刻画模态方差贡献、异常空间分布特征、时间系数的年际变化等方面存在明显误差;（2）模式能够合理预测大尺度环流和海表温度（SST）的变化特征,但是对中国东部夏季降水的总体预测技巧有限,这与模式不能准确刻画西太平洋副热带高压、大陆高压、中高纬阻塞高压等环流系统以及热带太平洋、印度洋SST变率对中国东部降水模态的影响有关;（3）针对1991~2003年回报试验数据中的500 hPa位势高度、850 hPa纬向风和经向风、SST变量,在全球范围内寻找并定位与中国东部站点降水关系最密切的预报因子,进而建立针对降水预测的单因子线性回归、多因子逐步和多元回归模型。采用2004~2013年回报试验对所建立的降水预测模型进行了独立检验,结果表明:所建立的降尺度预测模型能显著提高中国东部地区夏季降水的预报技巧。以6月1日起报试验为例,预测的第一模态（第二模态）与观测的空间相关系数由原始的0.12（0.48）提高到了0.58（0.80）,时间相关系数则从0.47（0.15）提高到0.80（0.67）;其它超前时间的预测试验中,降尺度预测模型的降水预测技巧相比模式原始预测技巧也同样明显提高。     

Variability and teleconnections of South and East Asian summer monsoons in present and future projections of CMIP5 climate models

Coupled Model Inter-comparison Project Phase 5 (CMIP5) model outputs of the South and East Asian summer monsoon variability and their tele-connections are investigated using historical simulations (1861-2005) and future projections under the RCP4.5 scenario (2006-2100). Detailed analyses are performed using nine models having better representation of the recent monsoon teleconnections for the interactive Asian monsoon sub-systems. However, these models underestimate rainfall mainly over South Asia and Korea-Japan sector, the regions of heavy rainfall, along with a bias in location of rainfall maxima. Indeed, the simulation biases, underestimations of monsoon variability and teleconnections suggest further improvements for better representation of Asian monsoon in the climate models. Interestingly, the performance of Australian Community Climate and Earth System Simulator version 1.0 (ACCESS1.0) in simulating the annual cycle, spatial pattern of rainfall and multi-decadal variations of summer monsoon rainfall over South and East Asia appears to more realistic. In spite of large spread among the CMIP5 models, historical simulations as well as future projections of summer monsoon rainfall indicate multi-decadal variability. These rainfall variations, displaying certain epochs of more rainfall over South Asia than over East Asia and vice versa, suggest an oscillatory behaviour. Teleconnections between South and East Asian monsoon rainfall also exhibit a multi-decadal variation with alternate epochs of strengthening and weakening relationship. Furthermore, large-scale circulation features such as South Asian monsoon trough and north Pacific subtropical high depict zonal oscillatory behaviour with east-west-east shifts. Periods with eastward or westward extension of the Mascarene High, intensification and expansion of the upper tropospheric South Asian High are also projected by the CMIP5 models.     

Forecasting quantitative rainfall over India using multi-model ensemble technique

A new approach to ensemble forecasting of rainfall over India based on daily outputs of four operational numerical weather prediction (NWP) models in the medium-range timescale (up to 5 days) is proposed in this study. Four global models, namely ECMWF, JMA, GFS and UKMO available on real-time basis at India Meteorological Department, New Delhi, are used simultaneously with adequate weights to obtain a multi-model ensemble (MME) technique. In this technique, weights for each NWP model at each grid point are assigned on the basis of unbiased mean absolute error between the bias-corrected forecast and observed rainfall time series of 366 daily data of 3 consecutive southwest monsoon periods (JJAS) of 2008, 2009 and 2010. Apart from MME, a simple ensemble mean (ENSM) forecast is also generated and experimented. The prediction skill of MME is examined against observed and corresponding outputs of each constituent model during monsoon 2011. The inter-comparison reveals that MME is able to provide more realistic forecast of rainfall over Indian monsoon region by taking the strength of each constituent model. It has been further found that the weighted MME technique has higher skill in predicting daily rainfall compared to ENSM and individual member models. RMSE is found to be lowest in MME forecasts both in magnitude and area coverage. This indicates that fluctuations of day-to-day errors are relatively less in the MME forecast. The inter-comparison of domain-averaged skill scores for different rainfall thresholds further clearly demonstrates that the MME algorithm improves slightly above the ENSM and member models.     

A dataset of future daily weather data for crop modelling over Europe derived from climate change scenarios

Coupled atmosphere-ocean general circulation models (GCMs) simulate different realizations of possible future climates at global scale under contrasting scenarios of land-use and greenhouse gas emissions. Such data require several additional processing steps before it can be used to drive impact models. Spatial downscaling, typically by regional climate models (RCM), and bias-correction are two such steps that have already been addressed for Europe. Yet, the errors in resulting daily meteorological variables may be too large for specific model applications. Crop simulation models are particularly sensitive to these inconsistencies and thus require further processing of GCM-RCM outputs. Moreover, crop models are often run in a stochastic manner by using various plausible weather time series (often generated using stochastic weather generators) to represent climate time scale for a period of interest (e.g. 2000 ± 15 years), while GCM simulations typically provide a single time series for a given emission scenario. To inform agricultural policy-making, data on near- and medium-term decadal time scale is mostly requested, e.g. 2020 or 2030. Taking a sample of multiple years from these unique time series to represent time horizons in the near future is particularly problematic because selecting overlapping years may lead to spurious trends, creating artefacts in the results of the impact model simulations. This paper presents a database of consolidated and coherent future daily weather data for Europe that addresses these problems. Input data consist of daily temperature and precipitation from three dynamically downscaled and bias-corrected regional climate simulations of the IPCC A1B emission scenario created within the ENSEMBLES project. Solar radiation is estimated from temperature based on an auto-calibration procedure. Wind speed and relative air humidity are collected from historical series. From these variables, reference evapotranspiration and vapour pressure deficit are estimated ensuring consistency within daily records. The weather generator ClimGen is then used to create 30 synthetic years of all variables to characterize the time horizons of 2000, 2020 and 2030, which can readily be used for crop modelling studies.     

A new daily weather generator to preserve extremes and low-frequency variability

This paper addresses deficiencies of stochastic Weather Generators (WGs) in terms of reproduction of low-frequency variability and extremes, as well as the unanticipated effects of changes to precipitation occurrence under climate change scenarios on secondary variables. A new weather generator (named IWG) is developed in order to resolve such deficiencies and improve WGs performance. The proposed WG is composed of three major components, including a stochastic rainfall model able to reproduce realistic rainfall series containing extremes and inter-annual monthly variability, a multivariate daily temperature model conditioned to the rainfall occurrence, and a suitable multi-variate monthly generator to fit the low-frequency variability of daily maximum and minimum temperature series. The performance of IWG was tested by comparing statistical characteristics of the simulated and observed weather data, and by comparing statistical characteristics of the simulated runoff outputs by a daily rainfall-runoff model fed by the generated and observed weather data. Furthermore, IWG outputs are compared with those of the well-known LARS-WG weather generator. The tested characteristics are a variety of different daily statistics, low-frequency variability, and distribution of extremes. It is concluded that the performance of the IWG is acceptable, better than LARS-WG in the majority of tests, especially in reproduction of extremes and low-frequency variability of weather and runoff series.     

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.     

澳门单站气象资料变化趋势的预报模型之比较

以澳门单站年和四季降水和温度两个气象要素的气象资料(1952~2001年)为主要研究对象,利用3种统计预报模型(谐波分析外推模型、开环门限自回归模型和主分量因子的逐步回归模型)进行拟合及试报,对澳门的降水及温度的变化做较深入的分析及预测,比较3种统计预报模型在研究澳门单站气象资料的变化趋势中的优劣。结果发现,3种预报模型在预报年和四季平均气温的方面都比较理想,但对降水量变化序列做拟合及试报则差异较大。总体而言,气候场的主分量逐步回归法对相同的气候资料建模做拟合及试报,结果拟合率是三者中最高的,复相关为0.821~0.911,预报效果除秋季较差外,其余都非常好。     

Intermittent convection, mixed boundary conditions and the stability of the thermohaline circulation

 Intermittent convection and its consequences on the stability of the thermohaline circulation are investigated with an oceanic global circulation model (OGCM) and simple box models. A two-box model shows that intermittency is a consequence of the non-linearity of the equation of state and of the ratio of heat and freshwater fluxes at surface versus the fluxes at depth. Moreover, it only occurs in areas, where the instability of the water column is caused by temperature or by salinity. Intermittency is not necessarily suppressed by long restoring times. Because intermittent convection causes temporal variations of the ocean-atmosphere fluxes, an OGCM cannot reach an exact equilibrium. After a switch to mixed boundary conditions, changes of the convective activity occur in areas where intermittency is observed. Intermittent convection becomes either continuous or is stopped depending on the method used for calculating the freshwater fluxes. Advective and diffusive fluxes between these regions and their surroundings change in order to balance the altered convective fluxes. A comparison between the OGCM and a six-box model illustrates that this may lead to an alteration of adjacent deep convection and of the related deep water formation. Received: 4 November 1997 / Accepted: 5 November 1998