A fine-scale point process model of rainfall with dependent pulse depths within cells

Abstract

A cluster point process model is considered for the analysis of fine-scale rainfall time series. The model is based on three Poisson processes. The first is a Poisson process of storm origins, where each storm has a random (exponential) lifetime. The second is a Poisson process of cell origins that occur during the storm lifetime, terminating when the storm finishes. Each cell has a random lifetime that follows an exponential distribution (or terminates when the storm terminates, whichever occurs first). During cell lifetimes, a third Poisson process of instantaneous pulses occurs. The model is essentially an extension of the well-known Bartlett-Lewis rectangular pulses model, with the rectangular profiles replaced with a Poisson process of instantaneous pulse depths to ensure more realistic rainfall profiles for fine-scale series. Model equations, derived in Cowpertwait et al. (2007 Cowpertwait, P., Isham, V. and Onof, C. 2007. Point process models of rainfall: developments for fine-scale structure. Proceedings of the Royal Society of London, Series A, 463: 2569–2587. [Crossref], [Web of Science ®] , [Google Scholar]), are used to fit different sets of properties to a 60 year record of 5-min data taken from Kelburn, New Zealand. As in the previous work, two superposed processes are used to account for two main and distinct precipitation types (convective and stratiform). By treating the within-cell pulses as dependent random variables, it is found, by simulation, that improved fits to extreme values and the proportion of dry intervals are obtained.

Citation Cowpertwait, P. S. P., Xie, G., Isham, V., Onof, C. & Walsh, D. C. I. (2011) A fine-scale point process model of rainfall with dependent pulse depths within cells. Hydrol. Sci. J. 56(7), 1110–1117.     

Spatial-temporal rainfall modelling for flood risk estimation

Some recent developments in the stochastic modelling of single site and spatial rainfall are summarised. Alternative single site models based on Poisson cluster processes are introduced, fitting methods are discussed, and performance is compared for representative UK hourly data. The representation of sub-hourly rainfall is discussed, and results from a temporal disaggregation scheme are presented. Extension of the Poisson process methods to spatial-temporal rainfall, using radar data, is reported. Current methods assume spatial and temporal stationarity; work in progress seeks to relax these restrictions. Unlike radar data, long sequences of daily raingauge data are commonly available, and the use of generalized linear models (GLMs) (which can represent both temporal and spatial non-stationarity) to represent the spatial structure of daily rainfall based on raingauge data is illustrated for a network in the North of England. For flood simulation, disaggregation of daily rainfall is required. A relatively simple methodology is described, in which a single site Poisson process model provides hourly sequences, conditioned on the observed or GLM-simulated daily data. As a first step, complete spatial dependence is assumed. Results from the River Lee catchment, near London, are promising. A relatively comprehensive set of methodologies is thus provided for hydrological application.     

A class of hidden Markov models for regional average rainfall

Abstract

Basic hidden Markov models are very useful in stochastic environmental research but their ability to accommodate sufficient dependence between observations is somewhat limited. However, they can be modified in several ways to form a rich class of flexible models that are useful in many environmental applications. We consider a class of hidden Markov models that incorporate additional dependence among observations to model average regional rainfall time series. The focus of the study is on models that introduce additional dependence between the state level and the observation level of the process and also on models that incorporate dependence at observation level. Construction of the likelihood function of the models is described along with the usual second-order properties of the process. The maximum likelihood method is used to estimate the parameters of the models. Application of the proposed class of models is illustrated in an analysis of daily regional average rainfall time series from southeast and southwest England for the winter season during 1931 to 2010. Models incorporating additional dependence between the state level and the observation level of the process captured the distributional properties of the daily rainfall well, while the models that incorporate dependence at the observation level showed their ability to reproduce the autocorrelation structure. Changes in some of the regional rainfall properties during the time period are also studied.

Editor D. Koutsoyiannis     

On the potential of Bartlett Lewis rectangular pulse models for simulating rainfall in Peninsular Malaysia

Abstract

The applicability of two versions of the Bartlett Lewis rectangular pulse model, the original and the modified model, is discussed for describing the temporal and spatial variation of rainfall patterns observed at 15 raingauge stations in Peninsular Malaysia over the period 1971–2008; 17 different sets of moment combinations are fitted to these models based on the generalized method of moments approach. The common statistics included in all sets are the mean, variance, lag-1 autocorrelation and the probability of dry based on the hourly rainfall data. The analysis was carried out on hourly rainfall data from all 15 stations for all months of the year. Two stations, Petaling Jaya and Kemaman, located on the west and east coasts of the Peninsula, respectively, are considered for illustration of the results, taking the months of July and November, which correspond to the driest and wettest months, corresponding to the southwest monsoon (May–August) and northeast monsoon (November–February), respectively. The best moment combination found for the illustrative results is based on the common statistics, as well as the mean and variance based on 24-h aggregated rainfall data, the inclusion of which successfully improved the model performance; the errors were significantly reduced. It was also found that the performance of the fitted models based on the mean absolute deviate error varies according to the type of Bartlett Lewis model applied: errors are much smaller for the fitted model based on the modified model as compared to the original model. In addition, the fitted statistics: mean, lag-1 autocorrelation and probability of dry are quite well fitted for several aggregated time scales; however, the variances are underestimated in both models for all aggregated time scales, particularly in the case of the original model. The results of extreme value analysis indicate that the modified model failed to reproduce the annual hourly and daily rainfall extremes satisfactorily.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Hanaish, I.S., Ibrahim, K., and Jemain, A.A., 2013. On the potential of Bartlett Lewis rectangular pulse models for simulating rainfall in Peninsular Malaysia. Hydrological Sciences Journal, 58 (8), 1690–1703.     

A spatial–temporal point process model of rainfall for the Thames catchment, UK

A spatial–temporal point process model of rainfall is fitted to data taken from 23 sites across the Thames catchment, London. For the period January 1970 to December 1988 the sites have daily data, whilst for the period January 1989 to November 2003 the sites have hourly data. In addition, the records contain missing values. The fitted model is used to infill the missing values, to disaggregate the daily data to hourly data and to generate spatially consistent series at a further 25 sites across the catchment. The model is validated by considering statistical properties that are not used in the fitting procedure, which include extreme values, the proportion of dry intervals, and annual totals. Overall the performance of the model is good, with the exception of an over-estimation in cross-correlation between pairs of sites for the disaggregated series.     

Propagation of uncertainty from rainfall to runoff: A case study with a stochastic rainfall generator

We explore the impact of uncertainties in the spatial–temporal distribution of rainfall on the prediction of peak discharge in a typical mountain basin. To this end, we use a stochastic generator previously developed for rainfall downscaling, and we estimate the basin response by adopting a semi-distributed hydrological model. The results of the analysis provide information on the minimum rainfall resolution needed for operational flood forecasting, and confirm the sensitivity of peak discharge estimates to errors in the determination of the power spectrum of the precipitation field.     

Simulation and spatio-temporal disaggregation of multi-site rainfall data for urban drainage applications

Abstract

For urban drainage and urban flood modelling applications, fine spatial and temporal rainfall resolution is required. Simulation methods are developed to overcome the problem of data limitations. Although temporal resolution higher than 10–20 minutes is not well suited for detailed rainfall—runoff modelling for urban drainage networks, in the absence of monitored data, longer time intervals can be used for master planning or similar purposes. A methodology is presented for temporal disaggregation and spatial distribution of hourly rainfall fields, tested on observations for a 10-year period at 16 raingauges in the urban catchment of Dalmuir (UK). Daily rainfall time series are simulated with a generalized linear model (GLM). Next, using a single-site disaggregation model, the daily data of the central gauge in the catchment are downscaled to an hourly time scale. This hourly pattern is then applied linearly in space to disaggregate the daily data into hourly rainfall at all sites. Finally, the spatial rainfall field is obtained using inverse distance weighting (IDW) to interpolate the data over the whole catchment. Results are satisfactory: at individual sites within the region the simulated data preserve properties that match the observed statistics to an acceptable level for practical purposes.     

On the influence of microphysics parametrization on the rainfall rates in numerical models of clouds

Accuracy of formulas for growth by accretion and evaporation of rain in bulk parametrization of these processes for the case of light and moderate precipitation is investigated. It is done by comparison of results from two simple models: with bulk approach and with exact calculations of growth or evaporation of drops in each size bin separately. Growth by accretion is accurately represented in bulk parametrization but rain evaporation is overpredicted. Corrected formula for rain evaporation is suggested.     

北京精细下垫面信息引入对暴雨模拟的影响

首先根据2000年环北京实际的精细下垫面布局资料（500m分辨率）,按美国USGS陆面资料分类标准（25类）对其提供的全球30 s经纬分辨率（≈1 km）下垫面分类资料进行了更新设计.进而针对一个北京夏季暴雨过程,利用10:3.3km双向双重嵌套的MM5V3.6-Noah LSM陆气耦合模式进行24h数值对比试验,研究了北京精细下垫面信息引入对暴雨的影响.分析表明：新设计的陆面资料更真实地反映了环北京区域的下垫面结构,尤其针对北京城区面积迅增特征;同时还修正了原资料将亚洲中纬度区域落叶阔叶林下垫面类型归属为热带(或亚热带)稀疏大草原类型的问题.其在数值天气模式中的引入会对短期暴雨过程的发生发展产生重要影响.对此次暴雨主要降水中心的模拟,12h差值分布范围远达30km以上,中心值相对差异可达30%.研究发现在城市下垫面和大气相互间存在一个重要的相互影响机制,即由于城区面积的扩大会导致自然植被减少,进而会减少地表蒸发及相应局地大气水分供应、加深边界层高度并增强大气水汽混合,这不利于降水的发生发展.     

Identification of physical processes inherent in artificial neural network rainfall runoff models

The emergence of artificial neural network (ANN) technology has provided many promising results in the field of hydrology and water resources simulation. However, one of the major criticisms of ANN hydrologic models is that they do not consider/explain the underlying physical processes in a watershed, resulting in them being labelled as black‐box models. This paper discusses a research study conducted in order to examine whether or not the physical processes in a watershed are inherent in a trained ANN rainfall‐runoff model. The investigation is based on analysing definite statistical measures of strength of relationship between the disintegrated hidden neuron responses of an ANN model and its input variables, as well as various deterministic components of a conceptual rainfall‐runoff model. The approach is illustrated by presenting a case study for the Kentucky River watershed. The results suggest that the distributed structure of the ANN is able to capture certain physical behaviour of the rainfall‐runoff process. The results demonstrate that the hidden neurons in the ANN rainfall‐runoff model approximate various components of the hydrologic system, such as infiltration, base flow, and delayed and quick surface flow, etc., and represent the rising limb and different portions of the falling limb of a flow hydrograph. Copyright © 2004 John Wiley & Sons, Ltd.     

Sensitivity of hydrological models to uncertainty in rainfall input

Abstract

Different approaches used in hydrological modelling are compared in terms of the way each one takes the rainfall data into account. We examine the errors associated with accounting for rainfall variability, whether in hydrological modelling (distributed vs lumped models) or in computing catchment rainfall, as well as the impact of each approach on the representativeness of the parameters it uses. The database consists of 1859 rainfall events, distributed on 500 basins, located in the southeast of France with areas ranging from 6.2 to 2851 km². The study uses as reference the hydrographs computed by a distributed hydrological model from radar rainfall. This allows us to compare and to test the effects of various simplifications to the process when taking rainfall information (complete rain field vs sampled rainfall) and rainfall–runoff modelling (lumped vs distributed) into account. The results appear to show that, in general, the sampling effect can lead to errors in discharge at the outlet that are as great as, or even greater than, those one would get with a fully lumped approach. We found that small catchments are more sensitive to the uncertainties in catchment rainfall input generated by sampling rainfall data as seen through a raingauge network. Conversely, the larger catchments are more sensitive to uncertainties generated when the spatial variability of rainfall events is not taken into account. These uncertainties can be compensated for relatively easily by recalibrating the parameters of the hydrological model, although such recalibrations cause the parameter in question to completely lose physical meaning.

Citation Arnaud, P., Lavabre, J., Fouchier, C., Diss, S. & Javelle, P. (2011) Sensitivity of hydrological models to uncertainty of rainfall input. Hydrol. Sci. J. 56(3), 397–410.     

A conceptually based stochastic point process model for daily stream‐flow generation

Based on the stochastic and phenomenological aspects of hydrological processes, a conceptually based stochastic point process (SPP) model for daily stream‐flow generation is proposed in this paper. In which, storms are defined by a stochastic point process with marked values. All the random variables defining the process are assumed to be mutually independent, which constitutes a compound Poisson point process. The direct surface runoff is regarded as occurring from storage in a cascade of surface linear reservoirs and is responsible for the short‐term variation of the daily stream flows. The baseflow component is considered as coming from subsurface/groundwater storage and is responsible for the long‐term persistence of the storm time‐series. This type of model is proposed as a more realistic model of daily stream flow than models based on pure stochastic processes. Studies on the instantaneous unit hydrograph and the mechanism of baseflow could thereby provide some parameters for this model. Copyright © 2002 John Wiley & Sons, Ltd.     

Evaluating the performance of climate models in reproducing the hydrological characteristics of rainfall events

ABSTRACT

Rainfall events largely control hydrological processes occurring on and in the ground, but the performance of climate models in reproducing rainfall events has not been investigated enough to guide selection among the models when making hydrological projections. We proposed to compare the durations, intensities, and pause periods, as well as depths of rainfall events when assessing the accuracy of general circulation models (GCMs) in reproducing the hydrological characteristics of observed rainfall. We also compared the sizes of design storm events and the frequency and severity of drought to demonstrate the consequences of GCM selection. The results show that rainfall and extreme hydrological event projections could significantly vary depending on climate model selection and weather stations, suggesting the need for a careful and comprehensive evaluation of GCM in the hydrological analysis of climate change. The proposed methods are expected to help to improve the accuracy of future hydrological projections for water resources planning.     

Run off-on-out method and models for soil infiltrability on hill-slope under rainfall conditions

Infiltration is the process of water penetrating into soil, generally referred to as the downward movement of water from the soil surface[1,2]. This process is af-fected by water supply and the soil infiltrability, de-termines the amounts of water entering into soil pro-file and the surface runoff. Infiltrability is defined as the infiltration flux of a unit area under atmospheric pressure and sufficient water supply. The actual infil-tration rate and/or the infiltrability is expressed in m/s …     

Integrative stochastic model standardization with genetic algorithm for rainfall pattern forecasting in tropical and semi-arid environments

ABSTRACT

Climate patterns, including rainfall prediction, is one of the most complex problems for hydrologist. It is inherited by its natural and stochastic phenomena. In this study, a new approach for rainfall time series forecasting is introduced based on the integration of three stochastic modelling methods, including the seasonal differencing, seasonal standardization and spectral analysis, associated with the genetic algorithm (GA). This approach is specially tailored to eradicate the periodic pattern effects notable on the rainfall time series stationarity behaviour. Two different climates are selected to evaluate the proposed methodology, in tropical and semi-arid regions (Malaysia and Iraq). The results show that the predictive model registered an acceptable result for the forecasting of rainfall for both the investigated regions. The attained determination coefficient (R²) for the investigated stations was approx. 0.91, 0.90 and 0.089 for Mosul, Baghdad and Basrah (Iraq), and 0.80, 0.87 and 0.94 for Selangor, Negeri Sembilan and Johor (Malaysia).     

Effect of rainfall uncertainty on the performance of physically based rainfall–runoff models

This paper analyses the effect of rain data uncertainty on the performance of two hydrological models with different spatial structures: a semidistributed and a fully distributed model. The study is performed on a small catchment of 19.6 km² located in the north‐west of Spain, where the arrival of low pressure fronts from the Atlantic Ocean causes highly variable rainfall events. The rainfall fields in this catchment during a series of storm events are estimated using rainfall point measurements. The uncertainty of the estimated fields is quantified using a conditional simulation technique. Discharge and rain data, including the uncertainty of the estimated rainfall fields, are then used to calibrate and validate both hydrological models following the generalized likelihood uncertainty estimation (GLUE) methodology. In the storm events analysed, the two models show similar performance. In all cases, results show that the calibrated distribution of the input parameters narrows when the rain uncertainty is included in the analysis. Otherwise, when rain uncertainty is not considered, the calibration of the input parameters must account for all uncertainty in the rainfall–runoff transformation process. Also, in both models, the uncertainty of the predicted discharges increase in similar magnitude when the uncertainty of rainfall input increase.     

Probabilistic radar rainfall nowcasts using empirical and theoretical uncertainty models

Weather radar has a potential to provide accurate short‐term (0–3 h) forecasts of rainfall (i.e. radar nowcasts), which are of great importance in warnings and risk management for hydro‐meteorological events. However, radar nowcasts are affected by large uncertainties, which are not only linked to limitations in the forecast method but also because of errors in the radar rainfall measurement. The probabilistic quantitative precipitation nowcasting approach attempts to quantify these uncertainties by delivering the forecasts in a probabilistic form. This study implements two forms of probabilistic quantitative precipitation nowcasting for a hilly area in the south of Manchester, namely, the theoretically based scheme [ensemble rainfall forecasts (ERF)‐TN] and the empirically based scheme (ERF‐EM), and explores which one exhibits higher predictive skill. The ERF‐TN scheme generates ensemble forecasts of rainfall in which each ensemble member is determined by the stochastic realisation of a theoretical noise component. The so‐called ERF‐EM scheme proposed and applied for the first time in this study, aims to use an empirically based error model to measure and quantify the combined effect of all the error sources in the radar rainfall forecasts. The essence of the error model is formulated into an empirical relation between the radar rainfall forecasts and the corresponding ‘ground truth’ represented by the rainfall field from rain gauges measurements. The ensemble members generated by the two schemes have been compared with the rain gauge rainfall. The hit rate and the false alarm rate statistics have been computed and combined into relative operating characteristic curves. The comparison of the performance scores for the two schemes shows that the ERF‐EM achieves better performance than the ERF‐TN at 1‐h lead time. The predictive skills of both schemes are almost identical when the lead time increases to 2 h. In addition, the relation between uncertainty in the radar rainfall forecasts and lead time is also investigated by computing the dispersion of the generated ensemble members. Copyright © 2013 John Wiley & Sons, Ltd.     

Incorporating rainfall intensity into daily rainfall records for simulating runoff and infiltration into soil profiles

Hydrological modelling often implies the use of rainfall data. Its quality and resolution directly affect the accuracy of the simulation results. This study illustrates that a simple approach of incorporating rainfall intensity information in daily rainfall records significantly improves the simulation of surface runoff and rainfall infiltration into soil profiles. The procedure is developed using a frequency analysis on rainfall data of the Royal Meteorological Institute of Belgium, collected with a resolution of 10 min and for a consecutive period of 61 years. The frequency analysis of the data allowed the incorporation of rainfall intensity information into daily rainfall records. To test the effect of this approach the surface runoff and water flow into three different soil types was simulated using the HYDRUS‐1D model for a typical dry, normal and wet year. The simulation results whereby the observed 10‐min rainfall data was used as input were considered as the reference. Comparative analysis revealed that the simulations using the 10 min rainfall data deducted from the incorporation of rainfall intensity into daily rainfall records, deviate a maximum 1·2% from the reference and produce much better results than the Soil Conservation Service (SCS) runoff curve‐number method because rainfall intensity is considered in the procedure presented. The SCS curve‐number method typical overestimates surface runoff during periods of low rainfall intensity (winter) and underestimate runoff during periods of high rainfall intensities (summer). Copyright © 2002 John Wiley & Sons, Ltd.     

Automated rainfall simulator for variable rainfall on urban green areas

Rainfall simulators can enhance our understanding of the hydrologic processes affecting the total runoff to urban drainage systems. This knowledge can be used to improve urban drainage designs. In this study, a rainfall simulator is developed to simulate rainfall on urban green surfaces. The rainfall simulator is controlled by a microcomputer programmed to replicate the temporal variations in rainfall intensity of both historical and synthetic rainfall events with constant rainfall intensity on an area of 1 m². The performance of the rainfall simulator is tested under laboratory conditions with regard to spatial uniformity of the rainfall, the kinetic energy of the raindrops, and the ability to replicate historical and synthetic rainfall events with temporally varying intensity. The rainfall simulator is applied in the field to evaluate its functionality under field conditions and the influence of wind on simulated rainfall. Finally, a field study is carried out on the relationship between runoff, soil volumetric water content, and surface slope. Performance and field tests show that the simulated rainfall has a uniform spatial distribution, whereas the kinetic energy of the raindrops is slightly higher than that of other comparable rainfall simulators. The rainfall simulator performs best in low wind speed conditions. The simulator performs well in replicating historical and synthetic rainfall events by matching both intensity variations and accumulated rainfall depth. The field study shows good correlation between rainfall, runoff, infiltration, soil water content, and surface slope.