Elevation effects on rainfall: A stochastic model

The variation in point precipitation with elevation is investigated using an event-based stochastic model of thunderstorm rainfall and empirical data. Parameters of the model correspond to the number of events per unit of time and the depth of rainfall per event. An increase in precipitation with elevation may be due to an increase in the number of events, in the amount of rainfall per event or to some combination of both possibilities. The distribution of the number of events per season is assumed to be a Poisson variate while the distribution of point rainfall depths may be taken as geometric. The summation of a random number of random variables is used to represent seasonal point precipitation. Assuming that the two parameters of the model increase linearly with elevation, then total seasonal rainfall increases as a quadratic polynomial with elevation. The use of the model allows one to obtain the return period of storm rainfall of a given magnitude despite a short historical record. An independent set of data was used to verify the procedure.     

A stochastic model describing the impact of daily rainfall depth distribution on the soil water balance

Simplified, vertically-averaged soil moisture models have been widely used to describe and study eco-hydrological processes in water-limited ecosystems. The principal aim of these models is to understand how the main physical and biological processes linking soil, vegetation, and climate impact on the statistical properties of soil moisture. A key component of these models is the stochastic nature of daily rainfall, which is mathematically described as a compound Poisson process with daily rainfall amounts drawn from an exponential distribution. Since measurements show that the exponential distribution is often not the best candidate to fit daily rainfall, we compare the soil moisture probability density functions obtained from a soil water balance model with daily rainfall depths assumed to be distributed as exponential, mixed-exponential, and gamma. This model with different daily rainfall distributions is applied to a catchment in New South Wales, Australia, in order to show that the estimation of the seasonal statistics of soil moisture might be improved when using the distribution that better fits daily rainfall data. This study also shows that the choice of the daily rainfall distributions might considerably affect the estimation of vegetation water-stress, leakage and runoff occurrence, and the whole water balance.     

A stochastic model for tropical rainfall at a single location

Modelling data that correspond to rainfall accumulated over fixed periods of time presents the challenging problem of dealing with a random variable that has a point mass at zero which corresponds to dry periods that occur with positive probability. One way to overcome this difficulty is to assume that the data correspond to a normal variate w, that has been truncated and transformed. The dry periods correspond to the (unobserved) negative values and the wet periods correspond to some power of the positive ones. The serial structure that is present in rainfall can be modelled by imposing a serial structure to w. We use a dynamic linear model on w using a Fourier representation to allow for the seasonality of the data, which in the case of tropical rainfall is very marked. The model is fitted using a Markov chain Monte Carlo method that uses latent variables to handle both dry periods and missing values. We use the model to estimate and predict both the amount of rainfall and the probability of a dry period. The method is illustrated with data collected in the Venezuelan state of Guárico.     

考虑降雨空间变化的随机产汇流模型

引入两个负指数型差值函数,估计降雨量的概率分布,以此描述流域降雨空间变异性问题.将降雨量空间统计分布与垂向混合产流模型耦合进行产流量计算,即对地表径流,采用超渗产流模式,根据降雨与土壤下渗能力的联合分布推求其空间分布;对地面以下径流,采用蓄满产流模式,以地表渗入量的均值作为输入,进行简化处理以提高其实用性;最终推导出总产流量概率分布函数计算公式.将流域概化成一个线性水库,并根据随机微分方程理论,推导任一计算时段洪水流量的概率分布,从而构建了一个完整的随机产汇流模型.以淮河支流黄泥庄流域为例进行应用研究,结果表明,该模型可提供洪水过程的概率预报,可用于防洪风险分析,若以概率分布的期望值作为确定性预报,亦具有较高精度.     

Evidence of large rainfall partitioning patterns by banana and impact on surface runoff generation

In this article the effect of redistribution of rainfall by banana on local water fluxes and the possible impact of these fluxes on surface runoff has been studied. First the water redistribution by a banana canopy at three development stages (vegetative, flowering, and bunch stage) was measured. The results showed a considerable stemflow, proportional to the leaf area index (LAI), which represented 18 to 26% of the incident rainfall volume according to the age of the crop. Consequently, the rainfall rate was 28‐fold higher at the plant collar for a fully developed banana canopy. For the throughfall, on average, the higher the LAI, the lower the mean throughfall. In addition, the spatial distribution of the throughfall varied according to the distance from the pseudostem. Notably, for the earlier stages, the area between the pseudostem and 0·5 m from it received weak throughfall. Secondly, simulations were carried out with a simple two‐compartment model simulating the total surface runoff volume. The simulations showed stemflow combined with the agronomical practice of furrowing has an effect on runoff compared to bare soil. A relative increase in surface runoff volume of three‐fold was encountered on a plot with a fully developed banana and a infiltration rate of 60 mm h^?1. However, the absolute increase was only a few percentage of the incident rainfall volume, although it represented large water volumes given the tropical rains. These features must be taken into account for hydrological management of such systems. Copyright © 2007 John Wiley & Sons, Ltd.     

Application of a stochastic model to the frequency and duration of monsoon rainfall

The paper deals with an application of a stochastic model to the frequency and duration of precipitation events. With the aid of the model, the magnitudes ofmth highest rainfall amount in 24 hours' duration with 97.5% probability are obtained for various climatic regimes over a tropical monsoon region. There is good agreement between them-day minimum rainfall estimated through the model and the observed value. The model satisfactorily explains the frequency of the extreme rainfall event.     

A Monte Carlo study of rainfall forecasting with a stochastic model

A procedure for short-term rainfall forecasting in real-time is developed and a study of the role of sampling on forecast ability is conducted. Ground level rainfall fields are forecasted using a stochastic space-time rainfall model in state-space form. Updating of the rainfall field in real-time is accomplished using a distributed parameter Kalman filter to optimally combine measurement information and forecast model estimates. The influence of sampling density on forecast accuracy is evaluated using a series of a simulated rainfall events generated with the same stochastic rainfall model. Sampling was conducted at five different network spatial densities. The results quantify the influence of sampling network density on real-time rainfall field forecasting. Statistical analyses of the rainfall field residuals illustrate improvement in one hour lead time forecasts at higher measurement densities.     

Multisite generalization of a daily stochastic precipitation generation model

The familiar chain-dependent-process stochastic model of daily precipitation, consisting of a two-state, first-order Markov chain for occurrences and a mixed exponential distribution for nonzero amounts, is extended to simultaneous simulation at multiple locations by driving a collection of individual models with serially independent but spatially correlated random numbers. The procedure is illustrated for a network of 25 locations in New York state, with interstation separations ranging approximately from 10 to 500 km. The resulting process reasonably reproduces various aspects of the joint distribution of daily precipitation observations at the modeled locations. The mixed exponential distributions, in addition to providing substantially better fits than the more conventional gamma distributions, are convenient for representing the tendency for smaller amounts at locations near the edges of wet areas. Means, variances, and interstation correlations of monthly precipitation totals are also well reproduced. In addition, the use of mixed exponential rather than gamma distributions yields interannual variability in the synthetic series that is much closer to the observed.     

Unsteady soil erosion due to rainfall impact: a model of sediment sorting on the hillslope

A new method is presented for predicting sediment sorting associated with soil erosion by raindrop impact for non-equilibrium conditions. The form of soil erosion considered is that which results from raindrop impact in the presence of shallow overland flow itself where the flow is not capable of eroding sediment. The method specifically considers early time runoff and erosion when sediment leaving an eroding area is generally finer and thus may have a higher potential for transport of sorbed pollutants. The new mechanism described is the formation of a deposited layer on the soil surface, which is shown to lead to sediment sorting during an erosion event. The deposited layer is taken to have two roles in this process: to temporarily store sediment on the surface between successive trajectories, and to shield the underlying soil from erosive stresses. Equations describing the dynamics of the suspended sediment mixture and the deposited layer are developed. By integrating these equations over the length of eroding land element and over the duration of the erosion event, an event-based solution is proposed which predicts total sediment sorting over the event. This solution is shown to be consistent with experimentally observed trends in enrichment of fine sediment. Predictions using this approach are found to only partly explain measured enrichment for sets of experimental data for two quite different soils, but to be in poor agreement for an aridsol of dispersive character. It is concluded that the formation of the deposited layer is a significant mechanism in the enrichment of fine sediment and associated sorbed pollutants, but that processes in the dispersive soil are not as well described by the theory presented.     

Extreme rainfall and its impact on cultivated landscapes with particular reference to Britain

Extreme rainfall events (>50 mm day^?1) falling on cultivated land which is relatively bare of vegetation cover, typically give rise to networks of rills and gullies with ephemeral gullies in depressions and valley bottoms. Farming practices such as the removal of field boundaries, the presence of wheelings and rolled surfaces encourage runoff. The coincidence of vulnerable crops such as maize, potatoes and sugar beet with erodible soils and sloping sites may lead to high rates of erosion associated with single events or wet seasons. Not all extreme rainfall events lead to runoff and erosion, this depends on timing with respect to the growing crop. Rates of erosion associated with extreme events may be high but when placed in a long‐term temporal context, they tend to be quite low. Extreme events frequently lead to off‐site impacts most notably muddy flooding of properties and the pollution of watercourses. Landscapes may be protected from extreme events by standard soil conservation techniques; off‐site impacts may similarly be alleviated by flood‐protection measures. In both cases, the challenge is to put in place adequate economic incentives, social pressures and governmental policy frameworks to incentivise effective action. Predicted rainfall changes in the future include wetter winters and increases in rain per rain‐day. In this case, the risk of erosion on cultivated land will increase. However, erosion mitigation strategies should still address the issue of the incidence of high‐risk crops on vulnerable sites. Copyright © 2015 John Wiley & Sons, Ltd.     

An analysis of the impact of spatial variability in rainfall on runoff and sediment predictions from a distributed model

This paper investigates the effect of introducing spatially varying rainfall fields to a hydrological model simulating runoff and erosion. Pairs of model simulations were run using either spatially uniform (i.e. spatially averaged) or spatially varying rainfall fields on a 500‐m grid. The hydrological model used was a simplified version of Thales which enabled runoff generation processes to be isolated from hillslope averaging processes. Both saturation excess and infiltration excess generation mechanisms were considered, as simplifications of actual hillslope processes. A 5‐year average recurrence interval synthetic rainfall event typical of temperate climates (Melbourne, Australia) was used. The erosion model was based on the WEPP interrill equation, modified to allow nonlinear terms relating the erosion rate to rainfall or runoff‐squared. The model results were extracted at different scales to investigate whether the effects of spatially varying rainfall were scale dependent. A series of statistical metrics were developed to assess the variability due to introducing the spatially varying rainfall field. At the catchment (approximately 150 km²) scale, it was found that particularly for saturation excess runoff, model predictions of runoff were insensitive to the spatial resolution of the rainfall data. Generally, erosion processes at smaller sub‐catchment scales, particularly when the sediment generation equation had non linearity, were more sensitive to spatial rainfall variability. Introducing runon infiltration reduced the total runoff and sediment yield at all scales, and this process was also most sensitive to the rainfall resolution. Copyright © 2011 John Wiley & Sons, Ltd.     

Conditional simulation of remotely sensed rainfall data using a non-Gaussian v-transformed copula

Quantification of rainfall and its spatial and temporal variability is extremely important for reliable hydrological and meteorological modeling. While rain gauge measurements do not provide reasonable areal representation of rainfall, remotely sensed precipitation estimates offer much higher spatial resolution. However, uncertainties associated with remotely sensed rainfall estimates are not well quantified. This issue is important considering the fact that uncertainties in input rainfall are the main sources of error in hydrologic processes. Using an ensemble of rainfall estimates that resembles multiple realizations of possible true rainfall, one can assess uncertainties associated with remotely sensed rainfall data. In this paper, ensembles are generated by imposing rainfall error fields over remotely sensed rainfall estimates. A non-Gaussian copula-based model is introduced for simulation of rainfall error fields. The v-transformed copula is employed to describe the dependence structure of rainfall error estimates without the influence of the marginal distribution. Simulations using this model can be performed unconditionally or conditioned on ground reference measurements such that rain gauge data are honored at their locations. The presented model is implemented for simulation of rainfall ensembles across the Little Washita watershed, Oklahoma. The results indicate that the model generates rainfall fields with similar spatio-temporal characteristics and stochastic properties to those of observed rainfall data.     

Identification and stochastic generation of representative rainfall temporal patterns in Hong Kong territory

In hydrosystem engineering design and analysis, temporal pattern for rainfall events of interest is often required. In this paper, statistical cluster analysis of dimensionless rainfall pattern is applied to identify representative temporal rainfall patterns typically occurred in Hong Kong Territory. For purpose of selecting an appropriate rainfall pattern in engineering applications, factors affecting the occurrence of different rainfall patterns are examined by statistical contingency tables analysis through which the inter-dependence of the occurrence frequency of rainfall patterns with respect to geographical location, rainfall duration and depth, and seasonality is investigated. Furthermore, due to inherent variability of rainfall mass curves or hyetographs within each classified rainfall pattern, a practical procedure to probabilistically generate plausible rainfall patterns is described. The procedure preserves the inherent stochastic features of random dimensionless rainfall hyetograph ordinates, which in general are correlated non-normal multivariate compositional variables.     

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.     

Multifractal analysis as a tool for validating a rainfall model

A multifractal analysis was carried out in order to validate the simulation of hourly rainfall records of a local climate model for the Iberian Peninsula. Observed and simulated hourly rainfall data from four locations in Andalusia (southern Spain) were used to carry out the study. In order to detect the influence of the length of the data series on the results, two different sizes were used for the real data: 4 years, and 20 years. The results show that algebraic tails are required to fit the probability distribution of extreme rain event sizes, and rain and dry event durations for both kinds of rainfall data. Similar results are found for the extreme rain event sizes and dry event durations fits when the real and synthetic data are considered. Nevertheless, some differences appear in the cases of rain event durations. The detection of the presence of a first‐order multifractal phase transition associated with a critical moment in the empirical moment scaling exponent function and the results of the extreme rain event sizes fits, reveal that real rainfall is a self‐organized criticality (SOC) process. That behaviour is less evident in the simulated rainfall series. The same ‘synoptic maximum’ value was found for each place with both types of rainfall data. A time clustering analysis was carried out applying the count‐based periodogram and the Fano factor methods. Some periodicities have been detected in the periodograms, especially for the longest real rainfall data series. Copyright © 2007 John Wiley & Sons, Ltd.     

PAR(<Emphasis Type="Bold">p</Emphasis>)-vine copula based model for stochastic streamflow scenario generation

Synthetic streamflow data is vital for the energy sector, as it feeds stochastic optimisation models that determine operational policies. Considered scenarios should differ from each other, but be the same from a statistical point of view, i.e., the scenarios must preserve features of the original time series such as the mean, variance, and temporal dependence structures. Traditionally, linear models are applied for this task. Recently, the advent of copulas has led to the emergence of an alternative that overcomes the drawbacks of linear models. In this context, we propose a methodology based on vine copulas for the stochastic simulation of periodic streamflow scenarios. Copula-based models that focus on single-site inflow simulation only consider lag-one time dependence. Therefore, we suggest an approach that incorporates lags that are greater than one. Furthermore, the proposed model deals with the strong periodicity that is commonly present in monthly streamflow time series. The resulting model is a non-linear periodic autoregressive model. Our results indicate that this model successfully simulates scenarios, preserving features that are observed in historical data.     

Let-It-Rain: a web application for stochastic point rainfall generation at ungaged basins and its applicability in runoff and flood modeling

We present a web application named Let-It-Rain that is able to generate a 1-h temporal resolution synthetic rainfall time series using the modified Bartlett–Lewis rectangular pulse (MBLRP) model, a type of Poisson stochastic rainfall generator. Let-It-Rain, which can be accessed through the web address http://www.LetItRain.info, adopts a web-based framework combining ArcGIS Server from server side for parameter value dissemination and JavaScript from client side to implement the MBLRP model. This enables any desktop and mobile end users with internet access and web browser to obtain the synthetic rainfall time series at any given location at which the parameter regionalization work has been completed (currently the contiguous United States and Republic of Korea) with only a few mouse clicks. Let-It-Rain shows satisfactory performance in its ability to reproduce observed rainfall mean, variance, auto-correlation, and probability of zero rainfall at hourly through daily accumulation levels. It also shows a reasonably good performance in reproducing watershed runoff depth and peak flow. We expect that Let-It-Rain can stimulate the uncertainty analysis of hydrologic variables across the world.     

An improved numerical implementation of Calder's stochastic model of rainfall interception — a note

Two stratagems are described that are necessary to ensure the successful implementation of Calder's stochastic model of rainfall interception for high-intensity rain storms in which condensation occurs over prolonged periods.     

Reproduction of temporal scaling by a rectangular pulses rainfall model

The presence of scaling statistical properties in temporal rainfall has been well established in many empirical investigations during the latest decade. These properties have more and more come to be regarded as a fundamental feature of the rainfall process. How to best use the scaling properties for applied modelling remains to be assessed, however, particularly in the case of continuous rainfall time‐series. One therefore is forced to use conventional time‐series modelling, e.g. based on point process theory, which does not explicitly take scaling into account. In light of this, there is a need to investigate the degree to which point‐process models are able to ‘unintentionally’ reproduce the empirical scaling properties. In the present study, four 25‐year series of 20‐min rainfall intensities observed in Arno River basin, Italy, were investigated. A Neyman–Scott rectangular pulses (NSRP) model was fitted to these series, so enabling the generation of synthetic time‐series suitable for investigation. A multifractal scaling behaviour was found to characterize the raw data within a range of time‐scales between approximately 20 min and 1 week. The main features of this behaviour were surprisingly well reproduced in the simulated data, although some differences were observed, particularly at small scales below the typical duration of a rain cell. This suggests the possibility of a combined use of the NSRP model and a scaling approach, in order to extend the NSRP range of applicability for simulation purposes. Copyright © 2002 John Wiley & Sons, Ltd.     

Evaluation of the impact of rainfall on soil moisture variability

The impact of rainfall on the spatial-temporal soil moisture variability is investigated by using a model of the soil moisture dynamics and two rainfall models, the noise-forced diffusive precipitation model and the WGR model. The study shows that the variability of the soil moisture field is impacted during the limited time of the storm period. During the interstorm period, the variability of the soil moisture field is closely related with the soil texture, as supported by the analysis of the Washita '92 data set. As the impact of rainfall on the variability of the soil moisture field is limited to the short time period of precipitation, the role of the rainfall is simplified as a source of water to the soil moisture field without any consideration of its variability and/or organization in space. A simulation study of the soil moisture field temporal evolution also supports this result, i.e. a strong relationship between the soil moisture field and the variability of its medium. Also, larger variabilities of the loss field coefficient result in easier removal of moisture from the soil.