Empirically-based modeling of spatial sampling uncertainties associated with rainfall measurements by rain gauges

In the quantitative evaluation of radar-rainfall products (maps), rain gauge data are generally used as a good approximation of the true ground rainfall. However, rain gauges provide accurate measurements for a specific location, while radar estimates represent areal averages. Because these sampling discrepancies could introduce noise into the comparisons between these two sensors, they need to be accounted for. In this study, the spatial sampling error is defined as the ratio between the measurements by a single rain gauge and the true areal rainfall, defined as the value obtained by averaging the measurements by an adequate number of gauges within a pixel. Using a non-parametric scheme, the authors characterize its full statistical distribution for several spatial (4, 16 and 36 km²) and temporal (15 min and hourly) scales.     

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.     

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.     

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.     

Rainfall stochastic disaggregation models: Calibration and validation of a multiplicative cascade model

The simulation of long time series of rainfall rates at short time steps remains an important issue for various applications in hydrology. Among the various types of simulation models, random multiplicative cascade models (RMC models) appear as an appealing solution which displays the advantages to be parameter parsimonious and linked to the multifractal theory. This paper deals with the calibration and validation of RMC models. More precisely, it discusses the limits of the scaling exponent function method often used to calibrate RMC models, and presents an hydrological validation of calibrated RMC models. A 8-year time series of 1-min rainfall rates is used for the calibration and the validation of the tested models. The paper is organized in three parts. In the first part, the scaling invariance properties of the studied rainfall series is shown using various methods (q-moments, PDMS, autocovariance structure) and a RMC model is calibrated on the basis of the rainfall data scaling exponent function. A detailed analysis of the obtained results reveals that the shape of the scaling exponent function, and hence the values of the calibrated parameters of the RMC model, are highly sensitive to sampling fluctuation and may also be biased. In the second part, the origin of the sensivity to sampling fluctuation and of the bias is studied in detail and a modified Jackknife estimator is tested to reduce the bias. Finally, two hydrological applications are proposed to validate two candidate RMC models: a canonical model based on a log-Poisson random generator, and a basic micro-canonical model based on a uniform random generator. It is tested in this third part if the models reproduce faithfully the statistical distribution of rainfall characteristics on which they have not been calibrated. The results obtained for two validation tests are relatively satisfactory but also show that the temporal structure of the measured rainfall time series at small time steps is not well reproduced by the two selected simple random cascade models.     

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.     

A stochastic model of surface contaminant releases to support assessment of site contamination at a former industrial site

An industrial site is usually contaminated by accidental (and occasionally intentional) releases of pollutants to the environment from various operations carried out on that site. Consequently, the pattern of contamination created during the life of the site depends in part, at least, on the pattern of operations. Thus, the assessment of the pattern of contamination over the site should be improved: if it is possible to identify the pattern of operations on the site, the duration of the different activities and the perceived likelihood of releases from the different operations. A stochastic model has been developed that can be used to simulate alternative realizations of contaminant releases (duration, extent and timing). The model employs release zones associated with particular activities or groups of activities on the site and the areas of each of the zones may be independent or overlapping. The period of activity in each zone is obtained from the site records, while the likelihood and extent of contamination in each zone is inferred from an analysis of the contamination data obtained by point sampling. The form of the model, the method of inference of the model parameter values from the site data and the application of the model to the study site are presented. The release model has been developed as part of a suite of stochastic models for site ground contamination analysis. The stochastic soil and transport models and the application of the integrated modelling system are described in separate papers.     

Decomposing InSAR LOS displacement into co-seismic dislocation with a linear interpolation model： A case study of the Kunlun Mountain Ms=8.1 earthquake

It has always been a difficult problem to extract horizontal and vertical displacement components from the InSAR LOS （Line of Sight） displacement since the advent of monitoring ground surface deformation with InSAR technique. Having tried to fit the firsthand field investigation data with a least squares model and obtained a preliminary result, this paper, based on the previous field data and the InSAR data, presents a linear cubic interpolation model which well fits the feature of earthquake fracture zone. This model inherits the precision of investigation data; moreover make use of some advantages of the InSAR technique, such as quasi-real time observation, continuous recording and all-weather measurement. Accordingly, by means of the model this paper presents a method to decompose the InSAR slant range co-seismic displacement （i.e. LOS change） into horizontal and vertical displacement components. Approaching the real motion step by step, finally a serial of curves representing the co-seismic horizontal and vertical displacement component along the main earthquake fracture zone are approximately obtained.