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A new approach is proposed for image denoising. The approach involves edge preservation relying on image multiresolution decomposition using a redundant wavelet transform.

This paper reports the results of statistical analyses for the detection of time trend in 48 rainfall records from sites in the Amazon Basin with more than 15 yr of record. Using a nonparametric test for trend in monthly rainfall, three results emerge: (a) irrespective of the statistical significance of time trends, positive and negative trends occur with approximately equal frequencies over the Brazilian Amazon hydrographic basin; (b) the number of statistically significant time trends, whether positive or negative, is very much greater than can be ascribed to chance variation; (c) significantly negative time trends are more common than significantly positive time trends in monthly rainfall. Over the period of approximately 30 yr covered by the records, during which deforestation has been rapid, negative trends seem to have occurred more frequently in two regions of western and central Amazonia, and positive trends more frequently in eastern Amazonia. There is some qualitative agreement between the disposition of contours defining regions of negative trend (reduced rainfall) in the rainfall records, and the contours defining regions of reduced rainfall following 50% deforestation, as predicted by the U.K. Hadley Centre for Climate Prediction and Research. However, the rainfall records show positive trends (increased rainfall, confirming the conclusion of Chu et al.) in some parts of the region where the Hadley Centre predicts reduced rainfall, following deforestation of 50% or more.

Regionalization of flow duration curves make up an important part of any project in water resources planning and development. Maximum likelihood estimators can be used to obtain asymptotically unbiased and minimum variance estimates for parameters of the flow-duration curve model. However, multivariate regression equations should be developed to improve derived confidence intervals for an estimated flow duration curve.

Abstract: Sediments produced from eroding cultivated land can cause on‐site and off‐site effects that cause considerable economic and social impacts. Despite the importance of soil conservation practices (SCP) for the control of soil erosion and improvements in soil hydrological functions, limited information is available regarding the effects of SCP on sediment yield (SY) at the catchment scale. This study aimed to investigate the long‐term relationships between SY and land use, soil management, and rainfall in a small catchment. To determine the effects of anthropogenic and climatic factors on SY, rainfall, streamflow, and suspended sediment concentration were monitored at 10‐min intervals for 14 years (2002–2016), and the land use and soil management changes were surveyed annually. Using a statistical procedure to separate the SY effects of climate, land use, and soil management, we observed pronounced temporal effects of land use and soil management changes on SY. During the first 2 years (2002–2004), the land was predominantly cultivated with tobacco under a traditional tillage system (no cover crops and ploughed soil) using animal traction. In that period, the SY reached approximately 400 t·km−2·year−1. From 2005 to 2009, a soil conservation programme introduced conservation tillage and winter cover crops in the catchment area, which lowered the SY to 50 t·km−2·year−1. In the final period (2010–2016), the SCP were partially abandoned by farmers, and reforested areas increased, resulting in an SY of 150 t·km−2·year−1. This study also discusses the factors associated with the failure to continue using SCP, including structural support and farmer attitudes. [ABSTRACT FROM AUTHOR]

A general method is proposed which measures the increase in uncertainty when sampling effort is reduced in sediment fingerprinting. The method gives quantitative measures of how reduced sampling of material in one of the source areas, and/or of suspended sediment in streams, increases the uncertainties in the proportions of sediment contributed from the sources. Because the proportions of sediment contributed by the source areas must add to one, standard errors of the estimated proportions cannot be used as the usual measures of uncertainty: the paper uses instead the volume of the joint 95% confidence region for the estimated proportions. The paper shows how the uncertainty in this volume changes as numbers of suspended sediment samples, and the numbers of samples collected from cropped fields, are reduced by successive steps from 24 ( 20, in the case of cropped fields) to 16, 12, 8, 4 and 2 samples. As expected, uncertainty increases rapidly as the number of samples - whether of suspended sediment or from cropped fields - is reduced drastically. The pattern of increasing uncertainty is similar both for reductions in suspended sediment sampling, and for reduced sampling from cropped areas. When the number of suspended sediment samples, and the number of samples from cropped fields, are reduced to the same values, the increase in uncertainty from fewer suspended sediment samples was always slightly greater than the increased uncertainty from the reduced sampling of cropped areas, although this finding took no account of differences in the costs of field sampling and laboratory analysis. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

When 'fingerprinting' is used to identify what proportions Ps ( s = 1, ..., g) of suspended sediment come from g different source areas, measures of the uncertainties in estimates of the Ps are also required. These uncertainties are influenced by two kinds of correlation whose effects are rarely recognized in the literature. These are (i) correlation between the estimated Ps because they must add to 1 and (ii) correlation between the geochemical tracers measured in sediment samples. This paper uses bootstrap procedures to identify joint confidence regions for the estimated proportions [responding to correlation of type (i)] and to explore alternatives to the 'standard' least-squares criterion used to estimate the proportions when tracer measurements are correlated [correlation of type (ii)]. Using a limited dataset with three sediment source areas for illustration ( g = 3), results were obtained from 5000 bootstrap samples, using two criteria (standard and generalized least squares, GLS) with two inequality constraints: (a) 0 ≤ Ps ≤ 1, where Ps is the fraction of suspended sediment contributed by the s-th source area ( s = 1, 2, 3) and (b) 0 < Ps < 1, which, the paper argues, better represents reality. Approximate 95% confidence regions for the Ps, given by the two criteria and two inequality constraints, were compared. Using inequality constraint (a), the confidence region given by the GLS criterion was slightly smaller than that given by the standard; using constraint (b), the two confidence regions' boundaries were almost identical, suggesting that the effects of correlations between tracers were not large for the dataset used. For both criteria, the scatter amongst estimated proportions Ps obtained by bootstrapping was large, raising issues concerning the efficiency of sampling and the allocation of sampling effort, both in source areas and in transported suspended sediment. The results suggest that apparently small differences in the constraints applied to the proportions Ps can give quite different numerical results. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Since the 1970s, there has been both continuing and growing interest in developing accurate estimates of the annual fluvial transport (fluxes and loads) of suspended sediment and sediment-associated chemical constituents. This study provides an evaluation of the effects of manual sample numbers (from 4 to 12 year−1) and sample scheduling (random-based, calendar-based and hydrology-based) on the precision, bias and accuracy of annual suspended sediment flux estimates. The evaluation is based on data from selected US Geological Survey daily suspended sediment stations in the USA and covers basins ranging in area from just over 900 km2 to nearly 2 million km2 and annual suspended sediment fluxes ranging from about 4 Kt year−1 to about 200 Mt year−1. The results appear to indicate that there is a scale effect for random-based and calendar-based sampling schemes, with larger sample numbers required as basin size decreases. All the sampling schemes evaluated display some level of positive (overestimates) or negative (underestimates) bias. The study further indicates that hydrology-based sampling schemes are likely to generate the most accurate annual suspended sediment flux estimates with the fewest number of samples, regardless of basin size. This type of scheme seems most appropriate when the determination of suspended sediment concentrations, sediment-associated chemical concentrations, annual suspended sediment and annual suspended sediment-associated chemical fluxes only represent a few of the parameters of interest in multidisciplinary, multiparameter monitoring programmes. The results are just as applicable to the calibration of autosamplers/suspended sediment surrogates currently used to measure/estimate suspended sediment concentrations and ultimately, annual suspended sediment fluxes, because manual samples are required to adjust the sample data/measurements generated by these techniques so that they provide depth-integrated and cross-sectionally representative data. Published 2014. This article is a U.S. Government work and is in the public domain in the USA. [ABSTRACT FROM AUTHOR]

An expression is derived for the variance of a regional linear trend in annual runoff (units: mm of runoff per km2 per year), averaged over P gauging sites, where the P individual runoff sequences are subject to both year-to-year and site-to-site correlations. At each site, it is assumed that mean annual runoff has a linear trend with serially correlated residuals modeled by an ARMA(1,1) process which can represent both short-term and long-term persistence in annual runoff. Extension to ARMA( p, q) processes is straightforward, and the procedure is also adapted to the case where runoff exhibits long-term persistence. In the case of the ARMA(1,1) model, the expression obtained for the variance of the regional trend need not assume Gaussianity, but if the assumption of Gaussianity is tenable, the note shows how the following hypotheses can be tested: (i) that the linear trend is zero at all P sites; (ii) that the linear trend is equal at all P sites. [ABSTRACT FROM AUTHOR]

A comparison of six procedures for estimating the linear trend parameter β in annual maximum 1 day river flows at five sites in southern Brazil showed marked differences between, on the one hand, estimates obtained by incorporating trend into the generalized extreme value (GEV) location parameter with all parameters estimated by maximum likelihood (ML) and on the other hand, estimates found by least squares, trend removal prior to fitting the GEV by ML, boot-strap sampling, and Theil-Sen estimation. ML estimates of trend were considerably smaller than those given by all other procedures. The same was true where trend had been incorporated into the Gumbel location parameter. Where 95% confidence intervals were calculated for the 'true' trend β by different procedures, some confidence intervals bracketed zero (indicating that the trend was not 'significant' at the 5% level), but there was no consistency between results from different procedures; Theil-Sen confidence intervals always bracketed zero, confidence intervals given by detrending never did. It is concluded that not only do different estimation procedures give different measures of trend uncertainty, as reported elsewhere, but the estimated trends themselves may differ, and the paper suggests an explanation why this may occur. Some philosophical issues relating to estimation of trend in climatological and hydrological extremes are discussed, and it is concluded that selection of a method to estimate trend must depend on context. [ABSTRACT FROM AUTHOR]

The paper compares forecasts of mean monthly water levels up to six months ahead at Ladário, on the Upper Paraguay River, Brazil, estimated from two long-range dependence models. In one of them, the marked seasonal cycle was removed and a fractionally differenced model was fitted to the transformed series. In the other, a seasonal fractionally differenced model was fitted to water levels without transformation. Forecasts from both models for periods up to six months ahead were compared with forecasts given by simpler "short-range dependence" Box-Jenkins models, one fitted to the transformed series, the other a seasonal autoregressive moving average (ARMA) model. Estimates of parameters in the four models (two "long-range dependence", two "short-range dependence") were updated at six-monthly intervals over a 20 year period, and forecasts were compared using root mean square errors (rmse) between water-level forecasts and observed levels. As judged by rmse, performances of the two long-range dependence models, and of the ARMA (1,1) short-range dependence model, were very similar; all three out-performed the seasonal short-range dependence ARMA model. There was evidence that all models performed better during recession periods, than on the hydrograph rising limb. [ABSTRACT FROM AUTHOR]

This paper discusses issues arising when Tropical Rainfall Measuring Mission (TRMM) estimates of rainfall characteristics are calculated for the sparsely gauged Brazilian Amazon. The particular issue considered is the calculation of statistical uncertainty in (1) comparisons between TRMM estimates of rainfall characteristics and their corresponding rain gauge estimates and (2) interpolated estimates of rainfall characteristics, which are conditional on local TRMM estimates near ungauged sites. Three characteristics selected for particular comparison are (1) mean annual rainfall, 1998-2005, (2) mean value, over these years, of the 95% quantile of within-year daily rainfall, and (3) mean number of days in the year with rainfall of 2 mm or more. The paper demonstrates how positive spatial correlation leads to underestimation of the uncertainty in the comparisons (i.e., the standard errors of differences), so that the significance of differences, when observed, is likely to be overestimated if spatial correlation is ignored. For the three characteristics mentioned, the Matérn spatial correlation function with shape parameter = 1/2, giving an exponential correlation function, was found to be adequate for modeling spatial correlation. It is also argued that the statistic 1 − b, where b is the slope of the regression of a rain gauge estimate of a rainfall characteristic on its counterpart derived from satellite instrumentation, is a measure of the errors in the satellite (spatially averaged) estimates. Finally, although issues of spatial correlation are discussed with particular reference to rainfall, it is argued that the same issues arise whenever satellite-derived estimates of a component of the water cycle must be combined with ground-based measurements. [ABSTRACT FROM AUTHOR]

Knowledge of hydrodynamic processes is essential for engineers who assess the stability of energy dissipation structures undergoing extreme pressure fluctuations caused by turbulence during high discharge. Methods are in particular required to evaluate the frequencies of occurrence of extreme pressures. This work explores the use of the generalized extreme value (GEV) distribution to represent frequencies of instantaneous pressures recorded in a structure designed for energy dissipation by a hydraulic jump in a hydroelectric power station at Porto Colombia in central Brazil. The goodness of fit of the GEV distribution was evaluated using probability plots and the Kolmogorov-Smirnov test. The results indicate that it is appropriate for studying the maximum and minimum pressures for a range of discharges corresponding to Froude numbers between 3.88 and 6.42. [ABSTRACT FROM AUTHOR]

This paper presents results of analyses by parametric methods of annual means of temperature, precipitation and discharge, and of seasonal maximum precipitation at 17, 28 and 10 Icelandic stations, respectively, for the period 1961-2000. Trends in mean seasonal temperature and precipitation are in broad agreement with results found by other authors using other methods. A positive trend appears in both mean annual temperature and mean temperatures in most seasons. Annual mean precipitation trends are positive in most seasons except for negative trends in the September-November season in the south. Additionally, positive trends appear in maximum one-, three- and five-day precipitation, both during the spring and autumn, except at a group of stations in central Iceland. Some of the positive trends in mean annual and seasonal precipitation may, however, be attributed to the positive trend in temperature which may have influenced gauge catch. Trends in mean annual and seasonal discharge are small and statistically insignificant; the trends found in temperature and precipitation do not all relate directly to trends in discharge but suggest hypotheses for further study of the relationships between them. [ABSTRACT FROM AUTHOR]

Gaps in measured discharge series are common in Iceland, especially during winter, but reconstructed series are needed for a number of applications. Modeled series are therefore sometimes used to fill the gaps to create a continuous series, but the modeled inserts may have different statistical characteristics from the observed series, whilst their initial and final values rarely coincide with the corresponding measured values. Where gaps are numerous, individual treatment of each gap is time-consuming and often impractical. A method for adjusting modeled sequences to be inserted into gaps was therefore designed with the objective of reducing the difference between model-generated inserts and recorded series. This paper reports on the performance of the method and shows how an improved fit can be attained by adjusting the model-generated inserts so as to smoothly match the discharges observed before and after a gap. [ABSTRACT FROM AUTHOR]

The article presents the study which explores the relationship between suspended sediment concentration (SSC) and turbidity for a small rural catchment in Brazil. It evaluates two calibration methods by comparing the SSC estimates obtained from the calibrated turbidity readings with direct measurements using the soil taxonomy system of the U.S. Department of Agriculture. The first method is derived by relating the turbidity reading to simultaneous measurements of concentration obtained from SSC samples collected from the vicinity of the turbidity probe during flood events, while the second is based on the readings obtained from the turbidity meter when the probe immersed in samples using soils collected from the catchment. The study shows the efficiency of the first method over the second.

Research to compare the performance of precipitation-runoff models (and indeed models of other hydrologic and geophysical processes) is increasingly reported in the literature. A characteristic of almost all such intercomparisons at present is that each model is tested only by the research group (the 'operator') that has developed it, so that differences between models are confounded with differences between operators. It has long been recognized that each model should be tested using data from a range of watersheds, giving replication of results under different conditions of climate, vegetation, geology, and other factors. This paper argues that in addition, models must be tested by more than one operator and that the other necessary feature of good experimental practice (namely, the use of randomization procedures where models are to be tested in sequence) is also needed in model intercomparison studies. This removes possible bias, inadvertent or otherwise, and allows the uncertainties in estimates of model performance to be calculated. In the context of intercomparison experiments, the paper discusses a number of issues: (1) experimental design as a means of eliminating operator bias; (2) the comparability between models for which different numbers of parameters must be estimated; (3) the consequence for estimates of uncertainty (as measured by standard errors of mean measures of model performance) of assuming that the watersheds used in an intercomparison experiment are sampled from a wider population of watersheds; (4) the 'representativity' of the hydrologic records used for calibration and validation of models; (5) whether the periods of record used in calibration/validation from different watersheds should be synchronized for each model run; and (6) procedures for estimating how well models would perform on ungaged basins. [ABSTRACT FROM AUTHOR]

The paper discusses evidence that common assumptions in the analysis of hydrological time series (homogeneous variability in random fluctuations about a constant mean value) may not be appropriate for some South American drainage basins. Relatively rapid changes have occurred, and are occurring, as a consequence of replacing mature forest by short crops and urban development. Some research claims to have detected non-linear trends in streamflow in rivers draining the south-eastern part of the sub-continent, together with decadal fluctuations and interannual peaks at ENSO timescales. The paper discusses the implications of such changes for hydrological practices now in widespread and largely unquestioned use. [ABSTRACT FROM AUTHOR]

For low-flow data sequences that can plausibly be assumed to have a Weibull distribution, possibly with time trend superimposed, both estimation of a linear trend parameter and tests for its statistical significance are more efficient where information about the underlying Weibull distribution is incorporated into estimation and testing procedures. Both maximum likelihood and linear-regression estimates of linear trend are unbiased in sample sizes commonly found in hydrological practice (from 30 to 50 years). In samples of this relatively limited size, maximum likelihood (ML) estimates of a linear trend parameter have smaller variance than the linear regression (LR) estimate, except when the Weibull parameter k is near to one, when the distribution reduces to an exponential form. For the larger sample size used in simulation, N = 50, empirical tests based on the distribution of the ML and LR estimates showed that those based on maximum likelihood were always more powerful. However, a critical assumption in the paper is that annual low flows are independently distributed, and this may not always be justified. [ABSTRACT FROM AUTHOR]

This paper shows how Gumbel-distributed data can be related to explanatory variables by using generalized linear models (GLMs) fitted by using a modified form of the iteratively weighted least squares algorithm (IWLS). Typical applications include (1) testing for trend in annual flood data, as a possible consequence of changing land cover or other factors; (2) testing for trend in annual maximum rainfall intensities of different durations, as a possible consequence of climate change; and (3) testing how annual maximum rainfall intensity is related to weather conditions at the times that annual maximum intensities were recorded. Given a first estimate of the Gumbel scale parameter α, the coefficients β of explanatory variables x are estimated by casting the model in GLM form, and the scale parameter α is updated by solution of relevant maximum likelihood equation for this parameter. The parameters α, β can be readily estimated using currently available statistical software for fitting GLMs, which can also be used to test the significance of trends in annual flood data for which the Gumbel distribution is a plausible hypothesis. A plotting procedure to indicate departures from the Gumbel hypothesis is also given. The proposed procedure avoids the illogicality in which, when a trend in flood data is suspected, it is tested either by linear regression methods that assume Normally distributed residuals, or by nonparametric methods, both of which discard the Gumbel hypothesis. Simulated samples from Gumbel distributions were used to compare estimates of linear trend obtained by (1) the GLM procedure and (2) straightforward use of a Newton-Raphson procedure to locate the maximum of the likelihood surface; the GLM procedure converged more rapidly and was far less subject to numerical instabilities. Simulated samples from Gumbel distributions were also used to compare estimates of a linear trend coefficient β given by the GLM procedure, with estimates of β obtained by simple linear regression (LR). The variance of the distribution of GLM estimates of β was less than the variance of the distribution of LR estimates, while comparison of the powers of the two tests showed that GLM was more powerful than LR at detecting the existence of small trends, although for large linear trends there was little to choose between the two methods. [ABSTRACT FROM AUTHOR]

Where changes in hydrologic regime occur, whether as a result of change in land use or climate, statistical procedures are needed to test for the existence of trend in hydrological data, particularly those expected to follow extreme value distributions such as annual peak discharges, annual minimum flows, and annual maximum rainfall intensities. Furthermore, where trend is detected, its magnitude must also be estimated. A later paper [ Clarke, 2002] will consider the estimation of trends in Gumbel data; the present paper gives results on tests for the significance of trends in annual and minimum discharges, where these can be assumed to follow a Weibull distribution. The statistical procedures, already fully established in the statistical analysis of survival data, convert the problem into one in which a generalized linear model is fitted to a power-transformed variable having Poisson distribution and calculates the trend coefficients (as well as the parameter in the power transform) by maximum likelihood. The methods are used to test for trend in annual minimum flows over a 19-year period in the River Paraguay at Cáceres, Brazil, and in monthly flows at the same site. Extension of the procedure to testing for trend in data following a generalized extreme value distribution is also discussed. Although a test for time trend in Weibull-distributed hydrologic data is the motivation for this paper, the same approach can be applied in the analysis of data sequences that can be regarded as stationary in time, for which the objective is to explore relationships between a Weibull variate and other variables (covariates) that explain its behavior. [ABSTRACT FROM AUTHOR]

This paper explores the utility of generalized linear models (GLMs) and generalized linear mixed models (GLMMs) for regionalization and record augmentation of flood data. Because both models allow the separation of site and year effects, each gives an estimate of a site's mean annual flood free from effects of the particular years in which floods were recorded. In addition, a GLM gives a measure of the extent to which a short flood record can be regarded as representative of a longer period. The way in which GLMs and GLMMs are formulated effectively unites two problems that have largely been regarded as separate: namely, regional regression and data augmentation. GLMM model structure implicitly includes correlation between flood records at neighboring sites, and both models contain facilities for testing whether time trends exist in flood data, for testing whether such trends are regionally uniform when they are found to exist, and for testing which climatological and/or physiographic variables are useful for information transfer. By appropriate selection of probability distribution and link function, biases are avoided that arise where log transformed data are back transformed to the scale on which flood flows are recorded. The paper illustrates GLMs and GLMMs by fitting them to flood records of variable length from 12 sites in the Ibicui drainage basin in southern Brazil. While the models are extremely flexible and are easily fitted for gamma-distributed data (and to data following certain other probability distributions), the assumptions on which they are based are arguably more complex than in more familiar methods, requiring careful checking procedures. [ABSTRACT FROM AUTHOR]

ABSTRACT The la Plata River basin is one of the largest in the world, with an area of about 3 million km2. It includes parts of five countries (Argentina, Bolivia, Brazil, Paraguay and Uruguay) and the water resources of the la Plata basin are essential for their economic development. The main tributaries are the rivers Parana, Paraguay and Uruguay. Some of the main developments having environmental impacts that influence the basin have been the following: (1) developments of many hydropower reservoirs in the Upper Parana River, in Brazil, from 1960-90; (2) deforestation in the Parana, Uruguay and Paraguay basins from 1950-90; (3) introduction of intensive agricultural practice after 1970; (4) urban developments with change to flood regimes; and (5) navigation and conservation of the Upper Paraguay River. Since 1970, flow increases have been observed which may have been caused by changes in vegetation cover, or by climate variation. The changes have raised important issues for both water resource development and environmental conservation. This paper discusses the water management and environmental issues, taking account of climate patterns and the development of the five countries sharing the basin. [ABSTRACT FROM AUTHOR]

This paper presents some new results for the transfer and extension of information at sites with short hydrological records. The results refer particularly to the transfer and extension of annual flood data. The methods described make use of incomplete or 'censored' data such as may be supplied by people living near a river or from records collected for nonhydrological purposes, and they constitute extensions to methods already described in the literature. For two specific censoring configurations, the gain in information is assessed analytically; it is shown that, under certain conditions, the gain in information can be substantial, but in general the gain is small, particularly where scale parameters are estimated. For other configurations of censored data, an analytical formulation is not possible, and integrals are given from which information gain may be assessed by numerical calculation. Another result extends the use of flood peaks exceeding some threshold value ('peaks over a threshold,' POTs); probabilistic models of flood frequency using POTs are, in effect, fitted using censored data. The value of the results presented in the paper is likely to be restricted by assumptions about the probabilistic structure of flood sequences: in one case that their distribution (at different sites) is bivariate lognormal, and, for the POT model, that floods occur as a Poisson process with POTs exponentially distributed. The results show, in strictly qualitative terms, the circumstances in which information might be gained by the use of censored data at two sites, and how large (or small) the gains might be. [ABSTRACT FROM AUTHOR]

This paper explores some of the statistical characteristics of estimators of sediment load which require the integration over time of the product of a concentration ( c) with a discharge ( q). Using a bivariate lognormal distribution for the discrete variables ( c i, q i), ( i = 1, ..., n), approximate confidence intervals are calculated for an unbiassed estimator of sediment yield, and the exact sampling distribution of the estimator is obtained by numerical integration of a Fourier transform. This permits an investigation of the rapidity with which the estimator tends to normality. Provided the data sequences are serially independent, the same technique can be used to obtain the distribution of an estimator without the assumption of bivariate lognormality. Some characteristics of an 'extrapolation' estimate of sediment yield are derived, in which power law regression is used to estimate concentration from discharge when measurements of the latter are more plentiful than the former. Subject to model assumptions, the extrapolation estimate is found to underestimate the true sediment load, although its variance is smaller; this confirms results obtained by other workers who use empirical sampling and alternative theoretical approaches. [ABSTRACT FROM AUTHOR]

Using a simplified representation of how a river basin stores precipitation, generates runoff, and loses water through evapotranspiration, we derive probabilistic relationships between precipitation, soil moisture deficit, and generated runoff. The 'distribution function model' is used to describe the soil moisture storage capacity of the basin: storage capacity, per unit of basin surface area, is regarded as a spatially variable quantity described by a density function. By routing the generated runoff through what is essentially a linear reservoir with stochastic inputs and outputs, we show how the median discharge can be calculated which corresponds to a rainfall input of some specified return period T time intervals. The return period for basin discharge can, with certain assumptions, also be calculated, thereby yielding probability statements relating the T-period rainfall to its resultant discharge. [ABSTRACT FROM AUTHOR]

A population of channels penetrates a soil matrix that is otherwise homogeneous. The channels are assumed to be vertical and of circular cross section with constant diameter, but channel depths and radii are allowed to vary over the population. This paper uses a model based on the Green-Ampt assumptions to predict infiltration rates through the walls and bases of channels, resulting in a mathematical description of the way in which infiltration develops in the soil and in which channels fill with water until eventually overland flow is initiated. This model takes account of the fact that there may be a random distribution of channels in space. Expressions for the expected mean and variance of infiltration volumes are derived. Some example results are given and show that below the matrix wetting front the variance of the change in water content with 30 and 50 channels per square meter may be of the same order as the mean change in water content. The presence of channels can lead to significant increases in predicted channel volumes. [ABSTRACT FROM AUTHOR]