ABSTRACT Process-based models of soil-vegetation-atmosphere interactions developed for small plots (points) define vertical transfers of water and energy. One can attempt to scale to larger heterogeneous land units by disaggregating the landscape into a set of elements and applying a vertical SVAT model independently to each element (Running et al., 1989; Pierce et al., 1992). Such applications fail to consider lateral transfers. A distributed parameter, three-dimensional SVAT (Topog-IRM) developed by the CSIRO Division of Water Resources (O'Loughlin, 1990; Hatton and Dawes, 1991; Hatton et al., 1992) is used to examine the importance of lateral transfers of water for prediction of water balance components at the small catchment scale.

Simulations are used to contrast the predicted water balances from a SVAT model with and without considerations of lateral subsurface and overland flow in complex terrain. Components of the catchment water balance are shown to scale linearly except in those cases where transient perched water tables develop in landscapes with sufficient slope and hydraulic conductivity to redistribute water effectively via subsurface lateral flow. In such cases, the prediction of catchment yield and the spatial pattern of soil moisture requires the explicit treatment of lateral transfers.

ABSTRACT Macroscale hydrological modelling is currently conducted using Global Climate Models (GCMs) coupled to a range of Soil-Vegetation-Atmosphere Transfer Schemes (SVATs). The most extreme type of simulation involves massive land use change. This paper reports on the results of a tropical deforestation experiment in which the tropical moist forest throughout the Amazon Basin and SE Asia has been replaced by a scrub grassland in a version of the NCAR Community Climate Model (Version 1) which also incorporates a mixed layer ocean and the Biosphere-Atmosphere Transfer Scheme (BATS). In the Amazon we find a smaller temperature increase than did all other previous experiments except Henderson-Sellers and Gornitz (1984); indeed temperatures decrease in some months. On the other hand, we find larger hydrological responses than all earlier experiments including runoff decreases and a larger difference between the changes in evaporation and precipitation which indicate a basin-wide decrease in moisture convergence. Disturbances extend beyond the region of land-surface change causing temperature reductions and precipitation increases to the south of the deforested area in S America. Changes to the surface climate in the deforested area take between 1 and 2 years to become fully established although the root zone soil moisture is still decreasing at the end of a 6-year integration. Besides temperature and precipitation, other fields show statistically significant alterations, especially evaporation and net surface radiation (both decreased). An important question raised by this type of simulation concerns the appropriateness of the microhydrological process models employed in SVATs to the GCMs in which they are currently used.

ABSTRACT A methodology is presented for downscaling GCM-output results to regional scale precipitation using atmospheric circulation patterns. A sequence of observed daily air pressure distributions is used to define circulation patterns. The classification of the circulation patterns is done with the help of a neural network. A multivariate stochastic model describes their link to observed daily precipitation amounts at a number of selected locations. To assess precipitation under changed climate circulation patterns derived from GCM output pressure values are used to condition the stochastic precipitation model. The methodology is demonstrated by results obtained for a selected location (Essen, Germany).

ABSTRACT Rainfall exhibits at every time scale a great variability which becomes extreme for short durations. We first tried to give rainfall occurrence a fractal dimension the main interest of which is to be time scale invariant. This geometrical approach appears to be of limited value, the fractal dimension being dependent upon the intensity threshold used to define the rainy character of a given period. This problem can be overcome by substituting multifractal fields to fractal sets.

The fundamental equation of such fields enables us to relate at every scale the fraction of space occupied by singularities to their probability of appearance. This equation depends only on two parameters characterizing respectively departures of the field under study from homogeneity and monofractality. A time scale invariant frequency-intensity-duration formula has been derived within this frame, which suggests the existence for all durations of a possible maximum precipitation.

ABSTRACT Two Monte Carlo simulation experiments which address the problem of radar-rainfall estimation are presented. One of the problems associated with hydrologic use of radar-rainfall data is the need to adjust radar rainfall estimates to raingage estimates. The adjustment, which is performed in real time, can be done in the mean field sense. The problem of development of such an adjustment scheme is difficult due to largely unknown statistical structure of radar errors and the fundamental sampling differences between these two sensors. To investigate the problem, mean field bias is modeled as a random process that varies not only from storm to storm but also over the course of a storm. State estimates of mean field bias are based on hourly rain gage data and hourly accumulations of radar rainfall estimates. The procedures are developed for the precipitation processing system to be used with products of the Next Generation Weather Radar (NEXRAD) system. To implement the state estimation procedure parameters of the bias model must be specified. The performance of the state estimation is investigated within a Monte Carlo simulation framework. The results highlight the dependence of the state estimation problem on the parameter estimation problem. The second experiment addresses the problem of converting radar-measured reflectivity into rainfall rate. This is typically done using a Z–R relationship. The parameters of such relationship can be estimated using climatological data and nonparametric estimation framework. In the paper the effects of thresholds imposed on the observations included in the estimation are investigated.

ABSTRACT If hydrological systems and properties of their input are changing year to year the stationarity assumption of hydrological time series could not hold any longer. The non-stationarity may occur due to the global climate changes and continued man-induced transformations of river basins. The assumption is made that the time series of annual values of hydrological variables are non-stationary, which in fact can be tested statistically. Then the question arises how to use such series in hydrological design if the structure is to be dimensioned on the statistical base. It seems reasonable to try to extend the existing statistical procedure to cover such a case. Following this line it is proposed to keep the type of probabilistic distribution constant and to allow its parameters to vary in time. Estimation of time dependent parameters is described. Various hypotheses regarding the form of time dependence can be compared and significance of the dependence tested. In order for a hydraulic structure to be dimensioned, its period of life shall be defined, while probability of exceedance or economic risk shall refer to this period. If the same trend in the parameter change is to be preserved in future, it will enable extrapolation of parameter values to every year of the life period and then to evaluate the probability distribution for the whole period of life.

ABSTRACT Different aspects and meanings of uncertainty are reviewed. This introductory review forms a basis for putting recent developments in hydrological and water resources applications of uncertainty concepts into perspective. The understanding of the term uncertainty followed herein is a logical sum of all the notions discussed. An attempt is made to justify the structure of the present volume and to sketch the areas of particular contributions in the volume and to point out their connections to different facets of uncertainty.

ABSTRACT Stochastic analysis of flow and transport in subsurface usually assumes that the soil permeability is a stationary, homogeneous stochastic process with a finite variance. Some field data suggest, however, that the permeability distributions may have a fractal character with long range correlations. It is of interest to investigate how the fractal character of permeability distribution influences the spreading process in porous media. Dispersion in perfectly stratified media with fractal distribution of permeability along the vertical was analyzed. Results were obtained for the transient and asymptotic longitudinal dispersivities. The results show that the macroscopic asymptotic dispersivity depends strongly on the fractal dimension of vertical permeability distribution. Macroscopic dispersivity was found to be problem-scale dependent in development and asymptotic phases.

ABSTRACT Some scaling properties of the distribution of rain rate in space are investigated. The scales of concern range from the radar coverage range (of the order of 400 km) down to individual raindrops. Preliminary results show that over this wide range of scales rain fields exhibit: preferential scales in the range of a few tens of kilometers; behaviour compatible with multifractal structure between scales of 0.5 to 12 km and some clustering properties of the distribution of the small raindrops in space probably related to raindrop collisions and breakup.

ABSTRACT The irrigation system design of pressurized networks is often dimensioned based on the probability of hydrant operation. Simple statistical techniques have been extensively used in the past to model the hydrants operation and to calculate the design capacity of each reach of the network. Such methods as, for example, Clemment's ‘on demand’ approach, are adopted by designers and agencies in the design of irrigation systems. The objective of this paper is to attempt to model the hydrants operation in the irrigation network using the Alternating Renewal Process in continuous time. Extensive data were gathered from collective irrigation networks in Crete. These data were used to estimate the parameters of the Alternating Renewal Process model. A graphical representation of the results could assist in drawing useful conclusions.

ABSTRACT Decision making in the process of control of water storage reservoirs is always combined with risk, whose evaluation is of utmost practical importance. Define the risk as the probability of failure within an operational control process, in the sense of water deficit or water surplus. The control is the sequence of interventions (releases) on future intervals. The risk is estimated on the basis of probability distributions of the total inflows within the horizon of an intervention. The stochastic process of total inflow is conceptualized as a non-stationary Markov chain of first or second order, under discrete time. The methodology is illustrated at the example of the water supply system of a cascade of reservoirs on the river Sola.

ABSTRACT In order to obtain a good description of the exceedances in a partial duration series it is often necessary to divide the year into a number (2–4) of seasons. Hereby a stationary exceedance distribution can be maintained within each season. This type of seasonal model may, however, not be suitable for prediction purposes due to the large number of parameters required. In the particular case with exponentially distributed exceedances and Poissonian occurrence times the precision of the T-year event estimator has been thoroughly examined considering both seasonal and non-seasonal models. The two-seasonal probability density function of the T-year event estimator has been deduced and used in the assessment of the precision of approximate moments. The non-seasonal approach covered both a total omission of seasonality by pooling data from different flood seasons and a discarding of nonsignificant season(s) before the analysis of extremes. Mean square error approximations (bias second order, variance first and second order) were employed as measures for prediction uncertainty. It was found that optimal estimates can usually be obtained with a non-seasonal approach.

ABSTRACT In the existing design methods consideration is given to stochastic processes of flood flows imposed on the structure in order for the hydrological uncertainty to be accounted. However, there are also various uncertainties associated with flood conveyance structures which have to be considered in the design of hydraulic structures. A static model integrating hydrological and hydraulical uncertainties in the design of the Ogee spillway is devised in the present contribution. Results show that the conventional method of the evaluation of risk, where hydrological risk only is accounted, produces underestimation of the risk of failure. This becomes particularly significant if the return period and the safety factor are large.

ABSTRACT Designing a system to monitor groundwater for contamination from landfills involves a tradeoff between cost, time of detection, and probability of detection. As monitoring wells are spaced more closely together, the probability of detecting a leak improves. Locating monitoring wells further downgradient of the landfill also improves detection probability because the plume disperses more and is less likely to move undetected between two monitoring wells. However, closer spacing costs more, and location further away from the source implies a greater time of detection and a greater probability that a water supply well will become contaminated.

An important problem in designing a monitoring system is that the hydraulic conductivity properties of the aquifer around and under the landfill are often poorly understood. It is possible to test for these properties only at points and interpolation between them may be done only with some uncertainty.

A method is discussed for designing a monitoring system under parameter uncertainty. This method places a given number of wells (the number selected by the analyst or user) in locations that maximize the probability of detection of a plume. The method requires some prior knowledge of the statistical properties of the conductivity parameters of the aquifer and some knowledge of the probability of a leak occurring at any given point in the landfill. The method is microcomputer based and currently runs on an advanced microcomputer workstation. The possibility for its adaptation to a more readily available microcomputer is discussed.

ABSTRACT Rainfall occurrence related to a particular location, denned as the set of rainy periods observed, can be regarded as a fractal object belonging to the 1-D space of time. The dimension of this object, which is bounded by 0 and 1, is estimated via the functional box counting method. A large number of West African rainfall time series has been analysed. The resulting dimension is a function of the time scale and of the accepted threshold of rainfall intensity. In all cases under study, for a given time scale, a decreasing fractal dimension of rainfall occurence with increasing rainfall intensity threshold was observed. A main time scale range of practical interest was found to be from some days to some months. It is possible to attribute a multifractal structure to the process of rainfall occurrence. It can be used for simulation and/or estimation purposes. Attempts to find regional patterns and trends, and to compare them to those of inter annual rainfall means were undertaken.

ABSTRACT The objective of this paper is to describe daily discharge series by a stochastic differential equation which is based on the mass balance of a linear reservoir. The input consisting of a series of jumps reflects the rainfall while the output refers to the discharges of a river basin. To account for random phenoma such as evaporation during the transformation process a perturbation term was introduced. The point process describing the shots (jumps) is based on an intensity function alternating randomly between two levels. Thus clustering of shots can be incorporated into the model.