ABSTRACT Evaluation of the applicability of the fuzzy sets theory in the area of hydrology and water resources management is attempted. In this respect, the determination of the membership functions and the interpretation of the results of operations on these functions are of crucial significance. Using water resources allocation problems as an example, the advantages of fuzzy set approaches vis a vis other techniques are demonstrated and discussed. Although the advantages of fuzzy approaches in the decision-making contexts are not always straightforward, these approaches seem to be very attractive in the various diagnostic and classification problems in hydrology and water resources management as well. This is illustrated by the application of some elements of fuzzy sets theory within the framework of a decision support system for a choice of an analog catchment.

ABSTRACT The p.d.f.s typically used in hydrology for determination of exceedance probability (e.g. design floods) are typically based on the parametric approach. In the two-or three-dimensional cases and in the case of regression problems the multivariate normal distribution is in common use. Nonparametric density estimators in multivariate random variables are a new approach to estimation and regression. As an alternative to the standard parametric estimators, the nonparametric multivariate Parzen estimator has been used in the analysis. The results of the analysis indicate that the parametric and nonparametric estimators are performing comparatively well. Some conclusions are offered concerning the applications of the nonparametric approaches.

ABSTRACT Plausibility analysis of annual maximum flows of Norwegian rivers is performed. The data embrace time series of 60 years (1921–80) gathered at 42 observation stations and time series of 30 years (1921–50 and 1951–80) collected at 86 and 83 observation stations, respectively. Six different tests for outliers detection have been used (Shapiro-Wilk, skewness, Student, RST, probability plot coefficient and Anderson-Darling). The tests are based on the assumption of normal distribution, so the normalization (logarithmic or cube root transformation) of the raw data may be a prerequisite. The empirical orthogonal functions approach was used to simulate regional samples with preserved first and second order moments. Outliers analysis of the simulated data was performed and the results were compared with observations.

ABSTRACT An outline of conceptual stochastic models for describing the concentration of pollutants from non-point sources in a river is presented. Pollutants are assumed to have originated from agricultural fields and to have reached a river attached to suspensa eroded from a watershed. The model consists of three parts: a module describing runoff of pollutants from the land into the river, a module for transport in the river, and a decision module which quantifies the consequences of the river pollution. The model serves as a guide for structuring an experimental programme being conducted at the University of Karlsruhe.

ABSTRACT The effect of spatial variation of the initial moisture contents on the distribution of soil moisture and the evaporation rate from the land surface is evaluated. The process of drying is described by a lumped, nonlinear model representing two stages of evaporation using the thermodynamic equation.

ABSTRACT The graphical curve fitting procedure has been favoured by many hydrologists and engineers, and the plotting positions are required both for the display of flood records and for the quantile estimation. The existing plotting position formulae which consider historical floods and palaeologic information are reviewed and discussed. The plotting positions for systematically recorded floods below the threshold of perception must be adjusted to reflect the additional information provided by the pre-gauging period if the historical flood data and the systematic records are to be analyzed jointly in a consistent and statistically efficient manner. However, all available formulae are unlikely to adjust these plotting positions properly. It is felt that the traditional rule and exceedance rule assumptions are inconsistent with the floods over and below the threshold of perception of historical floods. A new type of formula is proposed and examined. Simulation studies and numerical examples show that the new formula type performs better than the traditional rule and competitive to the exceedance rule. The Weibull based formulae result in large bias in quantile estimation. If an unbiased plotting position formula were required, then the proposed modified exceedance Cunnane formula would be the best selection.

ABSTRACT The transformation of white noise and Markov processes through the simplified St. Venant flood routing model is examined. This model has been derived from the linearized St. Venant equation for the case of a wide uniform open channel flow with arbitrary cross-section shape and friction law. The only simplification results in filtering out the downstream boundary condition. The cross-correlation and normalized autocorrelation functions are determined in analytical way.

ABSTRACT The utilization of operationally available radar data for improved shortterm predictions of mean areal rainfall on hydrologic scales can be accomplished by the use of a physically-based spatially-lumped rainfall prediction model. The state-space form of such a model admits covariance estimation algorithms for the determination of rainfall forecast variance. In particular, when the model is linear in the state, covariance analysis can be performed without the use of radar reflectivity data. Covariance analysis of a particular linear physically-based model indicates that the utility of the radar reflectivity data of various elevation angles is limited in mean areal rainfall predictions, even when a very small density of rain gauges exists over the region of interest and good quality radar data are used. This applies to both raw reflectivity and radar-rainfall data converted through a Z–R relationship. The ratio of mean areal rainfall prediction variances, defined as variance with radar data divided by variance without radar data, was found to be greater than 0.8 in most cases. On the other hand, the radar data reduced the estimated variance of the vertically-integrated liquid water content considerably, even when high density rain gauge data were present. The conclusions of this study are representative of covariance analyses procedures that require linear or linearized rainfall prediction models and, for such procedures, are independent of the particular model used. On the other hand, the model used is a spatially-lumped model and can not utilize information on storm velocity offered by the radar data time series.

ABSTRACT The plausibility analysis of the regional flood data of Southern Norway is performed with the help of geostatistical methods. As the data at a number of sites are analyzed, one can account the spatial relationships in the outliers detection problem. That is the results of outliers detection may differ in comparison to the non-structured (univariate) case. The geostatistical methods applied are block kriging and Switzer's location-specific covariance analysis, with catchment areas accounted.

ABSTRACT Point-rainfall data recorded by a fast-responding optical raingauge were analyzed. The methods used range from statistical analysis to the fractal and chaotic dynamics approaches. The study showed the evidence of scaling and chaotic dynamics. It is believed that the insight into the dynamics of rainfall data with very fine increment, gained in the course of the exercise, could be useful in advancing our capability to reliably estimate probable maximum rainfall for design purposes.

ABSTRACT Traditionally human beings predict future runoffs from present rainfalls. One of the recent methodologies of prediction stemming from the pattern recognition technique is presented. The possible range of values of the predicted runoff is estimated by the discriminant functions. The discriminant functions are derived from data sets on several events of rainfall and runoff in the same watershed. The predicted runoff is in good agreement with the observed one.

ABSTRACT Optimization (mainly dynamic programming) based operation of reservoir systems has proven its superiority over traditional techniques based on the concept of rule curve, at least in terms of the selected objective function. Stochasticity of the system can be considered in the optimization by using stochastic dynamic programming to derive longterm, expectation oriented optimal policies. Since the optimality of the operation can only be realized during an infinite operational period, the performance of a stochastic system should not be characterized for practically available time series alone by the expected (annual) value of the objective function. In addition to the traditional output figures a number of performance indices (PI) can be derived to describe the operational behaviour (especially reliability) of the system upon the application of a certain operational policy. These performance indices can be estimated by simulation of the system operation according to the operational policy to be tested.

The inclusion of these PIs in the overall judgment creates a multicriterion framework for decision making. Furthermore, these performance indices are believed to be more sensitive in reflecting the impact of certain constraints than the value of the objective function alone.

The validity of this hypothesis will be tested on a multiunit multipurpose reservoir system, the Victoria, Randenigala, Rantembe reservoir cascade situated on the river Mahaweli in Sri Lanka.

Based on the results of simulation, the PIs will be analyzed for their viability in practical applications.

ABSTRACT The daily rainfall and the daily mean temperature are modelled as processes coupled to atmospheric circulation. Atmospheric circulations are classified into a finite number of circulation patterns. Rainfall occurrence is linked to the circulation patterns using conditional probabilities. Rainfall Z is modelled using a conditional distribution (exponential or gamma) for the rainfall amount, and a separate process for rainfall occurrence using a normal process which is then transformed, delivering both rainfall occurrences and rainfall amounts with parameters depending on the actual circulation pattern. Temperature is modelled using a simple autoregressive approach, conditioned on atmospheric circulation. The simulation of other climatic variables like daily maximum and minimum temperature, and radiation, is briefly discussed. The model is applied using the classification scheme of the German Weather Service for the time period 1881–1989. Precipitation and temperature data measured at different locations for a period of 30 years are linked to the circulation patterns. Circulation pattern occurrence frequencies are analyzed, and anomalies due to a possible climate change are presented. A stationary model uses a semi-Markov chain representation of circulation pattern occurrence. The possibility of developing a non-stationary process representation using General Circulation Models is also presented.

ABSTRACT The design of groundwater contamination remediation based on hydraulic head gradient control method determines the locations of the pumping wells and their pumping rates. In a heterogeneous medium such a design will be sensitive to the spatial characteristics of the underlying geological parameters. The geological uncertainty is due to the heterogeneity of the hydraulic conductivity of the porous medium. Under conditions of uncertainty, incorporation of transmissivity fields with spatial characteristics that most influence the design will reduce the sensitivity of the design. A new class of artificial intelligence technique known as neural networks has been identified as appropriate for pattern association tasks. A neural network based screening tool is being developed to identify transmissivity fields with such spatial characteristics. The ongoing research embraces training a neural network to learn the association between transmissivity fields and their impact on the design, and using the trained network to classify randomly generated feasible transmissivity fields according to their level of impact on the design.