Abstract
This paper reviews some of the stochastic methods used in applied hydrology over the past thirty years, the period during which the power and availability of computers grew rapidly, and methods of time-series modelling and simulation came into use which had previously been computationally prohibitive. Where stochastic methods are used to estimate the frequencies with which extreme hydrological events (floods, droughts) will occur in the future, these methods assume that hydrological processes are stationary, so that rainfall and runoff records from past years can be used to estimate how often extreme events will occur in the future. But where there are changes in land use or climate, hydrological processes also change, and the past may not be a good guide to the future. In South America, there have been extensive changes in land use during the last thirty years, and there is increasing evidence that climate is also changing. Standard hydrological procedures, such as estimating annual events with T-year return period, and regionalization of annual floods, then become inappropriate. The paper argues that under conditions of climate and land-use change, good assessment of the future frequency of extremes must await better knowledge of the physical processes that determine the behaviour of atmosphere and the oceans.
Highlights
This paper reviews some of the stochastic methods used in applied hydrology over the past thirty years, the period during which the power and availability of computers grew rapidly, and methods of time-series modelling and simulation came into use which had previously been computationally prohibitive
A first definition of stochastic hydrology is that it is a set of procedures for computing quantities of hydrological interest, through analysis of a hydrological record, the values of which are regarded as observations of a random variable: that is, a variable subject to probabilistic laws
Whether we are dealing with observations of a single hydrological variable, or of several, the procedures of stochastic hydrology result in the calculation of quantities that are subject to uncertainty because they are derived from calculations using random variables
Summary
There is some confusion in the hydrological literature concerning the terms uncertainty and risk. The probability can be interpreted either in frequentist or subjective terms; from the frequentist viewpoint, the probability of the event A can be estimated from the number of times in the past that rainfall in the month considered has exceeded 100 mm. Risk is calculated from the uncertainties (probabilities) which in this simple example have the values p and 1 – p, together with loses (or, more generally, utilities). If L11 = 0 so that the farmer loses nothing if he buys the equipment when rainfall is insufficient, the risk of the decision d1 has the simple form (1-p).L12, or: risk = uncertaintyloss. The principle remains that the uncertainties in the events are measured by their probabilities, whilst the risk associated with each possible decision is the sum of the products of losses with probabilities
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