Elsevier

Journal of Hydrology

Volume 346, Issues 3–4, 30 November 2007, Pages 122-130
Journal of Hydrology

A method for coupling daily and monthly time scales in stochastic generation of rainfall series

https://doi.org/10.1016/j.jhydrol.2007.09.003Get rights and content

Summary

Stochastic generation of hydrological time series is a useful tool for the design and management of water resources systems. One of the shortcomings of many available models for stochastic generation of daily rainfall data is that they are unable to preserve satisfactorily key statistical properties simultaneously at daily, monthly and annual time scales. In this paper, a method for coupling two different time scales of stochastic hydrological time series models is introduced. The key feature of the method is to first generate two resembling time series, one preserving key statistical properties at a finer time scale and the other at a coarser time scale. Adjustment is then made to the finer time scale series so that this series becomes consistent with the coarser time scale series. Because the initial two time series resemble each other, the adjustment is kept small. In the paper, the technique for generating two resembling time series is described. The implementation of the method for coupling daily and monthly rainfall series is demonstrated. Test results of the method using rainfall data from a number of sites around Australia showed that the coupling method was able to generate daily rainfall time series that preserved satisfactorily some key statistical properties at daily, monthly and even annual time scales.

Introduction

Stochastic generation of hydrological time series is a useful tool for the design and management of water resources systems (e.g., Salas, 1993). There have been various models developed for stochastic generation of daily rainfall time series (For reviews, see Srikanthan and McMahon, 1985, Chapman, 1994, Chapman, 1995). The models vary considerably in complexity with the number of parameters ranging from fewer than 50 (e.g., Richardson, 1981) to 540 (Srikanthan and McMahon, 1985).

For many applications, it is important that the model is capable of reproducing key statistical characteristics at not only a daily level but also monthly and annual levels. For example, for the evaluation of water supply systems, it is necessary to model prolonged low rainfall and high rainfall periods, which give rise to critical conditions. At the same time, it is also necessary to model rainfall characteristics at shorter durations, which affect the amount of catchment runoff to storages of water supply systems because of the nonlinearity in rainfall and runoff processes. However, the daily rainfall time series models developed in the past tend to be designed to simulate persistence only at the daily time scales. Real rainfall processes display persistence also at larger time scales. For example, the rainfall processes can behave markedly differently in an El-Nino year from other years. For this reason, these daily rainfall time series models generally do not preserve well statistical characteristics, such as the coefficient of variation (CV) and skewness, at monthly and annual levels, although the more complex models tend to do better (Srikanthan and McMahon, 1985).

One of the approaches for overcoming this problem is to start with annual and monthly models and then to disaggregate the annual and monthly time series to a daily series. Koutsoyiannis (2003) provided a comprehensive review of disaggregation methods available for hydrological time series modelling. The review concluded that disaggregation methods that use simultaneously both coarser and finer time scales in one mathematical expression can not adequately reproduce key statistical properties at the finer time scale. Koutsoyiannis, 1994, Koutsoyiannis, 2001, Koutsoyiannis, 2003, Koutsoyiannis and Manetas, 1996, Koutsoyiannis and Onof, 2001 introduced a method for coupling time series of different time scales. It uses two unrelated models to generate two independent time series, one for a coarser time scale and another for a finer time scale. It then applies a coupling transformation to modify the finer time scale series so that this series becomes consistent with the coarser time scale series. A number of coupling transformation forms were proposed the simplest being proportional adjustment. To keep the size of the adjustment small, conditional sampling of the finer time scale series was also proposed so that the finally adopted finer time scale series to be adjusted, when aggregated to the coarser time scale, resembles the coarse time scale series to an acceptable level.

In this paper, a new method for coupling two different time scales of stochastic hydrological time series models is introduced. The key feature of the method is to first generate two resembling time series, one preserving key statistical properties at a finer time scale and the other at a coarser time scale. Then the coupling transformation technique (Koutsoyiannis, 2003) is applied to modify the finer time scale series so that this series becomes consistent with the coarser time scale series. Because the initial two time series resemble each other, the adjustment is automatically kept small. In the paper, the technique for generating two resembling time series is described. The implementation of the method for coupling daily and monthly rainfall series is demonstrated. Test results of the method using rainfall data from a number of sites around Australia are presented.

Section snippets

Generic formulation

The following introduces the method generically for broad applications. As a first step, a basic time series model is assumed for a finer time scale:x=x(a,F)where x is a vector representing a time series of the variable of interest, a a vector representing the parameters of the model, and F a vector representing a series of nonexceedance probabilities corresponding to the random elements that are used as inputs to the model to generate x. The parameters a are estimated by matching key

Discussion

The Basic and Coupled Models implemented in this paper have the same daily rainfall occurrence sequence. Only the daily rainfall amounts generated by the Basic Model are adjusted by the coupling procedure so that the final daily rainfall amounts produced by the Coupled Model preserve key statistical properties at the monthly time scale. In reality, it may be more appropriate to adjust the daily rainfall occurrence sequence rather than the daily rainfall amounts or to adjust both. However, a

Conclusions

A method for coupling two different time scales of stochastic hydrological time series models is presented. The key feature of the method is first to generate two resembling time series, one preserving key statistical properties at a finer time scale and the other at a coarser time scale. The resemblance of the two series with each other is achieved by using the finer time scale model as a building block for the coarser time scale model and using the same sequence of nonexceedance probabilities

Acknowledgements

We are grateful to Dr N. Nandakumar for useful discussion on stochastic data generation, to Dr R. Srikanthan and T. Chapman for providing data for testing, and to Professor T. McMahon for commenting on the manuscript. This work was undertaken when the first author was on study leave from the University of Melbourne and worked at the Sinclair Knight Merz Consulting. We are also grateful to D. Koutsoyiannis and another anonymous reviewer for their highly constructive comments on an early draft of

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