Abstract
The Multiplicative Discrete Random Cascade (MDRC) class of model is used to temporally disaggregate rainfall volumes through multiplying the volumes by random weights, which is repeated through multiple disaggregation levels. The model development involves the identification of probability density functions from which to sample the weights. The parameters of the probability density functions are known to be dependent on the rainfall volume. This paper characterises the volume dependency over the scarcely observed extreme ranges of rainfall, introducing the concept of volume-bounded MDRC models. Probable maximum precipitation (PMP) estimates are used to define theoretically-based points and asymptotes to which the observation-based estimates of the MDRC model parameters are extrapolated. Alternative models are tested using a case study of rainfall data from Brisbane, Australia covering the period 1908 to 2015. The results show that moving from a baseline model with constant parameters to incorporating the volume dependency of the parameters is essential for acceptable performance in terms of the frequency and magnitude of modelled extremes. As well as providing better estimates of parameters at each disaggregation level, the volume dependency provides an in-built bias correction when moving from one level to the next. A further, relatively small performance gain is obtained by extrapolating the observed dependency to the theoretically-based bounds. The volume dependency of the parameters is found to be reasonably time-scaleable, providing opportunity for advances in the generalisation of MDRC models. Sensitivity analysis shows that the subjectivities and uncertainties in the modelling procedure have mixed effects on the performance. A principal uncertainty, to which the results are sensitive, is the PMP estimate. Therefore, in applications of the bounded approach, the PMP should ideally be described by a probability distribution function.
Highlights
Since observed rainfall records tend to be more accurately and completely observed at daily or longer intervals than at sub-daily intervals, temporal disaggregation models are commonly used for the synthesis of sub-daily rainfall as part of flood estimation
Using the ‘microcanonical’ type of Multiplicative Discrete Random Cascade (MDRC) model, the probability distribution functions (PDFs) parameters are estimated for each disaggregation level independently, empirically derived scaling relationships may be used to generalise between levels
This paper proposes that the probable maximum precipitation (PMP) can be used to define a theoretical bound on the parameters of the PDFs used for MDRC models
Summary
Since observed rainfall records tend to be more accurately and completely observed at daily or longer intervals than at sub-daily intervals, temporal disaggregation models are commonly used for the synthesis of sub-daily rainfall as part of flood estimation. Using a MDRC model, the rainfall falling in any interval (say, one day) is divided into two or more sub-intervals (say, two intervals each of 12 h) using a set of weights, W. This is repeated over a number of disaggregation levels until the required time interval (say, one hour) is reached. This requires the probability distribution functions (PDFs) of W to be estimated from rainfall observations. Using the ‘microcanonical’ type of MDRC model, the PDF parameters are estimated for each disaggregation level independently, empirically derived scaling relationships may be used to generalise between levels
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