Reliability of daily and annual stochastic rainfall data generated from different data lengths and data characteristics

This paper assesses the performance of the singlesite stochastic daily rainfall model, TPMb, using data from 101 locations across Australia, as a function of the historical rainfall characteristics, geographical locations and the length of historical data used to calibrate the model. TPMb (Transition Probability Matrix with Boughton's correction) is one of the more robust and commonly used stochastic daily rainfall models in Australia. TPMb is one of the stochastic models in SCL (Stochastic Climate Library, www.toolkit.net.au), a software product in the Catchment Modelling Toolkit designed to facilitate the generation of stochastic climate data. The results here therefore also provide a perspective of the model performance that can be expected for different locations and historical data characteristics. Stochastic rainfall data provide alternative realisations that are equally likely to have occurred, and are often used as inputs into hydrological models to quantify uncertainty in environmental systems associated with climatic variability, allowing informed risk-based design and system operations decisions to be made. The TPMb model is used to generate 1000 replicates of 100-year daily rainfall time series for 101 locations across Australia, and the model performance is assessed by comparing key statistics in the stochastic replicates with those of the historical data. Two annual rainfall characteristics/statistics (mean annual rainfall and 5-year low rainfall total) and four daily rainfall characteristics (mean wet day rainfall, mean wet spell length, mean maximum 3-day rainfall and mean dry spell length) that are not used in calibrating the model are compared. The results indicate that TPMb can generally reproduce the historical rainfall data characteristics satisfactorily. The average of the statistic in the 1000 stochastic replicates is generally within 10% of the statistic of the historical data, and the 2.5^th percentile and 97.5^th percentile of the statistic in the stochastic replicates are almost always lower and higher respectively than the statistic in the historical data. Some of the main observations are: TPMb slightly overestimates the mean annual rainfall and mean wet day rainfall (but only when the coefficient of variation of annual rainfall is smaller than 0.4); the higher overestimations are in the southern parts of Australia; TPMb simulation of mean maximum 3-day rainfall is poorer for smaller mean maximum 3-day rainfall (<20 mm); TPMb simulation of mean dry spell length is poorer for higher mean dry spell length (>20 days); apart from these, there is no obvious relationship between the model performance and the historical data characteristics or geographical locations; and long historical records are required to derive reliable stochastic rainfall data, particularly the statistics that reflect longer-term variability.