Comparison of Two Stochastic Spatial Daily Rainfall Generation Approaches

Daily rainfall is a key input into models that simulate water resources, agricultural and ecological systems. Stochastic rainfall data provide alternative realisations that are equally likely to have occurred, and are often used to drive hydrological and other models to quantify uncertainty in environmental systems associated with climatic variability. This paper describes the comparison of two stochastic spatial daily rainfall generation approaches: a multi-site two-part model (M2P) and a transition probability matrix-random cascade model (CAS), using 101 years of rainfall data across the eastern Gippsland region in southeast Victoria, Australia. The M2P model consists of a two-state, first-order Markov chain for rainfall occurrences and a two-parameter Gamma distribution for rainfall amounts. It generates rainfall simultaneously at multiple locations by driving a collection of individual models with serially independent but spatially correlated random numbers. In the CAS approach, daily regional rainfall is first generated using a first-order transition probability matrix with a two-parameter Gamma distribution for rainfall amounts in the largest state. The spatial rain field is then simulated using a non-homogeneous random cascade model that utilises scaling invariance features in the historical rain field. The M2P and CAS models are used to generate 20 replicates of 101-year daily concurrent catchment average rainfall time series for five catchments (Tambo, Nicholson, Mitchell Low, Mitchell Up and Avon) across the eastern Gippsland region. These generated rainfall time series are then used as inputs into a calibrated daily conceptual rainfall-runoff model for each of the four major catchments (Tambo, Nicholson, Mitchell and Avon) to generate 20 replicates of 101-year daily concurrent catchment flow time series. The stochastic flow simulations using rainfall inputs from M2P and CAS are assessed by comparing key statistics (spatial and temporal) in the stochastic replicates with those of the historical data. The statistics assessed are: correlations of 1-day, 3-day and annual flows between catchments; mean annual flow, standard deviation of annual flow and 5-year low flow total in the four catchments; and 1-day and 3-day annual exceedance probabilities (AEPs) in the four catchments. Runoff (or flow), rather than rainfall, are assessed because it is the variable directly affecting catchment yield and flood studies. In any case, the general results for stochastic rainfall and flow simulations from the M2P and CAS models are similar, but with the errors accentuated in the flow. The results indicate that both models slightly overestimate mean annual flow, simulates the inter-annual variability well, and the 5-year low flow total reasonably. M2P underestimates the spatial 1-day and 3-day correlations slightly while CAS overestimates the correlations, which will lead to slight underestimations and overestimations respectively in regional flood estimates. M2P also underestimates the spatial annual correlations, which will lead to underestimation of droughts in system simulations. The CAS model simulates 1-day and 3-day flow AEP characteristics much better than the M2P model, and is therefore a better model for regional flood studies. Many of the limitations in the M2P model can be overcome with model improvements, and the paper provides some suggestions. The main limitation of the CAS model is the absence of space-time correlation of rain fields on consecutive days, and the limitation in simulating the clustering (i.e. spatial correlation) of daily rain field during extreme storm events, both of which are difficult to overcome and require further research.