Evaluation of the rainfall component of a weather generator for climate impact studies☆
Introduction
There is currently intense interest in understanding the impact of surface climate on the land surface, due to the requirement to predict the response of hydrological processes and terrestrial ecosystems in a greenhouse-gas enriched climate. Central to such understanding and prediction is the development and application of soil–vegetation–atmosphere-transfer models (SVATs), which emulate land atmosphere fluxes of momentum, heat, water vapour and carbon dioxide (where the latter might affect biome coverage in an altered climate). Predictions of SVAT schemes are highly dependent upon their driving conditions, predominantly the surface climatology, of which rainfall is a key determinant. These surface processes vary on timescales of the order of days or less, especially after major rainfall events. For this reason, in any modelling structure of land–atmosphere interactions, accurate descriptions of short timescale characteristics of rainfall are required.
Climate impact studies are frequently undertaken by forcing a land surface description with monthly climatologies for different scenarios of greenhouse gas emissions. Such climatologies are either based on collated measurements (e.g. the University of East Anglia Climatic Research Unit 0.5×0.5° dataset, New et al., 1999, New et al., 2000), derived from Global Circulation Models (GCMs) directly (typically at a scale of the order of 2.5°) or use simpler GCM-based ‘analogue models’ (e.g. that developed by Huntingford and Cox, 2000). Such studies are frequently undertaken ‘off-line’, which allows various hypotheses of surface behaviour to be tested without resort to full GCM simulations. However, large-scale surface climatologies based on measurements or derived from GCMs are generally only available on a monthly timescale. Hence, it is necessary to disaggregate such information to at least the daily level.
A large volume of literature deals with the problem of temporal disaggregation of hydrological time series (commonly streamflow and precipitation). The proposed stochastic methods attempt to produce a realization of the finer time series from the coarser one while preserving certain statistical properties of both. Valencia and Schaake (1973) presented one of the important contributions to disaggregation, which used fractional noise approximation models to preserve relevant statistics at all levels of aggregation in a generalized model. This model was further developed by Mejia and Rousselle (1976) to preserve the higher-order correlation at different time steps (e.g. correlation of monthly series in different years). Stedinger and Vogel (1984) advanced that model to include serial and spatial correlations of the fine-resolution series. More recently, Maheepala and Perera (1996) improved the method to explicitly preserve over-year monthly serial and cross-correlations. Other recent contributions include Lebel et al., 1998, Tarboton et al., 1998, Burian and Durran, 2002, and Guenni and Bárdossy (2002) amongst others.
Only a few contributions (e.g. Geng et al., 1986, Guenni and Bárdossy, 2002) deal specifically with the monthly-to-daily precipitation disaggregation problem. Disaggregation of daily precipitation to hourly or sub-hourly timesteps (e.g. Glasbey et al., 1995, Burian and Durran, 2002) or disaggregation of monthly or daily totals to storm events (e.g. Koutsoyiannis and Xanthopoulos, 1990, Koutsoyiannis and Onof, 2001) is much more common in the literature. In many of the techniques a distributional assumption about the disaggregated (finer) series is required and the distribution of sub-daily or storm events is usually different from that for daily time series.
The method of Guenni and Bárdossy (2002) is based on generating an initial daily rainfall series from the truncated normal model as a reference distribution followed by restructuring that series (by iterative reordering) to preserve selected statistics (autocorrelation function, scaling properties, seasonality) using a Markov Chain Monte Carlo (MCMC) based algorithm. This method is complex and has as yet not been widely used.
Geng et al. (1986) proposed a simple model to disaggregate monthly rainfall totals to the daily time-step by providing a method to estimate the parameters of a weather generator from monthly data. The weather generator, an extension of the original development of Richardson (1981), is then used to generate the daily time series. Rainfall ‘weather generator’ models have been developed over many years (refer to Wilks and Wilby (1999) for a review) for the purpose of generating long synthetic series from finite observed records. Weather generators produce series of the same temporal resolution (e.g. daily) as the observed record, while temporal disaggregation aims to produce a finer resolution series (e.g. daily or hourly) from a coarser resolution observed series (e.g. monthly or daily). Weather generators are statistical in concept, based on known distributions of rainfall, from which daily values are sampled using a random numerical generator. The probability of whether rainfall will occur on a given day is classically calculated by Markov Chain methods, whereby probabilities are conditioned on whether the previous day was wet or dry. Geng et al. (1988) developed their method into a simulation package called ‘SIMMETEO’, which has been widely used, especially in crop production studies (e.g. Austin et al., 1998, Lansigan et al., 2000, Hartkamp et al., 2003). The model developed by Geng et al. (1986) has relatively few parameters, and is therefore amenable to calibration using available datasets.
In this study, we focus on a critical review of the Geng model and suggest improvements. A specific aim is to represent the diversity of climatology over the Nile catchment; hence data from a network of Nile raingauges are used. The results are contrasted with data from a relatively dense raingauge network from the Blackwater Catchment, in the Southeast of the UK. The emphasis is placed on developing a simple robust rainfall generator, capable of disaggregating large-scale mean precipitation values. Two distinct applications are considered, although these are commonly confused. The model was originally developed for temporal disaggregation of gauge rainfall. However, the generator is required to predict mean daily rainfall across a region (corresponding to the gridbox of the known climatology or GCM output) from monthly time series. Here we use the Nile and UK raingauges to investigate spatial dependence of climate variables and parameters, making the Geng model applicable for point and large-scale grid-square estimates. Transferring the data across spatial scales (spatial downscaling) is not explicitly tackled, but algorithms could be built based upon the derived dependence of parameters on spatial scale.
Section snippets
The Nile basin
The Nile basin extends from approximately 4°S to 31°N in latitude and 21°E to 41°E in longitude and has an area of some 2.9 million km2. It can be divided into eight sub-basins with different climatic and hydrologic characteristics (Shahin, 1985, Conway and Hulme, 1993, Sutcliffe and Parks, 1999). These include a tropical climate (Lake Victoria and Eastern African Lakes) with bi-modal rainfall seasonality, arid and semi-arid climates (Central Sudan, Bahr El-Ghazal) with a single short (2-month)
The weather generator
The weather generator utilized in this study is an extension of the original Richardson (1981) model for weather generation. It predicts a set of five daily weather variables, namely, precipitation, temperature (maximum and minimum), radiation, and relative humidity, from monthly values. This paper is concerned with the parameterisation of precipitation, which is central in the Richardson model to the calculation of the other variables.
The model predicts rainfall occurrence on a particular day
Performance evaluation for single sites
To test the performance of the weather generator in disaggregation, time series of monthly rainfall amounts (P) and monthly wet fractions (Wf) were used for the four selected gauges. The weather generator parameters (PWD, PWW, α, and β) were calculated from Eqs. (3), (4), (5) for each month and each year using the original ‘Geng’ coefficients. Direct comparison between the generated (single realization) and observed series was performed and the statistics of the disaggregated series compared to
Transitional probabilities
The relationships derived by Geng et al. (1986) to estimate transitional probabilities from the monthly wet fraction (Eqs. (3), (4)), while simple (if b1 is set to zero, only a single parameter, a1, is required), have some limitations. As observed above, the Geng model fails in near-dry months, when both PWD and PWW are close to zero, and in the limiting case when Wf=0, PWW is set equal to 0.25, when in reality it is undefined. Another problem with the Geng model is that the difference between P
Spatial analysis
The main use of the weather generator is to disaggregate GCM and similar grid scale output in time. Therefore, it was necessary to investigate the relationships between rainfall properties and scale. The Blackwater region was divided into four equal grids (Fig. 2, inset) and rainfall properties were calculated for each grid as well as the whole region, providing areal averages at the scales of 500 and 2000 km2. The period 1981–2000 was selected for the analysis; stations with records starting
Estimation of wet fraction from monthly total
The monthly wet fraction is not saved in most GCM experiments, and sample daily data are not always readily available to calculate it. Therefore, in such circumstances, a method is required to estimate the monthly wet fraction from other available variables in order to be able to use the weather generator to disaggregate monthly totals. Error in estimating the wet fraction will not only affect the occurrence properties, but also the properties of rainfall amount as the Gamma distribution
Conclusions
This study investigates the performance of a disaggregation model for converting monthly rainfall totals into daily values across different scales and suggested improvements based on analyses of two catchments. The original weather generator preserves the mean properties of rainfall occurrence and amounts and overestimates their variability. Calibration of the estimation equations used to obtain the generator parameters using available gauge data reduces the variability overestimation. The
Acknowledgements
This study was conducted as part of the PhD research for the first author funded by the Islamic Development Bank Merit Scholarship Programme. Richard Chandler, University College London, UK, provided rainfall data for the Blackwater catchment, while the Nile Forecast Centre, Ministry of Water Resources and Irrigation, Egypt, with which the first author is affiliated, provided rainfall data for the Nile Basin. Prof. Daniel Wilks, Cornell University, USA, provided FORTRAN code to estimate the
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