Space-time simulation and disaggregation of observed precipitation using a copula based stochastic model

Abstract:

Precipitation is highly variable in space and time. It has traditionally been measured with rain-gauges at point locations and the records are overwhelmingly daily.

The target of this paper is disaggregation of daily data into hourly estimates using pluviometers which are likely to be in the minority of rain gauges in a chosen region.

The methodology is based on the observation that the wet hourly intervals in a subregion containing a few control pluviometers tend to match each other rather well. Furthermore, the amount of precipitation in each hour of the day at each control match quite closely, as far as ordering is concerned. These properties form the basis of the disggregation procedure. To briefly outline the new method, we disaggregate the daily totals to hourly using the distribution of rainfall amounts in each of the 24 hours, conditioned on

(i) the day's total precipitation catch at the target and

(ii) the statistical link between the hourly catch at each pluviometer in the control set over the 24 hours. The technique employed is a form of constrained simulation based on Monte Carlo Markov Chains (MCMC).

The method is using Gaussian copula based constrained simulation, and offers a very flexible combination of the different sources of information. As simulation methodology it can be directly used for uncertainty assessment. Using the statistical links between the transformed control and target hourly values, we simulate an arbitrary number of sets of transformed target hourly values, which yield desired statistics like expectations and selected quantiles.

The methodology is applied to a set of 75 stations with hourly data and 760 daily observations collected over 16 years in South-Germany (Bavaria). A cross validation was performed for all days exceeding 1 mm precipitation stations of the hourly precipitation network. The performance of the disaggregation was compared to other methods - Rescaled Nearest Neighbours and Rescaled Ordinary Kriging. The model shows good performance in the sense of expected values, and reproduces the distribution of wet amounts well. As a next step the daily amounts were disaggregated for subsequent use for hydrological modelling.

The procedure can be extended relatively simply to obtain daily values from monthly totals.