Statistical Modelling for a Randomised Trial of a Rainfall Modification Technology

Any technology that increases the amount of rain that reaches the ground has enormous potential for rainfall-poor countries. However the evaluation of such technologies and detection of any effect on rainfall is a complex undertaking, given the natural spatial and temporal variability in rainfall. Explicit or implicit control of the necessary experimental conditions for providing evidence for an effect is therefore extremely difficult. Rainfall modification trials based on randomized experimental designs have not so far reliably demonstrated sufficient statistical power to detect an enhancement signal because of the large level of background variation in rainfall. To a large extent this has been because the statistical models used to account for uncontrolled variation of observed meteorological covariates have usually been defined at a relatively aggregated scale. However, recent developments in spatio-temporal modelling of finer scale data collected in such trials provide a way of implementing more powerful methods of detecting this signal. This paper discusses the statistical issues faced when analysing rainfall data using such models, and some of the lessons learnt about the difficulty of making causal inferences when non-stationary environmental variation makes it impossible to use a randomisation-based approach to controlling for this variation, at least in the short to medium term. The statistical models described here are defined at the rain gauge by day level and use a hurdle specification to allow for days when no rain is recorded at a location. Positive rainfall on a day at a gauge is modelled as a mixture of fixed effects, based on meteorological and orographic covariates, plus random effects to account for both spatial and temporal correlations in the rain gauge data. A number of issues related to the statistical estimation of weather modification will be discussed in more detail in the paper, including: the effectiveness of randomisation for balancing the impact of varying meteorological conditions on the estimation of an effect; the limitations of rainfall modelling based on area and time aggregation of rainfall data; identification of the effective footprint of the technology; and the use of a block bootstrap for robust semiparametric inference of the effect of the technology on rainfall over the trial period. Finally, we note that the methodology described here is not necessarily limited to the analysis of the rainfall modification, but can be applied more generally to statistical analysis of potential intervention in the behaviour of weather systems.