Interpolation of rainfall observations during extreme rainfall events in complex mountainous terrain

Page, Trevor and Beven, Keith and Hankin, Barry and Chappell, Nick (2022) Interpolation of rainfall observations during extreme rainfall events in complex mountainous terrain. Hydrological Processes, 36 (11): e14758. ISSN 0885-6087

Abstract

The representation of rainfall in space is important for hydrological modelling. Accurate estimation of rainfall is particularly challenging in mountainous regions where observations are often sparse relative to the spatial variability of rainfall. In these regions, orographic processes lead to complex patterns of rainfall enhancement and rain shadow depletion. This study tests Natural Neighbour Interpolation (NNI), ordinary kriging (OK) and ordinary cokriging (CK), to determine if CK improves rainfall interpolation during three extreme rainfall events. Three different elevation indices were considered as secondary variables for CK. Preliminary analysis using long-term annual average rainfall totals, including additional high elevation rainfall observations, showed that CK with an effective elevation index (a directionally smoothed elevation, corrected for degree of ‘orographic processing’ and shifted to account for ‘wind-drift’ of rainfall) as a secondary variable performed better than NNI and OK with an overall improvement of around 40%. Using rainfall totals for long-term wind direction and wind speed rainfall classes, CK performance was variable but provided an improvement of approximately 15% for wind direction classes without an easterly wind component. For 15-minute timesteps during extreme rainfall events, there were comparatively small differences (cross-validation using RMSE) between interpolation methods, partly attributed to having only relatively low elevation rainfall observations, providing weak constraint. Using cross-validation and mean bias did, however, show an improvement for both high and low elevation observation classes. Importantly, cross-variogram estimation provided differing cross-validation results when estimated for different rainfall accumulation periods: 15-minutes, hourly, daily and long-term. Variograms and cross variograms estimated at a 15-minute timestep frequency were robust for many timesteps, but were difficult to fit automatically for others. Variograms estimated from longer periods were more reliably estimated, but tended to have lower variance and cross-variance and longer correlation ranges producing a smoother interpolated rainfall field. Given the weak cross-validation constraint, care must be taken in identifying the most appropriate method and variogram estimation period.