Improving rainfall gradients modeling by conditioning daily rainfall maps to monthly totals

Rainfall maps are key tools in hydrological sciences, with uses ranging from the understanding of rainfall climatology to distributed hydrological modeling. Due to the wide availability of rain gauge records and the high accuracy of these direct observations, daily rainfall maps are often derived from the spatial interpolation of rain gauge data.

Geostatistical methods are commonly used to create gridded rainfall maps from scattered rain gauge observations, and have the advantage of providing an estimation of the uncertainty associated with the interpolation process. However, the uncertainty in the resulting daily rainfall maps increases with the distance to the rain gauges, and the variance of the interpolation uncertainty tends to the variance of the rainfall signal itself at grid points far from any rain gauge. This also results in daily rainfall maps with over-smooth spatial gradients, in particular in mountains areas where rain gauge networks are relatively sparse and rainfall gradients strong.

To overcome this limitation, we propose to condition daily rainfall maps not only to daily rain gauge observations, but also to monthly totals that can be available at ungauged locations. These monthly totals can be derived for instance from monthly rainfall maps incorporating additional observations recorded by rain gauges operating at the monthly resolution, as well as information about long-term rainfall patterns (obtained from e.g., vegetation patterns or past rainfall monitoring campaigns). This task is complicated by the fact that the geostatistical model we use is complex due to the intention to account for the temporal variability of daily rainfall patterns, and we therefore resort to a Metropolis within Gibbs algorithm to perform the conditioning to monthly totals.

The performance of the method is assessed for the Island of Hawai‘i (state of Hawaii, USA) which is known to experience dramatic rainfall gradients. Results show that the proposed approach drastically improves the modeling of daily rainfall gradients in poorly gauges areas as well as at the edges of the modeling domain.