Spatial Rainfall Simulation: Trading Time for Space with Multiple Point Statistics.

Detailed rainfall spatial distribution plays an important role in various applications of hydrological management such as flood forecasting or recharge estimation. However, limited rain gauge network density often makes it difficult to characterize the small-scale variability of rainfall, and reduces the reliability of interpolations methods such as kriging. Here, we test a non-parametric technique that produces spatial rainfall fields by relying on time series data rather than dense spatial data sets. If the velocity of the rain cells is known, the time series can be projected into a one-dimensional space, reflecting the same type of variability observable in the direction of the rain cell displacement. Assuming spatio-temporal ergodicity for a small area, we estimate the mean rainfall cells displacement direction i and velocity vi by optimizing the cross correlation between two subsequent radar images at time t and t+dt. Then, given a time series in the same time lapse R([t,...,t+dt]) and applying the linear transformation R([t,...,t+dt])=S([t,...,t+dt]vi), we obtain a spatial series S generally more densely informed than the available rain-gauge network, used to represent the spatial variability in the direction i. For example, from a 1 min spaced time series R and an estimated velocity v=20 km/h, we obtain a 333 m spaced series S. The obtained spatial series are then employed as a basis to generate 2D spatial rainfall fields using the Direct Sampling (DS), a multiple-point technique that allows simulating complex statistical relations by respecting the similarity of multiple scales patterns. Here the DS is used to complete the 2D field by reproducing one-dimensional patterns borrowed from the spatial series. The approach is tested on the rain-gauge network of the Swiss plateau (Switzerland) and on radar data for the same region. The proposed technique has the potential to characterize realistic spatial fields even for sparse observation networks.