Convolutional Neural Networks for Predicting Orographic Precipitation Gradients: Outcomes from Leveraging Spatial Relationships

A convolutional neural network (CNN) was tested to predict observed orographic precipitation gradients (OPG) over the CONUS northern Rockies. Our target dataset was from prior work by our group: a 40-year observational dataset of orographic precipitation gradients (OPGs) of the western continental United States (CONUS). The terrain of the western CONUS was separated into mountain faces, referred to as facets, based on regional terrain orientation. Daily OPGs were formulated to facets with sufficient in-situ observations from the Global Historical Climatology Network-Daily as linear regressions. Daily wintertime OPGs were found to vary frequently from their climatological means due to the effects of large-scale circulation patterns. This suggested the potential for a CNN to predict wintertime OPGs based on these large-scale patterns.

Testing a CNN in the northern Rockies provided promising results, with 34% OPG variability explained and a mean absolute error of about 2.9 mm (1000 m)-1. When expanding the CNN to predict OPGs for the western CONUS, the OPG variability explained decreased, and mean absolute error increased mainly due to facets with shorter observational records. To improve the CNN’s predictions, we speculated that leveraging the spatial relationships between facets and OPGs could improve its predictions. This study evaluates the spatial characteristics of the target OPG dataset and CNN predictions, the implementation of hybrid loss functions, and the subsequent skill of the CNN to infill withheld OPG values.

Correlation coefficients and the mean absolute difference in OPGs were formulated between all facets of the western CONUS to parse out a spatial relationship of OPGs. The strength of the spatial relationship between facets was highly dependent on the length of the facets’ observational record. When filtering to facets with a greater than 30-year record, the correlation of facet OPGs by distance decayed exponentially, and the mean absolute differences in OPG increased with distance. The CNN predictions of OPGs captured a similar realistic decay of correlation by distance, with an overestimation of magnitude, and a similar increase in mean absolute differences between OPGs and distance, with an underestimation of magnitude. These results indicated that while the CNN is unaware of the facet locations, it predicts similar spatial relationships between them. Here, we present the results of implementing hybrid loss functions that penalize the CNN for over-correlating or under-predicting the differences in OPGs.