  Merging satellite and gauge data with machine learning produces
high-resolution precipitation datasets, but uncertainty estimates are often
missing. We address this gap by benchmarking six algorithms, mostly novel for
this task, for quantifying predictive uncertainty in spatial interpolation. On
15 years of monthly data over the contiguous United States (CONUS), we compared
quantile regression (QR), quantile regression forests (QRF), generalized random
forests (GRF), gradient boosting machines (GBM), light gradient boosting
machines (LightGBM), and quantile regression neural networks (QRNN). Their
ability to issue predictive precipitation quantiles at nine quantile levels
(0.025, 0.050, 0.100, 0.250, 0.500, 0.750, 0.900, 0.950, 0.975), approximating
the full probability distribution, was evaluated using quantile scoring
functions and the quantile scoring rule. Feature importance analysis revealed
satellite precipitation (PERSIANN (Precipitation Estimation from Remotely
Sensed Information using Artificial Neural Networks) and IMERG (Integrated
Multi-satellitE Retrievals) datasets) as the most informative predictor,
followed by gauge elevation and distance to satellite grid points. Compared to
QR, LightGBM showed improved performance with respect to the quantile scoring
rule by 11.10%, followed by QRF (7.96%), GRF (7.44%), GBM (4.64%) and QRNN
(1.73%). Notably, LightGBM outperformed all random forest variants, the current
standard in spatial interpolation with machine learning. To conclude, we
propose a suite of machine learning algorithms for estimating uncertainty in
interpolating spatial data, supported with a formal evaluation framework based
on scoring functions and scoring rules.
