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.

翻译：通过机器学习融合卫星与地面站点数据可生成高分辨率降水数据集，但往往缺乏不确定性估计。我们针对这一空白，系统评估了六种算法（其中多数为首次应用于该任务）在空间插值中量化预测不确定性的能力。基于美国本土（CONUS）15年月度数据，我们比较了分位数回归（QR）、分位数回归森林（QRF）、广义随机森林（GRF）、梯度提升机（GBM）、轻量梯度提升机（LightGBM）和分位数回归神经网络（QRNN）。利用分位数评分函数与分位数评分规则，评估了这些算法在九个分位水平（0.025, 0.050, 0.100, 0.250, 0.500, 0.750, 0.900, 0.950, 0.975）上输出预测降水分位数（近似完整概率分布）的能力。特征重要性分析表明，卫星降水数据（PERSIANN（基于人工神经网络的遥感信息降水估算）与IMERG（集成多卫星反演）数据集）是最具信息量的预测因子，其次为站点高程和距卫星格点距离。与QR相比，LightGBM在分位数评分规则上性能提升11.10%，其次为QRF（7.96%）、GRF（7.44%）、GBM（4.64%）和QRNN（1.73%）。值得注意的是，LightGBM优于所有随机森林变体（当前机器学习空间插值的标准方法）。最后，我们提出了一套基于评分函数与评分规则形式化评估框架的机器学习算法，用于估算空间数据插值的不确定性。