Global Climate Models (GCMs) are numerical models that simulate complex physical processes within the Earth's climate system and are essential for understanding and predicting climate change. However, GCMs suffer from systemic biases due to simplifications made to the underlying physical processes. GCM output therefore needs to be bias corrected before it can be used for future climate projections. Most common bias correction methods, however, cannot preserve spatial, temporal, or inter-variable dependencies. We propose a new semi-parametric conditional density estimation (SPCDE) for density correction of the joint distribution of daily precipitation and maximum temperature data obtained from gridded GCM spatial fields. The Vecchia approximation is employed to preserve dependencies in the observed field during the density correction process, which is carried out using semi-parametric quantile regression. The ability to calibrate joint distributions of GCM projections has potential advantages not only in estimating extremes, but also in better estimating compound hazards, like heat waves and drought, under potential climate change. Illustration on historical data from 1951-2014 over two 5x5 spatial grids in the US indicate that SPCDE can preserve key marginal and joint distribution properties of precipitation and maximum temperature, and predictions obtained using SPCDE are better calibrated compared to predictions using asynchronous quantile mapping and canonical correlation analysis, two commonly used bias correction approaches.

翻译：全球气候模型（GCMs）是模拟地球气候系统内复杂物理过程的数值模型，对于理解和预测气候变化至关重要。然而，由于对底层物理过程进行了简化，GCMs存在系统性偏差。因此，在使用GCM输出进行未来气候预测之前，需要对其进行偏差校正。然而，大多数常见的偏差校正方法无法保持空间、时间或变量间的依赖关系。我们提出了一种新的半参数条件密度估计（SPCDE）方法，用于对从网格化GCM空间场获取的日降水量和最高气温数据的联合分布进行密度校正。在密度校正过程中，采用Vecchia近似来保持观测场中的依赖关系，该过程通过半参数分位数回归实现。校准GCM预测联合分布的能力不仅在估计极端事件方面具有潜在优势，还能在潜在气候变化背景下更好地估计复合灾害，如热浪和干旱。基于美国两个5x5空间网格上1951-2014年历史数据的示例表明，SPCDE能够保持降水量和最高气温的关键边缘分布和联合分布特性，并且与异步分位数映射和典型相关分析这两种常用偏差校正方法相比，使用SPCDE获得的预测具有更好的校准效果。