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 assumptions about and 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 bias correction method based on conditional density estimation for the simultaneous bias correction of daily precipitation and maximum temperature data obtained from gridded GCM spatial fields. The Vecchia approximation is employed to preserve dependencies in the data, and conditional density estimation is carried out using semi-parametric quantile regression. Illustration on historical data from 1951-2014 over two 5 x 5 spatial grids in the US indicate that our method can preserve key marginal and joint distribution properties of precipitation and maximum temperature, and predictions obtained using our approach are better calibrated compared to predictions using asynchronous quantile mapping and canonical correlation analysis, two commonly used alternative 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，由于对基础物理过程的假设和简化，GCMs存在系统性偏差。因此，GCM输出数据在用于未来气候预测前需要进行偏差校正。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。本文提出一种基于条件密度估计的新偏差校正方法，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进行同步偏差校正。该方法采用Vecchia近似来保持数据中的依赖关系，并通过半参数分位数回归进行条件密度估计。基于1951-2014年美国两个5×5空间网格历史数据的实验表明，本方法能够保持降水量与最高气温的关键边缘分布和联合分布特性，且相较于异步分位数映射和典型相关分析这两种常用替代偏差校正方法，采用本方法获得的预测结果具有更好的校准性。