Statistical post-processing is an indispensable tool for providing accurate weather forecasts and early warnings for weather extremes. Most statistical post-processing is univariate, with dependencies introduced via use of an empirical copula. Standard empirical methods take a dependence template from either the raw ensemble output (ensemble copula coupling, ECC) or the observations (Schaake Shuffle, SSh). There are drawbacks to both methods. In ECC it is assumed that the raw ensemble simulates the dependence well, which is not always the case (e.g. 2-meter temperature in The Netherlands). The Schaake Shuffle is not able to capture flow dependent changes to the dependence and the choice of observations is key. Here we compare a reshuffled standard ensemble model output statistics (EMOS) approach with two multivariate bias adjustment approaches that have not been used before in a post-processing context: 1) the multivariate bias correction with N-dimensional probability density function transform (MBCn) and 2) multivariate ranks that are defined with optimal assignment (OA). These methods have the advantage that they are able to explicitly capture the dependence structure that is present in the observations. We apply ECC, the Schaake Shuffle, MBCn and OA to 2-m and dew point temperature forecasts at seven stations in The Netherlands. Forecasts are verified with both univariate and multivariate methods, and using a heat index derived from both variables, the wet-bulb globe temperature (WBGT). Our results demonstrate that the spatial and inter-variable dependence structure is more realistic in MBCn and OA compared to ECC or the Schaake Shuffle. The variogram score shows that while ECC is most skilful for the first two days, at moderate lead times MBCn is most skilful and at the longest lead times OA is more skilful than both ECC and MBCn. Overall, we highlight the importance of considering the dependence between variables and locations in the statistical post-processing of weather forecasts.

统计后处理是提供准确的天气预报和极端天气预警的必不可少的工具。大多数统计后处理都是单变量的，并且通过使用经验语系引入依赖关系。标准的经验方法从原始合奏输出（合奏copula耦合，ECC）或观测值（Schaake Shuffle，SSh）中获取依赖模板。两种方法都有缺点。在ECC中，假定原始集合很好地模拟了依存关系，但情况并非总是如此（例如，荷兰的2米温度）。Schaake Shuffle无法捕获与流量相关的依赖变化，因此观察的选择至关重要。ñ维概率密度函数变换（MBCn）和2）用最佳分配（OA）定义的多元等级。这些方法的优势在于它们能够显式捕获观察结果中存在的依存关系结构。我们将ECC，Schaake Shuffle，MBCn和OA应用于荷兰七个站点的2 m和露点温度预报。通过单变量和多变量方法以及使用从这两个变量得出的热指数湿球温度（WBGT）来验证预测。我们的结果表明，与ECC或Schaake Shuffle相比，MBCn和OA中空间和变量间的依存关系结构更现实。变异函数得分显示，虽然ECC在前两天最熟练，MBCn的交付周期适中，而ECC的交付周期最长，而MBCn的交付周期最长。总体而言，我们强调了在天气预报的统计后处理中考虑变量和位置之间的依存关系的重要性。