We assess the value of calibrating forecast models for significant wave height Hs, wind speed W and mean spectral wave period Tm for forecast horizons between zero and 168 hours from a commercial forecast provider, to improve forecast performance for a location in the central North Sea. We consider two straightforward calibration models, linear regression (LR) and non-homogeneous Gaussian regression (NHGR), incorporating deterministic, control and ensemble mean forecast covariates. We show that relatively simple calibration models (with at most three covariates) provide good calibration and that addition of further covariates cannot be justified. Optimal calibration models (for the forecast mean of a physical quantity) always make use of the deterministic forecast and ensemble mean forecast for the same quantity, together with a covariate associated with a different physical quantity. The selection of optimal covariates is performed independently per forecast horizon, and the set of optimal covariates shows a large degree of consistency across forecast horizons. As a result, it is possible to specify a consistent model to calibrate a given physical quantity, incorporating a common set of three covariates for all horizons. For NHGR models of a given physical quantity, the ensemble forecast standard deviation for that quantity is skilful in predicting forecast error standard deviation, strikingly so for Hs. We show that the consistent LR and NHGR calibration models facilitate reduction in forecast bias to near zero for all of Hs, W and Tm, and that there is little difference between LR and NHGR calibration for the mean. Both LR and NHGR models facilitate reduction in forecast error standard deviation relative to naive adoption of the (uncalibrated) deterministic forecast, with NHGR providing somewhat better performance.

翻译：我们评估了针对北海中部某地点，对来自商业预报提供商的有效波高Hs、风速W和平均谱波周期Tm的预报模型进行校准的价值，以改进零至168小时预报时效内的预报性能。我们考虑了两种简单的校准模型：线性回归（LR）和非齐次高斯回归（NHGR），并纳入了确定性预报、控制预报和集合平均预报作为协变量。研究表明，相对简单的校准模型（最多包含三个协变量）即可提供良好的校准效果，增加更多协变量并无充分理由。最优校准模型（针对某一物理量的预报均值）总是利用该物理量的确定性预报和集合平均预报，以及一个与不同物理量相关的协变量。最优协变量的选择在每个预报时效上独立进行，且最优协变量集在不同预报时效间表现出高度的一致性。因此，可以为校准给定的物理量指定一个一致的模型，该模型为所有预报时效纳入一组共同的三个协变量。对于给定物理量的NHGR模型，该物理量的集合预报标准差在预测预报误差标准差方面具有技巧性，对于Hs尤其显著。我们表明，一致的LR和NHGR校准模型能够将Hs、W和Tm的预报偏差降低至接近零，并且LR和NHGR在校准均值方面差异很小。相对于直接采用（未经校准的）确定性预报，LR和NHGR模型均有助于降低预报误差标准差，其中NHGR提供略优的性能。