Up to now, relatively little effort has been dedicated to the quantitative assessment of the differences in spatial patterns of model outputs. In this paper, we employed a variogram-based methodology to quantify the differences in the spatial patterns of root-zone soil moisture, net radiation, and latent and sensible heat fluxes simulated by three land surface models (SURFEX/ISBA, JULES and CHTESSEL) over three European geographic domains – namely, UK, France and Spain. The model output spatial patterns were quantified through two metrics derived from the variogram: i) the variogram sill, which quantifies the degree of spatial variability of the data; and ii) the variogram integral range, which represents the spatial length scale of the data. The higher seasonal variation of the spatial variability of sensible and latent heat fluxes over France and Spain, compared to the UK, is related to a more frequent occurrence of a soil-moisture-limited evapotranspiration regime during summer dry spells in the south of France and Spain. The small differences in spatial variability of net radiation between models indicate that the spatial patterns of net radiation are mostly driven by the climate forcing data set. However, the models exhibit larger differences in latent and sensible heat flux spatial variabilities, which are related to their differences in i) soil and vegetation ancillary datasets and ii) physical process representation. The highest discrepancies in spatial patterns between models are observed for soil moisture, which is mainly related to the type of soil hydraulic function implemented in the models. This work demonstrates the capability of the variogram to enhance our understanding of the spatiotemporal structure of the uncertainties in land surface model outputs. Therefore, we strongly encourage the implementation of the variogram metrics in model intercomparison exercises.

迄今为止，相对较少的精力用于定量评估模型输出的空间模式差异。在本文中，我们使用了基于变异函数的方法来量化由三种陆地表面模型（SURFEX / ISBA，JULES和CHTESSEL）模拟的根区土壤水分，净辐射以及潜热通量和感热通量的空间格局的差异。超过三个欧洲地理区域-英国，法国和西班牙。通过从变异函数得出的两个度量来量化模型输出的空间模式：i）变异函数基石，它量化了数据的空间变异性；ii）变异函数积分范围，代表数据的空间长度尺度。与英国相比，法国和西班牙的感热通量和潜热通量的空间变异性的季节变化较大，这与法国南部和南部夏季干旱期间土壤水分受限的蒸散量发生更为频繁有关。西班牙。模型之间净辐射的空间变异性的微小差异表明，净辐射的空间格局主要由气候强迫数据集驱动。然而，这些模型在潜热通量和感热通量的空间变异方面表现出较大差异，这与它们在以下方面的差异有关：i）土壤和植被辅助数据集； ii）物理过程表示。在模型之间的空间模式差异最大的是土壤湿度，这主要与模型中实现的土壤水力功能类型有关。这项工作证明了变异函数可以增强我们对地表模型输出不确定性的时空结构的理解。因此，我们强烈建议在模型比对练习中实施方差图指标。