Capability of the variogram to quantify the spatial patterns of surface fluxes and soil moisture simulated by land surface models

Abstract

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.

Interpolation and Synthesis of Sparse Samples in Exoplanet Atmospheric Modeling

“…(The nugget term is negligible for both cases.) The sill and range provide diagnostic quantities in addition to the graphical representation of the variogram that can be utilized in model intercomparisons (see Garrigues et al 2021).…”

“…The general problem was that obtaining drill core samples is expensive, and so only a sparse number of samples could be obtained over the field of interest. Kridge and Sichel developed methods for correlating and interpolating sparse samples that are today known as "kriging" and have been applied beyond mining to a wide range of problems, which include weather prediction and geographic information systems as well as climate science (e.g., Drignei 2009;Garrigues et al 2021) and astrophysics (e.g., Tremmel et al 2017). The application of kriging to the analysis of climate models was suggested by Drignei (2009), who demonstrated that sparse samples of computationally expensive GCM calculations can be combined with larger sets of less complex model calculations to make meaningful predictions without needing to run additional GCM cases.…”

Spatiotemporal Landscape Pattern Analyses Enhanced by an Integrated Index: A Study of the Changbai Mountain National Nature Reserve

“…The range parameter thus indicates the range of spatial correlation of the underlying variable [25]. If the value of the range is big, it means that the land cover type has a bigger range of spatial correlation and similar spatial features over a larger distance and vice versa [26][27][28].…”

“…Finally, conclusions were drawn about the dynamic changes of the landscape pattern in the Changbai Mountain National Nature Reserve. means that the land cover type has a bigger range of spatial correlation and similar spatial features over a larger distance and vice versa [26][27][28].…”