Geostatistical scaling of land surface parameters with spatial heterogeneities in the validation of remote sensing products

Scaling is a fundamental research issue in the geosciences and plays an essential role in the comparison and integration of datasets and in the calibration and validation of environmental models. Much environmental research suffers from a scale discrepancy between different data sources and models[1]. In the validation of remote sensing products, for instance, soil moisture is typically measured in situ at the scale of several dm3, while satellites measure soil moisture for grid cells at least several km2 in size[2]. Different spatial scales (supports) in the input and output cause the issue of scale transformation[3]. Various methods have been proposed to transfer the spatial scale of land surface parameters but most are appropriate only for homogeneity situations. In most real-world situations, heterogeneity is inevitably present. This article focuses on scaling methods for land surface parameters under spatial heterogeneity and develops a methodological framework for `scale transformation'. This framework is composed of two types of methods to handling the issue of scale transformation: (1) from multiple in situ observations at point support to obtain satellite footprint-scale estimates (area support), named as MOPTA; (2) from multiple in situ observations at footprint scale (area support) to obtain another footprint-scale estimate (area support), named as MOATA. Land surface parameters considered are soil moisture and evapotranspiration (ET). As to MOPTA, we investigates two cases of upscaling in situ soil-moisture observations to satellite footprint-scale estimates. The in situ observations are acquired by three types of ecohydrological wireless sensor network (WSNs) deployed in 5 cm depth, varying measurement precision. WSNs covers approximately 16 (4 × 4) MODIS 1-km spatial resolution pixels. In the first case, A block kriging (BK) upscaling strategy is used to scale up soil moisture to MODIS pixel averages with in situ observations of unequal precision[4]. Furthermore, when measurement times of ground-based and satellite-based observations are not the same, temporal variation in soil moisture must be taken into account. At this case, a spatio-temporal regression block kriging (STRBK) is used to upscale in situ soil moisture observations collected as time series at multiple locations to pixel-scale estimates for validating the Polarimetric L-band Multi-beam Radiometer (PLMR) retrieved soil moisture product in the Heihe watershed[5]. As to MOATA, two types of in situ observations are involved: eddy correlation (EC) which measurements are normally a few to hundreds of meters[6][7] and large aperture scintillometer (LAS) which measurements are integrated over a long transect of approximately 500-5000 m from the same or different underlying surfaces[6][7]. For the purpose of cross-validation and comparison, the scale transformation between EC observations and LAS observations needs to be carried out. A area-to-area regression kriging is used to handle the problem of the nonstationarity of a random function and the issue of scale transformation[8]. This framework will be further developed to handling more cases. When land surface parameter show high spatio(-temporal) heterogeneity within the footprint, the upscaling strategy will take this into account through modelling the mean and variance as non-constant values that depend on high-resolution covariates. We will do this both in the spatial and spatio-temporal setting, in the case of the latter making use of space-time geostatistics and the stochastic partial differential equation (PDE) approach.