A geostatistical approach to the field-scale pattern of heterotrophic soil CO₂ emission using covariates

Soil heterotrophic respiration fluxes at field scale may exhibit a substantial spatial variability. The aim of this study was (1) to elucidate the role of soil temperature and different carbon fractions on heterotrophic soil respiration and (2) to test by which of three different statistical approaches (multiple regression, external drift kriging and simulated annealing) such influences may be best represented. Chamber-based measurements of respiration fluxes were carried out within a 180 × 40 m bare soil plot. Soil temperature was measured simultaneously to the flux measurements. Further, we recorded total soil organic carbon content, apparent electrical conductivity as well as mid-infrared spectroscopy-based carbon fractions as co-variates in addition to basic soil properties like stone content and texture. A stepwise multiple linear regression procedure was used to spatially predict bare soil respiration from the co-variates. The results showed that the particulate organic matter (POM) fraction and terrain elevation were able to explain the spatial pattern of heterotrophic soil respiration (R ² = 0.45). In a second step we applied external drift kriging to determine the improvement of using co-variates in an estimation procedure in comparison to ordinary kriging. The maximum relative improvement using the co-variates in terms of the root mean square error was 16%. In a third step we applied simulated annealing to perform stochastic simulations conditioned with external drift kriging to generate more realistic spatial patterns of heterotrophic respiration at plot scale. The conditional stochastic simulations revealed a significantly improved reproduction of the probability density function, the G-statistics value increased from 0.36 to 0.92. Further, the error in the reproduction of the semivariogram of the original point data decreased by more than one order of magnitude. All this confirmed that the mapping of soil respiration patterns may be significantly improved when considering terrain elevation and spatial heterogeneity of POM in combination with a conditional stochastic simulation.