Abstract: Among the soil-based ecosystem services (ES), nutrient cycling and carbon sequestration have direct influence on the biogeochemical cycles and greenhouse gas emissions affecting provision of other ES that support human existence. We reviewed methods to assess the two key ES by identifying their strengths and weaknesses and have made suggestions for using appropriate methods for better understanding of the ecosystem functions for the provision of ES. Relevant papers for the review were chosen on the basis of (i) diversity of studies on the two key ES in different ecosystems, (ii) methodologies applied and (iii) detailed descriptions of the trial locations in terms of vegetation, soil type, location and climatic information. We concluded that (i) elemental stoichiometrical ratios could be a potential approach to assess the health of ecosystems in terms of provision of the two ES discussed, (ii) stoichiometric imbalances need to be avoided between the supply and the demand of the nutrients to maintain the ES provision in terrestrial ecosystems and (iii) stoichiometric ratios can act as a management tool at a field, farm and at landscape level, to complement other compositional biodiversity and functional diversity approaches to ensure sustainable provision of ES.

Abstract: Eddy covariance data from four European grassland sites are used to probabilistically invert the CARAIB (CARbon Assimilation In the Biosphere) dynamic vegetation model (DVM) with 10 unknown parameters, using the DREAM((ZS)) (DiffeRential Evolution Adaptive Metropolis) Markov chain Monte Carlo (MCMC) sampler. We focus on comparing model inversions, considering both homoscedastic and heteroscedastic eddy covariance residual errors, with variances either fixed a priori or jointly inferred together with the model parameters. Agreements between measured and simulated data during calibration are comparable with previous studies, with root mean square errors (RMSEs) of simulated daily gross primary productivity (GPP), ecosystem respiration (RECO) and evapotranspiration (ET) ranging from 1.73 to 2.19, 1.04 to 1.56 g C m(-2) day(-1) and 0.50 to 1.28 mm day(-1), respectively. For the calibration period, using a homoscedastic eddy covariance residual error model resulted in a better agreement between measured and modelled data than using a heteroscedastic residual error model. However, a model validation experiment showed that CARAIB models calibrated considering heteroscedastic residual errors perform better. Posterior parameter distributions derived from using a heteroscedastic model of the residuals thus appear to be more robust. This is the case even though the classical linear heteroscedastic error model assumed herein did not fully remove heteroscedasticity of the GPP residuals. Despite the fact that the calibrated model is generally capable of fitting the data within measurement errors, systematic bias in the model simulations are observed. These are likely due to model inadequacies such as shortcomings in the photosynthesis modelling. Besides the residual error treatment, differences between model parameter posterior distributions among the four grassland sites are also investigated. It is shown that the marginal distributions of the specific leaf area and characteristic mortality time parameters can be explained by site-specific ecophysiological characteristics.