Core Ideas: A community effort is needed to move soil modeling forward. Establishing an international soil modeling consortium is key in this respect. There is a need to better integrate existing knowledge in soil models. Integration of data and models is a key challenge in soil modeling. The remarkable complexity of soil and its importance to a wide range of ecosystem services presents major challenges to the modeling of soil processes. Although major progress in soil models has occurred in the last decades, models of soil processes remain disjointed between disciplines or ecosystem services, with considerable uncertainty remaining in the quality of predictions and several challenges that remain yet to be addressed. First, there is a need to improve exchange of knowledge and experience among the different disciplines in soil science and to reach out to other Earth science communities. Second, the community needs to develop a new generation of soil models based on a systemic approach comprising relevant physical, chemical, and biological processes to address critical knowledge gaps in our understanding of soil processes and their interactions. Overcoming these challenges will facilitate exchanges between soil modeling and climate, plant, and social science modeling communities. It will allow us to contribute to preserve and improve our assessment of ecosystem services and advance our understanding of climate‐change feedback mechanisms, among others, thereby facilitating and strengthening communication among scientific disciplines and society. We review the role of modeling soil processes in quantifying key soil processes that shape ecosystem services, with a focus on provisioning and regulating services. We then identify key challenges in modeling soil processes, including the systematic incorporation of heterogeneity and uncertainty, the integration of data and models, and strategies for effective integration of knowledge on physical, chemical, and biological soil processes. We discuss how the soil modeling community could best interface with modern modeling activities in other disciplines, such as climate, ecology, and plant research, and how to weave novel observation and measurement techniques into soil models. We propose the establishment of an international soil modeling consortium to coherently advance soil modeling activities and foster communication with other Earth science disciplines. Such a consortium should promote soil modeling platforms and data repository for model development, calibration and intercomparison essential for addressing contemporary challenges.

We compiled published and newly-obtained data on the directly-measured atmospheric deposition of total phosphorus (TP), filtered total phosphorus (FTP), and inorganic phosphorus (PO₄-P) to open land, lakes, and marine coasts. The resulting global data base includes data for c. 250 sites, covering the period 1954 to 2012. Most (82%) of the measurement locations are in Europe and North America, with 44 in Africa, Asia, Oceania, and South-Central America. The deposition rates are log-normally distributed, and for the whole data set the geometric mean deposition rates are 0.027, 0.019 and 0.14 g m⁻² a⁻¹ for TP, FTP and PO₄–P respectively. At smaller scales there is little systematic spatial variation, except for high deposition rates at some sites in Germany, likely due to local agricultural sources. In cases for which PO₄–P was determined as well as one of the other forms of P, strong parallels between logarithmic values were found. Based on the directly-measured deposition rates to land, and published estimates of P deposition to the oceans, we estimate a total annual transfer of P to and from the atmosphere of 3.7 Tg. However, much of the phosphorus in larger particles (principally primary biological aerosol particles) is probably redeposited near to its origin, so that long-range transport, important for tropical forests, large areas of peatland and the oceans, mainly involves fine dust from deserts and soils, as described by the simulations of Mahowald et al. (Global Biogeochemical Cycles 22, GB4026, 2008). We suggest that local release to the atmosphere and subsequent deposition bring about a pseudo-diffusive redistribution of P in the landscape, with P-poor ecosystems, for example ombrotrophic peatlands and oligotrophic lakes, gaining at the expense of P-rich ones. Simple calculations suggest that atmospheric transport could bring about significant local redistribution of P among terrestrial ecosystems. Although most atmospherically transported P is natural in origin, local transfers from fertilised farmland to P-poor ecosystems may be significant, and this requires further research.

Field observations and experimental data of effects of nitrogen (N) deposition on plant species diversity have been used to derive empirical critical N loads for various ecosystems. The great advantage of such an approach is the inclusion of field evidence, but there are also restrictions, such as the absence of explicit criteria regarding significant effects on the vegetation, and the impossibility to predict future impacts when N deposition changes. Model approaches can account for this. In this paper, we review the possibilities of static and dynamic multispecies models in combination with dynamic soil–vegetation models to (1) predict plant species composition as a function of atmospheric N deposition and (2) calculate critical N loads in relation to a prescribed protection level of the species composition. The similarities between the models are presented, but also several important differences, including the use of different indicators for N and acidity and the prediction of individual plant species vs. plant communities. A summary of the strengths and weaknesses of the various models, including their validation status, is given. Furthermore, examples are given of critical load calculations with the model chains and their comparison with empirical critical N loads. We show that linked biogeochemistry–biodiversity models for N have potential for applications to support European policy to reduce N input, but the definition of damage thresholds for terrestrial biodiversity represents a major challenge. There is also a clear need for further testing and validation of the models against long‐term monitoring or long‐term experimental data sets and against large‐scale survey data. This requires a focused data collection in Europe, combing vegetation descriptions with variables affecting the species diversity, such as soil acidity, nutrient status and water availability. Finally, there is a need for adaptation and upscaling of the models beyond the regions for which dose–response relationships have been parameterized, to make them generally applicable.