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.

Background and aimRecycled sources of phosphorus (P), such as struvite extracted from wastewater, have potential to substitute for more soluble manufactured fertilisers and help reduce the long-term threat to food security from dwindling finite reserves of phosphate rock (PR). This study aimed to determine whether struvite could be a component of a sustainable P fertiliser management strategy for arable crops.MethodsA combination of laboratory experiments, pot trials and mathematical modelling of the root system examined the P release properties of commercial fertiliser-grade struvite and patterns of P uptake from a low-P sandy soil by two different crop types, in comparison to more soluble inorganic P fertilisers (di-ammonium phosphate (DAP) and triple super phosphate (TSP)).ResultsStruvite had greatly enhanced solubility in the presence of organic acid anions; buckwheat, which exudes a high level of organic acids, was more effective at mobilising struvite P than the low level exuder, spring wheat. Struvite granules placed with the seed did not provide the same rate of P supply as placed DAP granules for early growth of spring wheat, but gave equivalent rates of P uptake, yield and apparent fertiliser recovery at harvest, even though only 26 % of struvite granules completely dissolved. Fertiliser mixes containing struvite and DAP applied to spring wheat have potential to provide both optimal early and late season P uptake and improve overall P use efficiency.ConclusionsWe conclude that the potential resource savings and potential efficiency benefits of utilising a recycled slow release fertiliser like struvite offers a more sustainable alternative to only using conventional, high solubility, PR-based fertilisers.Electronic supplementary materialThe online version of this article (doi:10.1007/s11104-015-2747-3) contains supplementary material, which is available to authorized users.

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19The readily available global rock phosphate (P) reserves may run out within the next 50-130 20 years, causing soils to have a reduced P concentration which will affect plant P uptake. Using 21 a combination of mathematical modelling and experimental data we investigated potential 22 plant-based options for optimising crop P uptake in reduced soil P environments. 23By varying the P concentration within a well-mixed agricultural soil, for high and low P (35.5 24 to 12.5 mg l -1 respectively, using Olsen's P index), we investigated branching distributions 25 within a wheat root system that maximise P uptake. 26Changing the root branching distribution from linear (evenly spaced branches) to strongly 27 exponential (a greater number of branches at the top of the soil), improves P uptake by 142%

The growth of rice in submerged soils depends on its ability to form continuous gas channels-aerenchyma-through which oxygen (O 2 ) diffuses from the shoots to aerate the roots. Less well understood is the extent to which aerenchyma permits venting of respiratory carbon dioxide (CO 2 ) in the opposite direction. Large, potentially toxic concentrations of dissolved CO 2 develop in submerged rice soils. We show using X-ray computed tomography and image-based mathematical modelling that CO 2 venting through rice roots is far greater than thought hitherto. We found rates of venting equivalent to a third of the daily CO 2 fixation in photosynthesis. Without this venting through the roots, the concentrations of CO 2 and associated bicarbonate (HCO 3 − ) in root cells would have been well above levels known to be toxic to roots.Removal of CO 2 and hence carbonic acid (H 2 CO 3 ) from the soil was sufficient to increase the pH in the rhizosphere close to the roots by 0.7 units, which is sufficient to solubilize or immobilize various nutrients and toxicants. A sensitivity analysis of the model showed that such changes are expected for a wide range of plant and soil conditions.

Management and irrigation of plants increasingly relies on accurate mathematical models for the movement of water within unsaturated soils. Current models often use values for water content and soil parameters that are averaged over the soil profile. However, many applications require models to more accurately represent the soil-plant-atmosphere continuum, in particular, water movement and saturation within specific parts of the soil profile. In this paper a mathematical model for water uptake by a plant root system from unsaturated soil is presented. The model provides an estimate of the water content level within the soil at different depths, and the uptake of water by the root system. The model was validated using field data, which includes hourly water content values at five different soil depths under a grass/herb cover over one year, to obtain a fully calibrated system for plant water uptake with respect to climate conditions. When compared quantitatively to a simple water balance model, the proposed model achieves a better fit to the experimental data due to its 2 ability to vary water content with depth. To accurately model the water content in the soil profile, the soil water retention curve and saturated hydraulic conductivity needed to vary with depth.

12Aims The readily available global rock phosphate (P) reserves may be depleted within the next 50-13 130 years warranting careful use of this finite resource. We develop a model that allows us to assess 14 a range of P fertiliser and soil management strategies for Barley in order to find which one 15 maximises plant P uptake under certain climate conditions. 16Methods Our model describes the development of the P and water profiles within the soil. Current 17 cultivation techniques such as ploughing and reduced till gradient are simulated along with fertiliser 18 options to feed the top soil or the soil right below the seed. 19Results Our model was able to fit data from two barley field trials, achieving a good fit at early 20 growth stages but a poor fit at late growth stages, where the model underestimated plant P uptake. 21A well-mixed soil (inverted and 25 cm ploughing) is important for optimal plant P uptake and 22 provides the best environment for the root system. 23Conclusions The model is sensitive to the initial state of P and its distribution within the soil profile; 24 experimental parameters which are sparsely measured. The combination of modelling and 25 experimental data provides useful agricultural predictions for site specific locations. 26 27

Aims Phosphorus (P) is an essential nutrient necessary for maintaining crop growth, however, it's often used inefficiently within agroecosystems, driving industry to find new ways to deliver P to crops sustainably. We aim to combine traditional soil and crop measurements with climate-driven mathematical models, to give insight into optimising the timing and placement of fertiliser applications. Methods The whole plant crop model combines an above-ground leaf model with an existing spatially explicit below-ground root-soil model to estimate plant P uptake and above ground dry mass. We let P-dependent photosynthesis estimate carbon (C) mass, which in conjunction with temperature sets the root-growth-rate. Results The addition of the leaf model achieved a better estimate of two sets of barley field trial data for plant P uptake, compared with just the root-soil model alone. Furthermore, discrete fertiliser placement increases plant P uptake by up to 10 % in comparison to incorporating fertiliser. Conclusions By capturing essential plant processes we are able to accurately simulate P and C use and water and P movement during a cropping season. The powerful combination of mechanistic modelling and experimental data allows physiological processes to be quantified accurately and Plant Soil (2016) useful agricultural predictions for site specific locations to be made.