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In semiarid zones, wind erosion is very significant and tillage erosion redistributes considerable amounts of soil at the field scale. However, water erosion is globally the most important and will be the focus of discussion here. The intensification of agriculture and changes in rainfall patterns with more intense rain events may increase rates of surface soil erosion.

The damage is not limited to the removal of productive soil top layer Pimental and Sparks, , but also affects surface water quality downstream stream and lake ecology, dam siltation, and enhanced pollution by agrochemicals and colloid facilitated transport. Soil erosion is strongly connected with drivers for climate change, as the mobilization of large amounts of soil organic carbon by soil transport may significantly contribute to atmospheric CO 2 emissions WMO, In addition, drier soil conditions associated with future climate extremes may limit rates of soil carbon accumulation, thereby reducing soil aggregation and enhancing vulnerability to wind erosion.

A host of soil conservation strategies for combating land degradation due to soil erosion offer additional benefits such as enhanced soil water storage Troeh et al. Soil erosion leads to significant loss of agricultural land and reduction in agricultural productivity, as soil loss diminishes soil water storage capacity, impacting crop growth and enhancing flood risk.

Soil erosion by water is a complex phenomenon resulting from soil detachment by raindrop impacts and overland flow, and transport of particles by rain splash and by sheet and channel flow Ellison, , Quantitative evaluation of erosion effects at the different scales requires modeling capabilities to deal with the complexity of the processes involved.

In the different modeling approaches, the driving and resisting forces are conceptually expressed by i flow erosivity an indicator of the erosive potential of rainfall and runoff and ii soil erodibility a measure of the susceptibility of soil particles to detachment and transport by rainfall and runoff. Both are state variables that respond to variations in local and regional conditions, making their evaluation the real challenge of erosion modeling. The flow erosivity requires data on the timing and amount of runoff Assouline et al. This is required for the nontrivial issue of modeling coupled infiltration and overland flow Furman, ; Chen et al.

Quantitative representation of the infiltration process itself requires multiscale information of soil hydraulic properties and its spatial variations, soil surface conditions, topography, soil profile initial conditions, and boundary conditions Assouline, Because of the multiscale nature of erosion, one can either focus on the microscale and consider soil particle detachment by rain splash and sediment transport using a process-based approach Eckern, ; Rose, ; Lane, ; Diaz et al.

At the macroscale, the most commonly used quantitative expression of soil erosion continues to be the multiplication-of-factors type empirical equation, as proposed by Neal, , where soil loss is a function of the product of soil erodibility and rain erosivity Wischmeier, ; Meyer and Harmon, ; Kinnell and Wood, ; Kinnell, ; Zhang et al.

Following this approach, soil erodibility is considered an intrinsic soil property independent of rainfall and slope conditions Lane et al. However, soil erodibility has been found to be dependent on infiltration and runoff Nearing et al. Soil erodibility also varies over the long term due to feedbacks between erosion and soil properties Govers et al. Another major problem with current macroscale assessments is that the procedures used for upscaling are sometimes inadequate, which may lead to a significant overestimation of erosion rates Cerdan et al.

Relatively little attention has been given to the modeling of soil transport across the landscape, in connection with soil, nutrient, and carbon delivery to stream and open waters. Whereas spatially distributed sediment routing using transport and deposition laws may offer better perspectives to understand sediment delivery, such modeling approaches have been relatively simple Van Rompaey et al.

Mitigating and controlling erosion require advance modeling tools to evaluate the appropriateness and efficiency of alternative approaches and methods. Compaction Soil compaction caused by human activities that reduces soil pore volume has been recognized as a worldwide problem Bridges, ; Soane and van Ouwerkerk, These changes can turn soil into a source for environmental CH 4 instead of a sink.

Furthermore, the platy structure caused by soil compaction reduces plant rootability. Compaction also decreases water infiltration, which increases water runoff, soil erosion, and the likelihood of flooding and debris flow. Efficient protection against unwanted soil compaction requires knowledge of the mechanical processes and properties of structured, unsaturated soils.

All soil deformation processes affect ecosystem services and soil functions in the short term and some, such as those involving irreversible dewatering and compaction of clay, in the long term as well. Soil compaction models use empirical simple cause—effect relationships , semi-empirical pedotransfer functions , and process-based approaches Keller et al. Process-based compaction modeling is generally a three-step approach. The first step describes the load situation e.

The second step quantifies the change in the stress field within the soil due to the load applied to the soil surface. The third step uses constitutive relationships to quantify soil deformation as a result of the change in the soil stress field. These three steps are typically incorporated into an analytical Soehne, ; Soehne, ; Horn, ; Van den Akker, ; Keller et al. Recently, progress was made toward improving the characterization of the pressure distribution at the soil surface Gysi et al.

This progress allowed for improved process-based compaction modeling that used a comprehensive framework to describe stress-deformation behavior due to vehicle traffic. Additionally, more soil information has become available because of georeferencing and global positioning systems GPSs that allows for soil compaction modeling at the field scale using pedotransfer functions. Horn and Fleige developed pedotransfer functions to estimate compaction sensitivity based on bulk density texture, organic matter content and soil structure as well as moisture status.

Horn and Fleige also addressed the changes in physical soil functions that were related to soil surface loads, for example, due to vehicle traffic Duttmann et al. Assouline a , b extended models for the soil water retention and hydraulic conductivity curves to account for structural changes in soils resulting from changes in porosity, enabling the prediction of the hydraulic properties of compacted or tilled soils.

For example, we have only a very limited quantitative understanding of soil structure and dynamics and how they influence the physical and mechanical processes and properties of soil Logsdon et al. Although the description of soil stress-deformation behavior has largely improved, the impact of soil deformation on soil hydrological processes, soil chemistry, and soil biology is still not well understood. Another limitation is that classical soil mechanics were developed for mostly static loads, whereas most soil compaction is caused by dynamic loads, such as soil deformation under a rolling wheel.

The differences between compaction caused by static and dynamic loads were studied only recently Wiermann et al. Finally, there is a huge gap in upscaling soil compaction properties and processes measured in the laboratory to the field scale, as well as understanding the effects of field-scale compaction on hydrological and ecological processes in the landscape.

For an ecosystem-scale soil model, we suggest that a simplified semi-empirical soil compaction modeling approach would likely be the most effective to improve the quantification of soil ecosystem processes and identify the key challenges.

ELUM: Ecosystem Land Use Modelling & Soil C Flux Trial

Soil Modeling and Ecosystem Services In this section we will deal with the role of soil models in understanding, quantifying, and delivering ecosystem services. We focus on two groups of ecosystem services as outlined in Fig. Regulating services include climate regulation and recycling of wastes and buffering and filtering capacity of soils; provisioning services include biomass production for food, fiber, and energy, as well as soil as habitat and physical support.

We discuss the role of soil models to determine the importance of the different soil properties, as affected by the different soil processes, for the different ecosystem services. At the end of this section, we formulate five key challenges on soil modeling and ecosystem services Table 4. Regulating Services Climate Regulation Climate regulation may be assessed in terms of the time scales of its regulatory function.

For example, at hydrological short time scales soil water storage affects various climate patterns e. Soil regulatory function could also be assessed through mechanistic feedbacks related to its properties and hydro-ecological functioning, such as effects of soil on plant communities that affect climate, surface albedo, land use patterns, and more.

The inextricable links between soil and climate were highlighted in the section on soil formation and have been quantified in various quantitative models for soil formation. Soil water storage features prominently in the definition of droughts Alley ; Dai et al. A recent study Trenberth et al.

Soil properties control soil evaporation dynamics and transition to stage 2 evaporation Or et al. This is linked to the amount and stability of estimated soil carbon stocks that vary with soil properties and function also with land use and climate. Changes in soil surface temperature affect the fate of carbon stocks in arctic regions and within a relatively short period, large tracts of land may become significant sources of GHG at high rates, for example, due to the rapid thawing of permafrost soils in northern latitudes Schuur et al.

On geologic time scales, rock weathering and formation of soils play a substantial role in supporting vegetation, accumulating carbon, and thus regulation of planetary climate e. Soil management practices, such as tillage and land clearing forests and grasslands , are among the main human activities that have significantly increased CO 2 emissions in the past centuries, with much of the emissions mediated by soil microbial processes. Additionally, the increase in fertilizer application to boost crop production part of what is known as the Green Revolution , has resulted in significant releases of nitrous oxides to the atmosphere, thereby reducing nutrient use efficiency and directly contributing to global warming.

Vinken et al. For natural systems at the northern lower latitudes, it is expected that soil warming and melting of permafrost will result in positive feedbacks of unknown magnitudes Schuur et al. In general, wide ranging estimates of negative feedbacks are projected with rising temperatures that could decrease net primary production. Hence, to understand the role of GHG emissions and to mitigate their adverse impacts, the soil community must endeavor to study the integrated soil system by linking physical, chemical and biological processes, and their variations with future climate patterns and introduce state-of-the-art knowledge on soil processes in existing and operational terrestrial biosphere models Fisher et al.

In particular, the assessment of the impact of management and land use practices on GHG emissions requires models that are based on a fundamental understanding of these processes. When considering regional soil carbon balances, one must take account of changes caused by soil erosion and soil formation longer time scales that affecting the soil organic matter pool and the balance between its decomposition and sequestration Lal, ; Amundson et al.

Soil models for climate regulation are listed in Table 2. Integrated modeling approaches informed by climate scenarios and feedback provide the necessary know-how for adapting agricultural and natural ecosystems to changing temperatures and soil moisture regimes that affect plants and crop yields as well as soil ecological functioning and long term sustainability. Buffering and Filtering We may define the buffering capacity of soil as including processes that involve storage and transformation of chemicals, including both anthropogenic and biogeogenic substances.

Addition and removal of chemicals disturbs the state of a soil, affecting biota as they require sufficiently stable conditions; however, such disturbances can be countered by biogeochemical processes. The modeling goal is to quantify the extent and spatiotemporal variability of such buffering. All soil related processes are connected with soil buffering and filtering. Relevant physical processes concern the exchange of carrier fluids, such as water and gas with groundwater, surface water, and atmosphere, as well as by physical filtration at phase interfaces, whereas important biogeochemical processes are chemical ad- and desorption, precipitation—dissolution, and transformation.

In addition, biological processes, like in the rhizosphere and biofilms may play an important role in filtering and buffering and have not been explicitly considered in modeling until recently Or et al. Because soil organic matter is a major sorbent for many important chemicals, buffering is intensively linked with the major cycling of N, P, and C. Connected with the unsaturated soil zone is the capillary fringe at the groundwater table. Since the capillary fringe is characterized by steep gradients in terms of hydraulic state variables and chemical e.

Moreover, this biogeochemically important transition zone changes very dynamically with time and depth Winter et al. Yet, our understanding of this important zone between the vadose zone and the groundwater is still limited, requiring more intensive research and an more improved incorporation of capillary fringe processes in soil models. Significant advances have been made during the past decades in understanding, quantifying, and modeling of buffering and filtering processes. General mineral equilibria models have been extended with validated ad- and desorption models for specific groups of solutes, such as metals Zhang et al.

Interaction between soil components is crucial for quantifying buffering and filtering; inorganic and organic components might compete either for sorption sites or for forming aqueous complexes increasing solubility or decreasing sorption. A number of numerical tools have been developed during the last decade accounting for these interactions, mainly based on principles of thermodynamic equilibrium Steefel et al.

The generic nature of these tools allows for implementing complex conceptual models for fate and transport Jacques et al. This includes nonequilibrium of water—air dynamics, as these interfaces control interactions and access to sorption sites, duration of interactions and local equilibrium assumption LEA validity, and biological activity.

Much of that dynamics is caused by soil heterogeneity, such as preferential and bypass flow. Many advances have been made in modeling soil heterogeneity both explicitly by Bellin et al. Linking inorganic and organic biogeochemistry seems crucial for understanding the fate of many solutes. For example, some heavy metals form strong complexes with dissolved organic matter, as described in Fig. Whereas modeling of inorganic chemical biogeochemistry often addresses specific components e.

For cases where the organic matter pool may change significantly, with increasing occurrences of drought or water logging with associated redox potential changes, links between organic and inorganic interactions must be investigated. The kinetics of abiotic soil chemical changes also requires attention Werner Stumm ; Schroder et al. In addition to the kinetic behavior of soil chemical processes, soil biological processes show similar rate-limited behavior, which is most likely controlled by chemical and structural soil properties.

In fact, whether certain biological processes as denitrification occur at all, depends on the presence of the necessary microbial populations. In addition, bioavailability of contaminants for microorganisms affects the leaching behavior in essence Beltman et al. Mercury cycle in soil systems. Oval shapes denote Hg sources, rectangles are for Hg sinks and rounded rectangles are components that can act as both sources and sinks.

In summary, integrating physical aspects of nonuniform flow and solute transport with chemical and biological processes will remain a prominent focus of soil-modeling research. Recycling of Anthropogenic Waste Many human activities produce waste that is often released to the soil, such as chemotoxic and radioactive elements, toxic organic compounds, and potentially harmful living organisms and viruses. Waste inputs range from feedlots dung and farm animals, irrigation by wastewater nonpoint pollution by atmospheric deposition, accidental spills to deliberate dumping of industrial byproducts in highly engineered waste landfills.

A specific pathway is soil amendment to reduce metal leaching or to control CO 2 sequestration Campbell et al. Supporting processes such as limiting water flow through waste zones, sorption of compounds, and biological degradation help to regulate contaminant release to the biosphere by dilution, dispersion, retardation, and decay e.

Related examples of available models are listed in Table 2. Impacts of soil contamination, waste disposal, or site remediation are typically assessed with risk assessment chemotoxic compounds or radiological impact radioactive waste models. Although the safety or protection provided by a disposal system is primarily focused on isolation and containment, quantification of dilution and dispersion and bioaccumulation in soils systems is highly relevant for impact calculations by biosphere models Smith et al.

Particularly within the framework of radiological impact studies, time scales could be several tens of thousands to hundreds of thousands of years. Generally, engineered covers are put in place in typical landfills with hazardous materials.

For near-surface disposal systems for low-radioactive waste disposal, as well as for high-radioactive wastes Rosenberger, , cement-based structures are buried under an engineered layered system of natural materials Flach et al. Although covers could have an isolation function, protecting humans and other biota from the waste, their main functions are related to provide a stable physical and chemical soil environment for the waste and to limit water flow into the waste zones. Stable chemical conditions are related to durability in physical terms e.

Geochemical degrading and leaching processes are driven by soil pore water composition Jacques et al. The engineered barrier will also limit the water flow through the waste zone. The properties of the engineered barriers could be optimized to favor the evaporative capacity of the barrier, that is, increasing water holding capacity of the top water to promote ET or the divergence capacity by increasing lateral flow.

When contaminants are released into the soil, their transport and fate are governed by similar physical, chemical, and biological processes and pose similar modeling challenges as described for both the buffering and filtering regulating services. The main variable of interest is the flux across environmental compartments, such as the groundwater, biosphere, and atmosphere. A particular challenge is the development of a soil-like profile in the engineered barrier that alters its relevant physical, hydrological, chemical, and biological properties thereby altering their required performance.

For that purpose, long-terms field experiments of years to decades Albright et al. To deal with extremely long time scales, models should be able to incorporate long-term changes in climate, landforms, and other relevant boundary conditions. Integrated methodological approaches need to be developed to verify such models beyond the time-scale of instrumental observations, for example, by including proxy variables serving as paleo indicators of past hydrological conditions e. As in simulating soil formation, many input variables are uncertain since they are in essence unknown for future conditions.

Nevertheless, soil waste modeling as described herein requires the same kind of scenario-like quantification, as well as collaborations with related modeling communities. Provisioning Services Biomass Production for Food, Fiber, and Energy By providing and storing nutrients and water, as well as serving as mechanical support for plants, soil plays a central role in biomass production. Soil also provides biochemical support for plant-essential symbionts.

Optimizing crop and biofuel production relies on a thorough understanding of plant requirements, soil water and nutrient availability, and on plant uptake mechanisms. This can be partly achieved via experimental work, but modeling is needed to investigate complex interactions and feedbacks between bulk soil, rhizosphere, and plant systems under environmental constraints.

Examples of models addressing this ecosystem service are listed in Table 2. Interacting biological, chemical, and physical processes affect crop root uptake and production Lynch, ; Hinsinger et al. The elements most often limiting to production are the macronutrients N, P, and K, although growth may be limited by supply of any of the essential elements.

Many soil processes are directly affected by plant activities, especially in the rhizosphere. Because of soil—root—microbial interactions, the biophysical and chemical properties of the rhizosphere are different from those of the bulk soil. To meet the crop nutrient demand, nutrients must be transported from the bulk soil into the rhizosphere toward the root surface Marschner and Marschner, The most simple single root uptake model considers soil nutrient transport by convection and diffusion, desorption of nutrients from the soil solid phase, and uptake at the root surface, as by Michaelis—Menten kinetics Darrah et al.

For nutrients of low mobility, uptake models include root hairs, root exudation, and arbuscular mycorrhizal fungi in either rhizosphere scale models Schnepf et al. In addition, nutrient uptake models have been coupled with water flow models Somma et al. Rhizosphere modeling includes root-induced changes in soil hydraulic properties through mucilage exudation and related effects on water and solute dynamics in the root zone as presented by Carminati and Vetterlein However, the release of rhizodeposits by roots and associated microbial activity enhances soil organic matter decomposition Kuzyakov and Domanski, and would require the inclusion of microbial and carbon dynamics Darrah, Besides nutrients, plants also need water.

The adequate description of water stress onset and water uptake distribution in soil is crucial for predicting plant growth transpiration flux and crop yield. Although we know water transpiration stream is driven by climatic demand and controlled by plant and soil, questions remain regarding the location and magnitude of controlling or regulating mechanisms for plant water flow Lobet et al. Bulk soil acts as a storage for water, and rhizosphere hydraulic properties control the availability of water to plants Couvreur et al.

Root segment—scale models called mesoscopic have been developed that explicitly solve axisymmetric Richards equation around a given root segment Philip, ; Gardner, ; Raats, and allow one to estimate the soil hydraulic resistance. Yet, soil compaction induced by root growth, shrinkage—swelling of roots and soil leading to gap formation between soil and root, and specific nonequilibrium processes induced by mucilage, for instance, challenge these equations. At the plant scale called macroscopic scale different approaches exist to account for root water uptake. Typically a sink term is included in the Richards equation, which includes soil resistance, plant root distribution, climatic demand, and sometimes a compensation term Javaux et al.

The challenge is to find a mathematical expression for the root water uptake or sink term that best represents the key mechanisms embedded in a numerically acceptable level of complexity for the application. The upscaling of complex and dynamic rhizosphere processes can be assessed with the help of mathematical modeling Roose and Schnepf, Different one-dimensional models have recently been proposed de Jong van Lier et al. Couvreur et al. Siqueira et al. Novel root growth models and tomography techniques have recently allowed the development of three-dimensional models Dunbabin et al.

At larger scale, the availability of many different models for root water uptake translates into high uncertainty in predicting transpiration. For land surface models, Wang and Dickinson showed that the ratio of transpiration to total ET ranged from 0. This uncertainty is due to the poor representation or validation of root water uptake modules, in particular under dry conditions Li et al.

An additional modeling challenge is to link soil—root zone processes at the rhizosphere scale to the spatially variable landscape scale Katul et al. Land surface or crop models typically have a grid size between and km 2 , in which plants uptake is modeled in zero or one dimension for the sake of simplicity and computational efficiency. In zero dimension, when spatially explicit information is not available, the effects of soil properties on nutrient and water uptake is treated simply by considering total availability and access of soil water and nutrients in the soil.

More advanced crop models apply one-dimensional soil modeling, using a simplified water balance and simple root depth models Gerwitz and Page, and thereby neglecting spatial variations in soil water or nutrient content and uptake rates. However, in spatially variable soil—root condition, the one-dimensional assumption does not hold and may lead to erroneous results of ET and crop yield, especially in soil-stressed conditions Roose and Fowler, Soil Physical Support Most terrestrial ecosystems rely on soil for their physical support and stability.

The functional design of plant roots is optimized for sufficient anchorage to the ground Coutts, , ; Coutts et al. Large trees and perennial shrubs especially have root systems that are intimately linked with the soil underneath, which enables them to support the enormous weight of their own biomass and external loads such as animals and snow as well as dynamic stresses from wind, debris flow, and surface runoff Stokes et al.

Soils also bear the weight of all terrestrial animals and provide habitat to burrowing animals including rodents, birds, and insects. At finer scales, soils provide physical support to microbial communities. The highly modified environment in the rhizosphere as well as biological soil crusts in many desert ecosystems provide stable microstructure that serves as a habitat for microbial communities.


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In summary, physical support service provided by soils is an essential ingredient for the health and sustainability of terrestrial ecosystems. Soils also provide direct support services to engineered structures as well as human activities. In many places, soil—in the form of mud bricks and dirt roofs—literally serves as a physical shelter.

Likewise, unpaved dirt roads and paths are vital access routes and essential in management of natural resources. A soil is able to provide the above stated services when its strength is sufficient to support the stresses exerted on it, yet not too strong to resist necessary deformations, such as for root growth and animal burrowing.

Therefore, a great deal of research related to soil as a physical support system has been directed toward understanding distribution and propagation of stress and strain in soil, as well as in quantifying the underlying rheological characteristics including elasticity, plasticity, and viscosity Baumgarten et al. The ability of heavy clay soils to provide physical support may also be compromised when they swell and shrink on wetting and drying, respectively.

In the United States alone, expansive soils cause billions of dollars of damage to civil structures Thomas et al. However, we need to include the aspect of rigidity in all our modeling approaches also because the shrink—swell processes alter the reference volume and may result in a complete overestimation of, for example, flux processes Horn et al. The latter is further exacerbated by progressive organic matter loss from drained soils Dawson et al.

Fundamentally, the ability of soils to provide physical support functions is a product of interplay between stabilizing and destabilizing processes. The key stabilizing processes include: soil aggregation, which is mediated by a variety of physical, chemical, and biological processes; cementation by mineral deposits; and stabilization by burrowing animals. Soil stabilization is continually countered by destabilizing processes, including shearing forces, dynamic mechanical stresses, static loads, and slaking. Theories and models of soil as a physical support system must involve the following key elements: i basic theories and modeling capability concerning mechanical strength, stress, strain, and their distribution in soils, which are generally well understood for most soil conditions over wide scale ranges; ii reliable techniques to quantifying stresses and strains, which are also well developed, especially for stress propagation under traffic; iii combined physical, chemical, and biological processes as the most influential parameters to strengthen soil systems, including the dynamic stress strength changes due to hydraulic processes also in mechanical theories; and iv quantitative understanding of particle-scale soil strengthening and further extrapolation from the interparticle to the meso- or macroscale.

The major open questions related to mechanistic understanding and modeling of physical support functions of soil include: i transient phenomena, including short-term elastic and elastoplastic responses, as well as transient coupled interactions between mechanical, hydraulic, and biogeochemical processes; ii stabilizing and destabilizing processes; and iii stress-dependent changes of soil hydraulic, thermal, and gas diffusion processes.

Soil and Biological Habitat Life in soil follows much the same pattern as human life on the surface of the planet. For life to persist, soil microbes require sufficient accessible food resources, water, safe refuges from predators, and gaseous and hydraulic transport pathways through which they move if motile and be active.

In terms of the soil geometry to provide the physical living habitat, key soil attributes are its porosity and its continuity and level of connectivity in space and time. Thus, soil pore and hydraulic connectivity, specific surface area, and tortuosity become key determinants of all processes that impact on soil life. The spatial distribution of porosity and nutrients determine distances between active microbes and roots , whereas the connected porosity determines the rate at which soil gases as CO 2 and O 2 can diffuse between microbial active sites.

Therefore, the soil water characteristic becomes one of the most important relationships in soil ecology Assouline, The latter has driven the majority of research in this area despite the fact that the level of aggregation is the relevant metric to capture and understand for most soils Young et al. Many conceptual models on aggregates exist Six et al. However, understanding the relevance of soil architecture within as it varies over time is a difficult task due to the complexity of the processes at hand and the significant spatial—temporal soil dynamics.

The challenge in relation to modeling habitat space is its linking to the relevant functions. Biodiversity research in soils has failed generally to account for the soil habitat that controls many of the relevant processes that generate soil biodiversity, the probability of movement of microbes and higher organisms, and the probability of gene transfer and the impact of pathogens on crop plants Therefore, the inclusion of the soil habitat in biodiversity modeling Young and Crawford, will ensure evaluations of the importance of soil geometry on soil biodiversity, including effects of spatial isolation and population connectedness Zhou et al.

Notwithstanding the difficult challenge of quantifying biological processes in any natural environment, modeling soil biological processes present specific challenges related to the complex and heterogeneous medium, limited observational capability into the opaque soil, and the wide range of scales where biological activity matters. The issue of scale is particularly difficult, as modelers are required to consider interactions taking place at the scale of microbial communities in pores Young and Crawford, ; Or et al. Description of dynamic changes in flow and transport and the response of biological agents to the changes in aquatic habitats for microbes Wang and Or, or the dynamic formation of microniches within soil aggregates that promote denitrification e.

Adding to the challenge is the soil opacity that hinders direct observations and thus necessitating surrogate measures and methods to obtain model parameters. Soil biological activity alter pore geometry characteristics, and related soil transport parameters. The changes and associated feedbacks may be gradual and slow root growth or occur overnight earthworm burrows, ants, and termites , thereby drastically modifying soil conditions. Challenges in Dealing with Soil Heterogeneity and Uncertainty Major challenges in soil modeling across all subdisciplines arise from the fact that the soil environment is very heterogeneous, that processes occur over a multitude of spatial and temporal scales, and that one has to deal with uncertainties in both models and data.

It is the objective of this section to discuss these issues. Heterogeneities and hierarchical structures may lead to different system behavior, requiring different model concepts to describe processes at different scales and locations. The second part discusses how appropriate model concepts and model parameters can be inferred from observations, bearing in mind that observations may be uncertain, variable in space, and not representative for the scale at which model predictions are made.

Sophisticated model concepts and parameterization procedures increase the precision of model predictions at the location where measurements used to parameterize the model are obtained. However, local conditions and predictions may not be representative, so the accuracy of precise local predictions may be low for the conditions and the region for which predictions are requested. The third part addresses the issue of prediction precision and accuracy and its consequences for model selection and parameterizations. Heterogeneity: Aggregate to Landscape, Microbe to Forest, Grains to Ecology Most soil processes and related soil ecosystem functions dealt with in this paper depend in one way or another on the architecture of soils, which determines the geometry and topology of the pore space inhabited by soil biota and through which water, gases, solutes, and particulate matter transit.

The architecture of soils is acknowledged as being heterogeneous at many different scales, all the way from the distribution of soils across the landscape down to microscopic pore networks and the molecular structure of biogeochemical interfaces. At large spatial scales field to landscape scale , the distribution of soils is mainly determined by geology, topography, climate, and land use, whereas at smaller scales pedon to pore scale the continuous flow of energy promotes physical and biochemical structure formation.

This produces characteristic soil architectures that typically change vertically along the main direction of flow and transport within soil profiles. Because of the nonlinearity of the different interacting processes of structure formation and decay, these changes are often distinct, leading to heterogeneous structures and vertical organization of soils e. An immediate consequence of the heterogeneous structure of the subsurface across spatial and temporal scales is that observed flow rates of water, gases, and solutes or the dynamics of state variables, such as soil moisture, temperature, and biological activity, typically depend on the scale of observation.

Thus, models of soil processes e. A major challenge when one attempts to model physical, chemical, or biological processes in soils is the opacity of soil materials that hampers the quantification of their architecture. For any reasonably sized soil volume, however, this is clearly neither possible due to the lack of detailed information and limited computing power, nor is it desirable because of the sheer flood of mostly redundant information.

The general approach to gain a representation at some larger macroscopic scale is to average the pertinent processes at the corresponding smaller microscopic scale over an appropriate domain. Necessary prerequisites for this approach to work are i that the macroscopic quantities are robust with respect to changes in the averaging domain and ii that the microscopic quantities are in thermodynamic equilibrium at the scale of the averaging domain. Given the wide temporal spectrum of forcings, for example, through precipitation, such an averaging is restricted to rather small domains.

The issue is further exacerbated by nonlinear processes like soil water flow, transport of reactive solutes, freeze—thaw cycles, or evaporation—condensation processes, which are all capable of generating sharp fronts and intricate patterns. The proper handling of such processes remains an open research question.

An example is the consideration of nonequilibrium phenomena by decoupling state variables through an additional equation at the larger scale Ross and Smettem, These effective parameters are typically gained from inverting physical numerical models. However, there is no evidence that the postulates are valid. It appears that proceeding to larger scales—to a field or even to a larger catchment—demands numerical simulations of the pertinent multiscale processes and quickly runs into supercomputer applications that include self-adaptive discretizations.

In the case of biological processes, such as microbial activity, subsurface heterogeneity fosters the coexistence of biochemical processes that cannot be captured or reproduced experimentally in homogenized materials. This is true for the concurrence of aerobic and anaerobic processes, as well as for the turnover of organic matter in general, which is promoted or hampered depending on the relative spatial distribution of soil biota and substrate.

While its importance is well recognized, it is still unclear how to represent this heterogeneity in modeling biological activity and organic matter turnover. Model Concepts Homogenization is a possible approach in the case when the various scales of heterogeneity are clearly separable, so that information from small scales can be transferred to larger scales in a meaningful way. In this case, small-scale heterogeneities can be averaged in time or space toward homogenized large-scale models that account for all the essential ingredients from the small-scale processes.

Separable scales might rather be expected at small scales when moving from soil pores to aggregates and up to soil horizons. Here we can identify different levels of macroscopic homogeneity. Examples for homogenization include derivation of the Darcy flow and Richards equation Daly and Roose, , solute movement in the soil with dual porous structure Zygalakis and Roose, , uptake of nutrients by root hairs Leitner et al. If the scales of heterogeneity are interlaced and nested, which is typically the case at the pedon scale and beyond, modeling soil processes needs to be adapted to the spatial or temporal scale representing the relevant heterogeneity at this scale.

In some cases, perturbations at a given scale may smear out when the observation scale becomes much larger. This may not be true when the perturbations at the microscopic scale are associated with microbial activity. However, this assumption applies, for example, for the transport of solutes through the soil pore network that develops towards a volume-averaged Fickian regime once the transport distance is much larger than the characteristic heterogeneities within the flow field. Another example is the rapid drainage or filling of single pores that translate into a smooth curve, known as the soil water retention curve, at the larger scale.

In both cases, the problem faced in reality is that heterogeneities at larger scales emerge before the limit of a well-defined macroscopic behavior is reached. A possible way to deal with this is to explicitly include the heterogeneity at the well-defined subscale, while heterogeneities at the sub-subscale and smaller scales are described by effective parameterizations and averaging Vogel and Roth, Examples, where this concept is typically applied include i water dynamics in soil profiles, where effective mean hydraulic properties are used for soil horizons; ii water and gas exchange between the soil and the atmosphere, where the lateral distribution of soil types is considered; and iii solute transport in groundwater, where only the coarse structure of the conductivity field is explicitly considered, while smaller scale heterogeneities are integrated into an effective dispersivity length.

Concerning biochemical processes, the vast abundance of biodiversity in soils may allow for simplified representations at larger scales since biological communities and their biological potential and activity are controlled by the local site conditions and the metabolism of individual organisms in any specific part of the pore space is not relevant.

This might be true for highly productive soils in humid regions. However, especially in water-scarce systems, the feedback between soil biota, organic matter, and water dynamics leads to complex patterns of system development Jenerette et al. Exploring Heterogeneity Several recent technologies and conceptual tools provide novel information on subsurface heterogeneity.

These methods differ widely in their capability, resolution, accuracy, and precision see "Modern Sources of Spatial and Temporal Data for Soil Modeling". Their most interesting aspects are the scales of resolution and view. Some may be used in an undisturbed field situation, while others are only applicable in carefully prepared lab environments. Some capture the entire volume of interest, others just its surface. Furthermore, the quantity of interest is often not observed directly, but only indirectly via a proxy. This requires the development of appropriate transfer functions that are often just empirical relations that need data-intensive calibration procedures.

In this context, top-down approaches can be highly attractive to make use of the multitude of available information, which will certainly increase in the near future, quantitatively as well as qualitatively. However, a bottom-up approach rooted in fundamental basic science observations is required to complement the top-down approach because ultimately the integration of the two, top-down and bottom-up approaches, and their synergy will enable the synthesizing of new scientific knowledge about soil systems. A joint analysis toward a consistent description of terrestrial systems may help an adequate representation emerge.

Soil Hydrology, Land Use and Agriculture: Measurement and Modelling by Manoj K. Shukla

Formalisms for Considering Uncertainties Related to Model Choice Uncertainties in soil models may arise on the conceptual level model choice , on the parameter level insufficient calibration data , through measurement errors, from stochasticity of system forcing, and from scaling issues. Multimodel ensemble simulations, e. Each model ensemble represents parametric within-model uncertainty, restricted to the available data though Bayesian updating conditional simulation. The BE value expresses how good a model including its uncertain parameters before conditioning matches the available data including their possible measurement errors , combined with a priori expert knowledge on model plausibility.

Unfortunately, the BMA approach is challenged by two issues. First, evaluating BE requires Monte-Carlo techniques to evaluate the fitting quality on average over its uncertain parameters of each model. This may become computationally prohibitive for models with long run times and with many uncertain parameters requiring very large ensembles in the BMA context. Instead, the study reviews and benchmarks a list of alternative numerical schemes for more efficient computation of BME that pose many additional future statistical and numerical research questions.

The second challenge in BMA is constructing a set of competing models to reflect conceptual uncertainty adequately i.

Session programme

In many applications, however, building a model is time-consuming and expensive, or only a single system conceptualization is readily available. Even if a large set of plausible models exists, the entire set may, in hindsight, seem inadequate on comparison to extensive and accurate data sets. Still, depending on the number of model parameters, the complexity of the problem and the data set size, MCMC can require up to 10 6 or more model evaluations. If MCMC is not feasible, uncertainty quantification is still possible when assuming that all model parameters and measurement errors follow multi-Gaussian distributions at least after transformation and that the model equations can be linearized, and then using linear error propagation Moore and Doherty, However, soil—plant models are typically highly nonlinear, so that linearized techniques must be treated with extreme care.

Because soil models often involve many state variables e. Different data types carry different information about the individual compartments and their respective processes Vereecken et al. In such situations, multiobjective optimization e. They also showed that an inadequate choice of calibration data sets may result in unrealistic parameter estimates and poor predictive performance, particularly for quantities that have not been included in model calibration.

Soil monitoring in the past has been largely restricted to a limited set of standard observations e.

Therefore, the worth of different and new data types for the performance and robustness of predictive models is an area of research that needs further attention. For local predictions, the processes and the parameters of the process model need to be described as precisely and accurately as possible.

Due to soil heterogeneity, information that is available about local soil parameters or about state variables or fluxes that are used to parameterize the model is very uncertain. This uncertainty is propagated into uncertainty about predictions, which may therefore be imprecise. However, for several practical applications, not the predictions at a certain given site and time, but the distribution of a certain variable in a specific region over a certain period are required. For predictions of the percentile of the distribution in a region the set of conditions in the region needs to be represented as precisely as possible.

This implies that the model should be able to represent the conditions in time and space that represent the distribution of conditions for the area and time period that is considered. The question arises therefore whether it is more important to have spatial and temporal coverage of information that is required to run a simplified and locally less precise model or whether it is better to use a more detailed and precise representation of the processes at a limited number of locations and time periods.

The problem of the second approach is that the relevance of the predictions for the region and time period of interest cannot be evaluated based on the lack of spatial and temporal coverage of the model parameters and boundary conditions. The distribution, which is predicted based on a limited number of conditions or situations, may therefore lack accuracy. An illustrative example is the process of pesticide risk assessment for pesticide registration Leterme et al. The general principles and questions may also be transferred to other soil processes and predictions.

The pesticide fate parameters sorption and degradation often vary strongly with location, but their variation cannot be predicted or derived from other soil properties, so these parameters are often treated as stochastic parameters.

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Figure 5 illustrates the effect of uncertainty of pesticide fate parameters on the predicted cumulative distribution of leachate concentrations in a certain region. In pesticide risk assessment, the question arises whether a prediction with a detailed process model that requires detailed information about soil properties including for instance a parameterization of preferential flow and transport and temporal information of meteorological variables rainfall data with high temporal resolution to capture rainfall intensities that trigger preferential flow is to be preferred over a prediction with a much simpler model that considers only yearly rainfall amounts and uses information about soil texture and organic matter.

The problem with the first approach is that an area-wide parameterization of a detailed model may not be possible due to a lack of data. The second problem is that computational resources may still be limiting to carry out simulations for millions of scenarios that are required to represent the distribution of soil, vegetation crop , and weather conditions and to consider uncertainties or spatial variability of stochastic parameters that cannot be mapped.

A workaround for this problem is to use meta-models that are calibrated on a limited number of simulation runs that are performed using more detailed models Tiktak et al. Such meta-models are simple regression models that make a direct link between available input parameters and the model output of interest.

The structure of the regression model can be based on analytical solutions of the process model that are obtained for certain boundary and initial conditions. Since they are much simpler, meta-models can easily be used to make predictions for a large number of scenarios and conditions. This allows evaluation of the effect of stochastic parameters on the spatial and temporal distribution of the prediction of interest, which generally requires a large number of simulations. In general, stochastic parameters lead to wider distributions of predictions in a certain region for a certain time period Heuvelink et al.

In addition, the error in meta-model predictions lack of precision could be treated similarly to the uncertainty due to stochasticity of the parameters. USD Sign in to Purchase Instantly. Overview Agriculture is strongly affected by changes in soil hydrology as well as by changes in land use and management practices and the complex interactions between them.

About the Author Manoj K. Remote sensing and soil hydrology.

Scientific challenge:

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