Upscaled exact solutions to root water uptake equations for earth system modelling

2020 ◽  
Author(s):  
Martin Bouda ◽  
Mathieu Javaux
Keyword(s):  
Soil Moisture ◽  
Exact Solutions ◽  
Water Uptake ◽  
Root Water Uptake ◽  
Hydraulic Redistribution ◽  
System Modelling ◽  
Pressure Gradients ◽  
Earth System ◽  
Plant Hydraulics ◽  
Discretisation Error

<p>Earth system models struggle to accurately predict soil-root water flows, especially under drying or heterogeneous soil moisture conditions, resulting in inaccurate description of water limitation of terrestrial fluxes. Recent descriptions of plant hydraulics address this by applying Ohm’s law analogues to the soil-plant-atmosphere hydraulic continuum.</p><p>While adequate for stems, this formulation linearises soil-root and within-root resistances by assumption, neglecting the nonlinearity of pressure gradients in absorbing roots. The resulting discretisation error is known to depend strongly on model spatial resolution. At coarse resolution, substantial errors arise in a form depending on the assumed configuration of resistances. In simulations of a drought at the Wind River Crane (WRC) flux site, a parallel Ohm model based on the rooting profile overpredicted hydraulic redistribution, while a series model overpredicted uptake in shallow layers at the expense of deep ones.</p><p>A conceptual alternative is to upscale exact solutions to the hyperbolic differential equation that describes root water uptake, by solving for the mean root water potential in each soil subdomain. Upscaled solutions show that multiple soil water potentials affect pressure gradients in each root segment, producing the nonlinearities absent in Ohm models. This upscaled model gave better predictions of WRC drought data and was significantly less prone to over-fitting than the two Ohm models, with more robust predictions beyond calibration conditions.</p><p>Analysis reveals classes of root systems of differing architectural complexity that yield a common upscaled model. In numerical experiments, using a simple upscaled model in situations of increasing complexity (e.g., adding individual plants), resulted in bounded errors that decreased asymptotically with increased complexity. The approach is thus a viable candidate for upscaling the effects of heterogenous soil moisture distributions on root water uptake.</p>

A general approach for analytically upscaling the exact root water uptake equations despite heterogeneous soil moisture at the soil-root interface

2021 ◽  
Author(s):  
Martin Bouda ◽  
Jan Vanderborght ◽  
Mathieu Javaux
Keyword(s):  
Soil Moisture ◽  
Exact Solutions ◽  
Root System ◽  
Water Uptake ◽  
Grid Cell ◽  
Earth System ◽  
Water Flows ◽  
Heterogeneous Soil ◽  
Soil Moisture Heterogeneity ◽  
Earth System Models

<p>Recent advances in scaling up water flows on root system networks hold promise for improving predictions of water uptake at large scales. These developments are particularly timely, as persistent difficulties in getting Earth system models to accurately represent soil-root water flows, especially under drying or heterogeneous soil moisture conditions, are now a major obstacle describing the water limitation of terrestrial fluxes.</p><p>One recently developed upscaling formalism has been shown to be both free of discretisation error in flow predictions regardless of scale and with computational cost linearly diminishing with the number of soil subdomains considered. What has been missing from this approach, however, is a proven method to apply it generally – i.e. to an arbitrary root system architecture discretised on an arbitrary grid.</p><p>The work presented here demonstrates a general algorithm that can be applied to a wide range of root system architectures (the only assumption being that only one lateral root originates at one point along a parent root) discretised on a grid consisting of a series of soil layers of variable thickness, as is common in Earth system models. It is further shown theoretically that both of these restrictions can in principle be relaxed and that this approach can in principle be extended to conditions of soil moisture heterogeneity – i.e. situations where each root segment in a soil grid cell faces a different water potential at the soil-root interface.</p><p>This work represents both a practical advance bringing broad applicability to this upscaling approach and a major theoretical advance as exact solutions for water uptake under conditions of soil moisture heterogeneity within grid cells were previously unknown. While obtaining exact solutions despite heterogeneity within the grid cell requires a way of finding the overall mean soil water potential faced by the plant, this advance nevertheless points to possible directions of future research for overcoming the major hurdle of soil moisture heterogeneity.</p>

C-dots as a novel silica-based fluorescent nanoparticle tracer to investigate plant hydraulics

2020 ◽  
Author(s):  
Kanishka Singh ◽  
Benjamin Hafner ◽  
James Knighton ◽  
M. Todd Walter ◽  
Taryn Bauerle
Keyword(s):  
Water Uptake ◽  
Plant Tissue ◽  
Imaging System ◽  
Root Water Uptake ◽  
Nano Particles ◽  
Water Isotopes ◽  
Hydraulic Redistribution ◽  
Severe Drought ◽  
Stable Water Isotopes ◽  
Plant Hydraulics

<p>Forest cover exerts a significant control on the partitioning of precipitation between evapotranspiration and surface runoff. Thus, understanding how plants take up and transpire water in forested catchments is essential to predict flooding potential and hydrologic cycling. A growing literature underscores the importance of integrating whole-plant hydraulics, including such processes as the spatial variability of root distribution and the temporally dynamic nature of root water uptake by depth in understanding the relationship between changes in vegetation and hydrology. The analysis of stable isotopes of water (<sup>18</sup>O and <sup>2</sup>H) sourced from soils and plant tissue has enabled the estimation of tree root water uptake depths and water use strategies. Despite the general acceptance of stable water isotopic data to estimate plant hydraulic dynamics, this methodology imposes assumptions that may produce spurious results. For example, end member mixing analysis neglects time-delays during tree-water storage. Also, it is likely that hydraulic redistribution processes of plants, which transport water across soil depths and both into and out of plant tissue, modify δ<sup>18</sup>O and δ<sup>2</sup>H; the isotopic signature of a collected sample may thus reflect a history of transport and exposure to fractionating processes not accounted for in analysis. We tested the feasibility of C-dots, core-shell silica polyethylene-glycol coated fluorescent nano-particles (5.1 nm diameter) in 20 µmol/l solution with H<sub>2</sub>O labeled with a near-infrared fluorophore, cyanine 5.5 (excitation maximum of 646 nm, emission maximum of 662 nm), as an alternative to stable water isotopes in the investigation of plant hydraulics. We examined the absorption and transport of C-dots through soil, as well as roots and aerial structures of Eastern hemlock (Tsuga canadensis), Eastern white pine (Pinus strobus), and white spruce (Picea glauca) saplings (n = 12 each) via an IVIS-200 luminescence in-situ imaging system. We compared the fluid mechanics, residence times and mixing schemes of C-dots with <sup>2</sup>H-labeled water during transport within these plant species to establish the nanoparticles as a viable alternative through a split-root hydraulic redistribution experiment under moderate and severe drought conditions. We present a residence-time distribution to elucidate the mixing scheme of C-dot solution and calibration curves to aid future studies. This research is the premier assessment of this nanoparticle as an alternative tracer to stable water isotopes, and as such may yield insights for broader applications.</p>

How to scale root water uptake from root scale to stands and beyond – a theoretical framework, practical lessons, and next steps

2020 ◽  
Author(s):  
Martin Bouda ◽  
Jan Vanderborght ◽  
Valentin Couvreur ◽  
Félicien Meunier ◽  
Mathieu Javaux
Keyword(s):  
Soil Moisture ◽  
Soil Water ◽  
Water Flow ◽  
Water Uptake ◽  
Root Systems ◽  
Root Water Uptake ◽  
Discretization Error ◽  
Persistent Problem ◽  
Plant Hydraulics ◽  
Soil Moisture Heterogeneity

<p>Estimating plant uptake of soil water has been a persistent problem in process-based earth system models (ESMs). Initially ignored altogether, plant access to soil water was long modelled with heuristic approaches at large scales. These formulations are currently being replaced as ESMs begin to incorporate more detailed plant hydraulics schemes based on the soil-plant-atmosphere continuum concept. While the new schemes greatly improve mechanistic description of above-ground plant hydraulics, they have given rise to various issues belowground, from excessive hydraulic redistribution to numerical instability. As detailed 3D descriptions of root systems and water flow equations on the soil-root domain have been established, the key challenge is how to scale them up to relevant scales, reducing computational cost to a trivial level without loss of accuracy.</p><p>Here, we set out a mathematical framework that incorporates recent advances in this area and allows us to relate them to each other. Comparing and contrasting different models, formulated in a novel matrix form of the water flow problem in the root system, allows us to make inferences about their suitability for use in upscaling. We are able to show how to avoid discretization error in the upscaled root scheme, as well as which upscaling method offers full generality, and which yields the computationally simplest forms. These theoretical results are fully supported by numerical simulations of fully explicit 3D root systems and their upscaled versions. Improved performance of the upscaled models is also demonstrated in an application to field data from the Wind River Crane flux tower site (reduced model bias, root mean squared error, and increased robustness of fitted parameters).</p><p>Root water uptake equations can now be scaled up without discretization error for arbitrary root systems. The chief remaining source of error is soil moisture heterogeneity within discretized soil elements where it is assumed uniform by any given model (e.g. within each vertical layer). The main task for future work thus becomes to achieve a correspondingly accurate description for soil moisture heterogeneity. Some of the upscaling approaches compared here offer hints at potential next steps in this direction.</p>

scholarly journals Effect of parameter choice in root water uptake models – the arrangement of root hydraulic properties within the root architecture affects dynamics and efficiency of root water uptake

2014 ◽  
Vol 18 (10) ◽  
pp. 4189-4206 ◽  
Author(s):  
M. Bechmann ◽  
C. Schneider ◽  
A. Carminati ◽  
D. Vetterlein ◽  
S. Attinger ◽  
...  
Keyword(s):  
Root System ◽  
Water Uptake ◽  
Root Length ◽  
Hydraulic Properties ◽  
Three Dimensional ◽  
Root Systems ◽  
Root Water Uptake ◽  
Hydraulic Lift ◽  
Hydraulic Redistribution ◽  
Young Root

Abstract. Detailed three-dimensional models of root water uptake have become increasingly popular for investigating the process of root water uptake. However, they suffer from a lack of information on important parameters, particularly on the spatial distribution of root axial and radial conductivities, which vary greatly along a root system. In this paper we explore how the arrangement of those root hydraulic properties and branching within the root system affects modelled uptake dynamics, xylem water potential and the efficiency of root water uptake. We first apply a simple model to illustrate the mechanisms at the scale of single roots. By using two efficiency indices based on (i) the collar xylem potential ("effort") and (ii) the integral amount of unstressed root water uptake ("water yield"), we show that an optimal root length emerges, depending on the ratio between roots axial and radial conductivity. Young roots with high capacity for radial uptake are only efficient when they are short. Branching, in combination with mature transport roots, enables soil exploration and substantially increases active young root length at low collar potentials. Second, we investigate how this shapes uptake dynamics at the plant scale using a comprehensive three-dimensional root water uptake model. Plant-scale dynamics, such as the average uptake depth of entire root systems, were only minimally influenced by the hydraulic parameterization. However, other factors such as hydraulic redistribution, collar potential, internal redistribution patterns and instantaneous uptake depth depended strongly on the arrangement on the arrangement of root hydraulic properties. Root systems were most efficient when assembled of different root types, allowing for separation of root function in uptake (numerous short apical young roots) and transport (longer mature roots). Modelling results became similar when this heterogeneity was accounted for to some degree (i.e. if the root systems contained between 40 and 80% of young uptake roots). The average collar potential was cut to half and unstressed transpiration increased by up to 25% in composed root systems, compared to homogenous ones. Also, the least efficient root system (homogenous young root system) was characterized by excessive bleeding (hydraulic lift), which seemed to be an artifact of the parameterization. We conclude that heterogeneity of root hydraulic properties is a critical component for efficient root systems that needs to be accounted for in complex three-dimensional root water uptake models.

scholarly journals Estimates of tree root water uptake from soil moisture profile dynamics

2019 ◽  
Author(s):  
Conrad Jackisch ◽  
Samuel Knoblauch ◽  
Theresa Blume ◽  
Erwin Zehe ◽  
Sibylle K. Hassler
Keyword(s):  
Time Series ◽  
Soil Moisture ◽  
Water Uptake ◽  
Sap Flow ◽  
Water Cycle ◽  
Xylem Sap ◽  
Root Water Uptake ◽  
Soil Conditions ◽  
Diurnal Changes ◽  
Moisture Profile

Abstract. Root water uptake (RWU) as one important process in the terrestrial water cycle can help to better understand the interactions in the soil water plant system. We conducted a field study monitoring soil moisture profiles in the rhizosphere of beech trees at two sites with different soil conditions. We infer RWU from step-shaped, diurnal changes in soil moisture. While this approach is a feasible, easily implemented method during wet and moderate conditions, limitations were identified during drier states and for more heterogeneous soil settings. A comparison with time series of xylem sap velocity reveals that RWU and sap flow are complementary measures of the transpiration process. The high correlation between the sap flow time series of the two sites, but lower correlation between the RWU time series, suggests that the trees adapt RWU to soil heterogeneity and site differences.

scholarly journals Using StorAge Selection functions to quantify ecohydrological controls on the time-variant age of evapotranspiration, soil water, and recharge

2018 ◽  
Author(s):  
Aaron A. Smith ◽  
Doerthe Tetzlaff ◽  
Chris Soulsby
Keyword(s):  
Soil Moisture ◽  
Surface Water ◽  
Soil Water ◽  
Water Uptake ◽  
Root Water Uptake ◽  
Soil Evaporation ◽  
Root Uptake ◽  
Water Fluxes ◽  
Near Surface ◽  
Moisture Conditions

Abstract. Quantifying ecohydrological controls on soil water availability is essential to understand temporal variations in catchment storage. Soil water is subject to numerous time-variable fluxes (evaporation, root-uptake, and recharge), each with different water ages which in turn affect the age of water in storage. Here, we adapt StorAge Selection (SAS) function theory to investigate water flow in soils and identify soil evaporation and root-water uptake sources from depth. We use this to quantify the effects of soil-vegetation interactions on the inter-relationships between water fluxes, storage, and age. The novel modification of the SAS function framework is tested against empirical data from two contrasting soil-vegetation units in the Scottish Highlands; these are characterised by significant preferential flow, transporting younger water through the soil during high soil moisture conditions. Dominant young water fluxes, along with relatively low rainfall intensities, explain relatively stable soil water ages through time and with depth. Soil evaporation sources were more time-invariant with high preference for near-surface water, independent of soil moisture conditions, and resulting in soil evaporation water ages similar to near-surface soil waters (mean age: 50–65 days). Sources of root-water uptake were more variable: preferential near-surface water uptake occurred in wet conditions, with a deeper root-uptake source during dry soil conditions, which resulted in more variable water ages of transpiration (mean age: 56–79 days). The simple model structure provides a parsimonious means of constraining the water age of multiple fluxes from the upper part of the critical zone during time-varying conditions improving our understanding of vegetation influences on catchment scale water fluxes.

scholarly journals Big root approximation of site-scale vegtation water uptake

2019 ◽  
Author(s):  
Martin Bouda
Keyword(s):  
Soil Moisture ◽  
Water Uptake ◽  
Land Surface ◽  
Land Surface Model ◽  
Root Water Uptake ◽  
Surface Model ◽  
Summer Drought ◽  
Ohm’S Law ◽  
Ohm's Law ◽  
Vegetation Water

AbstractLand surface model (LSM) predictions of soil moisture and transpiration under water-limited conditions suffer from biases due to a lack of mechanistic process description of vegetation water uptake. Here, I derive a ‘big root’ approach from the porous pipe equation for root water uptake and compare its predictions of soil moistures during the 2010 summer drought at the Wind River Crane site to two previously used Ohm’s law analogue plant hydraulic models. Structural error due to inadequate representation of root system architecture (RSA) in both Ohm’s law analogue models yields significant and predictable moisture biases. The big root model greatly reduces these as it better represents RSA effects on pressure gradients and flows within the roots. It represents a major theoretical advance in understanding vegetation water limitation at site scale with potential to improve LSM predictions of soil moisture, temperature and surface heat, water, and carbon fluxes.

Quantifying how plants with different species-specific water-use strategies cope with the same drought-prone hydro-ecological conditions

2020 ◽  
Author(s):  
Deepanshu Khare ◽  
Gernot Bodner ◽  
Mathieu Javaux ◽  
Jan Vanderborght ◽  
Daniel Leitner ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Drought Stress ◽  
Water Potential ◽  
Water Uptake ◽  
Hydraulic Properties ◽  
Root Water Uptake ◽  
Leaf Water ◽  
Plant Water ◽  
Soil Hydraulic Properties ◽  
Stomatal Control

<p>Plant transpiration and root water uptake are dependent on multiple traits that interact with site soil characteristics and environmental factors such as radiation, atmospheric temperature, relative humidity, and soil-moisture content. Models of root architecture and functions are increasingly employed to simulate root-soil interactions. Root water uptake is thereby affected by the root hydraulic architecture, soil moisture conditions, soil hydraulic properties, and the transpiration demand as controlled by atmospheric conditions. Stomatal conductance plays a vital role in regulating transpiration in plants. We performed simulations of plant water uptake for plants having different mechanisms to control transpiration, spanned by isohydric/anisohydric spectrum. Isohydric plants follow the strategy to close their stomata in order to maintain the leaf water potential at a constant level, while anisohydric plants leave their stomata open when leaf water potentials fall due to drought stress. Modelling the stomatal regulation effectively will result in a more reliable model that will regulate the excessive loss of water. We implemented hydraulic and chemical stomatal control<br>of root water uptake following the current approach where stomatal control is regulated by simulated water potential and/or chemical signal concentration. In order to maintain water uptake from dry soil, low plant water potentials are required, which may lead to reversible or permanent cavitation. We parameterise our model with field data, including climate data and soil hydraulic properties under different tillage conditions. This helps us to understand the behaviour of different crops under drought conditions and predict at which growing stage the stress hits the plant. We conducted the simulations for different scenarios to study the effect of hydraulic and chemical regulation on root system performance under drought stress.</p>

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