An optimality-based model of the coupled soil moisture and root dynamics

Authors:

Stanislaus J. Schymanski, Murugesu Sivapalan, Michael L. Roderick, Jason Beringer, Lindsay B. Hutley

Abstract:

The main processes determining soil moisture dynamics are infiltration, percolation, evaporation and root water uptake. Modelling soil moisture dynamics therefore requires an interdisciplinary approach that links hydrological, atmospheric and biological processes. Previous approaches treat either root water uptake rates or root distributions and transpiration rates as given, and calculate the soil moisture dynamics based on the theory of flow in unsaturated media. The present study introduces a different approach to linking soil water and vegetation dynamics, based on vegetation optimality. Assuming that plants have evolved mechanisms that minimise costs related to the maintenance of the root system while meeting their demand for water, we develop a model that dynamically adjusts the vertical root distribution in the soil profile to meet this objective. The model was used to compute the soil moisture dynamics, root water uptake and fine root respiration in a tropical savanna over 12 months, and the results were compared with observations at the site and with a model based on a fixed root distribution. The optimality-based model reproduced the main features of the observations such as a shift of roots from the shallow soil in the wet season to the deeper soil in the dry season and substantial root water uptake during the dry season. At the same time, simulated fine root respiration rates never exceeded the upper envelope determined by the observed soil respiration. The model based on a fixed root distribution, in contrast, failed to explain the magnitude of water use during parts of the dry season and largely over-estimated root respiration rates. The observed surface soil moisture dynamics were also better reproduced by the optimality-based model than the model based on a prescribed root distribution. The optimality-based approach has the potential to reduce the number of unknowns in a model (e.g. the vertical root distribution), which makes it a valuable alternative to more empirically-based approaches, especially for simulating possible responses to environmental change.

Reference:

Hydrology and Earth System Sciences, Vol. 12, 913-932.
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Figure 1: Cross-section of a simplified elementary watershed. Variables on the left hand side (in grey) denote spatial dimensions (see text), while the variables on the right hand side denote water fluxes (precipitation (Q_rain), infiltration (Q_inf), infiltration excess runoff (Q_iex ), soil evaporation from the saturated zone and the unsaturated zone (E_ss and E_su respectively), flow between saturated and unsaturated layer (Q_u) and outflow across the seepage face (Q_sf).

Figure 2: Conceptual catchment, with the unsaturated zone subdivided into three soil layers. Soil layers are given indices (i=1...n_layers), starting with 1 at the soil surface (right). The indices relating to fluxes refer to fluxes across the bottom boundary of the respective layer (left).

Figure 3: Simulated below-ground conditions 40 days after model initialisation. Vertical soil profiles show values for each soil layer between the surface and the variable water table. Daily root water uptake (Q_r,i, Plot (a)) and root surface area (S_Ar,i, Plot (b)) are highest in the deep layers of the root zone, while soil saturation (s_u,i, Plot (c)) is reduced in the layers where the water uptake took place. Plot (d) shows midnight snapshots of the observed and modelled soil moisture in the top soil layer for 12 months, with a round dot indicating the position in time of the other three plots.

Figure 4: Simulated below-ground conditions at the onset of the wet season rains (147 days after model initialisation). Vertical soil profiles show values for each soil layer between the surface and the variable water table. The distribution of soil saturation (s_u,i, Plot (c)) shows the wetted surface soil, leading to water uptake (Q_r,i, Plot (a)) by the top root layers and a slight release of water by the bottom root layer in the early wet season. This caused the root area distribution (S_Ar,i, Plot (b)) to start shifting towards the upper soil profile, with the bimodal distribution as an intermediate state. Plot (d) shows midnight snapshots of the observed and modelled soil moisture in the top soil layer for 12 months, with a round dot indicating the position in time of the other three plots.

Figure 5: Simulated below-ground conditions during the mid-wet season (200 days after model initialisation). Vertical soil profiles show values for each soil layer between the surface and the variable water table. The distribution of soil saturation (s_u,i, Plot (c)) shows the propagation of multiple wetting fronts through the soil profile, while the distributions of root surface area (S_Ar,i, Plot (b)) and root water uptake (Q_r,i, Plot (a)) in the soil profile are concentrated in the top soil with a spike in the lowest layer of the root zone. Plot (d) shows midnight snapshots of the observed and modelled soil moisture in the top soil layer for 12 months, with a round dot indicating the position in time of the other three plots.

Figure 6: Observed and modelled half-hourly surface soil moisture (θ_obs and θ_mod respectively, m³ m⁻³) (top) and their residuals (bottom) obtained using a dynamically optimised root profile. MAE denotes the mean absolute error of the model.

Figure 7: Comparison of the diurnal dynamics of simulated transpiration (E_t), total root water uptake (Q_r) and plant water storage per unit catchment area (M_q) for two different values of M_qx. (a) Optimising root distribution, with a water storage capacity (M_qx) of 3.1 kg m⁻²; (b) optimising root distribution, with a water storage capacity (M_qx) of 0.1 kg m⁻². Data shown for Day 100 of each model run (6 October 2004).

Figure 8: Comparison of modelled (E_t,mod) and observed (E_t,obs) transpiration rates. (a) Dynamically optimised root profile. (b) Prescribed, static root profile with root area index of 43. (c) Prescribed, static root profile with root area index.

Figure 9: Simulated below-ground conditions during the early wet season (147 days after model initialisation) simulated using a fixed root distribution. Vertical soil profiles show values for each soil layer between the surface and the variable water table. Note the substantial net water release by roots in certain soil layers on that day in Plot (a) in relation to the fixed root distribution in Plot (b) and the midnight snapshot of the soil moisture distribution in Plot (c). Plot (d) shows midnight snapshots of the observed (grey line) and modelled (black line) soil moisture in the top soil layer for 12 months, with a round dot indicating the position in time of the other three plots.

Figure 10: Observed and modelled half-hourly surface soil moisture (θ_obs and θ_mod respectively, m³ m⁻³) (top) and their residuals (bottom) obtained using a fixed root distribution. MAE denotes the mean absolute error of the model.