# VIC+ for water-limited conditions: A study of biological and hydrological processes and their interactions in soil-plant-atmosphere continuum

## Abstract

[1] The Three-Layer Variable Infiltration Capacity (VIC-3L) land surface model is extended to include biological and hydrological processes important to water, energy, and carbon budgets under water-limited climatic conditions: (1) movement of soil water from wet to dry regions through hydraulic redistribution (HR); (2) groundwater dynamics; (3) plant water storage; and (4) photosynthetic process. HR is represented with a process-based scheme and the interaction between HR and groundwater dynamics is explicitly considered. The impact of frozen soil on HR in the cold season is also represented. Transpiration is calculated by combining an Ohm's law analogy, where flow from the soil to leaves is buffered by plant water storage, with the Penman-Monteith method, where stomatal conductance is linked with photosynthesis. In this extended model (referred to as VIC+), water flow in plants and in the unsaturated and saturated zones, transpiration and photosynthesis are closely coupled, and multiple constraints are simultaneously applied to the transpiration process. VIC+ is evaluated with an analytical solution under simple conditions and with observed data at two AmeriFlux sites. Scenario simulations demonstrate the following results: (1) HR has significant impacts on water, energy, and carbon budgets during the dry season; (2) Rise of groundwater table, increase of root depth, HR, and plant water storage are favorable to dry-season latent heat flux; (3) Plant water storage can weaken the intensity of upward HR; (4) Frozen soil can restrict downward HR in the wet winter and reduce the soil water reserves for the dry season.

## Key Points

- Couple biological and hydrological processes into LSM for dry conditions
- Impacts of these processes and interactions between them are investigated
- Include multiple constraints to reduce model's degrees of freedom

## 1. Introduction

[2] Researchers have incorporated many physical and physiological processes occurring in vegetation and soil into land surface models, which are often employed in climate models, in hopes of properly reproducing and predicting water, energy and carbon cycles in the soil-plant-atmosphere continuum [e.g., *Sellers et al*., 1986, 1996; *Bonan*, 1995; *Foley et al*., 1996]. Identifying the important processes and implementing them into the models is crucial for modeling studies to achieve their goals [e.g., *Pitman*, 2003]. However, significance of a process may vary under different climatic and environmental conditions. Processes that are not important in the humid environment, for example, may have evident impacts on water, energy, and carbon cycles under water-limited conditions and thus, should not be ignored in the corresponding model simulations [e.g., *Lee et al*., 2005; *Wang*, 2011].

[3] Plant growth relies on climatic and environmental conditions. Plants have the ability to adjust their strategies to adapt to the environment. When dry climatic conditions appear, plants may try to cope with the adverse circumstances by taking advantage of some biological and hydrological processes (e.g., hydraulic redistribution, ground water dynamics, plant water storage, etc.) [e.g., *Caldwell et al*., 1998; *Wang et al*., 2002; *Soylu et al*., 2011]. Therefore, these processes can play important roles in the soil-plant-atmosphere continuum and should be included in models.

[4] Hydraulic redistribution (HR) is the movement of water from soil of higher water potential to soil of lower water potential, usually from moist regions to dry regions, through plant roots. HR has been verified to exist for many plant species at different geographical locations around the world [*Caldwell et al*., 1998]. Experimental and modeling studies show that HR is an important process not only in the arid and semiarid regions [*Caldwell and Richards*, 1989; *Dawson*, 1993; *Ryel et al*., 2002] but also in wet regions which experience dry seasons (e.g., partial region of the Amazonia) [*Lee et al*., 2005; *Wang*, 2011]. For example, it has been found that HR can contribute to dry-season transpiration and carbon assimilation [*Ryel et al*., 2002; *Lee et al*., 2005; *Amenu and Kumar*, 2008; *Wang*, 2011].

[5] HR has been investigated in a number of modeling studies. Most of these used conceptual formulae to represent the HR process [e.g., *Ryel et al*., 2002]. In some of these studies, conceptual representations of HR were incorporated into land surface models or General Circulation Models (GCMs) to investigate its impacts at large spatial scales [e.g., *Ren et al*., 2004; *Lee et al*., 2005; *Baker et al*., 2008; *Wang*, 2011; *Li et al*., 2012]. However, in those conceptual formulae for the HR process, it is challenging to estimate parameter values [*Ryel et al*., 2002; *Wang*, 2011; *Neumann and Cardon*, 2012]. In addition to conceptual formulae, some process-based schemes have also been put forward to model the HR process [e.g., *Mendel et al*., 2002; *Amenu and Kumar*, 2008; *Quijano et al*., 2012]. For parameters in these process-based schemes, physical meanings are straightforward and the parameter values can be estimated from the measured data. In the previous studies, process-based HR schemes have been coupled with other biological and hydrological processes. *Mendel et al*. [2002] considered interactions between HR, transpiration and groundwater in their model, and applied the model in a two-dimensional domain under a simplified condition. *Amenu and Kumar* [2008] coupled their process-based HR scheme with a big-leaf canopy model of plant transpiration, and applied the coupled model at the Sierra Nevada eco-region. This HR scheme was also used to model the HR processes of overstory and understory simultaneously and the interactions between vegetation species were investigated [*Quijano et al*., 2012]. In this study, a process-based HR scheme has been coupled with a few biological or hydrological processes (e.g., groundwater dynamics, plant water storage, etc.), which can play important roles under water-limited conditions. The HR scheme and representations of these processes have been integrated into the Three-layer Variable Infiltration Capacity (i.e., VIC-3L) land surface model and the dynamic interactions between HR and other biological and hydrological processes of land surface are represented.

[6] Groundwater can have significant impacts on the land surface and atmospheric processes under dry climatic conditions by way of mechanisms such as exerting influence on soil moisture of the root zone. Groundwater dynamics have been represented in some land surface models [e.g., *Liang et al*., 2003; *Kollet and Maxwell*, 2008]. HR influences the distribution of soil moisture in the root zone and can enhance the utilization of groundwater by plants. Previous experimental studies indicated that the existence of groundwater, together with the effect of HR, could provide more potential transpirational water to plants [e.g., *Dawson*, 1996]. Therefore, it is meaningful to consider the interaction between HR and groundwater in modeling studies. Groundwater was represented in a few previous modeling studies on HR. For example, *Mendel et al*. [2002] considered the HR-groundwater coupling in the context of a simplified scenario. In the HR modeling study by *Ryel et al*. [2002], the groundwater table is “fixed” at a certain position below the root zone (i.e., the depth from the ground surface to the groundwater table is assumed to be constant). In this study, the coupling between HR and groundwater dynamics is represented in the context of a land surface model. Water flow in the unsaturated zone and the saturated zone is simulated consistently. Thus, the fluctuations of the interface between the unsaturated zone and the saturated zone (i.e., the groundwater table) are explicitly represented. At the same time, The HR-groundwater coupling is integrated with other land surface processes in the model.

[7] Besides groundwater dynamics, frozen soil can also affect the amount of water stored in the soil. During the wet season, soil water in shallow layers may be transferred to the deep soil through downward HR, if the water potential of the shallow layer is higher than that of the deep soil [e.g., *Caldwell et al*., 1998; *Amenu and Kumar*, 2008; *Neumann and Cardon*, 2012]. However, if the wet season is in winter (e.g., the Mediterranean climate), soil water in the shallow layer may be frozen, thus reducing the magnitude of downward HR and decreasing the amount of water stored in the deep soil which can be used by plants during the dry periods. To our knowledge, the impact of frozen soil on downward HR has not been quantitatively investigated in modeling studies. In this study, the impact of frozen soil on HR is represented in the model, and the impact is evaluated with a few scenario simulations.

[8] Water absorbed by roots can be stored in plant tissues (e.g., stems and leaves) and used to partially supply transpiration at a later time when root uptake cannot satisfy the transpiration demand [e.g., *Katerji et al*., 1986; *Lhomme et al*., 2001]. Therefore, this plant storage can promote plant transpiration and hence latent heat flux, especially under dry soil conditions [e.g., *Wang et al*., 2002]. This process affects the water cycle in plants and causes time lag between root uptake and transpiration, as well as decreases maximum instantaneous rate of water uptake by roots [*Hunt et al*., 1991]. In this study, the representation of plant water storage (also referred to as “plant storage” in this article) is included in the VIC-3L model for the purpose of more realistically modeling the water and energy cycles in the soil-plant-atmosphere continuum, which can be affected by the plant storage process under water-limited conditions.

[9] In addition to the above biological and hydrological processes, the photosynthetic process is also coupled into the VIC-3L model. Stomata of leaves regulate both vapor flux and uptake of CO_{2} simultaneously and transpiration is closely related to photosynthesis [e.g., *Collatz et al*., 1991; *Daly et al*., 2004]. In this study, the transpiration process is coupled with the photosynthetic process through linking the stomatal conductance with carbon assimilation, using a variant of the Ball-Berry-Leuning model [*Tuzet et al*., 2003]. This Tuzet et al. model has a solid mechanistic basis and accounts for the effect of water stress on stomatal conductance. In addition, in this coupling method the photosynthetic capacity is effectively reduced under dry conditions, which can result in decreases of both photosynthesis and transpiration.

[10] In this article, the VIC-3L land surface model is extended in the above ways; the extended model is referred to as the VIC+ model. In the VIC+ model, processes of soil water dynamics, water transport along roots, water flow in above-ground stems, transpiration and photosynthesis are closely coupled. Moreover, a new modeling strategy is introduced in this study to partially overcome the ever increasing and challenging problem a model has—lack of enough constraints, especially when new processes are included. The idea of the new strategy is to represent the same process simultaneously from as many different aspects/perspectives/constrains/equations as possible to reduce the model's degrees of freedom. For example, in VIC+, transpiration is determined by coordinating the method of Ohm's law analogy and the Penman-Monteith method. Thus, transpiration is controlled by both the soil water potential of the root zone and the atmospheric conditions simultaneously. In addition, carbon assimilation is estimated by coordinating a diffusion method and a biochemical model. In this way, carbon assimilation calculation is constrained by stomatal and biochemical limitations simultaneously. These multiple constraints included in the modeling approach of this study reduce the model's degrees of freedom and thus, partially address the modeling problem of lacking enough constraints.

[11] The remainder of this paper is organized as follows: section 2 describes the approach for extending the VIC-3L model. Section 3 presents the evaluation of the extended VIC-3L model (i.e., VIC+). Section 4 presents the results and analyses of some scenario simulations. Summary and discussion are provided in section 5. Some technical details of the model are described in Appendices A–E.

## 2. Approach

### 2.1. Water Movement in the Soil and Roots

[12] In this study, water movement in the soil and root system is modeled simultaneously. We use the Richards equation to represent the soil water dynamics and the Poiseuille law to approximate the water transport along roots. The movement of water in the soil and in roots is connected through the water exchange at the interface between roots and the soil.

#### 2.1.1. Soil Water Dynamics

*Richards*, 1931]:

*θ*(m

^{3}m

^{−3}) is the volumetric soil water content (SWC);

*t*is time;

*z*(m) is the vertical coordinate originating from the ground surface with downward being positive;

*K*(m

_{s}^{2}·s

^{−1}·Pa

^{−1}) is the soil hydraulic conductivity;

*ψ*(Pa) is the soil water potential; (−

_{s}*ρ*) (Pa) is the gravitational potential;

_{w}gz*ρ*(kg·m

_{w}^{−3}) is the water density;

*g*(m·s

^{−2}) is the gravitational acceleration;

*F*(s

_{sr}^{−1}) is the water exchange between roots and the soil, and can be a sink term (roots absorb water) or source term (roots release water). Here “water potential” specifically refers to the pressure component of the total water potential. The pressure component can be either negative or positive.

[14] For unsaturated soil, the soil water content (*θ*) is linked to the soil water potential (*ψ _{s}*) through the equation of

*Van Genuchten*[1980]. The soil hydraulic conductivity (

*K*) is predicted from the soil water potential (

_{s}*ψ*) by using the Mualem–van Genuchten formula [

_{s}*Van Genuchten*, 1980]. The reason for using the van Genuchten equations instead of the Clapp-Hornberger type of equations for the

*θ*,

*ψ*, and

_{s}*K*relationship is that the former leads to a smoother transition for the soil moisture profile from the unsaturated zone to the saturated zone.

_{s}[15] Flux boundary conditions are used for the Richards equation. At the upper boundary, the fluxes are infiltration and evaporation. At the lower boundary zero flux is prescribed since it is assumed that the soil domain is underlain by impervious bedrock.

#### 2.1.2. Water Transport in the Root System

*K*(m

_{ra}^{2}·s

^{−1}·Pa

^{−1}) is the axial hydraulic conductivity of roots per unit area; and

*ψ*(Pa) is the root water potential. The meanings of other symbols are the same as that of equation 1. The derivation of equation 2 is presented in Appendix Appendix A:. Similar approaches were adopted by

_{r}*Mendel et al*. [2002] and

*Amenu and Kumar*[2008].

[17] *K _{ra}* is estimated based on the distribution of primary roots in the vertical direction and the specific hydraulic conductivity per unit lumen area. The former is described by an asymptotic equation [

*Gale and Grigal*, 1987;

*Jackson et al*., 1996]. The latter can be measured [e.g.,

*Pate et al*., 1995] or be approximately estimated using the Poiseuille law.

[18] For this equation, the upper boundary condition is the sap flux at the root collar (i.e., the interface between the plant stem and roots). This sap flux can be derived from the calculation of plant transpiration which will be discussed below. At the lower boundary zero flux is assumed.

#### 2.1.3. Water Exchange Between Roots and the Soil

*Steudle and Peterson*, 1998]. The uptake flux can be considered to be proportional to the difference between the soil water potential and the root water potential [

*Fiscus*, 1975;

*Herkelrath et al*., 1977;

*Landsberg and Fowkes*, 1978]. In this study, the water exchange between roots and soil is represented by the following equation, similar to that of Landsberg and Fowkes:

*K*(m·s

_{rr}^{−1}·Pa

^{−1}) is the root radial hydraulic conductivity per unit of root surface area;

*S*(m

_{r}^{2}·m

^{−3}) is the surface area of roots which absorb or release water per unit volume of soil;

*ψ*(Pa) is the soil water potential;

_{s}*ψ*(Pa) is the root water potential.

_{r}[20] The water exchange (*F _{sr}*) can be positive (roots absorb water) or negative (roots release water) depending on the potential difference between the soil water potential and the root water potential.

[21] *K _{rr}* can be measured and varies for different species [e.g.,

*Sands et al*., 1982;

*Huang and Nobel*, 1994]. In this study, it is assumed that the root permeability is symmetric and the same

*K*value is used regardless of whether roots absorb water or release water.

_{rr}[22] Assuming the water exchange occurs at live fine roots, *S _{r}* is the surface area density of live fine roots. It is derived from the distribution function of live fine roots and the LFRAI (Live Fine Root Area Index, i.e., the total surface area of live fine roots per unit ground area). The distribution of live fine roots in the vertical direction is described by an asymptotic equation [

*Gale and Grigal*, 1987;

*Jackson et al*., 1997]. The LFRAI value is from the study by

*Jackson et al*. [1997].

[23] It is worth mentioning that the root axial hydraulic conductivity (*K _{ra}*) is the flux density per unit of potential gradient and the root radial hydraulic conductivity (

*K*) is the flux density per unit of potential difference. The units of these two parameters are different.

_{rr}[24] Effect of osmotic potential on the water exchange is not taken into account since HR is primarily a hydraulic process, which is also supported by *Mendel et al*. [2002] through numerical simulations.

#### 2.1.4. Representation of the Saturated Zone

[25] The Richards equation (i.e., equation 1) is also employed to describe the water dynamics of the saturated zone [e.g., *Van Dam and Feddes*, 2000]. The Richards equation is simultaneously solved for the unsaturated zone and the saturated zone. Solutions of soil water potential for the equation will indicate whether the soil is saturated or not. When the soil water potential value becomes zero or positive, it means that the soil is saturated. Positive soil water potential reflects hydrostatic pressure. The interface between the unsaturated zone and the saturated zone (i.e., the groundwater table) is dynamic, since the unsaturated soil can become saturated and vice versa.

[26] The sink or source term (*F _{sr}*) of equation 1 appears whether the soil is saturated or not, as long as there are roots in the soil. If the soil becomes saturated, the water exchange between the roots and the saturated soil can also be simulated.

#### 2.1.5. Frozen Soil

[27] The primary part of the frozen soil algorithm in the VIC-3L land surface model [*Cherkauer and Lettenmaier*, 1999; *Jeong*, 2009] is kept in this VIC+ model. The VIC-3L model uses a multilayer snow submodel [*Jeong*, 2009]. The thermal fluxes in the snowpack and the soil are simultaneously solved, and the solution gives the temperature profiles in the snowpack and the soil column in the vertical direction. At different depths in the soil column, if the local soil temperature drops below the freezing point, then partial soil water turns into ice and the ice content is calculated. Water movement in the soil and roots is computed after the ice content is updated. When the ice content increases, flow paths in the soil become narrower and unfrozen soil water decreases, which reduce moisture fluxes in the soil and water uptake by roots. In the cold and wet winter, the high ice content of the shallow soil layer restrains root uptake and decreases the amount of downward HR.

#### 2.1.6. Solving the Coupled Equations

[28] The soil water dynamics (equation 1) and the water transport in roots (equation 2) are linked via the sink or source term (*F _{sr}*) given by equation 3. Equations 1-3 are simultaneously solved with a finite difference method in which central difference is used for the space derivative and implicit backward difference is used for the time derivative. The soil domain is divided into

*n*layers with

*n*+ 1 nodes. For each node, there are two difference equations: one for the soil water flow and the other for the root water flow.

[29] At the upper boundary, the water balance equation for the top half layer is discretized to get the difference equation of the soil water flow for the top node. This approach is employed for the stability and mass conservation of the computation, especially when the boundary fluxes vary rapidly [*Šimůnek et al*., 2005]. At the lower boundary, the same treatment is applied. The resulting algebraic equations are solved using the Gaussian elimination algorithm. For each time step, an iterative process is used to obtain the solution when prescribed convergence criteria are satisfied. For all nodes of the unsaturated zone, the relative change in soil water content between two successive iterations needs to be less than a specified tolerance. For the saturated zone, the soil water potential (hydrostatic pressure) results of two successive iterations need to meet a prescribed convergence criterion.

[30] After a solution is obtained for soil water potential and root water potential, mass balance is checked for both the soil and the root systems. For the soil porous media, the amount of water entering (e.g., infiltration), and exiting (e.g., water uptake by roots) should be balanced by the change in water storage. For the root system, the summation of water exchange between roots and the soil should be equal to the sap flux at the root collar.

### 2.2. Plant Transpiration

[31] Plant transpiration plays an important role in the soil-plant-atmosphere continuum. In this study, plant transpiration is estimated by combining the method of Ohm's law analogy, where plant water storage is considered, with the Penman-Monteith method, where stomatal conductance is linked with the photosynthetic process. That is, transpiration is simultaneously constrained by the hydraulic and stomatal limitations, which lead to the simulation of the leaf water potential as a consequence of two coordinated hydrological processes. Furthermore, the photosynthetic process is simultaneously constrained by biochemical and stomatal limitations to simulate CO_{2} concentration within the leaf as a consequence of the interplay of the two. In addition, the modified Farquhar biochemical model and the diffusive method are combined in determining the carbon assimilation rate for the photosynthetic process. Such a combined approach (see Appendices B–D for details) allows for more constraints to be simultaneously included in representing the plant transpiration process.

[32] In the Ohm's law analogy, the water movement in plants is represented by the capacitance-resistance circuit shown in Figure 1, which is similar to some of the previous studies [e.g., *Landsberg et al*., 1976; *Katerji et al*., 1986; *Lhomme et al*., 2001]. The water flux in plants is equal to the ratio between the water potential difference and the hydraulic resistance. Water can be stored in the plant and used for transpiration at a later time. The direction of the plant-storage flux depends on the comparison of the plant storage water potential to the leaf water potential. Details of this method are described in Appendix Appendix B:.

[33] The Ohm's law analogy approach is combined with the Penman-Monteith method to determine the proper leaf water potential and the plant transpiration. In the Penman-Monteith method, the stomatal conductance is a key variable. It is estimated through establishing the link with the parameterization of photosynthesis [*Ball et al*., 1987; *Leuning*, 1995; *Tuzet et al*., 2003; *Daly et al*., 2004; *Runkle*, 2009]. The stomatal conductance is expressed as a function of the net carbon assimilation in the Ball-Berry-Leuning model [*Ball et al*., 1987; *Leuning*, 1995]. *Tuzet et al*. [2003] proposed a variant of the Ball-Berry-Leuning model that accounts for the effect of leaf water potential on stomatal conductance and is more appropriate for plants under water-stress conditions. The method of *Tuzet et al*. [2003] is adopted in this study. The detailed procedure for estimating the stomatal conductance is described in Appendix Appendix C:.

[34] The net carbon assimilation is derived by combining the diffusion method and the modified Farquhar model [e.g., *Daly et al*., 2004]. With this approach, carbon assimilation is concurrently constrained by stomatal and biochemical limitations. In the diffusion method, carbon assimilation rate is estimated as the ratio of the CO_{2} concentration difference, between the ambient air and the substomatal cavity, to the resistance. In the modified Farquhar model, carbon assimilation rate primarily depends on a few factors such as photosynthetically active radiation, CO_{2} concentration, leaf temperature, and leaf water potential. Through the function of leaf water potential, this model reflects the reduction of carbon assimilation under water-stress conditions. Details for calculating the carbon assimilation rate are described in Appendix Appendix D:.

[35] The calculation procedure for plant transpiration is illustrated in Figure 2. At first, the leaf water potential of the current time step is assumed and a preliminary value of plant transpiration (*E _{tr}*

_{1}) can be estimated with the Ohm's law analogy described in Appendix Appendix B:. A trial-and-error method is used to search for the proper CO

_{2}concentration within the leaf (

*C*) at which the assimilation rate from the diffusion method is the same as that from using the modified Farquhar model. Then the assimilation rate is substituted into the variant of the Ball-Berry-Leuning model (i.e., equation C1) to obtain the CO

_{i}_{2}stomatal conductance which is then converted to stomatal conductance. This stomatal conductance is employed to obtain a second value of plant transpiration (

*E*

_{tr}_{2}) using the Penman-Monteith equation. If

*E*

_{tr}_{2}is different from

*E*

_{tr}_{1}, the leaf water potential is adjusted and the above steps are repeated. The calculation is completed when the difference between

*E*

_{tr}_{2}and

*E*

_{tr}_{1}is smaller than a prescribed criterion.

### 2.3. Coupling with Three-Layer Variable Infiltration Capacity (VIC-3L) Model

[36] The approach for representing the water movement in the soil and roots is implemented as a soil-root module. The approach for representing the plant transpiration is implemented as a new transpiration module. These two modules are incorporated into the Three-Layer Variable Infiltration Capacity (VIC-3L) land surface model. The coupling approach is depicted in Figure 3. For details of the VIC-3L model and its previous versions the reader is referred to *Liang et al*. [1994, 1996a, 1996b, 1999, 2003], *Cherkauer and Lettenmaier* [1999], *Liang and Xie* [2001], and *Huang and Liang* [2006].

#### 2.3.1. Incorporation of the Soil-Root Module

[37] The land-surface water balance calculation in the VIC-3L model provides the water flux at the ground surface. The water flux can be infiltration or soil evaporation and is used as the upper boundary condition for the Richards equation in the soil-root module. The new transpiration module provides the sap flux at the root collar which is the upper boundary condition for the water transport in roots (i.e., equation 2). Driven by these boundary conditions, the soil-root module can update the distribution of soil moisture content (or soil water potential) in the soil domain. As described in section 2.1, the soil domain is divided into *n* layers when the finite difference method is applied to solve the coupled differential equations for the water movement in the soil and the root system. The specific number of layers depends on the maximum depth of the soil domain and the thicknesses of the soil layers. The *n* layers are referred to as sublayers hereinafter in order to distinguish them from the three layers in the VIC-3L model, which are abbreviated to “VIC layer” hereinafter. The sublayers are finer than the VIC layers. Therefore, each of the three VIC layers comprises a number of the sublayers.

[38] Soil moisture values of sublayers are averaged to provide soil moisture values to the three VIC layers, respectively. For example, the soil moisture value of the top VIC layer is obtained by averaging all the soil moisture values of the sublayers within this VIC layer. The soil moisture values of the top and the second VIC layers will be used to calculate soil evaporation and surface runoff, respectively, in the next time step. The soil moisture value of the bottom VIC layer is used by the ARNO algorithm [*Franchini and Pacciani*, 1991] to calculate the subsurface runoff, which is subsequently deducted from the sublayers contained in the bottom VIC layer.

[39] After the soil moisture adjustment, the soil water potential values of the sublayers within the root zone are used to calculate the weighted average soil water potential of the root zone. For each sublayer, the weighting coefficient is the ratio of the live fine roots in the current sublayer to the total live fine roots in terms of biomass. The weighted average soil water potential is used by the new transpiration module to calculate the transpiration for the next time step.

[40] It is worth mentioning that in the VIC+ model, the dynamic movement of the ground water table is calculated based on the mixed form of the Richards equation (i.e., equation 1) when the soil water potential becomes zero using the finite difference method described in section 2.1. In other words, the calculation of the groundwater table is not based on the moving boundary approach which uses the finite element method and is coupled with the VIC-3L model [*Liang et al*., 2003]. The two main reasons are: (1) to use a consistent numerical method (i.e., finite difference method) to deal with the unsaturated and saturated zones rather than using the finite difference method for the unsaturated zone and the finite element method for the saturated zone and (2) to have the entire VIC+ model in C language rather than C and Fortran combined since the moving boundary approach associated with the finite element method is written in Fortran language.

#### 2.3.2. Incorporation of the New Transpiration Module

[41] The net radiation and the ground heat flux from the VIC-3L model and the weighted average soil water potential of the root zone mentioned above are provided to the new transpiration module which subsequently gives the water flux results, including the sap flux at the root collar and the plant transpiration. The sap flux is supplied to the soil-root module. The plant transpiration is then used in the energy balance calculation of the VIC-3L model.

## 3. Model Validation

### 3.1. Validation of Soil-Root Module under a Simplified Condition

[42] A simple numerical experiment is used to evaluate the VIC+ model simulation results related to water movement in roots and the soil, where interactions between the unsaturated and saturated zones are considered. First we analytically derived a hydrostatic equilibrium soil moisture distribution along the vertical direction in the soil domain. Using this distribution as the initial condition of the soil domain and assuming that there is no water flux at all boundaries of the soil domain and the root system, we run the new coupled model for a period of time and check whether the initial soil moisture profile is maintained.

[43] If there is no water flux at all boundaries of the study soil domain and the corresponding root system, namely there is no infiltration, soil evaporation, subsurface flow, and plant transpiration, then soil water should be at the hydrostatic equilibrium state and the total water potential (i.e., matric potential plus gravitational potential) should be a constant within the soil domain. Based on this principle, the new coupled model can be evaluated under a given ideal condition. In this test, we use the van Genuchten formulation to represent the relationship between soil moisture and soil matric potential, and derive the ideal steady state soil moisture distribution within the soil domain to compare with the numerical results from VIC+.

[44] In this simple numerical experiment, the soil domain is composed of loam and has a depth of 3.44 m. The groundwater table depth is set to be 2 m. The vertical coordinate originates from the ground surface with upward being positive. Therefore, the constant total water potential of the hydrostatic equilibrium state is −2 m. The derived steady state soil moisture distribution is shown in Figure 4.

[45] In the numerical simulation, the soil domain is evenly discretized into 100 layers of which each is 3.44 cm thick. The time step is hourly. The theoretical steady state soil moisture distribution derived is used as the initial condition of the soil domain and all the boundary conditions are set to be zero flux for the soil domain and the root system. The model was run for 30 days and the initial soil moisture profile was found to be always maintained. This result verifies that the VIC+ model is reliable in terms of its numerical modeling of the soil water dynamics. This model does not have the numerical deficiencies of the Community Land Model, version 3 (i.e., CLM3) when it includes the groundwater module of *Niu et al*. [2007] as indicated by *Zeng and Decker* [2009]. This result also demonstrates that the simulation for the coupling of soil water dynamics and root water transport is reliable under the simplified condition of this numerical experiment.

### 3.2. Validation at Duke Site

#### 3.2.1. Site Description and Model Setup

[46] The VIC+ model is tested using the observed data from an AmeriFlux site (Duke Forest Loblolly Pine (US-Dk3)) located within the Blackwood Division of Duke Forest near Durham, North Carolina, USA (35.98°N, 79.09°W). The average elevation is about 163 m above sea level. The vegetation is dominated by *Pinus taeda L*. (loblolly pine) trees, which were uniformly planted in 1983, with a mean canopy height of about 19 m in 2006. The understory is composed of different hardwood species. The soil types are loam and clay. The climate is characterized by mean annual precipitation of 1145 mm and mean air temperature of 15.5°C. This site is chosen because there are usually dry periods during a year. The biological and hydrological processes included in the VIC+ model are expected to play important roles in the water, energy, and carbon cycles under dry conditions. Also, the observed soil moisture data there shows a nighttime increase in soil moisture which seems to indicate the existence of hydraulic redistribution. In addition, previous studies have observed the HR phenomenon for the same vegetation (i.e., loblolly pine) in that area [e.g., *Domec et al*., 2010].

[47] The soil information is from the Web Soil Survey (WSS) database, which is operated by Natural Resources Conservation Service (NRCS) of United States Department of Agriculture (USDA). At this site, the typical soil profile is composed of sandy clay loam (from the ground surface to 30 cm depth), clay (from 30 to 80 cm depth) and loam (below 80 cm depth).The WSS data indicate that the soil depth is greater than 80 inches (203 cm), but the maximum soil depth is unknown. For each soil class, class-average values of soil parameters, including saturated hydraulic conductivity, porosity, residual soil water content, and van Genuchten parameters, are obtained from the database of the ROSETTA model developed by the Agricultural Research Service of USDA. The leaf area index (LAI) data are from a study performed at the Duke Free Air CO_{2} Enrichment (FACE) experiment [*McCarthy et al*., 2007]. The Duke FACE facilities are located in the same forest as the AmeriFlux tower.

[48] The climatic input data for the VIC+ model includes precipitation, air temperature, wind speed, atmospheric pressure, vapor pressure, short wave radiation, downward long wave radiation, and CO_{2} concentration in the atmosphere. The data of years 2004 and 2005 from the website of the AmeriFlux network is used. For years 2004 and 2005, the annual precipitation values are 983 and 935 mm, and the mean air temperature values are 14.8°C and 14.7°C, respectively.

[49] The dominant vegetation, loblolly pine, is known to have a deep taproot. In the model simulations, the maximum root depth is set as 5 m. The soil depth is set to be larger than 5 m so that the groundwater table in the soil can either rise into the root zone or drop below the root zone. In the trial model simulations using the forcing data of years 2004 and 2005, the modeled groundwater table depths are always shallower than 6.5 m. Therefore, the soil depth of 7 m is adopted. The 7 m thick soil domain is evenly discretized into 350 sublayers, i.e., each sublayer's thickness is 2 cm, in the finite difference method of the model simulation. One advantage of having this uniform discretization configuration is that the ground water table can move upward or downward smoothly. The time step is hourly.

[50] The 30 cm top soil layer is underlain by a less pervious clay layer. In addition, the slope of this area is from 2% to 6%. These features make lateral flow in the top soil layer possible [*Schäfer et al*., 2002]. In order to represent such specific characteristic of this site, an additional subsurface runoff calculation with the ARNO algorithm is implemented in the top layer.

[51] In the model simulations a few parameters, which cannot be adequately estimated based on the available information, are adjusted to obtain a better match between the modeled results and the observations. The goodness of fit is judged using the root mean square error. These parameters include the soil moisture capacity shape parameter associated with the VIC-3L model, the parameter in the ARNO parameterization and the hydraulic resistance from the soil to leaves. Values and some discussions of these parameters are provided in Appendix Appendix E:. The modeled results are compared to the observations as follows.

#### 3.2.2. Comparison to Observations

[52] The modeled soil water content (SWC) values are compared with the observed data at the Duke site for the years 2004 and 2005 (Figure 5). Both the modeled results and the observed data are average values of the surface soil layer from 0 to 30 cm depth (abbreviated as “surface layer” hereinafter in this section). The model captures the daily variations of soil moisture fairly well (Figures 5a and 5c). The coefficients of determination (*R*^{2}) between modeled and observed soil moisture for years 2004 and 2005 are 0.86 and 0.94, respectively. The root mean square errors (RMSEs) for years 2004 and 2005 are 0.029 and 0.026, respectively. For some time periods (e.g., Day 210–230 of year 2004 and Day 110–135 of year 2005), the differences between the modeled results and the observations are evident. One possible reason may be the spatial heterogeneity of soil moisture at this site. The modeled results represent the spatially averaged soil moisture of the site. The observed data are the average soil moisture value across four different locations at the site, and may not represent the true average condition of the site, since the actual soil moisture varies across this site due to heterogeneity of factors such as precipitation and soil characteristics. For example, Figure 5 shows the range of soil moisture values obtained at the four locations of the site. The range of SWC can be as large as 0.1.

[53] Figures 5b and 5d show hourly SWC values of 14 days in years 2004 and 2005, respectively. On the two subfigures, we can see nighttime increases in the observed soil moisture values of the surface layer. This phenomenon could be due to combined reasons such as HR, diffusion of soil water, and impacts of the soil temperature on the soil moisture instrument. Note that “Soil moisture” specifically refers to soil moisture of the surface layer hereinafter in this section. At this site, the nighttime increases in the observed soil moisture data are relatively large. For example, in Figure 5b, the increases are usually as large as 0.01, which means that a 3 mm depth of water is imported into the 30 cm depth of surface layer. Such a large nighttime soil moisture increase is probably mainly contributed by HR since the increase due to diffusion [e.g., *Warren et al*., 2007] and instrument is small.

[54] As shown in the literature, the water fluxes of the upward liquid or vapor diffusion process are usually much smaller than those caused by HR [e.g., *Warren et al*., 2007]. This is also partially supported by the model simulations of this study. For the surface soil layer, nighttime inward water fluxes through direct upward soil water diffusion (*W*_{DIFF}) and through the HR process (*W*_{HR}) are, respectively, calculated each day. The ratio (*W*_{DIFF}/*W*_{HR}) ranges from close to zero to about 16% for the time periods when upward soil water diffusion exists.

[55] The fluctuations in the observed soil moisture values due to the impacts of soil temperature on the instrument device are also examined in this study. At this site, the soil moisture data were obtained with time domain reflectometry (TDR, CSI CS615 model). The SWC readings obtained by TDR may be affected by soil temperature as shown by some previous studies [*Pepin et al*., 1995; *Wraith et al*., 1995; *Or and Wraith*, 1999; *Wraith and Or*, 1999]. Based on the sensitivities of the TDR-measured SWC to the variation of soil temperature from previous studies and the variation range of soil temperature during nighttime at this site, it is deduced that the maximum possible increase in SWC readings caused by soil temperature is much smaller than the increase in the observed soil moisture data.

[56] Based on the above analyses, we conclude that nighttime increases in the observed soil moisture data are primarily caused by HR. That is, at nighttime soil water is redistributed from the deep soil to the surface layer through roots, when the surface layer is much drier than the deep soil. This is a typical HR process which is evident in the observed data at this site. This phenomenon is captured by the VIC+ model simulation as there exists a nighttime increase in the modeled soil moisture as shown in Figures 5b and 5d. This result validates, to some extent, the effectiveness of the HR scheme used in the VIC+ model.

[57] The modeled latent heat flux results are compared to the observed data at the daily scale for year 2004 (Figure 6a). The model can reproduce the latent heat flux fairly well. The *R*^{2} and RMSE between modeled and observed latent heat flux are 0.88 and 18.0 W/m^{2}, respectively. The modeled daily gross primary productivity (GPP) results are compared with the observations for year 2004 (Figure 6b). The daily variations of GPP are captured by the model reasonably well. The *R*^{2} and RMSE between modeled and observed GPP are 0.73 and 2.38 μmol m^{−2} s^{−1}, respectively.

### 3.3. Validation at Blodgett Site

#### 3.3.1. Site Description and Model Setup

[58] The VIC+ model is also applied at another AmeriFlux site (Blodgett Forest (US-Blo)) located in the Sierra Nevada range near Georgetown, California, USA (38.90°N, 120.63°W). The average elevation is about 1315 m above sea level. The site is in a mixed-evergreen coniferous forest dominated by even aged ponderosa pine. Other trees and shrubs make up less than 30% of the biomass. The soil characteristics are relatively uniform and the primary soil type is loam. The average annual precipitation is 1226 mm and the average air temperature is 11.1°C. The Mediterranean-type climate is characterized by wet winter and a long dry summer. Precipitation mainly occurs from October through May and there are very few rainfall events from June to September. During the dry summer, plants are primarily sustained by water stored in the unsaturated and saturated zones. So in the later period of the summer, plants will be under water-limited conditions. In this circumstance, the biological and hydrological processes included in the VIC+ model (e.g., HR, groundwater dynamics, and plant water storage) will play important roles in the water, energy, and carbon cycles. Therefore, it is convenient to investigate and demonstrate the impacts of these processes on the water, energy, and carbon cycles. In addition, the wet season in winter at this site can facilitate evaluating the impact of frozen soil on downward HR.

[59] This site is situated in a region where vegetation is known to have deep roots. In order to investigate the function of deep roots, in this modeling study, the maximum root depth is set as 8 m, which is similar to the root depths adopted by previous studies at this site [e.g., *Quijano et al*., 2012]. The soil depth is set to be larger than 8 m to allow for fluctuation of the groundwater table in the soil. In the trial model simulations using the forcing data of year 2004, the modeled groundwater table depths are always smaller than 11 m. Therefore, the soil depth of 12 m is used. The whole soil column is evenly discretized into 600 sublayers, each of which is 2 cm thick, in the numerical simulations. Values of soil parameters are obtained from the database of ROSETTA model developed by USDA. The LAI data are from the MODIS Land Product Subsets developed by the Oak Ridge National Laboratory. The climatic data of year 2004 from the website of the AmeriFlux network are used. The annual precipitation and mean air temperature are 1025 mm and 11.6°C, respectively. The annual precipitation is lower than the average annual value by 16.4%. Similar to the application at the Duke site, a few parameters are adjusted in the model simulation. Values and some discussions of these parameters are provided in Appendix Appendix E:. The modeled results are compared with the observed data in the following section.

#### 3.3.2. Comparison to Observations

[60] The HR process is considered in the simulation of the “HR” scenario. The modeled soil moisture results of the “HR” scenario are compared to the observations at the depth of 10 and 30 cm, respectively (Figure 7). The *R*^{2} between modeled and observed soil moisture for 10 and 30 cm depth are 0.94 and 0.96, respectively. The RMSEs for 10 and 30 cm depth are 0.036 and 0.020, respectively. At a depth of 10 cm, the modeled results are close to the observations during most of the wet season, but are obviously higher than the observations in the dry season (Figure 7a). Some previous studies at the Blodgett site found similar results [e.g., *Quijano et al*., 2012]. One possible reason may be that the model does not properly simulate the distribution of root uptake in the vertical direction, namely roots absorb less water in the shallow soil and absorb more water in the deep soil, as compared to the actual root uptake. Another reason may be that the modeled amount of soil evaporation at the ground surface is lower than the real amount. At the depth of 30 cm, in the dry season the modeled results are closer to the observations (Figure 7b) than at the depth of 10 cm.

[61] Results of the “no-HR” scenario are also shown in Figure 7. In the “no-HR” scenario, the HR process is shut down, namely roots cannot release water to the soil. It is demonstrated that during the dry season HR has evident impacts on soil moisture of the shallow soil layer. Soil moisture results of the “HR” scenario are higher than that of the “no-HR” scenario because water in the deep soil is pumped up to the shallow layer through the HR process. On the other hand, during the wet season, the soil moisture results of the “HR” scenario are sometimes slightly lower than that of the “no-HR” scenario. This is the consequence of the downward HR process, namely water is transferred from the shallow soil to the deep soil through roots.

[62] The modeled latent heat flux results of the “HR” scenario are compared to the observed data at the daily scale (Figure 8a). The *R*^{2} and RMSE between modeled and observed latent heat flux are 0.90 and 12.7 W/m^{2}, respectively. In the later period of the dry season (i.e., August and September), the observed latent heat flux drops down dramatically as the result of water limitation. This decline of latent heat flux is also captured by the model. The latent heat flux results of the “no-HR” scenario are also included in Figure 8a. It is shown that HR promotes latent heat flux during the dry season and does not have visible impacts on latent heat flux in the wet season. The HR process leads to an increase of the average latent heat flux of 3 months (July, August, and September) by 11.7 W/m^{2} (relative increase of 15.9%).

[63] The daily GPP results of the “HR” scenario are compared to the observations (Figure 8b). The *R*^{2} and RMSE between modeled and observed GPP are 0.55 and 1.27 μmol m^{−2} s^{−1}, respectively. Figure 8b also shows the GPP results of the “no-HR” scenario. It is shown that the HR process promotes GPP during the dry season. The increase of the average GPP of 3 months (July, August, and September) is 0.27 μmol m^{−2} s^{−1} and the relative increase is 8.0%.

## 4. Scenario Simulations and Analyses

[64] In this section, the impacts of hydraulic redistribution (HR), groundwater, root depth, and plant water storage on the water and energy cycles in the soil-plant-atmosphere continuum, as well as the interactions among these factors, are demonstrated through the results of a few scenario simulations. In addition, the effect of frozen soil on HR is also revealed with scenario simulations. These simulations are conducted at the Blodgett site. This site has a long dry summer when the four factors (i.e., HR, groundwater, root depth, and plant storage) are expected to have evident impacts on the water and energy processes. The wet winter of this site is favorable to evaluate the effect of frozen soil on downward HR.

### 4.1. Impacts of Hydraulic Redistribution, Groundwater, and Plant Storage

[65] For the purpose of studying the individual impacts exerted by HR, groundwater dynamics, and plant storage, respectively, on the water and energy processes, several scenario simulations are carried out. These simulations are divided into two groups which differ in the maximum root depth (2 m for one group and 8 m for the other group). Each group consists of five scenarios. The setup of the five scenarios is shown in Table 1. In the first scenario (benchmark), the groundwater table is comparatively deep and neither HR nor plant storage is considered in the simulation. Depth of the groundwater table is controlled by changing one parameter (i.e., the maximum daily subsurface runoff) of the ARNO algorithm through which to determine the amount of the subsurface runoff. In scenarios 2, 3, and 4, the three factors (i.e., HR, groundwater table depth and plant storage) are changed one by one. In the last scenario (HRGWC), the groundwater table is comparatively shallow and both HR and plant storage are included in the simulation. The simulated latent heat flux results of the other four scenarios are compared with that of the benchmark scenario (see Figure 9 and Table 2).

Scenarios | Considering Hydraulic Redistribution | Groundwater Table | Considering Plant Water Storage |
---|---|---|---|

1 (Benchmark) | No | Deep | No |

2 | Yes | Deep | No |

3 | No | Shallow | No |

4 | No | Deep | Yes |

5 (HRGWC) | Yes | Shallow | Yes |

^{a}This table shows scenarios of one group. Two groups of scenario simulations are conducted. The maximum root depth is 2 m for one group and 8 m for the other group.

Max Root Depth (m) | Scenarios | Average Latent Heat Flux of Jul., Aug., and Sep. (W/m^{2}) |
Increase From the Benchmark (W/m^{2}) |
Relative Increase From the Benchmark (%) |
---|---|---|---|---|

2 | 1 (Benchmark) | 33.3 | – | – |

2 | 44.1 | 10.9 | 32.7 | |

3 | 51.7 | 18.4 | 55.3 | |

4 | 40.1 | 6.8 | 20.5 | |

5 (HRGWC) | 60.7 | 27.4 | 82.3 | |

8 | 1 (Benchmark) | 59.8 | – | – |

2 | 73.6 | 13.8 | 23.0 | |

3 | 66.7 | 6.9 | 11.6 | |

4 | 67.6 | 7.8 | 13.1 | |

5 (HRGWC) | 84.3 | 24.5 | 40.9 |

[66] Figure 9a shows that HR evidently promotes latent heat flux during the dry season and does not have obvious impact on latent heat flux during the remaining period of the year. HR increases the average latent heat flux of 3 months (abbreviated as LE3Mo hereinafter; the 3 months are July, August, and September) by 10.9 W/m^{2} and the relative increase is 32.7%. When the root depth is 8 m, HR increases LE3Mo by 13.8 W/m^{2} and the relative increase is 23.0% (Figure 9e).

[67] HR can increase dry-season latent heat flux. The main reason is that at nighttime the HR process transfers water from the deep soil to the shallow soil where most roots concentrate. This process is favorable for plant transpiration and hence promotes latent heat flux. Figure 10 shows profiles of annual total root uptake at daytime and nighttime, respectively. When HR is considered in the simulation, it is clear that at nighttime roots absorb water in the deep soil and release water in the shallow soil. During the daytime, the root uptake of “HR” scenario is much higher than that of “no-HR” scenario in the shallow soil. The root uptake profiles in the shallow layer (0–1 m) are similar for the scenarios of different root depths (i.e., 2 versus 8 m). One important reason is that the distributions of the live fine roots in the shallow layer are assumed to be identical for these different scenarios. Therefore, the total mass of live fine roots is larger for the scenarios with deeper maximum root depths.

[68] When the root depth is 2 m, the rise of groundwater table (the mean annual groundwater table depth decreases from 7.2 to 2.8 m) promotes latent heat flux of the dry season dramatically (Figure 9b). The LE3Mo is increased by 18.4 W/m^{2} and the relative increase is 55.3%. The main reason is that the rise of groundwater table makes the root zone wetter and increases the amount of soil water available to plant transpiration. However, when the root depth is 8 m, the rise of groundwater table (the mean annual groundwater table depth decreases from 8.3 to 4.1 m) does not have such a large impact on latent heat flux of the dry season. The LE3Mo is increased by 6.9 W/m^{2} and the relative increase is 11.6%. Deep roots can access water from deep wet layers even if the groundwater table is comparatively deep [*Caldwell et al*., 1998; *Jackson et al*., 2000]. In this case, the rise of the groundwater table increases the soil-water amount available to plant transpiration but to a lesser extent as compared with the shallow-root case.

[69] Figures 9c and 9g demonstrate that plant storage can increase latent heat flux and that the effect is more obvious during the dry season. Plant storage can store water absorbed by roots at nighttime and supply water to transpiration during the daytime if root uptake cannot satisfy the transpiration requirement. The LE3Mo is promoted by plant storage to the similar extent for the shallow root and deep root cases (6.8 and 7.8 W/m^{2}, respectively).

[70] If both HR and plant storage are considered in the simulation, and at the same time, there is an evident rise of the groundwater table, latent heat flux of the dry season will be promoted to a large extent (Figures 9d and 9h). When the root depth is 2 m, the LE3Mo is increased by 27.4 W/m^{2} and the relative increase is 82.3%, and the primary contributing factor is the rise of groundwater table. When the root depth is 8 m, the LE3Mo is increased by 24.5 W/m^{2} and the relative increase is 40.9%, and the primary contributing factor is HR.

### 4.2. Interactions Among the Impacts of Root Depth, Hydraulic Redistribution, and Groundwater

[71] Roots, groundwater, and the HR process are linked with each other, thus there are interactions among them. For example, in the above section, it is shown that the impacts of HR or groundwater on latent heat flux can be sensitive to the root depth. The interactions among roots, groundwater, and HR are investigated through a few scenario simulations. These scenarios are divided into four groups as shown in Table 3. Each group consists of four scenarios with different root depths (i.e., 2, 4, 6, and 8 m). The plant storage is not considered in these scenarios. The LE3Mo values (the average latent heat flux of July, August, and September) of these scenarios are shown in Figure 11a. Data points of the four scenarios belonging to the same group are connected by line segments, and the corresponding group number is labeled beside the line. The mean annual groundwater table depths of the 16 scenarios are shown in Figure 11b.

Group No. | With hydraulic Redistribution | Groundwater Table |
---|---|---|

1 | Yes | Shallow |

2 | Yes | Deep |

3 | No | Shallow |

4 | No | Deep |

^{a}Each group consists of four scenarios with different root depths (i.e., 2, 4, 6, and 8 m).

#### 4.2.1. Impact of Root Depth

[72] For each of the four groups, it is clear that the dry-season latent heat flux (LE3Mo) rises as the root depth increases (Figure 11a). For example, when HR is considered and the groundwater table is shallow, dry-season latent heat flux rises from 58.1 to 78.1 W/m^{2} as the root depth increases from 2 to 8 m (Line 1 in Figure 11a). During the dry season, plant transpiration is mainly sustained by water stored in the soil. The increase of root depth makes more soil water available to plant transpiration. So the plant transpiration and hence the latent heat flux are higher when roots are deeper. This result demonstrates that deep roots are significant for plant growth during the dry season.

[73] Figure 11a also shows that the influence of root depth on the dry-season latent heat flux is larger when the groundwater table is deeper, no matter whether HR is considered (Line 1 versus Line 2) or not (Line 3 versus Line 4). For example, when HR is not considered and the root depth increases from 2 to 8 m, the latent heat flux increase is 26.5 W/m^{2} (the relative increase is 79.7%) for deep groundwater table condition (Line 4) and 15.1 W/m^{2} (29.1%) for shallow groundwater table condition (Line 3). The corresponding mean annual groundwater table depths are from 7.2 to 8.3 m for the deep groundwater table condition and from 2.8 to 4.1 m for the shallow groundwater table condition (Figure 11b). This result indicates that, in the water-limited circumstance, deep roots play a more important role when the groundwater table is deep, as compared with the shallower groundwater table condition.

#### 4.2.2. Impact of Hydraulic Redistribution

[74] Under the shallow groundwater table condition, impacts of HR on the dry-season latent heat flux become larger as the root depth increases from 2 to 8 m (Line 1 versus Line 3). The HR induced-increase of the latent heat flux is comparatively small (6.4 W/m^{2}) when the root depth is 2 m. There is an evident growth in such an increase (from 6.4 to 9.9 W/m^{2}) as the root depth increases from 2 to 4 m. However, as the root depth increases from 4 to 8 m, the increase in latent heat flux slows down (from 9.9 to 11.4 W/m^{2}). Similar phenomenon is observed under the deep groundwater table condition (Line 2 versus Line 4). This result indicates that shallow rooting depths limit the impact/role of HR in promoting the latent heat flux. Impacts of HR on water and energy processes become significant as the root depth increases within a certain range (e.g., from 2 to 4 m in the above cases).

[75] By comparing the differences between Line 1 and Line 3 with the differences between Line 2 and Line 4, it is demonstrated that, for all of the four root depths cases, the HR induced-increase of the dry-season latent heat flux is higher under the deep groundwater table conditions, as compared with the shallower groundwater table conditions. When the groundwater table is deep, groundwater cannot be effectively utilized by plants to satisfy the transpiration demand during the daytime. However, the HR process can pump the deep groundwater to the shallow layer at nighttime and facilitate the transpiration process in the next day. Therefore, under the water-limited condition, the impact of HR on latent heat flux is more significant when the groundwater table is deeper.

#### 4.2.3. Impact of Groundwater

[76] Figure 11a shows that the rise of the groundwater table evidently promotes dry-season latent heat flux no matter whether HR is included (Line 1 versus Line 2) or not (Line 3 versus Line 4). However, this promotion is smaller when HR is included, as compared to no-HR scenarios. The main reason is that HR can enhance the utilization of groundwater by plants, even though the groundwater table is deep. This makes the plant transpiration and hence latent heat flux less sensitive to the fluctuations of the groundwater table.

[77] When HR is not considered, the increase of the dry-season latent heat flux caused by the rise of groundwater table (differences between Line 3 and Line 4) declines from 18.4 to 6.9 W/m^{2} as the root depth increases from 2 to 8 m. Similar phenomenon is observed when HR is considered (Line 1 versus Line 2). The reason is that deep roots enhance the capability of plants to utilize groundwater and reduce the impact of groundwater table fluctuation on the plant transpiration.

### 4.3. Impact of Plant Storage on Hydraulic Redistribution

[78] Connection between the plant storage flow (i.e., flow into/out of plant storage) and the HR process is explicitly represented in the VIC+ model. Therefore, the interaction between plant storage and HR is modeled in the simulations. This interaction is demonstrated by some of the modeled results. For example, variation of the amount of hydraulically redistributed water (HRW) can reveal the impact of plant storage on HR.

[79] Hydraulically redistributed water refers to water flow from roots into the soil. Figure 12a shows daily HRW amounts from ground surface to 30 cm depth for two scenarios (considering and not considering plant storage) when the root depth is 2 m. Positive HRW amount means that soil water is redistributed from the deeper soil to the surface layer (0–30 cm) through the HR process. Higher HRW amount implies larger impact of HR on the water and energy processes. It is shown that the HRW is evident during the dry season, which indicates that HR plays a more important role during the dry season than during other periods of the year.

[80] It is interesting to note that the HRW amounts decrease significantly for most of the dry season while plant storage is considered in the simulation. In other words, this phenomenon demonstrates that plant storage can weaken the intensity of the HR process. Table 4 shows annual total HRW amounts in the surface soil layer (0–30 cm) for different scenarios. When the maximum root depth is 2 m, including plant storage reduces the HRW amount by 28.9 mm and the relative decrease is 28.0%. Water stored in plant storage is depleted by transpiration during the daytime. At nighttime plant storage is replenished by water coming from root uptake. On the other hand, the HR process also occurs at nighttime under the dry climatic conditions. Usually water from the deeper soil is pumped up and released into the shallow layer. Therefore, both plant storage and the shallow soil layer obtain water tranferred from the deeper soil. The inclusion of plant storage into the simulation reduces the water amount redistributed to the shallow layer.

Max Root Depth (m) | Without Plant Storage (mm) | With Plant Storage (mm) | Difference (mm) | Relative Difference (%) |
---|---|---|---|---|

2 | 103.2 | 74.3 | 28.9 | 28.0 |

8 | 140.7 | 119.2 | 21.5 | 15.3 |

^{a}The values are annual total HRW amounts in the surface soil layer (0–30 cm).

[81] Comparison between Figures 12a and 12b shows that the HRW amounts increase when the root depth is increased; at the same time the effect of plant storage on the HRW amounts decreases. This phenomenon is also demonstrated in Table 4. As roots extend into deeper soil, more soil water can be utilized by plants [e.g., *Jackson et al*., 2000; *Amenu and Kumar*, 2008]. At nighttime, the increase of root uptake in the deep soil favors water release by roots into the shallow layer. At the same time, more water is provided to replenish plant storage and the impact of plant storage on HR is weakened.

### 4.4. Impact of Frozen Soil on Hydraulic Redistribution

[82] For general simulations, the freezing process of soil water is represented, namely partial soil water turns into ice when soil temperature is lower than the freezing point. These general simulations are also referred to as “Frozen soil” scenario simulations hereinafter. For evaluating the effect of frozen soil on HR, we conducted a few special simulations where soil water does not turn into ice when soil temperature is below the freezing point. These special simulations are also referred to as “No frozen soil” scenario simulations hereinafter.

[83] These simulations are conducted at the Blodgett site which has a Mediterranean-type climate. During the wet winter, frozen soil may have impact on the downward HR. At first, the observed forcing data of year 2004 are used. The amounts of downward HRW (hydraulically redistributed water) for the “Frozen soil” scenario and the “No frozen soil” scenario are 131.1 and 135.7 mm/y, respectively. It appears that frozen soil does not have an obvious impact on downward HR. However, examination of the forcing data shows that the weather of year 2004 is not very cold at the Blodgett site. For 526 h out of 8784 h in this year (6.0% of the time steps in simulations), the average air temperature values are below 0°C. The comparatively warm weather is one important reason why the results do not show evident impact of frozen soil on HR.

[84] The “Frozen soil” and “No frozen soil” scenario simulations are repeated with modified forcing data of year 2004 with air temperature values lowered by 3°C. The results exhibit obvious impacts of frozen soil on HR. The amounts of downward HRW for the “Frozen soil” scenario and the “No frozen soil” scenario are 107.3 and 125.3 mm/y, respectively. Figure 13 shows the daily downward-HRW amounts of the two scenarios and the corresponding daily air temperature and precipitation. The figure demonstrates that the downward-HRW amount of the “Frozen soil” scenario is lower than that of the “No frozen soil” scenario when the air temperature is around 0°C. Figure 14 shows the profiles of total root uptake during the cold periods (Day 1–Day 69 and Day 292–Day 366) for the two scenarios. This figure demonstrates that root uptake is restricted in the shallow layer and at the same time roots release less water into the deep soil when the freezing process is considered in the simulation.

## 5. Summary and Discussion

[85] In this study, the VIC-3L model is extended to VIC+ by including representations of several important biological and hydrological processes under water-limited conditions, which are hydraulic redistribution (HR), groundwater dynamics, plant water storage and photosynthesis. In the VIC+ model, HR is represented by a process-based scheme and its interaction with groundwater dynamics is explicitly considered. Plant transpiration is calculated by combining the the Ohm's law analogy, where plant storage is considered, with the Penman-Monteith method which is coupled with the calculation of carbon assimilation. In the VIC+ model, the new biological and hydrological processes are closely coupled and at the same time they interact with the other water and energy processes of the VIC-3L model. The integration approach involved in VIC+ includes a new concept of modeling strategy—representing the same processes (e.g., transpiration process and photosynthetic process) with multiple simultaneous equations/constraints. Such a new modeling strategy leads to a simulation of certain variables (e.g., leaf water potential and CO_{2} concentration within the leaf) as a consequence of multiple coordinated hydrological processes. Such an approach increases constraints applied to the model and thus reduces the model's degrees of freedom. This new modeling strategy can partially address the modeling problem of lacking enough constraints, especially when new processes are added.

[86] The VIC+ model is first evaluated with an analytical solution under a simple condition for its modeling of water flow process in the soil and roots (Figure 4). The result, to some extent, verifies the reliability of VIC+ for modeling water flows in roots, the unsaturated zone and the saturated zone.

[87] The VIC+ model is also applied to two AmeriFlux sites. One is the “Duke Forest Loblolly Pine (US-Dk3)” site located in North Carolina, USA. The Duke site experienced some dry periods during the years of 2004 and 2005. The existence of HR in a loblolly pine plantation in a region close to the Duke site has been reported in previous studies. This application shows that the VIC+ model can reproduce the observed soil moisture, latent heat flux and gross primary productivity (GPP) at the daily time scale fairly well (Figures 5 and 6). There exist nighttime increases in the observed soil moisture data of this site (Figures 5b and 5d); it is deduced that this phenomenon is primarily caused by HR. This phenomenon is also captured by the VIC+ model.

[88] The other one is the “Blodgett Forest (US-Blo)” site located in California, USA. This site has a long dry summer each year. In the later period of the summer, plants are under water-limited conditions. In this circumstance the biological and hydrological processes investigated in this study are expected to play important roles in the water, energy, and carbon cycles. Our results show that the observed soil moisture, latent heat flux, and GPP are reproduced by the model reasonably well at the daily time scale (Figures 7 and 8). The modeled results are also compared with the results of the “no-HR” scenario, where the HR process is shut down. The comparison shows that soil moisture in the shallow layer is increased by HR in the dry season and decreased by HR in the wet season, while the impacts are more evident in the dry season (Figure 7). The comparison also shows that the latent heat flux and GPP are supported by HR in the dry season and are not obviously affected by HR in the wet season (Figure 8).

[89] A group of scenario simulations are performed at the Blodgett site to investigate the impacts of HR, groundwater dynamics, plant storage and root depth on the water, and energy cycles (Table 1). The modeled results demonstrate that each of the three factors (i.e., HR, groundwater dynamics and plant storage) can evidently increase latent heat flux in the dry season, while they do not have obvious impacts on the latent heat flux in the wet season, no matter whether the maximum root depth is shallow (2 m) or deep (8 m) (Figure 9 and Table 2). The combined effects of the three factors can exert larger impacts on the dry-season latent heat flux than each of the three factors alone and can increase the latent heat flux by 82.3% and 40.9%, when the maximum root depth is 2 m and 8 m, respectively.

[90] As the new biological and hydrological processes in the VIC+ model are closely coupled with each other, it enables an investigation of the interactions among these processes. The interactions among roots, groundwater table, and HR are investigated through a series of scenario simulations. The modeled results reveal that the impact of one factor (i.e., maximum root depth, groundwater table depth or HR) on dry-season latent heat flux may be influenced by the other two factors (Figure 11): (1) The increase of root depth is favorable for dry-season latent heat flux, which is more sensitive to root depth when the groundwater table is deeper; (2) The dry-season latent heat flux is promoted by HR more obviously when either the groundwater table or the root depth is deeper; (3) The rise of groundwater table will increase the dry-season latent heat flux and the effect is more evident when there is no HR or when the root depth is shallow. In addition, the interaction between plant storage and HR is demonstrated by comparing two scenarios in terms of the amount of hydraulically redistributed water in the shallow soil layer (Figure 12). It is found that plant storage can weaken the intensity of the upward HR in the dry summer (Figure 12 and Table 4).

[91] In the wet season, soil water of the shallow layer may be transferred to the deep soil via downward HR. However, downward HR may be restricted by frozen soil in the shallow layer if the wet season is in winter. The effect of frozen soil on the downward HR is investigated with scenario simulations and the results show that frozen soil can evidently reduce the downward HR in winter (Figures 13 and 14), which decreases water amount stored in the deep soil and hence can reduce transpiration during the dry season.

[92] Although important biological and hydrological processes for water-limited environments are coupled within the VIC+ model and their impacts on water, energy, and carbon budgets are investigated through a series of scenario simulations, our understanding of these processes is still limited. In addition, although the biological and hydrological processes are closely coupled in this study so that the model's degrees of freedom can be reduced and the interactions among these processes can be investigated, this new modeling strategy needs to be further explored and tested. The model parameter uncertainties may be further reduced through the reduction of the number of parameters when more important constraints (e.g., biological constraints) are discovered and included. Such advancement would require more understanding of the processes and their interactions within the soil-plant-atmosphere continuum.

## Acknowledgments

[112] The authors are thankful to the four reviewers, the Editor and the Associate Editor for their valuable comments and suggestions. We thank Seongeun Jeong for his work on the snow processes in the VIC-3L model. We also thank the scientists who worked at the two AmeriFlux sites for their data. The AmeriFlux research is supported by the U.S. Department of Energy and National Aeronautics and Space Administration. Juan C. Quijano is acknowledged for the helpful discussion on the data of the Blodgett site. This work was partially supported by the DOE grant of DEFG0208ER64586 and by the NOAA grant of NA09OAR4310168 to the University of Pittsburgh.

## Appendix A:: Derivation of the Equation for Water Transport in the Root System

*Frensch and Steudle*, 1989]. Therefore, the total flow rate

*Q*

_{vessel}(m

^{3}·s

^{−1}) in all vessels which go through the area

*S*(m

^{2}) can be approximated by

*n*is the number of vessels;

*k*

_{a}_{,}

*(m*

_{i}^{4}·s

^{−1}·Pa

^{−1}) is the axial hydraulic conductance of vessel

*i*;

*ψ*

_{r}_{,}

*(Pa) is the root water potential in vessel*

_{i}*i*; and the meanings of other symbols are the same as that of equation 1. For flow rate

*Q*

_{vessel}upward is positive.

*S*, one obtains the expression of vessel flux per unit area as:

*q*

_{vessel}is (m·s

^{−1});

*K*(m

_{ra}^{2}·s

^{−1}·Pa

^{−1}) is the axial hydraulic conductivity of roots per unit area and is equal to ; and

*ψ*(Pa) is the root water potential.

_{r}## Appendix B:: The Method of Ohm's Law Analogy

*E*(m·s

_{tr}^{−1})] is assumed to be the sum of the sap flux [

*F*(m·s

_{ru}^{−1})] at the root collar and the plant-storage flux [

*q*(m·s

^{−1})]:

*Van den Honert*[1948] as

*ψ*

_{soil}(Pa) is the lumped soil water potential in the root zone;

*ψ*(Pa) is the leaf water potential; and

_{l}*R*(Pa·s·m

^{−1}) is the total hydraulic resistance from the soil to leaves.

*ψ*(Pa) is the water potential of plant storage; and

_{p}*r*(Pa·s·m

^{−1}) is the hydraulic resistance between plant storage and leaves.

*C*(m·Pa

^{−1}) is the parameter representing the capacity of plant water storage; and

*t*is time.

*S*is the weighted average soil saturation degree of all sublayers in the root zone. For each sublayer, the weighting coefficient is the ratio of the live fine roots in the current sublayer to the total live fine roots in terms of biomass.

*R*

_{0}is a reference resistance.

*α*and

*β*are empirical coefficients.

## Appendix C:: Stomatal Conductance

[102] Stomatal conductance for water vapor is related to the stomatal conductance for CO_{2}. The former
can be assumed to be equal to the latter
multiplied by 1.6 [*Jones*, 1992]. The stomatal conductance
is in the unit of (mol·m^{−2}·s^{−1}) while in the Penman-Monteith equation the stomatal conductance (*g _{s}*) is in the unit of (m·s

^{−1}). The unit conversion can be done using the method of

*Pearcy et al*. [1989].

*Tuzet et al*. [2003] proposed a variant of the Ball-Berry-Leuning model [

*Ball et al*., 1987;

*Leuning*, 1995] to express the CO

_{2}stomatal conductance as a function of the net carbon assimilation.

*g*

_{0}(mol·m

^{−2}·s

^{−1}) is the residual conductance; and

*a*is an empirical coefficient;

*A*(mol·m

_{n}^{−2}·s

^{−1}) is the net carbon assimilation per unit leaf area (also referred to as “carbon assimilation rate” or “assimilation rate” in this paper);

*c*(mol·mol

_{i}^{−1}) is the CO

_{2}concentration within the leaf; Г* (mol·mol

^{−1}) is the CO

_{2}compensation point which depends on leaf temperature; and

*f*(

*ψ*) is an empirical function which is given by

_{l}*ψ*(Pa) is the leaf water potential;

_{l}*S*(Pa

_{f}^{−1}) is a sensitivity parameter; and

*ψ*(Pa) is a reference potential.

_{f}## Appendix D:: Carbon Assimilation Rate

[104] The diffusion method and the modified Farquhar model are combined to derive the carbon assimilation rate.

### D1. Diffusion Method

*Daly et al*., 2004]

*c*(mol·mol

_{a}^{−1}) is the CO

_{2}concentration in the ambient air; and

*c*(mol·mol

_{i}^{−1}) is the CO

_{2}concentration within the leaf. The conductance (mol·m

^{−2}·s

^{−1}) is calculated by

_{2}stomatal conductance and assumed to be equal to ; is the CO

_{2}leaf boundary layer conductance and is equal to ; and is the atmospheric conductance and is equal to

*g*in value.

_{a}### D2. Modified Farquhar Model

*Daly et al*., 2004]:

*ψ*(Pa) is the leaf water potential; (Pa) is the leaf water potential value indicating well-watered conditions; and (Pa) is the leaf water potential value below which assimilation is reduced to zero.

_{l}[107]
in equation D3 is the assimilation rate under well-watered condition and primarily depends on photosynthetically active radiation (*ϕ*), CO_{2} concentration within the leaf (*c _{i}*), and leaf temperature (

*T*). It is given by the minimum of

_{l}*A*,

_{q}*A*, and

_{c}*A*. The daytime respiration (

_{s}*R*) usually accounts for a small fraction of assimilation and is neglected here.

_{d}*A*is the assimilation rate limited by RuBP (Ribulose-1,5-bisphosphate) regeneration when

_{q}*ϕ*is low. It is given by

*J*is the electron transport rate which depends on

*ϕ*and

*T*; Г* is the CO

_{l}_{2}compensation point which depends on

*T*.

_{l}*A*is the assimilation rate restricted by rubisco activity (i.e., restricted by

_{c}*c*) and is expressed as

_{i}*V*

_{c}_{,max}is the maximum carboxylation rate which depends on

*T*;

_{l}*o*is the oxygen concentration;

_{i}*K*and

_{c}*K*are the Michaelis-Menten coefficients for CO

_{o}_{2}and O

_{2}, respectively, and they depend on

*T*.

_{l}*ϕ*or

*c*, the maximum assimilation rate is given by

_{i}## Appendix E:: Parameter Values

[111] Values of model parameters for this study are listed in Table A1. Some values are based on the literature and some values are estimated through model calibration. The soil moisture capacity shape parameter (referred to as b-parameter hereinafter) is an indicator of the spatial variation of the storage capacity of soil moisture in the upper layer of the soil column [e.g., *Liang and Xie*, 2001]. Reducing the b-parameter value can decrease the surface runoff and increase the infiltration and soil moisture. The b-parameter values adopted in this study fall within the typical range of (0, 5) indicated in the literature [e.g., *Huang et al*., 2003]. The maximum subsurface runoff (*D _{m}*) in the ARNO algorithm controls the magnitude of subsurface runoff. Increasing the

*D*value can lower the groundwater table and decrease soil moisture. The

_{m}*D*values used in this study are consistent with the typical range (from 0 to 40 mm/day) indicated in the literature [

_{m}*Huang and Liang*, 2006]. The reference resistance (

*R*

_{0}) is close to the total resistance from the soil to leaves when the root zone is moist. The increase of the reference resistance can reduce plant transpiration. The reference resistance values adopted in this study are comparable to the values in the literature [

*Hunt et al*., 1991;

*Lhomme et al*., 2001].

Parameter | Symbol | Units | Duke Site | Blodgett Site |
---|---|---|---|---|

Empirical coefficient in equation C1 | a |
– | 2a | 2 |

Soil moisture capacity shape parameter | b |
– | 0.5 | 0.4 |

Capacity of plant water storage (equation B4) | C |
m·MPa^{−1} |
2.6 × 10^{−4}b |
1.8 × 10^{−4}c |

Maximum subsurface runoff of one day in ARNO algorithm | D_{m} |
mm·day^{−1} |
0.5 | 0.3 |

Maximum root depth | D_{root} |
m | 5 | 8 |

Maximum soil depth | D_{soil} |
m | 7 | 12 |

Axial hydraulic conductivity of roots per unit area (equations 2, A2, and A4) | K_{ra} |
m^{2}·s^{−1}·MPa^{−1} |
8.9 × 10^{−6}−3.8 × 10^{−4}d |
8.9 × 10^{−6}−3.8 × 10^{−4} |

Radial hydraulic conductivity of roots per unit of root surface area (equation 3) | K_{rr} |
m·s^{−1}·MPa^{−1} |
1.4 × 10^{−7}e, f |
1.4 × 10^{−7} |

Oxygen concentration (equation D6) | o_{i} |
mol·mol^{−1} |
0.209g | 0.209 |

Reference resistance (equation B5) | R_{0} |
MPa·s·m^{−}^{1} |
1.4 × 10^{7} |
2.0 × 10^{7} |

Sensitivity parameter (equation C2) | S_{f} |
MPa^{−1} |
3.2a | 3.2 |

Empirical coefficient in equation B5 | α |
– | 10 | 10 |

Empirical coefficient in equation B5 | β |
– | 0.2 | 0.2 |

Reference leaf water potential (equation C2) | ψ_{f} |
MPa | −1.9a | −1.9 |

Leaf water potential below which assimilation is reduced to zero (equation D4) | ψ_{l}_{A1} |
MPa | −4.5g | −4.5 |

Leaf water potential indicating well-watered condition (equation D4) | ψ_{l}_{A1} |
MPa | −0.5g | −0.5 |