## 1. Introduction

The connection between terrestrial, ecologic, and atmospheric processes has been recognized and studied since at least the 1970s (Eagleson 1978). The feedbacks between vegetation dynamics and the hydrologic system have been shown to affect the landscape-scale spatial and temporal structure of topography, soil moisture, and transpiration patterns; the distribution of vegetation; and the resiliency of hydrologic systems (Caylor et al. 2006; Dietrich and Perron 2006; Florinsky and Kuryakova 1996; Ivanov et al. 2008; Jones et al. 2012; Peterson et al. 2009; Porporato et al. 2002; Rodriguez-Iturbe 2000; Vivoni et al. 2010). Even at short time scales, environmental change affects the dynamics of vegetation. In turn, vegetation has the ability to modify the atmospheric boundary layer and to reportion the land energy and water balance. Because vegetation plays a critical role in the terrestrial hydrologic cycle, it is important that we include in our models the feedbacks between vegetation, hydrology, and the atmosphere to build a more integrated and realistic description of the hydrologic, ecologic and atmospheric processes (Rodriguez-Iturbe 2000). While many models integrate boundary layer processes and hydrology (e.g., Liang et al. 1994; Peters-Lidard et al. 1997; Wigmosta et al. 1994), there are relatively few models currently available that integrate vegetation dynamics in the description of the energy and water exchanges at the landscape scale (e.g., Oleson et al. 2010; Tague and Band 2004).

New climate research challenges have fostered the development of land–vegetation–atmosphere energy and water transfer schemes that can be used in conjunction with climate models. One approach is to fully integrate these schemes in the atmospheric models providing a two-way feedback mechanism between surface and climate. Examples of this approach include the Biosphere–Atmosphere Transfer Model (Dickinson et al. 1993) that eventually evolved into the Community Land Model scheme (Oleson et al. 2010 for current version 4.0) used in the Community Climate System Model and the Community Atmosphere Model. Another example is the Pleim–Xiu model (Pleim and Xiu 1995) and the Noah land surface model (Chen et al. 1996) used in fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model, version 3 (MM5v3; Grell et al. 1995) and Weather Research and Forecasting model, version 3 (WRFv3; Michalakes et al. 1998). This integrated approach offers a sophisticated vertical description of the atmospheric boundary layer but at the expense of simplifying the vegetation and hydrologic components or incurring high computational expenses.

An alternative approach is the one-way linkage. In this approach, the output from the atmospheric model provides the input to the ecohydrologic component that is then run offline. This approach permits running the model using data generated by sources other than atmospheric models and allows for a more flexible description of the vertical energy and water exchanges. It also typically allows for faster run times, more detail in the spatial representation of the ecohydrologic processes, and more flexibility in the temporal resolution used to run the model. The TOPMODEL-based Land–Atmosphere Transfer Scheme (TOPLATS; Famiglietti and Wood 1994; Peters-Lidard et al. 1997) is an example of models in this category. It presents a one layer vertical energy and water balance scheme and uses a TOPMODEL approach (Beven and Kirby 1979) to describe horizontal water transfers in the landscape but does not include a snow component or vegetation dynamics and does not allow for subpixel heterogeneity. The Variable Infiltration Capacity (VIC) model (Liang et al. 1994) was formulated to include subpixel variations in the soil cover and has evolved to include snow processes, multilayer description of soil processes, and water routing (Cherkauer et al. 2003; Lohmann et al. 1998) but does not include vegetation dynamics.

A description of the dynamics of vegetation was not incorporated into hydrologic models until later. Traditionally, mechanistic forest growth models vary in the complexity of the description of the physiological and biochemical processes involved in the growth of vegetation but do not have a rigorous description of the hydrologic cycle. These models use precipitation, prescribed hydrologic indices, or empirical parameters to account for the effect of hydrologic conditions on vegetation growth. Two models that have a thorough description of vegetation dynamics and the associated biogeochemical cycles that have been used in conjunction with atmospheric models are Biome–Biogeochemical Cycles (BIOME-BGC; Running and Hunt 1993) and CENTURY (Parton et al. 1993), but even these sophisticated models do not take into consideration the hydrologic connectivity of the landscape or the impact of vegetation on the hydrologic conditions of the soil. The Regional Hydro-Ecologic Simulation System (RHESSyS; Mackay and Band 1997; Tague and Band 2004) couples a TOPMODEL-type description of lateral hydrologic fluxes to BIOME-BGC. This model offers a detailed account of carbon and nitrogen cycling at the landscape scale with a hydrologic component of intermediate complexity, but the energy transfer mechanism relies on a semiempirical approach rather than the fully physical description used by other models. Tribs+Veggie (Ivanov et al. 2008) and the Community Land Model (CLM) (Oleson et al. 2010) implement a higher level of sophistication in the description of the energy and carbon dynamics. However, Tribs+Veggie is intended to be used for semiarid regions and does not include a snow component, and CLM does not have a lateral water transfer component. Recently, a new watershed-scale ecohydrologic model (Fatichi et al. 2013) improves on Tribs+Veggie by including snowpack dynamics. Further advances toward a more detailed description of the processes driving energy, water, and vegetation dynamics are included in a new formulation of the Noah land surface model (Niu et al. 2011). This new development improves over the Noah land surface model (Noah-LSM) by calculating energy balances separately for the canopy and soil surface, improved multilayer snow and frozen soil dynamic and short-term leaf dynamics. Lateral water transfers are simulated using a TOPMODEL approach for surface runoff and an exponential decay function of the aquifer depth to simulate subsurface runoff.

In this paper, we present an ecohydrologic model designed to be run using outputs from a regional climate model. It is unique in that it maintains a balance between a comprehensive description of fluxes with a strong physics base and a parsimonious implementation that results in an agile model that is fast and easy to run. It implements a simplified forest growth module, a first-order local-closure scheme for the turbulent energy exchanges, and a kinematic hydrologic model. The energy balance equation is solved for the canopy and the surface layers and includes a snow component. The model allows for subpixel surface cover variability by solving the energy balance for different vegetation units and for bare soil within each computational cell. Both rainfall-excess and saturation-excess runoff generation mechanisms are simulated together with a kinematic description of subsurface water routing. The primary productivity and forest growth components are based on the Physiological Principles Predicting Growth (3PG) model (Landsberg and Waring 1997) and TREEDYN3 (Bossel 1996). The model is programmed in C++ with an object-oriented structure that allows for easy expansion of new modules and features and is parallized for shared-memory multicore computers using OpenMP. Spatial inputs and outputs to and from the model are in the cross-system format (CSF) compatible with PCRaster (http://pcraster.geo.uu.nl/) to provide full free GIS functionality for data pre- and postprocessing and for visualization.

## 2. Overview

The model has three major components: a vertical energy balance scheme that simulates soil–vegetation–atmosphere energy dynamics based on flux–gradient similarity approach; a hydrologic component based on the kinematic wave that provides lateral water transfer and ensures the hydrologic articulation of the landscape; and a forest growth component that includes carbon uptake, carbon allocation, leaf and root turnover, and tree growth based on allometric relationships. The models are tightly coupled to ensure they capture the main feedbacks between vegetation, hydrology, and climate. Figures 1 and 2 depict the main components of the energy balance component and of the water balance component included in the model, respectively. An outline of the main parts of the forest growth component is shown in Figure 3.

Simulated feedbacks between the components include the effect of plant growth and phenology on the atmospheric boundary layer and on turbulent energy transfers. The leaf growth cycle impacts the transmission of shortwave radiation to the understory (shading), the emission of longwave radiation, and the partition of sensible and latent heat fluxes. It also affects the interception of rain and snow by the canopy and the transpiration volumes. In turn, water and energy availability affect stomatal resistance; carbon uptake rates by vegetation; leaf and root turnover rates; and carbon allocation ratios to leaves, stem, and roots. Lateral redistribution of soil moisture affect the bulk heat capacity of soil and hence its temperature variation, it also affects the spatial pattern of water availability and the runoff generation areas.

### Model domain

The model domain is constructed and determined by a regularly gridded raster digital elevation model (DEM) that defines the topography and the drainage network and establishes the finite-differences grid on which the governing equations are solved. Conservation of mass and energy are enforced at each time step and computational unit.

Boundary conditions at the top are given by the atmospheric forcing: shortwave radiation, downwelling longwave radiation, air temperature, relative humidity, wind speed, and precipitation. Boundary conditions for the upstream cells and for the bottom of the domain are no-flow boundaries (i.e., it is assumed that the edge of the domain is the water divide for surface and subsurface water and that the bottom of the considered subsurface layer is impervious). Initial conditions include soil moisture, soil temperature, snow water equivalent on the ground, leaf area index, tree height, and tree basal area. The model grid size and time step can be chosen by the user, although the energy and hydrologic equations are most meaningful at hourly time steps. The solution of the kinematic wave is unconditionally stable for any ratio of time step to grid size, although a grid size that is commensurate with the time step and the speed of lateral hydrologic flows to maintain the Courant number below unity is recommended.

Each grid cell in the model can have more than one vegetation type in addition to areas of bare soil. Vegetation types are differentiated in terms of its physiologic properties and structure rather than in terms of species. Thus, it is possible to have a cell with forest of one species at two growth stages (one plot with large mature trees and another plot with saplings) forming two vegetation types or a cell with several species of similar characteristics forming a single vegetation type. The area occupied by a vegetation type is defined in terms of the proportion of canopy coverage in the cell. Allometric relationships are used to relate biomass to the number of individual trees and stem and canopy dimensions. In this version of the model competition between cover types is proportional to canopy coverage. Reduced growth by crowding is also taken into account. Different competition schemes will be introduced in the future.

## 3. Model description

This section presents the mathematical framework for implementing the processes described by the model. The energy, hydrologic, and forest growth components are described in different sections. The connection between the components is done through shared variables representing local processes or states. For convenience, we have included the list of symbols used in this paper in Table 1. Forest cover types are identified by the index *p*. Each cell has *P* cover types *p* = 1, 2, … , *P*, where the first *P* − 1 values of the index represents different vegetation types and *P* represents bare soil. The energy and water balances are solved for each vegetation type and integrated over the cell area to produce the fluxes at the cell scale as explained in sections 3.1 and 3.2.

List of symbols.

### 3.1. Energy balance scheme

#### Canopy energy balance

*P*− 1 times). At the canopy level it is assumed that the storage of heat by vegetation is negligible and the available energy (net radiation) is partitioned into radiative and turbulent components. The total energy balance for the pixel is calculated by taking the sum of the fluxes for each vegetation type weighted by the proportion of the pixel they occupy

*f*,

_{p}*R*is net radiation for the canopy (W m

_{nc}^{−2}),

*ρ*is water density (kg m

_{w}^{−3}),

*λ*

_{υ}is latent heat of vaporization (J kg

^{−1}),

*E*is evaporation flux (m s

_{c}^{−1}),

*ρ*

_{w}λ_{υ}

*E*(W m

_{c}^{−2}) is latent heat flux into the atmosphere due to evaporation, Tp

_{c}is transpiration flux (m s

^{−1}),

*ρ*

_{w}λ_{υ}Tp

_{c}(W m

^{−2}) is latent flux into the atmosphere due to transpiration, and

*H*is sensible heat flux between the canopy and the atmosphere (W m

_{c}^{−2}). The subscript [

*p*] indicates that the flux of energy is for the

*p*vegetation type. All terms in the balance equation are nonlinear functions of canopy temperature

*T*, which is calculated using the Newton–Raphson method to solve Equation (1).

_{c}*R*into the

_{nc}*p*vegetation type is calculated as the sum of the absorbed fraction of incoming shortwave radiation (W m

^{−2}) [fraction of incident radiation that is not reflected or transmitted through the canopy; first term in Equation (2)], absorbed incoming longwave radiation (W m

^{−2}) [second term in Equation (2)], and the longwave radiation emitted by the canopy [third term in Equation (2)],

*α*is albedo of the

*p*vegetation type (no unit),

*k*is an exponential attenuation coefficient (as per Beer's law), LAI is leaf area index of the

*p*vegetation type,

*ɛ*is the emissivity and absorptivity of the

_{c}*p*vegetation type (no unit), σ is the Stefan–Boltzmann constant (W m

^{−2}K

^{−4}), and

*T*is the canopy temperature of the

_{c}*p*vegetation type (K).

*p*and the atmosphere due to evaporation of intercepted water is calculated as

*ρ*is the density of air (kg m

_{a}^{−3}),

*c*is the specific heat capacity of air (J m

_{a}^{−1}K

^{−1}),

*γ*is the psychrometric function (Pa K

^{−1}) (appendix A),

*r*

_{a}_{υ}is the aerodynamic resistance between the surface of the leaves from the

*p*vegetation cover and the atmosphere (s

^{−1}m) (appendix B),

*e*is the vapor pressure in the air at reference elevation

_{a}*z*(appendix A),

_{a}_{Cs}is the relative humidity in the canopy; RH

_{Cs}is considered a function of canopy storage,

*z*and

_{a}*C*

_{s}_{max}and

*C*are maximum canopy water storage and canopy water storage (see section 4.2).

_{s}*r*is the canopy resistance of vegetation

_{c}*p*to latent heat flux that depends on the soil moisture content, atmospheric conditions, and vegetation characteristics [see Equation (43) in section 5].

*p*canopy type and the atmosphere is calculated as

*T*is air temperature.

_{a}### 3.2. Surface energy balance

*P*times. The solution of the energy balance allocates the available energy into energy used to evaporate water, reduce the cold content of the snowpack, heat the air, and heat the ground. The total energy balance for the pixel is calculated by taking the sum of the fluxes for each of the vegetation types weighted by the proportion of the pixel they occupy

*f*,

_{p}*R*is net radiation at the surface (W m

_{n}^{−2}),

*ρ*is water density (kg m

_{w}^{−3}),

*λ*

_{υ}is latent heat of vaporization water (J kg

^{−1}),

*E*is flux of water vapor due to soil evaporation (m s

^{−1}),

*ρ*(W m

_{w}λ_{υ}E^{−2}) is latent heat flux into the atmosphere due to soil evaporation,

*H*is sensible heat flux into the atmosphere (W m

^{−2}),

*G*is ground heat flux (W m

^{−2}),

*S*is heat flux into the snowpack (W m

^{−2}), LM is latent heat of snowmelt (W m

^{−2}), and

*R*is sensible heat advected by rainfall/throughfall (W m

^{−2}). The subscript [

*p*] indicates that the flux of energy is for the

*p*soil cover type. All terms in the balance equation are nonlinear functions of surface skin temperature

*T*, which is calculated using the Newton–Raphson method to solve Equation (7).

_{s}The snowpack is assumed to be a dimensionless energy sink with lumped properties. When snow is present, soil skin and snow temperatures are assumed to be the same, energy exchanges with the ground are assumed to be negligible (*G* is zero), and *T _{s}* represents the temperature of the snow–soil interface.

*R*

_{s}_{↓}(1 −

*α*) (

_{s}*e*

^{−kLAI}) (W m

^{−2}), where

*α*is the albedo of the surface under cover type

_{s}*p*(no unit). Longwave radiation emitted by canopy layer

*p*that contributes to heating the soil is

*ɛ*

_{s}ɛ_{c}σT_{c}^{4}(W m

^{−2}), where

*ɛ*is the emissivity of the canopy and

_{c}*ɛ*is the absorptivity of the surface. The atmospheric longwave radiation not intercepted by the canopy that contributes to heating the soil is the fraction absorbed by the surface

_{s}*ɛ*(1 −

_{s}*ɛc*)

*R*

_{l}_{↓}(W m

^{−2}). The radiation output is the longwave radiation emitted by the surface

*ɛ*(W m

_{s}σT_{s}^{−2}), where

*ɛ*is the emissivity of the surface (no unit), σ is the Stefan–Boltzmann constant (W m

_{s}^{−2}K

^{−4}), and

*T*is the surface temperature (K). The subscript

_{s}*p*indicates that the vegetation properties inside the brackets are evaluated for the

*p*vegetation type. These terms are set to zero during the solution of the (bare soil) land-cover type (i.e., when

*f*=

_{p}*P*),

*ρ*is the density of air (kg m

_{a}^{−3}),

*c*is the specific heat capacity of air (J m

_{a}^{−1}K

^{−1}),

*γ*is the psychrometric relationship (Pa K

^{−1}),

*r*is soil resistance to evaporation (s

_{s}^{−1}m),

*r*is the combined (surface and canopy) aerodynamic resistance of the surface (s

_{as}^{−1}m) (appendix B),

*T*under vegetation type

_{s}*p*, and

*e*is the vapor pressure in the air. Vapor pressure in soil is adjusted by a function RH

_{a}_{θ}that approximates relative humidity in the soil pores (Lee and Pielke 1992)

*β*is a function of soil moisture (Kondo et al. 1990; Lee and Pielke 1992),

*θ*

_{10}and

*θ*

_{fc}represent the average volumetric soil moisture of the top 10 cm of soil calculated assuming a hydrostatic soil moisture profile (appendix C) and soil moisture at field capacity, respectively. Equation (10) assumes that vapor pressure in the soil pores reaches saturation when soil moisture is at field capacity or above.

*T*and

_{s}*T*(K) are soil and air temperature, respectively.

_{a}_{g[p]}is the heat flux at depth

*d*,

_{g}*d*is the depth of the top thermal layer, and

_{g}*c*(

_{s}*θ*) (J m

^{−3}K

^{−1}) is soil volumetric heat capacity [Equation (17)]. Both

*d*and

_{g}*c*are considered constant during the time step. The flux at depth

_{s}*d*is approximated by assuming that the heat wave is dampened with depth according to the analytical solution of the heat diffusion equation using a sinusoidal forcing at the soil surface. The dampening depends on the thermal properties of the soil and the period

_{g}*P*of the forcing, which we assume daily if the time step is less than 1 day or yearly if the simulation time step is longer. The heat flux at the top thermal layers is approximated as (Arya 2001; Liebethal and Foken 2007)

_{e}*K*(

_{T}*θ*) (W m

^{−1}K

^{−1}) is the soil thermal conductivity [function of soil moisture: Equation (18)],

*T*is the temperature of the surface of the top thermal layer, and

_{s}*T*is the average temperature of the bottom thermal layer. The depth of the top thermal layer depends on the thermal conductivity of the soil and is defined to be half the depth at which the thermal wave has been dampened by 37% (Arya 2001, p. 53),

_{d}*T*is updated every time step,

_{d}^{+}*d*is the depth to the bottom of the lower thermal layer, chosen deep enough so heat fluxes across this boundary can be considered to be zero.

*η*is soil porosity;

*ρ*,

_{p}*ρ*, and

_{w}*ρ*are the density of soil solid particles, water, and air, respectively;

_{a}*c*,

_{p}*c*, and

_{w}*c*(J kg

_{a}^{−1}K

^{−1}) are the heat capacities of the soil solid particles, water, and air; and

*K*,

_{p}*K*, and

_{w}*K*(W m

_{a}^{−1}K

^{−1}) are the thermal conductivities of the soil particles, water, and air, respectively.

*T*and heat exchanges with the ground are assumed to be zero. Fluxes of energy into the snowpack under vegetation type

_{s}*p*,

*S*

_{[p]}, can increase or decrease the snowpack cold content, changing its average temperature. In the case of continuous positive energy inputs, the temperature of the snowpack increases until it reaches the melting temperature of ice,

*c*is the specific heat capacity of frozen water (J kg

_{i}^{−1}K

^{−1}),

*h*is the snow water equivalent of the snowpack (m),

_{i}*λ*is the latent heat of fusion (J kg

_{f}^{−1}), and

*T*is the temperature of the melting point (K). At the melting temperature (

_{m}*T*), any extra energy input generates snowmelt,

_{s}= T_{m}*μ*is an empirical melt coefficient (m K

_{M}^{−1}). The min function ensures that no more latent heat of fusion is extracted than the total existing amount in the snow of each cell. In Equation (20),

*ρ*/Δ

_{w}λ_{f}h_{i}*t*is the total amount of latent heat needed to melt the current snowpack with a water equivalent

*h*.

_{i}*R*(W m

^{−2}). The model assumes that the temperature of the raindrops equals air temperature (Dingman 2002),

## 4. Water balance

### 4.1. Precipitation input

*P*(m s

_{t}^{−1}) during the time step is prorated into snowfall

*P*(m s

_{s}^{−1}) and rainfall

*P*(m s

_{r}^{−1}) by the fraction of the temperature range in the time step that falls below the rain–snow transition temperature

*T*currently set at 1°C,

_{rs}### 4.2. Canopy water balance

*P*− 1 vegetation types,

*C*

_{stor}is the current canopy water storage (m) and

*C*is the canopy drainage (dripping from the canopy) (m s

_{t}^{−1}).

*C*

_{stor max},

*p*is a function of the current leaf area index,

*X*

_{stor max}is a species-dependent maximum canopy storage parameter (m) that reflects the depth of water that the species can hold per unit leaf area index.

*C*is the amount of canopy drainage occurring as snow and

_{s}*C*is the amount of canopy drainage occurring as rain.

_{r}### 4.3. Surface water balance and fluxes

Precipitation on bare soil and canopy drainage from trees reach the surface and increase the snowpack storage or the ponding storage depending on weather they reach the ground as snow or as rain. From the point of view of the hydrologic component, the snowpack is a dimensionless storage of water on top of any liquid water storage on the soil surface: both snowpack and ponded water on the surface can coexist in the cell and routing of precipitation or canopy drainage through the snow happens instantaneously.

*h*is the snow water equivalent of the snowpack in the cell (m), the first

_{i}*P*− 1 terms on the right-hand side are the snow canopy drainage from the

*P*− 1 vegetation types in the cell, the

*P*th term is the amount of snowfall on the bare ground fraction of the cell, and the last

*P*terms are the amount of snowmelt

*M*(m s

_{i}^{−1}) from the snowpack under each of the

*P*land-cover types.

*h*is the depth of surface water in the cell (m), the first

_{w}*P*− 1 terms on the right-hand side are the canopy drainage as rain from the

*P*− 1 vegetation types in the cell, the

*P*th term is the amount of rainfall onto the bare ground fraction of the cell, the following

*P*terms are the amount of snowmelt water

*M*(m s

_{i}^{−1}) contributed from the snowpack under each of the

*P*land covers,

*q*

_{rtn}is return flow rate from the subsurface (m s

^{−1}) (section 4.4),

*q*

_{up}(m s

^{−1}) is overland run-on from the upstream cell, and the last term

*I*is the infiltration rate into the soil (m s

_{f}^{−1}). The fraction of

*h*that does not infiltrate by the end of the time step becomes runoff. Runoff in one cell becomes run-on for the downstream cell, where it may reinfiltrate. The calculation is performed in a cascading form following the local drain direction determined by the steepest descent D8 algorithm performed over a raster DEM until the basin outlet or a cell with a channel is reached. Once overland flow reaches a channel, no further losses by reinfiltration are allowed. In the current version, overland flow is assumed to be able to run the entire drainage network each time step (i.e., overland flow exits the basin in one time step). Overland flow at each channel cell is the sum of inflows from upstream cells (channel and nonchannel cells) plus inflows from the subsurface system

_{w}*q*

_{chan}, as explained in section 4.4.

*K*is saturated hydraulic conductivity in the vertical direction (m s

_{s}^{−1}),

*ψ*

_{ae}is the soil air entry pressure (m),

*η*is effective porosity,

*θ*is the average volumetric soil water content for the soil layer, and

*S*is effective saturation [i.e., S

_{θ}_{θ}= (

*θ*−

*θ*)/(

_{r}*η*−

*θ*), where

_{r}*θ*is residual soil water content]. The depth of water that infiltrates and the associated increase in soil moisture depends on the antecedent moisture conditions and the available water for infiltration

_{r}*h*as follows: potential infiltration depth

_{w}*F*(m) is the lesser between the available water for infiltration on the surface (ponding depth

_{p}*h*) and the potential infiltration rate integrated over the time before ponding occurs

_{w}*t*≤ Δ

_{p}*t*,

*F*(m) increases the average soil moisture of the cell over the hydrologically active soil depth

*d*(Δ

_{s}*F*= Δ

*θd*),

_{s}*t*is the time at which ponding occurs. Note that

_{p}*d*represents the depth of the subsurface hydrologic layer, which may be deeper than the actual soil depth if the soil lays on weathered bedrock that can store and transmit water. Equation (32) is solved iteratively for Δ

_{s}*θ*using the Newton–Raphson scheme.

### 4.4. Subsurface water balance and fluxes

*h*in the soil in excess of field capacity will move downslope under the force of gravity,

_{g}*Q*(m

_{g}^{2}s

^{−1}) is assumed to be proportional to the slope of the bedrock and to some effective hydraulic conductivity value,

*K*

_{eff}and

*S*are locally constant (locally independent of

_{x}*x*) and noting that

*h*is the depth of gravitational flux, yields the kinematic wave approximation, which is linear in

_{g}*h*and does not contain diffusive terms (Singh 1997, p. 191),

_{g}*h*is the water depth in the soil free to move downslope (m),

_{g}*t*is time (s),

*x*is distance (m),

*K*

_{eff}is some effective conductivity of the soil (m s

^{−1}),

*S*is the slope of the bedrock in the downslope direction,

_{x}*q*

_{rch}(m s

^{−1}) is the amount of recharge to the saturated layer per unit area,

*q*

_{rtn}(m s

^{−1}) is the return flow rate to the surface system when subsurface water depth exceeds the soil storage capacity,

*q*

_{cap}(m s

^{−1}) is the rate of water transfer from the free gravitational pool of water to the capillary water pool to satisfy the soil water deficit if average soil moisture is lower than field capacity, and

*q*

_{chan}(m s

^{−1}) is the rate of water transfer from the subsurface system to channel cell per unit area. Equation (35) is solved using a space and time backward finite-differences scheme.

*q*

_{cap}).

*j*and subscript

*i*indicate temporal and spatial positions of the associated flux in the finite-difference solution grid, respectively. The transfer of water from the subsurface to the channel is calculated using an exponential decay function controlled by a parameter,

*b*(m

^{−1}), that represents the resistance to flow of the channel–subsurface system interface,

## 5. Ecological processes

### Forest growth

*p*[gross primary productivity (GPP); kg m

^{−2}] to the amount of photosynthetically active energy during the time step (

*R*

_{par}; J m

^{−2}) and to the amount of transpired water (Tp

_{c}; m) occurring over the time step. This is a modification with respect to Landsberg and Waring (Landsberg and Waring 1997) that permits a tighter coupling of the forest growth module to the energy and water components by explicitly introducing transpiration into the equation

*ξ*is the quantum efficiency of vegetation type

_{c}*p*(kg J

^{−1}), which prescribes how much mass of carbon is assimilated per unit of energy absorbed;

*R*

_{par}is assumed to be 47% of

*R*

_{s}_{↓}; and

*ξ*is the water-use efficiency of vegetation type

_{w}*p*(kg m

^{−1}), which indicates how much mass of carbon is assimilated per unit depth of water transpired. The effect of vegetation age and the phenological cycle of vegetation are controlled by the last two dimensionless efficiency factors (0–1),

*f*

_{GPP}(age) and

*f*

_{GPP}(

*T*), respectively. Note that the effect of LAI and other environmental condition on GPP are accounted for in Equation (40) through the calculation of transpiration.

_{a}*p*(years) and age

_{max}(years) is the maximum age a tree of its type can achieve.

*T*

_{opt}and will stop when temperatures drop below or exceed certain temperature thresholds,

*T*

_{min}and

*T*

_{max}, respectively (Landsberg and Waring 1997),

*r*is the inverse of canopy conductance,

_{c}*ζ*is a shelter factor (0–1) that accounts for the shade that leaves project on each other (Dingman 2002, p. 298) and

*f*(

_{gc}*R*

_{s}_{↓}),

*f*(

_{gc}*T*),

_{a}*f*(

_{gc}*e*), and

_{a}*f*(

_{gc}*θ*) are canopy conductance efficiency factors related to solar radiation, air temperature, vapor pressure, and soil moisture, respectively. These factors are calculated as follows (Cox et al. 1998; Landsberg and Waring 1997; Stewart and Verma 1992):

*φ*

_{s}_{↓},

*φ*, and

_{ea}*φ*are empirical coefficients and

_{θ}*θ*

_{wp}and

*θ*

_{fc}are the volumetric soil moisture content at wilting point and at field capacity, respectively.

^{−2}) is determined by a constant conversion factor of GPP,

*C*

_{NPP}is the proportionality constant found to be 0.47 ± 0.04 for a wide range of forests (Landsberg and Waring 1997).

*M*

_{root}, Δ

*M*

_{stem}, and Δ

*M*

_{leaf}(kg m

^{−2}) are increments of the root, stem, and foliage mass over the time step, respectively, and

*η*,

_{r}*η*, and

_{s}*η*(

_{f}*η*+

_{r}*η*+

_{s}*η*= 1) are the partition factors to allocate NPP to roots, stem, and leaves, respectively. These factors are functions of the effective age of the stand of vegetation type

_{f}*p*, air temperature, and soil moisture,

*p*is a partition function dependent on species-specific parameters,

_{fs}*F*

_{prn},

*F*

_{pra},

*S*

_{prn}, and

*S*

_{pra}are vegetation-dependent empirical parameters; and DBH is the total diameter at breast height of the sum of the individual trees of species [

*p*] in the pixel (m).

_{LAI}is the specific leaf area index (m

^{2}g

^{−1}) of vegetation type

*p*, δ

_{f}is a constant base leaf turnover rate for vegetation type

*p*(s

^{−1}),

*δ*and

_{fw}*δ*are foliage loss coefficients due to hydrologic and temperature stresses, and Δ

_{fT}*t*is the time step size (s).

_{fw[p]max}and δ

_{fT[p]max}are maximum leaf decay rates (s

^{−1}) due to hydrologic and temperature factors, respectively, and

*γ*and

_{δw}*γ*are dimensionless empirical shape parameters. Soil moisture stress

_{δT}*β*is defined as

_{δw}*β*= max{0, min[1, (

_{δw}*θ*−

*θ*

_{fc})/(

*θ*

_{wp}−

*θ*

_{fc})]} and temperature stress is

*β*defined as

_{δw}*β*= max(0, min{1, [

_{δw}*T*− (

_{a}*T*

_{cold}− 5)]/5}). In this last function,

*T*

_{cold}is a species-dependent temperature threshold that accelerates foliage loss. The increment in root mass is similarly calculated by

^{−2}) and δ

_{r}is the base root turnover rate (s

^{−1}).

*p*] with units of mass per tree (kg tree

^{−1}), which is calculated by dividing total stem mass (kg m

^{−2}) by the stem density {number of trees per area of the patch (tree m

^{−2}) in patch [

*p*]}. The term

*ρ*

_{wood}is the density of wood (kg m

^{−3}); π is the constant (3.141 59…);

*H*is the average tree height (m) in the patch; and

_{t}*F*

_{hd}is a growth factor that depends on the height-to-diameter ratio of the tree and the conditions of the patch (Peng et al. 2002),

*F*

_{hdmin}and

*F*

_{hdmax}are the maximum and minimum growth factors allowed for a given species and Stc is a crowding factor that is depends on the number of trees in the patch and the crown coverage,

*ω*is the crown to stem diameter ratio and

*N*

_{trees}is the number of trees of vegetation type

*p*in the cell.

## 6. Case studies

We present two case studies that demonstrate the performance of the different components of the model at two different spatial and temporal scales. The first case study has a focus on the radiative components of the model. Soil temperature and the different components of the radiation balance were compared to observational data to test the model's energy balance scheme. In a second case study, we used data for the Goodyears Bar subbasin of the Yuba River watershed in Northern California. We examined simulated gross primary productivity, evapotranspiration, leaf area index, snow dynamics, and streamflow and compared the model results with remote sensing data and U.S. Geological Survey (USGS) stream discharge data.

### 6.1. Case study 1: Energy balance

In this study, we run the model for the Shidler Tallgrass Prairie Fluxnet station in north-central Oklahoma. This site was chosen to provide a controlled evaluation of the model in a simplified setting with a minimum number of free unknown model parameters. The plot is predominantly open grasslands and is located at an elevation of 355 m. The climate consists of cold dry winters and warm humid summers with the bulk of the precipitation falling in September. Soil characteristics are silty clay loam texture in the upper 0.6 m underlaid by clay. The study plot consists of a 10 m × 10 m gently sloping domain, which was resolved to 1 m for the simulation. Soil parameters were obtained from the literature (see Table 2). Some manual adjustment was done for the aerodynamic roughness parameter *z*_{0s} and the depth of the bottom soil thermal layer.

Relevant parameter values and sources used during case study 1.

The model was run using a half-hourly time step. Inputs to the model came directly from the Fluxnet site data acquisition. Atmospheric longwave radiation was estimated using the method described by Swinbank (Swinbank 1963). Climate data presented here span a period of 14 days from the end of September through the beginning of October 1997. This time period was chosen because it provides information over a variety of conditions.

Figure 4 shows the temperature, precipitation, radiative forcing, wind speed, and air relative humidity during the study period. The data show a mix of sunny, clear-sky days with large daily air temperature swings as well as overcast days with rain and smaller daily temperature swings (Figures 4a–c). Relative humidity was lower during the day when temperatures were higher and increased at night (Figure 4d). Overall relative humidity was at a maximum during the unstable weather of the first three days. Measured wind speed (Figure 4e) varied between 0.3 and 9.4 m s^{−1} with generally higher wind speeds during the day.

Figure 5a shows the simulated and observed soil temperature. Overall, the fit was satisfactory with an *R*^{2} of 0.61 and an RMSE of 2.45°C. In interpreting this graph it is worth noting that the simulated signal is the average temperature for the soil thermal layer while the measurements capture the temperature signal of a narrower soil volume. The simplification of the soil with two thermal layers of homogeneous properties may explain the observed low bias and earlier peak in the simulated daily soil temperature compared to the measurements. Still, a qualitative visual inspection of the graphs indicates that the simulated signal captured the main features of the observed signal, including a dampened diurnal cycle during the overcast period at the beginning of the study period.

The simulation of net radiation (Figure 5b) also showed satisfactory statistics with an *R*^{2} of 0.99 and an RMSE of 54.15 W m^{−2}. The daytime peaks were remarkably well simulated but the nighttime lows were consistently underestimated. This was likely due to enhanced heat transfers to the soil surface from the aerodynamic resistance formulations during the stable nighttime periods, where radiative outgoing fluxes should dominate the energy balance.

Ground heat (Figure 5c) estimates from the simulation further show the ability of the model to predict energy exchanges in the study plot (*R*^{2} = 0.48 and RMSE = 25.46 W m^{−2}). While the modeled values show more variability (hence the lower *R*^{2} value), the overall peaks and valleys are well captured in timing and magnitude. Other nonradiative exchanges that were captured include sensible heat and latent heat (Figures 5d,e). As expected, larger outgoing (negative) fluxes of sensible heat occurred during the day when the soil temperature reached maximum value. Small incoming fluxes of sensible heat occurred during nighttime hours. The simulation tends to overpredict outgoing fluxes during high wind events. Overall, the *R*^{2} is 0.91 and the RMSE is 52.77 W m^{−2} for the comparison between observed and simulated values. Similar to sensible heat, latent heat also peaked during the daytime, when evaporation was the highest, especially during the sunnier days. During the first few overcast and rainy days of the study period and during 8 October, latent heat is suppressed because of higher atmospheric relative humidity. Goodness-of-fit statistics for latent heat estimates include an *R*^{2} of 0.77 and an RMSE of 32.95 W m^{−2}.

### 6.2. Case study 2: Watershed-scale application of the model

In this case study, we run the model at the watershed scale. Goodyears Bar (GYB) is a 648 km^{2} gauged catchment in the North Yuba River basin in the Sierra Nevada range of Northern California (Figure 6) ranging from 850 to 2500 m and with a mean elevation of 1735 m. The basin has no dams or major water diversions and most of its land cover is composed of evergreen needleleaf forests. Most of the western and eastern sections along valley bottoms are dominated by ponderosa pine. Fir and spruces dominate the central region of the basin and at moderate and high elevation (Figure 7). The basin is densely forested, with more than 80% of the area covered by canopies in the low- and mid-elevation regions of the basin. Canopy cover decreases to 50% or below in high-elevation regions in the northern and northeastern sections of the basin (Figure 8) dominated by fir and lodgepole pine.

Climate conditions for the area include hot, dry summers and cool, wet winters. The simulation covers the 3-yr period from 1 September 2000 through 31 August 2003 using daily time steps. Climate forcing for the model were provided by the Weather Research and Forecasting (WRF) model at 4-km resolution. WRF was run using boundary conditions from the Global Forecasting System (GFS) reanalysis as described in Pan et al. (Pan et al. 2010). The simulated years include first a relatively dry, low-flow year followed by a higher flow year with a wetter winter and spring.

A 1000-m-resolution digital elevation model was used to determine GYB boundaries and geometry obtained by resampling the 1/3 arc-s elevation dataset available in the National Map Seamless Data Server (http://nationalmap.gov/viewer.html). We simulated two types of needleleaf evergreen trees. One parameterization is for pine and was applied to the ponderosa and lodgepole pine regions of the basin. Another parameterization simulates a combination of fir and spruce and was applied to the regions of the basin dominated by fir and spruce, including Douglas fir. The main vegetation and soil parameters and the sources are listed in Table 3. Canopy coverage and forest cover types (Figures 2 and 3) were obtained from the National Atlas Database (USDA 2012). The model was started with uniform initial conditions (uniform soil temperature, soil moisture, and leaf area index) and was spun up until the spatial distribution of soil moisture, leaf area index, and the base outflow reached equilibrium (typically 12–15 simulated years). Subsequent spinup runs use the state of the basin in a previous run to initialize the model. Discharge and remotely sensed information of snow cover area, leaf area index, evapotranspiration, and gross primary productivity were used to evaluate the model performance. Daily discharge at the outlet for the simulated period was obtained from the USGS National Water Information System (site 11411500). The 8-day, 500-m-resolution Moderate Resolution Imaging Spectroradiometer (MODIS) snow-covered area (SCA) MOD10A2 version 5 product (Hall et al. 2006) was used to evaluate the model's ability to describe the dynamics of SCA.

Relevant parameter values and sources used during case study 2. Note that adjusted values are values that have been manually adjusted to improve match with observations. Values with blank source are guessed values based on anecdotal data or expert knowledge.

The ability of the model to describe vegetation processes was evaluated using three other MODIS products. The 8-day, 1000-m resolution MODIS LAI (MOD15A2) version 5 product (Myneni et al. 2002) was used to evaluate the spatial distribution of time-averaged LAI over the basin and to evaluate the temporal dynamics of spatially integrated LAI. The ability of the model to reproduce evapotranspiration was evaluated by comparing the spatial distribution of time-averaged simulated evapotranspiration and the temporal dynamics of spatially averaged evapotranspiration with evapotranspiration obtained from the 8-day, 1000-m-resolution Numerical Terradynamic Simulation Group (NTSG) MODIS evapotranspiration (ET) (MOD16A2) product (Mu et al. 2007). GPP was evaluated by comparing the dynamics of the basin-averaged primary productivity with the 8-day, 1000-m-resolution NTSG MODIS GPP (MOD17A2) product (Zhao et al. 2005).

Figure 9 shows the simulated dynamics of the SCA and the MODIS estimate. The model simulates well both the onset of the snow season and the recession of the snow (coefficient of determination between the two estimates is *R*^{2} = 0.71). Much of the mismatch occurs during periods of high coverage. Our simulations tend to underestimate the high values of SCA, most clearly during the third year, compared to the MOD10 estimates. Despite this partial bias, the dynamics and recessions are reasonably well captured and the length of the simulated snow season is within the snow season dates bracketed by the satellite estimates. These results need to be interpreted bearing in mind that the model is run with atmospheric inputs at a 4-km resolution, whereas the MOD10 product has a 500-m resolution and can therefore observe the effect of topography at a finer scale. This is evident in the simulated spatial distribution of snow cover. Figure 10 shows the fraction of time that each computational element is covered with snow during the study period. The simulation of the spatial distribution of snow cover shows the effect of the WRF coarser grid while the finer grid of MOD10 permits a better capture of the effect of topography. Note the heterogeneity at a sub-4-km scale observed in the simulated spatial distribution of snow cover. This reflects the effect of vegetation and other processes that are resolved at the 1000-m model pixel scale on the spatial distribution of snow. Overall, when compared with MOD10, the spatial pattern of the relative duration of the snowpack is very similar. Lower fractions of time occupied by snow cover are simulated along the river network and longer snow seasons are simulated in the high-elevation areas in the northern and eastern sections of the basin.

Figure 11 shows the simulated and measured streamflow at the basin outlet. The first year represents a low-flow year while the second and third years were wetter with a much larger water yield. The onset of spring flow, base flow, and the recession of the hydrographs were well captured, but the magnitude of the flows was overestimated and the high-resolution details of the streamflow time series were less well represented. The relatively large simulated volume of subsurface input to the channel prevented the simulated flow from receding at the observed rates. Streamflow is an integrated expression of all the ecohydrologic processes occurring in the basin. Because of the complexity of interdisciplinary mechanistic models, troubleshooting the exact reasons for inaccurate simulation of high-frequency variations in the response hydrograph is very difficult. An inadequate parameterization of the soil hydraulic properties or even shortcomings in the kinematic representation of subsurface flows can contribute to problems in the representation of outflows. Also, WRF is known to overestimate precipitation over regions of complex terrain (Argüeso et al. 2011; Caldwell et al. 2009; Silverman et al. 2013), which could be a direct cause of the high simulated streamflow volumes. A closer look at the simulated state of the basin suggests that the high and sustained simulated flow inputs to the channel may be caused by a large pool of available subsurface water connected to the stream. This may explain why high flows were maintained during the high-flow season, where simulated flow spanned different observed runoff subevents, especially during the second year. Because the size and connection of the subsurface water pool are very sensitive to the distribution of the parameters that determine the total soil water storage (soil depth and porosity) and release (effective hydraulic conductivity and water retention parameters of the soil), a specific calibration of these parameters may likely further correct the response of the model regarding outflows.

The ecologic output of the model was evaluated against the remotely sensed estimation of LAI, GPP, and ET. Figure 12 shows the temporal dynamics of spatially integrated values for these variables. The temporal dynamics of spatially averaged productivity for the basin are well represented (Figure 12a) according to MOD17 (RMSE = 0.66 gC m^{−2} day^{−1}; *R*^{2} = 0.7) The productivity of the three years is very similar, peaking between 3 and 4 gC m^{−2} day^{−1}. The third year shows a slower (less steep) onset of the growing season, which is also well captured in the model. The sensitivity of the model to high-frequency atmospheric inputs causes a relatively high variation in the daily estimates of GPP, which is responsible for the spread observed in the scatterplot (Figure 12a, inset), although the estimates are almost unbiased (mean absolute bias = 0.05 gC m^{−2} day^{−1}).

The temporal dynamics of spatially averaged evapotranspiration is also well represented as per MOD16 (Figure 12b; RMSE of the estimation is 0.7 kg m^{−2} day^{−1}; *R*^{2} = 0.67). The model simulates higher evapotranspiration rates than MOD16 during the summer, inducing a high bias (mean absolute bias = 0.32 kg m^{−2} day^{−1}) with respect to the MOD16 estimates. How much of this bias is real is an open question since MOD16 is estimated to have a bias of about 0.3–0.4 kg m^{−2} day^{−1} with respect to tower measurements (Mu et al. 2011). While the temporal dynamics of spatially averaged metrics of GPP and ET may be considered satisfactory, we still need to assess the ability of the model to capture the associated spatial patterns. Figure 13 shows the time-averaged spatial distribution of evapotranspiration during the study period (since GPP and ET are related and show very similar spatial patterns we only present the spatial distribution of ET).

A visual comparison of this figure shows that the evapotranspiration range and main elements of the spatial patterns of evapotranspiration are consistent. Average annual evapotranspiration ranges from ~200 to over 1000 mm yr^{−1}, with high values of evapotranspiration following the stream network, where more water and vegetation is concentrated, and low values at high elevation, where less dense vegetation and a longer period of snow cover preclude evapotranspiration. It is important to note that, even though the atmospheric forcing to the model is provided at a coarser resolution, it is not reflected in the spatial pattern of evapotranspiration. This highlights the importance of the lateral redistribution of water and the effect of the heterogeneity of vegetation as a major driver for evapotranspiration.

Figure 12c shows the simulated temporal dynamics of the spatially averaged leaf area index and the MODIS (MOD15) estimates. The low leaf turnover rates quoted in the literature for needleleaf evergreen trees (White et al. 2000) produce very modest seasonal fluctuations of leaf area index. For some individually monitored pixels these fluctuations are of about one unit LAI between peak and low LAI, but these fluctuations are smoothed to about 0.2 units of LAI when spatially averaged (Figure 12c). The simulated seasonal variability of LAI is much smaller than the MODIS estimate, but the satellite estimate presents unrealistically low values of LAI, approaching zero during winter for a densely forested basin with perennial trees.

The larger-than-expected seasonal variation in the estimates of LAI given by MODIS for perennial needleleaf forests is known and attributed to seasonality in the background signal due to the dynamics of the understory and to changes in the optical properties of the leaves and the effect of snow (Tian et al. 2004; Yang et al. 2006) and not to an actual change in the quantity of leaves. Since the model does not simulate seasonal grass or understory vegetation and without a third source of information, no further parameter adjustment was attempted to recreate the MODIS LAI seasonality. We may speculate that the actual seasonality of LAI may be somewhere between the modeled estimates and those estimated by MODIS.

The spatial distribution of leaf area index (Figure 14) closely followed that of production and evapotranspiration. High LAI values (>4) are found in the western part of the basin, where the densest pine forests are found. The highest values are found following the valley bottoms where water converges and hydrologic stresses are minimal. This effect is more pronounced in the simulated distribution of LAI but clear lines of high LAI along valleys can be observed in the MODIS estimate as well. The regions where firs and spruces dominate show lower values of LAI. Fir and spruce occupy moderate- and high-elevation zones of the basin, with shallower soils and smaller contributing areas that cannot maintain high levels of soil moisture once the snowpack disappears. The density of the forest is also lower in these regions and the proportion of time that these regions are occupied by snow is relatively larger. A comparison of the figures shows that the central northern and southeastern parts of the basin have the lowest value of LAI (~1 and below).

We note that much of the observed variability in Figure 14a is produced by the hydrologic connectivity of the basin and the distribution of atmospheric inputs since the models were spun up from spatially homogeneous leaf area index values. Since precipitation inputs increase with elevation, the enhanced productivity observed in the valley bottoms rely on lateral contributions of water from upslope in order to maintain high transpiration rates. This redistribution of water is determined by the hydrologic network, which in turn determines to a large extent the distribution of biomass (e.g., Caylor et al. 2005; Rodriguez-Iturbe et al. 2009).

## 7. Summary and conclusions

Vegetation is increasingly recognized as a fundamental dynamic component of the hydrologic cycle that adapts to changing hydrologic conditions and in turn affects its hydrologic environment. Vegetation is a major water and energy user and can significantly alter the energy and water balance. It shades the ground, dissipates energy as latent heat during transpiration, intercepts water, and removes water from the soil storage at rates that are dependent on the availability of water and energy. On the other hand, changes in the hydrologic and energy cycle affect the amount of vegetation that the physical system can support. This synergistic relationship between vegetation and the environment induces a still poorly understood nonlinearity in the climate–surface hydrology relationship that may dampen or exacerbate the effects of climate change or other environmental impacts on the available water resources.

This paper describes a model that captures the biophysical dynamics of vegetation and the hydrologic cycle at the watershed scale. The model is designed to balance the complexity of introducing a strong physical and physiological description of the different elements and the need for simplicity to produce an agile model that is parsimonious and can run on long time steps for extended runs. A number of independently developed and well-tested models are at the foundation of the forest dynamics component implemented in the presented model. The soil–vegetation–atmosphere energy exchange component is based on a solution of the nonlinear energy balance equation; the hydrologic component uses the Green and Ampt equation to calculate infiltration and a kinematic wave model to route subsurface water through the drainage network. The model is demonstrated at two different spatial and temporal scales in two case studies.

The object-oriented design of the code makes it easy to modify the model to include alternative descriptions of different processes or expand the model to include new components. Current work is being done to include two hydrologic soil layers to separate root zone processes from deep subsurface processes. Planned future work includes the inclusion of grass growth, seed dispersal and vegetation encroachment, stomatal dependency on carbon dioxide, and a simplified description of the nitrogen cycle to accommodate cases where nutrients are a limiting factor.

## Acknowledgments

This work was supported by grants from the Montana Water Resources Association and the Montana Space Grant Consortium as well as by a startup grant by the University of Montana and the National Science Foundation EPSCoR Cooperative Agreement EPS-1101342.

## Appendix A

### Calculation of Atmospheric Properties

*c*or

*s*) are calculated from their respective temperatures using Swinbank's (Swinbank 1963) empirical relationship (temperature in degrees Celsius),

*T*is given in degrees Celsius and saturation vapor pressure is calculated in pascals.

## Appendix B

### Aerodynamic, Canopy, and Soil Resistances

Aerodynamic resistance is calculated assuming a logarithmic wind profile over the canopies and over bare soil and an exponential wind profile below and within plant canopies (Figure B1) (Arya 2001; Bonan 2008). The equations are local first-order closure approximation of the governing equations for momentum, vapor, and energy in the surface boundary layer. Neutral conditions and identical resistance for the vertical transfer of vapor and energy are assumed.

*r*

_{a}_{υ}and over surfaces with no trees

*r*assume logarithmic wind speed profiles that arise from integrating the shear stress equations. For local first-order closure using the K approach and assuming identical diffusion coefficients for momentum, mass, and energy (Arya 2001; Foken 2008), aerodynamic resistance is as commonly used in the Penman–Monteith equation (Allen et al. 1998),

_{as}*υ*is wind speed (m s

_{a}^{−1});

*z*is the elevation at which wind speed has been measured (m);

_{a}*z*,

_{do}_{u}is a reference elevation (zero-plane displacement) for the overstory (subscript

*o*) or the understory (subscript

*u*) (m); and

*z*

_{0o},

_{u}is the roughness height of the overstory or understory (m), which is a measure of the unevenness of the surface. Parameters

*z*,

_{do}_{u}and

*z*

_{0o},

_{u}are calculated for the canopy and for the surface as per Equations (B4)–(B6).

*υ*→ 0, and therefore the equation shuts down latent and sensible heat transfers under low wind speed conditions. Because of this, in addition to Equation (B1), a choice of an alternative formulation proposed by Thom and Oliver (Jackson et al. 1988; Thom and Oliver 1977) is offered for situations of atmospheric instability and low wind. This formulation uses a modification of the logarithmic wind profile equation that puts a finite limit to aerodynamic resistance as

_{a}*υ*→ 0. This limit presents a simplification of the effect of buoyancy when free convection replaces turbulent diffusion as the main heat transfer mechanism under windless conditions,

_{a}*z*is the height over the canopies where wind speed is being measured,

_{a}*z*is the zero-plane displacement the canopy layer,

_{do}*z*

_{0o}is the roughness height of the canopy layer,

*z*is the apparent sink of momentum/heat/vapor (

_{t}*z*=

_{t}*z*+

_{du}_{z0o}), and

*H*is the effective height of trees. The factor

_{t}*n*is a decay coefficient that depends on the LAI of the canopy and the height of the tree (Campbell and Norman 1998; Foken 2008),

_{c}*lm*is a coefficient that Campbell and Norman (Campbell and Norman 1998) equate to the average separation of leaves; in this case, we have constrained

*lm*so

*n*is bounded between 1 and 4 to ensure that Equation (B2) yields feasible values. Equation (B1) is not bound to a finite value as

_{c}*υ*→ 0.

_{a}Aerodynamic resistance for the canopy layer *r _{a}*

_{υ}is calculated as

*r*

_{a}_{υ}=

*r*using the appropriate roughness parameters for the overstory [subscript

_{a}*o*in Equations (B5) and (B6)].

*p*<

*P*) is the sum of the resistance of the exponential and logarithmic wind speed regions. For bare soil areas, aerodynamic resistance equals

*r*using the appropriate roughness parameters for bare soils [Equation (B7)],

_{a}*z*,

_{o}*z*,

_{d}*r*(m s

_{s}^{−1}), is added in the soil evaporation formulation [Equation (9)]. We use an expression by Sellers et al. (Sellers et al. 1996) as used in Ivanov et al. (Ivanov et al. 2008),

*θ*

_{10}is the average volumetric moisture content of the top 10 cm of soil (m

^{3}m

^{−3}) (see appendix C),

*θ*is the residual volumetric soil water content (m

_{r}^{3}m

^{−3}), and

*θ*

_{fc}is soil moisture at soil field capacity (m

^{3}m

^{−3}).

## Appendix C

### Soil Hydraulic Functions

*H*is the depth to the local subsurface saturated layer and

_{u}*d*equals soil depth

_{u}*d*if (

*H*−

_{u}*d*) >

*ψ*or otherwise

_{ae}*d*= (

_{u}*H*−

_{u}*ψ*) (i.e., integrate over soil depth if the depth to

_{ae}*ψ*is larger than soil depth; otherwise, integrate to depth of

_{ae}*ψ*). For the running average soil moisture content in the soil

_{ae}*θ*, Equation (C1) is solved for

*H*to obtain the corresponding hydrostatic equilibrium profile. This soil moisture profile is used to calculate the average soil moisture of the top 10 soil centimeters,

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