In this study, we used the integrated hydrologic model, ParFlow, to study the MPB-induced perturbations in plant processes on the complete, coupled, terrestrial water and energy balances in a forested Rocky Mountain watershed. In the configuration used here, ParFlow simulates three-dimensional, variably saturated groundwater flow, and fully integrated overland flow; subsurface and overland flow equations are solved simultaneously, allowing non-linear feedbacks between the surface and subsurface flows (Kollet and Maxwell, 2006; Sulis et al., 2010). ParFlow was coupled to the Common Land Model (CLM) (Dai et al., 2003; Maxwell and Miller, 2005), which calculates the water and energy fluxes at the land surface including evaporation from the canopy and ground surface, transpiration from vegetation, ground heat flux, and snow water equivalent (SWE). CLM is forced with atmospheric data such as precipitation, solar radiation, wind, temperature, humidity and pressure. Complete details on the equations coupled in CLM and ParFlow can be found in the literature (Maxwell and Miller, 2005; Maxwell and Kollet, 2008; Kollet et al., 2009), and a summary of the relevant equations can be found in the section on Coupled Numerical Model: Summary of Equations.
Coupled numerical model: summary of equations
Although complete details of the solution approach that ParFlow uses to solve for coupled surface–subsurface flow are given in (Jones and Woodward, 2001; Kollet and Maxwell, 2006), a brief summary of the equations is presented here. Fundamentally, ParFlow solves the Richards equation for variably saturated flow in three spatial dimensions given as
In these expressions, h is the pressure head [unit is defined as length (L)], z is the vertical coordinate (L), Ks(x) is the saturated hydraulic conductivity tensor (length per unit time), k is the relative permeability (−), Ss is the specific storage coefficient (L−1), ϕ is the porosity (−), Sw is the relative saturation (−), and qr is a general source–sink term that represents transpiration, wells, and other fluxes (length per unit time). The specific volumetric (Darcy) flux is denoted by q (length per unit time).
Overland flow is represented in ParFlow by the two-dimensional kinematic wave equation included as the overland flow boundary condition resulting from application of continuity conditions for pressure and flux (Kollet and Maxwell, 2006):
where νsw is the two-dimensional, depth-averaged surface water velocity (length per unit time); h is the surface ponding depth (L), if h > 0; qr(x) is a general source–sink (e.g. rainfall, ET) rate (length per unit time); and k is the unit vector in the vertical. Note that ‖h, 0‖ indicates the greater value of the two quantities, that the lhs of Equation (3) represents vertical fluxes (e.g. in–exfiltration) across the land surface boundary, and that the overland flow condition assumes that pressure h represents both surface pressure and the ponding depth at the ground surface under saturated conditions (Kollet and Maxwell, 2006). Equation (3) represents the connection between surface and subsurface flow processes.
The primary equations used to represent evapotranspiration and interception in CLM are summarised succeedingly. A more comprehensive description of CLM and the equations used can be found in Dai et al., 2003. Total ET is taken as the sum of evaporation from bare ground Eg, evaporation from vegetation Ew (i.e. direct evaporation from wetted foliage), and plant transpiration Etr.
The maximum transpiration, Etrmax is given by
where froot,j, the root fraction within soil layer j is
and wLT is a factor that varies between 0 at the permanent wilting point to 1 at saturation.
σf is the fraction of vegetation excluding the part buried by snow, LAI is the leaf area index, and wLT is a function of φmax,sat,j the maximum, saturated and soil matrix potential at layer j.
When transpiration is not at a maximum, Etr is defined by
ET is now also a function of LSAI (the stem plus leaf area index), δ(Efpot) which is a step function and is equal to one for a positive Efpot (the potential ET) where
and zero when Efpot is zero or negative. ρa is the density of air, qfsat is the saturated specific humidity and qaf is the air specific humidity within the canopy space. Ld is the dry fraction of the foliage surface where
rb and rs the leaf boundary and stomatal resistances where rb is defined by
where Cf if the coefficient of transfer between the canopy air and underlying ground (0.01 m/s1/2), Uaf (the magnitude of the wind velocity incident on the leaves) is
and Df is the characteristic dimension of leaves in the wind direction. Va is the wind at reference height, Cd is the coefficient of drag and ram is the aerodynamic resistance for momentum.
ET is limited by the stomatal resistance rs, which is inversely related to leaf photosynthesis and is defined by
where m is an empirical parameter, A is leaf photosynthesis, cs is the CO2 concentration at the leaf surface, es is the vapour pressure at the leaf surface, ei is the saturation vapour pressure inside the leaf at the vegetation temperature, ps is the atmospheric pressure and b is the minimum stomatal conductance (2000 µmol m−2 s−1).
Evaporation from bare ground Eg and vegetation Ew are calculated by Equations (14) and (15), respectively:
where qg is the air specific humidity at the ground surface [kg/kg]; qa is the specific humidity at reference height zq, obtained from the prescribed atmospheric forcing [kg/kg]; and rd is the aerodynamic resistance of evaporation between the ground surface and canopy air, computed based on Monin–Obukhov similarity theory; is the wetted fraction of the canopy [−].
Precipitation arriving at the top of the canopy is either intercepted by foliage, or directly falls through the gaps of leaves to the ground. In CLM, the rate of direct through-fall is proportional to P, the rate of precipitation (mm/s) and is given by
and the maximum water capacity of the canopy is given by
where the maximum storage of solid water is assumed to be the same as that of liquid water.
The land energy budget includes conduction of heat through both soil and snow layers. The snow-pack in CLM is modelled with up to five layers depending upon total snow depth. Three mechanisms are used for changing snow characteristics: destructive, overburden, and melt, and snow albedo decays over time owing to accumulation of dirt and growth of snow grain size. Previous simulations show the snow model compares well with observations of SWE and the land-energy model with ground temperature (Maxwell and Miller, 2005).
Problem domain and setup
Figure 1 shows the physical processes in our simulated hillslope. In our simulations, the water table begins 3 m below the ground surface on the left side of the domain and meets the ground surface on the right side of the domain. Bedrock is assumed to be 12.5 m below the ground surface and is a no flow boundary. Once water reaches the confines of the domain as either subsurface lateral flow or overland flow, it crosses the boundary and is no longer considered to be part of the domain, leading to subsurface storage losses or gains depending on the scenario.
Figure 1. Displays the governing processes in the three simulated watersheds. Arrow lengths indicate flux magnitudes. P is precipitation, ET is evapotranspiration, O is overland flow, and I is infiltration.
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This hillslope-scale study was simulated with a hypothetical domain, 500 m (x-direction) by 1000 m (y-direction) by 12.5 m (z-direction). The domain was discretised using Δx = 100 m, Δy = 200 m and Δz = 0.5 m. Three different simulations were run with topographic slopes of 0.01, 0.08 and 0.15 m/m (Figure 1) that were selected to represent the topography found both in high-elevation, mountainous, MPB-infested watersheds in the Rocky Mountain West, along with the flatter MPB-infested watersheds found in southern Wyoming. The saturated hydraulic conductivity was set to 0.1 m/h. Porosity and vanGenuchten parameters were assigned for the watershed. Porosity was held constant throughout at 0.390 (−) and the van Genuchten parameters were set as follows: α = 3.5 (1/m), n = 2 and Sres = 0.01 to represent an idealised, relatively fast draining, sandy clay loam soil. Soils in mountain hillslopes are of course very heterogeneous with great uncertainty about both point values and spatial distribution. The assumption of homogeneity invoked here is used to isolate the impacts of land-cover changes on the hydrology of the system, whereas minimising other confounding signals. Approaches that directly include heterogeneity at the hillslope scale (Rihani et al., 2010; Atchley and Maxwell, 2011) are beyond the scope of this current study and are excellent topics for future work.
Hourly meteorological forcings were taken from the North American Land Data Assimilation System (NLDAS), forcing dataset (Cosgrove et al., 2003) for the 2008 water year (1 September 2007 to 31 August 2008) at Pennsylvania Gulch, Blue River, Colorado. The climate during 2008 was typical of an average year for this region by comparing precipitation with seasonal averages, and therefore a good representation of what a climatological weather pattern will be in the Rocky Mountains, yet still including high-frequency (hourly) variability. The model was run for each phase for 3 years, re-running the 2008 meteorological data for each year, to minimise the influence of initial conditions (but not running the model to equilibrium) on simulated results with results focusing on the third year.
In the model simulations, we defined the process of mortality in an affected tree to have four distinct phases: (1) green phase: the tree is alive and transpiring; (2) red phase: the tree has been attacked and has ceased transpiring and interception has slightly decreased; (3) grey phase: the tree is dead, has no remaining needles, transpiration has ceased, and interception is significantly decreased; and (4) dieback phase: the tree has fallen to the ground and begun decomposing as new vegetation begins to take its place. During an actual MPB infestation, the vegetation distribution throughout the four phases is likely to be heterogeneous; however, for the sake of simplicity and to understand the magnitudes of difference in the hydrologic and energy regimes between each phase, we are assuming a homogeneous distribution of vegetation during each phase.
The hydrologic and land-energy impacts of each of the four phases of MPB infestation were simulated by perturbing two vegetative parameters: stomatal resistance and leaf area index. Table 1 shows how we defined each phase of MPB infestation, along with its corresponding land surface classification, maximum and minimum LAI (depending on season, recall that LAI is dynamically calculated in CLM) and the minimum stomatal conductance. When the MPB infects a stand of trees, it introduces a blue-stain fungi (Ceratostomella montia and Europhium clavigerum) that essentially clogs the xylem and phloem tubes (Amman, 1978). This renders the tree unable to take up water and nutrients from its roots. Stomatal resistance was manipulated to represent this phenomenon during the red and grey stages of infestation by increasing the minimum stomatal conductance until it was maximised and transpiration approached zero. During the red and grey phases, it is assumed that there is no new undergrowth in the pine stands, transpiration approaches zero in the entire watershed and bare-ground evaporation is the only energy land-surface flux occurring.
Table 1. Parameters used in Parflow-CLM for distinguishing the four different mountain pine beetle phases.
|Phase||Land surface classificationa||Maximum LAI||Minimum LAI||Minimum stomatal conductance (µmol m−2 s−1)|
|Green||Evergreen needleleaf forest||6||5||2000|
|Red||Evergreen needleleaf forest||5||4||2.0E+06|
|Grey||Evergreen needleleaf forest||1||1||2.0E+06|