3.1. Definition of an Archetypical Meadow
 The approach adopted here is to gain insight into the hydroecologic function of meadow systems in the Last Chance watershed by employing a modeling framework. To this end, we define an archetypical meadow for which we simulate the groundwater flow and vegetation patterning under pristine, incised, and restored conditions. Recognizing that our simulated meadow system is somewhat stylized, our purpose nevertheless is to (1) reproduce the salient hydroecologic features observed in the meadows at our field site and (2) compare directly the hydroecologic response of the simulated meadows under the different meadow conditions.
 We have historical accounts that two of the meadows in this study, (Big Flat and Alkali Flat) have experienced pristine, degraded, and restored conditions. Unfortunately we only have data available for the current condition. By making a substitution of space for time, we are able to make general comparisons between how the archetype meadow condition changes through various degradation states (time) with the field observations collected at various locations (space).
 Figure 6a displays the simulation domain of the pristine and degraded cases. The simulated meadow is ∼180 m wide in the widest portion and narrows to ∼30 m in the upstream and downstream regions. On the basis of topographic surveys presented in Text S1 (section S5), the down-valley surface slope is 0.2°, and the meadow sediments have a constant thickness of 5 m. The location of the stream is as shown, also with a bed slope of 0.2°. The depth to the streambed was varied to simulate different states of stream incision. Figure 6b represents the restored case and has exactly the same outer boundary as shown in Figure 6a. In the model of the restored case, the incised channel is replaced with a series of six, 3.5 m-deep ponds and a new 0.5 m-deep channel to represent pond-and-plug restoration. In the model, the new channel is more sinuous than the incised one; as noted by Benoit and Wilcox , the incised channels are typically straighter than remnant channels (see active and remnant channels of Figures 3a and 3b). At the downstream end of the restoration project area, the new channel is routed back into the incised channel through an outflow control structure. In the field, each control structure consists of a series of pools created with rip-rap to step the stream down to the position of the incised channel and to prevent channel incision from propagating upstream into the new unincised channel.
Figure 6. Model domain used for numerical simulations of (a) the pristine and degraded cases and (b) the restored case. Dimensions of both domains are identical.
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3.2. Vegetation Threshold Hydrographs
 It has long been recognized that different vegetation communities have various water requirements. Particularly in semiarid meadow environments, depth to groundwater has been identified as a critical parameter determining the type of vegetation that will flourish at a given location [Allen-Diaz, 1991; Ridolfi et al., 2006]. However, understanding these water requirements has proven difficult because they are dependent not only on the species present, but also on environmental conditions such as climate, nutrient limitations, and soil type, amongst others. According to McKinstry , a critical gap in our knowledge of the ecology of mountain meadows is the water requirements of meadow species.
 High groundwater levels are particularly critical for supporting groundwater-dependent ecosystems. Because the meadows are GDEs, we believe depth to the water table is the primary driver of vegetation patterning. We maintain that differing depth-to-water requirements of mesic versus xeric plant types are time variant, and quantitative relationships must be developed that describe this time dependency as it relates to specific communities.
 The depth-to-water characteristics that differentiate wet meadow vegetation from sagebrush/dryland grass vegetation communities are in fact related to the phenology of these plants. The phenology of Nebraska Sedge (Carex nebraskensis), a species found in wet meadow vegetation communities, was reported by Ratliff  in the Sierra National Forest. He found that initiation of new growth occurred between 22 May and 4 June. The reproductive stage was reached by 48% of individuals by 2 July. Full bloom was reached by 30 July, and continued into mid-August. The seed continued to ripen until late September. These important phenologic events help us interpret the observed depth-to-water requirements discussed below.
 The required depth-to-water characteristics as a function of plant community type are shown in Figure 7, where a vegetation threshold hydrograph is introduced. Regions on the graph were determined using the water table hydrographs in Figure 5 and the characterization of the vegetation at each site (mesic/wet meadow, mixed, or xeric) on the basis of species composition. On the basis of the data, we define three curves. The upper, middle, and lower vegetation threshold hydrographs define the thresholds between exclusively wet meadow/dominantly wet meadow, dominantly wet meadow/dominantly dryland, and dominantly dryland/exclusively dryland vegetation communities, respectively. The middle vegetation threshold hydrograph differentiates between the two vegetation communities by providing a threshold above which the water table would support wet meadow vegetation and below which the area would be dominated by sagebrush and dryland grasses.
Figure 7. On the basis of the data shown in Figure 5, vegetation threshold hydrographs separating sites of wet meadow vegetation from those with xeric vegetation are shown.
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 There are two portions of this threshold curve that are particularly important and may be related to phenological patterns during typical growing seasons. First, the most critical feature of the vegetation threshold hydrograph is that water levels are very near, or above, the land surface during April and May. If the water table is within 0.5 m of the surface during this period of growth initiation, the very high moisture content in the root zone will cause waterlogging and mortality of xeric vegetation. Second, it appears as though the water table must remain within ∼1 m of the surface through June and July to maintain sufficient soil moisture for the wet meadow species to reach full bloom during the annual dry period. This depth may be related to the rate at which rooting depth can increase through the growing season in an attempt to reach the water table [Martin and Chambers, 2002]. Through August (and later), the wet meadow species begin to senesce, water requirements are reduced, and a shallow water table is no longer required to supply water to the vegetation. The upper and lower vegetation hydrographs are included in recognition of the fact that the threshold is not precisely defined and is perhaps better thought of as a transition from wet meadow to dryland vegetation communities.
3.3. Groundwater Flow Modeling Techniques
 The effect of stream incision on groundwater flow and vegetation patterning is explored through numerical modeling in the archetypical meadow described in section 3.1. The stream is incised to various degrees in five simulated cases. In the pristine case, the streambed is located 0.5 m below the meadow surface. Increasing severity of meadow degradation is simulated by lowering the streambed elevation to 1 m, 2 m, and 4 m below the meadow surface. A fifth case, that of a restored meadow, is simulated by creating a domain in which a series of ponds and plugs replaces the original channel and a secondary, meandering channel is added with a streambed elevation 0.5 m below the meadow surface. Toward the downstream end of the meadow, the stream course is located in the incised channel (4 m deep) to simulate the transition into an unrestored reach. The conceptual model in all cases includes (1) infiltration at the meadow surface during the winter months, which peaks during the spring snowmelt, (2) a stream that is represented as a time-dependent, specified pressure head boundary (i.e., ψ(t)), (3) a basal influx that represents the contribution of water from the regional groundwater flow system, and (4) evapotranspiration from the root zone that is vegetation- and time-dependent during the growing season. The model does not include surface water routing, overland flow, or meadow flooding.
 Three-dimensional, variably saturated, transient groundwater flow modeling was performed using Richards' equation as shown below:
where θ is the water content (−), θR is the residual water content (−), θS is the water content at saturation (−), ψ is the pressure head (L), K(ψ) is the unsaturated hydraulic conductivity (L/T), C(ψ) = ∂θ/∂ψ (1/L), ρf is the density of the fluid (M/L3), g is the gravitational constant (L/T2), xf is the compressibility of the fluid (1/P), xp is the compressibility of the solid (1/P), and Qs is a source/sink term (1/T). The functional forms of the characteristic curves given by van Genuchten  were used and are shown below:
where KS is the saturated hydraulic conductivity (L/T), and α (1/L), n (−), and m (−) are empirical coefficients with m = 1 − 1/n. On the basis of measured values reported in Text S1 (section S4), the following hydraulic properties were used in the simulations: K = 7 × 10−6 m/s, α = 1.5 m−1, n = 2, θs = 0.65; and θr = 0.2. The aquifer compressibility was 1 × 10−6 Pa−1. The ponds are represented as an extension of this domain with θs = 1, θr = 0, a high hydraulic conductivity (100 times that of the meadow sediments), and a very steep characteristic curve to approximate an open water body. Representing the hydraulic behavior of the ponds as an effective porous media with high hydraulic conductivity and porosity of 100% allows the ponds to act as regions with low resistance to flow and high water storage capability while allowing them to communicate with the nearby sediments. In terms of their hydrologic impact, the ponds were treated as groundwater sinks because of evaporation.
 Comsol Multiphysics version 3.2® [Comsol, 2005], a finite element software package for solving user-defined partial differential equations, was used to solve equation (1). The time-dependent solver was used in combination with a linear geometric multigrid (GMRES) solver using the LU preconditioner; the results were checked using a much less memory efficient direct solver (UMFPACK) with excellent agreement. The domain was discretized into ∼160,000 elements, and ∼220,000 nodes. The simulations were run on a Sun v40z with 32 GB of memory. The simulations were each run for a water year (beginning 1 October).
 The boundary conditions at the edges of the meadow are all defined as no-flow boundaries and are set by prescribing a zero head gradient (∇(ψ + z) = 0). An upward flux is specified at the base of the model domain at a rate of 1 × 10−8 m/s to represent a deep groundwater contribution as a constant flux boundary condition; the rationale for selecting this flux rate is presented in Text S1 (section S6). The top of the domain is represented by a time-dependent downward flux describing the infiltration rate. In the model, the infiltration rate is 2 × 10−8 m/s from 1 November to 1 March when winter storms typically occur. The majority of the recharge due to infiltration occurs during the spring snowmelt; this is represented as an infiltration rate of 2 × 10−7 m/s from 1 March to 1 April. The maximum total infiltration is 73 cm/yr, representing more than the annual precipitation because both surface flow from the hillslopes and stream water from meadow flooding infiltrate into the meadow sediments during the spring snowmelt. During the remainder of the year, there is no infiltration in the model. The values of both of the inflow terms (infiltration and deep groundwater) are specified at rates less than their respective maximum rates if the meadow is completely saturated; at all locations, the reduced inflow rates are linearly interpolated between the maximum value and zero by scaling between the pressure head that indicates saturation (in a hydrostatic state) and a pressure head 10 cm higher than saturation. This is to represent the fact that surface waters accumulate on the meadow surfaces, but great depths do not occur. Neither streamflow routing nor surface water storage are included in the model.
 To represent ET, water extraction by roots occurs within the top two meters of the meadow, regardless of whether this zone is saturated or unsaturated; there is no bare surface evaporation. The extraction rate is determined as a function of time, vegetation type, and soil water pressure head. From data in Text S1 (section S3), the time dependency of transpiration over the growing season was determined by analysis of diurnal water table fluctuations using the methods of White  and Loheide et al. . We introduce a vegetation index (vi) in which “1” represents mesic, wet meadow vegetation and “0” represents xeric vegetation, and intermediate values represent mixtures of the two vegetation communities. Loheide and Gorelick  determined that near-peak evapotranspiration rates for xeric meadow vegetation and wet meadow vegetation were 1.5–4.0 and 5.0–6.5 mm/day, respectively. The ET rate in the model is determined by linearly scaling between the values of 3 mm/d and 6 mm/d for these end member vegetation types given the temporal pattern determined previously (Figure S2). Figure 8 shows the ET that would be specified for vegetation indices of 1.00, 0.50, and 0.00 under the condition when water is not strongly limiting ET. If soil water tension is less than −10.0 m, ET is further reduced in a linear manner until it is zero at the wilting point (−140.0 m). Evaporation from the ponds is specified using the daily rate function shown in Figure 8 for vi = 1.
Figure 8. Growing season evapotranspiration rates used in simulations for vegetation indexes (vi) of vi = 1 (100% mesic), vi = 0.5 (50% mesic and 50% xeric), and vi = 0.0 (100% xeric).
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 The stream stage is represented as a time-dependent specified pressure head; using a lookup table with eleven equally spaced time and stage data pairs, the values specified for this boundary condition are interpolated from the function presented in Text S1 (section S2) on the basis of typical annual stream stage (Figure S1). This boundary condition is imposed at the streambed. In the pristine case, the streambed is located 0.50 m below the meadow surface. Under low flow conditions, the surface of the stream is 0.2 m above the streambed and the high flow conditions are 0.5 m above the streambed. Therefore in the pristine case, the stream surface is 0.3 m below the meadow surface under low flow conditions and at the surface during high flow.
 The only two differences between the model of the pristine case and that of the degraded cases are that (1) the streambed and the stream boundary condition are lowered to a depth below the meadow surface of 1 m, 2 m, and 4 m in the degraded cases and (2) the ET rates are different because the predicted vegetation maps are different. In the restored case, the streambed is relocated, but the streambed depth is 0.5 m as in the pristine meadow case.
 A several year warm-up period was simulated to obtain reasonable initial soil moisture/pressure head conditions needed for the coupled groundwater/vegetation model. Because the same boundary conditions are applied during repeated years, a dynamic equilibrium develops in which the water table (and pressure head) response is the same in successive warm-up years. To start this warm-up period, we assumed hydrostatic conditions and a planar water table with a slope and elevation that are equivalent to that of the stream surface on the first day of the water year (1 October). A one year period was simulated that included infiltration, groundwater flow, and ET. The simulated pressure head values at the final time step of the year were then used as the initial conditions for the next simulation under the same conditions of system stresses and boundary conditions. This process was repeated until a stable (<1 cm difference) annual water table hydrograph was obtained in successive years. For this warm-up period, a constant vegetation type was assumed (i.e., vi = 0.0, 0.5, 1.0, 1.0, and 1.0 for the degraded 4 m, degraded 2 m, degraded 1 m, the pristine, and restored cases, respectively). A constant vegetation type was assumed, as no better estimate was available for the initial simulation and was retained through the warm-up period. The results from the final time step of this warm-up period were used as initial conditions when the groundwater and vegetation models were linked.
3.4. Linking the Groundwater Flow and Vegetation Models
 Springer et al.  and Rains et al.  significantly advanced the ability to predict vegetation patterning through a one-way coupling of a saturated groundwater flow model to a vegetation model. In both studies, groundwater flow and vegetation patterning were influenced by connected surface water bodies with regulated flows and stages. Depth to the water table was used to predict vegetation type under various surface water reservoir operation scenarios; Rains et al.  focused on vegetation surrounding a reservoir whereas Springer et al.  considered the downstream effects of reservoir releases on riparian vegetation communities. We build on these efforts in several ways by considering (1) a three- dimensional, transient, variably saturated groundwater flow system, (2) a time-dependent vegetation model, and (3) feedback between the vegetation community and the groundwater flow system.
 Similar to Springer et al.  and Rains et al. , we predict vegetation patterning on the basis of depth to the water table. Our predictive vegetation model is based on the vegetation threshold hydrograph (Figures 7 and 9) determined using field data. However, instead of using a mean or steady state depth to the water table, we use the simulated depth to the water table at three critical times in the life cycle of these vegetation communities. The three dates we chose for this analysis are 1 May, 1 June, and 1 July. At the earliest date, if a very high water table is present, the root zone of xeric vegetation will be waterlogged and anaerobic [Dwire et al., 2006], causing the xeric species to die out. Near 1 June, sufficient water must be present for initiation of growth of the mesic communities. By 1 July, the water table must still be accessible by mesic vegetation to ensure reproductive success. Because the reproductive stages have already been reached by early August, it is likely that even very dry conditions will not negatively impact the long-term success of the mesic communities. On each of these dates, a vegetation index (vi) ranging from 0 to 1 is estimated on the basis of the depth to the water table. A vegetation index of 1 indicates 100% mesic/wet meadow vegetation (0% xeric) and a value of 0 indicates 0% mesic/wet meadow vegetation (100% xeric). If the depth to the water table is above the upper vegetation threshold hydrograph, a vi = 1 is predicted. If the depth to the water table is equal to the middle vegetation threshold hydrograph, a vi = 0.5 is predicted. If the depth to the water table is at or below the lower vegetation threshold hydrograph, a vi = 0 is predicted. In this vegetation model, vi values at intermediate water table depths are linearly interpolated as shown in Figures 9a, 9b, and 9c for the 1 May, 1 June, and 1 July, respectively. The overall vi is calculated as the equally weighted mean of these three estimates, and is used as the vegetation map for the next model iteration.
Figure 9. Curves relating depth to the water table to the fraction of mesic and xeric vegetation expected for (a) 1 May, (b) 1 June, and (c) 1 July. These relationships were created by assuming vegetation communities are 100% mesic at sites where the water table depths are above the upper vegetation threshold. Similarly, vegetation communities are assumed 100% xeric at sites where the water table depths are below the lower vegetation threshold. Vegetation communities at sites with water table depths that are exactly at the middle vegetation threshold are 50% mesic and 50% xeric. The relationships are linear between these points.
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 There is a two-way coupling between the water table and the vegetation pattern. Because different vegetation types transpire at different rates, updating the vegetation map in the model affects the groundwater system. When applying the vegetation threshold hydrograph to determine vegetation type, we used the post warm-up simulated depth to the water table to update our initial guess of a constant vegetation type for the warm-up simulations. Then, pressure head values at the final time step are used as initial conditions in the subsequent simulation, and an annual simulation is rerun using the updated vegetation map. Water table depth resulting from this simulation is again used to update the vegetation map using the vegetation threshold hydrograph at the three evaluation dates. The flow model is rerun, with the updated vegetation conditions. This iterative process is repeated until the water table configuration and vegetation patterning reach an equilibrium condition (Δvi < 0.01).