Raquel H.FLINKERM.Bayani CARDENASTodd G.CALDWELLGerald N.FLERCHINGERRoy RICH and Peter B.REICH6 tment of Geological SciencesThe University of Texas at AustinAustin 787(USA)

2 Bureau of Economic Geology，The University of Texas at Austin，Austin 78713(USA)

3 Agricultural Research Ser vice，United States Depar tment of Agriculture，Boise 83712(USA)

4 Smithsonian Environmental Research Center，Edgewater 20137(USA)

5 Depar tment of Forest Resources，University of Minnesota，St.Paul 55108(USA)

6 Hawkesbur y Institute for the Environment，Wester n Sydney University，Sydney 2753(Australia)

ABSTRACT Free-air carbon dioxide(CO2)enrichment(FACE)experiments provide an opportunity to test models of heat and water f low under novel，controlled situations and eventually allow use of these models for hypothesis evaluation.This study assesses whether the United States Department of Agriculture SHAW(Simultaneous Heat and Water)numerical model of vertical one-dimensional soil water f low across the soil-plant-atmosphere continuum is able to adequately represent and explain the effects of increasing atmospheric CO2 on soil moisture dynamics in temperate grasslands.Observations in a FACE experiment，the BioCON(Biodiversity，CO2，and Nitrogen)experiment，in Minnesota，USA，were compared with results of vertical soil moisture distribution.Three scenarios represented by different plots were assessed:bare，vegetated with ambient CO2，and similarly vegetated with high CO2.From the simulations，the bare plot soil was generally the wettest，followed by a drier high-CO2 vegetated plot，and the ambient CO2 plot was the driest.The SHAW simulations adequately reproduced the expected behavior and showed that vegetation and atmospheric CO2 concentration signif icantly affected soil moisture dynamics.The differences in modeled soil moisture amongst the plots were largely due to transpiration，which was low with high CO2.However，the modeled soil moisture only modestly reproduced the observations.Thus，while SHAW is able to replicate and help broadly explain soil moisture dynamics in a FACE experiment，its application for point-and time-specif ic simulations of soil moisture needs further scrutiny.The typical design of a FACE experiment makes the experimental observations challenging to model with a one-dimensional distributed model.In addition，FACE instrumentation and monitoring will need improvement in order to be a useful platform for robust model testing.Only after this can we recommend that models such as SHAW are adequate for process interpretation of datasets from FACE experiments or for hypothesis testing.

Key Words: carbon dioxide，FACE experiment，soil water f low，vadose zone，vegetation

INTRODUCTION

The increasing carbon dioxide(CO2)concentration in the atmosphere has now passed 410 ppm(410 mg L-1)，which is 130 ppm(130 mg L-1)higher than pre-industrial levels.Numerous studies are being conducted to investigate how these increases affect different aspects and components of the Earth system and how well numerical models can represent these impacts.Higher atmospheric CO2leads to a decrease in plant transpiration and an increase in water use efficiency by lowering stomatal conductance(Fieldet al.，1995，1997;Leeet al.，2009;Adairet al.，2011)，consequently enhancing soil moisture storage(Drakeet al.，1997;Fieldet al.，1997).Higher soil moisture in response to higher atmospheric CO2environments has been observed in open-top chamber experiments(Fieldet al.，1997;Fredeenet al.，1997;Nelsonet al.，2004;Dermodyet al.，2007)and free-air CO2enrichment(FACE)experiments(Adairet al.，2011).The covariance has also been simulated in large ecosystem manipulation models(Grünzweig and Korner，2001).However，less research has been conducted on the associated subsurface hydrologic processes(Ainsworth and Long，2005).

In FACE experiments，the atmosphere in controlled plots are enriched with CO2(http://www.bnl.gov/face/)in order to investigate the effects of higher atmospheric CO2.Such FACE experiments have been conducted for a number of years in many different ecosystems，but the focus has generally been on the response of plant communities，soil respiration，and microbes to changing conditions(Kimballet al.，2002;Ainsworth and Long，2005;Adairet al.，2011).Comprehensive modeling of vertically-distributed soil moisture and energy balance in FACE experiments is seldom conducted.Using a year’s data(2006)from a FACE experiment，the BioCON(Biodiversity，CO2，and Nitrogen)，Adairet al.(2011)showed that elevated CO2increased volumetric soil water content by 23%on average(113%maximum)and total water storage by 53%on average(182%maximum).They showed that the effect of CO2weakened at very low and high volumetric soil water content and at the end of the growing season，when plant activity declined.Also，during post-rainfall events，soil intervals at 0—17 and 42—59 cm depths stayed moist longer in the elevated CO2plots than in the ambient CO2plots.We expand on the work of Adairetal.(2011)by conducting more complex biophysical modeling and considering more recent data.

The overall question this study sought to address was:can the SHAW(Simultaneous Geat and Water)model replicate soil moisture dynamics in plots where vegetation is potentially responding to increasing atmospheric CO2concentration?In testing whether SHAW can adequately represent soil moisture dynamics，we also assessed two basic concepts:i)The presence of vegetation contributes to an increase in evapotranspiration and a decrease in soil moisture，and ii)higher atmospheric CO2concentrations lead to smaller evapotranspiration values and，consequently，to higher soil moistures.For the f irst concept，the hydrology of bare and vegetated soils was modeled and compared to each other，while for the second idea，the hydrology of vegetated soils at different atmospheric CO2concentrations was modeled and compared.The main point behind the assessment is that if a model such as SHAW succeeds in replicating the soil moisture dynamics and plant water uptake across different treatments in BioCON，then such models have explanatory value and can be used for mechanistic hydrologic-biophysical interpretation of the unique observations offered by a FACE site.These models may also be useful for providing complete spatially distributed，time-series information on soil moisture and f luxes in light of limited measurements in time and space.

The broader objective of this work was，therefore，to characterize and model soil moisture dynamics for different atmospheric CO2concentrations and plant presence to ultimately determine how each affects soil moisture simulations on grasslands of central Minnesota，USA.The BioCON experiment data and the SHAW model，which solves the Richards equation for unsaturated zone water f low coupled to a comprehensive energy balance model，are used for this evaluation.

METHODS

Description of the BioCON FACEsite

The FACE experiments provide the ideal replicated environment of elevated atmospheric CO2around an ecosystem.In the past，experimental manipulation of enriched concentrations of atmospheric CO2was possible only in growth chambers and greenhouses，all of which require containment.These containments alter the ecosystem’s relationship to the natural environment，but the FACE setup largely overcomes this problem(Ainsworth and Long，2005).

The BioCON experiment(Reichetal.，2001b)is a FACE experiment that has been continuously run since 1997(for more information，visit http://www.biocon.umn.edu)in the Cedar Creek Ecosystem Science Reserve in East Bethel，Minnesota(45°24′N，93°11′E，218 m above sea level).Mean annual precipitation(1982—2009)at the BioCON experiment site is 800 mm and summer is the wettest season of the year(Adairet al.，2011).The BioCON experiment investigates plant community response to three key environmental variables:increased nitrogen，increased atmospheric CO2，and decreased biodiversity(Reichet al.，2001a，b，2004，2006;Adairet al.，2011;Reich and Hobbie，2013).The BioCON experiment consists of 371 plots(2 m×2 m)，arranged into six circular areas or“rings”that are 20 m in diameter.Three of the six rings are fumigated with CO2-enriched air(ca.560 ppm(560 mg L-1)CO2)during the day throughout the growing season and the remaining rings have ambient atmospheric CO2levels(Adairet al.，2009).Elevated CO2levels were set to approximately 180 ppm(180 mg L-1)higher than the ambient levels at the start of the experiment and only during the daytime when plants are photosynthesizing.Each of the 371 plots was randomly planted with 0，1，4，9，or 16 species of herbaceous perennial prairie taxa，either native or naturalized to the Cedar Creek area.All sixteen plant species belonged to one of the four following functional groups:C4 grasses，C3 grasses，nitrogen-f ixing legumes(C3)，or non-nitrogen-f ixing herbaceous plants(C3).There were four plant species of each of the four functional groups available for planting(Reichet al.，2001b).The studies at BioCON have investigated the effects of treatments on different plant species’photosynthetic responses(Ellsworthet al.，2004;Crouset al.，2010;Leeet al.，2011).The soils in the region are sandy and primarily classif ied as Nymore loamy sand，a mixed，frigid Typic Udipsamment，following the United States Natural Resources Conservation Service classif ication，with low soil organic matter and nitrogen(Dijkstraet al.，2006).

In-situ soil moisture measurements

The f ield soil moisture was measured in all of the plots by BioCON researchers at four 17-cm intervals(0—17，22—39，42—59，and 83—100 cm)multiple times during each growing season from 2007 to 2012.The soil moisture data from a few plots were analyzed and used for comparison with the SHAWsimulations.

A Trime FM3 Time Domain Ref lectometry(TDR)system，version P3 with a T3 tube-access probe(IMKO Micromodultechnik GmbH，Ettligen，Germany)，was used for soil moisture measurements(Adairet al.，2011).The TDR measurements were calibrated according to calculated volumetric soil water contents from coincident gravimetric soil moisture and bulk density measurements(Adairetal.，2011).Only a single calibration was done as，according to Dijkstraet al.(2006)，“Soils(Argic Udipsamments)in this nearly level area are very homogenous，sandy(93%sand，3%silt，and 4%clay)，and poor in soil organic matter.”The volumetric water content measuring range of the instrument was 0.0—0.6 m3m-3.Its measuring accuracy was 0.02 m3m-3in the 0.0—0.4 m3m-3range.Due to the measuring accuracy of the equipment，all water content measurement values smaller than or equal to 0.02 m3m-3were not considered in model performance evaluations.

Soil moisture and energy balance modeling with SHAW

We assessed and used the SHAW model for the hydrologic-biophysical modeling of each of the three plot treatments(Flerchinger and Saxton，1989a，b;Flerchinger，2000;Flerchingeretal.，2012).The SHAWmodel is a vertical one-dimensional heat and water transport numerical model for the soil-plant-atmosphere continuum.It simulates heat，water，and solute transfer through plant cover，dead plant residue，snow，and soil(Flerchinger and Pierson，1991，1997).The ability of SHAW to model the soil-plant-atmosphere continuum has been demonstrated in several studies and the reader is referred to these studies for further details and additional examples of its applications(Flerchinger and Pierson，1997;Wanget al.，2010).Meteorological conditions and soil hydraulic parameters are necessary input parameters.The iterative Newton-Raphson technique is used to numerically solve the implicit f inite-difference energy and water balance equations for each time step(Flerchinger and Saxton，1989a).

The SHAWmodel Version 3.0(Flerchinger，2013)was selected for these detailed small-scale hydrologic simulations because it allows for plant-water uptake and uses a water and energy balance approach to represent freeze-thaw processes(Flerchinger and Saxton，1989a)，which occur at BioCON.The model was parameterized using a combination of f ield and laboratory estimates of soil properties.The following sections describe the boundary conditions and some important equations used in the model.More detailed information on the components of the model can be found in its manual(Flerchinger，2000).

Soil water f lux modeling

The SHAWmodel solves the modif ied Richards equation for water f low in the unsaturated zone.This equation takes into account freezing and thawing of the soil(Flerchinger and Saxton，1989a)and reads as:

whereθlis the volumetric liquid water content(m3m-3)，θiis the volumetric ice content(m3m-3)，ρiis the density of ice(kg m-3)，ρlis the density of liquid water(kg m-3)，tis the time(s)，zis the soil depth(m)，Kis the unsaturated hydraulic conductivity(m s-1)，Ψis the soil matric potential(m)，qvis the vapor f lux through the soil(kg m-2s-1)，andUis the sink term representing root water extraction(m3m-3s-1).

The SHAWmodel calculates the energy and water f luxes at the land surface based on inputs of daily or hourly weather data of air temperature，wind speed，relative humidity，precipitation，and total solar radiation measured on a horizontal surface.The energy balance at the surface is:

whereRnis the net radiation(W m-2)，His the sensible heat f lux(W m-2)，Lvis the latent heat of evaporation(J kg-1)，Eis the total evapotranspiration from the soil surface and plant canopy(kg m-2s-1)，andGis the ground heat f lux(Wm-2)(Flerchinger and Saxton，1989a).

The f luxes through the one-dimensional vertical soilplant-atmosphere system are computed for each time step by a f inite-difference approximation between model nodes.Adjustments for precipitation，snowmelt，settling of the snowpack，interception，and inf iltration are made at the end of each time step(Flerchinger and Saxton，1989a).Evaporation from the soil or residue surface is computed directly from the gradient in vapor density between the surface and the bottom canopy node(Flerchinger and Pierson，1997).

Water f lux through the plant residue is described by the following equation:

whereρvis the vapor density within the residue layer(kg m-3)，Kvis the convective vapor transfer coefficient within the residue(m s-1)，hris the relative humidity within the residue elements，ρ′vsis the saturated vapor density at the temperature of the residue elements，andrhis the resistance(s m-1).

Water f low through plants is physically dependent on the soil-plant-atmosphere continuum，as plants draw water stored in the soil and transpire it through the stomata.This f lux is regulated by atmospheric demand but also by resistances directly related to the soil，roots，plant xylem，and leaf water potential.It is calculated according to the equation below(Flerchinger and Pierson，1997):

whereTris total transpiration rate(kg m-2s-1)for a given plant species，Ψs，mis the water potential(m)in layermof the soil，Ψxis the water potential(m)in the plant xylem，Ψl，iis the water potential(m)in the leaves of canopy layeri，NS is the number of the soil layer，NC is the number of the canopy layer，rr，mis the resistance to water f low(m3s kg-1)through the roots of layermand xylem up to locationx，rl，iis the resistance to water f low(m3s kg-1)through the xylem above locationxand through the leaves of layeri，Liis the leaf area index within canopy layeri，ρvs，iis the vapor density within the stomatal cavities，ρv，iis the vapor density of the air within the canopy layer，rs，iis the stomatal resistance(s m-1)，andrh，iis the resistance to convective transfer(s m-1).

Water f low within the plant is dependent mainly on the stomatal resistance(rs)，typically the largest of the abovementioned resistance variables:

wherersois the stomatal resistance with no water stress(m s-1)，Ψcis the critical leaf water potential(m)，andnis an empirical coefficient(Flerchinger and Pierson，1991).

Parameterization and boundar y and initial conditions of the model

The main boundary conditions for the system are temperature and soil water potential at the lower boundary and daily or hourly weather conditions at the upper boundary(Flerchinger and Pierson，1997).The initial conditions for soil temperature and water content at each node need to be specif ied.The initial soil water content and temperature for the simulations were based on f ield measurements and data from the Cedar Creek weather station.

Meteorological information is necessary for forcing the energy balance model and also for def ining mass boundary conditions.Initially，we intended to use weather data from the Cedar Creek Ecosystem Science Reserve weather station.Unfortunately，due to malfunctions，data from the station had several gaps and inconsistencies，making its use limited.Therefore，we used hourly National Aeronautics and Space Administration(NASA)Land Data Assimilation Systems(NLDAS)Phase 2 Forcing File A data for the(1/8)°-wide cell containing the study site.

Since 1979，NLDAS-2 data are available for the continental United States.Precipitation is calculated based on a temporal disaggregation of a gauge-only Climate Prediction Center(CPC)analysis of daily precipitation.The other weather parameters were obtained from the National Centers for Environmental Prediction(NCEP)North American Regional Reanalysis(NARR)based on NCEP data，models，data assimilation systems，and additional datasets(Mesingeret al.，2006).For our study period(2007—2012)，the average annual precipitation in the region was 735 mm and the air temperature was 8.3°C.The average January and July air temperatures were-10.6 and 24.8°C，respectively(Fig.1).In addition to hourly air temperature(°C)and precipitation(mm)，similar time-series for wind speed at 10-m height(m s-1)，relative humidity(%)，and incoming short-wave solar radiation(Wm-2)were used in these simulations.

Fig.1 Daily precipitation(column)and average daily air temperature(line)at the BioCONexperiment site in the Cedar Creek Ecosystem Science Reserve in East Bethel，Minnesota，USA.The data were from the National Aeronautics and Space Administration(NASA)Land Data Assimilation Systems(NLDAS)Phase 2 Forcing File A(NLDAS-2).

The soil is described by 88.4%sand，10.7%silt，and 1.0%clay following additional grain-size analysis as part of this study.Table I includes a summary of these analyses.These values are consistent with previous analyses and conf irm the homogeneity of the soil at BioCON.

TABLE I Grain size statistics for soil samples collected at various depths and adjacent to each ring in the BioCON experiment conducted in the Cedar Creek Ecosystem Science Reserve in East Bethel，Minnesota，USA

Soil hydraulic parameters were based on the pedotransfer functions def ined by Saxton and Rawls(2006)，which calculate the parameters for the Brooks and Corey model for soil-moisture retention and saturation-hydraulic conductivity based on soil texture data(Table II).

Plant characteristics and assessment of their conceptualization in SHAW

To simplify the model，the nine random plant species present in the vegetated plots(Table III)were combined and simulated as one“effective”species represented by“generic”grass.This generic grass was used to represent the plant species present in the plot，regardless of which plant species they were.

The parameters of this“generic”grass were obtained from Campbell and Norman(1998)，Leeet al.(2011)，the SHAW User’s Manual，and BioCON data.Some plant characteristics were f ixed in time and others varied depending on the season(Fig.2，Table IV).Monthly time-variant plant parameters included plant height(m)，leaf width(cm)，dry biomass(kg m-2)，leaf area index，and effective rooting depth(cm).The following plant residue parameters also changed over time:thickness of the layer(cm)，dry weight(kg m-2)，and fraction of surface area covered by residues.

Fig.2 Time-variable plant properties prescribed in the Simultaneous Heat and Water(SHAW)model simulations for the Biodiversity，CO2，and Nitrogen(BioCON)experiment conducted in the Cedar Creek Ecosystem Science Reserve in East Bethel，Minnesota，USA:leaf dimension(cm，dot line)，effective root depth(m，long-dash line)，plant height(m，solid line)，and leaf area index(LAI).The LAI values presented have been divided by 10 for both the ambient CO2(dash-dot line)and high CO2(short-dash line)conditions.

Three plant parameters differed depending on the CO2concentration:stomatal resistance，dry plant biomass，and plant residue dry weight.These differences are likely necessary in order for soil moisture modeled by SHAW to match the observations and，therefore，could help explain any differences across treatments.

TABLE II Brooks and Corey soil hydraulic parameters used in the SHAW model simulations for the BioCON experiment conducted in the Cedar Creek Ecosystem Science Reserve in East Bethel，Minnesota，USA

TABLE III Plants present in each vegetated plot investigated in the BioCON experiment conducted in the Cedar Creek Ecosystem Science Reserve in East Bethel，Minnesota，USA

At higher CO2concentrations，stomatal resistance，dry plant biomass，and plant residue dry weight have been shown to increase(Drakeet al.，1997;Fieldet al.，1997;Leeet al.，2011).This occurs as plants have more CO2to photosynthesize and grow and can increase stomatal resistance as CO2is abundant.The values for stomatal resistance under ambient and elevated CO2conditions were based on BioCON data from Leeet al.(2011).For maximum dry plant biomass，the ambient CO2condition value was based on grass values from the SHAW User’s Manual and Documentation.The maximum dry plant biomass for elevated CO2conditions was 10%higher than for ambient CO2conditions.Moreover，the leaf area index(LAI)was also modif ied accordingly.This variation was based on dry biomass variations measured at BioCON under the different CO2conditions.For the maximum plant residue dry weight，the ambient and elevated CO2conditions values were based on the SHAW User’s Manual and Documentation for different grassland disturbance conditions.A list of the main plant parameters and their sources can be found in Table IV，and their time variation is illustrated in Fig.2.

TABLE IV Main vegetation and residue parameters used in the SHAW model simulations for the BioCON experiment conducted in the Cedar Creek Ecosystem Science Reserve in East Bethel，Minnesota，USA

Energy balance model

Although it is not the focus of this study，SHAW also simultaneously models heat transport within the soil through the heat advection-conduction-dispersion equation.In addition to transport，SHAW includes phase changes(freezing and thawing)，which are relevant for our study due to the freezing conditions in winter.The thermal properties of the soil were calculatedviastandard equations following the volumetric proportions of sand，clay，water，and ice(see SHAW Documentation).

General properties of the implemented SHAW model and its application for hypothesis testing

The SHAW simulations were run for the different plot types using the hourly weather NLDAS data for the weather boundary conditions and soil properties obtained from f ield and laboratory tests.The simulations started in April 2007 and ended in December 2012.

The vertical one-dimensional model consisted of 2-m depth of soil discretized into 18 nodes，which have irregular spacing denser near the surface.The nodes were located at 0.0，0.01，0.02，0.05，0.085，0.1，0.2，0.305，0.4，0.505，0.6，0.7，0.8，0.915，1.0，1.2，1.5，and 2.0 m.Unit gradient water f low(i.e.，gravity f low)was assumed for the lower boundary condition(2 m).The initial water contents and soil temperatures were based on f ield measurements and data from the Cedar Creek weather station for the starting date.Additional model details are presented in Table V.Unless otherwise stated，the parameters and properties listed in Tables II—V were kept the same and no calibration or tuning of any parameters was performed.

TABLE V Inputs of the SHAW model for the BioCON experiment conducted in the Cedar Creek Ecosystem Science Reserve in East Bethel，Minnesota，USA

In order to test whether SHAW can model soil moisture dynamics under varied key plant characteristics that change with CO2concentration(e.g.，stomatal resistance)，we modeled three representative plots from BioCON.These plots represented the following conditions:a bare plot(the base case)，a vegetated plot under ambient CO2conditions，and a vegetated plot under high CO2conditions.Following the naming system at BioCON，these plots correspond to Ring 1-plot 61，Ring 2-plot 106，and Ring 1-plot 26，respectively.Hereafter，these cases are referred to as bare，vegetated-ambient CO2，and vegetated-high CO2.The ambient and high CO2vegetated plots had a similar mix of C3 and C4 grasses，forbs，and legumes(Table III).

RESULTS AND DISCUSSION

Comparison of measured in situ soil moisture(θ)between plots

Each of the three plots had dynamicθfrom the top to the bottom of their prof iles(Fig.3).Near the surface(z=8.5 cm)，θbetween the plots were very similar through time and tended to cluster tightly.However，the vegetated-high CO2plot tended to be the driest during very dry periods.At intermediate depth(z=50.5 cm)，some differences were observed.The vegetated-ambient CO2plot was typically the driest，followed by the bare plot，and the vegetated-high CO2plot was generally the wettest.However，in all plots and during most observation times，there was substantial variability inθ.These observations support that the differences inθcould be useful for further testing of hydrologic and biophysical processes that are in action and how these are represented in SHAW.

Fig.3 Comparison of observed volumetric soil moisture(θ)at different soil depths of 8.5(a)，50.5(b)，and 91.5 cm(c)in the bare plots(circle)，vegetated plots with ambient CO2(cross)，and vegetated plots with high CO2(square)of the Biodiversity，CO2，and Nitrogen(BioCON)experiment conducted in the Cedar Creek Ecosystem Science Reserve in East Bethel，Minnesota，USA.

SHAW model results of soil moisture

Some of the observed soil moisture dynamics near the surface were captured by the model simulations.However，the models poorly reproduced observations at the deepest location.The measurements are integrated over 17 cm depth(the length of the TDRprobe)，while the SHAWmodel results are for a point or node location.To make the model results and observations comparable，model nodes were precisely positioned to be in the middle of theθmeasurement interval.

Bare plots

Soil moisture in the bare plots remained within a narrower and higher range relative to the two vegetated plots(Figs.4，5，and 6).The model was able to reproduceθobservations for the bare plot(Fig.4)only within a narrow range(ca.0.1 to 0.14).The model generally failed to reproduce the driest observedθ(ca.0.05 and less，see scatter plot in Fig.4).However，like the observations，the model is able to replicate broad drying trends during summer(e.g.，around April 2011and May 2012)，except for the deepest location at 91.5 cm.There were some very dry moments in the deepest location(e.g.，around June 2007 and July 2008)，that the model did not show.

Fig.4 Comparison of modeled and observed volumetric soil moisture(θ)in the bare plots of the BioCON experiment conducted in the Cedar Creek Ecosystem Science Reserve in East Bethel，Minnesota，USA.The left graphs show the time-series of the modeled(line)and observed(circle)θfor different soil depths of 8.5(a)，30.5(b)，50.5(c)，and 91.5 cm(d).Each tick is separated by 180 d and a tick’s month and year label does not necessarily denote the start of the month.Also shown in each left panel is the corresponding root-mean-square-error(RMSE)between the modeled and observedθ(not applicable for the 30.5 cm depth as no observedθfor this soil depth).The right graph(e)shows the scatter diagram forθ.In this graph，the solid line is the f itted line，and the dash line is the ideal line(1:1).The graph shows the f itted a，with 95%conf idence bounds in the parentheses，and R 2 and RMSE for the f it.

We assessed model performance quantitatively in two ways.The f irst is through the calculation of the root-meansquare-error(RMSE)for each model depth node.The second is more integrated:viascatter plots of all the model resultsvs.observations and by f itting a line to these with the intercept set at 0.TheR2and RMSE values are determined for the f its and visually compared with the line of perfect correlation(1:1).Thus，there are two RMSEs，a node-based one and one for the ensemble.

The node RMSE values were 0.017 and 0.020 m3m-3in the shallow and intermediate depths，respectively;this is similar to the TDR’s accuracy，which is 0.02—0.03 m3m-3.However，the RMSE was 0.036 m3m-3at the deepest measurement location(z=91.5 cm)，which is about twice the instrument’s accuracy.In general，the SHAWmodel was able to simulate wetting and drying events atz=8.5 cm and at the deeperz=50.5 cm.Periods whenθwas constant or‘f lat-lined’correspond to frozen conditions.These were most apparent at the shallowest location(z=8.5 cm)but were also simulated up to 50.5 cm depth.However，this was not observed at the deepest location(z=91.5 cm)，and thus the maximum depth of the freezing front was somewhere between 50.5 and 91.5 cm.The SHAW model generally simulated slightly wetter conditions relative to the observations in the deepest measurement location.However，at this location，the observed wetting and drying events were also captured by SHAW.

The scatter plot shows a general over-estimation ofθby SHAW.The poor and negativeR2shows that there is little predictive capacity of the observations.This indicates that the mean is just as predictive as any of the actual model results.However，the RMSE based on all the results of 0.024 m3m-3is small and within the accuracy of the TDR measurements as noted above.The metrics suggest that the SHAWmodel may be able to capture the mean behavior or the mean soil moisture state，but inaccurately captures the instantaneous point values.

Vegetated plots under ambient CO2 conditions

The vegetated plots under ambient CO2conditions had more dramatic changes inθacross all depths(Fig.5).Compared with the bare plots，there were more pronounced drying and wetting events in the summers.The SHAWmodel was able to capture the dynamics of these events，with drying and wetting at the same times and of similar magnitudes(e.g.，in June/July 2007，July 2008，and June/July 2012).However，the model failed to capture the observed dynamics in the deepest location(z=91.5 cm).The node RMSE values for the vegetated-ambient CO2plots(Fig.5)were also generally low(0.032—0.069 m3m-3)but a little higher than those in the bare plot(Fig.4).The RMSE values were nonetheless similar to that of the measurement error of the TDR probe，but slightly outside the range.The simulated and observedθwas more dynamic in the vegetated-ambient CO2plots relative to the bare plots.The drying and wetting events led to a broaderθrange.Nonetheless，the SHAW model was able to qualitatively capture these events for the f irst three measurement depths.However，the deepest location displayed larger differences between the simulated and measuredθ，and this is also ref lected by the highest RMSE of 0.069 m3m-3.The SHAWmodel simulated relatively wetter conditions at the deepest location.Flat-liningθ(frozen)was also simulated only in the shallower three locations，similar to the bare plots.

The scatter plot analysis showed that SHAW tends to over-estimateθwhen the soil is drier(ca.0.05 m3m-3and less)，similar to the model behavior for the bare plots.There were f ive observations that fell outside the range illustrated in Fig.5，ranging from 0.20 to 0.46 m3m-3.However，the corresponding modeled values did not reach this range and stayed between 0.12 to 0.15 m3m-3.The SHAW model failed to reproduce these few highθvalues and drastically under-estimated them.Similar to the bare plot comparison，the negativeR2shows that there is little predictive capacity of the observations.The over-all RMSE of 0.038 m3m-3is higher than that of the bare plots，but still close to the range of the TDR accuracy.

Fig.5 Comparison of modeled and observed volumetric soil moisture(θ)in the vegetated ambient CO2 plots of the BioCON experiment conducted in the Cedar Creek Ecosystem Science Reserve in East Bethel，Minnesota，USA.The left graphs show the time-series of the modeled(line)and observed(circle)θ for different soil depths of 8.5(a)，30.5(b)，50.5(c)，and 91.5 cm(d).Each tick is separated by 180 d and a tick’s month and year label does not necessarily denote the start of the month.Also shown in each left panel is the corresponding root-mean-square-error(RMSE)between the modeled and observedθ.The right graph(e)shows the scatter diagram forθ.In this graph，the solid line is the f itted line，and the dash line is the ideal line(1:1).The graph shows the f itted a，with 95%conf idence bounds in the parentheses，and R 2 and RMSE for the f it.

Vegetated plots under elevated CO2 conditions

The simulatedθvalues in the vegetated-high CO2plots were very similar to those in the vegetated-ambient CO2plots(Figs.6 and 5).This is expected since the only difference between the two model scenarios is the decreased stomatal resistance，which resulted in slightly wetter soil conditions.However，the differences are not visibly obvious in the time-series plots ofθ.In this case，SHAW was able to replicate the observed drying and wetting events.The SHAW model resulted in similar node RMSE values of around 0.03—0.04 m3m-3as the previous two plots at the f irst three depths，and higher RMSE in the deepest location.However，in this case，the RMSE of 0.084 m3m-3for the deepest location was relatively much higher，with observations showing much wetter and more dynamic conditions than what SHAW simulated.In general，the observedθvalues were higher than what the model produced.Nonetheless，the node RMSE values here，as in the other two cases，indicate that the dominant dynamics are captured by the SHAWsimulations.

The scatter plot further highlights that SHAW tends to over-estimateθin drier conditions，and under-estimates them in wetter conditions(Fig.6).TheR2for the f itting was similarly poor and also negative，indicating almost no predictive capacity.However，the over-all RMSE of 0.036 m3m-3was reasonably low，again indicating that SHAW is mostly representing the mean conditions.

Fig.6 Comparison of modeled and observed volumetric soil moisture(θ)in the vegetated high CO2 plots of the Biodiversity，CO2，and Nitrogen(BioCON)experiment conducted in the Cedar Creek Ecosystem Science Reserve in East Bethel，Minnesota，USA.The left graphs show the time-series of the modeled(line)and observed(circle)θfor different soil depths of 8.5(a)，30.5(b)，50.5(c)，and 91.5 cm(d).Each tick is separated by 180 d and a tick’s month and year label does not necessarily denote the start of the month.Also shown in each left panel is the corresponding root-mean-square-error(RMSE)between the modeled and observedθ.The right graph(e)shows the scatter diagram forθ.In this graph，the solid line is the f itted line，and the dash line is the ideal line(1:1).The graph shows the f itted a，with 95%conf idence bounds in the parentheses，and R 2 and RMSE for the f it.

Total water storage and f luxes modeled by SHAW

In order to further highlight and analyze the differences in the simulation results，here we focus on the total amount of water stored and the evaporation and transpiration f luxes.One representative year，2012，is chosen for this analysis.

The total amount of water stored over the model domain of 2 m is calculated by vertical integration of the simulatedθprof ile，ranging from 0.2—0.3 m of water(Fig.7)，with increases and decreases in the summer due to precipitation input and evapotranspiration output.The bare plot always stored the most water，but all the plots had more similar，if not the same，amount of water during the wet period(early spring).However，after the period of peak wetness，the vegetated plots dried up more，reducing soil water storage.This increasing dryness is clearly driven by transpiration(Fig.7c).During the mid-to-late summer period of late July to early August，the transpiration f luxes generally exceeded evaporation f luxes in the vegetated plots.As expected，the ambient CO2plots showed slightly higher transpiration during this period，and generally throughout the period of active transpiration.However，the differences between the vegetated-ambient CO2and high CO2are relatively small compared to the overall evapotranspiration differences between the bare soil and vegetated plots.

Note that Fig.7 compares transpiration between the SHAWsimulations only.It shows that transpiration rates for the vegetated-ambient CO2conditions are higher than for the vegetated-elevated CO2conditions.Table VI also presents time-averaged values for evaporation and transpiration.The observations show this in a much more accentuated manner.As the observed soil moisture for the vegetated-ambient CO2is smaller than the simulation，the transpiration in this case is probably even higher than what was simulated.For the vegetated-elevated CO2conditions，the observed soil moisture was higher than the simulation，suggesting that the real transpiration rates were even smaller than what was simulated.

Fig.7 Modeled total water storage(a)，evaporation(b)，and transpiration(c)in 2012 for the bare plots(solid line)，vegetated-ambient CO2 plots(dot line)，and vegetated-high CO2 plots(dash line)of the BioCON experiment conducted in the Cedar Creek Ecosystem Science Reserve in East Bethel，Minnesota，USA.

Potential reasons for the mixed results of the comparison and recommendations

The main sources of uncertainty in this study were related to temporally limited f ield soil moisture data，soil hydraulic properties，and plant properties.On average，f ield soil moisture was only measured and results were available for eight times each year，with each measurement taken at different months.This limitation generates uncertainty in our comparison of f ield data to the simulations.For future work，it would be interesting to have continuous daily soil moisture observations.The plant species present in each plot were simplif ied to an“effective”grass.In the future，if sufficient data become available，it would be benef icial to represent each species separately and to see how this affects the model results.The lack of local weather data adds some uncertainty to this study.

The two decades of observations from the BioCONFACE experiments have led to substantial insights into the effects of various perturbations on grassland ecosystems.However，BioCON was not expressly designed for testing hydrologicbiophysical process models，although it clearly offers some potential for this.This is what we set out to test and our analysis has revealed some issues.Overall，the SHAWmodels we set up seem to capture primarily the mean soil moisture state of the plots.However，there are persistent discrepancies when point and instantaneous results are observed.These suggest that the current monitoring design of the BioCON site is not adequate for a robust test.Our modeling has attempted to minimize calibrations and varying parameters.The most logical values of input parameters were assumed when they were not constrained by observations.While these are also reasons for the discrepancies，analysis of each of the potentially dozens of parameters is beyond the scope of this study.We attempted to be as parsimonious as possible in the model design and construction，given the limited observations.Following this，here we speculate on other sources of error.

The plots at BioCON are 2 m wide.It is possible that there is lateral soil moisture transport between each plot，especially when there are lateral soil moisture gradients.Given the observed differences between the bare and vegetated plots，such lateral gradients and variability are likely.The one-dimensional(vertical)formulation of SHAWdoes not represent such effects.However，attempting to assess plot-plot soil moisture transport would require a fully threedimensional model since there are several plots within one ring at BioCON.

TABLE VI Comparison of simulated evaporation(E)and transpiration(T)f luxes in the bare plots，vegetated-ambient CO2 plots，and vegetated-high CO2 plots of the BioCON experiment conducted in the Cedar Creek Ecosystem Science Reserve in East Bethel，Minnesota，USA

The soil columns and other soil hydraulic and thermal properties are considered homogeneous.While grain-size analysis of samples from BioCON has indicated relative consistency in soil texture across plots and rings，it is likely that the soil columns have individually evolved through time，and of course，that there had always been inherent vertical and lateral variability that was not mapped.Moreover，BioCON，because it was designed to assess vegetation，obviously has roots.Some roots were also plucked for analysis.The roots and root extraction produced macropores.Our SHAWmodels do not represent any macropores.Mapping centimeter to perhaps decimeter scale variability in soil physical properties was not an early goal of the initial characterization of the sites，and monitoring any changes is close to impossible given all other measurements being done.Unfortunately，this is the scale over which such models such as SHAW are implemented，and some inputs may even vary over f iner scales in the real world.One indicator of these issues in spatially varying soil hydraulic properties is the very dynamic soil moisture in the deepest location at 91.5 cm.This location goes from very wet to very dry，both aspects missed by the SHAW models.Since this behavior is unlikely driven by plants given the depth，this is likely the outcome of a unique combination of soil hydraulic properties.Soil water has to be able to go through this zone like a relative fast piston，which would indicate a texture that is coarser than prescribed.

The plant properties we imposed(e.g.，those in Fig.2)may also vary from year to year and could exhibit some higher frequency variations，but the latter is less likely.Interannual variations could possibly lead to memory effects with signals from previous years affecting those of the following year.One of the critical plant parameters in SHAW，and any biophysical model，is the stomatal resistance.The values we used here are based on limited measurements.Thus，there is some uncertainty introduced with imposing the measured stomatal resistance values.They may have also varied through time and the values imposed may not be the most representative.

The FACE sites offer a unique but challenging opportunity for testing distributed models of soil water f low across the soil-plant-atmosphere continuum.However，the typical instrumentation and monitoring design of a site like BioCON may prevent a robust test for whether models are representing the myriad processes correctly and where improvements are needed.Doing so would，unfortunately，require more detailed measurements of soil moisture and soil physical properties in space and time.These are not only time-and resource-intensive，but their invasive nature may run counter to the primary goals of the FACE experiments.

The detailed representation of many physical and physiological processes within models such as SHAWresults in endless possibilities of parameter combinations.This led us to the strategy of simply imposing most parameters following observations or standard values representative for the specif ic vegetation and soils present in the studied plots.This study is certainly just a start.We recommend that a more robust test of a soil water f low model includes frequent，if not continuous，soil moisture monitoring and a broad analysis of some parametersvia，e.g.，Monte Carlo simulations.

Some biophysical implications following the model results

The higher water use efficiency by vegetation at high CO2levels is not a surprise，as it is a prescribed feature of the SHAWmodels implemented.However，here we showed that the observed differences in stomatal resistance can produce noticeable differences in the modeled soil water budget，even when LAI is higher than what was observed independently and empirically in the f ield experiment(Adairet al.，2011).Thus，our study further suggests that CO2fertilization leads to less transpiration and potentially wetter soils in the grassland ecosystems of Minnesota，and likely in ecosystems where the relative shifts in stomatal resistance and LAI are of comparable magnitudes.However，increasing CO2levels imply other changes，e.g.，increasing temperatures.Temperature increases could lead to higher evapotranspiration rates，which could completely counteract the increase in soil moisture caused by the higher water use efficiency of plants.The SHAW model is a potentially useful modeling framework for investigating these changes.

CONCLUSIONS

We simulated soil moisture at the BioCON FACE site using the SHAWnumerical model.Three representative sites were considered:a bare plot，a vegetated plot with ambient CO2，and a vegetated plot with high CO2.The simulations were populated by f ield-observed parameters and boundary conditions.The SHAWmodel qualitatively reproduced patterns of observed soil moisture dynamics across a vertical soil section without any calibration.However，quantitative comparisons revealed that the model inadequately predicted point and instantaneous values of soil moisture.The model mostly captured the mean state and behavior.

The SHAW model was able to simulate the expected result of higher evapotranspiration and lower total water content for vegetated soil than for bare soil.The higher total water content for the bare plots occurs due to the lack of the transpiration.Evapotranspiration at high CO2conditions was smaller and water content was higher when compared to ambient CO2conditions.The difference is primarily due to higher imposed stomatal resistance at elevated CO2conditions as well as higher plant and residue biomass.Thus，given that SHAWreproduces soil moisture patterns for the different vegetation-CO2treatments，the simplif ied biophysical representation of transpiration and the soil-plant-atmosphere continuum in SHAW appears to be adequate and holds promise for future applications in assessing the impacts of increasing atmospheric CO2.However，the limited measurements available for model testing so far indicate some delinquencies in the model or how they are parameterized.The available soil moisture measurement and observations of input parameters prevent a robust and conclusive analysis of whether SHAW is capturing or missing certain local，instantaneous or broad dynamics for the right reasons.We conclude that a hydrologic-biophysical model such as SHAWremains a promising complement for FACE and other manipulation experiments，given that the pitfalls can be overcome.

ACKNOWLEDGEMENTS

The BioCON experiment and the author PBR were supported by the National Science Foundation(NSF)Long-Term Ecological Research(LTER)grants(Nos.DEB-0620652，DEB-1234162，and DEB-1831944)，Long-Term Research in Environmental Biology(LTREB)grants(Nos.DEB-1242531 and DEB-1753859)，and Biological Integration Institutes grant(No.NSF-DBI-2021898).The authors MBC and RHFwere supported by the Geology Foundation at The University of Texas at Austin.The author RHFwas supported by an Ivanhoe Foundation Fellowship.