The 3-dimensional 3-D volume averaged soil-moisture transport VAST formulation is derived from the Richards equation to incorporate the lateral flow and subgrid hetero- geneity due to t
Land Surface Models 2 QC Q Q Q Q Q Vy 1
As climate models progress with higher resolutions, their complexity demands sophisticated land-surface parameterization to capture intricate processes at smaller scales Advanced Land Surface Process Models (LSPMs) have emerged to meet this need, evolving from basic bucket models to incorporate photosynthesis simulations and dynamic vegetation dynamics These models play a crucial role in representing processes such as ecohydrology and biogeochemistry, but their efficacy depends on characterizing water cycle processes at finer scales than currently implemented Additionally, determining the processes that become more prominent at higher resolutions and developing appropriate modeling approaches is vital for enhancing the predictability and applicability of these models at smaller scales.
Principal among these issues is the question of the impact of the heterogeneity of land- surface processes that are induced by a variety of factors such as vegetation, soil-properties, topography, etc Satellite remote sensing products have played a significant role in improving the predictability of many of these processes, both through better model parameter estimates and increasingly sophisticated assimilation schemes Although topographic data is one of the most readily available high resolution products with continental and global coverage, hetero- geneity induced by topographic characteristics, such as slopes and curvatures, is generally not well represented in the models Topographic variability influences a variety of processes including soil-moisture flux, snow accumulation and melt and the associated albedo, vege- tation response to climate variability, watershed-floodplain-stream transition processes, etc Availability of high resolution Digital Elevation Model (DEM) data offers unprecedented opportunity for representing and dealing with the scaling issues of these processes, at least to the extent that topographic attributes are a controlling factor This will also reduce large model errors that sometimes result in complete inability to predict certain important processes, such as subsurface moisture convergence in the topographic hollows or riparian vegetation controls on watershed-atmosphere feedback The model errors, in the absence of appropriate parameterizations, often manifest as non-linear drifts in the dynamical response Constraining the model through assimilation of observations serves to only temporarily al- leviate the problem without any significant improvement in either process understanding or predictability of the model
Effects of topographic variability for land-atmosphere interaction studies have been in- corporated through the development of basin-scale hydrologic models These include the
“catchment” model of Koster et al (2000) and “Large Area Basin scale” (LABs) model of Chen and Kumar (2001) These models have been implemented using model scale statistics derived from GTOPO30 DEM data (1-km resolution) Basin scale representation enables us to account for lateral sub-surface flow as well as spatial heterogeneities induced on en- ergy fluxes by the variability of soil-moisture state Chen and Kumar (2001, 2002, 2004) have shown that modeling the topographic control has significant impact on the water table dynamics and on the predictability of moisture and energy fluxes Further, in regions of
ENSO influence they are able to better characterize the inter-annual variations of deep layer moisture and energy (temperature) variations
However, as the model resolutions improve, some of the underpinnings of hydrologic parameterizations so crucial in the predictions of energy and moisture fluxes become invalid Chief among these is that they use moisture transport equations that either have no physical basis at the scale of the model (1-D Richards equation valid for a differential scale but not at the scales implemented in climate models) or the assumptions are not valid at multiple scales (water table parallel to the topographic surface as in Topmodel (Beven and Kirkby 1979)) These models are being implemented in sophisticated assimilation schemes utilizing high resolution satellite data such as from the Terra and Aqua platforms However, owing to the model deficiencies resulting from the unrealistic assumptions, several processes tied to the moisture state have limited predictability Often these model deficiencies impact the estimates of other variables and related fluxes such as surface energy, surface runoff and stream flow With increasing resolution of the climate models it is now possible to perform finer resolution prediction and better assess climate impact on terrestrial processes However, for such studies to be successful, the predictability has to improve at the sub-monthly time scale and spatial scale of the order of km These scales are significantly smaller than what is possible now It is important to note that although model predictions currently are performed at very small time scales the validity of the results are assessed at the monthly to seasonal and annual time scale averages
Topography's small-scale variability, particularly in complex terrains, significantly contributes to uncertainties in climate models' predictions of processes like elevation, slopes, and curvatures This variability, often unresolved at the global and regional scales used in climate models, can substantially impact these predictions.
They are essential to model for improved predictability related to studies of land-atmosphere interaction and terrestrial impact of climate variability
Within this context, the objectives of this research are:
Objective 1: Develop a 3-Dimensional Volume Averaged Soil-moisture Transport (VAST) formulation that scales from a point to model grid scale and accounts for sub-grid variability
Objective 2: Develop appropriate data sets for the implementation of the new coupled model
Objective 3: Perform new coupled model simulations by VAST-based Common Land Model (CLM) using North American Regional Reanalysis (NARR) forcing data
One of the most important components of the Soil-Vegetation-Atmosphere-Transport (SVAT) schemes is the terrestrial soil-moisture transport scheme determining surface and subsurface runoff processes that have a large effect on the surface energy balance However, soil-moisture transport equations remain so simplistic that most land surface models in the SVAT schemes consider only vertical mean soil-moisture transport within a closed bucket of soil layers with neither lateral flow nor subgrid flux contribution Recently the new layer averaged formulation based on the Richard’s equation has illustrated that the lateral transport driven by topographic attributes can be a significant component of the total soil- moisture flux (Kumar 2004) Besides, it is common in most land surface models coupled with the climate model that meteorological processes interacting with hydrological predictions occur in a rectangular grid mesh and grid-scale soil-moisture values are simulated for energy flux forecasts For the better prediction of hydrologic processes in the SVAT schemes, the first objective of this research focuses on developing the VAST formulation incorporating lateral and subgrid fluxes due to topographic characteristics at a grid-scale Parameters characterizing subgrid variability are represented as a scale dependent function with second order approximations These parameterizations incorporate statistical properties related to
4 soil-moisture variability dependence on subgrid topographic attributes such as slopes and curvatures The analyses through analytical and numerical methods show that the lateral and subgrid flux contribution plays a significant role in total soil-moisture dynamics, and the flux due to subgrid spatial variability is as much or larger than grid averaged flux, especially in drier condition Numerical implementation of the model is done using a time splitting scheme applying an explicit method for lateral flow after a fully implicit method for vertical flow In addition, this VAST model is implemented with a surface flow routing scheme through resolved flow directions at the model grid scale while most current models roughly estimate the runoff from the soil water budget without any explicit routing schemes This conjunctive surface-subsurface flow scheme can better predict runoff due to both rainfall excess and soil-surface saturation
Surface Boundary Conditions (SBCs) are required for VAST-based land-atmosphere cou- pled model simulations The SBCs are constructed for the CWRF model which is the climate extension of the next-generation Weather Research and Forecasting (WRF) model (Klemp et al 2000, Michalakes 2000, Chen and Dudhia 2000), incorporating all WRF functionali- ties for Numerical Weather Predictions (NWP) while enhancing the capability for climate applications The second objective of the research focuses on the construction and imple- mentation of appropriate SBCs specifically designed for general CWRF mesoscale modeling applications Existing observational databases have various resolutions, and a wide range of map projections and data formats, and often contain missing values or inconsistencies between variables This presents significant challenges and requires labor-intensive efforts to process the data onto the Regional Climate Model (RCM)-specific grid mesh and input data format Horizontal data remapping uses Geographic Information System (GIS) software tools to determine the geographic conversion information from a specific map projection of raw data to the identical CWRF grid system using the best observational data combined with or chosen from various dataset sources Finally, ArcInfo’s Arc Macro Language (AML) programs are created for processing procedures corresponding to each raw data source used to construct any specific CWRF domains over the globe For U.S applications, the domain is centered at (37.5N, 95.5W) using the Lambert conformal map projection and a 30-km hor- izontal grid spacing, with total grid points of 195 (west-east) x 138 (south-north) The do- main covers the entire continental U.S and represents the regional climate that results from interactions between the planetary circulation and the North American surface processes, including orography, vegetation, soil and coastal oceans The primary SBCs include surface topography (mean elevation, slopes, curvatures, and their standard deviations); bedrock, lakebed, or seafloor depth; soil sand, and clay fraction profiles; surface albedo localization factor; bottom soil temperature; surface characteristic identification; land cover category; fractional vegetation cover; leaf and stem area index; sea surface temperature, salinity, and current; and sea temperature and salinity profiles
The third objective of the research is to perform land-atmosphere model simulations using the VAST model that is incorporated into the CLM (Dai et al 2003), a state-of-the-art SVAT and already coupled with CWRF, with numerous crucial updates for land processes This new coupled model provides a more accurate, flexible, efficient, and consistent coupling with other components of regional and global models The new coupled model (CLM + VAST) simulations using realistic SBCs and NARR forcing data provide substantial im- provements in understanding of the role of topography in terrestrial hydrologic processes and predictability of the model
This research consisting of three parts is schematically illustrated in Fig 1.1.
Model Development Construction of | Topographic Impact |
Richards Various raw data NARR quation | ] Meteorological
30,000, we use the resistance coefficient for wide channels suggested by Yen (1991, 2002) as
1 ke 1.95\]7~? fa= 1 | (ly + am | > (4.14) where k, is the equivalent sand grain roughness size and this equation is available at the relative roughness k,/h < 0.05
The diffusion wave equation in a wide rectangular channel can be obtained by combining
Oh oh Oh p,, at Ox 9z2 ° (4.15)
94 where cy is the diffusion wave celerity, which can be approximated for gentle-slope case as
3 3 ah cq = su = Cy h| So ch - — |, (4.16) 4.16 and Dy, is the hydraulic diffusivity expressed as
For the small pressure gradient, cq and D), can be further simplified as follows: ca“ 5V hSo 3 (4.18)
There can be many converging junctions in the channel network generated from the DEM The boundary conditions for mass and energy conservation at any junction is required for a channel network simulation (Sevuk and Yen 1973, Choi and Molinas 1993, Jha et al 2000) The continuity equation assuming no change in storage volume at the junction can be expressed as
` Qout _ ằ Qin = 0, (4.20) where @ is discharge through the whole channel cross section The subscripts in and out denote inflow and outflow channels, respectively, at the junction The equation of energy conservation for each branch is approximated as
4.2.3 Coupling of surface and subsurface flows
A common internal boundary condition by comparison between the supplied rainfall and the potential infiltration capacity is required for coupling the surface flow (Eq (4.15)) and subsurface flow (Eq (4.1)) models
The net water supply rate P, on the surface is
Pr = Py +Sm—- Ey, (4.22) where P, is the rainfall rate reaching the ground including interception captured by, through- fall passing through, or drip along the edge of the plant canopy S,, is the snow melt rate, and E, is the evaporation rate from the ground surface
The water supply rate P, by the total available flow depth h + P,,At on the surface for a time-increment At is
The maximum infiltration rate, Jp, is determined assuming saturated surface soil moisture during rainfall events and a linear moisture profile from the surface to the center of the first soil layer This assumption is based on the work of Mahrt and Pan (1984), Abramopoulos et al (1988), and Boone and Wetzel (1996) Consequently, the upper boundary condition at the top of each soil column is computed as Jp for rainfall events.
Fz, = — min|P;, jạ|, (4.24) where Fz, is the vertical flux at the top of each soil column
The subsurface flow calculation is performed using Eq (4.1) under the surface boundary condition (Eq (4.24)), and the available surface flow depth is updated by infiltration as h = max|0, h — TạAl] (4.25)
The water supply rate exceeding the maximum infiltration rate causes the surface runoff as
Ry = max (0, P; — lạ — h/Atl, (4.26) where Ry is rainfall excess surface runoff due to the excess precipitation intensity over the soil infiltration rate
Another type of runoff can occur when the moisture content exceeds soil storage capacity at the surface layer as
Rp = max (0, 6 ~x 6; 4] "Ai" AZ, (4.27) where ỉ,; is the porosity, and AZ; is the thickness of the first layer i#p is the satura- tion surface runoff that occurs when subsurface flow saturates the soil If precipitation exceeds evapotranspiration and interception by canopy, the infiltrating water may collect above bedrock layers, which may cause excess water greater than porosity near the surface (see also Section 4.4.4)
Finally, the total available surface runoff is obtained from the summation of the two Eqs (4.26) and (4.27) as
When either of the two surface runoffs occur, the surface flow calculation starts using Eq (4.15)
The flow chart for the conjunctive surface-subsurface flow scheme is shown in Fig (4.1) This computation routine needs iterations until solutions are stable for both surface and subsurface flows before the next computation time step But, the numerical scheme used for this conjunctive model decouples subsurface flow and surface flow computations, and solves the two equations separately only once during a computational time step At because of the slow response of subsurface flow to the variation of surface flow depth This decoupled method can reduce the computational time significantly without a large influence on the
97 accuracy of the results (Akan and Yen 1981a, Singh and Bhallamudi 1997, and Morita and Yen 2002) See also Appendix D.4
Rainwater Supply Rate Maximum Infiltration Rate
Ps H/At = h/Att Pa lo ~fh(1)
Boundary Condition for Subsurface Flow
Update Flow Depth Subsurface Flow Calculation h =maxth -loAt, 0} for New Soil-moisture
Ru miax{ Ps - lo-h/At, 0] Ro = max{1-Os,1, JAZ At h=0 and Rs=0 Update
Rs = Ru +.Rp h>0 or Rs>O
Surface Flow Calculation for New Flow Depth h
Figure 4.1: Flow chart of the conjunctive surface-subsurface flow model calculation
Implementation c Q Q Q Q c Q ng g vn v v21 v2 99
4.3.1 Numerical scheme for subsurface flow
For the discretization of a vertical soil column in CLM (Dai et al 2001) a soil layer at the node depth d; [m] is given as d, = — (sá-? ~ 1) | k=1,2, ,N (4.29) where NV is the total number of soil layers
The thickness AZ, [m] of each layer is
AZ = § 0.5(der1 —dy-1), k=2,3, ,N-1 (4.30) dp, - đụ ~1, k = N
The depth Z¿ [m]| at the interface is
For more efficient implementation of the VAST, we use time splitting numerical scheme that applies a fully implicit method for vertical flow and an explicit method for lateral flow
We can rewrite equation (2.26) as
99 where © is an operator formed by the sum of two time-independent operators Oy and O, for vertical flow and lateral flow, respectively
The first step is to evaluate the points on the grid for the vertical transport using the implicit scheme as
6° = 6" + AtOy (6°), (4.33) where 6° is a temporary quantity computed at the first fractional step s
The second step is to use this temporary value 6° to evaluate the points on the grid for the lateral transport using the explicit scheme as grt? = 9° + AtO,(6°) (4.34)
Thus, all points on the grid mesh are updated at the new time level n +1 (t+ At) The details on this time splitting scheme for the vertical flow are described in Appendix D
4.3.2 Numerical scheme for surface flow
The MacCormack finite difference scheme (MacCormack 1971) is one of splitting methods which is an explicit scheme with second-order accuracy in both space and time This scheme was first introduced to solve nonlinear fluid dynamics aeronautical problems and is now used to solve various types of surface flow equations (Zhang and Cundy 1989, Singh and Bhallamudi 1997, 1998, Kazezyilmaz-Alhan et al 2005) It consists of the predictor step using a forward difference and the corrector step using a backward difference in space This scheme is known to be computationally more efficient than the Leapfrog scheme (Playan et al., 1994) Kazezyilmaz-Alhan et al (2005) also shows that the MacCormack scheme is comparable to the 4-point implicit scheme in accuracy and the most efficient method for practical purpose See Appendix D for the details of the MacCormack finite difference method used for the surface flow calculation
New Model Application 0.0.0.0 00000000 cee ee 101
This subsection presents the application of the new coupled land surface model, VAST- based CLM model (CLM+VAST), for a study domain including the Ohio Valley around the Appalachian mountain region Figure 4.2 shows the study domain with the size of 750km (25 x 30km) by 600km (20 x 30km), which is a part of the computational domain with a 30-km horizontal grid spacing in a current RCM (Liang et al 2004) The land cover types are dryland cropland and pasture, cropland/woodland mosaic, deciduous broadleaf forest, evergreen needleleaf forest, and mixed forest The conjunctive surface-subsurface model based on the VAST model is substituted for the existing terrestrial hydrologic scheme in the latest version of CLM as shown in Fig 4.3 While the current CLM model performs all computations for each component at an individual soil column, the lateral subsurface flow and surface runoff are calculated after the vertical subsurface calculation is done using a time-splitting method in the CLM+VAST model The other schemes in the latest version of CLM are identically used for the CLM+VAST model simulation See the CLM document (Dai et al 2001, 2003) for the detailed descriptions for radiation, energy flux, canopy, snow, and so on
This new land surface model simulation is performed using North American regional reanalysis (NARR, http://www.emc.ncep.noaa.gov/mmb/rreanl/) forcing data from 1995 to 2000
Figure 4.2: Study domain around the Ohio Valley region including 30-km resolved flow directions (blue arrows) for 30-km computational girds (25 x 20) representing DEM (green- brown pizels) with overlays of 1-km HYDROIK stream network (red lines), level-4 basin boundaries (white polygons), and four USGS stream flow gauge stations (red spots) selected within the study domain
The CLM, a state-of-the-art model for Soil-Vegetation-Atmosphere Transfer (SVAT), was incorporated into the CWRF Major CLM characteristics include: a 10-layer prediction of soil temperature and moisture; a 5-layer prediction of snow processes (mass, cover, and age); an explicit treatment of liquid and ice water mass and their phase change in soil and snow; a runoff parameterization based on the Topmodel concept (Beven and Kirkby 1979); a canopy photosynthesis-conductance scheme that describes the simultaneous transfer of carbon dioxide and water vapor to and from vegetation; a tiled treatment of subgrid fraction of energy and water balance; and high-resolution geographic distributions of land cover, vegetation, and root and soil properties The CLM has been evaluated extensively in stand-
Dai et al (2003) demonstrated the accuracy of the 102 alone mode through field measurements, indicating its ability to realistically simulate soil moisture, soil temperature, snow water equivalent, and flux terms such as net radiation, latent and sensible heat fluxes, and runoff.
CLM clmetl CLM clmctl netsolar leafinterception netsolar leafintereeption newsnow thermal newsnow thermal snowcompaction snowlayerscombine snowlayersdivide snowage lake seafluxes snowcompaction snowlayerscombine snowlayersdivide snowage lake seafluxes
Figure 4.3: Comparison of model structures between the latest version of CLM and the coupled CLM+VAST models
The latest version CLM incorporates several important updates and new modules Major updates include a two-leaf (sunlit and shaded) canopy treatment for temperature, radiation, and photosynthesis-stomatal resistance; a two-stream approximation for canopy albedo; the bedrock depth effect on soil thermal and hydrological processes; a new canopy interception treatment accounting for partitioning between convective and stable precipitation; turbulent transfer under the canopy; an efficient iterative solution for leaf temperature; separation of surface and subsurface runoff; rooting fraction and water stress on transpiration; and perfect energy and water balance within every time-step A dynamic vegetation module (DVM) that integrates the interactive canopies with the full carbon and nitrogen cycling mechanism (Dickinson et al 1998, 2002) has been added to represent two-way interactions between
103 climate and biosphere processes over a wide range of temporal scales from minutes to decades The DVM combines process-based representations of terrestrial vegetation dynamics and land-atmosphere carbon, nitrogen, and water exchanges in a modular framework Features include feedbacks through canopy conductance between photosynthesis and transpiration and between these "fast" and other "slow" ecosystem processes, such as tissue turnover, and soil organic matter and litter dynamics See the CLM document (Dai et al 2001) for the detailed descriptions for each subroutine in the latest CLM model
A comprehensive set of SBCs based on the best observational data for CWRF general appli- cations are constructed in Chapter 3 The required parameters for land are HSFC, HSDV, HSLD, DBED, SAND, CLAY, SALF, SCI, LCC, FVC, LAI and SAI in Table 3.1 In addi- tion, the 30-km resolved flow direction is needed for the surface flow calculation The flow direction derived from a coarse resolution (30-km) DEM may not represent well the feature of the real stream network Following Lear et al (2000), the Double Maximum Algorithm (DMA) is used to determine the most realistic representation of the upscaled river network at a 30-km grid spacing Figure 4.2 shows the 30-km resolved flow directions along with the HYDROIK stream network for the study domain
Meteorological forcing data and initial conditions
The NARR data are used in this study for the forcing data from the atmosphere to drive the models as listed in Table 4.1 The NARR data is a long term set of consistent climate data on a regional scale for the North America domain The 32-km resolution NARR at a time step of 3 hours are linearly interpolated and remapped for the model computational domain with a 30-km horizontal grid spacing for the period of simulations (1995-2000) Although
104 the hydrologic scheme of the CLM model is run at a computational time step of 10 minutes, the spatially interpolated NARR data are also linearly interpolated to the model time step without the temporal variability The NARR data values at the first simulation time step (January 1, 1995 00:00) are used to initially drive the models Initialization is done using a spin-up strategy The model run is repeated two times using the 1995 data set, and the conditions at the end of the second run are used to obtain the initial conditions for the simulations from 1995 to 2000
Table 4.1: Atmospheric forcing data required to drive the CLM model
Variable Unit pressure at the lowest atmospheric layer Pa temperature at the lowest atmospheric layer K specific humidity at the lowest atmospheric layer kg/kg zonal wind at the lowest atmospheric layer m/s meridional wind at the lowest atmospheric layer m/s the lowest atmospheric layer height m pressure at surface Pa convective rainfall mm resolved rainfall mm snow mm planetary boundary layer height m downward longwave radiation onto the surface W/m? downward short wave flux at ground surface W/m?
The observed daily stream flow discharges during 1995 - 2000 are obtained from the USGS
National Water Information System (http://waterdata.usgs.gov/nwis/sw) for the model val- idation We select four stations near each outlet on the four basins which are not connected to the outside of the study domain; Kanawha River at Charleston, WV (03198000), Ken- tucky River at Lock 4 at Frankfort, KY (03287500), Green River at Lock 2 at Calhoun,
KY (03320000), and Tennessee River AT Chattanooga, TN (03568000) These locations are marked on Fig 4.2 and the details are summarized in Table 4.2
Table 4.2: Stream flow gauge stations for validation of model simulations The drainage area for each station is documented by USGS and the computational grids are selected corresponding to each drainage area for the four basins
Station Name (Station ID) Drainage Area Contributing Area
[km?] in the Model [km?]
Kanawha River at Charleston, WV (03198000) 27,060.2 28,800
Kentucky River at Lock 4 at Frankfort, KY (03287500) 13,706.2 13,500 Green River at Lock 2 at Calhoun, KY (03320000) 15,622.8 15,300
Tennessee River at Chattanooga, TN (03568000) 55,425.7 56,700
At the top of each soil column, the flux Fz, computed in Eq (4.24) represents the actual infiltration rate The maximum rate of the potential infiltration is defined as
The above equation is derived from the saturated surface assumption during rainfall events used in soil models (Mahrt and Pan 1984, Abramopoulos et al 1988, and Boone and Wetzel 1996) This infiltrability also cannot exceed the maximum possible influx caculated using the soil water budget at the first layer as
F29,mox = Fz, + Ey + (65,1 — ĐT AZ, (4.36)
The other key property in hydrologic modeling is the bedrock profile which is generally neglected or roughly assumed as the lowest model layer in most LSMs It may over estimate soil-moisture memory in deeper zones resulting in unrealistic representation of the terrestrial hydrology and the regional water recycling processes The bedrock acts as a bottom lid that effectively prevents downward water flux, and the bedrock is one of the factors affecting the sub-surface moisture dynamics It raises the water table and limits moisture storage available in the soil column, which has significant impact on surface energy and water flux dynamics (Chen and Kumar 2001) Although water may rarely penetrate the fresh bedrock, the moisture flux can occur through fractures, fissures, and cracks in the rock However, it is difficult to model the mechanism of the fracture flow in the bedrock, and moreover the bedrock information and rock property data are not sufficient to use To estimate
107 drainage through bedrocks we use a drainage parameter w as introduced in soil models such as SSiB (Simplified Simple Biosphere; Xue et al., 1991), GISS (Goddard Institute for Space Studies; Abramopoulos et al., 1988), PLACE (Parameterization for Land-Atmosphere- Cloud-Exchange; Boone and Wetzel, 1996), SiB2 (Simple Biosphere; Sellers at al., 1996b), and so on We assume that the saturated hydraulic conductivity of bedrocks is 1% of K,, at the lowest soil layer above the bedrock layer We extend one more layer from the current 10-layer model for the model to contain the ground water level or bedrock depth within the model soil layers Since the last layer may be located below either the bedrock or water table depths, the vertical gradient of soil-moisture can be negligible Hence, the diffusion terms are neglected and drainage terms work for the vertical flux at the lower boundary as
Summary 2 ee eg 139
Although the subsurface subgrid and lateral flows have a significant impact on the spatial soil-moisture variability and the surface runoff is also one of the important components for the terrestrial hydrologic cycle, most LSMs simplistically estimate or totally neglect them in the surface water budget In most existing LSMs, soil-moisture transport occurs only in the vertical direction and the surface runoff is estimated from the net water flux which is effective precipitation minus evapotranspiration on the surface and surface soil-moisture storage Therefore, a conjunctive surface-subsurface flow model that can be coupled to the current LSMs is required for the comprehensive terrestrial water and energy predictions In this sudy, the new conjunctive surface-subsurface flow model based on the VAST model is developed to incorporate subgrid and lateral fluxes, and surface flow routing which are not modeled in most current LSMs This new terrestrial hydrologic scheme is implemented by the mixed numerical methods The 3-D VAST model is implemented using a time splitting scheme by separating the vertical and lateral components of the equation After the vertical flow is solved by a fully implicit method using the linearized form of the discretized equation for the first fractional time step, an explicit method applies for the lateral flow calculation for the next time level quantities For the surface flow calculation, 1-D diffusion wave model is solved by the MacCormack finite difference scheme which is an explicit scheme with the second-order accuracy in both space and time
The existing hydrologic scheme in the Community Land Model (CLM) is replaced with a new conjunctive surface-subsurface flow model to enhance model predictability and investigate the effects of topography-induced parameterizations on the terrestrial water and energy balance This updated model is applied to the Ohio Valley region using the NARR forcing dataset.
1995 to 2000 in the off-line mode All model simulations are performed using the published model parameter values without calibration for them except for the reference depth Z, for
139 the saturated hydraulic conductivity and the anisotropy ratio ¢ Their values are examined through the sensitivity analysis and then a parameter set is chosen The selected values of the two parameters are identical to the values published in Chen and Kumar (2001) The predicted stream flow hydrographs are compared with the observations at the four USGS stream gauges selected within the study domain although it is difficult to compare model predictions with observations because of the regulations due to dams and reservoirs The heavy snowfall events in every winter season during 1995-2000 cause the high flow results as compared with observations The recession curves in the hydrographs from the new model decline more quickly than observations It seems to be due to the lack of base flow and channel flow schemes in the current CLM model In general, the predictions from the new model capture the trend and variability in the observations except for the high winter flow This study shows that the surface flow routing and its interaction with the subsurface flow can improve the stream flow prediction significantly and has a large impact on the surface energy balance as well Ignoring the role of surface flow depth on the infiltration rate causes errors in both surface and subsurface flow modeling The surface runoff contribution to the water supply rate on the top soil layer increases the soil-moisture water contents and the latent heat flux on the surface, and this increased latent heat flux is compensated by a re- duction in the sensible heat flux especially during summer as a result The spatial variability of subsurface moisture has a large impact on the surface water and energy balance, which is sensitive to climate variability and change
In the new model scheme, the infiltrating water to the soil layer can be over estimated when the surface water in a grid along the overland flow lines infiltrates through the whole grid area if the underneath soil-grids are not saturated This can be improved when the mosaic subgrid scheme and saturation fraction are incorporated in the future CLM
Summary and Conclusions 0 0 000.0 ce ee eee ee 141
Regional Climate Models (RCMs) allow us to downscale the results of Global Climate Models (GCMs) to the resolution of tens of kilometers Winds and other predictions from GCMs are used for the initial and lateral boundary conditions of RCMs RCM simulations at higher resolutions are necessary for resource management and impact assessment, for example, climate change effects on water resources, ecosystem, extreme weather, hurricane frequency, etc As the resolution increases, the Land Surface Model (LSM) component in RCMs needs to incorporate more sophisticated linkages and process interactions at small scales to represent their aggregated effect on larger scales This requires improved parameterizations of key subgrid processes, especially for terrestrial hydrologic schemes whose description remains more simplistic as compared to the remarkable increase in the details describing the canopy processes In particular, the heterogeneity effects induced by topographic characteristics within a model grid are poorly modeled or totally neglected in most existing LSMs, although topographic data are readily available at fine resolution (< 1 km) for the globe
Using a novel terrestrial hydrologic scheme, this study aims to enhance the predictive capabilities of current land surface models (LSMs) The scheme captures the spatial variability of subsurface moisture induced by topography, significantly influencing the surface water and energy balance By coupling this improved hydrologic module with the Climate extension of the next-generation Weather Research and Forecasting (CWRF) model, we aim to deepen our understanding of the intricate interactions between land-atmosphere processes and climate variability.
141 for advanced regional, continental, and global hydroclimatological studies and assessments This chapter provides a brief summary of the study, the obtained results, and limitations of this work, and proposes future research tasks to leap into an unprecedented evolution of LSMs
Topographic attributes, such as elevation, slope, and curvature, have a significant impact on the spatial variability of subsurface moisture flux transport To account for these effects, a 3-D Volume Averaged Soil-moisture Transport (VAST) model has been developed, which incorporates topographic variability into subsurface moisture dynamics through scalable parameterization By decomposing the moisture transport equation into mean and fluctuation components, the VAST model explicitly incorporates the variability of moisture flux and lateral flow due to topographic attributes, in addition to the grid-mean moisture flux This formulation allows for the estimation of model parameters at the scale of interest and can be integrated into existing Land Surface Models (LSMs) for accurate representation of subsurface moisture dynamics.
I analytically examine the contribution of new variability terms to the grid-mean flux terms in the VAST formulation Two offline tests for the VAST model are also done using the realistic Surface Boundary Conditions (SBCs) with/without the consistent North American Regional Reanalysis (NARR) meteorological forcing data for a study domain with a basin size of 176,400 km? around the Ohio Valley region The first test compares the simulation result from the full VAST model with that from its 1-D vertical mean transport only version that resembles a traditional LSM scheme The simulations are done under an initially saturated condition without any source and sink terms during the model integration 3-D VAST results show the spatial soil-moisture redistribution by subgrid and lateral fluxes incorporated in the new model In the second test, the VAST model is coupled to the Common Land Model
(CLM), which is a state-of-the-art LSM Both CLM and CLM+VAST are initialized and subsequently driven by the NARR forcing data as the best proxy of observations during June to August in 1995 Besides the subgrid topographic effects, the CLM+VAST incorporates, at the 30-km grid resolution, all other spatial variability of local-controls, such as precipitation, evapotranspiration, vegetation and radiation, as included in the CLM Substantial regional differences are identified with the incorporation of lateral and vertical subgrid fluxes induced by topographic effects
From results through both analytical and numerical investigation, I conclude that: [1] The flux contribution of the subgrid variability is larger than or comparable to that of mean flux, particularly under drier moisture conditions; [2] In general, the VAST model simulates drier soils on the hillslopes as the topography-induced lateral and subgrid fluxes move water toward lower valleys; [3] The CLM+VAST simulates overall drier soil moisture in layers near the root zone because the VAST model includes the additive lateral and vertical subgrid fluxes The spatial moisture distribution at the first soil layer also depends on local-control factors such as the evapotranspiration rate on the surface; and [4] It is evident from both analytical and numerical tests that the new terms due to topographic features included in the VAST model play a significant role in determining total soil-moisture dynamics
This research also focuses on developing high-quality surface boundary conditions for general use in mesoscale regional climate models This new SBC development is motivated by the limitations and inconsistencies of existing SBCs incorporated into RCM simulations
So, the primary effort is in the thoughtfulness given to the data quality and the product accuracy The utility of this set of SBCs should stand on its own given the myriad of scientific justifications and quality-controlled procedures that are underpinning its creation Although the SBCs are constructed onto the 30-km CWRF domain, they can be readily incorporated into any RCMs suitable for the U.S climate and hydrology simulations I also elaborate in
143 detail processing and validation procedures, by which SBCs (especially those derived from remote sensing data) can be constructed for any specific domain over the globe Although
I have strived for the best-available quality data, comprehensive processing procedures, and diligence to ensure of consistency between alternative sources, the SBCs so constructed do carry over uncertainties inherent in the raw data
Given the current understanding of physical processes and data uncertainties, I conclude that: [1] RCMs should incorporate 3-D soil characteristics by integrating geographically varying bedrock depth with soil sand and clay fraction profiles, rather than using verti- cally constant quantities based on soil texture categories; [2] RCMs can combine the static fractional vegetation cover with varying leaf plus stem area indices to represent vegetation spatial and temporal variations, for which both data from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensors and the Advanced Very High Resolution Radiometer (AVHRR) satellites must be corrected to create a long coherent record while removing the obvious error and discontinuity The monthly leaf area index (LAI) data from MODIS are systematically less than those from AVHRR data, particularly for the growing season in croplands [3] RCMs need to prescribe daily Sea Surface Temperature (SST) variations us- ing the most appropriate Real-Time Global (RTG) SST data currently available or otherwise the iterative, conservative spline-fit to the weekly Optimum Interpolation (OI) SST data, but presently prohibited from the direct use of the new fine-resolution MODIS data that suffer from large gaps and errors
The surface runoff is also one of the important components for the terrestrial hydrologic cycle However, most LSMs simplistically estimate the surface runoff using the soil water budget without any explicit simulation or routing schemes Moreover, this roughly generated runoff is not used as the boundary condition for the subsurface flow calculation, which may result in a mass balance error in the water cycle Ignoring the role of surface flow depth on the
144 infiltration rate causes errors in both surface and subsurface flow calculations Therefore, a conjunctive surface-subsurface flow model is necessary for the comprehensive terrestrial hydrologic simulation I have developed a 1-dimensional diffusion wave model interacting with the VAST model for better surface flow predictions in LSMs at a large scale
The developed formulations are implemented using the mixed numerical schemes for each flow component The 1-D diffusion wave model is solved by the MacCormack finite difference scheme, and the 3-D VAST model is implemented using a time splitting scheme by separating the vertical and lateral components of the equation An explicit method is used to solve the lateral flow after a fully implicit method for vertical flow Since the spatial variability of the surface and subsurface water is not well captured in the current LSMs using a 1-dimensional simplistic flow scheme, this conjunctive surface-subsurface flow scheme is substituted for the existing 1-D scheme in the CLM, to improve the model predictability Consequently, the new model includes subgrid heterogeneity, subsurface lateral flow, and surface flow routing and its interaction with subsurface flow These components are partially modeled using crude parameterizations or totally neglected in current models
The coupled model (CLM+VAST) driven by SBCs and NARR climate forcing data was evaluated in off-line mode with a 10-minute time step for 1995-2000 over the Ohio Valley region CLM+VAST simulations were initialized using a spin-up strategy, and parameters were estimated through sensitivity analysis The coupled model's performance was assessed by comparing simulated runoff with streamflow observations from USGS gauge stations The results indicate that the new conjunctive flow scheme enhances soil moisture and latent heat flux, while reducing streamflow peaks and sensible heat flux Furthermore, the surface flow routing scheme improves streamflow simulation.
Limitations and FutureResearch cu
The contribution of this research is the necessary initial steps towards improving the ter- restrial hydrologic scheme in current LSMs through a conjunctive surface-subsurface flow scheme based on the new soil-moisture transport equation incorporating topography-driven subgrid and lateral fluxes However, this work has some limitations and requires future research tasks as follows The main limitations relate to closure parameterizations and the lack or shortcoming of adjoint hydrologic schemes
In this research, I hypothesize that topography is a controlling factor of subgrid mois- ture flux for large-scale land surface simulations I isolate subgrid topographic attributes from other properties, and perform closure parameterizations for the dependence of subgrid soil-moisture on topography only, although the hydraulic conductivity and diffusivity terms embedded in the VAST equation are functions of soil properties as well Topographic data is easily available at fine scales to enable subgrid parameterizations, while soil properties and other data are largely at coarse resolutions, often only interpolated at their resolu- tions without providing any information for subgrid parameterizations To represent the nonlinear complex effects of soil properties on the total soil-moisture dynamics, the VAST equation needs to be extended by closure terms representing the variance and joint variabil-
Soil and topography uncertainties pose challenges for modeling the transport of water and energy To address this, a future model would incorporate all subgrid components, including soil properties, vegetation, and meteorological forcing However, current models are limited in their ability to handle the unknown covariance properties among these elements The VAST model's initial closure parameters, derived from field measurements with limited soil-moisture data, utilize the moisture-based Richards equation due to its prevalent use and perfect mass conservation While the VAST equation has limitations, the parameterizations presented here illustrate the importance of subgrid variability Validation and expansion of these parameters require both real-world flux data and the comparison of VAST model output to upscaled output from a fine-resolution model.
Some hydrologic schemes, such as channel flow, base flow, snow melt, and saturation fraction schemes, need to be added or improved in the current CLM model for better predic- tions The developed hydrologic scheme in this research still needs a couple of schemes such as channel flow and base flow calculations The developed surface flow routing scheme is based on the overland flow, which is unable to capture the channel storage effects In channel flow routing scheme of LSMs, geomorphological studies are also required for the upscaled channel network at a scale of LSMs, for instance, the upscaled channel geometry data such
The existing CLM model lacks explicit schemes for subsurface flows, including both unsaturated and saturated conditions While the VAST model incorporates topography-controlled lateral flow, its moisture-based equation is limited to soil-moisture transport in unsaturated zones In saturated conditions, the lateral moisture flux is primarily driven by topographic gradient, necessitating an explicit or empirical equation for groundwater flow calculations Additionally, the snow melt scheme in the current CLM model requires scrutiny as it may release snow melt immediately after snowfall events The current model also disregards the impact of human activities on water quantity and quality, such as aquifer recharge, water withdrawal, and consumptive use, which are crucial factors in hydrologic modeling.
It will be interesting to study on the influence of the spatial variability of slope, soil properties, and bedrock profiles on surface runoff hydrographs The variation of surface runoff hydrographs due to the spatial variability of soil properties has been examined in some previous studies But, the impact on the surface flow interacted with subsurface flow by geographical and geological features such as slope and bedrock profiles has been not investigated yet The spatial variability of these factors is crucially related to infiltration and affects runoff prediction significantly In addition, this new conjunctive surface-subsurface flow model can be used for a non-point source management program by coupling the overland flow scheme with a water quality module for predictions of the pollution due to non-point sources such as nutrient and soil erosion
In this study, novel model simulations were conducted offline using the NARR forcing dataset To fully evaluate model performance and its influence on atmospheric models (GCMs or RCMs), future research should focus on fully coupling the model with these systems.
One of the further research tasks is to couple this new land surface model to a climate model (CWRF) The fully coupled climate system model is required for comprehensive predictions for seasonal and interannual variability of climate and water resources, since the fully coupled model can simulate soil moisture feedback to precipitation and atmospheric circulations and its effects on the available energy into latent and sensible heat exchanges The fully coupled model (CLM+VAST+CWRF) is expected to provide credible information on climate and impacts of climate variations on terrestrial hydrologic processes, as a scientific basis for decision makers to select optimal pathways to achieve future economic, societal and environmental goals
Alternative Form of VAST Model
Leveraging Kumar's (2004) layer averaging approach and extending it to the volume, we integrate equation (2.2) over a grid cell with area A and horizontal scales Lx and Ly, and a layer of thickness ΔZ (bounded by vertical coordinates Zt and Zt-1) to derive a volume-averaged equation.
II be [5 ode drdụ = | | | = P9055 | dz* dx dy in 2k—t v;_ 5U om Ze-1 On} Ox*
(A.1) where (X;, Y;) denotes the center location of each grid-cell (i, 7)
=_ A0, ||e 6-2287” +[e-/ec-z8Mảs£ Oz* Jig, _— Oz* TT”) | | Ze | (A.2)
-1 where C; = ae is a representative value for each grid-cell Q¢ = 5E(E — la’ is a coefficient related to the spatial variability of soil-moisture where € is a linear function of b
l Vertical diffusion © 2.0.00 0000 0000 eee eg 150
‘ : v„+T xi+# using an integral operator [, da for Jy lý J xo dz dy
2k~t + Càng xa) 2k~1 | (a8) where Cy = ans is a grid-representative value
| [ Fe [Da = Fe ae da = (A2 =e: ( pee + ene) (a) where the summation over x; € {x,y} is implied and each integral term Z; = [ 5 ‘Fl eS -2r) GE dz where € is a linear function of 6 and đ
Ox) Ox] ồ C2ệ2t.-2+i 0 C2Q2p43°V2 8 C2€)2p+373 au, ( a(b+1) ỉs,Z2y~ứ+3 | + ụm, “a(b-+1) 1) ỉs,Zzu— as) +3 += (eos La ơ)
The above equation can be written in the following alternative form as
+ Ơg, (= (Spo + Ba; \a(b + 1) T-g44} + 2m \ ab+1) T2b— 8+5 Ừs,, C2Ơsya
+ Xq,CoLan+3 + Xx,C2Q2p432o5~2643 + (i225—6+3 + Taap— 24 tẩm e3)| :
(A9) where 9,, and Xx, are spatial means of slopes and curvatures, respectively, and ỉs, 1s the standard deviation of slopes The coefficients +, y2, and y3 represent the parameterization of the correlation between the slope and soil-moisture
Collecting all the relevant terms from equations (A.2), (A.3), (A.4), and (A.5), and using the volume averaged soil-moisture 6, over the volume of AAZ; for each grid-cell (2, 7, k) defined as 0, = Tai Ja Jz,_, 9 dz* da, we can write an alternative form of the VAST model a 7 as
Ci | fe 2m + [e oe z Zu-1 z Zu-1
L mean term variability term Â