A Conjunctive Surface–Subsurface Flow Representation for ...

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A Conjunctive Surface–Subsurface Flow Representation for Mesoscale Land Surface Models HYUN IL CHOI Department of Civil Engineering, Yeungnam University, Gyeongsan, South Korea

XIN-ZHONG LIANG Department of Atmospheric and Oceanic Science, and Earth System Science Interdisciplinary Center, University of Maryland, College Park, College Park, Maryland

PRAVEEN KUMAR Department of Civil and Environmental Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois (Manuscript received 10 November 2012, in final form 28 March 2013) ABSTRACT Most current land surface models used in regional weather and climate studies capture soil-moisture transport in only the vertical direction and are therefore unable to capture the spatial variability of soil moisture and its lateral transport. They also implement simplistic surface runoff estimation from local soil water budget and ignore the role of surface flow depth on the infiltration rate, which may result in significant errors in the terrestrial hydrologic cycle. To address these issues, this study develops and describes a conjunctive surface– subsurface flow (CSSF) model that comprises a 1D diffusion wave model for surface (overland) flow fully interacted with a 3D volume-averaged soil-moisture transport model for subsurface flow. The proposed conjunctive flow model is targeted for mesoscale climate application at relatively large spatial scales and coarse computational grids as compared to the traditional coupled surface–subsurface flow scheme in a typical basin. The CSSF module is substituted for the existing 1D scheme in the common land model (CoLM) and the performance of this hydrologically enhanced version of the CoLM (CoLM1CSSF) is evaluated using a set of offline simulations for catchment-scale basins around the Ohio Valley region. The CoLM1CSSF simulations are explicitly implemented at the same resolution of the 30-km grids as the target regional climate models to avoid downscaling and upscaling exchanges between atmospheric forcings and land responses. The results show that the interaction between surface and subsurface flow significantly improves the stream discharge prediction crucial to the terrestrial water and energy budget.

1. Introduction Mesoscale regional climate models (RCMs) are recognized as an essential tool to address scientific issues concerning climate variability, changes, and impacts at regional to local scales. As the model resolution increases, land surface models (LSMs) coupled with RCMs need to incorporate more comprehensive physical processes and their nonlinear interactions. This has been Corresponding author address: Dr. Xin-Zhong Liang, Department of Atmospheric and Oceanic Science, University of Maryland, College Park, 5825 University Research Court, Suite 4001, College Park, MD 20740-3823. E-mail: [email protected] DOI: 10.1175/JHM-D-12-0168.1 Ó 2013 American Meteorological Society

the trend in recent developments (Stieglitz et al. 1997; Chen and Kumar 2001; Warrach et al. 2002; Niu and Yang 2003; Niu et al. 2005; Oleson et al. 2008; Choi and Liang 2010), but most LSMs still contain simplistic parameterizations that need improvements for terrestrial hydrologic processes. As a result, LSMs may produce nonlinear drifts in their dynamic responses to external forcings (e.g., Yuan and Liang 2011), which in turn feed back to the coupled climate system and ultimately lead to significant errors in predicting surface water and energy budgets. Improved parameterizations of key land surface processes, especially for the terrestrial hydrologic cycle, are needed to get better performance from RCMs.

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Most current LSMs model only vertical moisture transport and therefore cannot capture spatial variability of soil water induced by topographic characteristics; thus, they are limited in predicting surface fluxes. Such one-dimensional models are unable to represent subsurface lateral transport induced by topography or moisture gradients. As one of the critical components in the terrestrial hydrologic cycle, runoff is estimated using the soil water budget without any explicit or parameterized routing treatment in most current models. As shown below, these models that disregard flow routing or runoff travel time over the basins predict surface runoff hydrographs with unrealistic sharp peaks and steep declining recessions. Moreover, ignoring the role of surface flow depth on the infiltration rate causes errors in both infiltration and surface flow calculations (Schmid 1989; Singh and Bhallamudi 1997; Wallach et al. 1997). Therefore, this study presents a numerical model based on a conjunctive solution of surface and subsurface flow interactions, typically applied for smallscale modeling, here specifically targeting for use in mesoscale land surface parameterizations over a continental scale to improve regional climate modeling, especially for the spatiotemporal distribution of surface and subsurface water that has significant influence on terrestrial water and energy budget. To develop the improved runoff treatment in LSMs, this study has chosen the Common Land Model (CoLM) as the basic LSM that originally utilizes simplistic assumptions and crude parameterizations for the terrestrial hydrologic cycle, especially runoff processes as most LSMs do. The CoLM is an advanced soil–vegetation– atmosphere transfer model (Dai et al. 2003, 2004), which has been incorporated into the state-of-the-art mesoscale Climate–Weather Research and Forecasting (CWRF) model (Liang et al. 2005a,b,c,d, 2006, 2012) with numerous crucial updates and improvements for land processes (Choi 2006; Choi et al. 2007; Choi and Liang 2010; Yuan and Liang 2011). The original Community Land Model (CLM) and CoLM have been extensively evaluated for good performance against field measurements in a stand-alone mode as driven by the observational forcings (Dai et al. 2003; Niu and Yang 2003; Niu et al. 2005; Maxwell and Miller 2005; Qian et al. 2006; Niu and Yang 2006; Niu et al. 2007; Lawrence and Chase 2007; Lawrence et al. 2007; Oleson et al. 2008). Our own experience, however, has shown that a direct application of the CoLM for the CWRF at a 30-km grid spacing leads to serious problems in predicting the hydrologic cycle, especially runoff processes and basin discharge (Choi and Liang 2010; Yuan and Liang 2011). A number of attempts have been made to couple explicit runoff schemes with LSMs. Walko et al. (2000)

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incorporated a modified form of Topography-based Hydrological Model (TOPMODEL) into the Land Ecosystem– Atmosphere Feedback model (LEAF-2) for land–surface processes in the Regional Atmospheric Modeling System (RAMS) in order to represent surface and subsurface downslope lateral transport of groundwater. M€ olders and R€ uhaak (2002) coupled with an atmospheric model a hydrothermodynamic soil–vegetation scheme that incorporates surface and channel runoff. Since the runoff component was solved at a 1-km grid that differs from other terrestrial hydrologic schemes at a 5-km grid, the coupling using aggregation and disaggregation was required to introduce the runoff processes. Gochis and Chen (2003) developed a hydrologically enhanced form of the NOAH LSM incorporating a cell-to-cell surface flow routing scheme through disaggregated routing subgrids coupled to a quasi-steady state model for subsurface lateral flow. Maxwell and Miller (2005) added in the CoLM a variably saturated groundwater model ParFlow without explicit surface runoff scheme. As such, the model was mainly targeted to improve water table depth prediction, but it could not capture observed monthly runoff variations. Kollet and Maxwell (2006) incorporated an overland flow simulator into the ParFlow, followed by an evaluation against published data and an analytical solution for a V catchment (1.62 km 3 1 km). Richter and Ebel (2006) developed a fully integrated atmospheric– ocean–hydrology model, the Baltic Integrated Model System (BALTIMOS), where the regional climate model REMO is coupled to the mesoscale hydrological model LARSIM for simulating the water balance of large river basins continuously. Fan and Miguez-Macho (2011) simulated lateral groundwater flow using estimates from three participants of the National Aeronautics and Space Administration’s (NASA) Global Land Data Assimilation System (GLDAS) (Rodell et al. 2004) such as CLM, Mosaic, and Noah at 1-km spacing to improve water table depth prediction over North America. Along with these attempts, we have been continuously seeking improved representations for the terrestrial hydrology in the CWRF. Choi (2006) and Choi et al. (2007) developed the 3D volume-averaged soil-moisture transport (VAST) model based on the Richards (1931) equation to incorporate the lateral flow and subgrid heterogeneity due to topographic characteristics introduced in the work of Kumar (2004). It was demonstrated that both the lateral flow and subgrid flux have important effects on total soil-moisture dynamics and spatial distribution. In general, soil-moisture moves from hillslopes to the lower regions by lateral and subgrid fluxes in the VAST model. Since the water would converge along topographic concave hollows, any water exceeding soil porosity needs to be transported to the

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vertical soil layers and then treated as lateral surface runoff. Hence, the improved terrestrial hydrologic scheme based on the VAST model also requires an explicit surface flow computation scheme. Choi (2006) incorporated a non-inertial diffusion wave model to account for the downstream backwater effect. This was an approximate form of the Saint-Venant (1871) equation, known for its efficiency in accuracy and computation (Ponce et al. 1978; Akan and Yen 1981; Hromadka et al. 1987; Morita and Yen 2002; Kazezyilmaz-Alhan et al. 2005). Choi and Liang (2010) incorporated the baseflow allocation scheme along with improved terrestrial hydrologic representations such as realistic bedrock depth, dynamic water table, exponential decay profile of the saturated hydraulic conductivity, minimum residual soil water, and maximum surface infiltration limit. This model, however, still simulates steep declining recession curves and relatively small total runoff, primarily because it underestimates the baseflow (Choi and Liang 2010). Therefore, this study has developed and implemented in the CoLM a new conjunctive surface–subsurface flow (CSSF) module that comprises an 1D diffusion wave model for the surface (overland) flow interacted with the 3D VAST model for the unsaturated subsurface flow and an 1D topographically controlled baseflow for the saturated subsurface flow, where all the components are designated at the 30-km grid scale. A new formulation is introduced for the baseflow to depict the effects of surface macropores and vertical hydraulic conductivity changes. The RCM grid-based overland flow routing process is introduced in this study for mesoscale LSMs to realistically predict the temporal variation of the spatial distribution of flow depth and runoff. Such coupling enables the CSSF to explicitly simulate surface runoff that results from both rainfall excess and moisture saturation in the whole soil column as well as its interactions with neighboring grids. This conjunctive flow model is solved by the mixed numerical implementation for each flow component and then substituted for the existing 1D hydrologic scheme in the CoLM. Most hydrologic parameterization schemes in LSMs, including the CoLM and CLM, have been tested with field measurements at small catchment scales (Stieglitz et al. 1997; Warrach et al. 2002; Dai et al. 2003; Niu et al. 2005; Niu and Yang 2006), while directly applied in much coarser resolution climate models. Given the strong scale dependence, terrestrial hydrologic parameterizations, especially for runoff, must be tuned and evaluated at the same resolution as their host climate models. Therefore, we assess the new CSSF module as coupled with the current CoLM built in the CWRF for their designated application at the 30-km grid, focusing on the representation of surface and subsurface runoff.

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All schemes are explicitly implemented at the 30-km grids rather than hydrologic basins or catchments to avoid downscaling and upscaling exchanges between CWRF atmospheric forcings and land responses (Choi 2006; Choi et al. 2007; Choi and Liang 2010; Yuan and Liang 2011). This is an important advance to most previous LSMs that couple hydrologic and atmospheric schemes usually at different scales. Furthermore, the CSSF scheme with the scalable parameterization can be substituted for the terrestrial hydrologic scheme in most LSMs at any current and future finer spatial resolutions within the mesoscale range. As demonstrated below, the CoLM1CSSF extension generates runoff variations much closer to observations. Section 2 presents a brief description of the original CoLM with our previous improvements. Section 3 elaborates the key features of the new CSSF parameterizations. Section 4 depicts the numerical implementation of the CSSF into the CWRF–CoLM at 30-km grids. Section 5 evaluates the CSSF skill enhancement in runoff processes and discharge predictions against daily observations at catchment-scaled study basins over the Ohio Valley. The final conclusions are given in section 6.

2. State of development of the CoLM The original CoLM is well documented in Dai et al. (2003, 2004). Its major 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; and a two-big-leaf model for canopy temperature, photosynthesis, and stomatal conductance. In coupling with the CWRF, the CoLM was consistently integrated with comprehensive surface boundary conditions (Liang et al. 2005a,b) and an advanced dynamic–statistical parameterization of land surface albedo (Liang et al. 2005c). Recently, Choi and Liang (2010) identified several deficiencies in the CoLM formulations for terrestrial hydrologic processes and developed better solutions with a focus on stream discharge predictions. In particular, they have incorporated a realistic geographic distribution of bedrock depth to improve estimates of the actual soil water capacity, replaced an equilibrium approximation of the water table with a dynamic prediction to produce more reasonable variations of the saturated zone depth, used an exponential decay function with soil depth for the saturated hydraulic conductivity to consider the effect of macropores near the ground surface, formulated an effective hydraulic conductivity of the liquid part at the frozen soil interface

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FIG. 1. Schematic diagram for the key terrestrial hydrologic processes represented in the current CoLM and the new CSSF parameterizations.

and imposed a maximum surface infiltration limit to eliminate numerically generated negative or excessive soil moisture solution, and considered an additional contribution to subsurface runoff from saturation lateral runoff or baseflow controlled by topography. The above improvements enable the CoLM to more realistically reproduce observations of terrestrial hydrologic quantities, where the skill enhancement is especially significant for runoff at peaks discharges under high-flow conditions. For convenience, the original model with these improvements is referred to as the CoLM in the subsequent sections, unless specifically noted otherwise. However, this model, using the current TOPMODEL equation, still underestimates the baseflow and thus results in steep declining recession curves and relatively small total runoff (Choi and Liang 2010). Therefore, we develop the CSSF approach below to further reduce these CoLM deficiencies so identified.

3. New CSSF parameterizations Figure 1 illustrates the key terrestrial hydrologic processes represented in the current CoLM and the new CSSF module. Below we describe the new parameterizations introduced into the CSSF, including the treatments for various runoff components as shown in Fig. 2a and the surface flow routing scheme as illustrated in Fig. 2b. The CSSF also couples the VAST model to explicitly incorporate additive lateral and subgrid moisture transport fluxes due to local variations of topographic attributes.

a. Soil-moisture transport scheme Choi et al. (2007) developed a soil-moisture transport formulation, the VAST model, based on the Richards (1931) equation, incorporating both the grid-mean and subgrid fluxes for each vertical and lateral direction:

8 8 0 1 0 1 > > > > > > > B C > B C > > > > B C B ›w ›D C > > › > > B C B C ›D › ›w > > - C 1 BDm 1 > > BD C (Vertical diffusion) 1 z (Lateral diffusion) 1 > > > > m B B ›z C ›z ›z > > ›xl B ›xl ›xl C > > C @|fflfflffl{zfflfflffl} |ffl{zffl} A > > |fflfflffl{zfflfflffl} |ffl{zffl} > > @ A mean variability ›u ›F < ›F < mean variability 5 1 0 1 ›t ›z > ›xl > 0 1 > > > > > > > > B C > > > > B C C > > ›B > > C ›B >2 B > Km 1 K- C (Vertical drainage) > > B C (Lateral drainage), B C > > K 1 z 1 K 1 K 1 ›z@ |{z} |ffl{zffl} A > > m B C > > 1 2 ›x > > @ l |{z} |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}A > > : : mean variability mean variability

(1)

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FIG. 2. (a) Schematic diagram for surface runoff and subsurface runoff components at a single grid cell and (b) concept sketch for the developed conjunctive flow model for the four horizontal grid cells with multiple soil layers in the new CoLM1CSSF model.

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where u is the volumetric water content for a soil element, F is the soil water flux, t is time, z is the vertical coordinate, and the summation over the coordinates xl 2 fx, yg is implied, which represents the x–y plane following the land surface terrain. The variable w is the effective soil wetness (saturation) defined in Eq. (A3), and z is an anisotropic factor first introduced in LSMs by Chen and Kumar (2001) for the desired streamflow predictions [see Eq. (A10)]. Given the functional relationships of Eqs. (A1)–(A9) and the closure parameterization in Choi et al. (2007), the diffusivity D and conductivity K functions (subscript m represents the grid-mean term and -1 and -2 denote the subgrid variability terms) are calculated by Eqs. (A11)–(A15). Note that all variables and coefficients represent grid volume-averaged values in Eq. (1). The VAST model formulation and resulting effects were documented in details by Choi et al. (2007).

b. Subsurface runoff representation scheme The original CoLM predicts subsurface runoff as the sum of only bottom drainage and saturation excess. Recent studies have shown important additional contribution from saturation lateral runoff or baseflow that is controlled by topography (Stieglitz et al. 1997; Chen and Kumar 2001; Warrach et al. 2002; Niu and Yang 2003; Niu et al. 2005; Choi and Liang 2010). In the new CSSF model, subsurface runoff consists of four components as Rsb 5 Rsb,bas 1 Rsb,dra 1 Rsb,int 1 Rsb,sat ,

(2)

where Rsb,bas , Rsb,dra , Rsb,int , and Rsb,sat denote subsurface runoff from baseflow, bottom drainage, interflow, and saturation excess, respectively. Their formulations are presented below. Subsurface runoff is calculated directly from the above four components in each soil column without any interacting or routing schemes for horizontal adjacent soil grids. Note that baseflow runoff is dominant in subsurface runoff for the study basins since all other subsurface runoff components are negligible for the given conditions in this study.

1) BASEFLOW RUNOFF The subsurface lateral flow mainly driven by complex terrain is collecting water along lower-valley regions. The lateral subsurface flow from the VAST model is limited to the vadose zone, the so-called interflow or throughflow, because it is modeled by the u-based Richards equation. Since the VAST model is insufficient to capture the real feature of baseflow in the saturated zone, we need the further improvement of the baseflow calculation scheme associated with the water table depth variation.

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Following Sivapalan et al. (1987), most TOPMODELbased models (Beven and Kirkby 1979) represent subsurface saturated lateral runoff (baseflow) induced by topographic control as Rsb,bas 5

zKs (0) 2l 2fz e e $, f

(3)

where Ks (0) is the saturated hydraulic conductivity approximated by Eq. (A4) on the surface of the top soil layer and f is the decay factor of the saturated hydraulic conductivity obtained by calibrating the recession curve in the observed hydrograph [see Eq. (A8)]. The quantity l is the grid cell mean value of the topographic index defined as l 5 ln(a/tanb), where a is the drainage area per unit contour length and tanb is the local surface slope. The z$ is the water table depth. This topographic index is a scale-dependent variable and has uncertainties due to coarse-resolution digital elevation model (DEM) data available for the regional and continental studies (Kumar et al. 2000). Because of difficulty in defining parameters in Eq. (3) on global scales, some models (Niu and Yang 2003; Niu et al. 2005; Niu and Yang 2006; Choi and Liang 2010) introduce the simplified parameterization using a single calibration parameter, the maximum baseflow coefficient Rsb,max , instead of zKs (0)e2l /f . Hence, Eq. (3) can be rewritten as Rsb,bas 5 Rsb,max e2fz$ .

(4)

However, neither Eqs. (3) nor (4) can represent contribution to baseflow because of the variation of hydraulic conductivity corresponding to different soil texture layers, surface macropores, and the frozen soil area. In particular, the use of a single parameter Rsb,max in Eq. (4) is inappropriate for a large heterogeneous region. Choi and Liang (2010) pointed out that these formulations may not capture observed recession curves (underestimation) or may produce negative or less remaining soil moisture content than the residual value (overestimation). Therefore, we compute baseflow directly from each saturated layer, starting with an assumption that the water table is parallel to the surface, which is the basic assumption of Eqs. (3) and (4) also. The saturated lateral flow qb beneath a water table at a depth z can be written as qb (z) 5 Fliq (z)zKs (z) tanb,

(5)

where Fliq is the unfrozen part of soil water as defined in Eq. (A17). The total baseflow runoff from a grid cell is computed by integrating Eq. (5) through the entire saturated soil layer and along the channel length as

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ð ðz

N

Rsb,bas 5

Qb 5 A ð ðz

N

5

L z$

L z$

Fliq (z)zKs (z) tanb dz dL A

T( j) 1 5

Note that most existing LSMs incorporate a baseflow allocation scheme without considering the limitation of actual water availability in soils [the second part of Eq. (8)]. The baseflow is finally computed as follows:

qb dz dL A

"

N

å

Rsb,bas 5

#

T(k) tan(bL)

k5j11

A

,

(6)

where L is channel length assumed to be the orthogonal straight line to the grid mean flow direction, A is the grid cell area, zN is the bottom of the lowest soil layer, N is the total number of model soil layers, and j is the layer index with the water table. The quantity T is a transmissivity varying nonlinearly with depth and can be computed for each discrete layer as: T(k) 5

ðz

k

zk21

5

Fliq (z)zKs e2f (z2zc ) dz

8 e2f (zk 2zc ) f (z 2z ) > > Fliq (k)zKs [e k $ 2 1], > > < f

k5j

, > > > e2f (zk 2zc ) f Dz > : Fliq (k)zKs (e k 2 1), k 5 j 1 1, N f (7)

where zc is the compacted depth representing macropore effect (Beven 1982a) near the soil surface, especially in vegetated areas [see also Eq. (A8)]. The quantity Dzk is a layer thickness between vertical coordinates zk and zk21 for the layer k. Because the saturated lateral flow cannot exceed the available soil liquid water for mass conservation, qb (k) for each saturated layer below the water table is determined as * qb (k) 5 min

T(k) tan(bL) , A

fuliq (k) 2 max[ur (k) 2 uice (k), 0]gDz0k

+

Dt

,

(8)

where Dz0k 5

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N

å qb (k) .

(9)

k5j

Baseflow from each saturated layer is employed as a sink term, and the soil liquid water is updated by using the following equation: uliq (k) 5 uliq (k) 2

qb (k)Dt . Dzk

(10)

2) BOTTOM DRAINAGE RUNOFF The vertical gradient of soil moisture is generally very small in the lower portion of the soil column, and the lowest soil layer (eleventh-layer bottom is 5.7 m depth in the CoLM) may be located below the bedrock or water table depth. Hence, the vertical diffusion flux of soil moisture is negligible, and the drainage water flux Rsb,dra from the soil bottom can be estimated by Rsb,dra 5 Km (zN ) 1 K- (zN ) ,

(11)

1

where Km (zN ) and K-1 (zN ) are hydraulic conductivity terms of the vertical mean and variability fluxes in Eq. (1) [see also Eqs. (A13) and (A14)], respectively, at the bottom of the lowest soil layer zN . This drainage flux is the lower boundary condition for the vertical soil water movement in the VAST model and treated as a source of subsurface runoff since the CoLM lacks a deep aquifer component in soil water dynamics. Its contribution to the total subsurface runoff is small when the actual bedrock is located in the model soil layers. Moreover, the exponential decay profile of the saturated hydraulic conductivity Ksz as defined in Eq. (A8) substantially reduces bottom drainage, causing a negligible contribution to total subsurface runoff. Ksz is so small in this study domain where the exponential decay factor of the vertical hydraulic conductivity f is large and the bedrock is above the model soil bottom that this runoff component is insignificant.

3) INTERFLOW RUNOFF for k 5 j zk 2 z$ , zk 2 zk21 for k 5 j 1 1 to N

uliq is the partial volume of liquid soil water, uice is the ice content in frozen soil, ur is the residual moisture content at the hygroscopic condition, and Dt is a computational time increment.

The interflow is computed by lateral components in the VAST model and significantly contributes to the spatial distribution of soil water between horizontal grids. Because it can be treated as subsurface runoff at the computational domain boundary grids only, the interflow runoff causes a minor contribution to the total subsurface runoff. The interflow runoff is computed as

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Rsb,int 5

å å uout (k)Dzk B k51

,

Dt

(12)

where uout (k) is the outgoing soil moisture by the lateral flux terms in the VAST model and B indicates all boundary grid cells. Note that the interflow runoff does not occur for this study domain with a buffer zone on all four sides, where the same moisture content is assumed to each boundary soil column, but it is considered for grids bordered laterally by and located vertically above water bodies (e.g., lakes and oceans) in the CWRF as coupled with the CSSF.

where Qrain , Qdew , and Qmelt are rainfall, dewfall, and snowmelt rate at the surface, respectively. Surface runoff is generated by the Horton and the Dunn mechanisms. Horton runoff occurs as rainfall intensity exceeds soil infiltration rate while Dunn runoff takes place when precipitation falls over the saturated area. For the comprehensive surface and subsurface coupling, we consider the influence of overland flow depth on both infiltration rate and surface runoff. The net surface runoff on the exchange of water between the surface and the subsurface is Rs 5 (1 2 Fimp ) max(0, Qw 2 Imax ) 1 Fimp Qw 2 h/Dt , |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflffl{zfflfflfflfflffl} Hortonian

4) SATURATION EXCESS RUNOFF

Rsb,sat 5 max 0,

N

N

k51

k51

å u(k)Dzk 2 å us (k)Dzk

where Fimp is the impermeable area fraction consisting of the fractional saturated area Fsat and the frozen area Ffrz as follows: Fimp 5 (1 2 Ffrz ) Fsat 1 Ffrz ,

#, ) Dt , (13)

where us is the soil moisture content (porosity) at saturation approximated by the pedo-transfer function in Eq. (A6). Note that the numerically generated excessive soil-moisture solution rarely occurs in this study by incorporating a maximum surface infiltration limit condition and the effective hydraulic conductivity function at the interface of unfrozen areas [see Eq. (A18)] from Choi and Liang (2010).

ð Fsat 5

l$l1fZ$

g(l) dl ,

Fsat 5 Fmax e20:5fz$ ,

(14)

(17)

where g(l) is the probability density function of the topographic index l. Woods and Sivapalan (1997) showed a similarity for the cumulative distribution functions of the topographic index among a variety of catchments. Such similarity lends strong support to the simplification made by Niu and Yang (2003) as:

1) SURFACE RUNOFF The total available water supply rate Qw on the surface is computed, incorporating the flow depth h for a time increment Dt as:

(16)

where the frozen area Ffrz is defined in Eq. (A16) and the fractional saturated area Fsat is determined by the topographic characteristics and soil moisture state:

c. Surface runoff representation scheme

Qw 5 Qrain 1 Qdew 1 Qmelt 1 h/Dt ,

Dunnian

(15)

In cases where the soil water exceeds its moisture capacity (porosity) numerically at any single layer, the excess water is recharged to the unsaturated layers above the water table. If the entire soil column becomes supersaturated, saturation excess runoff occurs: ( "

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(18)

where Fmax is the maximum saturated fraction. The exponent coefficient 0.5 is derived by making the result in agreement with the three-parameter gamma distribution of Niu et al. (2005). The remaining variable Imax in Eq. (15) is defined as

  c (1)b1 Imax 5 Fliq (1)Ks (1) 1 2 s [1 2 wu (1)] z d1 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl} mean flux   1 b1 1322b 2 1 Fliq (1)Ks (1)a (2b1 1 3)(b1 1 1) 2 b1 (b1 1 2)[1 2 wu (1) ] , z 2 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} variability flux

(19)

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where (1) or subscript 1 denotes for the top soil layer. The quantity cs is the saturated suction head, the exponent b is the pore size distribution index, and a and b are parameters characterizing the dependence of moisture variability on the mean in the VAST model. The value d is the node depth of a soil layer, and wu is soil wetness for the permeable unsaturated area and calculated from grid-mean soil wetness w as # " w(1) 2 Fimp (1) , Fimp (1) , 1, (20) wu (1) 5 max 0, 1 2 Fimp (1) where w is the effective soil wetness (saturation) defined in Eq. (A3). Equation (20) is derived from an assumption that the surface layer is saturated during rainfall events (Mahrt and Pan 1984; Entekhabi and Eagleson 1989; Abramopoulos et al. 1988; Boone and Wetzel 1996). This infiltrability also cannot exceed the maximum possible influx calculated using the soil water budget at the first layer as Imax # us (1)[1 2 wu (1)]

Dz1 1 Fz 1 E1 , 1 Dt

(21)

where Fz1 and E1 are the soil water flux and the evapotranspiration flux, respectively, at the first soil layer. Hence, the vertical flux Fz0 at the top of each soil column z0 (the upper boundary condition) is computed as Fz 5 2min(Qw, Imax ) .

(22)

0

For the lateral boundary conditions, the buffer adjacent soil columns are assumed to have the same water content to each boundary soil grid.

2) SURFACE FLOW ROUTING One approximated solution for unsteady surface flow is the non-inertial wave model neglecting local and convective inertia term in the full dynamic wave equations, known as the Saint-Venant equation (Tsai and Yen 2001; Morita and Yen 2002). The diffusion wave equation in a wide rectangular section can be written for a unit width element as ›h ›h ›2 h 5 Dh 2 1 Rs , 1 cd ›t ›xc ›xc

(23)

where h is a flow depth, xc is longitudinal flow direction coordinate, and cd is the diffusion wave celerity, which can be approximated for gentle-slope case as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   3 3 ›h cd 5 V 5 h So 2 , (24) 2 2 ›xc and Dh is the hydraulic diffusivity expressed as

c h Vh 5  , Dh 5  d ›h ›h 2 So 2 3 So 2 ›xc ›xc

(25)

where V is flow velocity averaged over a flow depth h and So is bottom slope in the flow direction. There can be many converging junctions in the flow network generated from the DEM. The boundary conditions for mass and energy conservation at any junction are required for a flow 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

åQs,out 5 åQs,in ,

(26)

where the subscripts in and out denote inflow and outflow, respectively, at the junction. Qs is the surface flow discharge through the flow cross section. The equation of energy conservation for each branch is given as 2 Vin 1 ghin 5 2

ðx

cout

xcin

dV V2 dxc 1 out 1 ghout 1 ghf , dt 2

(27)

Ðx where xcincout (dV/dt) dxc is the energy loss due to acceleration of flow, g is the gravitational acceleration, and hf is the head loss due to fraction and other local losses. If we ignore the change of velocity and head loss at a junction, Eq. (27) is simply approximated as hout 5 hin .

(28)

As such, the 30-km grid-based overland flow routing formulations are incorporated into the CSSF model without any disaggregation and aggregation procedures to realistically predict the temporal variation of the spatial distribution of flow depth and runoff at regional– local scales. As delineated in Fig. 2b, in the hydrologically enhanced version of the CoLM, the surface flow equation in Eq. (23) relies on the exchange flux Rs between the surface and subsurface flow in Eq. (15). The spatial and temporal variation of the surface water depends on the exchange flux Rs (induced by vegetation, topography, soil texture, etc.) as well as climatic factors such as rainfall and temperature.

d. Total runoff representation scheme Total runoff is composed of surface and subsurface runoff results. To estimate total runoff at a given grid point, surface flow discharge divided by the total grid cell area contributing to the target grid point is added to the averaged subsurface runoff as

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FIG. 3. Plots of 30-km resolved flow directions (arrows), 1-km HYDRO1K stream network (curved lines), basin boundaries (black closed curves), model basin grid boundaries (white polygons), and the three USGS streamflow gauge stations (white circles) overlaid with spatial distributions of (a) the 30-km terrain elevation (black–gray gradation pixels) and (b) the 30-km USGS land cover type (graytoned pixels), along with (c) a background map for study basin locations.

Rtot 5

Qs 1 Rsb , nfa A

(29)

where Rtot is total runoff, nfa is the flow accumulation number at the target grid point, and Rsb is the averaged subsurface runoff for the total grid cells located upstream of the target grid point. Total runoff variation with time is the specific discharge hydrograph, which can be used to compare with stream discharge observations.

4. Implementation of the new CoLM1CSSF model The CSSF model is substituted for the existing terrestrial hydrologic representation in the CoLM. While

the CoLM performs all computations independently at individual soil columns, the lateral subsurface flow and surface flow in the CSSF depend on neighboring grids and hence are calculated after the vertical subsurface water movement is computed using a time-splitting method. Since the performance of the terrestrial hydrologic schemes depends strongly on the spatial scale, the CSSF skill enhancement in predicting runoff is evaluated over a relatively large catchment using the actual CWRF– CoLM 30-km grid mesh targeted for regional climate applications. To facilitate model comparison with observations, the experiments are conducted in a stand-alone mode, where the CoLM with or without the CSSF is

TABLE 1. The selected USGS streamflow gauge stations for evaluation of the model performance. The drainage area for each station is documented by the USGS and the computational drainage grids are determined by 30-km flow directions for each of the three study basins.

USGS station ID

Station name

Drainage area for the station (km2)

Contributing area in the model (km2)

03198000 03287500 03320000

Kanawha River at Charleston, WV Kentucky River at Lock 4 at Frankfort, KY Green River at Lock 2 at Calhoun, KY

27 060 14 014 19 596

28 800 13 500 18 000

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TABLE 2. Summary of terrain elevation, bedrock depth ranges, and major land use types for the three study basins. Basin name Kanawha River Kentucky River Green River

Elevation range (m) Bedrock depth range (m) 269–991 235–481 140–338

1.17–4.19 0.87–4.18 0.93–4.97

driven by the most realistic surface boundary conditions (SBCs) and meteorological forcings. This avoids the complication from errors of atmospheric processes and surface–atmospheric feedbacks in the fully coupled CWRF. To implement the CSSF into the CoLM, a mixed numerical integration approach is adopted for different flow components. The 3D VAST is integrated using a time-splitting algorithm by separating the vertical and lateral components. An explicit method solves the lateral flow after a fully implicit method solves the vertical flow. The 1D diffusion wave model is solved by the MacCormack (1971) scheme with second-order accuracy in both space and time. The evaluation procedures on the CoLM1CSSF simulations are described below.

a. Study catchments To appropriately evaluate the performance of the CSSF in the CoLM, we select three catchments around the Ohio Valley within the CWRF U.S. domain. These basins have observed records of streamflow discharges from the U.S. Geological Survey (USGS) National Water Information System (http://waterdata.usgs.gov/nwis/sw),

Major land use types Deciduous broadleaf forest mixed forest Cropland/woodland mosaic deciduous broadleaf forest mixed forest Cropland/woodland mosaic deciduous broadleaf forest

and each contains the headwater of the stream. We choose one gauge station near each basin outlet: Kanawha River at Charleston, West Virginia (03198000), Kentucky River at Lock 4 at Frankfort, Kentucky (03287500), and Green River at Lock 2 at Calhoun, Kentucky (03320000). Figure 3 marks their locations while Table 1 gives more specifications. Figure 3 also illustrates the portion of the CWRF computational domain for U.S. climate applications (Liang et al. 2004) that covers the entire three study catchments. It contains a rectangular size of 690 km (23 grid cells) by 360 km (12 grid cells) at a 30-km spacing.

b. Surface boundary conditions The CoLM, as coupled with the CWRF, incorporates the most comprehensive SBCs based on the best observational data over North America constructed by Liang et al. (2005a,b). These include surface topography, bedrock depth, sand and clay fraction profiles, surface albedo localization factor, surface characteristic identification, land cover category, fractional vegetation cover, and leaf and stem area index for the 30-km grid scale constructed from raw data at the finest possible

FIG. 4. Comparison of (top) the benchmark efficiency and (bottom) correlation coefficient with the decay factor f and the maximum baseflow coefficient Rsb,max of the current CoLM (Choi and Liang 2010) for the total runoff of the three study catchments in 1995.

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FIG. 5. Comparison of the (top panels for each z value) benchmark efficiency and (bottom panels for each z value) correlation coefficient with the decay factor f and the maximum baseflow coefficient Rsb,max of the new CoLM1CSSF using the different anisotropic ratio z 5 (a) 500, (b) 1000, (c) 1500, and (d) 2000 for the total runoff of the three study catchments in 1995.

resolution. The spatial distributions of terrain elevation and land cover types are shown in Fig. 3, all at the CWRF 30-km grids, with major features summarized in Table 2. Figures 3a and 3b depict the distributions at the CWRF 30-km grid over the three study catchments for terrain elevation ranging from 140 to 991 m and land

cover types consisting of cropland–woodland mosaic, deciduous broadleaf forest, and mixed forest. The bedrock depth distribution over these catchments, ranging from 0.87 to 4.97 m, is illustrated in Table 2. The new CSSF model requires additional SBCs for each 30-km grid, such as standard deviations of subgrid

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FIG. 5. (Continued)

local terrain slopes in the two horizontal coordinate directions, and eight surface flow directions to incorporate the topographic effects on soil moisture transport as well as lateral surface and subsurface flows. These fields were also constructed from the same 1-km DEM data. Following Lear et al. (2000), the double maximum algorithm (DMA) based on the eight-direction pour-point model is used to determine the flow direction that most

realistically represents the dominant direction of the river network within the 30-km grid box. The maximum flow accumulation is first calculated from the 1-km DEM, and then the DMA uses a unique division of the 30-km grid box into four subsections generated from two offset 30-km meshes overlaid with the 1-km grids. Finally, the DMA extracts river networks from the 1-km resolution and upscales them to the CWRF 30-km

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computation grid resolution. Figure 3 shows that the so-derived 30-km flow directions represent well the feature of the Global Hydrological 1 kilometer database (HYDRO1K) stream network. See Liang et al. (2005a,b) and Choi (2006) for the details of data sources and construction methods for SBCs.

c. Meteorological forcings and initial conditions The stand-alone simulations of the CoLM with and without the CSSF model are driven by the same meteorological forcings constructed from the best available observational North American Regional Reanalysis (NARR; Mesinger et al. 2006). The NARR adopts a 32-km grid, close to that of CWRF, and provides 3-hourly atmospheric and land data over an extensive area that completely includes our U.S. computational domain. The outcome represents a major improvement upon the earlier global reanalysis datasets in both resolution and accuracy. The required atmospheric variables to drive the CoLM stand-alone simulations are pressures at the lowest atmospheric layer and the surface (Pa), temperature at the lowest atmospheric layer (K), specific humidity at the lowest atmospheric layer (kg kg21), zonal and meridional winds at the lowest atmospheric layer (m s21), the lowest atmospheric layer height (m), convective and resolved rainfalls [mm (3 h)21], snow [mm (3 h)21], planetary boundary layer height (m), and downward longwave and shortwave radiations onto the surface (W m22). They are remapped onto the CWRF 30-km grid by linear spatial interpolation. Note that the NARR data for soil temperature and moisture are given only in four layers of 0–10, 10–40, 40–100, and 100–200 cm below the surface. Mass conservative vertical interpolation for the 11 soil layers in the CoLM along with a conventional LSM spinup strategy is adopted to initialize the CoLM. Specifically, the CoLM integration is started at 0000 UTC on 1 January 1995 and run continuously throughout the whole year of 1995 as driven by the NARR data. This is repeated for five cycles with the same 3-hourly NARR forcings of 1995. The resulting conditions at the end of the fifth cycle are considered to be fully consistent with the atmospheric forcings and hence used as the initial conditions for the subsequent CoLM simulation to be evaluated against observations.

5. Runoff simulation results The performance for the existing improved CoLM (Choi and Liang 2010) and the hydrologically enhanced version of the CoLM (CoLM1CSSF) is evaluated against the baseline CoLM model (Dai et al. 2003) by using a normalized benchmark efficiency (Schaefli and Gupta 2007) BE and the correlation coefficient R:

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TABLE 3. Comparison of the model performance measured by the benchmark efficiency BE and the correlation coefficient R of the modified CoLM and the new CoLM1CSSF models with each selected calibration parameter set for the three study river basins based on the simulation result in 1995.

CoLM

BE R BE R

CoLM1CSSF

Kanawha River

Kentucky River

Green River

0.128 0.170 0.681 0.715

0.131 0.420 0.819 0.797

20.192 0.316 0.782 0.717

N

å (Oi 2 Si )2

BE 5 1 2 i51 N

å (Oi 2 Bi )

,

(30)

2

i51

"

# N 1 N å (Si Oi ) 2 N å Si å Oi i51 i51 i51 R 5 v"ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 #" !2 # , u N N N N u 1 1 t å (Si )2 2 N å Si å (Oi )2 2 N å Oi i51 i51 i51 i51 N

(31) where N is the total number of raw data cells, Oi and Si denote the observed and simulated values at day i, and Bi is the benchmark results from the baseline runoff scheme in the original CoLM (Dai et al. 2003). The normalized benchmark efficiency BE measures the model ability to simulate the observed runoff amplitudes over the reference model results, and the correlation coefficient R depicts the temporal correspondence of the model results with observations. Note that the closer both the BE and R values are to 1, the more accurate the model is. Total runoff consists of surface and subsurface parts. For surface runoff over each basin, the CoLM alone calculates only the basinwide mean, while the coupling with the CSSF simulates surface outflow at each outlet grid. For subsurface runoff, the CoLM with and without the CSSF both simulates the basin average. We have first examined the sensitivity of the existing CoLM modified by Choi and Liang (2010) to two calibration parameters, the decay factor f (2–10 m21) and the maximum baseflow coefficient Rsb,max (1 3 1024 to 4 3 1024 mm s21) for a simulation of the year 1995. Overall, the benchmark scores are low and the maximum score occurs with different values of calibration parameters for each study river basin as shown in Fig. 4. The decay factor f of 4 m21 and the maximum baseflow coefficient Rsb,max of 2 3 1024 mm s21 are selected for the model calibration parameters over the three study watersheds. As Choi and Liang (2010) demonstrated,

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FIG. 6. Comparison of daily time series of model simulated specific discharges of the total runoff from the baseline model (the original CoLM) by Dai et al. (2003), the CoLM modified by Choi and Liang (2010), and the new CoLM1CSSF in this study, along with the daily observations from the three USGS gauge stations in 1995. The hyetographs of the observed total precipitation are plotted along the righthand vertical axis.

the change of the exponential decay factor f does not affect much the runoff results mainly because of smaller soil water availability and less baseflow generation in the CoLM.

The sensitivity analysis of the new CoLM coupled with the CSSF is performed for the two cases, the CoLM1CSSF simulations with and without the new baseflow scheme. When the new baseflow scheme is

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FIG. 7. Comparison of daily time series of the specific discharges and water table depth (z$ ) simulated from the CoLM alone and the new CoLM1CSSF models, along with the daily observed streamflow from the three USGS gauge stations during 1995–99.

coupled, calibration is done for the two parameters: the decay factor f (2–10 m21) and the anisotropic ratio z (500–2000). Note that additional calibration is required for the maximum baseflow coefficient Rsb,max when the new baseflow scheme is uncoupled. Based on the sensitivity analysis depicted in Fig. 5, f 5 8 m21 and z 5 1000 enable the CoLM1CSSF model to produce the highest BE and R scores. It also demonstrates that the new baseflow scheme plays a significant role in capturing the seasonal streamflow patterns (see more discussion later). A larger f value in the CoLM1CSSF model facilitates a significant surface flow depth contribution to infiltration enhancing the baseflow generation, solving the lowsensitivity problem in the existing CoLM without the CSSF. This is reasonable because the incorporation of the realistic bedrock depth may confine soil water in upper layers and a larger decay factor may enhance the

saturated hydraulic conductivity [Eq. (A8)] and baseflow [Eq. (7)] above the root zone (;1 m). We obtain a smaller value for the anisotropic ratio (z 5 1000) as compared with the result (z 5 2000) in Chen and Kumar (2001). This occurs because the larger f value along with subsurface interflow in the VAST model somewhat contributes to the horizontal water movement. Table 3 summarizes the BE and R scores for total runoff from the CoLM and CLM1CSSF models with each selected calibration parameter set. When the CSSF is coupled, the results are significantly improved where much higher values are obtained for both scores than the CoLM results. Figure 6 compares the time series of daily specific discharges (per unit drainage area) during 1995 observed and simulated by the baseline CoLM (Dai et al. 2003) and the improved CoLM (Choi and Liang 2010) with–without coupling the CSSF at the three gauge

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stations in the study domain. The original and current CoLM without CSSF schemes produce discharges as pulse fluctuations as a result of quick response to rainfall events, causing no recession time and overall underestimation of runoff, whereas the hydrologically enhanced version of the CoLM with the CSSF captures the seasonal variability of streamflow quite realistically. With each set of the selected calibration parameters, the CoLM uncoupled and coupled with the CSSF were run continuously for 5 yr from January 1995 to December 1999. As shown in Fig. 7, the runoff simulated by the CoLM alone shows an overestimate for the peaks but an underestimate in recession periods, while the coupling with the CSSF results in a significant improvement by capturing observations much more closely over the three study catchments. It is also clear that the coupling with the CSSF significantly improves the CoLM performance in representing the basin flow dynamics. Figure 7 and Table 4 demonstrate that the CoLM1CSSF incorporating the role of surface flow depth contribution to infiltration results in shallower water table depth and enhanced baseflow generation. In the CoLM1CSSF the routed surface flow depth and the large f value allow more water recharged to soil layers to raise the water table and increase subsurface flow. The CoLM predicts very little subsurface runoff, even after incorporating more advanced representations, including realistic bedrock depth, dynamic water table, exponential decay profile of the saturated hydraulic conductivity, minimum residual soil water, and maximum surface infiltration limit (Choi and Liang 2010). In general, when total runoff is dominated by its surface component, LSMs tend to overestimate runoff peaks and underestimate runoff recession. This may partially explain why the CoLM simulates extremely weak seasonal– interannual soil moisture variability (Yuan and Liang 2011). On the other hand, the CoLM coupled with the CSSF produces much larger subsurface runoff by incorporating the effects of surface flow depth and surface macropores on the baseflow generation. The ratios of subsurface to total runoff increase from 62.0%, 33.9%, and 50.3% to 89.2%, 65.5%, and 57.4%, respectively, for the Kanawha River, the Kentucky River, and the Green River basins (Table 4). The study demonstrates that the baseflow generation is extremely important for capturing streamflow observations. Note that baseflow runoff is comparable to total subsurface runoff in the CoLM with the CSSF because other subsurface components are confined by the use of the bedrock depth and the supersaturation prevention scheme. Figure 8 illustrates that the baseflow is predominant in low-flow seasons while surface runoff is more important during the high-flow

TABLE 4. Comparison of 5-yr-averaged simulation results from the CoLM alone and the new CoLM1CSSF models along with observations for the three study river basins. that the quantity Pt is total precipitation (mm yr21), Rt is total runoff (mm yr21), rR is the ratio of simulated Rt to observed Rt , rsb is the ratio of simulated subsurface runoff to simulated total runoff, The ET is the evapotranspiration rate (mm yr21), and z$ is the water table depth (m). All values are the 5-yr-averaged basinwide mean.

Observations CoLM

CoLM1CSSF

Pt Rt Rt rR rsb ET z$ Rt rR rsb ET z$

Kanawha River

Kentucky River

Green River

1056 510 104 0.204 0.620 912 1.70 413 0.810 0.892 972 0.81

1222 403 235 0.584 0.339 968 1.55 339 0.842 0.655 1008 0.75

1285 582 280 0.481 0.503 1006 1.61 622 1.069 0.574 1038 0.66

season, especially May–June. One exception is for the Kanawha River basin, where no considerable storm events occurred over that period. Therefore, the new CSSF parameterizations that enforce interactions between the routed surface flow and the subsurface flow with topographic subgrid soil-moisture variation and baseflow generation simulate total runoff more realistically, especially in the recession part of the hydrograph. Relative to observations for the Kanawha River, the Kentucky River, and the Green River basins, the 5-yr-averaged runoff is only 20.4%, 58.4%, and 48.1%, respectively, in the CoLM, but increased to 81.0%, 84.2%, and 106.9% in the CoLM1CSSF (Table 4 and Fig. 9). However, this hydrologically enhanced version of the CoLM still cannot capture the recessions in the early spring flooding events. As shown in Fig. 9, the simulated monthly flow volumes for each of the study basins are in general less than observations during February–April. One possible reason is that the new model does not yet include aquifer recharge, regulation storage, deep aquifer groundwater flow, and channel flow routing. In addition, the snowmelt scheme may also contribute to the model–observation discrepancy (Yuan and Liang 2011). These factors warrant further investigation.

6. Conclusions and summary Most existing LSMs predict soil moisture transport only in the vertical direction and estimate surface runoff from local net water flux (precipitation minus surface evapotranspiration and soil-moisture storage). However, we found that subsurface subgrid and lateral fluxes

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FIG. 8. Modeled 5-yr-averaged climatology of monthly total model runoff consisting of surface runoff and baseflow components in the new CoLM1CSSF model simulation for (top to bottom) the three study river basins.

have significant impacts on soil-moisture spatial variability (Choi et al. 2007), and an explicit surface flow routing scheme is required for the comprehensive terrestrial hydrologic cycling in LSMs (Choi 2006; Choi et al. 2007; Choi and Liang 2010). They should be incorporated in a fully interactive manner to affect the hydrologic cycle both locally and in adjacent areas. To this end, we

have developed the CSSF module that comprises the 1D diffusion wave surface flow model coupled with the 3D VAST subsurface flow model and the 1D topographically controlled baseflow to substitute the existing hydrologic module in the CoLM. The CSSF is implemented into the CoLM by a time-split mixed numerical approach, where the subsurface flow model is

FIG. 9. Comparison of 5-yr-averaged climatology of monthly total runoff from the CoLM and the new CoLM1CSSF models along with observations for (top to bottom) the three study river basins.

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separated for the vertical component by an implicit differencing method and the lateral component by an explicit method, and the surface flow model is solved by the MacCormack scheme. The implementation and verification of the CSSF in coupling with the CoLM is unique as compared with the conventional approach in that the hydrological and atmospheric components interact directly at the identical mesoscale grid mesh without aggregation or disaggregation. The model performance is evaluated using standalone simulations of the CoLM with and without the CSSF driven by realistic SBCs and reliable NARR climate forcing data around the Ohio Valley on the same 30-km grid over the U.S. domain of the coupling CWRF to be applied. The CSSF incorporates advanced representations for the lateral and subgrid soil-moisture transport, the surface flow routing and interaction with subsurface flow, and the topographically controlled baseflow. As a result the coupling with the CSSF simulates the total runoff much closer to observations than the CoLM alone, especially for the declining recession curves of hydrographs. The CSSF so developed demonstrates a significant surface flow depth contribution to infiltration causing enhanced baseflow generation. Although the soil-moisture simulation performance is not directly evaluated due to lack of observations in the study basins, Yuan and Liang (2011) have also demonstrated the superiority of the CSSF in simulating the observed Illinois soil moisture variations from an offline test against the CoLM and CLM. The terrestrial water dynamics by full interactions between surface and subsurface flow in the hydrologically enhanced version of the CoLM with the CSSF represents an important advance to the simple soil water budget used in the original and our modified CoLM (Choi and Liang 2010). Ignoring these new processes in the CoLM can cause significant model errors and, consequently, unrealistic model parameters targeted for calibration. The redistribution of surface and subsurface water by the new model may also have a large impact on the prediction of the surface energy balance as well. Note that the original CoLM has been demonstrated by numerous studies for its good performance in global climate models (see the introduction in section 1). We contend that a resolution increase must couple with advanced model physics representation at that scale to realize improved predictions. The newly developed CSSF model provides a suite of improved modeling capability for the CoLM to better characterize surface water and energy fluxes crucial to climate variability and change studies at regional–local scales. The CSSF model, albeit with many new advances, has yet to incorporate a more complete list of important factors for comprehensive terrestrial hydrologic simulations

over larger basins, including aquifer recharge, regulation storage, consumptive use, and channel and groundwater flow routing across the basin boundaries. In the current CSSF mode, the overland-based surface flow scheme cannot fully capture the storage effect of real streams, and the topographically controlled baseflow scheme associated with the water table depth neglects the possible contribution from the deeper aquifer underlying the bottom of the LSM soil column. These areas will be our future targets to improve. Acknowledgments. The research was supported by the NOAA Education Partnership Program (EPP) COM Howard 00073421000037534, Climate Prediction Program for the Americas (CPPA) NA11OAR4310194 and NA11OAR4310195, Environmental Protection Agency RD83418902, National Science Foundation ATM-0628687, and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF2013R1A2A2A01008881).

APPENDIX Soil Hydraulic Conductivity The hydraulic conductivity K and matric potential c are expressed as a function of soil wetness w (Brooks and Corey 1964): K(w) 5 Ks w2b13 ,

(A1)

c(w) 5 cs w2b ,

(A2)

where w is the effective soil wetness (saturation) defined as

w5

8 uliq 1 uice 2 ur > > > , uice , ur > > us 2 ur > < > > > > > > :

, uliq us 2 uice

,

(A3)

uice $ ur

where uliq (mm mm21) is the partial volume of liquid soil water, uice (mm mm21) is the ice content in frozen soil, and ur (mm mm21) is the residual moisture content at the hygroscopic condition, which is estimated as ur 5 us (2316 230/cs )21/b (see Bonan 1996). The Ks (mm s21), cs (mm), and us (mm mm21) are the compacted hydraulic conductivity, the suction head, and soil moisture content (porosity) at saturation, respectively, and the exponent b is the pore size distribution

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index. They are approximated by pedo-transfer functions in terms of soil sand and clay fractions (Cosby et al. 1984; Bonan 1996) as Ks 5 0:007 055 6 3 1020:88411:533sand ,

(A4)

cs 5 2102:8821:313sand ,

(A5)

us 5 0:489 2 0:126 3 sand ,

(A6)

b 5 2:91 1 15:9 3 clay.

(A7)

(A8)

z

where Ksz is the vertical saturated hydraulic conductivity and zc is the compacted depth representing macropore effect (Beven 1982a) near the soil surface, especially in vegetated areas. It is assumed that the saturated conductivity has reached the compacted value at the plant root depth of 1 m (Stieglitz et al. 1997; Chen and Kumar 2001). When zc is assumed 1 m, Ksz is 7.13–1.41 times greater than Ks in the CoLM soil layers 1–7 located above zc , whereas Ksz is much less than Ks in the rest of the lower soil layers, as shown in Table 2 of Choi and Liang (2010). As such, vertical transport of soil moisture near the surface is much faster with the Ksz profile because of the effect of macropores. The value f is the decay factor of Ksz , which can be obtained by comparison of the recession curve in the observed hydrograph. We also assume that soil properties (Ks , cs , us , b) are constant and uncorrelated with each other within a grid volume (Choi et al. 2007) and use a grid-representative value using the layer-averaging method as

zk21

Ks e

2f (z2zc )

y

(A10)

z

where z is an anisotropic factor first introduced by Chen and Kumar (2001) for the desired streamflow predictions. Also, the diffusivity D and conductivity K functions in Eq. (1) are calculated as: Ks cs b Dm 5 2 z wb12 , us

(A11)

1 D- 5 2 Ks cs b(b 1 2)a2 wb1322b , 2 z

(A12)

Km 5 Sx Ks w2b13 ,

(A13)

l

z

K- 5 Sx Ks (2b 1 3)(b 1 1)a2 w2b1322b , 1

l

(A14)

z

K- 5 sS Ks (2b 1 3)aw2b132b (g1 1 g2 w 1 g3 w2 ) , 2

xl

z

where subscript m represents the grid-mean term, and -1 and -2 denote the subgrid variability terms. The quantity Sxl is the grid-mean slope and sSxl is the standard deviation of local slopes for each grid where the summation over the coordinates xl 2 fx, yg is implied. The variables a and b are parameters characterizing the dependence of moisture variability on the mean, and g1 , g 2 , and g3 are parameters characterizing the dependence of moisture on slopes, which are estimated by the closure parameterization in Choi et al. (2007). In addition, we need to determine the effective hydraulic conductivity and diffusivity functions for the liquid part at the frozen soil interface. Choi and Liang (2010) demonstrated that the new scheme using the minimum of the unfrozen areas in the two adjacent soil elements produces a mass-conserved and numerically stable solution of soil-moisture profiles. They parameterized the frozen part as a function of soil liquid and ice water contents at soil layer k: Ffrz (k) 5

ðz

k

Ks 5 Ks 5 zKs ,

(A15)

Ks 5 Ks e2f (z2zc ) ,

1 Ks (k) 5 z Dzk

where Dzk is a layer thickness between vertical coordinates zk and zk21 for the layer k. The Ksz is treated constant within a grid volume, but can vary from one grid to the next vertically and horizontally. The lateral hydraulic conductivity is larger than vertical to account for anisotropy (Freeze and Cherry 1979): x

To improve estimates of the actual soil water capacity, we adopt the geographically distributed bedrock depth profiles as constructed at the CWRF 30-km grid by Liang et al. (2005b). To approximate the water drainage through bedrocks, we assume the hydraulic properties of bedrocks whose porosity is 0.05 and saturated hydraulic conductivity is 1% of that in the soil layer right above, as similarly introduced in many LSMs (Abramopoulos et al. 1988; Xue et al. 1991; Boone and Wetzel 1996; Sellers et al. 1996). We assume that the saturated hydraulic conductivity follows an exponential decay with depth as developed by Beven and Kirkby (1979), Beven (1982b, 1984), and Elsenbeer et al. (1992):

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dz

e2f (zk 2zc ) f Dz 5 Ks (e k 2 1), f Dzk

uice (k) , uliq (k) 1 uice (k)

(A16)

and the unfrozen part of soil moisture is (A9)

Fliq (k) 5 1 2 Ffrz (k) .

(A17)

OCTOBER 2013

CHOI ET AL.

Hence, the effective functions for unfrozen areas at the interface are computed as   x 1 x k11 , xk11/2 5 min[Fliq (k), Fliq (k 1 1)] k 2

(A18)

where x represents all diffusivity and conductivity functions. The quantities k and k 1 1 denote one soil element and another adjacent one, respectively, and k 1 1/2 denotes the interface of the two in the vertical or horizontal direction. Note that x zk [ xk11/2 in vertical direction discretization. This interblock function can reduce negative or supersaturated soil moisture solution caused by numerical problems from the existing parameterization in most current LSMs (Choi and Liang 2010). REFERENCES Abramopoulos, F., C. Rosenzweig, and B. Choudhury, 1988: Improved ground hydrology calculations for Global Climate Models (GCMs): Soil water movement and evapotranspiration. J. Climate, 1, 921–941. Akan, A. O., and B. C. Yen, 1981: Diffusion-wave flood routing in channel networks. J. Hydraul. Eng., 107, 719–732. Beven, K. J., 1982a: Macropores and water flow in soils. Water Resour. Res., 18, 1311–1325. ——, 1982b: On subsurface stormflow: An analysis of response times. Hydrol. Sci. J., 27, 505–521. ——, 1984: Infiltration into a class of vertically non-uniform soils. Hydrol. Sci. J., 29, 425–434. ——, and M. J. Kirkby, 1979: A physically based, variable contributing area model of basin hydrology. Hydrol. Sci. Bull., 24, 43–69. Bonan, G. B., 1996: A land surface model (LSM version 1.0) for ecological, hydrological, and atmospheric studies: Technical description and user’s guide. NCAR Tech. Note NCAR/ TN-4171STR, 150 pp. [Available online at ftp://ftp.daac.ornl. gov/data/model_archive/LSM/lsm_1.0/comp/NCAR_LSM_ Users_Guide.pdf.] Boone, A., and P. J. Wetzel, 1996: Issues related to low resolution modeling of soil moisture: Experience with the PLACE model. Global Planet. Change, 13, 161–181. Brooks, R. H., and A. T. Corey, 1964: Hydraulic properties in porous media. Hydrology Paper No. 3, Colorado State University, 27 pp. [Available online at http://www.wipp.energy.gov/ library/cra/2009_cra/references/Others/Brooks_Corey_1964_ Hydraulic_Properties_ERMS241117.pdf.] Chen, J., and P. Kumar, 2001: Topographic influence of the seasonal and interannual variation of water and energy balance of basins in North America. J. Climate, 14, 1989–2014. Choi, G. W., and A. Molinas, 1993: Simultaneous solution algorithm for channel network modeling. Water Resour. Res., 29, 321–328. Choi, H. I., 2006: 3-D volume averaged soil-moisture transport model: A scalable scheme for representing subgrid topographic control in land-atmosphere interactions. Ph.D. dissertation, University of Illinois at Urbana-Champaign, 189 pp. ——, and X.-Z. Liang, 2010: Improved terrestrial hydrologic representation in mesoscale land surface models. J. Hydrometeor., 11, 797–809.

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