A Conjunctive Surface–Subsurface Flow Representation for Mesoscale LandSurface 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 trans-

port 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 ter-

restrial 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 con-

junctive 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 rec-

ognized as an essential tool to address scientific issues

concerning climate variability, changes, and impacts at

regional to local scales. As the model resolution in-

creases, land surface models (LSMs) coupled with RCMs

need to incorporate more comprehensive physical pro-

cesses and their nonlinear interactions. This has been

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 pa-

rameterizations 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 en-

ergy budgets. Improved parameterizations of key land

surface processes, especially for the terrestrial hydro-

logic cycle, are needed to get better performance from

RCMs.

Corresponding author address: Dr. Xin-Zhong Liang, Depart-

ment of Atmospheric and Oceanic Science, University of Mary-

land, College Park, 5825 University Research Court, Suite 4001,

College Park, MD 20740-3823.

E-mail: xliang@umd.edu

OCTOBER 2013 CHO I ET AL . 1421

DOI: 10.1175/JHM-D-12-0168.1

� 2013 American Meteorological Society

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 sub-

surface lateral transport induced by topography or mois-

ture gradients. As one of the critical components in the

terrestrial hydrologic cycle, runoff is estimated using

the soil water budget without any explicit or parame-

terized 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 er-

rors 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 small-

scale modeling, here specifically targeting for use in me-

soscale land surface parameterizations over a continental

scale to improve regional climate modeling, especially

for the spatiotemporal distribution of surface and sub-

surface water that has significant influence on terrestrial

water and energy budget.

To develop the improved runoff treatment in LSMs,

this study has chosen the CommonLandModel (CoLM)

as the basic LSM that originally utilizes simplistic as-

sumptions and crude parameterizations for the terres-

trial 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 numer-

ous crucial updates and improvements for land pro-

cesses (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 measure-

ments in a stand-alone mode as driven by the observa-

tional forcings (Dai et al. 2003; Niu and Yang 2003; Niu

et al. 2005;Maxwell andMiller 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 applica-

tion 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 ex-

plicit runoff schemes with LSMs. Walko et al. (2000)

incorporated a modified form of Topography-based Hy-

drologicalModel (TOPMODEL) into theLandEcosystem–

Atmosphere Feedbackmodel (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 in-

corporates 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 sub-

grids 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 pre-

diction, 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 (1.62km3 1km). Richter and

Ebel (2006) developed a fully integrated atmospheric–

ocean–hydrology model, the Baltic Integrated Model Sys-

tem (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 Assimila-

tion System (GLDAS) (Rodell et al. 2004) such as CLM,

Mosaic, andNoah at 1-km spacing to improvewater table

depth prediction over North America.

Along with these attempts, we have been continu-

ously seeking improved representations for the terres-

trial hydrology in theCWRF. Choi (2006) andChoi 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 in-

troduced in the work of Kumar (2004). It was demon-

strated 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 con-

verge along topographic concave hollows, any water ex-

ceeding soil porosity needs to be transported to the

1422 JOURNAL OF HYDROMETEOROLOGY VOLUME 14

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 sur-

face 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 rep-

resentations 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, how-

ever, still simulates steep declining recession curves and

relatively small total runoff, primarily because it un-

derestimates the baseflow (Choi and Liang 2010). There-

fore, 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 3DVAST

model for the unsaturated subsurface flow and an 1D

topographically controlled baseflow for the saturated

subsurface flow, where all the components are desig-

nated 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 spa-

tial distribution of flow depth and runoff. Such coupling

enables the CSSF to explicitly simulate surface runoff

that results from both rainfall excess and moisture satu-

ration 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 parameteriza-

tions, especially for runoff, must be tuned and evaluated

at the same resolution as their host climate models.

Therefore, we assess the new CSSFmodule 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.

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 pre-

vious 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 res-

olutions 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 elab-

orates the key features of the new CSSF parameteriza-

tions. 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 ad-

vanced 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 partic-

ular, they have incorporated a realistic geographic dis-

tribution of bedrock depth to improve estimates of the

actual soil water capacity, replaced an equilibrium ap-

proximation of the water table with a dynamic pre-

diction to produce more reasonable variations of the

saturated zone depth, used an exponential decay func-

tion with soil depth for the saturated hydraulic con-

ductivity to consider the effect of macropores near the

ground surface, formulated an effective hydraulic con-

ductivity of the liquid part at the frozen soil interface

OCTOBER 2013 CHO I ET AL . 1423

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 hydro-

logic 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 re-

sults 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 pro-

cesses represented in the current CoLM and the new

CSSF module. Below we describe the new parameteri-

zations introduced into the CSSF, including the treat-

ments 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 mois-

ture 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:

›u

›t5

›F

›z

8>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>:

1›

›z

0BBBBB@Dm

›w

›z|fflfflffl{zfflfflffl}mean

1›D-

›z|ffl{zffl}variability

1CCCCCA (Vertical diffusion)

2›

›z

0BBBB@ Km|{z}

mean

1 K-1|ffl{zffl}

variability

1CCCCA (Vertical drainage)

1›F

›xl

8>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>:

1 z›

›xl

0BBBBBB@Dm

›w

›xl|fflfflffl{zfflfflffl}mean

1›D-

›xl|ffl{zffl}variability

1CCCCCCA (Lateral diffusion)

1 z›

›xl

0BBBB@Km|{z}mean

1 K-11K-

2|fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}variability

1CCCCA (Lateral drainage),

(1)

FIG. 1. Schematic diagram for the key terrestrial hydrologic processes represented in the

current CoLM and the new CSSF parameterizations.

1424 JOURNAL OF HYDROMETEOROLOGY VOLUME 14

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 hori-

zontal grid cells with multiple soil layers in the new CoLM1CSSF model.

OCTOBER 2013 CHO I ET AL . 1425

where u is the volumetric water content for a soil ele-

ment, 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 pre-

dictions [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 result-

ing 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 con-

tribution from saturation lateral runoff or baseflow that

is controlled by topography (Stieglitz et al. 1997; Chen

andKumar 2001;Warrach et al. 2002; Niu andYang 2003;

Niu et al. 2005; Choi and Liang 2010). In the new CSSF

model, subsurface runoff consists of four components as

Rsb 5Rsb,bas1Rsb,dra1Rsb,int 1Rsb,sat , (2)

whereRsb,bas,Rsb,dra,Rsb,int, andRsb,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 hori-

zontal adjacent soil grids. Note that baseflow runoff

is dominant in subsurface runoff for the study basins

since all other subsurface runoff components are neg-

ligible 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 VASTmodel is limited

to the vadose zone, the so-called interflow or through-

flow, because it is modeled by the u-based Richards

equation. Since the VAST model is insufficient to cap-

ture the real feature of baseflow in the saturated zone,

we need the further improvement of the baseflow cal-

culation scheme associated with the water table depth

variation.

Following Sivapalan et al. (1987), most TOPMODEL-

based models (Beven and Kirkby 1979) represent sub-

surface saturated lateral runoff (baseflow) induced by

topographic control as

Rsb,bas 5zKs(0)

fe2le2fz$ , (3)

where Ks(0) is the saturated hydraulic conductivity ap-

proximated 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 l5 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 parame-

terization using a single calibration parameter, the maxi-

mum baseflow coefficient Rsb,max, instead of zKs(0)e2l/f .

Hence, Eq. (3) can be rewritten as

Rsb,bas 5Rsb,maxe2fz$ . (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 re-

maining soil moisture content than the residual value

(overestimation). Therefore, we compute baseflow di-

rectly from each saturated layer, starting with an as-

sumption 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)5Fliq(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

1426 JOURNAL OF HYDROMETEOROLOGY VOLUME 14

Rsb,bas5Qb

A5

ðL

ðzN

z$

qb dz dL

A

5

ðL

ðzN

z$

Fliq(z)zKs(z) tanbdz dL

A

5

"T( j)1 �

N

k5j11

T(k)

#tan(bL)

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 trans-

missivity varying nonlinearly with depth and can be

computed for each discrete layer as:

T(k)5

ðzk

zk21

Fliq(z)zKse2f (z2z

c) dz

5

8>>>><>>>>:

Fliq(k)zKs

e2f (zk2z

c)

f[ef (zk2z$) 2 1], k5 j

Fliq(k)zKs

e2f (zk2z

c)

f(efDzk 2 1), k5 j1 1,N

,

(7)

where zc is the compacted depth representing macro-

pore effect (Beven 1982a) near the soil surface, espe-

cially in vegetated areas [see also Eq. (A8)]. The

quantity Dzk is a layer thickness between vertical co-

ordinates zk and zk21 for the layer k. Because the satu-

rated 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)5min

*T(k) tan(bL)

A,

fuliq(k)2max[ur(k)2 uice(k), 0]gDz0kDt

+, (8)

where

Dz0k 5�zk 2 z$ for k5 j

zk 2 zk21 for k5 j1 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 con-

tent at the hygroscopic condition, and Dt is a computa-

tional time increment.

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:

Rsb,bas5 �N

k5j

qb(k) . (9)

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)2qb(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 5.7m 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,dra5Km(zN)1K-1(zN) , (11)

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 contri-

bution 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) sub-

stantially 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

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 in-

terflow runoff causes a minor contribution to the total

subsurface runoff. The interflow runoff is computed as

OCTOBER 2013 CHO I ET AL . 1427

Rsb,int5

�B�N

k51

uout(k)Dzk

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.

4) SATURATION EXCESS RUNOFF

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:

Rsb,sat5max

(0,

"�N

k51

u(k)Dzk 2 �N

k51

us(k)Dzk

#Dt

),

,

(13)

where us is the soil moisture content (porosity) at satu-

ration approximated by the pedo-transfer function in

Eq. (A6). Note that the numerically generated excessive

soil-moisture solution rarely occurs in this study by in-

corporating a maximum surface infiltration limit condi-

tion and the effective hydraulic conductivity function at

the interface of unfrozen areas [see Eq. (A18)] fromChoi

and Liang (2010).

c. Surface runoff representation scheme

1) SURFACE RUNOFF

The total available water supply rate Qw on the sur-

face is computed, incorporating the flow depth h for

a time increment Dt as:

Qw 5Qrain1Qdew1Qmelt 1h/Dt , (14)

where Qrain, Qdew, and Qmelt are rainfall, dewfall, and

snowmelt rate at the surface, respectively. Surface run-

off is generated by the Horton and the Dunn mecha-

nisms. Horton runoff occurs as rainfall intensity exceeds

soil infiltration rate while Dunn runoff takes place when

precipitation falls over the saturated area. For the com-

prehensive 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 sub-

surface is

Rs 5 (12Fimp)max(0,Qw2 Imax)|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}Hortonian

1 FimpQw|fflfflfflfflffl{zfflfflfflfflffl}Dunnian

2 h/Dt ,

(15)

where Fimp is the impermeable area fraction consisting

of the fractional saturated area Fsat and the frozen area

Ffrz as follows:

Fimp5 (12Ffrz)Fsat1Ffrz , (16)

where the frozen areaFfrz is defined inEq. (A16) and the

fractional saturated area Fsat is determined by the to-

pographic characteristics and soil moisture state:

Fsat 5

ðl$l1fZ$

g(l) dl , (17)

where g(l) is the probability density function of the to-

pographic 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 simplifica-

tion made by Niu and Yang (2003) as:

Fsat5Fmaxe20:5fz$ , (18)

where Fmax is the maximum saturated fraction. The ex-

ponent coefficient 0.5 is derived by making the result in

agreement with the three-parameter gamma distribu-

tion of Niu et al. (2005).

The remaining variable Imax in Eq. (15) is defined as

Imax5 Fliq(1)Ksz(1)

�12

cs(1)b1d1

[12wu(1)]

�|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

mean flux

1 Fliq(1)Ksz(1)a2

�(2b11 3)(b11 1)2

1

2b1(b11 2)[12wu(1)

b11322b]

�|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

variability flux

, (19)

1428 JOURNAL OF HYDROMETEOROLOGY VOLUME 14

where (1) or subscript 1 denotes for the top soil layer.

The quantity cs is the saturated suction head, the expo-

nent 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

wu(1)5max

"0,

w(1)2Fimp(1)

12Fimp(1)

#, Fimp(1), 1, (20)

wherew is the effective soil wetness (saturation) defined

in Eq. (A3). Equation (20) is derived from an assump-

tion that the surface layer is saturated during rainfall

events (Mahrt and Pan 1984; Entekhabi and Eagleson

1989; Abramopoulos et al. 1988; Boone andWetzel 1996).

This infiltrability also cannot exceed the maximum pos-

sible influx calculated using the soil water budget at the

first layer as

Imax# us(1)[12wu(1)]Dz1Dt

1Fz11E1 , (21)

where Fz1 and E1 are the soil water flux and the evapo-

transpiration flux, respectively, at the first soil layer.

Hence, the vertical flux Fz0 at the top of each soil col-

umn z0 (the upper boundary condition) is computed as

Fz052min(Qw,

Imax) . (22)

For the lateral boundary conditions, the buffer adjacent

soil columns are assumed to have the same water con-

tent 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 equa-

tions, 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

›t1 cd

›h

›xc5Dh

›2h

›x2c1Rs , (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

cd 53

2V5

3

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih

�So2

›h

›xc

�s, (24)

and Dh is the hydraulic diffusivity expressed as

Dh 5cdh

3

�So 2

›h

›xc

�5Vh

2

�So 2

›h

›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 con-

ditions 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 vol-

ume at the junction can be expressed as

�Qs,out 5�Qs,in , (26)

where the subscripts in and out denote inflow and out-

flow, 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

V2in

21 ghin 5

ðxcout

xcin

dV

dtdxc1

V2out

21 ghout1 ghf , (27)

whereÐ xcoutxcin

(dV/dt) dxc is the energy loss due to accel-

eration of flow, g is the gravitational acceleration, and hfis 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 en-

hanced 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 rain-

fall 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

OCTOBER 2013 CHO I ET AL . 1429

Rtot 5Qs

nfaA1Rsb , (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 up-

stream 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 CoLM1CSSFmodel

The CSSF model is substituted for the existing ter-

restrial 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 obser-

vations, 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 Kanawha River at Charleston, WV 27 060 28 800

03287500 Kentucky River at Lock 4 at Frankfort, KY 14 014 13 500

03320000 Green River at Lock 2 at Calhoun, KY 19 596 18 000

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 (gray-

toned pixels), along with (c) a background map for study basin locations.

1430 JOURNAL OF HYDROMETEOROLOGY VOLUME 14

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 lat-

eral flow after a fully implicit method solves the verti-

cal 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),

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 applica-

tions (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 ob-

servational data over North America constructed by

Liang et al. (2005a,b). These include surface topogra-

phy, 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

TABLE 2. Summary of terrain elevation, bedrock depth ranges, and major land use types for the three study basins.

Basin name Elevation range (m) Bedrock depth range (m) Major land use types

Kanawha River 269–991 1.17–4.19 Deciduous broadleaf forest mixed forest

Kentucky River 235–481 0.87–4.18 Cropland/woodland mosaic deciduous broadleaf forest mixed forest

Green River 140–338 0.93–4.97 Cropland/woodland mosaic deciduous broadleaf forest

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.

OCTOBER 2013 CHO I ET AL . 1431

resolution. The spatial distributions of terrain eleva-

tion 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 991m and land

cover types consisting of cropland–woodland mosaic,

deciduous broadleaf forest, and mixed forest. The bed-

rock depth distribution over these catchments, ranging

from 0.87 to 4.97m, is illustrated in Table 2.

The new CSSF model requires additional SBCs for

each 30-km grid, such as standard deviations of subgrid

FIG. 5. Comparison of the (top panels for each z value) benchmark efficiency and (bottompanels for each z value) correlation coefficient

with the decay factor f and the maximum baseflow coefficientRsb,max of the new CoLM1CSSF using the different anisotropic ratio z5 (a)

500, (b) 1000, (c) 1500, and (d) 2000 for the total runoff of the three study catchments in 1995.

1432 JOURNAL OF HYDROMETEOROLOGY VOLUME 14

local terrain slopes in the two horizontal coordinate di-

rections, 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. Fol-

lowing 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

FIG. 5. (Continued)

OCTOBER 2013 CHO I ET AL . 1433

computation grid resolution. Figure 3 shows that the

so-derived 30-km flow directions represent well the

feature of the Global Hydrological 1 kilometer data-

base (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 mete-

orological 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 reso-

lution 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), spe-

cific humidity at the lowest atmospheric layer (kg kg21),

zonal and meridional winds at the lowest atmospheric

layer (ms21), the lowest atmospheric layer height (m),

convective and resolved rainfalls [mm (3h)21], snow

[mm (3h)21], planetary boundary layer height (m), and

downward longwave and shortwave radiations onto the

surface (Wm22). 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

NARRdata. This is repeated for five cycleswith the same

3-hourly NARR forcings of 1995. The resulting condi-

tions 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 simu-

lation 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:

BE5 12

�N

i51

(Oi 2Si)2

�N

i51

(Oi 2Bi)2

, (30)

R5

"�N

i51

(SiOi)21

N�N

i51

Si �N

i51

Oi

#ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi"�N

i51

(Si)22

1

N

�N

i51

Si

!2#"�N

i51

(Oi)2 2

1

N

�N

i51

Oi

!2#vuut,

(31)

where N is the total number of raw data cells, Oi and Sidenote 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 nor-

malized benchmark efficiency BE measures the model

ability to simulate the observed runoff amplitudes over

the reference model results, and the correlation co-

efficient 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 sub-

surface 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 cali-

bration parameters, the decay factor f (2–10m21) and

the maximum baseflow coefficient Rsb,max (1 3 1024 to

4 3 1024mm s21) for a simulation of the year 1995.

Overall, the benchmark scores are low and the maxi-

mum score occurs with different values of calibration

parameters for each study river basin as shown in Fig. 4.

The decay factor f of 4m21 and the maximum baseflow

coefficient Rsb,max of 2 3 1024mm s21 are selected for

the model calibration parameters over the three study

watersheds. As Choi and Liang (2010) demonstrated,

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.

Kanawha

River

Kentucky

River

Green

River

CoLM BE 0.128 0.131 20.192

R 0.170 0.420 0.316

CoLM1CSSF BE 0.681 0.819 0.782

R 0.715 0.797 0.717

1434 JOURNAL OF HYDROMETEOROLOGY VOLUME 14

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

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 CoLMmodified 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 right-

hand vertical axis.

OCTOBER 2013 CHO I ET AL . 1435

coupled, calibration is done for the two parameters: the

decay factor f (2–10m21) 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 sen-

sitivity analysis depicted in Fig. 5, f5 8m21 and z5 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 infiltra-

tion enhancing the baseflow generation, solving the low-

sensitivity 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 base-

flow [Eq. (7)] above the root zone (;1m). 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 con-

tributes 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

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.

1436 JOURNAL OF HYDROMETEOROLOGY VOLUME 14

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 rain-

fall events, causing no recession time and overall un-

derestimation 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 parame-

ters, 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 simu-

lated 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 signifi-

cant improvement by capturing observations much

more closely over the three study catchments. It is also

clear that the coupling with the CSSF significantly im-

proves the CoLM performance in representing the ba-

sin flow dynamics. Figure 7 and Table 4 demonstrate

that the CoLM1CSSF incorporating the role of surface

flow depth contribution to infiltration results in shal-

lower water table depth and enhanced baseflow gen-

eration. 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 sub-

surface flow.

The CoLM predicts very little subsurface runoff, even

after incorporating more advanced representations, in-

cluding realistic bedrock depth, dynamic water table,

exponential decay profile of the saturated hydraulic con-

ductivity, minimum residual soil water, and maximum

surface infiltration limit (Choi and Liang 2010). In gen-

eral, when total runoff is dominated by its surface com-

ponent, LSMs tend to overestimate runoff peaks and

underestimate runoff recession. This may partially ex-

plain 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 in-

corporating the effects of surface flow depth and sur-

face 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 captur-

ing 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 super-

saturation prevention scheme. Figure 8 illustrates that

the baseflow is predominant in low-flow seasons while

surface runoff is more important during the high-flow

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 be-

tween the routed surface flow and the subsurface flow

with topographic subgrid soil-moisture variation and base-

flow generation simulate total runoff more realistically,

especially in the recession part of the hydrograph. Rela-

tive to observations for theKanawhaRiver, theKentucky

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 can-

not 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 war-

rant 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

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 (mmyr21),Rt is total runoff (mmyr21), 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 evapo-

transpiration rate (mmyr21), and z$ is the water table depth (m).

All values are the 5-yr-averaged basinwide mean.

Kanawha

River

Kentucky

River

Green

River

Observations Pt 1056 1222 1285

Rt 510 403 582

CoLM Rt 104 235 280

rR 0.204 0.584 0.481

rsb 0.620 0.339 0.503

ET 912 968 1006

z$ 1.70 1.55 1.61

CoLM1CSSF Rt 413 339 622

rR 0.810 0.842 1.069

rsb 0.892 0.655 0.574

ET 972 1008 1038

z$ 0.81 0.75 0.66

OCTOBER 2013 CHO I ET AL . 1437

have significant impacts on soil-moisture spatial vari-

ability (Choi et al. 2007), and an explicit surface flow

routing scheme is required for the comprehensive terres-

trial 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 topo-

graphically controlled baseflow to substitute the existing

hydrologic module in the CoLM. The CSSF is im-

plemented into the CoLM by a time-split mixed nu-

merical approach, where the subsurface flow model is

FIG. 8. Modeled 5-yr-averaged climatology of monthly total model runoff consisting of

surface runoff and baseflow components in the new CoLM1CSSFmodel simulation for (top to

bottom) the three study river basins.

FIG. 9. Comparison of 5-yr-averaged climatology of monthly total runoff from the CoLM and the

new CoLM1CSSFmodels along with observations for (top to bottom) the three study river basins.

1438 JOURNAL OF HYDROMETEOROLOGY VOLUME 14

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 stand-

alone simulations of the CoLM with and without the

CSSF driven by realistic SBCs and reliable NARR cli-

mate 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 rep-

resentations for the lateral and subgrid soil-moisture

transport, the surface flow routing and interaction with

subsurface flow, and the topographically controlled base-

flow. 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 infiltra-

tion 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 su-

periority 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 pro-

cesses in the CoLM can cause significant model errors

and, consequently, unrealistic model parameters targeted

for calibration. The redistribution of surface and sub-

surface 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 ad-

vanced model physics representation at that scale to re-

alize 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 fac-

tors 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 asso-

ciated 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 Pro-

gram 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) (NRF-

2013R1A2A2A01008881).

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)5Ksw2b13 , (A1)

c(w)5csw2b , (A2)

wherew is the effective soil wetness (saturation) defined

as

w5

8>>>>>><>>>>>>:

uliq 1 uice 2 ur

us 2 ur, uice, ur

uliq

us 2 uice, uice $ ur

, (A3)

where uliq (mmmm21) is the partial volume of liquid

soil water, uice (mmmm21) is the ice content in frozen

soil, and ur (mmmm21) is the residual moisture con-

tent 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 (mmmm21) are the com-

pacted hydraulic conductivity, the suction head, and

soil moisture content (porosity) at saturation, respec-

tively, and the exponent b is the pore size distribution

OCTOBER 2013 CHO I ET AL . 1439

index. They are approximated by pedo-transfer func-

tions in terms of soil sand and clay fractions (Cosby

et al. 1984; Bonan 1996) as

Ks 5 0:007 055 63 1020:88411:533sand , (A4)

cs 52102:8821:313sand , (A5)

us 5 0:4892 0:1263 sand, (A6)

b5 2:911 15:93 clay. (A7)

To improve estimates of the actual soil water ca-

pacity, we adopt the geographically distributed bed-

rock 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 sat-

urated 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):

Ksz

5Kse2f (z2z

c) , (A8)

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 con-

ductivity has reached the compacted value at the plant

root depth of 1m (Stieglitz et al. 1997; Chen and Kumar

2001). When zc is assumed 1m, Ksz is 7.13–1.41 times

greater thanKs 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

Ksz(k)5

1

Dzk

ðzk

zk21

Kse2f (z2z

c) dz

5Ks

e2f (zk2z

c)

fDzk(efDzk 2 1), (A9)

where Dzk is a layer thickness between vertical co-

ordinates 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 ver-

tical to account for anisotropy (Freeze and Cherry 1979):

Ksx

5Ksy

5 zKsz

, (A10)

where z is an anisotropic factor first introduced by Chen

andKumar (2001) for the desired streamflow predictions.

Also, the diffusivityD and conductivityK functions in

Eq. (1) are calculated as:

Dm 52Ks

zcsb

uswb12 , (A11)

D- 521

2Ks

z

csb(b1 2)a2wb1322b , (A12)

Km 5 SxlKs

zw2b13 , (A13)

K-15 Sx

lKs

z(2b1 3)(b1 1)a2w2b1322b , (A14)

K-25sS

xl

Ksz

(2b1 3)aw2b132b(g11 g2w1 g3w2) ,

(A15)

where subscriptm represents the grid-mean term, and-1

and -2 denote the subgrid variability terms. The quan-

tity Sxl is the grid-mean slope and sSxlis the standard

deviation of local slopes for each grid where the sum-

mation 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, g2, and g3 are parameters characterizing the de-

pendence of moisture on slopes, which are estimated by

the closure parameterization in Choi et al. (2007).

In addition, we need to determine the effective hy-

draulic 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 parame-

terized the frozen part as a function of soil liquid and

ice water contents at soil layer k:

Ffrz(k)5uice(k)

uliq(k)1 uice(k), (A16)

and the unfrozen part of soil moisture is

Fliq(k)5 12Ffrz(k) . (A17)

1440 JOURNAL OF HYDROMETEOROLOGY VOLUME 14

Hence, the effective functions for unfrozen areas at the

interface are computed as

xk11/25min[Fliq(k),Fliq(k1 1)]

�xk 1xk11

2

�, (A18)

where x represents all diffusivity and conductivity func-

tions. The quantities k and k1 1 denote one soil ele-

ment and another adjacent one, respectively, and k1 1/2

denotes the interface of the two in the vertical or

horizontal direction. Note that xzk[ xk11/2 in vertical

direction discretization. This interblock function can

reduce negative or supersaturated soil moisture solution

caused by numerical problems from the existing param-

eterization in most current LSMs (Choi and Liang 2010).

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