Hydrology Group
Biological and Environmental Engineering
Cornell University
Working Paper
Comparison of TOPMODEL and STOPMODEL:
Conceptualizations and Implementations
Dawn Sedorovich, M.Todd Walter, Pierre Garard-Merchant, Tammo S. Steenhuis,
Abstract
TOPMODEL (Beven and Kirkby 1979) is a popular physically-based watershed model capable
of simulating variable source area processes (Anderson et al. 1997). STOPMODEL is a refined
conceptualization of TOPMODEL for systems in which the variable source area processes are
driven by shallow, transient, interflow (Walter et al. 2002). Although the landscape drainage
expressions are very similar for TOPMODEL and STOPMODEL, it is unclear how
STOPMODEL’s refined conceptualization will alter model results. Figure 1 illustrates the
conceptual differences between TOPMODEL and STOPMODEL. The following is a summary
of the implementations of each model.
Model Structures
TOPMODEL
STOPMODEL
Both models perform a suite of local water balance calculations for each topographic index, i,
representing a discrete area of a watershed, Ai. These calculations are (1) – (7).
(1)
The first operation is to determine the local saturation deficit, Si.

S i  max S     i ,0
Calculate the root zone water deficit:
RZ i  RZ
t 1
i

Determine the local soil water:
(2)
SWi  SATi  Si
P
Update SWi using the Thronthwaite-Mather
methodology.
If RZ < 0, then the drainage into the unsaturated
zone, DUZi = RZi and RZi is set to zero.
If SWi > FCi, then there is drainage into the deep
groundwater, Di, equal to the saturated hydraulic
conductivity of the restricting layer, Ks.
Bulk drainage, Dgw = Dgw + DiAi
The soil water is updated:
(3)
SWi  SWi  Di
Water in the unsaturated zone, UZi is updated:
If SWi > SATi, then the overland flow is:
UZi  UZ it 1  DUZ i
OFi  SWi  SATi Ai
If UZi > Si then the overland flow is:
SWi is set to SATi.
The net change in soil water, SW = SW + SW
OFi  UZi  S i Ai
(4)
(5)
Bulk overland flow is OF = OF + OFi
If Si > 0, then there will be drainage to the deep
saturated groundwater region:
 UZ
DSZ i  f  i
 Si



For simplicity, STOPMODEL assumes all water
leaving the root zone goes directly to the
groundwater. We may want to modify this later.
Make sure no more water drains from the
unsaturated zone than is available:
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(6)
Hydrology Group
Biological and Environmental Engineering
Cornell University
If DSZi > UZc, DSZi = UZi and UZi = UZi – DSZi
The bulk drainage, DSZ = DSZ + DSZi
Working Paper
The root zone deficit is updated, taking into
account evaporation:
This was done in (1)
(7)
RZ i  RZ i  ET
The following calculations are done on a bulk, or watershed basis at the end of each time step.
The drainage from the landscape, or baseflow, is
calculated as:
The drainage from the landscape, or interflow, is
calculated as:
(8)
The average soil water deficit is updated:
(9)
Qb = Qo exp S 
S
Qb = Qo exp  
m
The average saturation deficit is updated:
S
t 1
 S  Qb  DSZ
S
t 1
 S  Qb  SW is:
The groundwater is updated:
GW
t 1
(10)
 GW  Dgw
Base flow is calculated using a linear reservoir
assumption:
Q gw   GW 
Streamflow is calculated:
Streamflow is calculated:
Streamflow  OF  Qb
Streamflow  OF  Qb  Q gw
(11)
References
Anderson, M, N.E. Peters, and D. Walling. (eds). 1997. Special Issue: TOPMODEL. Hydrol.
Proc. J. 11(9): 1069-1356.
Beven, K.J. and M.J. Kirkby. 1979. A physically based variable contributing area model of basin
hydrology. Hydrol. Sci. Bull. 24(1):43-69
Walter, M.T., T.S. Steenhuis, V.K. Mehta, D. Thongs , M. Zion, E. Schneiderman. 2002. A
Refined Conceptualization of TOPMODEL for Shallow-Subsurface Flows. Hydrol.
Proc.16(10): 2041-2046.
9/26/2001
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Hydrology Group
Biological and Environmental Engineering
Cornell University
ET
Soil Reservoir
R
Working Paper
Precipitation
Saturated at the
Surface
z
Streamflow = Qb+Runoff
ST
(a)
Shallow
Restrictive Layer
ET
Precipitation
D
Saturated at the
Surface
R
SS
Leakage
to
Groundwater
(b)
Reservoir
Streamflow = Qb+Qgw+Runoff
Vgw
Figure 1: Schematics of the conceptual design for TOPMODEL (a) and STOPMODEL (b). ST
and SS indicate the physical locations where TOPMODEL and STOPMODEL, respectively, store
the water that controls variable source areas. Also note the different interpretations of recharge,
R.
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