JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION FEBRUARY
AMERICAN WATER RESOURCES ASSOCIATION
2005
RUNOFF MODELING OF A MOUNTAINOUS CATCHMENT USING TOPMODEL: A CASE STUDY1
Nageshwar R. Bhaskar, Laura K. Brummett, and Mark N. French2
ABSTRACT: The rainfall-runoff response of the Tygarts Creek Catchment in eastern Kentucky is studied using TOPMODEL, a hydrologic model that simulates runoff at the catchment outlet based on the concepts of saturation excess overland flow and subsurface flow. Unlike the traditional application of this model to continuous rainfall-runoff data, the use of TOPMOEL in single event runoff modeling, specifically floods, is explored here. TOPMODEL utilizes a topographic index as an indicator of the likely spatial distribution of rainfall excess generation in the catchment. The topographic index values within the catchment are determined using the digital terrain analysis procedures in conjunction with digital elevation model (DEM) data. Select parameters in TOPMODEL are calibrated using an iterative procedure to obtain the best-fit runoff hydrograph. The calibrated parameters are the surface transmissivity, To, the transmissivity decay parameter, m, and the initial moisture deficit in the root zone, Sr0. These parameters are calibrated using three storm events and verified using three additional storm events. Overall, the calibration results obtained in this study are in general agreement with the results documented from previous studies using TOPMODEL. However, the parameter values did not perform well during the verification phase of this study. (KEY TERMS: runoff; TOPMODEL; runoff modeling; topographic index; subsurface flow.)
occurs as subsurface flow often referred to as “macropore flow.” The amount of subsurface runoff is linked to catchment topography, subsurface geology, and soil moisture. Hence, any runoff modeling effort must recognize the characteristics that control overland or surface runoff (referred to as quick return flow) as well as subsurface runoff (referred to as intermediate flow). These two components of direct runoff depend on the subsurface soil profile that controls the moisture storage capacity (which includes the spatial variation of the hydraulic conductivity, porosity, soil thickness) and the catchment topographic characteristics. Wolock (1993) reinforces the importance of these two sources of runoff generation within catchments. TOPMODEL (TOPography based hydrologic MODEL) was first introduced by Kirkby and Weyman (1974) to simulate runoff from a catchment based on the concept of saturation excess overland flow and subsurface flow. TOPMODEL is a physically based rainfall-runoff model, which places emphasis on the role of catchment topography in the runoff generation process (Beven and Kirkby, 1979). An implicit assumption is that the local ground water table has the same slope as the watershed surface. This allows for the modeling of subsurface saturated flow using the surface topographic slope. The topography dominated rainfall-excess generation process is described by using a topographic index, λi = ln (ai/tanβi), where ai is upslope catchment area per unit contour length draining to a point i in the catchment and tanβi is the local surface topographic slope (assumed equal to the hydraulic gradient of the saturated zone) at the same location. This index is used to calculate the average
Bhaskar, Nageshwar R., Laura K. Brummett, and Mark N. French, 2005. Runoff Modeling of a Mountainous Catchment Using TOPMODEL: A Case Study. Journal of the American Water Resources Association (JAWRA) 41(1):107-121.
INTRODUCTION Catchment direct runoff response to rainfall involves generation of rainfall excess (runoff response) and the transfer of this excess to the catchment outlet via the land surface and through linked channels (channel response). However, in hilly catchments there is evidence that a portion of the runoff
1Paper No. 04012 of the Journal of the American Water Resources Association (JAWRA) (Copyright © 2005). Discussions are open until August 1, 2005. 2Respectively, Professor, Department of Civil and Environmental Engineering, University of Louisville, Louisville, Kentucky 40292; Project Engineer, QK4, Inc., 815 West Market Street, Louisville, Kentucky 40202; and Professor, Department of Civil and Environmental Engineering, University of Louisville, Louisville, Kentucky 40292 (E-Mail/Bhaskar:
[email protected]).
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BHASKAR, BRUMMETT, AND FRENCH data. The average topographic index, λ, was 6.58, value of T o = 0.504 m 2 /h, and parameter m was 0.0344 m. Beven and Wood (1983) also studied the 456 km2 North Fork Rivanna catchment in Virginia. The average topographic index, λ, in this study was 7.64, value of To = 11.75 m2/h, and parameter m was equal to 0.0092 m. With the above discussion in mind, the objective of this study is to investigate the use of TOPMODEL for modeling runoff in the hilly catchments of eastern Kentucky. To accomplish this, TOPMODEL: version 95.02 (Beven et al., 1995b) is used to simulate runoff from the Tygarts Creek catchment in the Appalachian Mountains located near Olive Hill, Kentucky (refer to Figure 1). Modeling is accomplished using single and subcatchment model representations as illustrated in Figure 2. In either case, TOPMODEL parameters are calibrated using three storm events and verified using three additional storm events. Dividing a catchment into subcatchments allows for any spatial variation of subsurface soil characteristics such as the transmissivity value, and rainfall. Some versions of TOPMODEL utilize a soil topographic index, ln (a/Totanβ), where the transmissivity value, To, can change for each location within a catchment whenever an index value is calculated. Overall, the calibration results obtained in this study are in general agreement with the results documented from previous studies using the TOPMODEL. However, the parameter values do not perform as well during the verification phase of this study. For the single catchment and subcatchment models, the storm events on December 18, 1990, and January 5, 1993, produced similar TOPMODEL calibration results. However, the storm event on August 13, 1993, produced parameters somewhat different for the subcatchment model. The calibration results are validated using the storm events occurring on March 26, 1991, December 3, 1991, and August 6, 1995, but the result does not produce hydrographs that fit as well as the calibration storm events. Based on this, it is apparent from the results of this study that the TOPMODEL parameters are dependent on the storm event used in the calibration process.
moisture deficit over the entire catchment and the local moisture deficit at any location i within the catchment. Hence, it can be used to characterize how the moisture deficit at any particular location within the catchment deviates from the average moisture deficit of the entire catchment. Since the development of TOPMODEL, a number of researchers have investigated the role of its modeling components in simulating catchment runoff. These studies include the derivation and use of the topographic index in simulating catchment runoff, effects of digital elevation model (DEM) data resolution on topographic index (Wolock and Price, 1994; Quinn et al., 1995; Wolock and McCabe, 1995) and interpretation of TOPMODEL parameters in runoff simulations (Franchini et al., 1996). The TOPMODEL parameters examined in past studies are the surface transmissivity, T o , and the transmissivity decay parameter, m. According to Beven (1997), the concept of transmissivity, as used in TOPMODEL, does not have the traditional meaning of ground water mechanics, where transmissivity refers to the rate at which water is transmitted through a unit width of aquifer under unit hydraulic gradient. The transmissivity values obtained using TOPMODEL are for downslope subsurface flow, where the unit hydraulic gradient is equal to the surface topographic slope. The other TOPMODEL parameter m reflects the decay rate of the assumed transmissivity profile (relationship between the subsurface transmissivity, T, at any depth to the surface transmissivity, To). Types of profiles that have been investigated are exponential, parabolic, and linear, the choice of which depends on observed streamflow recession curves within the catchment (Ambroise et al., 1996). Hence, the shape of streamflow recession curves during periods of no recharge to the ground water table can be analyzed to get an initial estimate of the parameter m. Past studies have shown this parameter to range from 0.003 to 0.038 m (Beven, 1997). Beven (1997) gives an excellent summary of the results of previous studies using TOPMODEL. Three specific studies are mentioned here. The topographic characteristics of the 70 km2 Réal Collobrier catchment in France was studied by Obled et al. (1994) using a DEM file resolution of 60 m. Based on digital terrain analysis (DTA), the average topographic index value, λ, was 7.31. The calibrated values of the TOPMODEL parameters m and T o were 0.017 m and 1,765 m2/h, respectively. These values were obtained using a constant velocity channel routing. Beven and Wood (1983) did a similar investigation using the 105 km 2 Davidson catchment in North Carolina. Although DEM data were not used by Beven and Wood, the topography was digitized from contour
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TOPMODEL THEORY Runoff Production in TOPMODEL TOPMODEL primarily generates estimates of runoff at the catchment outlet from saturation excess at the surface and from subsurface flow. The rainfallrunoff equations used are derived from: (1) Darcy’s 108
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Figure 1. Tygarts Creek at Olive Hill Catchment Location Map.
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Figure 2. Tygarts Creek at Olive Hill Subcatchments Used in TOPMODEL.
law, (2) the continuity equation, and (3) the assumption that the saturated hydraulic conductivity decreases exponentially as depth below the land surface increases. The equations used in this study follow the developments of Beven et al. (1995a) and for the sake of brevity only the important ones are included here. Darcy’s law in TOPMODEL takes the form, qi = To(tanβi)e(-Si/m), where the index i refers to a specific location in the catchment, qi is the downslope flow beneath the water table per unit contour length (m2/h), tanβi refers to the average inflow slope angle, To is the surface transmissivity (m2/h) at location i, m is a transmissivity decay parameter (m), and Si is the moisture deficit (amount of moisture required to saturate the soil) at location i (m). The continuity equation is represented by the quasi-steady-state recharge rate to the water table, qi = riai, where ri is the recharge rate (m/h) to the water table and ai is the upslope contributing area per unit contour length (m2/m) at any location i in the catchment. Combining these equations and rearranging gives an expression for the moisture deficit, Si, at any particular location i within the catchment (Beven et al., 1995a), Si = - m ln {ri ai / Totanβi}
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The variable, S i , in the above equation can be – expressed in terms of the average moisture deficit, S , for the entire catchment or subcatchment as – Si = S - m {(λi - λ) - (ln To - lnTe)}
(2)
where λi = ln (ai / tanβi ) is the local topographic index and Te is defined as the average transmissivity value for the entire catchment or subcatchment and is equal to (1/A) ∑ lnTo. The catchment average topographic index value, λ, in Equation (2) is equal to (1/A) ∑ ln i (ai/tanβi), where A is the entire area of the catchment or subcatchment. Equation (2) is the fundamental equation for describing runoff production within TOPMODEL because it defines the degree of saturation for each topographic index value λi at any location within the catchment. If one assumes Te equal to – To in Equation (2), Si depends on S and the deviation of the local topographic index, λi, from λ. Since small values of Si are associated with larger values of the topographic index, λ i , the higher the topographic index value at any location in the catchment, the smaller amount of moisture that will be needed to saturate the soil profile for that location. In the TOPMODEL version used in this study (Beven et al., 1995b), it is assumed that the hydraulic conductivity, K, decreases exponentially with depth.
(1)
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RUNOFF MODELING OF A MOUNTAINOUS CATCHMENT USING TOPMODEL: A CASE STUDY The hydraulic conductivity and transmissivity have the relation T = Kb, where b is the assumed average depth of the soil moisture deficit zone. Hence the transmissivity below the catchment surface can be expressed as T = T o e (-Si/m) , where T (m 2 /h) is the transmissivity value for a local moisture deficit, Si. This relationship is used in the development of Equation (2) above. There are three main soil profile zones considered for runoff production in TOPMODEL. They are the root zone, the unsaturated zone, and the saturated zone (Beven et al., 1995a). When the root zone exceeds the field capacity of the soil, excess moisture contributes to moisture storage in the unsaturated zone. Beven et al. (1995a) describe in detail the equations describing flow through the unsaturated and saturated zones in TOPMODEL. A brief summary follows. The vertical flux through the unsaturated zone is represented by qvi = Suz/(Si td)
The recharge rate to the saturated zone, Qv (refer to Equation 4) and the subsurface flow from the saturated zone, Q b , (refer to Equation 5) are used to update the value of the average moisture deficit, , in the catchment at each time step ∆t (h). This is represented by – – S t = S t-1 + (Qb, t-1 - Qv, t-1). ∆t
where the subscript t represents the current time – interval. Note that the initial value of S (i.e., when t = 0) is calculated from Equation (5) using the initial value of the observed hydrograph as Qb. The total contribution to the catchment outlet at any time step, Qi (simulated flow), is the sum of the subsurface flow, Qb, and the saturation excess overland flow, Qovr. The overland flow, Qovr is calculated as the product of the depth of saturation excess and the fractional area of the topographic index values that are generating the saturation excess. Routing is necessary to recognize the effects of travel time within the catchment. The routing method used in TOPMODEL resembles Clark’s (1945) method, which is a time area routing method. In the time area method of catchment routing, the travel time in the catchment is divided into equal intervals. At each time interval, it is assumed that the area within the catchment boundaries and the specific distance increment will contribute to the flow at the catchment outlet. The partial flow at the catchment outlet from each subarea is equal to the product of the rainfall excess produced times the area of the contributing portion of the catchment. Summing the partial flows of all contributing areas at each time step gives the total flow at the catchment outlet for each time step in the hydrograph (Ponce, 1989).
(3)
where, qvi has units of (m/h), Suz is the moisture storage in the unsaturated zone at each time step at location i (m), Si is the moisture deficit in the unsaturated zone at location i at each time step (m), and td is the time delay per unit depth of deficit (h/m). In the above equation, the term in the denominator, Sitd, represents a time constant that increases with the soil moisture deficit. The recharge rate to the saturated zone at any time step from the unsaturated zone is qviAi, where Ai is the fractional area (fraction of total catchment area at location i) associated with topographic index class i. This recharge is summed over the total number of topographic index classes, n, to get the total recharge to the saturated zone Qv (m/h) = ∑ qvi Ai i
(4)
STUDY PROCEDURE
at the current time step. Once Qv enters the saturated zone, the flow in the saturated zone or subsurface flow, Qb (m/h), is —
Qb = Qoe(-S /m)
Study Area The Tygarts Creek catchment used in this study is located in the Appalachian Mountains of eastern Kentucky near Olive Hill (refer to Figure 1). The catchment is composed of a forested hilly terrain underlain predominantly with silty clay soil and deeper by fissured limestone. A U.S. Geological Survey (USGS) streamflow gage at Olive Hill (No. 03216800) is located in the northeast corner of the catchment, which has a drainage area of approximately 156 km2 and an average slope of 7 percent. The catchment draining to the stream gage at Olive Hill is divided into seven
(5)
The flow Qb can also appear at the surface when the soil profile is fully saturated, such as at the bottom of a hillslope. Qo (m/h) in Equation (5) is the subsurface flow when the soil is fully saturated (i.e., – when S = 0) and is equal to Ae-γ, where A is the total catchment area and γ is the average soil-topographic index, given by (1/A)[∑ln(ai/Totanβi)]. Note that for constant transmissivity, To, within the catchment, γ = l/To, where λ is the average value of the topographic index for the catchment. JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION
(6)
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BHASKAR, BRUMMETT, AND FRENCH subcatchments (based on principal flow paths) as shown in Figure 2.
necessary topographic and hydrologic data associated with the catchment and each subcatchment are available within the WMS. Table 1b summarizes these data for the Tygarts Creek catchment and subcatchments. The streams are divided into several segments and the slopes and lengths of each are determined. These physical attributes are used for channel and routing velocity calculations.
Data Collection The data necessary to implement TOPMODEL and its components are a USGS DEM, the streamflow data for the select storm events from the USGS gage station, and the precipitation data for each storm event from the appropriate National Weather Service gage. The 1:250,000 scale (rectangular grid size of 75.2 m by 90.5 m) Huntington-West USGS DEM was used in the analysis. The streamflow and precipitation data for the storm events of December 18, 1990, January 5, 1993, and August 13, 1993, are used for model calibration, and the storm events on March 26, 1991, December 3, 1991, and August 6, 1995, are used for model verification. The characteristics of these storm events are shown in Table 1a.
TABLE 1b. Catchment and Subcatchment Characteristics.
TABLE 1a. Storm Event Characteristics.
Storm Date*
Rainfall Depth* (mm)
Total Runoff Depth* (mm)
Type
Area (km2)
Slope (m/m)
Average Topographic Index λ
Single* 1 2 3 4 5 6 7
155.97 21.11 15.98 35.97 15.36 14.89 33.33 19.32
0.076 0.081 0.071 0.077 0.078 0.070 0.076 0.074
8.95 8.84 8.95 9.11 8.96 9.16 9.00 8.97
*Single refers to the entire Tygarts Creek at Olive Hill catchment *used in the single catchment model.
Total Runoff To Total Rainfall* (percent)
Topographic Index Values
Calibration Event December 18, 1990 January 5, 1993 August 13, 1993
69.60 17.78 88.90
56.59 13.31 16.15
The topographic index values are determined using the DTA procedure referred to as GRIDATB (a subroutine in TOPMODEL). For a detailed discussion of this procedure, refer to Quinn et al. (1995). GRIDATB uses a multiple flow direction algorithm that requires a DEM with square grid cells as input. The procedure groups the topographic index values into 30 classes and is used in TOPMODEL. A topographic index value is determined for all grid cells, except those that are sinks. A sink is defined as a cell that has flow going into it, but no flow going out in any direction. If sinks are not removed, an average local terrain slope is assumed so flow will pass through the cell, but a topographic index value is not assigned. GRIDATB is implemented for the entire Tygarts Creek catchment and for each subcatchment to obtain the topographic index values shown in Table 1b and graphically illustrated in Figure 3.
81.31 74.86 18.17
Verification Event March 26, 1991 December 3, 1991 August 6, 1995
25.65 83.57 139.70
9.83 39.93 20.12
38.32 47.78 14.40
*Data obtained from French et al (1996).
Delineation of the Catchment and Subcatchments Before DEM data are used in the TOPMODEL framework, it is imported into the Watershed Modeling System (WMS) Version 5.1 (Brigham Young University, 1997) for the purpose of delineating the catchment and subcatchments. The WMS uses the internal program TOPAZ (a DTA routine) to determine the flow directions and flow accumulations from each grid cell in the DEM, where the latter is used to identify streams. The catchment can be delineated once the user defines the outlets of the catchment or subcatchments. Once this is accomplished, all JAWRA
Channel and Routing Velocities and Distance Area Data Channel velocity refers to the velocity within a stream segment or within a distance increment. 112
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Figure 3. Topographic Index Curves for the Catchment and Each Subcatchment.
Routing velocity refers to the velocity that translates runoff from a given location to the catchment outlet. The average channel and routing velocities are estimated in the following manner. The equivalent stream slopes are determined for each subcatchment using the equation Savg = [∑n Li/(∑n (Li//Si)]2 (Ponce, 1989), where Li is the length of stream segment i, Si is the slope of stream segment i, and n is the total number of stream segments. The approximate average velocities for different stream types based on the stream slope can be found in hydrologic literature (Chow et al., 1988). The distance area data are used to determine the routing velocity time to the catchment outlet. The streams in the catchment are divided into equal distance segments. An approximate average velocity is determined, as discussed in the previous section. This velocity, referred to as the routing velocity, is assumed to be constant in all the stream segments. The travel time necessary for a specific area to reach the catchment outlet is determined. The distance area data are specified in the following manner. At the catchment outlet, the distance and the fractional contributing area are zero. Thereafter, each distance and associated fractional area given are cumulative, as one moves to the catchment divide upstream from the outlet, with the final accumulated fractional area being JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION
equal to one. When studying a subcatchment model, the first distance given is the distance from the subcatchment outlet to the main catchment outlet. The associated fractional area is still zero since the area accumulated at the subcatchment outlet at the beginning of the first time interval is zero. The final accumulated area for each subcatchment is also one. TOPMODEL Calibration Using TOPMODEL, the single catchment and subcatchment models are calibrated using a trail-anderror procedure for three storm events of December 18, 1990, January 5, 1993, and August 13, 1993 (refer to the first three storm events listed in Table 1a). The criteria used in the calibration process determine the parameter set yielding the highest Nash and Sutcliffe efficiency value defined as (Beven et al., 1995a): n n 2 E = 1 − (Q obs − Q i ) / (Q obs − Qav )2 i = 1 i=1
∑
∑
(7)
where Qobs is the observed stream flow, Qi is the simulated stream flow, Q av is the average observed
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BHASKAR, BRUMMETT, AND FRENCH model requires several hundred trials since four parameters, m, ln To, td, and Sr0, are evaluated for all seven subcatchments. All hydrographs generated in TOPMODEL are in units of m3/h/m2 (or m/h), however, the results are shown in m3/s. The calibrated TOPMODEL parameters are shown in Table 2. It is clear from this table that the calibration for each storm event produces similar values of the parameters m and To. Table 3 compares the simulated peak flows and time-to-peak values with the observed for each storm event used in the calibration phase. Also included in this table are the values of the Nash and Sutcliffe efficiency value, E (refer to Equation 7). For all three events, the value of E is above 0.87 (or 87 percent), indicating a good fit of observed and simulated streamflow values. The subcatchment model is calibrated using the same storm events as the single catchment model. Referring to Table 2, calibrating the storm events on January 5, 1993, and December 18, 1990, produces similar values of m and To, and these values are generally in agreement with those calibrated for the single catchment model. The values of m range from 0.003 m to 0.011 m and the ln To values range from -2.3 to 14. The storm event on August 13, 1993, however, produces parameters that are different (by one order of magnitude) from the other two events. The m values have a longer range, from 0.010 m to 0.055 m and the ln To values are generally lower but remain consistent with other events ranging from -1.3 to 4.6. The calibrated parameter values are all similar to the results of previous studies using TOPMODEL (Beven, 1997). The hydrographs for the single catchment and subcatchment models are illustrated in Figure 4 along with the observed hydrographs. Calibration procedures show that parameters m and To have the most effect on model efficiency, E. During the calibration process, if m decreases, then To increases, and vice versa. Beven et al. (1995a) state that smaller values of m, together with larger values of To, signify a soil profile with a shallow effective soil depth and a pronounced transmissivity decay. Although the Sr0 values chosen also affect the model efficiency, a definitive value could not be determined for Tygarts Creek catchment. This value will vary based on the moisture in the soil before rainfall commences. The time delay parameter, td, is initially set to 1 h/m for each storm event. Any variation in this parameter during calibration does not change the model efficiency, E. Since the time delay is equal to the computational time interval, it implies that there is no storage in the unsaturated zone for any time period longer than the time step. Beven et al. (1995a) states that it could be difficult to relate the calibrated parameters to the actual properties of the soil since the calibration process often
stream flow and n is the total number of time steps used in the flow simulation. According to Equation (7), if the simulated and observed flows are equal, the value of E will be equal to 1 or 100 percent. The two TOPMODEL parameters, m and ln To, are considered for calibration. The parameters td and Sr0 are also calibrated since these values are initially unknown. To calibrate the single catchment model, all parameters are assigned initial values. The parameter td is initially set equal to the quasi steady-state computational time interval, ∆t, of 1 h/m. Starting with m, the value is varied, holding all other parameters at the values previously set, to determine which value of m yields the highest Nash and Sutcliffe efficiency value, E. With this value of m and all other parameters held constant, ln T o is varied with an effort to further maximize this efficiency. The other parameters are then varied until a final parameter set is obtained that shows little or no improvement in the efficiency, E. The parameters for all seven subcatchments in the subcatchment model are calibrated in the same manner. TOPMODEL Verification The single catchment and subcatchment models are verified using the last three storm events of March 26, 1991, December 3, 1991, and August 6, 1995, as shown in Table 1a. These storm events are completely independent of the ones used in the calibration phase of the study. Four parameter sets are selected for each storm event. Parameters in the first (Parameter Set 1) and third (Parameter Set 3) sets contain the average of parameters calibrated for each storm event for the single catchment and subcatchment models during the calibration phase of this study. The parameters in the second (Parameter Set 2) and fourth (Parameter Set 4) sets contain the average values of the calibrated parameters from the storm events on December 18, 1990, and January 5, 1993. The reason for not including the calibrated parameters from the storm event of August 13, 1993, is that their values were quite different from the first two events.
DISCUSSION OF RESULTS
Calibration Results The single catchment model requires an average of 100 trials of parameter sets and the subcatchment JAWRA
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RUNOFF MODELING OF A MOUNTAINOUS CATCHMENT USING TOPMODEL: A CASE STUDY TABLE 2. Calibrated TOPMODEL Parameters for Single and Subcatchment Models.
Date of Event
Subcatchment
Average Transmissivity Topographic Decay Index Parameter λ) (λ m(m)
Transmissivity of Saturated Soil ln To To (m2/h)
Initial Moisture Deficit in Root Zone Sr0 (m)
Initial Average Moisture Deficit – S (m)
Single Catchment Model December 18, 1990 January 5, 1993 August 13, 1993
na na na
8.95 8.95 8.95
0.007 0.004 0.017
2.0 1.2 1.0
7.40 3.30 2.70
0.006 0.000 0.008
0.019 0.010 0.082
Subcatchment Model December 18, 1990
1 2 3 4 5 6 7
8.84 9.11 8.96 8.88 9.16 9.00 8.97
0.006 0.008 0.005 0.009 0.007 0.005 0.011 0.007
3.4 3.5 2.3 3.8 2.0 1.2 13.0 3.8
29.96 33.12 9.97 44.70 7.39 3.32 4.4x105
0.003 0.013 0.005 0.009 0.009 0.008 0.001 0.007
0.025 0.032 0.015 0.040 0.017 0.009 0.150
1 2 3 4 5 6 7
8.84 9.11 8.96 8.88 9.16 9.00 8.97
0.004 0.005 0.003 0.005 0.005 0.003 0.005 0.004
0.7 14.0 3.4 12.0 14.0 -2.3 11.0 5.7
2.01 1.2x106 29.96 1.6x105 1.2x106 0.10 6x104
0.000 0.000 0.001 0.000 0.000 0.003 0.000 0.001
0.007 0.075 0.013 0.066 0.074 -0.002 0.060
1 2 3 4 5 6 7
8.84 9.11 8.96 8.88 9.16 9.00 8.97
0.040 0.012 0.011 0.055 0.018 0.010 0.030 0.022
-1.3 4.6 0.6 0.9 0.4 0.3 0.6 0.7
0.27 99.48 1.82 2.46 1.49 1.35 1.82
0.043 0.007 0.024 0.038 0.038 0.021 0.050 0.030
0.108 0.010 0.049 0.267 0.073 0.014 0.134
Average January 5, 1993
Average August 13, 1993
Average
TABLE 3. Runoff Simulation Results of Calibration Phase.
Storm Event
TOPMODEL Peak Flow Q (m3/s)
TOPMODEL Time-to-Peak (hours)
Observed Peak Flow Q (m3/s)
Observed Time-to-Peak (hours)
Nash and Sutcliffe Efficiency E
122.0 47.3 59.2
33 8 18
0.993 0.870 0.871
122.0 47.3 59.2
33 8 18
0.998 0.953 0.957
Single Catchment Model December 18, 1990 January 5, 1993 August 13, 1993
128.5 42.4 54.0
32 10 18 Subcatchment Model
December 18, 1990 January 5, 1993 August 13, 1993
122.5 43.2 57.0
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Figure 4. TOPMODEL Calibration: Comparison of Runoff Hydrographs for Single Catchment and Subcatchment Models.
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RUNOFF MODELING OF A MOUNTAINOUS CATCHMENT USING TOPMODEL: A CASE STUDY tends to make up for any errors in model structure. However, the calibrated values in this study may be high for downslope transmissivity due to the large grid size of 83 m. As previously discussed by Franchini et al. (1996), a large grid size used in the DTA can cause the calibrated transmissivity values, To, to be higher, when compared to the use of a smaller grid size. For comparison purposes, an approximate T value for each type of soil found in Tygarts Creek catchment is listed in Table 4. The T values used for comparison are determined in the following manner. The saturated hydraulic conductivity values, K, for various types of soils and rock are obtained from a ground water hydrology text such as Todd (1980). These values are then converted to transmissivity values, T, using the depth b of the soil moisture deficit zone, which is calculated as the ratio of the average value of the maximum capacity of the unsaturated zone, SDav, and the effective porosity, θ, of silty clay soil assumed equal to 0.385 (Chow et al., 1988). The value SDav is calculated by averaging the local moisture deficit values, SDi, over all topographic index values at each time step. The T values for each storm event are calculated using T = Toe(-Si/m), with Si equal to 0.015 m and m equal to its value calibrated for each storm event. A possible reason for the differences in the calibrated values of m and To for the storm event on August 13, 1993, as compared to the other two storm events is the low percentage of total runoff to total rainfall recorded by the rainfall and streamflow gages. Referring to Table 1a, the percentage of total runoff to total rainfall for this storm event is 18.2 percent, suggesting a larger amount of storage within the catchment. Also, by using single gage rainfall data, it is assumed that the rainfall is uniform over the entire catchment.
This assumption is often inappropriate for larger catchments. It is also possible that parameters m and To are not only dependent on the topography of the catchment, but on rainfall as well. Verification Results To verify the calibration of TOPMODEL the single catchment and subcatchment models are revisited, using three additional storm events, occurring on March 26, 1991, December 3, 1991, and August 6, 1995. All trial parameter sets are shown in Table 5 for comparison. As seen in this table, a different parameter set gave the best efficiency value for each storm event used in the verification phase. Thus, it appears that the TOPMODEL parameters are to some degree storm dependent. For all verifications, the timing of the simulated peak flows occurs within three hours of the observed peak flows. However, the magnitude of simulated peak flows is quite different than the observed in most cases. Figures 5 and 6 illustrate the simulated hydrographs for each storm event. Table 5 shows the parameter values and Table 6 compares the simulated and observed hydrographs for each verification storm event. The August 6, 1995, storm event is shown using Parameter Sets 3 and 4. Using Parameter Set 4 greatly improves the results for this storm event. However, the use of Parameter Set 4 for the other two storm events has the opposite effect. Hence, the simulated hydrographs for the December 3, 1991, and March 26, 1991, storm events are illustrated using Parameter Set 3.
TABLE 4. Comparison of Approximate Transmissivity Values.
Soil or Rock Type Silt
Clay
Fissured Limestone
Hydraulic Conductivity K* (m/h)
Transmissivity of Saturated Soil, To, for Each Storm Event January 5, 1993 August 13, 1993 December 18, 1990 (m2/h) (m2/h) (m2/h)
Aquifer SDav/2** (m)
Transmissivity T (m2/h)
4.17 x 10-5 to 4.17 x 10-4
0.039
1.62 x 10-6 to 1.62 x 10-6
6.92 x 10-5 to 6.92 x 10-4
3.93 x 10-6 to 3.93 x 10-5
1.39 x 10-5 to 1.39 x 10-4
8.33 x 10-6 to 3.33 x 10-3
0.039
3.25 x 10-7 to 1.30 x 10-4
1.38 x 10-5 to 5.52 x 10-3
7.85 x 10-7 minus 3.14 x 10-4
2.77 x 10-6 to 1.11 x 10-3
0.039
0.039
0.00152
0.06467
0.00368
0.01297
**From Todd (1980). **The value of SDav for all three storms is 0.015; effective porosity θ = 0.385.
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BHASKAR, BRUMMETT, AND FRENCH Most of the studies summarized by Beven (1997) report average values slightly less than those presented here. Based on TOPMODEL detailed output files reported in Krauth (1999), it could be concluded that subsurface flow from the saturated zone, Q b , is responsible for approximately 50 percent of the flow at the catchment outlet. The other 50 percent is from saturation excess overland flow, Qovr. This was determined by summing the flow values, Qb and Qovr, over all time steps and comparing the sums. The level of moisture deficit in the catchment and each subcatchment follows a similar trend as the simulated runoff hydrograph.
TABLE 5. TOPMODEL Parameter Values for Verification Models.
Storm Event
Subcatchment
m (m)
ln To
Sr0 (m)
Single Catchment Model August 6, 1995 Parameter Set 1 August 6, 1995 Parameter Set 2 December 3, 1991 Parameter Set 1 March 26, 1991 Parameter Set 1
na
0.010
1.4
0.005
na
0.006
1.6
0.003
na
0.010
1.4
0.005
na
0.010
1.4
0.005
Subcatchment Model August 6, 1995 Parameter Set 3
1 2 3 4 5 6 7
0.017 0.008 0.006 0.023 0.010 0.006 0.015
0.9 7.4 2.1 5.6 5.5 -0.3 8.2
0.015 0.007 0.010 0.016 0.016 0.011 0.017
August 6, 1995 Parameter Set 4
1 2 3 4 5 6 7
0.005 0.007 0.004 0.007 0.006 0.004 0.008
2.1 8.8 2.9 7.9 8.0 -0.6 12
0.002 0.007 0.003 0.005 0.005 0.006 0.001
December 3, 1991 Parameter Set 3
1 2 3 4 5 6 7
0.017 0.008 0.006 0.023 0.010 0.006 0.015
0.9 7.4 2.1 5.6 5.5 -0.3 8.2
0.015 0.007 0.010 0.016 0.016 0.011 0.017
March 26, 1991 Parameter Set 3
1 2 3 4 5 6 7
0.017 0.008 0.006 0.023 0.010 0.006 0.015
0.9 7.4 2.1 5.6 5.5 -0.3 8.2
0.015 0.007 0.010 0.016 0.016 0.011 0.017
CONCLUSIONS The purpose of this study is to examine the application of TOPMODEL to a catchment of moderate size in eastern Kentucky. In particular, the two main parameters that drive TOPMODEL, namely, the surface transmissivity, To, and the transmissivity decay parameter, m, are calibrated using three storm events. The time delay parameter, td, and the initial moisture deficit in the root zone, Sr0, are also calibrated since these values are initially unknown. The calibration results for m and To are in agreement with previous studies using TOPMODEL. However, the calibrated parameters do not perform as well when used in three additional storm events in the verification part of the study. Consequently, a universal set of TOPMODEL parameters cannot be recommended for simulating runoff from Tygarts Creek catchment. However, this conclusion may be reversed if more storm events are used in the calibration phase of this study. In any event, it is apparent from this study that TOPMODEL parameters depend on the storm events used in the calibration procedure. The relationship between the TOPMODEL parameters, the topographic index, and the resulting simulated hydrographs is also examined. The topographic index curves obtained for the Tygarts Creek catchment and each of its subcatchments are in close agreement, as are the average index values. However, the average index values are higher than those documented from previous studies. This may be partly due to the large grid size of 83 m that is used for analysis. Since the parameters m and To, the average topographic index value, and the resulting streamflow values are all directly connected, the large grid size will also affect the calibrated values of m and To.
Overall Performance The use of DEM data with a large grid size can result in higher topographic index values. In this study, the average topographic index value for catchment and subcatchment ranges from 8.84 to 9.11.
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RUNOFF MODELING OF A MOUNTAINOUS CATCHMENT USING TOPMODEL: A CASE STUDY
Figure 5. TOPMODEL Verification Results: Comparison of Runoff Hydrographs for Single Catchment and Subcatchment Models.
ACKNOWLEDGMENTS
LITERATURE CITED
The authors would like to thank the staff at the U.S. Geological Survey, Louisville District Office, Louisville, Kentucky, for providing the data and other help to complete this study and wish to acknowledge the editor and the reviewers for taking the time to review this paper. Their valuable input is greatly appreciated. Finally, the authors wish to extend their sincere appreciation to Professor Keith Beven of Lancaster University, Bailrigg, Lancaster, United Kingdom, for providing the TOPMODEL code, references, and valuable input and guidance on the application of this model.
Ambroise, B., K. Beven, and J. Freer, 1996. Toward a Generalization of the TOPMODEL Concepts: Topographic Indices of Hydrological Similarity. Water Resources Research 32(7):21352145. Beven, K., 1997. TOPMODEL: A Critique. Hydrological Processes 11:1069-1085. Beven, K. and M.J. Kirkby, 1979. A Physically Based Variable Contributing Area Model of Catchment Hydrology. Hydrological Sciences Bulletin 24:43-69. Beven, K., R. Lamb, P. Quinn, R. Romanowicz, and J. Freer, 1995a. TOPMODEL. In: Computer Models of Watershed Hydrology, Vijay P. Singh (Editor). Water Resources Publications. Highlands Ranch, Colorado, pp. 627-668.
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BHASKAR, BRUMMETT, AND FRENCH
Figure 6. TOPMODEL Verification Results: Comparison of Runoff Hydrographs for Single Catchment and Subcatchment Models.
Beven, K., P. Quinn, R. Romanowicz, J. Freer, J. Fisher, and R. Lamb, 1995 b. TOPMODEL AND GRIDATB: A Users Guide to the Distributed Versions (95.02). CRES Technical Report TR110 (2nd Edition), Centre for Research on Environmental Systems and Statistics, Institute of Environmental and Biological Sciences, Lancaster United Kingdom. Beven, K. and E.F. Wood, 1983. Catchment Geomorphology and the Dynamics of Runoff Contributing Areas. J. Hydrol. 65:139-158. Brigham Young University, 1997. WMS: Watershed Modeling System. Reference Manual. Engineering Computer Graphics Laboratory, Provo, Utah. Chow, V.T., D.R. Maidment, and L.W. Mays, 1988. Applied Hydrology. McGraw Hill , Inc., New York, New York, 572 pp.
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Clark, C.O., 1945. Storage and the Unit Hydrograph. Transactions, ASCE 110:1416-1446. Franchini, M., J. Wendling, C. Obled, and E. Todini, 1996. Physical Interpretation and Sensitivity Analysis of the TOPMODEL. J. Hydrol. 175:293-338. French, M.N., N.R. Bhaskar, and G.K. Kyiamah, 1996. Flash Flood Monitoring and Modeling in Kentucky. Research Report No. 195, Kentucky Water Resources Research Institute, University of Kentucky, Lexington, Kentucky. Kirkby, M.J. and D.R. Weyman, 1974. Measurements of Contributing Areas in Very Small Drainage Basins. Seminar Series B, No. 3, Department of Geography, University of Bristol, Bristol, United Kingdom.
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RUNOFF MODELING OF A MOUNTAINOUS CATCHMENT USING TOPMODEL: A CASE STUDY TABLE 6. Runoff Simulation Results From the Verification Phase.
Storm Event
TOPMODEL Peak Flow Time-to-Peak (m3/s) (hours)
Observed Peak Flow Time-to-Peak (m3/s) (hours)
Nash and Sutcliffe Efficiency E
Single Catchment Model August 6, 1995 Parameter Set 3
21.9
14
87.5
12
0.238
August 6, 1995 Parameter Set 4
54.9
14
87.5
12
0.720
278.1
19
169.9
18
0.535
59.1
11
57.2
8
0.397
December 3, 1991 Parameter Set 1 March 26, 1991 Parameter Set 1
Subcatchment Model August 6, 1995 Parameter Set 3
25.2
12
87.5
12
0.264
August 6, 1995 Parameter Set 4
69.9
12
87.5
12
0.864
259.2
15
169.9
18
0.739
45.4
10
57.2
8
0.469
December 3, 1991 Parameter Set 3 March 26, 1991 Parameter Set 3
Krauth, L.G., 1999. Hydrologic Modeling of Floods in an Eastern Kentucky Catchment Using TOPMODEL. M. Engg. Thesis, Department of Civil and Environmental Engineering, University of Louisville, Louisville, Kentucky, 78 pp. Obled, C., J. Wendling, and K.J. Beven, 1994. The Role of Spatially Variable Rainfalls in Modeling Catchment Response: An Evaluation Using Observed Data. Journal of Hydrology 159:305-333. Ponce, V.M., 1989. Engineering Hydrology. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 640 pp. Quinn, P.F, K. Beven, and R. Lamb, 1995. The ln (a/tanb) Index: How to Calculate It and How to Use It Within the TOPMODEL Framework. Hydrological Processes 9:161-182. Todd, D.K., 1980. Groundwater Hydrology (Second Edition). John Wiley and Sons, Inc., New York, New York, 535 pp. Wolock, D.M., 1993. Simulating the Variable-Source-Area Concept of Streamflow Generation With the Watershed Model TOPMODEL. U.S. Geological Survey, Water Resources Investigations Report 93-4124, Lawrence, Kansas, 33 pp. Wolock, D.M. and G.J. McCabe, Jr., 1995. Comparison of Single and Multiple Flow Direction Algorithms for Computing Topographic Parameters in TOPMODEL. Water Resources Research 31(5):1315-1324. Wolock, D.M. and C.V. Price, 1994. Effects of Digital Elevation Model Map Scale and Data Resolution on a Topography-Based Watershed Model. Water Resources Research 30(11):3041-3052.
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