- Email: [email protected]
A rainfall and snowmelt runoff modelling approach to flow estimation at ungauged sites in British Columbia
Journal of Hydrology 226 (1999) 101–120 www.elsevier.com/locate/jhydrol
A rainfall and snowmelt runoff modelling approach to flow estimation at ungauged sites in British Columbia Z. Micovic*, M.C. Quick 1 Department of Civil Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada Received 5 May 1999; accepted 7 October 1999
Abstract Streamflow was calculated from meteorological data using the UBC Watershed Model for 12 heterogeneous watersheds in British Columbia. These watersheds varied in drainage area, climate, topography, soil type vegetation and geology, which indicates that statistical regionalization of streamflow is likely to be unreliable. The model results indicated that an average set of model parameters could be applied to all the watersheds, provided that representative meteorological data was available and the impermeable fraction of the watersheds could be determined from independent sources such as natural vegetative cover and surficial geology. The averaged model parameter set gave Nash–Sutcliffe statistical results only slightly lower than results from a full calibration. Therefore the method appears to be useful for complete pre-calibration of ungauged watersheds so that flows can be generated for these ungauged sites. The method has been successfully tested on an independent watershed in British Columbia and another watershed in the Himalayas. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Watershed calibration; Model parameterization; Ungauged sites; Regionalization
1. Introduction Most of the streams in the province of British Columbia are either ungauged or have a short period of gauging record. However, for various engineering applications, estimates of design flows for these sites are required. One approach that has been used previously (Leith, 1975; Waylen and Woo, 1981) is to use a regional flood frequency analysis in which, for a homogenous region, regression equations are developed by regressing flood quantiles estimated at gauged basins against measured basin characteristics. It is then assumed that these equations can be applied * Corresponding author. Fax: 11-604-822-6901. E-mail addresses: [email protected] (Z. Micovic); mquick@ civil.ubc.ca (M.C. Quick) 1 Fax: 1604-822-6901.
to any basin in that region. However, regional regression equations have many shortcomings and standard errors of the predicted quantiles are often quite high. Also, these equations sometimes incorporate physically weak basin characteristics or two or more strongly correlated basin characteristics (e.g. basin area and main channel length). An extensive survey of many statistically based studies of this type are reviewed and discussed by Riggs (1973). In the present work, an alternative approach using a rainfall and snowmelt runoff model is used. The first aim was to calibrate the model for several watersheds in a hydrologically homogeneous region and then to use the model to generate flows for ungauged sites. However, as the work progressed, it was found that the approach could be extended to non-homogeneous regions across the whole province of British
0022-1694/99/$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S0022-169 4(99)00172-9
102
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Fig. 1. Locations of the study watersheds.
Columbia. The UBC Watershed Model was used for this study. Therefore, the objective of this study was to calibrate the UBC Watershed Model for various watersheds across British Columbia with different physical characteristics and to examine the variability of model parameters among the watersheds. It was then possible to identify parameters with small variability and average their values so that they could be applied to all of the watersheds. Finally, the reliability of the resulting streamflow estimates was evaluated and the method was validated by applying it to two catchments not used in deriving the average parameter values. The flows were calculated as if these test watersheds were ungauged and the results were then compared with the measured flows. It was found from this analysis that constant values could be assigned to most of the parameters, so that the number of remaining parameters to be determined
was minimized to two, as will be discussed later. This considerably simplified model still produced reliable results for physically different watersheds, indicating that it can be universally applied for ungauged basins in a region which is not homogeneous.
2. Study watersheds In this study, hydrological behavior of 12 watersheds in British Columbia was analyzed. Locations of the watersheds are shown in Fig. 1, (the shaded areas give an indication of basin size and shape). They are chosen to be heterogeneous, with different sizes of drainage area, climate, topography, soil types, geology and hydrologic regime. Some key factors are summarized in Table 1.
Drainage area (km 2) Barlow Creek 70.7 Bone Creek 268 Bridge River 984 Campbell River 1194 Coquihalla River 742 Illecillewaet River 1150 Jordan River 272 Little Swift River 133 Naver Creek 658 Stitt Creek 139 Tabor Creek 113 Watching Creek 80
Average surface slope
Glaciated Forested Mean annual fraction fraction flood (%) (%) (m 3/s/km 2)
Mean annual precipitation (mm)
Origin of the annual floods
0.0503 0.3576 0.2500 0.2934 0.3501 0.3732 0.3776 0.1509 0.0754 0.4034 0.1450 0.1183
0 11.5 18.29 0 0 6.61 1.54 0 0 13.31 0 0
480 1420 1380 2430 1800 1715 1925 900 800 1530 595 560
1. Snowmelt 2. Rainfall 580 Mainly snowmelt 700 Snowmelt 750 Rainfall 215 Rainfall or snowmelt 90 Snowmelt 520 Snowmelt 540 1. Snowmelt 2. Rainfall 1065 1. Rainfall 2. Snowmelt 600 Snowmelt 790 1. Rainfall 2. Snowmelt 645 Snowmelt 900
87 53 53 72 93 74 61 87 95 41 85 100
0.0689 0.1840 0.2232 0.6697 0.3212 0.2333 0.4042 0.1875 0.1217 0.2725 0.0837 0.0623
Minimal altitude (m)
Altitude range (m)
Mean altitude (m)
Impermeable fraction (%)
395 2280 2186 2065 2105 2740 2060 915 1076 2135 625 930
745 1889 1845 977 1203 1717 1593 1466 961 1947 823 1384
27 47 24 28 29 25 45 48 18 27 29 27
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Table 1 Physical characteristics of the study watersheds
103
104
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
3. Methodology 3.1. The conceptual design of the UBC watershed model The UBC Watershed model was presented by Quick and Pipes (1977), although the earliest ideas date back to 1963 and, thus, a very early version of the model was used for the Fraser River flood forecasting in 1964. Further developments of the model have been presented since that time and now incorporate many user-friendly features, Quick (1995). The model calculates daily watershed outflow using precipitation and maximum and minimum temperatures as input. The model was designed primarily for the calculation of streamflow from mountainous watersheds where streamflow consists of snowmelt, rain and glacier outflow. Since the hydrological behavior of the mountainous watershed is a function of elevation, the model uses the area-elevation bands concept. This concept accounts for orographic gradients of precipitation and temperature, which are assumed to behave similarly for each storm and are dominant gradients of behavior in mountainous areas. Besides the daily streamflow estimates, the UBC Watershed Model provides information on area of snow cover, snowpack water equivalent, energy available for snowmelt, evapotranspiration and interception losses, soil moisture, groundwater storage and surface and sub-surface components of runoff. All this information is available for each elevation band separately as well as for the whole watershed (average values). This is a continuous hydrologic model, which means that it will provide streamflow output as long as meteorological input is available. The physical description of a watershed is given for each elevation band separately in the form of different variables such as area of the band, forested fraction and forest density, glaciated fraction, band orientation and fraction of impermeable area. The UBC Watershed Model was designed to run from a minimum of meteorological and flow data, because these data are often sparse in the mountainous regions. In addition, most of these sparse data are from the valley stations. As a result of these constraints, an important aspect of the model is the elevation distribution of data. A schematic diagram representing the UBC Watershed Model structure is shown in Fig. 2. The model is made up of several submodels:
The meteorological sub-model distributes the point values of precipitation and temperatures to all elevation zones of a watershed. The variation of temperature with elevation controls whether precipitation falls as rain or snow and also controls the melting of the snowpacks and glaciers. The soil moisture sub-model represents the nonlinear behavior of a watershed. All the non-linearity of the watershed behavior is concentrated into this soil moisture sub-model which sub-divides the water input (rain and snowmelt) into four components of runoff namely, fast, medium (interflow), slow (upper groundwater) and very slow (deep groundwater). The impermeable area is the fast responding region of a watershed and is assumed to be adjacent to a well developed stream channel system. This area changes as a function of soil moisture deficit (variable source area). The routing sub-model: routing is linear which leads to great simplifications of model structure. It guarantees conservation of mass and a simple and accurate water budget balance. It should be mentioned that the majority of the parameters in the UBC Watershed Model are pre-calibrated and are kept constant. These parameters include all snowmelt, temperature lapse rate, evapotranspiration and interception parameters. The snowmelt algorithm uses an energy approach, which is discussed in detail in Quick (1995) and can account for forested and open areas, aspect and latitude. Glacier melt is also computed using this same method and parameters. 3.2. Developing a watershed description To develop a watershed description it is necessary to decide how many elevation bands it comprises. This is done by surveying topographical maps and aerial photographs for each particular watershed. By dividing a watershed into more elevation bands we account for more heterogeneity, but also increase computational time. Thus the number of elevation bands varies from watershed to watershed and varied from 4 to 12 in this study. Once we have determined the number of elevation bands into which the watershed will be divided, the general procedure is to do the following for each band: 1. From the maps, determine the altitude of the mid-point of the band.
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
105
Fig. 2. UBC Watershed Model—diagram of the structure.
2. Measure the band area. 3. Determine the fraction of the band that is forested, and the density of the forest canopy. 4. Determine the fraction of the band that is impermeable. 5. Establish the relative north/south orientation of the band. 6. Determine whether or not a glacier is present in the
band. If a glacier is present, estimate the area of the band that is covered by glaciers, and the fraction of the glaciated area that is south facing. Physical characteristics such as forested and glaciated fractions, orientation and density of the forest canopy can be easily measured from the topographic maps and aerial photographs. A rather difficult problem is
106
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Table 2 Starting ranges for the model parameters used in the optimization P0SREP
P0RREP
2 1 to 1 P0DZSH 0–1 a
2 1 to 1
C0IMPA (%) 0–70
E0LMID (m) 1/4–3/4 a
P0GRADL (% per 100 m) 1–10
P0GRADM (% per 100 m) 1–10
P0PERC (mm/day) 0–50
P0FRTK (days) 0–2
P0FSTK (days) 0–2
P0IRTK (days) 1–10
P0ISTK (days) 1–10
P0DZTK (days) 100–250
P0UGTK (days) 10–50
E0LMID is the minimum elevation 11/4 to 3/4 of the watershed’s elevation range
to determine the fraction of impermeable area in each elevation band. 3.3. Calibration of watershed model to study watersheds Model performance is evaluated visually and statistically. The visual criterion involves plotting the calculated hydrograph and comparing it with the measured flow. The statistical criterion used in the UBC model is the model efficiency suggested by Nash and Sutcliffe (1970), based on the ratio of explained and total variances of observed and calculated flow, as follows: n X i1 E! 1 2 X n
Qiobs 2 Qical 2 Qiobs
2 Q obs 2
1
i1
where, n X
Q obs
Qiobs
i1
n
2
and n is the number of days for daily runs or hours for hourly runs, Qiobs the observed flow on day (hour) i and Qical the calculated flow on day (hour) i. The model efficiency, E! relates how well the calculated and observed hydrographs compare in volume and shape. A negative value of E! means that the observed mean flows are closer to observed flows than the flows calculated by the model. The coefficient of determination D! relates how well the calculated hydrograph compares in shape to the observed, and therefore, depends only on timing, but not on volume. The volume error, d V is the third important statistic
used in calibration and is presented as: Q 2 Qcal dV obs Qobs
3
For a successfully calibrated model, the values of E! and D! should be close to 1, with dV kept close to zero. The UBC Watershed Model has a built-in automatic optimization procedure designed to assist the user in the calibration of a watershed. The user has to define reasonable ranges for the parameters and the computer then searches for optimum values. The parameter ranges used in this study are shown in Table 2. The optimization module optimizes three groups of parameters separately. The first group, precipitation parameters, is optimized until the calculated runoff volumes begin to compare with the observed values. Once the annual volumes of observed and calculated flow are reasonably close, the second group, water distribution, distributes the rain and the snowmelt to surface runoff, interflow and groundwater through the soil moisture budget. The third group of parameters, the routing constants, adjusts the time constants for each runoff component controlling the length of time taken to pass through the watershed. The coefficients of efficiency and determination and the volume error for the given period are then calculated. This procedure can be run for any number of iterations, after which the watershed is updated with the parameter values giving the best efficiency. The study watersheds were calibrated for available periods of continuous historical streamflow and meteorological records. The calibration was not done on a year-by-year basis, but was carried out for the whole calibration period for each watershed. However, the calibration statistics for one of the watersheds are shown in Table 3 on a year-by-year basis as well as for the whole period. Where data was available, the calibration was verified for a different
Table 3 Calibration and verification statistics for the Illecillewaet River watershed Mean Qest (m 3/s/d)
Tot Qobs (m 3/s)
Tot Qest (m 3/s)
Tot Qobs2Tot Qest
Coefficient of efficiency (E!)
Coefficient of determination (D!)
57.0 52.3 52.9 49.4 54.3 51.9 49.4 47.3 51.8
53.6 49.2 45.3 47.9 49.1 52.2 52.6 50.6 50.1
2078.7 19083.0 19376.0 18045.5 19804.5 18934.2 18065.4 17255.7 151352.0
19579.3 17960.6 16561.5 17490.7 17924.7 19045.2 19225.2 18451.2 146268.4
1208.4 1122.4 2814.5 554.8 1879.8 2111.0 21189.8 21195.6 5083.6
0.9124 0.9200 0.8948 0.9429 0.9172 0.9125 0.8940 0.9003 0.9130
0.9227 0.9228 0.9131 0.9454 0.9246 0.9173 0.9089 0.9354 0.9178
63.1 43.0 59.6 47.5 65.5 44.7 50.3 49.9 53.0
59.2 41.6 51.5 49.3 59.5 47.2 44.8 52.4 50.7
23096.9 15681.8 21768.6 17327.2 23978.2 16303.4 18352.2 18218.3 154726.7
21653.9 15179.4 18803.7 18000.9 21786.4 17236.5 16335.5 19131.7 148127.9
1442.9 502.5 2964.9 2673.7 2191.7 2933.2 2016.7 2913.4 6598.8
0.9491 0.9308 0.9487 0.9252 0.9176 0.9327 0.9048 0.9380 0.9345
0.9518 0.9316 0.9649 0.9283 0.9264 0.9388 0.9163 0.9533 0.9359
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Original calibration: 1981–1989 Year (811001–820930) Year (821001–830930) Year (831001–840930) Year (841001–850930) Year (851001–860930) Year (861001–870930) Year (871001–880930) Year (881001–890930) Whole Period (81101–890930) Verification: 1971–1979 Year (711001–720930) Year (721001–730930) Year (731001–740930) Year (741001–750930) Year (751001–760930) Year (761001–770930) Year (771001–780930) Year (781001–790930) Whole period (71101–790930)
Mean Qobs (m 3/s/d)
107
108
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
period of years, also shown in Table 3. Note that for this watershed the verification statistics were even better than the statistics of the original calibration. 3.3.1. Precipitation distribution The precipitation data used in this study are point measurements and thus, have to be distributed over the watershed. Particularly important parameters are the snowfall (P0SREP) and rainfall (P0RREP) adjustment factors. They are used to adjust precipitation at each meteorological station. If the data from a meteorological stations are representative for the watershed, P0SREP and P0RREP are equal to 0. If this is not the case, precipitation amounts are increased or decreased by certain percentages compared to those recorded at the meteorological station, until the best possible efficiency (i.e. agreement with the observed flow) is achieved. For example, a P0SREP value of 20.15 means that snowfall is reduced by 15%. In mountain regions precipitation increases as a moist air mass is driven by wind across mountain barriers. This orographic enhancement of precipitation is modeled by the precipitation gradients. On the weather side, these gradients are generally the highest on lower mountain slopes, and get smaller close to the top of the mountain. On the lee side, however, an inverse situation may occur; high precipitation on the weather side of the range extends over to the lee side, but then decreases very sharply. This applies for both rain and snow, but snow shows greater spill-over effect because of its lower fall velocity. It is often possible that considerable precipitation will occur at high elevations on the lee side, but precipitation decreases so sharply that no precipitation at all may fall in the lee side valley region. Therefore, data from the lee side valley meteorological stations may be useless for estimating runoff potential from the higher mountain slopes. It is clear that the best data would be from high on the mountain slopes, but in the majority of situations the meteorological data is from valley stations. All this emphasizes the significance of the good data sets we can obtain from the few meteorological stations at high elevations. Only two precipitation gradients were used in this study, even though the UBC Watershed Model has a capability of using three different gradients in a single watershed. Hence, for this study, the precipitation gradients were represented through the three
parameters, namely P0GRADL, P0GRADM and E0LMID, where E0LMID is an elevation below which precipitation gradient P0GRADL applies and above which the P0GRADM applies. The starting values of the precipitation gradients may be judged from snowcourse measurements to some extent. Alternatively, in a given sub-region precipitation gradients may have to be assessed from the nearest similar watershed. If no such information exist, the values for the orographic gradients of precipitation have to be obtained by a trial-and-error optimization procedure. Once determined, the estimated or calibrated values of the precipitation parameters are kept constant for a given watershed. In summary, a good calibration of the precipitation parameters is the first and most important step in model calibration, because these parameters control the amount of water available for runoff. Therefore, their high sensitivity (Fig. 3) is not surprising. 3.3.2. Fraction of impermeable area This parameter is the main subdivision between the water entering the subsurface and water flowing as fast runoff and is a very important variable for each watershed. Therefore, this study has examined whether this parameter can be determined from watershed information such as forest or vegetative cover, topography, surficial geology and soil maps. When such information is not available, trial-anderror optimization was used to find the impermeable fraction which provided the best model efficiency. These values of the impermeable fractions are called “calibrated values” and are plotted on Fig. 4 against the starting estimates based on natural lack of vegetation from the topographic maps. In some of the watersheds, a natural lack of vegetation estimated from a topographic map was a good indicator of impermeable area in the watershed. Also, in some of the watersheds (e.g. Stitt Creek), the topographic map indicated a presence of “moraine or scree” deposits on the unvegetated areas. The areas with these deposits are permeable and, thus, estimated values of impermeable fraction based on a lack of vegetation should be reduced in these cases (Fig. 6). For the rest of the watersheds, estimates of impermeable area based only on topographic maps proved to be below optimal values. In those cases, surficial geology maps can help estimate the fraction of impermeable area in
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
109
Fig. 3. Sensitivity of the precipitation parameters for the Bone Creek watershed
the watershed. For example, the Watching Creek watershed is 100% covered with forest. Therefore, an estimate of impermeable fraction based on lack of vegetation would be 0%, which is hardly possible in a natural watershed. According to the surficial geology map for this region, about 18% of the
watershed is an area of rock outcrop or near-surface rock and 7% is covered with glacio-lacustrine deposits with ridged or kettled topographic expression (Fig. 5). Both of these areas can be considered impermeable. Therefore, the percentage of impermeable area based on a surficial geology map for this
110
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Fig. 4. Starting estimates of the impermeable fraction of the basin versus calibrated values.
Fig. 5. Surficial geology of the Watching Creek watershed near Kamloops, British Columbia.
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
111
Fig. 6. Improved estimates of the impermeable fraction of the basin versus calibrated values.
watershed is about 25%, which is very close to the calibrated (optimized) value of 27%. Unfortunately, surficial geology maps are available for only a small portion of British Columbia, and were available for four out of twelve of the study watersheds. Percentage of impermeable area can also be estimated from soil maps, because certain types of soil (e.g. luvisolic soils) develop an impervious layer as a result of clay accumulation in the subsoil. Estimation of impermeable fraction for 12 watersheds in this study can be summarized as follows: • For five watersheds, estimates of impermeable area were based on topographic maps which showed natural lack of vegetation and moraine or scree deposits. • For the next four watersheds starting estimates were improved considerably after use of surficial geology maps. These improvements are shown in Fig. 6. For the remaining three watersheds, fraction of unvegetated area in the watershed does not correspond with the fraction of impermeable area. The use of surficial geology maps for those regions would help improve estimates of impervious areas, but they are unavailable at the present time. A sensitivity analysis
of this parameter is conducted for all 12 watersheds and a typical result for one is shown in Fig. 7. 3.3.3. Time distribution of runoff The time distribution of runoff determines the hydrograph shape, and is controlled by two groups of parameters. The parameters from the first group allocate water input as fast runoff, interflow, upper groundwater and deep groundwater reservoirs respectively. The fraction of impermeable area divides water input into fast flow and the part that infiltrates to subsurface flow. Infiltrated water must first satisfy the soil moisture deficit. A majority of the infiltrated water then infiltrates to groundwater, and the rest goes to the interflow. This is determined by “groundwater percolation” parameter (P0PERC). The groundwater is further divided into an upper groundwater and a deep groundwater reservoirs by the “deep zone share” parameter (P0DZSH). This water allocation by the soil moisture sub-model is estimated in each of the watershed altitude zones. Each runoff component is then routed to the watershed outlet and this is accomplished by the second group of parameters, the routing time constants for each of the four runoff mechanisms. These parameters are: • Snowmelt and rainfall fast runoff time constants
112
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Fig. 7. Sensitivity of the fraction of impermeable area for the Bone Creek watershed.
(P0FSTK and P0FRTK). • Snowmelt and rainfall interflow time constants (P0ISTK and P0IRTK). • Upper groundwater time constant (P0UGTK). • Deep zone groundwater time constant (P0DZTK). Parameters affecting the time distribution of runoff are calibrated by trial-and-error optimization procedure. However, the starting values of these recession constants can be determined from the observed hydrograph, because of the different time delay signatures of fast, medium, slow and very slow runoff components. For example, the recession constants for upper groundwater can be analyzed by selecting a recession flow period, such as the end of summer when snowmelt has ceased, or after a large rain event when recessional flows dominate. The deep groundwater constant can be estimated from overwinter recession. The fast runoff constants are estimated from the peak flow response to rainstorms or high snowmelt. 4. Calibration results All twelve studied watersheds were calibrated until a high efficiency was obtained. The results of the calibration in the form of hydrographs for the two
watersheds are shown on Fig. 8. The calibration and verification statistics for the Illecillewaet River are presented in Table 3. 4.1. Parameter variability among the study watersheds The calibrated values for the parameters affecting time distribution of runoff for all 12 watersheds are shown in Table 4 and it is clear that these parameters show rather low variability among the watersheds, even though the watersheds are very heterogeneous in many aspects. The low variability of these parameters and the fact that they do not depend on drainage area indicates the possibility of assuming that these parameters can be taken to be constant for all watersheds in the studied region, which in this case is the province of British Columbia. Reliability of the streamflow estimates based on this assumption can then be evaluated. Thus, parameters from Table 4 were averaged and results were rounded to the nearest reasonable number. The set of averaged parameters is shown in Table 5. The model was then rerun for each of the twelve watersheds using this fixed set of averaged parameters
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
113
Fig. 8. Observed and calculated flows for the Bone and Illecillewaet River watersheds.
from Table 5, instead of the original parameter values from Table 4. The results, in the form of hydrographs, are plotted in Fig. 9. The thin lines (Qcal) represent the model results with original parameters, as previously shown in Fig. 8. The thick lines (Qcal(avr)) are obtained by running the model with the set of averaged parameters from Table 5. Fig. 9 shows that model results obtained through the full calibration procedure do not differ significantly from those using the fixed set of averaged parameters for all 12 watersheds.
4.2. Reliability of the results obtained by averaged set of parameters The model performances for both the “full calibration procedure” and the “averaged parameters” were measured statistically using the statistical measures defined previously, namely coefficients of efficiency, determination and volume error. A sample calculation for the Illecillewaet River watershed is shown in Table 6. It can be seen that coefficients of efficiency and determination (E! and D!) for the run
114
Barlow Creek Bone Creek Bridge River Campbell River Coquihalla River Illecillewaet River Jordan River Little Swift River Naver Creek Stitt Creek Tabor Creek Watching Creek
P0PERC (mm/day)
P0DZSH
P0FRTK (days)
P0FSTK (days)
P0IRTK (days)
P0ISTK (days)
P0UGTK (days)
P0DZTK (days)
7 38 37 18 10 31 39 34 29 43 30 23
0.23 0.79 0.04 0.46 0.20 0.25 0.38 0.40 0.15 0.61 0.20 0.29
0.55 1.18 0.57 0.38 0.50 0.78 0.67 0.89 0.68 0.94 1.04 1.63
0.80 1.30 1.10 0.40 0.50 1.00 0.70 1.00 0.70 1.5 1.10 1.9
2 4 3 2 2 2 4 5 3 5 3 6
4 3 8 2 2 3 4 5 5 7 4 6
18 29 36 22 8 17 44 8 7 24 8 39
122 196 184 72 150 168 139 190 133 133 123 226
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Table 4 Calibrated values for the parameters affecting the time distribution of runoff
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
115
Table 5 Averaged values for the parameters affecting the time distribution of runoff P0PERC (mm/day)
P0DZSH
P0FRTK (days)
P0FSTK (days)
P0IRTK (days)
P0ISTK (days)
P0UGTK (days)
P0DZTK (days)
25
0.30
0.6
1
3
4
20
150
with the averaged set of parameters are only slightly less than those for the run with the calibrated parameters. In addition, the volume errors dV are only a little greater. The same analysis was carried out for all
12 watersheds and results are summarized in Table 7. In most cases, the differences in overall model efficiency between the two approaches appear insignificant.
Fig. 9. Flows calculated with the calibrated (Qcal) and the averaged (Qcal(avr)) parameters.
116
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Table 6 Statistical measures of the model performance for both runs (Illecillewaet River) Year
81/82 82/83 83/84 84/85 85/86 86/87 87/88 88/89
Method
E! (%)
Calculated Average Calculated Average Calculated Average Calculated Average Calculated Average Calculated Average Calculated Average Calculated Average Average differences
91.24 91.01 92.02 90.94 89.48 88.62 94.28 94.03 91.70 91.63 91.28 90.74 89.38 88.71 89.99 90.32
E! cal 2 E! avr (%) 0.23 1.08 0.86 0.25 0.07 0.54 0.67 20.33
D! cal 2 D! avr (%)
D! (%) 92.27 92.03 92.03 91.19 91.31 90.51 94.54 94.22 92.44 92.34 91.76 91.25 90.89 90.14 93.54 93.67
0.42
0.24 1.11 0.80 0.32 0.10 0.51 0.75 20.13
dV (%)
dV cal 2 dV avr (%)
5.80 6.69 5.84 5.57 14.52 14.71 3.03 3.04 9.42 9.56 0.53 0.87 6.60 6.46 6.99 6.91
20.89 0.27 20.19 20.01 20.14 20.34 0.14 0.08 20.136
0.46
5. Method validation—the case studies
These results indicate that reasonably reliable flow estimates can be obtained by assuming constant values for the parameters affecting the time distribution of runoff regardless of watershed size, soil type or geology of the watershed. Therefore after defining topography, precipitation and fraction of impermeable area, the model can be run using a fixed set of parameters for any watershed. This considerably simplifies model calibration and is an excellent first step in obtaining a full calibration, or is very useful for estimating runoff from an ungauged catchment.
The above method will now be validated by testing the same averaged parameters on two catchments which were not used to derive the average parameters values. The catchments used for method validation are the Slocan River watershed, located in British Columbia, and Astore River watershed located in the Great Himalayan Range in Pakistan. For the purpose of this study, no calibration was performed, and the resulting calculated flows were then compared with the measured flows.
Table 7 Average statistical differences between flows calculated with calibrated and those with averaged parameters
Barlow Creek Bone Creek Bridge River Campbell River Coquihalla River Illecillewaet River Jordan River Little Swift River Naver Creek Stitt Creek Tabor Creek Watching Creek
Average decrease in E! (%)
Average decrease in D! (%)
Average decrease in dV (%)
2.98 8.26 5.55 1.71 5.85 0.42 5.37 0.94 7.81 5.84 4.14 11.28
0.27 2.74 4.38 2.57 7.95 0.46 1.27 1.22 9.63 1.03 3.31 10.56
1.09 2.41 20.57 0.35 0.21 20.14 0.38 0.02 1.27 21.55 20.16 21.20
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
117
Fig. 10. Calculated and measured snowpack water equivalents.
5.1. Slocan River watershed Slocan River is a right tributary to the Kootenay River and is located some 30 km northeast of the Kootenay River’s confluence with the Columbia River. This mountainous watershed spans elevations from 500 to 2700 m and covers an area of 3360 km 2, about 80% of which is covered with vegetation. The flow is generated mainly from seasonal snowmelt. The watershed was divided into ten elevation bands and its physical description was established according to the rules explained in the Section 3.2. In absence of surficial geology maps for this region, the fraction of impermeable area in the watershed was assumed to be equal to the lack of vegetative cover which averaged about 20% in this case. The precipitation distribution over the watershed was simulated using two meteorological stations; one of them, Castlegar, is located at the watershed outlet at the altitude of 494 m, and another, Rossland-Maclean, is located about 20 km south of the watershed at an altitude of 1085 m. Since comparison with the observed flow was not used, and therefore model calibration was not performed, both meteorological stations were assumed reliable and representative for the area, i.e. precipitation adjustment factors P0SREP and
P0RREP were set to zero. The meteorological data (minimum and maximum temperatures and precipitation) from the Castlegar meteorological station (494 m) were applied to the first four elevation bands (up to 1200 m), while for the higher part of the watershed the data from the Rossland-Maclean (1085 m) meteorological station was used. This division was based on the elevation of the stations and therefore E0LMID was set to 1200 m. The precipitation recorded at the Castlegar meteorological station was assumed to increase according to one rate (P0GRADL) up to 1200 m, where the precipitation from the Rossland-Maclean meteorological station takes over and increases at a different rate (P0GRADM). These precipitation gradients, P0GRADL and P0GRADM were estimated from available snow survey measurements, as described below. The UBC Watershed Model distinguishes between snow and rain by using the mean daily temperature (T) at a given altitude such that if T , 08C; all precipitation is snow and if T . 28C; all precipitation is rain. For the temperatures between 0 and 28C, a simple algorithm divides the precipitation into rain and snow fractions. The model also calculates snowmelt. Therefore the model can calculate snowpack
118
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Fig. 11. Flows calculated by the proposed method Qcal(avr) and the observed flows Qobs.
accumulation and depletion over time at any elevation within a watershed. Using the temperatures and precipitation recorded at Castlegar the value of the precipitation gradient (P0GRADL) was found which correctly estimated the snowpack recorded at the Sandon snow survey station located within the Slocan River watershed at the elevation of 1070 m, as shown in Fig. 10. The same procedure was followed for the determination of the precipitation gradient applied to the upper part of the watershed (P0GRADM), except that data from Rossland-Maclean meteorological station and Harlow
Creek snow survey station (elevation 1920 m) were used. Final values for the precipitation gradients P0GRADL and P0GRADL were 3 and 7, respectively. These values are fairly typical of the precipitation behavior on the lee side of a mountain range, as explained previously in this paper. Once the topography, fraction of impermeable area and precipitation distribution have been defined, the model was run using the developed fixed set of parameters without any calibration. The simulated hydrographs for five consecutive years were then compared with the observed flows and the results, both
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120 Table 8 Statistics for the flows calculated using the proposed method Water year (Oct. 01 to Sept. 30) Slocan River watershed 1983/84 1984/85 1985/86 1986/87 1987/88 Astore River watershed 1990/91 1991/92 1992/93 1993/94 1994/95
E (%)!
D! (%)
dV (%)
86.73 90.93 90.80 84.72 90.33
97.33 95.00 94.65 90.46 92.47
3.78 6.95 22.15 11.91 12.80
94.32 90.28 80.61 86.50 89.79
94.94 92.82 85.42 86.90 92.84
3.15 0.55 0.12 2.82 1.59
hydrographs and statistics were quite satisfactory (Fig. 11, Table 8).
5.2. Astore River watershed Astore River watershed is located within the Indus River basin in the Himalayas. This watershed spans elevations from 2000 to 7000 m and covers an area of 3955 km 2, only 5% of which is covered with forest and 20% with glaciers. The flow is generated mainly from seasonal snowmelt and glacier melt. The watershed was divided into seven elevation bands and its physical description along with the estimates of the impermeable fraction was provided by the Pakistan Water and Power Development Authority. The precipitation distribution over the watershed was simulated using only meteorological station Astore located at the elevation of 2630 m. The precipitation gradients were provided by the Pakistan Water and Power Development Authority, and were probably calibrated values. However, it is interesting to note that the same set of averaged parameters used in British Columbia gave quite good results even in this very high Himalayan environment. The model was run using the same fixed set of averaged parameters for five consecutive years. The calculated flows showed a good agreement with the flows recorded at the gauging station (Fig. 11, Table 8).
119
6. Discussion 6.1. The regional watershed model calibration Examination of the parameters derived from individual calibration of each watershed revealed that there was a very similar and consistent set of parameters for everything except the fraction of impermeable area and the precipitation gradients. For an ungauged watershed, the precipitation gradients may be judged from snowcourse measurements to some extent, and also, in any sub-region may have to be assessed from the nearest similar watershed. The fraction of the impermeable area, for some of the watersheds, was found to correspond with the fraction of unvegetated area determined from a topographic map. However, this is not always the case. The best way to obtain estimates of this parameter is through the surficial geology maps. These maps provide information on impermeable areas such as areas of rock outcrop or near surface rock within a watershed. There are many parameters which have been pre-calibrated from earlier, detailed studies and are held constant, such as the snowmelt, temperature lapse rates, evapotranspiration and interception parameters. Also for the whole region of this study, parameters affecting the time distribution of runoff, groundwater percolation and groundwater deep zone share, showed relatively low variability, and therefore these parameters were assigned constant values. Each of the twelve study watersheds was re-run with this fixed set of parameters. This simplified approach produced quite reliable results, with only slight reduction in the coefficients of efficiency compared to the full calibration procedure. The differences in the volume errors between the two approaches appear negligible. 6.2. Implications for watershed behavior The pathways for water flow in a watershed consist of a hillslope land phase and a stream network, channel phase. The travel time of the water through the system depends on many controlling factors— basin topography and physical properties and depths of the soils being the most important. However, considering previous velocity measurements in different zones of the land phase (Ishihara
120
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
and Kobatake (1975); Dunne (1978); Kirkby (1988)), it can be concluded that the water velocity in the channel network is several orders of magnitude greater than that of the land phase. Therefore, the effect of travel time of the flow in the channel phase seems very small when compared with the observed land phase runoff delays and can be neglected in the watershed routing procedure. The results of this study conducted on the watersheds ranging from 71 to 1194 km 2 in area, show that routing time constants for all four runoff components (fast runoff, interflow, upper and deep zone groundwater) do not increase with drainage area of the watershed. This supports the idea that the land phase controls the runoff process, since, in the land phase, the length of flow paths to the nearest channel is likely to be independent of watershed size, whereas the length of channel network changes considerably with watershed size. Therefore the main delay in runoff is in the land phase. Once this land phase runoff reaches the channel, it is routed relatively quickly to the watershed outlet, because the channel flow is very fast and of much shorter duration than the previous land phase flow. 6.3. Final comments The results of this study show that the model can be essentially pre-calibrated except for two aspects— precipitation distribution and permeability characteristics of the watershed. Such a pre-calibrated model can then be used for generating design flows for ungauged watersheds. This method was tested on twelve watersheds in British Columbia and gave excellent results. These watersheds are quite heterogeneous as shown in Table 1. The implication is that the same parameters may be applicable to any watershed within the studied area regardless of size, topography, climate, soil, geology or hydrological regime, provided that impermeable fraction of the
watershed can be estimated and precipitation input is adequate. Given a good meteorological record, continuous flows could be generated and used for various studies. For example, an annual series of floods or low flows could be generated and used in a frequency analysis. Finally, the same approach was tested on two other watersheds, one in British Columbia and one in the Great Himalayan Range, which were not part of the original study, and the results confirm that good estimation of streamflow can be made.
References Dunne, T., 1978. Field studies of hillslope flow processes. In: Kirkby, M.J. (Ed.). Hillslope Hydrology, Wiley, Chichester, UK, pp. 227–293. Ishihara, Y., Kobatake, S., 1975. The roles of slope and channel processes in storm runoff in the Ara experimental basin. International Symposium on the Characteristics of River Basin, December 1–8, 1975, Tokyo, Japan. IAHS Publ., vol. 117, pp. 75–86. Kirkby, M.J., 1988. Hillslope runoff processes and models. Journal of Hydrology 100, 315–339. Leith, R.M., 1975. Streamflow Regionalization in British Columbia, No. 1. Regression of Mean Annual Floods on Physiographic Parameters, Inland Waters Directorate Report Series, 40. Environment Canada, Ottawa, Ontario, pp. 42. Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models. Part I—a discussion of principles. Journal of Hydrology 10, 282–290. Quick, M.C., 1995. The UBC watershed model. In: Singh, V.J. (Ed.). Computer Models of Watershed Hydrology, Water Resources Publications, Colorado, USA, pp. 233–280. Quick, M.C., Pipes, A., 1977. UBC watershed model. Hydrological Sciences Bulletin XXI 1 (3), 285–295. Riggs, H.C., 1973. Regional analyses of streamflow characteristics, Techniques of Water Resources Investigations of the U.S. Geol. Survey United States Government Printing Office, Washington, DC Book 4, chap. B3. Waylen, P., Woo, M., 1981. Regionalization and prediction of annual floods in the Fraser River catchment, British Columbia. Water Resources Bulletin 17 (4), 655–661.
A rainfall and snowmelt runoff modelling approach to flow estimation at ungauged sites in British Columbia Z. Micovic*, M.C. Quick 1 Department of Civil Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada Received 5 May 1999; accepted 7 October 1999
Abstract Streamflow was calculated from meteorological data using the UBC Watershed Model for 12 heterogeneous watersheds in British Columbia. These watersheds varied in drainage area, climate, topography, soil type vegetation and geology, which indicates that statistical regionalization of streamflow is likely to be unreliable. The model results indicated that an average set of model parameters could be applied to all the watersheds, provided that representative meteorological data was available and the impermeable fraction of the watersheds could be determined from independent sources such as natural vegetative cover and surficial geology. The averaged model parameter set gave Nash–Sutcliffe statistical results only slightly lower than results from a full calibration. Therefore the method appears to be useful for complete pre-calibration of ungauged watersheds so that flows can be generated for these ungauged sites. The method has been successfully tested on an independent watershed in British Columbia and another watershed in the Himalayas. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Watershed calibration; Model parameterization; Ungauged sites; Regionalization
1. Introduction Most of the streams in the province of British Columbia are either ungauged or have a short period of gauging record. However, for various engineering applications, estimates of design flows for these sites are required. One approach that has been used previously (Leith, 1975; Waylen and Woo, 1981) is to use a regional flood frequency analysis in which, for a homogenous region, regression equations are developed by regressing flood quantiles estimated at gauged basins against measured basin characteristics. It is then assumed that these equations can be applied * Corresponding author. Fax: 11-604-822-6901. E-mail addresses: [email protected] (Z. Micovic); mquick@ civil.ubc.ca (M.C. Quick) 1 Fax: 1604-822-6901.
to any basin in that region. However, regional regression equations have many shortcomings and standard errors of the predicted quantiles are often quite high. Also, these equations sometimes incorporate physically weak basin characteristics or two or more strongly correlated basin characteristics (e.g. basin area and main channel length). An extensive survey of many statistically based studies of this type are reviewed and discussed by Riggs (1973). In the present work, an alternative approach using a rainfall and snowmelt runoff model is used. The first aim was to calibrate the model for several watersheds in a hydrologically homogeneous region and then to use the model to generate flows for ungauged sites. However, as the work progressed, it was found that the approach could be extended to non-homogeneous regions across the whole province of British
0022-1694/99/$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S0022-169 4(99)00172-9
102
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Fig. 1. Locations of the study watersheds.
Columbia. The UBC Watershed Model was used for this study. Therefore, the objective of this study was to calibrate the UBC Watershed Model for various watersheds across British Columbia with different physical characteristics and to examine the variability of model parameters among the watersheds. It was then possible to identify parameters with small variability and average their values so that they could be applied to all of the watersheds. Finally, the reliability of the resulting streamflow estimates was evaluated and the method was validated by applying it to two catchments not used in deriving the average parameter values. The flows were calculated as if these test watersheds were ungauged and the results were then compared with the measured flows. It was found from this analysis that constant values could be assigned to most of the parameters, so that the number of remaining parameters to be determined
was minimized to two, as will be discussed later. This considerably simplified model still produced reliable results for physically different watersheds, indicating that it can be universally applied for ungauged basins in a region which is not homogeneous.
2. Study watersheds In this study, hydrological behavior of 12 watersheds in British Columbia was analyzed. Locations of the watersheds are shown in Fig. 1, (the shaded areas give an indication of basin size and shape). They are chosen to be heterogeneous, with different sizes of drainage area, climate, topography, soil types, geology and hydrologic regime. Some key factors are summarized in Table 1.
Drainage area (km 2) Barlow Creek 70.7 Bone Creek 268 Bridge River 984 Campbell River 1194 Coquihalla River 742 Illecillewaet River 1150 Jordan River 272 Little Swift River 133 Naver Creek 658 Stitt Creek 139 Tabor Creek 113 Watching Creek 80
Average surface slope
Glaciated Forested Mean annual fraction fraction flood (%) (%) (m 3/s/km 2)
Mean annual precipitation (mm)
Origin of the annual floods
0.0503 0.3576 0.2500 0.2934 0.3501 0.3732 0.3776 0.1509 0.0754 0.4034 0.1450 0.1183
0 11.5 18.29 0 0 6.61 1.54 0 0 13.31 0 0
480 1420 1380 2430 1800 1715 1925 900 800 1530 595 560
1. Snowmelt 2. Rainfall 580 Mainly snowmelt 700 Snowmelt 750 Rainfall 215 Rainfall or snowmelt 90 Snowmelt 520 Snowmelt 540 1. Snowmelt 2. Rainfall 1065 1. Rainfall 2. Snowmelt 600 Snowmelt 790 1. Rainfall 2. Snowmelt 645 Snowmelt 900
87 53 53 72 93 74 61 87 95 41 85 100
0.0689 0.1840 0.2232 0.6697 0.3212 0.2333 0.4042 0.1875 0.1217 0.2725 0.0837 0.0623
Minimal altitude (m)
Altitude range (m)
Mean altitude (m)
Impermeable fraction (%)
395 2280 2186 2065 2105 2740 2060 915 1076 2135 625 930
745 1889 1845 977 1203 1717 1593 1466 961 1947 823 1384
27 47 24 28 29 25 45 48 18 27 29 27
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Table 1 Physical characteristics of the study watersheds
103
104
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
3. Methodology 3.1. The conceptual design of the UBC watershed model The UBC Watershed model was presented by Quick and Pipes (1977), although the earliest ideas date back to 1963 and, thus, a very early version of the model was used for the Fraser River flood forecasting in 1964. Further developments of the model have been presented since that time and now incorporate many user-friendly features, Quick (1995). The model calculates daily watershed outflow using precipitation and maximum and minimum temperatures as input. The model was designed primarily for the calculation of streamflow from mountainous watersheds where streamflow consists of snowmelt, rain and glacier outflow. Since the hydrological behavior of the mountainous watershed is a function of elevation, the model uses the area-elevation bands concept. This concept accounts for orographic gradients of precipitation and temperature, which are assumed to behave similarly for each storm and are dominant gradients of behavior in mountainous areas. Besides the daily streamflow estimates, the UBC Watershed Model provides information on area of snow cover, snowpack water equivalent, energy available for snowmelt, evapotranspiration and interception losses, soil moisture, groundwater storage and surface and sub-surface components of runoff. All this information is available for each elevation band separately as well as for the whole watershed (average values). This is a continuous hydrologic model, which means that it will provide streamflow output as long as meteorological input is available. The physical description of a watershed is given for each elevation band separately in the form of different variables such as area of the band, forested fraction and forest density, glaciated fraction, band orientation and fraction of impermeable area. The UBC Watershed Model was designed to run from a minimum of meteorological and flow data, because these data are often sparse in the mountainous regions. In addition, most of these sparse data are from the valley stations. As a result of these constraints, an important aspect of the model is the elevation distribution of data. A schematic diagram representing the UBC Watershed Model structure is shown in Fig. 2. The model is made up of several submodels:
The meteorological sub-model distributes the point values of precipitation and temperatures to all elevation zones of a watershed. The variation of temperature with elevation controls whether precipitation falls as rain or snow and also controls the melting of the snowpacks and glaciers. The soil moisture sub-model represents the nonlinear behavior of a watershed. All the non-linearity of the watershed behavior is concentrated into this soil moisture sub-model which sub-divides the water input (rain and snowmelt) into four components of runoff namely, fast, medium (interflow), slow (upper groundwater) and very slow (deep groundwater). The impermeable area is the fast responding region of a watershed and is assumed to be adjacent to a well developed stream channel system. This area changes as a function of soil moisture deficit (variable source area). The routing sub-model: routing is linear which leads to great simplifications of model structure. It guarantees conservation of mass and a simple and accurate water budget balance. It should be mentioned that the majority of the parameters in the UBC Watershed Model are pre-calibrated and are kept constant. These parameters include all snowmelt, temperature lapse rate, evapotranspiration and interception parameters. The snowmelt algorithm uses an energy approach, which is discussed in detail in Quick (1995) and can account for forested and open areas, aspect and latitude. Glacier melt is also computed using this same method and parameters. 3.2. Developing a watershed description To develop a watershed description it is necessary to decide how many elevation bands it comprises. This is done by surveying topographical maps and aerial photographs for each particular watershed. By dividing a watershed into more elevation bands we account for more heterogeneity, but also increase computational time. Thus the number of elevation bands varies from watershed to watershed and varied from 4 to 12 in this study. Once we have determined the number of elevation bands into which the watershed will be divided, the general procedure is to do the following for each band: 1. From the maps, determine the altitude of the mid-point of the band.
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
105
Fig. 2. UBC Watershed Model—diagram of the structure.
2. Measure the band area. 3. Determine the fraction of the band that is forested, and the density of the forest canopy. 4. Determine the fraction of the band that is impermeable. 5. Establish the relative north/south orientation of the band. 6. Determine whether or not a glacier is present in the
band. If a glacier is present, estimate the area of the band that is covered by glaciers, and the fraction of the glaciated area that is south facing. Physical characteristics such as forested and glaciated fractions, orientation and density of the forest canopy can be easily measured from the topographic maps and aerial photographs. A rather difficult problem is
106
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Table 2 Starting ranges for the model parameters used in the optimization P0SREP
P0RREP
2 1 to 1 P0DZSH 0–1 a
2 1 to 1
C0IMPA (%) 0–70
E0LMID (m) 1/4–3/4 a
P0GRADL (% per 100 m) 1–10
P0GRADM (% per 100 m) 1–10
P0PERC (mm/day) 0–50
P0FRTK (days) 0–2
P0FSTK (days) 0–2
P0IRTK (days) 1–10
P0ISTK (days) 1–10
P0DZTK (days) 100–250
P0UGTK (days) 10–50
E0LMID is the minimum elevation 11/4 to 3/4 of the watershed’s elevation range
to determine the fraction of impermeable area in each elevation band. 3.3. Calibration of watershed model to study watersheds Model performance is evaluated visually and statistically. The visual criterion involves plotting the calculated hydrograph and comparing it with the measured flow. The statistical criterion used in the UBC model is the model efficiency suggested by Nash and Sutcliffe (1970), based on the ratio of explained and total variances of observed and calculated flow, as follows: n X i1 E! 1 2 X n
Qiobs 2 Qical 2 Qiobs
2 Q obs 2
1
i1
where, n X
Q obs
Qiobs
i1
n
2
and n is the number of days for daily runs or hours for hourly runs, Qiobs the observed flow on day (hour) i and Qical the calculated flow on day (hour) i. The model efficiency, E! relates how well the calculated and observed hydrographs compare in volume and shape. A negative value of E! means that the observed mean flows are closer to observed flows than the flows calculated by the model. The coefficient of determination D! relates how well the calculated hydrograph compares in shape to the observed, and therefore, depends only on timing, but not on volume. The volume error, d V is the third important statistic
used in calibration and is presented as: Q 2 Qcal dV obs Qobs
3
For a successfully calibrated model, the values of E! and D! should be close to 1, with dV kept close to zero. The UBC Watershed Model has a built-in automatic optimization procedure designed to assist the user in the calibration of a watershed. The user has to define reasonable ranges for the parameters and the computer then searches for optimum values. The parameter ranges used in this study are shown in Table 2. The optimization module optimizes three groups of parameters separately. The first group, precipitation parameters, is optimized until the calculated runoff volumes begin to compare with the observed values. Once the annual volumes of observed and calculated flow are reasonably close, the second group, water distribution, distributes the rain and the snowmelt to surface runoff, interflow and groundwater through the soil moisture budget. The third group of parameters, the routing constants, adjusts the time constants for each runoff component controlling the length of time taken to pass through the watershed. The coefficients of efficiency and determination and the volume error for the given period are then calculated. This procedure can be run for any number of iterations, after which the watershed is updated with the parameter values giving the best efficiency. The study watersheds were calibrated for available periods of continuous historical streamflow and meteorological records. The calibration was not done on a year-by-year basis, but was carried out for the whole calibration period for each watershed. However, the calibration statistics for one of the watersheds are shown in Table 3 on a year-by-year basis as well as for the whole period. Where data was available, the calibration was verified for a different
Table 3 Calibration and verification statistics for the Illecillewaet River watershed Mean Qest (m 3/s/d)
Tot Qobs (m 3/s)
Tot Qest (m 3/s)
Tot Qobs2Tot Qest
Coefficient of efficiency (E!)
Coefficient of determination (D!)
57.0 52.3 52.9 49.4 54.3 51.9 49.4 47.3 51.8
53.6 49.2 45.3 47.9 49.1 52.2 52.6 50.6 50.1
2078.7 19083.0 19376.0 18045.5 19804.5 18934.2 18065.4 17255.7 151352.0
19579.3 17960.6 16561.5 17490.7 17924.7 19045.2 19225.2 18451.2 146268.4
1208.4 1122.4 2814.5 554.8 1879.8 2111.0 21189.8 21195.6 5083.6
0.9124 0.9200 0.8948 0.9429 0.9172 0.9125 0.8940 0.9003 0.9130
0.9227 0.9228 0.9131 0.9454 0.9246 0.9173 0.9089 0.9354 0.9178
63.1 43.0 59.6 47.5 65.5 44.7 50.3 49.9 53.0
59.2 41.6 51.5 49.3 59.5 47.2 44.8 52.4 50.7
23096.9 15681.8 21768.6 17327.2 23978.2 16303.4 18352.2 18218.3 154726.7
21653.9 15179.4 18803.7 18000.9 21786.4 17236.5 16335.5 19131.7 148127.9
1442.9 502.5 2964.9 2673.7 2191.7 2933.2 2016.7 2913.4 6598.8
0.9491 0.9308 0.9487 0.9252 0.9176 0.9327 0.9048 0.9380 0.9345
0.9518 0.9316 0.9649 0.9283 0.9264 0.9388 0.9163 0.9533 0.9359
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Original calibration: 1981–1989 Year (811001–820930) Year (821001–830930) Year (831001–840930) Year (841001–850930) Year (851001–860930) Year (861001–870930) Year (871001–880930) Year (881001–890930) Whole Period (81101–890930) Verification: 1971–1979 Year (711001–720930) Year (721001–730930) Year (731001–740930) Year (741001–750930) Year (751001–760930) Year (761001–770930) Year (771001–780930) Year (781001–790930) Whole period (71101–790930)
Mean Qobs (m 3/s/d)
107
108
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
period of years, also shown in Table 3. Note that for this watershed the verification statistics were even better than the statistics of the original calibration. 3.3.1. Precipitation distribution The precipitation data used in this study are point measurements and thus, have to be distributed over the watershed. Particularly important parameters are the snowfall (P0SREP) and rainfall (P0RREP) adjustment factors. They are used to adjust precipitation at each meteorological station. If the data from a meteorological stations are representative for the watershed, P0SREP and P0RREP are equal to 0. If this is not the case, precipitation amounts are increased or decreased by certain percentages compared to those recorded at the meteorological station, until the best possible efficiency (i.e. agreement with the observed flow) is achieved. For example, a P0SREP value of 20.15 means that snowfall is reduced by 15%. In mountain regions precipitation increases as a moist air mass is driven by wind across mountain barriers. This orographic enhancement of precipitation is modeled by the precipitation gradients. On the weather side, these gradients are generally the highest on lower mountain slopes, and get smaller close to the top of the mountain. On the lee side, however, an inverse situation may occur; high precipitation on the weather side of the range extends over to the lee side, but then decreases very sharply. This applies for both rain and snow, but snow shows greater spill-over effect because of its lower fall velocity. It is often possible that considerable precipitation will occur at high elevations on the lee side, but precipitation decreases so sharply that no precipitation at all may fall in the lee side valley region. Therefore, data from the lee side valley meteorological stations may be useless for estimating runoff potential from the higher mountain slopes. It is clear that the best data would be from high on the mountain slopes, but in the majority of situations the meteorological data is from valley stations. All this emphasizes the significance of the good data sets we can obtain from the few meteorological stations at high elevations. Only two precipitation gradients were used in this study, even though the UBC Watershed Model has a capability of using three different gradients in a single watershed. Hence, for this study, the precipitation gradients were represented through the three
parameters, namely P0GRADL, P0GRADM and E0LMID, where E0LMID is an elevation below which precipitation gradient P0GRADL applies and above which the P0GRADM applies. The starting values of the precipitation gradients may be judged from snowcourse measurements to some extent. Alternatively, in a given sub-region precipitation gradients may have to be assessed from the nearest similar watershed. If no such information exist, the values for the orographic gradients of precipitation have to be obtained by a trial-and-error optimization procedure. Once determined, the estimated or calibrated values of the precipitation parameters are kept constant for a given watershed. In summary, a good calibration of the precipitation parameters is the first and most important step in model calibration, because these parameters control the amount of water available for runoff. Therefore, their high sensitivity (Fig. 3) is not surprising. 3.3.2. Fraction of impermeable area This parameter is the main subdivision between the water entering the subsurface and water flowing as fast runoff and is a very important variable for each watershed. Therefore, this study has examined whether this parameter can be determined from watershed information such as forest or vegetative cover, topography, surficial geology and soil maps. When such information is not available, trial-anderror optimization was used to find the impermeable fraction which provided the best model efficiency. These values of the impermeable fractions are called “calibrated values” and are plotted on Fig. 4 against the starting estimates based on natural lack of vegetation from the topographic maps. In some of the watersheds, a natural lack of vegetation estimated from a topographic map was a good indicator of impermeable area in the watershed. Also, in some of the watersheds (e.g. Stitt Creek), the topographic map indicated a presence of “moraine or scree” deposits on the unvegetated areas. The areas with these deposits are permeable and, thus, estimated values of impermeable fraction based on a lack of vegetation should be reduced in these cases (Fig. 6). For the rest of the watersheds, estimates of impermeable area based only on topographic maps proved to be below optimal values. In those cases, surficial geology maps can help estimate the fraction of impermeable area in
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
109
Fig. 3. Sensitivity of the precipitation parameters for the Bone Creek watershed
the watershed. For example, the Watching Creek watershed is 100% covered with forest. Therefore, an estimate of impermeable fraction based on lack of vegetation would be 0%, which is hardly possible in a natural watershed. According to the surficial geology map for this region, about 18% of the
watershed is an area of rock outcrop or near-surface rock and 7% is covered with glacio-lacustrine deposits with ridged or kettled topographic expression (Fig. 5). Both of these areas can be considered impermeable. Therefore, the percentage of impermeable area based on a surficial geology map for this
110
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Fig. 4. Starting estimates of the impermeable fraction of the basin versus calibrated values.
Fig. 5. Surficial geology of the Watching Creek watershed near Kamloops, British Columbia.
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
111
Fig. 6. Improved estimates of the impermeable fraction of the basin versus calibrated values.
watershed is about 25%, which is very close to the calibrated (optimized) value of 27%. Unfortunately, surficial geology maps are available for only a small portion of British Columbia, and were available for four out of twelve of the study watersheds. Percentage of impermeable area can also be estimated from soil maps, because certain types of soil (e.g. luvisolic soils) develop an impervious layer as a result of clay accumulation in the subsoil. Estimation of impermeable fraction for 12 watersheds in this study can be summarized as follows: • For five watersheds, estimates of impermeable area were based on topographic maps which showed natural lack of vegetation and moraine or scree deposits. • For the next four watersheds starting estimates were improved considerably after use of surficial geology maps. These improvements are shown in Fig. 6. For the remaining three watersheds, fraction of unvegetated area in the watershed does not correspond with the fraction of impermeable area. The use of surficial geology maps for those regions would help improve estimates of impervious areas, but they are unavailable at the present time. A sensitivity analysis
of this parameter is conducted for all 12 watersheds and a typical result for one is shown in Fig. 7. 3.3.3. Time distribution of runoff The time distribution of runoff determines the hydrograph shape, and is controlled by two groups of parameters. The parameters from the first group allocate water input as fast runoff, interflow, upper groundwater and deep groundwater reservoirs respectively. The fraction of impermeable area divides water input into fast flow and the part that infiltrates to subsurface flow. Infiltrated water must first satisfy the soil moisture deficit. A majority of the infiltrated water then infiltrates to groundwater, and the rest goes to the interflow. This is determined by “groundwater percolation” parameter (P0PERC). The groundwater is further divided into an upper groundwater and a deep groundwater reservoirs by the “deep zone share” parameter (P0DZSH). This water allocation by the soil moisture sub-model is estimated in each of the watershed altitude zones. Each runoff component is then routed to the watershed outlet and this is accomplished by the second group of parameters, the routing time constants for each of the four runoff mechanisms. These parameters are: • Snowmelt and rainfall fast runoff time constants
112
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Fig. 7. Sensitivity of the fraction of impermeable area for the Bone Creek watershed.
(P0FSTK and P0FRTK). • Snowmelt and rainfall interflow time constants (P0ISTK and P0IRTK). • Upper groundwater time constant (P0UGTK). • Deep zone groundwater time constant (P0DZTK). Parameters affecting the time distribution of runoff are calibrated by trial-and-error optimization procedure. However, the starting values of these recession constants can be determined from the observed hydrograph, because of the different time delay signatures of fast, medium, slow and very slow runoff components. For example, the recession constants for upper groundwater can be analyzed by selecting a recession flow period, such as the end of summer when snowmelt has ceased, or after a large rain event when recessional flows dominate. The deep groundwater constant can be estimated from overwinter recession. The fast runoff constants are estimated from the peak flow response to rainstorms or high snowmelt. 4. Calibration results All twelve studied watersheds were calibrated until a high efficiency was obtained. The results of the calibration in the form of hydrographs for the two
watersheds are shown on Fig. 8. The calibration and verification statistics for the Illecillewaet River are presented in Table 3. 4.1. Parameter variability among the study watersheds The calibrated values for the parameters affecting time distribution of runoff for all 12 watersheds are shown in Table 4 and it is clear that these parameters show rather low variability among the watersheds, even though the watersheds are very heterogeneous in many aspects. The low variability of these parameters and the fact that they do not depend on drainage area indicates the possibility of assuming that these parameters can be taken to be constant for all watersheds in the studied region, which in this case is the province of British Columbia. Reliability of the streamflow estimates based on this assumption can then be evaluated. Thus, parameters from Table 4 were averaged and results were rounded to the nearest reasonable number. The set of averaged parameters is shown in Table 5. The model was then rerun for each of the twelve watersheds using this fixed set of averaged parameters
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
113
Fig. 8. Observed and calculated flows for the Bone and Illecillewaet River watersheds.
from Table 5, instead of the original parameter values from Table 4. The results, in the form of hydrographs, are plotted in Fig. 9. The thin lines (Qcal) represent the model results with original parameters, as previously shown in Fig. 8. The thick lines (Qcal(avr)) are obtained by running the model with the set of averaged parameters from Table 5. Fig. 9 shows that model results obtained through the full calibration procedure do not differ significantly from those using the fixed set of averaged parameters for all 12 watersheds.
4.2. Reliability of the results obtained by averaged set of parameters The model performances for both the “full calibration procedure” and the “averaged parameters” were measured statistically using the statistical measures defined previously, namely coefficients of efficiency, determination and volume error. A sample calculation for the Illecillewaet River watershed is shown in Table 6. It can be seen that coefficients of efficiency and determination (E! and D!) for the run
114
Barlow Creek Bone Creek Bridge River Campbell River Coquihalla River Illecillewaet River Jordan River Little Swift River Naver Creek Stitt Creek Tabor Creek Watching Creek
P0PERC (mm/day)
P0DZSH
P0FRTK (days)
P0FSTK (days)
P0IRTK (days)
P0ISTK (days)
P0UGTK (days)
P0DZTK (days)
7 38 37 18 10 31 39 34 29 43 30 23
0.23 0.79 0.04 0.46 0.20 0.25 0.38 0.40 0.15 0.61 0.20 0.29
0.55 1.18 0.57 0.38 0.50 0.78 0.67 0.89 0.68 0.94 1.04 1.63
0.80 1.30 1.10 0.40 0.50 1.00 0.70 1.00 0.70 1.5 1.10 1.9
2 4 3 2 2 2 4 5 3 5 3 6
4 3 8 2 2 3 4 5 5 7 4 6
18 29 36 22 8 17 44 8 7 24 8 39
122 196 184 72 150 168 139 190 133 133 123 226
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Table 4 Calibrated values for the parameters affecting the time distribution of runoff
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
115
Table 5 Averaged values for the parameters affecting the time distribution of runoff P0PERC (mm/day)
P0DZSH
P0FRTK (days)
P0FSTK (days)
P0IRTK (days)
P0ISTK (days)
P0UGTK (days)
P0DZTK (days)
25
0.30
0.6
1
3
4
20
150
with the averaged set of parameters are only slightly less than those for the run with the calibrated parameters. In addition, the volume errors dV are only a little greater. The same analysis was carried out for all
12 watersheds and results are summarized in Table 7. In most cases, the differences in overall model efficiency between the two approaches appear insignificant.
Fig. 9. Flows calculated with the calibrated (Qcal) and the averaged (Qcal(avr)) parameters.
116
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Table 6 Statistical measures of the model performance for both runs (Illecillewaet River) Year
81/82 82/83 83/84 84/85 85/86 86/87 87/88 88/89
Method
E! (%)
Calculated Average Calculated Average Calculated Average Calculated Average Calculated Average Calculated Average Calculated Average Calculated Average Average differences
91.24 91.01 92.02 90.94 89.48 88.62 94.28 94.03 91.70 91.63 91.28 90.74 89.38 88.71 89.99 90.32
E! cal 2 E! avr (%) 0.23 1.08 0.86 0.25 0.07 0.54 0.67 20.33
D! cal 2 D! avr (%)
D! (%) 92.27 92.03 92.03 91.19 91.31 90.51 94.54 94.22 92.44 92.34 91.76 91.25 90.89 90.14 93.54 93.67
0.42
0.24 1.11 0.80 0.32 0.10 0.51 0.75 20.13
dV (%)
dV cal 2 dV avr (%)
5.80 6.69 5.84 5.57 14.52 14.71 3.03 3.04 9.42 9.56 0.53 0.87 6.60 6.46 6.99 6.91
20.89 0.27 20.19 20.01 20.14 20.34 0.14 0.08 20.136
0.46
5. Method validation—the case studies
These results indicate that reasonably reliable flow estimates can be obtained by assuming constant values for the parameters affecting the time distribution of runoff regardless of watershed size, soil type or geology of the watershed. Therefore after defining topography, precipitation and fraction of impermeable area, the model can be run using a fixed set of parameters for any watershed. This considerably simplifies model calibration and is an excellent first step in obtaining a full calibration, or is very useful for estimating runoff from an ungauged catchment.
The above method will now be validated by testing the same averaged parameters on two catchments which were not used to derive the average parameters values. The catchments used for method validation are the Slocan River watershed, located in British Columbia, and Astore River watershed located in the Great Himalayan Range in Pakistan. For the purpose of this study, no calibration was performed, and the resulting calculated flows were then compared with the measured flows.
Table 7 Average statistical differences between flows calculated with calibrated and those with averaged parameters
Barlow Creek Bone Creek Bridge River Campbell River Coquihalla River Illecillewaet River Jordan River Little Swift River Naver Creek Stitt Creek Tabor Creek Watching Creek
Average decrease in E! (%)
Average decrease in D! (%)
Average decrease in dV (%)
2.98 8.26 5.55 1.71 5.85 0.42 5.37 0.94 7.81 5.84 4.14 11.28
0.27 2.74 4.38 2.57 7.95 0.46 1.27 1.22 9.63 1.03 3.31 10.56
1.09 2.41 20.57 0.35 0.21 20.14 0.38 0.02 1.27 21.55 20.16 21.20
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
117
Fig. 10. Calculated and measured snowpack water equivalents.
5.1. Slocan River watershed Slocan River is a right tributary to the Kootenay River and is located some 30 km northeast of the Kootenay River’s confluence with the Columbia River. This mountainous watershed spans elevations from 500 to 2700 m and covers an area of 3360 km 2, about 80% of which is covered with vegetation. The flow is generated mainly from seasonal snowmelt. The watershed was divided into ten elevation bands and its physical description was established according to the rules explained in the Section 3.2. In absence of surficial geology maps for this region, the fraction of impermeable area in the watershed was assumed to be equal to the lack of vegetative cover which averaged about 20% in this case. The precipitation distribution over the watershed was simulated using two meteorological stations; one of them, Castlegar, is located at the watershed outlet at the altitude of 494 m, and another, Rossland-Maclean, is located about 20 km south of the watershed at an altitude of 1085 m. Since comparison with the observed flow was not used, and therefore model calibration was not performed, both meteorological stations were assumed reliable and representative for the area, i.e. precipitation adjustment factors P0SREP and
P0RREP were set to zero. The meteorological data (minimum and maximum temperatures and precipitation) from the Castlegar meteorological station (494 m) were applied to the first four elevation bands (up to 1200 m), while for the higher part of the watershed the data from the Rossland-Maclean (1085 m) meteorological station was used. This division was based on the elevation of the stations and therefore E0LMID was set to 1200 m. The precipitation recorded at the Castlegar meteorological station was assumed to increase according to one rate (P0GRADL) up to 1200 m, where the precipitation from the Rossland-Maclean meteorological station takes over and increases at a different rate (P0GRADM). These precipitation gradients, P0GRADL and P0GRADM were estimated from available snow survey measurements, as described below. The UBC Watershed Model distinguishes between snow and rain by using the mean daily temperature (T) at a given altitude such that if T , 08C; all precipitation is snow and if T . 28C; all precipitation is rain. For the temperatures between 0 and 28C, a simple algorithm divides the precipitation into rain and snow fractions. The model also calculates snowmelt. Therefore the model can calculate snowpack
118
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
Fig. 11. Flows calculated by the proposed method Qcal(avr) and the observed flows Qobs.
accumulation and depletion over time at any elevation within a watershed. Using the temperatures and precipitation recorded at Castlegar the value of the precipitation gradient (P0GRADL) was found which correctly estimated the snowpack recorded at the Sandon snow survey station located within the Slocan River watershed at the elevation of 1070 m, as shown in Fig. 10. The same procedure was followed for the determination of the precipitation gradient applied to the upper part of the watershed (P0GRADM), except that data from Rossland-Maclean meteorological station and Harlow
Creek snow survey station (elevation 1920 m) were used. Final values for the precipitation gradients P0GRADL and P0GRADL were 3 and 7, respectively. These values are fairly typical of the precipitation behavior on the lee side of a mountain range, as explained previously in this paper. Once the topography, fraction of impermeable area and precipitation distribution have been defined, the model was run using the developed fixed set of parameters without any calibration. The simulated hydrographs for five consecutive years were then compared with the observed flows and the results, both
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120 Table 8 Statistics for the flows calculated using the proposed method Water year (Oct. 01 to Sept. 30) Slocan River watershed 1983/84 1984/85 1985/86 1986/87 1987/88 Astore River watershed 1990/91 1991/92 1992/93 1993/94 1994/95
E (%)!
D! (%)
dV (%)
86.73 90.93 90.80 84.72 90.33
97.33 95.00 94.65 90.46 92.47
3.78 6.95 22.15 11.91 12.80
94.32 90.28 80.61 86.50 89.79
94.94 92.82 85.42 86.90 92.84
3.15 0.55 0.12 2.82 1.59
hydrographs and statistics were quite satisfactory (Fig. 11, Table 8).
5.2. Astore River watershed Astore River watershed is located within the Indus River basin in the Himalayas. This watershed spans elevations from 2000 to 7000 m and covers an area of 3955 km 2, only 5% of which is covered with forest and 20% with glaciers. The flow is generated mainly from seasonal snowmelt and glacier melt. The watershed was divided into seven elevation bands and its physical description along with the estimates of the impermeable fraction was provided by the Pakistan Water and Power Development Authority. The precipitation distribution over the watershed was simulated using only meteorological station Astore located at the elevation of 2630 m. The precipitation gradients were provided by the Pakistan Water and Power Development Authority, and were probably calibrated values. However, it is interesting to note that the same set of averaged parameters used in British Columbia gave quite good results even in this very high Himalayan environment. The model was run using the same fixed set of averaged parameters for five consecutive years. The calculated flows showed a good agreement with the flows recorded at the gauging station (Fig. 11, Table 8).
119
6. Discussion 6.1. The regional watershed model calibration Examination of the parameters derived from individual calibration of each watershed revealed that there was a very similar and consistent set of parameters for everything except the fraction of impermeable area and the precipitation gradients. For an ungauged watershed, the precipitation gradients may be judged from snowcourse measurements to some extent, and also, in any sub-region may have to be assessed from the nearest similar watershed. The fraction of the impermeable area, for some of the watersheds, was found to correspond with the fraction of unvegetated area determined from a topographic map. However, this is not always the case. The best way to obtain estimates of this parameter is through the surficial geology maps. These maps provide information on impermeable areas such as areas of rock outcrop or near surface rock within a watershed. There are many parameters which have been pre-calibrated from earlier, detailed studies and are held constant, such as the snowmelt, temperature lapse rates, evapotranspiration and interception parameters. Also for the whole region of this study, parameters affecting the time distribution of runoff, groundwater percolation and groundwater deep zone share, showed relatively low variability, and therefore these parameters were assigned constant values. Each of the twelve study watersheds was re-run with this fixed set of parameters. This simplified approach produced quite reliable results, with only slight reduction in the coefficients of efficiency compared to the full calibration procedure. The differences in the volume errors between the two approaches appear negligible. 6.2. Implications for watershed behavior The pathways for water flow in a watershed consist of a hillslope land phase and a stream network, channel phase. The travel time of the water through the system depends on many controlling factors— basin topography and physical properties and depths of the soils being the most important. However, considering previous velocity measurements in different zones of the land phase (Ishihara
120
Z. Micovic, M.C. Quick / Journal of Hydrology 226 (1999) 101–120
and Kobatake (1975); Dunne (1978); Kirkby (1988)), it can be concluded that the water velocity in the channel network is several orders of magnitude greater than that of the land phase. Therefore, the effect of travel time of the flow in the channel phase seems very small when compared with the observed land phase runoff delays and can be neglected in the watershed routing procedure. The results of this study conducted on the watersheds ranging from 71 to 1194 km 2 in area, show that routing time constants for all four runoff components (fast runoff, interflow, upper and deep zone groundwater) do not increase with drainage area of the watershed. This supports the idea that the land phase controls the runoff process, since, in the land phase, the length of flow paths to the nearest channel is likely to be independent of watershed size, whereas the length of channel network changes considerably with watershed size. Therefore the main delay in runoff is in the land phase. Once this land phase runoff reaches the channel, it is routed relatively quickly to the watershed outlet, because the channel flow is very fast and of much shorter duration than the previous land phase flow. 6.3. Final comments The results of this study show that the model can be essentially pre-calibrated except for two aspects— precipitation distribution and permeability characteristics of the watershed. Such a pre-calibrated model can then be used for generating design flows for ungauged watersheds. This method was tested on twelve watersheds in British Columbia and gave excellent results. These watersheds are quite heterogeneous as shown in Table 1. The implication is that the same parameters may be applicable to any watershed within the studied area regardless of size, topography, climate, soil, geology or hydrological regime, provided that impermeable fraction of the
watershed can be estimated and precipitation input is adequate. Given a good meteorological record, continuous flows could be generated and used for various studies. For example, an annual series of floods or low flows could be generated and used in a frequency analysis. Finally, the same approach was tested on two other watersheds, one in British Columbia and one in the Great Himalayan Range, which were not part of the original study, and the results confirm that good estimation of streamflow can be made.
References Dunne, T., 1978. Field studies of hillslope flow processes. In: Kirkby, M.J. (Ed.). Hillslope Hydrology, Wiley, Chichester, UK, pp. 227–293. Ishihara, Y., Kobatake, S., 1975. The roles of slope and channel processes in storm runoff in the Ara experimental basin. International Symposium on the Characteristics of River Basin, December 1–8, 1975, Tokyo, Japan. IAHS Publ., vol. 117, pp. 75–86. Kirkby, M.J., 1988. Hillslope runoff processes and models. Journal of Hydrology 100, 315–339. Leith, R.M., 1975. Streamflow Regionalization in British Columbia, No. 1. Regression of Mean Annual Floods on Physiographic Parameters, Inland Waters Directorate Report Series, 40. Environment Canada, Ottawa, Ontario, pp. 42. Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models. Part I—a discussion of principles. Journal of Hydrology 10, 282–290. Quick, M.C., 1995. The UBC watershed model. In: Singh, V.J. (Ed.). Computer Models of Watershed Hydrology, Water Resources Publications, Colorado, USA, pp. 233–280. Quick, M.C., Pipes, A., 1977. UBC watershed model. Hydrological Sciences Bulletin XXI 1 (3), 285–295. Riggs, H.C., 1973. Regional analyses of streamflow characteristics, Techniques of Water Resources Investigations of the U.S. Geol. Survey United States Government Printing Office, Washington, DC Book 4, chap. B3. Waylen, P., Woo, M., 1981. Regionalization and prediction of annual floods in the Fraser River catchment, British Columbia. Water Resources Bulletin 17 (4), 655–661.