Scientific Investigations Report 2007–5205
U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2007–5205
Models were developed for gaged and ungaged perennial-stream watersheds and ungaged ephemeral-stream watersheds in the study area. Watershed models for four gaged perennial watersheds were calibrated for this study; Daggett Creek (watershed 5g), Fredericksburg Canyon (watershed 12g), Pine Nut Creek (watershed 13g), and Buckeye Creek (watershed 14g; fig. 3, table 1). Models were then developed for the 10 ungaged perennial watersheds in the Carson Range (fig. 3 and table 1) having estimates of daily mean runoff from a previous study (watersheds 1u–4u and 6u–11u; Maurer and Berger, 2007).
Models for the ungaged perennial watersheds were developed using the calibrated models for either the Daggett Creek or Fredericksburg Canyon watersheds as an index model, meaning that PRMS parameters of the index model were used in building the preliminary model for the ungaged watersheds. Selection of which gaged watershed model to use as an index model was based on the similarity between gaged and ungaged watersheds of (1) major bedrock type, and (2) runoff as a percentage of precipitation as determined by Maurer and Berger (2007, p.29). The Daggett Creek watershed is underlain by granitic bedrock and about 21 percent of precipitation becomes runoff (table 1), whereas the Fredericksburg Canyon watershed is underlain by a mixture of granitic and metamorphic bedrock and a relatively large amount, about 45 percent, of precipitation becomes runoff.
Finally, models were developed for ephemeral watersheds to estimate the quantity of ephemeral runoff tributary to Carson Valley and the potential for ground-water inflow from ephemeral watersheds. Models were developed for 10 of the larger ephemeral watersheds of the Carson Range (watersheds 1e–10e, fig. 3) and a large area near the Pine Nut Mountains where runoff is ephemeral (watershed 11e) Similar to the models developed for the ungaged perennial watersheds, either the Daggett Creek or Fredericksburg Canyon watershed models were used as index models for the ephemeral watershed models of the Carson Range. Because the volume of ephemeral runoff is uncertain, selection of the index model was based only on the bedrock type underlying the ephemeral watershed. The Buckeye Creek model (table 1) was used as an index model for the area of ephemeral runoff on the eastern side of the valley. The Buckeye Creek model was used rather than the Pine Nut Creek model because the overall geology underlying the Buckeye Creek watershed is more similar to that of the area of ephemeral runoff. It consists of a mixture of consolidated rocks, semiconsolidated sediments, and alluvial fans (fig. 3). Index model parameters were used for the ephemeral watershed models without adjustment, except for an adjustment of the precipitation correction factor as discussed in the section, “Runoff and Climate Data.”
Conceptually, perennial and ephemeral drainages such as those on the eastern and western sides of Carson Valley can be described in terms of a few key hydrologic processes that, working in combination, result in measured runoff variations (Beven, 2001). The model used in this study is the Precipitation-Runoff Modeling System (PRMS; Leavesley and others, 1983). PRMS is a process-based, distributed-parameter modeling system designed to analyze the effects of precipitation, climate, and land use on runoff and watershed hydrology (Leavesley and others, 1983).
The term “process-based” refers to the use of mathematical equations to simulate the physical processes of the various water-budget components. The term “distributed-parameter” refers to the representation of the watershed with spatially varying hydrologic characteristics, which is represented numerically as a collection of hydrologic response units (HRUs) that each have a unique set of physical-parameter values. The term “parameters” used throughout this report refers to quantities that define certain relatively constant characteristics of the watershed system. When evaluating the mathematical representation of the watershed, the independent variables are varied, while the parameters are held constant. The system may then be reevaluated or reprocessed with different parameter values, to simulate a system with different behavior.
The PRMS computer program is part of a larger modeling system, the Modular Modeling System (MMS) (http://wwwbrr.cr.usgs.gov/projects/SW_precip_runoff/software/software.shtml). MMS combines a library of modules that simulate separate components of the hydrologic system including water, energy and biochemical processes.
In distributed-parameter precipitation-runoff models, the hydrologic processes are parameterized to account for the spatial and temporal variability of basin characteristics. Although partitioning methods differ, the intent of distributed-parameter models is to better conceptualize hydrologic processes, to represent these processes at time and space scales similar to those in nature, and to reduce model input error, thereby improving overall model performance.
The spatial variability of land characteristics that affect runoff within watersheds is accounted for in the model by dividing the modeled area into Hydrologic Response Units (HRUs). A critical assumption is that the hydrologic response to uniformly distributed precipitation and simulated snowmelt is homogeneous within each HRU. HRUs are thus characterized by those physiographic properties that determine hydrologic response: altitude, slope, aspect, vegetation, soil, geology, and climate. HRUs may consist of noncontiguous or contiguous areas of similar properties. Water and energy balances reflecting physical and hydrologic characteristics and the climate conditions for that day are computed daily for each HRU. The HRU is indexed to one or more nearby climate stations and precipitation is adjusted within the PRMS model with monthly correction factors. Monthly temperature lapse rates and precipitation-correction factors are used to extrapolate measured daily air temperature and precipitation from nearby climate stations to individual HRUs, thereby accounting for spatial and altitude differences. The form of precipitation (rain, snow, or mixed) is dependent on relations between a specified snow-rain threshold temperature and minimum and maximum temperatures for each HRU.
Responses to climate events can be simulated in terms of water and energy balances, streamflow regimes, flood peaks and volumes, soil-water relations, and ground-water recharge (represented by the term ground-water sink in fig. 6). Ground-water recharge from the watersheds moves in the subsurface to become ground-water inflow to the basin-fill aquifers in Carson Valley.
The watershed system is conceptualized as a series of interconnected reservoirs, whose collective output produces the total hydrologic response (fig. 6). The water-budget components (rectangular boxes) denote the storage and collection of water and energy. Daily precipitation, daily maximum and minimum air temperature, and a surrogate for daily solar radiation are inputs that drive the model. The surrogate for solar radiation is estimated from daily temperature using a modified degree-day method and adjusted for slope and aspect. This method is appropriate for use in the study area because predominantly clear skies prevail on days without precipitation (Frank and Lee, 1966; Swift, 1976). Snowmelt is a significant component of the water budget for mountainous watersheds. Snowpack components of PRMS simulate the initiation, accumulation, and depletion of snow on each HRU. The snowpack is simulated both in terms of its water storage and as a dynamic-heat reservoir (Anderson, 1973; Obled and Rosse, 1977; Leavesley and others, 1983). A snowpack water balance is computed daily within each HRU, and a snowpack energy balance is computed each day and night. For moderate-altitude, snow-dominated watersheds such as in the Carson Range and the Pine Nut Mountains, the importance of seasonal differences in temperature and precipitation is reflected in snowpack accumulation and melt rates, and ultimately the timing of runoff.
Potential evapotranspiration (PET) was computed using a modified version of the Jensen Haise method (Jensen and Haise, 1963; Jensen and others, 1969) to account for forest canopies and changes in altitude and humidity. Annually simulated PET estimates were compared to regional PET values for verification (Farnsworth and others, 1982). PET is first satisfied in the model by vegetation canopy-interception storage, followed by sublimation (snowpack evaporation) and impervious-surface evaporation. When snow is present and there is no transpiration, sublimation is computed as a percentage of the total PET (PRMS assumes no sublimation when plants are transpiring). The remaining PET demand is satisfied by evaporation from the soil surface and soil-zone storage after transpiration begins. The transpiration period depends on the plant type and altitude zone contained within each HRU. For each year of simulation, a cumulative degree-day index is computed (using daily mean temperature) to determine the start of transpiration, allowing for earlier or later initiation of the transpiration period during warmer or cooler springs, respectively.
PRMS simulates the soil zone as a simplified two-layer system: a shallow, upper zone (called the recharge zone in figure 6) where water losses are from soil evaporation and transpiration, and a deeper, lower zone where the soil-moisture depletion is by transpiration, ground-water and subsurface recharge. In this study, the subsurface is defined as the unsaturated zone below the root zone and above the water table. The total soil profile depth for each HRU is defined as the average rooting depth of the dominant vegetation. Actual evapotranspiration (AET) losses from the soil zone are simulated as proportional to the remaining PET demand and the ratio of currently available soil moisture to the maximum water-holding capacity of the soil profile. In PRMS, infiltration into the soil-zone reservoir depends on the daily snowmelt or net rainfall rates (total precipitation minus canopy interception), soil field capacities, specified maximum infiltration rates (for snowmelt), and antecedent soil-moisture conditions (water in the soil zone prior to infiltration). Infiltration thresholds are defined depending on whether the water is derived from rain or snowmelt.
The subsurface reservoir represents the pathways that the soil-water excess takes in percolating through the shallow unsaturated zones to stream channels, arriving at the streams above the water table. Soil water in excess of field capacity is first used to satisfy recharge to the ground-water reservoir and is assumed to have a maximum daily limit. Once this limit is reached, further percolation of soil water is routed to the subsurface reservoir. Water can then be further allocated to the ground-water reservoir or routed directly to the stream channel from the subsurface reservoir (fig. 6). The latter is referred to as interflow and is computed as a non-linear rate using the storage volume of the subsurface reservoir and user-defined routing coefficients. Flow from the ground-water reservoir is the source of baseflow in the stream. Movement of ground water outside the modeled watershed is simulated by decreasing the ground-water storage. This portion of the water budget is referred to as a ground-water sink. In this study, the ground-water-sink flux represents ground-water inflow to the basin-fill aquifers of Carson Valley.
Runoff, as simulated by PRMS, is a summation of three components: (1) overland runoff from saturated soils or runoff from impervious surfaces, (2) interflow from the unsaturated zone below the root zone as described above, and (3) baseflow. A basic assumption in PRMS is that the runoff travel time, from the headwaters to the outlet of a defined model area (a tributary watershed, for example) is less than or equal to the daily time step, and thus daily runoff need not be explicitly routed along stream channels.
In PRMS, the ground-water reservoir can be thought of as a bucket from which water in storage is released at a rate that satisfies the baseflow component of the measured hydrograph (the seasonal runoff recessions). Baseflow is designed to respond more slowly to hydrologic fluctuations than interflow. The interflow component typically is represented in the stream hydrograph as the more immediate response to snowmelt, though less rapid than the overland flow component, which occurs when net precipitation or snowmelt exceed infiltration thresholds.
The development of the PRMS model required delineating subbasins or watersheds for gaged and ungaged perennial and ephemeral watersheds, compiling daily time series of runoff and climate data, delineating HRUs, and computing initial index-model parameters for gaged watersheds. PRMS parameters of the index models were used in building the preliminary models for the ungaged perennial and ephemeral watersheds. While the HRU-dependent parameters were determined and computed for watershed-specific areas, the non-HRU dependent parameters were initially derived using the index model then transferred to the models of the ungaged and ephemeral watersheds. Parameters of particular relevance are those used in the routing of water through the soil zones and the shallow subsurface reservoir, the ground-water flow coefficients, and most importantly, those used for simulating ground-water inflow to the basin-fill aquifers of Carson Valley.
Index model parameters for the ungaged perennial watershed models were adjusted to closely match reconstructed runoff, whereas index model parameters were used without adjustment for the ephemeral watershed models, except for adjusting the precipitation correction factor, as discussed in the section, “Runoff and Climate Data.” The modeling and calibration periods were restricted by the lengths of the climate and runoff records.
Geographic Information System (GIS) software, the Weasel Toolbox (Viger and Leavesley, 2006: http://wwwbrr.cr.usgs.gov/weasel/, accessed on November 1, 2005) was used to manage spatial data and to characterize model drainages and HRUs in terms of slope, aspect, altitude, vegetation-cover densities and types, and soil types and depths. Analyses of these characteristics provided estimates of spatially varying HRU-specific model parameters. Initial global model parameters, whose values apply over the entire basin, were quantified from PRMS parameter values for similar watershed studies in the region (Jeton and others, 1996; Jeton, 1999a and 1999b). The gaged and ungaged perennial watersheds are hydrographically defined basins, defined as land areas that drain to a downstream point, whereas the ephemeral watersheds are aggregated areas whose boundaries were arbitrarily defined outside of the Weasel Toolbox, and imported for use in HRU delineation.
A 10-meter digital elevation model (DEM) was used as the basis for computing the watershed boundary (U.S. Geological Survey, 1999). Other digital data include slope and aspect (derived from the 10-meter DEM), soils [1:250,000 State Soil Geographic (STATSGO) database; (U.S. Department of Agriculture, 1991)], and land cover for computing vegetation type and canopy density.
Preliminary HRUs were delineated as subbasin areas with more emphasis on hydrography than on other physical characteristics. These HRUs were further subdivided by altitude resulting in the final physiographic delineation of the HRUs. The final digital HRU data layer was intersected with measurements of altitude, slope, aspect, vegetation, and soils and averaged values were assigned to each HRU.
Figure 7 shows an example of HRU delineation and the distribution of slope, aspect, land cover, and land-surface altitude zones in the Daggett Creek watershed. The GIS-derived parameters are “static,” meaning they are simulated as constant through time and are not adjusted during model calibration. Typically, watershed models are run using several years of daily climate data as model input and land cover and density are assumed to be constant over time. In the present study, however, vegetation-cover type and canopy density for the western and eastern sides of Carson Valley have undergone some changes attributed to recent wildfires. The vegetation data reflect conditions from 1998 to 2000, as mapped in the digital land-cover data sets, with some modifications made to the land cover for the eastern side of Carson Valley.
For the present study, the altitude (DEM) dataset was re-classified into 1,000-foot altitude bands and used to restrict the altitude range within a single HRU to about 1,000 ft (fig. 7D). Point precipitation and temperature measurements from climate stations at lower or higher altitudes than the HRUs were distributed to the HRU using orographic corrections based on the mean HRU altitude. Restricting the range in altitude within a single HRU decreases the magnitude of the orographic corrections.
Digital land-cover data for the Carson Range was obtained from the U.S. Forest Service (Kathy Braton, U.S. Forest Service, Carson City, Nevada, written commun., 2006). These data are a modified version of the 1:24,000 Toiyabe National Forest vegetation layer (http://www.fs.fed.us/r5/rsl/clearinghouse/sec-gbasin.shtml), which was mapped using imagery from 2000 (Ralph Warbington, U.S. Forest Service, Remote Sensing Laboratory, oral commun., 2006). For the Pine Nut Mountains, land cover was derived from the 30-meter resolution Southwest Regional Gap Analysis Program (GAP) data (Kepler and others, 2005) for vegetation type and density as mapped between 1998 and 2000. Canopy densities from the Southwest Regional GAP data appeared to be too high based on visual inspection, and arbitrary adjustments were made to lower the density for shrub and pinion-juniper woodlands. HRU vegetation densities primarily affect simulated snowmelt and runoff timing rather than overall runoff volume. Accurate simulation of runoff timing was less of a concern in the present study, however, because the water-budget components were aggregated to annual and mean annual values for comparison with estimates of Maurer and Berger (2007).
Daily mean runoff is available for model calibration for 4 gaged perennial watersheds (watersheds 5g and 12g–14g; fig. 3 and table 2) and 10 ungaged perennial watersheds (watersheds 1u–4u and 6u–11u; fig. 3) in the Carson Range. Daily mean runoff for the ungaged watersheds was estimated by Maurer and others (2004, p. 8) using multivariate regressions of more than 400 individual discharge measurements against selected continuously gaged streams in and near Carson Valley. In the remainder of this report, the term “reconstructed” runoff is used for the runoff statistically generated to distinguish the estimates from other estimated runoff values. The term “measured” runoff is used for measured or continuously gaged runoff, and “simulated” runoff is defined as runoff simulated by the watershed models. The reconstructed daily mean runoff was estimated by Maurer and others (2004, p. 17) to have an uncertainty of about 30 percent, and measured daily mean runoff of the gaged watersheds was estimated to have an uncertainty of about 15 percent.
Climate input-data requirements for PRMS are daily total precipitation and daily maximum and minimum air temperature. Daily precipitation from six stations in and near Carson Valley (stations 1p–6p; table 2, fig. 3) was used to determine daily precipitation for each HRU in each watershed model. The stations used for each watershed model initially were selected by their proximity to the watershed and the altitude distribution within the watershed. For the Carson Range, high-altitude climate data were limited to climate stations at Daggett Pass (station 2p at 7,330 ft) and Heavenly Valley (station 3p at 8,582 ft). PRMS simulations using the Minden climate station (station 5p at 4,709 ft), located on the valley floor east of the Carson Range, tended to underestimate precipitation, underscoring the rainshadow effect of the Carson Range. Simulations using Sheridan Acres climate station (station 4p at 4,774 ft), located near the base of the Carson Range, appeared more suitable for estimating precipitation for HRUs with altitudes lower than 7,000 ft.
For the eastern side of Carson Valley, daily precipitation data were limited to Fish Springs, at an altitude of 5,120 ft (station 6p, table 2, fig. 3). Mean annual precipitation for Fish Springs averaged 7.7 in. during 1991–2002. Two storage gaging stations, Lower and Upper Pine Nut Mountains at altitudes of 6,440 ft and 7,201 ft in the Pine Nut Creek watershed, recorded annual precipitation of 13.6 and 15.2 in., respectively, for 1984–2002 (Maurer and Halford, 2004, p. 26). Annual averages for the storage gaging stations were used to compare simulated precipitation estimates for the 1981–97 modeling period.
Initial PRMS model simulations in this study used an HRU precipitation correction factor that increased precipitation 15–20 percent for each 1,000 ft of altitude gain above the valley floor. This initial correction factor was derived from local lapse rates calculated using low- and high-altitude precipitation stations and differences in mean HRU altitude. Maximum and minimum daily temperatures were adjusted in the PRMS model with an altitude correction factor of 3.5°F of cooling for every 1,000 ft of altitude gain, which corresponds to regional temperature lapse rates used in similar watershed modeling studies.
Additional adjustments of simulated precipitation were made during model calibration, so that simulated mean annual precipitation was similar to previous mean annual precipitation estimated by Maurer and Berger (2007, p. 29) for the watersheds using the linear relations of Maurer and Halford (2004) for 1971–2000. This was done to assure that the precipitation input to watershed models was consistent with that used previously for estimating ground-water inflow to Carson Valley. Maurer and others (2004, p. 15) reported that mean annual precipitation for 1990–2002 was similar to that for 1971–2000 at Minden, 8.45 and 8.38 in/yr, respectively, and at Heavenly Valley, near the crest of the Carson Range, 33.3 and 32.9 in/yr, respectively.
Precipitation was estimated by Maurer and Halford (2004) using two linear relations between precipitation and altitude, one for the western side and one for the eastern side of Carson Valley, based on data from 14 stations in and near Carson Valley. An areal distribution of precipitation was estimated by applying these relations to a DEM of the study area (Maurer and Halford, 2004, p. 28). In this study, the resulting gridded data set was combined with HRU areas for each modeled watershed and the precipitation estimates of Maurer and Halford (2004) were used to adjust the HRU precipitation correction.
Sensitivity analyses during model calibration typically help to determine the extent to which parameter-value uncertainties result in acceptable runoff predictions. Although this modeling study was focused on estimating ground-water inflow, the hydrologic data to which the watershed model is calibrated is runoff, with ground-water inflow simulated as water in the ground-water reservoir in excess of what reaches the stream channel as baseflow.
The model sensitivities to PRMS parameter values for the present study can be understood from previous watershed modeling studies in the East Fork Carson River basin (Jeton and others, 1996), the Lake Tahoe basin (Jeton, 1999a), and the catchment area of the Truckee River (Jeton, 1999b). The hydroclimatic setting of these earlier studies is similar to that of the watersheds in the present study area with appropriate adjustments made for precipitation distribution. Previous studies of similar watersheds list the parameters modified during calibration (for example, Jeton, 1999b, p. 17).
Sensitivity analyses show that runoff simulations are most sensitive to the (1) snow threshold temperature that determines precipitation form, (2) precipitation-correction factor for snow and rain (similar to a precipitation lapse rate where the measured precipitation is adjusted for differences in altitude between the climate station and the HRU), (3) monthly temperature lapse rates (typically between 3.5 and 4.5°F for every 1,000 ft), (4) monthly evapotranspiration coefficients for the Jensen-Haise potential-evapotranspiration computation (Jensen and Haise, 1963), and (5) coefficient for transmission of solar radiation through winter plant canopies to snow surface, which affects snowmelt timing.
The watershed models also were sensitive to soil moisture storage, and the flow-routing coefficients for interflow and ground-water reservoirs used to simulate ground-water inflow. Parameters that determine flows to and from the ground-water reservoirs were adjusted to fit the observed shapes of the seasonal recession of runoff. Interflow influences the quicker response seen as spikes in the hydrograph in response to snowmelt or rain events and exhibits a short lag in timing. Overland runoff from the rock outcrop or otherwise barren, more impervious areas, reflects a near instantaneous runoff response.
Calibration of PRMS models is an iterative process where, after each adjustment of model parameters, simulated runoff is visually and statistically compared with measured or reconstructed runoff, with special attention paid to matching flow volumes for seasonal and annual time periods, and runoff timing for large events. Ground-water inflow is a component that is not measured but modeled as a residual component of the water budget. If the dominant gains to the system (precipitation) and losses (evapotranspiration) are adequately modeled, and the simulated hydrograph matches the measured hydrograph overall, water in excess of that which reaches the stream channel can be considered as an adequate representation of ground-water inflow. The simulations are run on a daily time step; however, ground-water inflow is evaluated on a mean annual basis to allow for comparison to previously derived estimates. Seasonal and annual water-budget components derived from the models were of most interest and the detailed timing of runoff and ground-water inflow was not crucial.
Effort was made during calibration to provide the best fit to measured or reconstructed runoff during wet years from 1993 to 1998 for watersheds in the Carson Range, and 1982–83 and 1986 for Pine Nut and Buckeye Creeks (fig. 4). This was done because initial watershed modeling showed that ground-water inflow was greatest or occurred primarily during wet years.
For comparison with previous water-budget estimates, and because reconstructed runoff was available for ungaged watersheds for the same time period, a calibration period of water years 1990–2002 was selected for watershed models of the Carson Range. For Pine Nut Creek and Buckeye Creek watershed models, a calibration period of water years 1981–97 was selected, because it coincides with the period of record of measured runoff for the streams (table 2). Simulations of the Pine Nut Creek and Buckeye Creek watersheds were extended to include water years 1998–2002 using the models developed for the 1981–97 calibration period. To provide simulation results for the same period as the Carson Range models, Pine Nut and Buckeye Creek models were run for the 1990–2002 period.
No single calibration of a PRMS model will simulate all runoff regimes with equal accuracy. The goal in modeling is threefold: (1) little to no bias, (2) small simulation error, and (3) realistic parameter values reflecting the conditions being modeled. The goals for calibration are to maintain a good visual fit between the simulated and measured hydrographs, to keep mean annual biases to within 5 percent, and to keep relative error to within 10 percent. In watershed modeling, common measures of simulation error include the sum of errors and bias. Bias is computed to determine the presence of systematic error or an indication of central tendency (that is, whether the simulations show a tendency towards under- or overestimating with respect to the measured runoff). Absolute errors (defined as the difference between simulated and measured runoff) tend to be dominated by a few large events (Haan and others, 1982), unless normalized by the measured values to form “relative error,” as used in this report. The un-normalized root mean square error (RMSE) provides a common measure of the magnitude of simulation errors that complements the relative measures provided by the bias and relative errors.
Normalizing runoff error by dividing it by the measured value presents a problem when the extremely low flows result in very large relative errors even though the absolute error may be small (Haan and others, 1982). Though much of the measured runoff of Carson Range watersheds represents low flows, no runoff data for these watersheds were omitted in the error analysis primarily to allow for comparisons between reconstructed and measured runoff. For the east side watersheds, the Buckeye Creek gaging record indicates numerous days with zero flows, possibly due to poor site location of the gaging station downstream of a losing reach, and the Pine Nut Creek simulations resulted in months with zero flow. For this reason, only months with non-zero flows were included in the error analysis.
Model calibration biases, relative errors, and RMSEs for the four watershed models of gaged watersheds are given in table 3. Error statistics were not calculated for models calibrated using reconstructed runoff because of the considerable uncertainty associated with the reconstructed daily mean runoff. The error statistics are presented as seasonal, mean monthly, and mean annual summaries for the simulation period, with the exception of Buckeye Creek watershed model. For Buckeye Creek, error statistics are presented only for February–April due to the prevalence of zero runoff in the measured record during other times of the year. For the remaining watershed models, monthly error statistics were computed for four seasons; October–December, January–March, April–June, and July–September. Each of these seasons represents a particular hydroclimatic regime with October–December characterized by early winter rain, snow, and mixed rain and snow events, and July–September characterized by low-flow conditions and occasional summer convective storms. January–March are characterized by winter snow and occasional rain-on-snow events, and the spring runoff season; April–June tends to produce the most water available for ground-water inflow to basin-fill deposits of Carson Valley. Lastly, the term “runoff efficiency” is used to compare the percentage of precipitation that becomes runoff, which indirectly is a measure of losses to evapotranspiration and infiltration. Runoff efficiencies were simulated for the 1990–2002 period of record and compared to previous estimates.
Daily mean runoff simulated by the models and measured for the Daggett Creek and Fredericksburg Canyon watersheds provides the best fit for wet years (fig. 8). The hydrographs show a distinct increase in baseflow in 1995 and 1996 with another, smaller increase in 1997. The increase in 1997 is the result of a very heavy snow accumulation and melt period in early 1997. Wet conditions continue into 1998 before returning to dry conditions for the remaining years of the modeling period.
With the exception of April–June, calibration statistics for the Daggett Creek model are satisfactory for seasonal, monthly, and annual time scales (table 3). Simulated mean monthly and mean annual runoff show a tendency to slightly underestimate runoff with low associated errors, and a mean annual RMSE of 1.1 in. Based on visual inspection, a satisfactory overall fit was obtained between simulated and measured daily mean runoff for Daggett Creek for the 1993–98 period of high runoff (fig. 8).
The pattern of simulating, on average, an earlier than recorded spring runoff (fig. 8), particularly evident for water years 1995–2000 results in an overestimation of runoff for January–March and a subsequent underestimation of runoff for April–June (table 3). This may be due to cooler temperatures than were modeled resulting in a later measured spring runoff. Comparisons of measured and simulated annual mean runoff and ground-water inflow are illustrated in figure 9. Overall, the Daggett Creek model under-estimates annual runoff for dry (or below normal) years and overestimates runoff for wet years. The mean annual runoff efficiency using the simulated runoff was 20 percent, comparable to the efficiency calculated with the measured flow (table 1).
Mean monthly and mean annual statistics for the Fredericks Canyon model (table 3) indicate a slight bias to overestimate runoff. Mean monthly and mean annual relative errors were about 15 and 12 percent, respectively, and mean annual RMSE was 6 in. For April–June, the bias and relative error are large and indicate a tendency to overestimate runoff during this period. Statistics for the other seasonal aggregates (table 3) indicate an adequate fit between simulated and measured values.
The simulated and measured runoff indicate that spring runoff in general and the baseflow recession for 1993 and 1995–97 match well (fig. 8), but annual runoff for 1998–99 is overestimated. For the drier years (water years 1990–92 and 1994), baseflow and annual runoff are overestimated. Beginning in 1993, precipitation appears to have recharged subsurface storage sufficiently to increase baseflow for subsequent years, only returning to baseflow conditions similar to 1990 by water year 2001 (fig. 8). For 1997, the measured snowmelt recession curve shows an erratic response (fig. 8), possibly attributed to poor data. Runoff for most days of the year is less than 2 ft3/s for dry years and increases to more than 10 ft3/s only during spring runoff for wet years (fig. 8).
The recorded January 1997 flood peak for Fredericksburg Canyon of 5,000 ft3/s (Bonner and others, 1998, p. 152) is considered to be highly unlikely when compared to the same flood peaks in other Carson Range watersheds (Mike Nolan, U.S. Geological Survey, oral commun., 2006). For this study, the January 1997 peak was therefore arbitrarily adjusted to 100 ft3/s (rather than omitted), to not unduly skew the statistical analyses. Measured runoff for January–May 1997 has numerous days when the runoff had been estimated (Bonner and others, 1998, p. 152) and overall the record for this water year is rated as poor. The runoff efficiency calculated for the 1990–2001 period is 45 percent, comparable to that calculated using measured runoff (table 1).
The period of record of the runoff used for calibration of the Pine Nut Creek and Buckeye Creek watersheds differs from the Carson Range watersheds, and represents an earlier period from water years 1981–97. Both the Buckeye Creek and Pine Nut Creek watershed models used a combination of precipitation data from the Minden station for 1981–91, and the Fish Springs station for 1992–2002 as input data.
There is considerably more uncertainty associated with the watershed models on the eastern side than with those on the western side for the following reasons: (1) the Pine Nut Mountains are subjected to more convective storm activity and without local precipitation data (Minden and Fish Springs stations may be too far from the modeled drainages to accurately estimate their precipitation), and lacking high-altitude data, the models may not adequately simulate the spatial and temporal distribution of precipitation; (2) the model-input precipitation time series is based on a combination of two stations (Minden and Fish Spring climate stations) that have different periods of record and slightly different altitudes but the model applies the same precipitation adjustments to each station record; (3) the Buckeye Creek watershed may be too large to fit the assumption that runoff and subsurface flow reach the stream channel within a daily time step; and (4) there is uncertainty about the soil-water holding capacity, which affects simulated evapotranspiration, runoff, and ground-water inflow to basin-fill aquifers of Carson Valley.
Mean monthly and mean annual bias and relative error are large in the Pine Nut Creek watershed model, and indicate systematic underestimations for mean annual and mean monthly runoff, though less so for the latter. As illustrated in figure 10, the model underestimates annual runoff for all years with the exception of 1982 and 1993 and wet years from 1995 to 1997.
Precipitation volumes for the Pine Nut Creek model were not adjusted to exactly match the 1971–2000 mean annual precipitation volumes determined by Maurer and Berger (2007, p. 29; table 4), which estimated a mean annual rate of 16 in., resulting in excessive simulated runoff. Precipitation amounts were decreased to better match the mean annual precipitation of about 14 in. at the Lower Pine Nut storage gage (Maurer and Halford, 2004, p. 26). Simulating runoff using the adjusted precipitation amounts improved runoff comparisons for the currently underestimated dry years, yet for the wet years particularly 1993, and 1995–97, the model-overestimated runoff resulted in a relative error ranging from 19 percent in 1997 to more than 100 percent in 1993 (fig. 10). Overall, the model underestimates runoff for the dry years when runoff typically was less than 2 ft3/s. The runoff efficiency for the model estimates is about 2 percent as compared to the 8 percent computed by Maurer and Berger (2007, p. 29).
As with all other watershed models presented in this study, the PRMS method for computing ground-water inflow affects the baseflow period for the dry years in a more pronounced manner when adjusting ground-water inflow to minimize overestimation of runoff during the wet years. This resulted in days with zero simulated runoff for the Pine Nut Creek model. Due to the use of a normalized error, only months with non-zero simulated runoff were included in the seasonal error analyses. The only seasonal aggregate with a reasonable bias is April–June. The tendency however, is to overestimate spring runoff during the wet years from water years 1995–97, resulting in an overall relative error of about 22 percent for April–June.
Although the Buckeye Creek watershed is considered to be a perennial watershed, records indicate periods of very low to zero runoff for much of the year, thus characterizing this watershed as more of an ephemeral- than perennial-stream watershed. The Buckeye Creek gaging station is downstream of a losing reach and has many days with zero flows except during the early spring snowmelt. For that reason, error statistics were computed for mean annual runoff, and the February–April aggregate, the latter for years with measured flow (table 3).
Overall, the simulated hydrograph indicates that the model simulates a much quicker response to precipitation than what is measured at the gage and it tends to overestimate mean annual runoff by as much as 12 percent relative to the measured runoff (fig. 10: table 3) However, for the February–April period, the only season with consistently measured runoff greater than zero, seasonal simulations underestimate runoff. For water years 1981–97, mean annual relative error is 102 percent. However, removing water year 1994 from the analysis, when the annual difference in simulated and measured runoff exceeds 1,000 percent (0.046 in. simulated versus 0.003 in. measured), reduces the relative error to about -5 percent (table 3).
The ground-water inflow component of the water budget is greater than zero for those years with above normal precipitation (fig. 9). For wet years (1982–83, 1986, 1993, 1995–97), ground-water inflow ranges from 20 percent of the precipitation in 1982 to more than 40 percent in 1997. The runoff efficiency for Buckeye Creek watershed is estimated to be 2 percent (table 1) indicating most of the precipitation is lost to evapotranspiration and infiltration.
Whether computed ground-water inflow from the Buckeye Creek watershed is reasonable depends primarily on the accuracy of the precipitation inputs. Simulated daily hydrographs for individual years with above normal precipitation (fig. 10) reasonably fit measured hydrographs for most of the winter to early spring runoff peaks, although there is a tendency for the model to underestimate March–April runoff. Conversely, during dry or below average precipitation years, not only is the runoff well below 1 ft3/s for every day during the year, but there are a larger number of measured summer runoff peaks that the model did not simulate.
The precipitation-runoff model is a mathematical representation of the physical processes that occur in the watershed. The quality of the model results depends on the accuracy of the representation of the physical processes (model error), the quality and accuracy of the precipitation and air-temperature input time series and runoff calibration time series (data error), and the accuracy of the calibrated model parameters (parameter error: van Heeswijk, 2006).
Those error sources most affecting the watershed models for Carson Valley include: the assumption that the ungaged perennial and ephemeral watersheds are hydrologically similar to the index watersheds, the scale of available soil data, the adequacy of available climate data and accuracy of precipitation estimates using the precipitation distribution of Maurer and Halford (2004), the accuracy of the reconstructed daily mean runoff used for calibration of the ungaged perennial watersheds, and the sensitivity of the model in simulating baseflow during years of below normal precipitation. Watersheds are dynamic systems. Land-cover type, density, and the percentage of impervious or barren areas are static parameters in PRMS, and therefore reflect land cover conditions for 1998–2000, when the digital maps were compiled.
The hydrologic similarity of ungaged watersheds to index watersheds cannot be further addressed without additional, definitive measurements of runoff from the ungaged watersheds. The effect of index model selection for ephemeral watersheds of the Carson Range is evaluated in the section, “Uncertainty in Estimates of Simulated Ground-Water Inflow.”
The scale of available soil data limits the extent to which the watershed models can represent the actual hydrologic system. The STATSGO soils data are mapped at a scale of 1:250,000, resulting in a 1,000-m grid resolution and a minimum mapping unit of 1,544 acres, an area larger than many of the modeled watersheds. Most of the Carson Range watersheds are characterized as having either one or two soil types, reflecting the dominance of granitic or metamorphic bedrock. Watersheds on the eastern side of Carson Valley have from four to five different soil types reflecting a more varied geologic landscape that includes crystalline volcanic rocks, Tertiary sediments, and alluvial-fan deposits.
The soil-water holding capacity was adjusted upward for most of the HRUs, reflecting an increase from 30 to more than 100 percent of the initial value computed from the STATSGO data to better match the reconstructed or measured runoff. The soil parameters influence the distribution of water between the surface and subsurface reservoirs and ultimately affect the distribution of interflow or shallow subsurface flow, baseflow, and ground-water inflow. In addition, the amount of actual evapotranspiration (AET) is influenced by the generalized PRMS soil designation of sand, loam or clay (derived from STATSGO), and the ratio of available water to the maximum soil-water storage at a given simulation time step.
The dominance of one flow coefficient over the other influences the shape of the simulated hydrograph. The simulated ground-water inflow is set at a constant rate in the model for the selected modeling period. The constant rate affects low-runoff years more visibly than the above-average precipitation years. In low runoff years, less water is routed to the subsurface reservoirs and thus, less water is available for baseflow. This results in a tendency to underestimate baseflow for the drier years, when adjusting the model to better fit wet years. Though there can be remaining soil-moisture storage at the end of a simulated water year, this may be underestimated compared to the actual year-to-year subsurface storage. Propogated over several consecutively low precipitation years, the tendency to underestimate baseflow can potentially increase the modeling error for the period of record.
The rainshadow effect of the Carson Range influences precipitation in Carson Valley as much as altitude. The Sheridan Acres, Daggett Pass, and Heavenly Valley climate stations (stations 4p, 2p, and 3p in fig. 3, respectively) adequately represent the range in precipitation distribution for the Carson Range while the Minden station (station 5p) appears to be influenced by the Carson Range rainshadow effect. The Fish Spring station (station 6p) in the Pine Nut Creek drainage recorded data from 1991 to 2002. The Minden data were used to complete the earlier part of the record and used to model both Buckeye Creek and Pine Nut Creek watersheds. The Pine Nut Mountains are more influenced by localized, convective storm activity, which may not be adequately represented by the Minden or Fish Springs climate stations. There may be some error introduced at the scale of daily runoff simulations in the use of one low-altitude climate station in simulating air temperatures for the higher altitude HRUs, and the use of regional monthly temperature lapse rates to adjust for differences in HRU altitude.
Precipitation inputs were corrected to closely match the long-term precipitation estimates for each watershed determined by Maurer and Berger (2007, p. 29) using the linear relations developed by Maurer and Halford (2004) for 1971–2000. Although the simulated mean annual volume of precipitation may correlate well with the previous estimates of Maurer and Berger (2007; table 4), there is uncertainty as to the interannual variability introduced by the model in using the same monthly HRU precipitation correction factor from year to year. Maurer and Halford (2004) report an uncertainty estimate of 15 percent of the total precipitation estimated for Carson Valley, however, the uncertainty associated with precipitation estimates for high-altitude areas is unknown.
Lastly, the reconstructed runoff time series to which the simulated runoff for ungaged perennial watersheds in the Carson Range was compared during model calibration, have an estimated uncertainty of about 30 percent. Sparse measurements accompany this data set and thus comparison of reconstructed and simulated daily mean runoff is most reliably done on an annual basis. The PRMS models generally exhibit a quicker runoff response to precipitation than most of the reconstructed time series, which use a composite of Carson River flows and gaged records from nearby watersheds. The overall effect is to minimize the daily variations typically present in the measured runoff. This is particularly evident for those watersheds with barren or rock exposure where runoff tends to be more immediate, reflecting the low infiltration during periods of rapid snowmelt or heavy rain.
U.S. Department of the Interior | U.S. Geological Survey
URL: https://pubs.usgs.gov/sir/2007/5205
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Page Last Modified: Thursday, 01-Dec-2016 19:50:48 EST
