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J. Martinec
Consulting Hydrologist
Davos, Switzerland
A. Rango, R. Roberts
USDA Hydrology Laboratory
Agricultural Research Service
Beltsville, Maryland, USA
The Snowmelt Runoff Model (SRM) is a simple degree-day model that requires remote sensing input in the form of basin or zonal snow cover extent. The model has been tested successfully on over 60 basins worldwide in the simulation and forecast modes. Model variables are derived from actual observations of temperature, precipitation, and snow covered area. Model parameters can either be derived from measurements or estimated by hydrological judgement taking into account the basin characteristics, physical laws, and theoretical or empirical relationships. To facilitate use of SRM, a microcomputer version of the program has been developed for IBM compatible personal computers. The program itself features user-oriented input and multiple self-help screens which allow the user to select the kind of data input employed and the output products desired.
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1.0 PREFACE
This new edition of the User's Manual and new personal computer (PC) program (Version 3.2) for the Snowmelt Runoff Model (SRM) feature in particular:
1. The possibility of inputting separate climate station data for each elevation zone.
2. Automatic printout of modified depletion curves of the snow coverage for day-to-day and seasonal runoff forecasts.
3. More guidance for selection of model parameters and for eliminating errors.
4. Improved handling of rainfall peaks.
5. Assessment of the impact of a changed climate on the snow cover and snowmelt runoff.
So far, about 100 diskettes with PC program Version 1 and 2.01 for SRM have been distributed to users in different parts of the world. This Manual corresponds to the more recent improved Versions 3.0, 3.1, 3.11, and 3.2 (which is now available).
Furthermore, elements of a SRM expert system had been designed to assist the user in difficult conditions (Engman et al., 1989). At the same time, the authors will be glad to help the user with special problems which may have not been foreseen for inclusion in this Manual.
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The Snowmelt-Runoff Model (SRM; also referred to in the literature as the "Martinec Model" or "Martinec-Rango Model") is designed to simulate and forecast daily streamflow in mountain basins where snowmelt is a major runoff factor. SRM was developed by Martinec (1975) in small European basins. Thanks to the progress of satellite remote sensing of snow cover, SRM has been applied to larger and larger basins. The largest basin where SRM has been applied so far is about 122000 km². Runoff computations by SRM appear to be relatively easily understood. To date the model has been applied by various agencies, institutes and universities in about 60 basins situated in 19 different countries as listed in Table 1. About 30% of these applications have been performed by the model developers and 70% by independent users. Some of the localities are shown in Figure 1. SRM also successfully underwent tests by the World Meteorological Organization with regard to runoff simulations (WMO, 1986) and to partially simulated conditions of real time runoff forecasts (WMO, 1992).
Figure 1 Selected locations where SRM has been tested
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3.0 RANGE OF CONDITIONS FOR MODEL APPLICATION
SRM can be applied in mountain basins of almost any size (so far from 0.76 to 122000 km²) and any elevation range (for example 305-7690 m a.s.l.). A model run starts with a known or estimated discharge value and can proceed for an unlimited number of days, as long as the input variables - temperature, precipitation and snow covered area - are provided. As a test, a 10-year period was computed without reference to measured discharges (Martinec and Rango, 1986). In addition to the input variables, the area-elevation curve of the basin is required. If other basin characteristics are available (forested area, soil conditions, antecedent precipitation, and runoff data), they are of course useful for facilitating the determination of the model parameters.
SRM can be used for the following purposes:
1. Simulation of daily flows in a snowmelt season, in a year, or in a sequence of years. The results can be compared with the measured runoff in order to assess the performance of the model and to verify the values of the model parameters. Simulations can also serve to evaluate runoff patterns in ungauged basins and in a hypothetically changed climate.
2. Short term and seasonal runoff forecasts. The microcomputer program (Micro-SRM) includes a derivation of modified depletion curves which relate the snow covered areas to the cumulative snowmelt depths as computed by SRM. These curves enable the snow coverage to be extrapolated manually by the user several days ahead by temperature forecasts so that this input variable is available for discharge forecasts. The modified depletion curves can be also used to evaluate the snow reserves for seasonal runoff forecasts. The model performance may deteriorate if the forecasted air temperature and precipitation deviate from the actual values, but the inaccuracies can be reduced by periodic updating.
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4.0 MODEL STRUCTURE
Each day, the water produced from snowmelt and from rainfall is computed, superimposed on the calculated recession flow and transformed into daily discharge from the basin according to Eq. (1):
If the elevation range of the basin exceeds 500 m, it is recommended that the basin be subdivided into elevation zones of about 500 m each. For an elevation range of 1500 m and three elevation zones A,B,C, the model equation becomes
In the simulation mode, SRM can function without updating. The discharge data serve only to evaluate the accuracy of simulation. In ungauged basins the simulation is started with a discharge estimated by analogy to a nearby gauged basin. In the forecasting mode, the model provides an option for updating by the actual discharge every 1-9 days.
Eqs. (1) and (2) are written for the metric system but an option for model operation in English units is also provided in the computer program.
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8.0 RUNOFF SIMULATION FOR A FUTURE CHANGED CLIMATE
Because all parameters of SRM are predetermined and not calibrated, the model is suitable for computing snowmelt runoff in ungauged basins and, in response to a recently emerging problem, in a changed climate. If temperature can be forecasted several months ahead, predicted with a certain probability for an unspecified year, or just hypothetically assumed, SRM is applicable for computing the resulting runoff hydrograph. To this effect, it is necessary to derive the changed depletion curves of snow covered areas with the use of the modified depletion curves, MDC. Possible changes in precipitation may also influence the new runoff patterns (Rango and van Katwijk, 1990b). The opinion now prevails that the climate will become warmer and not colder. It is of course possible to simulate the effect of both options and to consider various changes of future precipitation.
If SRM is used only to predict snow covered areas in a changed climate (for example in mountain areas which are not hydrological basins), the computer program requires the following data:
The following example (Martinec and Rango, 1989b) explains the effect of a warmer climate on the snowmelt runoff in a mountain basin. It is assumed that the seasonal snow cover of 1 April 1983 will exist in a future year when temperatures will be higher by + 3 °C each day during the snowmelt period than temperatures of 1983. Figure 25 shows the MDC derived by the computer program for the snowmelt season of 1983. The same occurrence of summer snowfalls is assumed so that the melt depth is obtained, for this purpose, by totalizing, starting on 1 April, the computed daily melt depths of the seasonal old snow cover as well as of the intermittent new snow. Recalling Figure 20, this MDC does not indicate the snow accumulation on 1 April. It can be read off that a totalized melt depth of 30 cm had the effect of reducing the snow covered area to 55%. The conventional depletion curve of snow covered areas in Figure 26 shows that this occurred on 28 May 1983. With temperatures increased by + 3 °C, the computed daily melt rates are higher so that the total of 30 cm is reached already on 10 May of a future year, and with it the snow covered area of 55%. In this manner, the depletion curve of 1983 is shifted to earlier dates. The new depletion curve reflects the effect of a warmer climate and indicates snow covered areas for each day which are needed to compute the new runoff hydrograph. The climate-shifted depletion curves are automatically derived by SRM computer program Version 3.2 for any selected change of temperature and precipitation.
Figure 25 Modified snow cover depletion curve (melt depth includes new snow) for zone B
(2926-3353 m a.s.l.) of the Rio Grande basin in 1983 (Martinec and Rango, 1989b).
Figure 26 Conventional snow cover depletion curve for zone B of the Rio Grande basin in 1983 and a
predicted shifted curve for teh temperature increase of +3°C (Martinec and Rango, 1989b).
The adjustment of CDCclim(MA) is carried out by the computer program as follows: If CDCclim shows more than one S-value on a date (the curve decreases vertically), the first S-value (the highest) is used. If there is no S-value on a date, the S-value of the previous day is used until there is a new S-value. Consequently, CDCclim(MA) has one S-value on each day as required for SRM runoff computation.
Due to the time shift by the changed climate, S-values may be missing towards the end of the computation period. The last available S-value is then repeated by the described adjustment so that CDCclim(MA) becomes a horizontal line. This part of the curve must be used for runoff computation. The user can either derive realistic S-values to use instead or stop the runoff computation at this point.
If such a horizontal line occurs in the original CDC, it usually indicates a glacier within the elevation zone in question. In this case, the horizontal line which also appears in CDCclim and CDCclim(MA) is valid and the S-values can be used for runoff computation.
The derivation of CDCclim includes the following steps:
The computer program takes care of the changed snow/rain conditions: with higher temperatures, some of the spring or summer snowfalls now become rainfalls. When these changes of input variables are also carried out in the remaining zones of the basin, the new runoff hydrograph is computed in the usual manner. Figure 27 shows that the warmer climate would increase the runoff and discharge peaks in the Rio Grande basin in the first half of the snowmelt season and reduce the runoff in the second half. The seasonal runoff volume appears to be slightly higher because the high flows are shifted to April and May when relatively high values of the runoff coefficient are assumed.
However, the resulting conditions in the warmer climate may imply that adjustments of the runoff coefficients are necessary as well. So far, the effect of a future climate change is evaluated only for the duration of the snowmelt season. The existing snow accumulation at the beginning of the snowmelt season is assumed to be unchanged. However, if the warmer climate would be extended to the winter months, the snow accumulation would be reduced. Consequently, a lower modified depletion curve MDCexcl would have to be used as a starting point to derive the snow covered areas as well as the redistribution of winter and summer runoff in the new climate. The adjustment of MDCexcl by the changed winter climate is in the research stage. New patterns can be simulated also by various assumptions regarding precipitation changes, but already the given example reveals some aspects of the climate change:
Figure 27 Simulated change in runoff on the Rio Grande basin for 1983 as a result of a 3°C
increase in temperature (T+3) (Martinec and Rango, 1989b).
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