«Chapter 7 Step 5 - Calibration of Hydrologic Models Introduction Now that all the needed information is available, the variability of physical and ...»
Step 5 - Calibration of Hydrologic Models
Now that all the needed information is available, the variability of physical and climatological fa
ctors have been assessed, the calibration locations and periods of record to use were selected, an
d the data have been checked, analyzed, and put in the proper form, it is finally time to calibrate t
he hydrologic models. In order to simulate conditions over an entire river basin many models a
nd procedures must be used. Most of these contain variables that must be determined. Some c an be determined directly by analyzing physical or experimental data, such as reservoir storage elevation relationships and spillway rating curves or the drainage area of a particular watershed o r local area. Other variables, which constitute the majority, are model parameters that vary fro m one area to another based on changes in physical factors and climatology. Methods exist for estimating the parameters for many models in an a priori fashion based on various information.
Such parameter estimates may be satisfactory for some applications, but seldom provide the acc uracy needed for river forecasting. To use the models to produce reliable forecasts both in the s hort term and for extended periods into the future, requires that a thorough calibration be conduct ed to determine the appropriate values of the parameters.
This manual will primarily focus on strategies and procedures for calibrating the NWSRFS SNO W-17 and Sacramento soil moisture models, however, in order to compute the flow in the rivers, a number of other models must be used. Even for a headwater drainage with no complications, a model of the channel system is required to convert the runoff into the channel network to disch arge at the streamgage location. For downstream local areas, some kind of routing model is nee ded to translate the flows from upstream to the downstream locations. For points with more co mplexity within their drainage area, models of reservoir operations, irrigation demands, glacial e ffects, etc. could be required. These other models will be mentioned in this chapter though not i n the same detail as the snow and Sacramento models.
There are many references in the literature to calibration procedures and techniques. The vast majority of these deal with the calibration of models to an individual drainage area, usually a hea dwater area with few complications. While this manual includes strategies and procedures for c alibrating an individual drainage, the primary emphasis is the calibration of an entire river basin which eventually leads to the calibration of the entire area of responsibility of an RFC. To calib rate the models needed for an entire RFC area for river forecasting applications, requires a calibr ation process that is efficient, that results in spatially consistent parameter values, and that accura tely simulates streamflow and other variables under a full range of climatic conditions. If calibr ation of an entire RFC area is conducted as a series of largely independent efforts with various in dividuals working on one watershed at a time with only minor coordination, the results will not o nly fall short of the objectives, but will take much longer to complete than necessary. The strat egies and procedures given in this chapter are aimed at fully meeting calibration objectives in the minimum amount of time.
There are three basic objectives when calibrating conceptual hydrologic models to an entire river basin for river forecasting applications.
1. Produce a good reproduction of the observed hydrograph at each individual point on the ri ver system. The aim is to achieve a fit that contains the minimum amount of bias possible, i.e. all errors are random. This includes all types of bias including overall bias, bias related t o the magnitude of flow, seasonal bias patterns, and bias related to specific snow and soil mo isture conditions such as during an abnormally large snow accumulation year or after a long dry spell. Also intermediate variables such as snow water equivalent and soil moisture defi cits should compare realistically to any observations of these variables. The amount of rand om error should be largely a function of the random error associated with the input variables, especially precipitation. Errors in the amount of precipitation, as categorized by the typica l spatial variability of this input variable, are the primary reason that lumped models do not p roduce satisfactory results in some areas of the country as was discussed back in Chapter 1 a nd illustrated in Figure 1.1.
2. The parameters of the models should function as they are intended. Both the SNOW-17 and Sacramento models are conceptual models which represent, although in a simplistic fashi on, the main physical processes that occur in nature. These models were designed to have a physical basis and the parameters control portions of the models that represent specific com ponents of the overall process. The parameters of the Sacramento model were designed to r epresent items such as the timing and maximum contribution of various runoff components, t he maximum soil moisture deficits that can occur, and the rate of the movement of water wit hin the soil profile with changing moisture conditions. The snow model parameters represe nt such items as the seasonal variation in melt rates when the area is completely snow covere d, the areal depletion pattern as the snow melts, and the amount of liquid water that can be he ld within the snow cover. The effects of each parameter are designed to be reflected in spec ific sections of the simulated hydrograph under specific soil moisture or snow cover conditio ns. In order to be consistent with the physical basis of the models and to produce results tha t will not only best reproduce the full range of historical observations, but also be most likely to extrapolate correctly beyond what was observed in the available historical record, each p arameter of the models should be used as it was intended.
3. There should be a realistic variation in parameter values from one area (headwater, local, o r subdivision within a drainage) to another within the river basin and with areas just across th e divide in adjacent river basins. Changes in parameter values from one area to the next sho uld be explainable based on changes in physiographic factors, climatic conditions, or hydrogr aph response. Not only is this objective reasonable from a physical point of view, but if adh ered to, makes it much easier to monitor and understand operational variations and run time a djustments to state variables.
7−2 One question that is often asked, especially by those first learning how to calibrate conceptual hy drologic models, is “when am I done.” Basically the answer is that you are done when the obje ctives have been met, i.e. when all possible bias has been removed, when the portions of the hydr ograph controlled by each parameter are checked to make sure that the parameter is acting as inte nded, and when any changes in parameter values from one area to another are consistent with the assessment that was made of the spatial variability of hydrologic factors across the region.
When trying to judge whether the objectives have been met, it is important to remember that ther e is often considerable noise in the input data being used for calibration, especially the precipitati on input. The amount of noise varies with the region of the country and the gage network. Th ere may not only be considerable noise in the data for a given watershed, but the amount of noise can vary from one watershed to another depending on the number of gages available, as well as their location and accuracy of the measurements. Noise in the input data can make it not only d ifficult to determine the appropriate parameter values for a given watershed, but the variation in t he amount of noise from one watershed to another can affect the spatial consistency of the results. This is why the strategy recommended in this chapter starts with calibrating the watershed tha t has the least noise in the data record. This is also one of the reasons why a sufficiently long p eriod with considerable climatic variability is needed for calibration. Such a period should mini mize “curve fitting”, though there still may be considerable uncertainty in the value of parameter s that control portions of the models that are seldom activated. Verifying the results on indepen dent data periods should help to reduce this uncertainty and further minimize any “curve fitting”.
After the initial watershed in the basin is calibrated, one must be careful that realistic spatial c onsistency patterns are not destroyed by “curve fitting” during the calibration of the other draina ges in the basin. In order to achieve the proper balance between the calibration objectives, give n the amount and variation of noise in the data, the reproduction of the observed hydrograph, at l east as measured by goodness of fit statistics, may have to be sacrificed somewhat in order to ach ieve spatial consistency of the parameters.
It is stated in objective one that all possible bias should be removed. When working with a lum ped model, there are certain types of bias that are inherent in how the model is applied. In addit ion, there are certain model limitations that will cause trends in the results. These factors result
in bias that typically cannot be removed including:
• An under simulation of the highest flows. A lumped application of a model uses the avera ge amount of precipitation over an area, whereas in nature the amount of precipitation is seld om uniform. Since the rainfall-runoff process is non-linear, those portions of an area that ha ve rainfall or snowmelt amounts that are greater than the mean areal value will produce relati vely more runoff than parts of the area where the amounts are below the mean. This results in the actual runoff being greater than what would be produced by applying the mean value t o the entire area. Adjustments to some model parameters, especially the percolation curve i n the Sacramento model, can partly adjust for this tendency, but especially in regions where t here is typically a large variation in intensity levels during storms over individual drainage ar eas, a lumped application of a model will under compute runoff during high flow events.
• A over simulation of low flows. When most models are applied in a lumped fashion it is t ypically assumed that baseflow is being generated over the entire area based on the contents of the groundwater storages, at least that is the case with the Sacramento model. Under the lowest flow conditions, this is likely not the case in nature. Thus, there is a tendency for a l umped application of the Sacramento model to over simulate the lowest flow levels.
• In mountainous areas where snowmelt dominates runoff production, the simulated spring s nowmelt typically occurs too early during years with a much below normal snow cover. Th is occurs because the snow primarily only covers the highest portion of the upper elevation z one, whereas the lumped application assumes the snow is distributed over the entire zone.
This situation is described further in Section 6-1 and illustrated in Figure 6-1-3.
• Some biased results when snowmelt is not occurring over the entire area. The model assu mes that either melt is taking place over the entire snow covered area or it is not. Especially in mountainous areas, early in the melt season snowmelt may only be occurring at the lowes t elevations and on south facing slopes. This can result in some bias in simulating runoff du ring the first week or so of the snowmelt period.
• The largest snowmelt runoff events are typically under simulated, particularly in regions w here high winds and dew-points are associated with major snowmelt situations. This is part ly due to the lumped application of the model, but primarily due to using an index to comput e snowmelt. In the SNOW-17 model air temperature is used as the sole index to snowmelt.
While temperature is a good indicator of melt under most conditions, during some extreme snowmelt situations the typical relationship between temperature and melt doesn’t hold. E specially in the northeast, major snowmelt events are associated with high dew-points and wi nd speeds. This causes large amounts of latent and sensible energy exchange and alters the normal relationship between air temperature and melt. There are other situations when the r elationship between temperature and melt varies from the normal, but these are not associate d with a particular level of melt and thus tend to randomly affect flow interval bias computati ons.
• Rainfall events that occur late in the snowmelt season on watersheds with a prolonged sno w depletion period, generally mountainous areas, typically are over simulated. In these situ ations the soil has dried out in portions of the area that have been bare of snow for sometime, whereas as long as the areal average melt computed by the model, which is coming from on ly a small part of the area, exceeds the evaporation rate, the soil will remain wet. This can b e minimized by using additional elevation zones, but the use of too many zones can cause op erational difficulties (see Section 6-1).
• Baseflow recharge can’t be modeled consistently when there is a lower zone tension water deficit in the Sacramento model. This is caused by the model assuming that a constant fract ion of the area (PFREE parameter) contributes to recharge during this situation when in realit y the fraction should undoubtedly vary depending on the size of the deficit, i.e. the ratio of L ZTWC/LZTWM. If the ratio is 0.0, little recharge should occur. As the lower zone beco
Calibration Methods There are two basic methods used for the calibration of hydrologic models. The first is a guide d trial and error procedure where the users knowledge of the model and how each parameter affe cts the results are used to control changes to parameter values. Decisions as to which parameter s to change are made primarily by comparing simulated versus observed values, especially hydro graph plots. This procedure is most effective when interactive, graphical software is available t o view the results and make parameter changes. The calibration is finished when the user subje ctively determines that the objectives have been met.