The flow at a control point can be correlated to storage at that control point. The model may also be used to relate the flow at a downstream control point to reservoir storage in one or more reservoirs located upstream. This is relevant only for the SFF method of assigning probabilities. Determining which reservoirs influence the flow at a control point of interest is an important issue that requires attention.
The Linear Correlation Coefficient and the Spearman Rank Correlation Coefficient can be used to determine the strength of the relationship between flows at one or more control points and storage at a reservoir or combination of reservoirs. For example, the coefficients can be used to determine if the flow at a point located
downstream of two reservoirs is more closely correlated with storage in only one of the reservoirs or the total storage in both.
Correlations between initial storage and naturalized flows tend to be strongest for a single control point, assuming there is storage at the control point. If there is no storage associated with a control point of interest, the correlation coefficients should be used to determine which reservoirs or combination of reservoirs are more highly correlated with flows at that point.
Including more control points in the summation quickly reduces the correlation to an unusable degree. If no clear correlation exists between storage and flow, the SFF option should not be used. The FF or equal weight options should be used instead. Salazar (2002) provides a detailed analysis of reservoir combinations.
6.3. Hydrologic Period-of-Analysis
For CRM applications, a long hydrologic period-of-record is desirable, even if data extension introduces greater modeling uncertainties. Short-term simulations are less sensitive to data extension techniques because the period-of-record is divided into many shorter sequences and each sequence is run by itself. It follows that short-term reliability and frequency estimates are based on the results of many simulations, so each simulation carries less weight. In a long-term simulation, on the other hand, only one long sequence is estimated, so reliabilities and frequencies are more impacted by modeling uncertainties.
The maximum recommended simulation length should consider the length of the hydrological period-of-record in order to ensure sufficient number of hydrologic sequences to perform a meaningful CRM analysis. While there is no minimum number of hydrologic sequences, the more the better. CRM is generally more accurate for shorter simulation lengths. A simulation length equal to the period-of-record is equivalent to a long-term simulation. If the period-of-record is less than 50 years, consider using the monthly cycle to generate more sequences.
6.4. Initial Storage Content
The effect of initial storage content on the assigning of probabilities depends on the storage frequency curve for the individual reservoir. That is, it depends on whether the reservoir tends to be full or empty. Consider a reservoir that is always 10% full. If the initial storage is 10%, then each hydrologic sequence will be equally likely, regardless of the method used to assign probabilities. On the other hand, consider a reservoir that is usually 100% full, but not always. If at the beginning of the simulation, the storage is now at 10%, the probabilities assigned will be very different between methods. The storage frequency curve of the reservoir of interest needs to be studied to determine the influence of the initial storage condition.
The reservoir storage contents of the primary reservoirs can be set to actual storage conditions or any storage condition of interest. The primary reservoirs contain greater than 95% of the storage capacity in the basin. A condensed dataset will contain only primary reservoirs. For the complete WAM, the storage contents of secondary
reservoirs can be set to the average percent full of the primary reservoirs. Initial storage conditions are specified in the BES file.
The results presented here apply to Granger reservoir and are generally applicable to reservoirs that tend to be full. If reservoir storage is low, and the simulation length is 6 months or less, the SFF method of assigning probabilities is recommended. If the reservoir storage is low or medium, and the simulation length is between 6 months and 2 years, the FF method with storage intervals is recommended. Beyond 2 years, the unrestricted FF and equal weight methods can be used, as the influence of the initial storage condition on simulation results becomes negligible.
6.5. Choice of Cycling Option
The CRM features of WRAP use two methods for dividing a long period of hydrology into several shorter ones: the monthly cycling option and the annual cycling option. The monthly cycle has up to 12 times more sequences, while the annual cycle preserves seasonality. The choice between the two options is essentially a choice between quantity and quality. The most appropriate cycling option depends on the application.
The time it takes for the influence of starting month to become negligible depends on watershed hydrology. For Lake Granger, the monthly cycling option is recommended for simulations lengths greater than 24 months. It is in the best interest of the user to use as many sequences as possible, because preservation of seasonality is less of an issue. For simulation lengths less than 24 months, the annual cycle is
recommended. If the user is interested in average or generalized trends, the monthly cycle can be used for simulation lengths less than 24 months.
6.6. Starting Month
The shorter the length of simulation, the more the starting month influences the computation. With a long enough simulation length, the effect of the starting month becomes negligible. In a drainage area that is wet most of the time, simulations starting in seasonally dry months will differ more from the monthly cycle. The reverse is true for watersheds that tend to be dry.
For modeling studies using the annual cycling option, simulation sequences should start in the month of interest. Alternatively, an appropriate starting month is May, the end of April. April represents a transition from a wet to a dry period. CRM is a practical tool for water management during the dry season.
6.7. Length of Simulation
The SFF option is recommended for use where the correlation between storage and flow permits. Otherwise, the FF option or the equal-weight option should be used. As a general rule, the SFF method for assigning probabilities is applicable to simulation lengths of 6 months or less. However, for certain reservoirs and multiple-reservoir combinations, the recommended length of simulation may be longer or shorter than 6 months.
The Spearman and Linear Correlation Coefficients are calculated by the 5COR record within the CRM features of WRAP. These correlation coefficients should be used to determine the appropriate length of simulation for the SFF option. The higher the correlation, the more accurate the SFF option becomes. The SFF option should not be used for correlations below zero for the Spearman Coefficient and the Linear Coefficient. For Granger reservoir, this occurs around 48 months for a simulation starting in January. The SFF option is recommended for Spearman Coefficients above 0.5. For Granger, this occurs around 5 months for a simulation starting in January. A coefficient above 0.2 is considered strong enough to build the regression relationship. Granger reservoir has a coefficient above 0.2 for simulation lengths up to 19 months for simulations starting in January.
For the purposes of CRM, the user should put more confidence in the Spearman Rank Correlation Coefficient. The Linear Correlation Coefficient (r) assumes that a linear relationship exists between initial storage and naturalized flow, which may not always be the case. The Spearman Correlation assumes that a linear relationship exists between the ranks of the storages and flows, which is more reasonable.
Values for the correlation coefficients change depending on the period-of- analysis, the reservoir or group of reservoirs being analyzed, the cycling option, starting month, and length of simulation.
When the SFF option is unusable, the FF option or the equal-weight option should be used. If the simulation length is between 6 months and 24 months, the FF option is recommended for use with storage intervals. The storage intervals restrict the
assigning of probabilities to those hydrologic sequences that occurred while the reservoir storage contents (or sum of reservoir storage contents for multiple reservoir systems) were within the specified interval.
Setting storage intervals for the FF and SFF options can greatly improve a CRM analysis, but may require knowledge of reservoir storage patterns. For Granger, eliminating all of the sequences that occurred while the reservoir was full may be sufficient. For others, like Hubbard, it may be appropriate to eliminate the top 15% and bottom 15%, and only consider the middle 70%.