Development of a Consumptive Use Operation for the
National Weather Service River Forecast System
Joseph A. Pica
Civil Engineering
Portland State University
Advisor: Dr. Roy Koch
October 27, 1997
Abstract
Today, the Northwest River Forecast Center (NWRFC) manually specifies future diversion flows to adjust long and short-term streamflow forecasts. As part of the implementation of the National Weather Service River Forecast System (NWSRFS), a method for providing these same streamflow forecasts is necessary. A consumptive use operation has been developed which accounts for the impacts of surface water irrigation with the use of the SCS Blaney-Criddle evapotranspiration estimation method. The consumptive use model is a lumped model which assumes an equivalent crop over the irrigated area, limits diversions to the natural flow, and maintains "return flow". Design of this consumptive use operation relied heavily on coordination with the Sacramento Soil Moisture Accounting operation in order to maintain the basin water balance. A test calibration performed on a watershed in the Upper Snake drainage indicates potential for the operation. Additional implementation is required to further evaluate the effectiveness of the consumptive use operation.
Introduction
The development of a consumptive use (agricultural diversion) operation will benefit the hydrologic forecasting of the National Weather Service (NWS). Today, the Northwest River Forecast Center (NWRFC) manually specifies future diversion flows for the long and short-term forecasts generated by the Streamflow Synthesis and Reservoir Regulation (SSARR) system. As part of a national effort to modernize hydrologic services, the NWRFC is discontinuing the use of SSARR and implementing the National Weather Service River Forecast System (NWSRFS), a nationally supported, continuous modeling system. While techniques are available in NWSRFS which provide the ability to manually specify agricultural diversions, they are not timely and offer no improvement in forecasting ability over SSARR. A consumptive use operation may provide for both timeliness and improvement in forecast ability. A diversion model will enable the NWRFC to transition more effectively from SSARR to NWSRFS in regions with extensive surface water irrigation.
Project Scope
The goal of the consumptive use project is to create an NWSRFS operation that improves the forecast ability of the NWS by accounting for the impacts of irrigation in a watershed. Operationally, it will provide for daily and long-term streamflow forecasts. The designed operation is intended to run in conjunction with the hydrologic models and techniques already contained in NWSRFS. This project does not focus on developing a new soil-moisture model, merely maintaining the water balance in conjunction with the existing model in NWSRFS.
Data requirements, model simplicity, and compatibility with other NWSRFS operations were the main considerations in creating this operation. The typical operational data for a watershed is flow at the forecast point and regional meteorological data. Diversion data is often incomplete or not available. Due to the complexity of the calibration process and the amount of data supporting the combination of NWSRFS models, a consumptive use model with fewer degrees of freedom is preferred. Coordination with other NWSRFS operations will need to be addressed with input, output, model parameters, and the basin water balance. In addition, the independence of operations within NWSRFS requires that the operation only address consumptive use contained in a single watershed.
Background - SSARR
Currently, SSARR is the operational forecast system at the NWRFC for watersheds which have considerable consumptive use. Each day, the NWRFC manually estimates and specifies future flows for watersheds which are not modeled due to irrigation impacts. Specified flows in SSARR can range from slightly positive flows in the Winter to large negative withdrawals of 14,000 cubic feet per second in the Summer. For example, the monthly average Milner specified flows are shown in Table 1. Milner is located in the Snake river basin of Southern Idaho. Of the total basin area of 3600 square miles, approximately 1250 square miles (800,000 acres) are irrigated by diversions (Brennan 1996).
TABLE 1. Milner Specified Flows (NWRFC 1996)
| Month | Specified Flow (cfsd) |
| January | 520 |
| February | 414 |
| March | -374 |
| April | -3490 |
| May | -9138 |
| June | -10336 |
| July | -12033 |
| August | -10699 |
| September | -7097 |
| October | -2309 |
| November | 67 |
| December | 520 |
Another example of specified flows in the SSARR model is Shelley Diversions. Shelley local has a total basin area of 500 square miles with approximately 420 square miles (270,000 acres) that are irrigated. There are also considerable subsurface losses to the Snake river aquifer from Shelley local (Brennan 1996). In Chart 1, Shelley observed flows for May through June, 1996, are shown against the SSARR average diversions which are used as guidelines in specifying future diversions.
Chart 1. Shelley Observed vs. Average Diversions (NWRFC 1996)
Typically, forecasters specify future diversions based on recently observed data and trend them towards the monthly average diversions during the next few days. A diversion model based on forecast meteorological data may provide the forecaster with a better indication of future diversions. Chart 2 on the following page shows these same observed specified flows with the precipitation and temperature observed at Idaho Falls Airport. From this diagram, it is apparent that the additional supply of water from rainfall leads to decreased diversions. Although it is not obvious from Chart 2, it has been observed at the NWRFC that higher diversions for irrigation generally result when temperatures are higher in the basin.
Chart 2. Shelley Diversions w/ Meteorological Conditions (NWRFC 1996; NCDC 1996)
Contact with other agencies in the Northwest, primarily the US Bureau of Reclamation(USBR), indicates that the same manual estimation of diversions occurs. However, work in being done by the US Geological Survey (USGS) to assist the USBR in modeling irrigation diversions in the Yakima river basin in Washington. References are available at the NWRFC that show adjusted streamflow due to consumptive use throughout the Columbia River basin (A.G. Crook Company 1993).
Background - NWSRFS
As mentioned previously, the NWRFC is in the process of implementing a new forecast system, NWSRFS. NWSRFS is a collection of hydrologic techniques, models, and procedures for forecasting streamflows in the short and long-range time scales. Calibration, operational forecast, and extended streamflow prediction (ESP) systems are the three components of NWSRFS. In the calibration of a basin, historical precipitation and temperature time-series are generated, and model parameters are optimized. Operational forecasts are made utilizing the same models with real-time observed and short-term forecast meteorological information. Model states are maintained in this process. The same models can be run with historical precipitation and temperature time-series in the ESP system to generate probabilistic long-term forecasts (NWS 1996).
The capabilities exist in NWSRFS to account for diversions using the same methodology as in SSARR. The channel-loss operation can be used to specify a monthly loss or gain of streamflow, but this can not be adjusted operationally. So, future diversions would always trend towards the monthly average. The individual flow time-series could be adjusted manually to better represent diversions. These alternatives are not timely and represent no increase in the forecast ability of the NWRFC. For long-range forecasting with ESP, there is a need to parameterize the diversion process to simulate withdrawals without the manual forecaster intervention.
Irrigation Overview
Irrigation exists where normal rainfall over agricultural lands is inadequate for satisfying crop requirements and water can be supplied from elsewhere. Crop water requirements can be equated to crop evapotranspiration (ET). Virtually all of the water used in plant growth (photosynthesis) leaves the plant into the atmosphere. ET depends on the type of crop, stage in the crop's growing cycle, and meteorological conditions (ASCE 1990). Water can be supplied from surface waters by various methods to meet crop moisture deficiencies. While water can be supplied from groundwater and across watersheds, this project is limited to basins with self-contained surface water irrigation. Water rights and law can play a role in consumptive use, but are not considered as well.
A possible lumped model of surface water irrigation could be described as follows. The total volume of water required by the crops is the ET less any precipitation (infiltration) over the entire irrigated area. Water is diverted, but is limited by the natural flow in the river. Due to the inefficiencies in transporting water from the river to the crops, more volume is diverted than meets the crop requirements. The inefficiencies in diverting water to the crops include the addition to groundwater storage termed "return flow" and other losses. A fraction of this diversion, "return flow", returns to the river after some delay. Other losses refer to any diverted water not accounted for by crop demand or "return flow" and would include deep aquifer recharge and evaporation during transport to the fields. This description of surface water irrigation is shown in figure 1.
Figure 1.
Evapotranspiration (ET) Estimation
Several methods exist for the empirical estimation of crop ET. These include temperature, pan evaporation, radiation, and combination methods, referring to the data requirements of each method. Combination methods such as the Penman Equation require air temperature, dew point temperature, wind speed, and radiation information, reflecting meteorological parameters influencing ET. All methods use empirical coefficients to compute crop ET which depends on the crops and climate of a region (ASCE 1990). When considering the real-time, historical, and future data requirements of each estimation method, the only alternative available for the consumptive use operation is a temperature method. The SCS Blaney-Criddle method, which has been used in the Western United States, was chosen for estimating ET. This estimation method was originally developed to compute ET on a monthly basis, but can be modified to estimate daily values of ET with mean daily temperature (ASCE 1990). Since more accurate mean areal potential evapotranspiration time-series may become available, the option to input this time-series for the consumptive use operation is included.
Consumptive Use Model
An agricultural diversion model was designed which emulates the lumped model shown previously and utilizes the SCS Blaney-Criddle ET estimation method. ET is computed from mean daily temperature, daily percent of annual daylight hours, and monthly empirical coefficients (ASCE 1990). This calculation is shown in equation (1). Temperature, latitude, and Julian day must be input, while monthly empirical coefficients would be determined in calibration. Daily percent of annual daylight hours is computed using latitude and Julian day information.
ET = k * t * p / 100 (1) ET - daily crop ET (L) k - daily empirical crop & meteorological coefficient t - mean daily temperature (T) p - daily percent of annual daytime hours
With precipitation and irrigation area input, ET minus the precipitation is multiplied by the irrigation area to determine the crop demand. An equivalent crop is assumed over the entire irrigated area. Equation (2) illustrates this formulation.
CD = ( ET - P ) * A (2) CD - crop demand (L3) P - daily precipitation (L) A - irrigated area (L2)
The diversion is the crop demand divided by an irrigation efficiency as shown in equation (3). Irrigation efficiency is another parameter which would be determined in calibration.
DQ = CD / e (3) DQ - net diversion (L3) e - irrigation efficiency
Irrigation contributes to additional groundwater supply called "return flow". To account for the delay in getting back to the river, "return flow" is modeled as a single, well-mixed reservoir. Inflow is a percentage of the net diversion, while outflow is first-order decay of storage as shown in equations (4, 5, & 6).
d(RFstor)/dt = RFin - RFout (4) RFin = DQ * c1 (5) RFout = RFstor * c2 (6) RFstor - return flow storage (L3) RFin - return flow in (L3) RFout - return flow out (L3) c1 - return flow accumulation rate c2 - return flow decay rate (1/T)
The accumulation and decay rates are calibration parameters, while an initial "return flow" storage would need to be specified at the beginning of a simulation.
There are constraints associated with the consumptive use calculations to make sure water is not created in the basin. The first is shown in equation (7). In case this constraint is not met, the diversion will be reduced to satisfy the constraint, and resulting flows are recomputed.
Q = NQ + RFout - DQ > 0 (7) Q - adjusted flow (L3) NQ - natural flow (before diversions, L3)
The second constraint recognizes the maximum portion of the diversion available for return flow accumulation after crop demand is fulfilled. This constraint is shown in equation (8).
c1 < 1 - e (8) c1 - return flow accumulation rate e - irrigation efficiency
For accounting purposes, losses in transport to evaporation or to the subsurface aquifer can be computed as shown in equation (9).
OL = DQ - CD - Rfin (9) OL - other losses (transport, subsurface, L3)
Figure 2 is an illustration of all of the equations together on the previously shown irrigation diagram. Note that the differential equation for return flow storage has been converted to its finite difference explicit form with a daily time step.
Figure 2.
NWSRFS Operation Design
The intention was to perform the consumptive use computations in a NWSRFS operation. However, the order of the operation in the forecast segment scheme and accounting of the basin water balance came into question. Since precipitation and ET are input for both the soil moisture accounting and consumptive use models, the water balance is not maintained. Modifications to the models and operations were considered to remedy the situation. First, the irrigation area should be modeled as its own subbasin with its own SAC-SMA operation. Second, coordination needs to be done between the Sacramento Soil Moisture Accounting (SAC-SMA) and Consumptive Use (CONS_USE) operations to best simulate streamflow and to maintain the basin water balance.
Required input to the consumptive use model is natural flow, mean areal temperature, mean areal precipitation, and possibly potential ET. Since natural flow is required as input to the consumptive use model, the CONS_USE operation has to follow any operations that compute the natural flow, including routing operations. The primary output from the CONS_USE operation is adjusted and diversion flow, which is necessary for forecasting streamflow. Secondary output is needed for water balance accounting and includes the "return flow" in, "return flow" out, other losses, crop demand, and crop ET.
Two options were considered for satisfying the redundant calculation of ET in the soil moisture accounting and consumptive use models. First, if the actual ET computed in the soil moisture model was output as a time-series, then input into the consumptive use model, crop ET could be adjusted to satisfy the water balance. The SAC-SMA operation would need to be modified to output the actual ET as a time-series for input into the consumptive use operation. This alternative complicates the calculations, requires modification of the SAC-SMA operation, and does not reflect conditions of an irrigated basin in the soil moisture model. The second alternative would be to set the potential evaporation to zero in the SAC-SMA operation during the crop's growing season. With ET only being calculating in one model on a given date, the water balance would be satisfied. It would also mean that water would not be depleted in the soil moisture model, better reflecting the conditions of an irrigated basin. However, the initial soil moisture contents in the model may be low and be cause for errors early in the growing season. Computations are more straight forward in the second alternative and do not require modifications to the SAC-SMA operation.
Precipitation is input for both the SAC-SMA and CONS_USE operations, leading to questions about the basin water balance. One alternative for addressing the precipitation concerns would be to calculate an infiltration amount based on input mean areal precipitation (MAP). Crop demand would be reduced and more accurately reflect the actual diversion. However, this input precipitation would have already gone into the SAC-SMA operation, and been accounted for in the soil contents or runoff. An alternative which solves the water balance question is simply to exclude it from the CONS_USE operation. The diversion would then be computed as if there was no rain. MAP input would go to runoff in the SAC-SMA instead of going to crop ET. This additional runoff would then be removed in the CONS_USE operation as diversion. The actual diversion flows are not accurate in this situation. Also, the problem arises early in the season when the MAP input goes only to tension water storage and does not show up in the river. The consumptive use operation would want to take water out of the river which will not get there.
The resulting design of the CONS_USE operation involved a cooperative effort with the SAC-SMA operation. ET should be set to zero in the SAC-SMA operation during the growing season, while the consumptive use coefficients should be set to zero outside the growing season. The MAP was input solely into the SAC-SMA, which in turn would become runoff from a sub-basin with tension water contents full. The consumptive use computed will take the necessary water back out of the runoff which actually went to the crops. Considering the scarcity of precipitation over much of the West during the growing season and the small percentage of irrigation area, this may not prove to be a significant error in the model. This handling of precipitation still needs to be evaluated, especially in basins with a large percentage of irrigated area.
NWSRFS Operation Construction & Evaluation
FORTRAN subroutines were written that are required for NWSRFS (Anderson 1996). Synthetic data was used to test the computations during operation construction. Sample calculations were also performed during a test calibration, which are contained in Appendix A.
The logic and computational part of the operation was verified during construction, but applicability to streamflow forecasting was evaluated with a test calibration. A test calibration was begun for the Portneuf river at Pocatello in the Upper Snake river basin. This is a 1,250 square mile headwater basin with nearly ten percent of the area irrigated (Brennan 1996). Temperature and precipitation data from the region were acquired and checked for consistency. Mean areal temperature and precipitation time-series were created using the standard methodology of the NWRFC. USGS records indicate that the watershed has had approximately the same amount of irrigated land over the past thirty years (Brennan 1996). While the Portneuf river at Pocatello has a historical record back to 1948, the calibration simulation will only be done for the latest consistent period of record due to changes in irrigation practices with time. Consumptive use coefficients were initially estimated based on the primary crops grown in the region: potatoes, sugar beets, and grains (A. G. Crook Company 1990).
The test calibration proved, as expected, to be somewhat more complex than a basin with no consumptive use. It still requires some adjustments, but there are indications of the value of the consumptive use operation. A multiyear statistical summary and hydrographs from the test calibration are contained in Appendix B. While the annual runoff, overall correlation coefficient, and hydrographs indicate a fairly good calibration, the monthly biases in the Summer and Fall are high. Long-term simulations and limited volume water years are simulated well with the CON_USE operation, while daily simulations leave room for improvement. The daily root mean square errors are highest in the Summer when the flows are at zero. Often, the flow goes to zero in the Summer instead of some minimum required flow in the river. This results from an assumption that all available runoff can be used for irrigation. The high bias in the fall is partially due to keeping the potential ET at zero in the SAC-SMA model, maintaining the full contents of the upper zone tension water contents into the Fall. In reality, less irrigation will occur near the end of the season when farmers are letting the fields dry for harvesting. Additional optimization of CONS_USE "return flow" and SAC-SMA maximum tension water content parameters could also be done. Further evaluation of this calibration is ongoing.
Conclusions & Recommendations
In general, the consumptive use operation can provide for streamflow forecasts and performs well over the long-term, especially in water years with a limited supply of water. On a daily basis, it may indicate trends but does not simulate as well. Since the SCS Blaney-Criddle estimation method was originally developed to be used on a monthly basis, this was not entirely unexpected. The ability to modify the daily empirical coefficients is needed operationally. Minimum flow needs to be added as a parameter in the consumptive use model. It is unlikely that all runoff is available for diversions, and this would improve the Summer simulations. Since the continuing of the zero ET specification in the SAC-SMA does not allow for depletion of the tension water contents before the Fall rains, an investigation could be performed to see if overlapping ET specification in the SAC-SMA and CONS_USE operations would alleviate the problem. While it appears that the exclusion of precipitation from the CONS_USE operation did not adversely affect the test calibration, it remains to be seen if this is the case for a basin with a large percentage of irrigated area. I recommend that precipitation be included in the consumptive use operation to examine the impacts in basins with large irrigated areas and to see if it improves the daily streamflow simulation. As others try to implement the consumptive use model, further evaluation can be done.
References
A.G. Crook Company. Technical Appendix for Development of Modified Streamflows, 1928-1989, Columbia River & Coastal Basins. Prepared for Bonneville Power Administration. June, 1993.
American Society of Civil Engineers (ASCE). "Evapotranspiration and Irrigation Water Requirements". Manuals and Reports on Engineering Practice. ASCE. No. 70. New York, New York, 1990.
Anderson, Eric. "How to Add a Forecast Component Operation". NWS River Forecast System User's Manual. NWS. Section VIII.4. July, 1996.
Brennan, T.S., Lehmann, A.K., O'Dell, I., and Tungate, A.M. Water Resources Data - Idaho, Water Year 1995, Volume 1. Great Basin and Snake River Basin Above King Hill. USGS, Idaho District. Boise, Idaho. May, 1996. pp. 121, 140, & 161.
Burnash, R. and Ferral, L. "Conceptualization of the Sacramento Soil Moisture Accounting Model". NWS River Forecast System User's Manual. NWS. Section II.3. July, 1996.
Norvitch R.F., Thomas, C.A., and Madison, R.J. Water Information Bulletin No. 12: Artificial Recharge to the Snake Plain Aquifer in Idaho; an Evaluation of Potential and Effect. Prepared by United States Geological Survey in cooperation with Idaho Department of Reclamation. August, 1969.
National Climatic Data Center (NCDC). Idaho Climatological Data. NCDC. Vol. 099, No. 05-06. May-June, 1996.
NWS. "Overview of NWSRFS". NWS River Forecast System User's Manual. NWS. Section I.1.1. July, 1996.
NWRFC. SSARR Upper Snake Spring Forecast Book. NWRFC. Stub=3/12/93. May-June, 1996.
APPENDIX A. Sample Calculations
MCP3 Output: Input Parameters
0******************** 0CONS_USE OPERATION NAME=PIHI1 0******************** CONSUMPTIVE USE - VERSION 1 PORTNEUF R AT POCATELLO -- DIVERSIONS OPTION 0 ET ESTIMATION WITH TEMPERATURE INPUT TIME SERIES ID CODE MEAN AREAL TEMPERATURE PIHI1L MAT POTENTIAL EVAPORATION NONE NONE MEAN DAILY NATURAL FLOW PIHI1 SQME PRIMARY OUTPUT TIME SERIES MEAN DAILY ADJUSTED FLOW PIHI1A SQME MEAN DAILY DIVERSION FLOW PIHI1D SQME SECONDARY OUTPUT TIME SERIES MEAN DAILY RETURN FLOW IN RFIN SQME MEAN DAILY RETURN FLOW OUT RFOUT SQME MEAN DAILY OTHER LOSSES OL SQME MEAN DAILY CROP DEMAND CD SQME CROP EVAPOTRANSPIRATION CE MAPE GENERAL IRRIGATION BASIN PARAMETERS LATTITUDE (+NORTH/-SOUTH, DEGREES) 42.70 IRRIGATED AREA (KM^2) 225. IRRIGATION EFFICIENCY (0-1) .65 MID-MONTH EMPIRICAL COEFFICIENTS JAN FEB MAR APR MAY JUN ---- ---- ---- ---- ---- ---- .00 .00 .00 .35 .65 .70 JUL AUG SEP OCT NOV DEC ---- ---- ---- ---- ---- ---- .70 .65 .60 .30 .00 .00 RETURN FLOW PARAMETERS RETURN FLOW ACCUMULATION RATE .25 RETURN FLOW DECAY RATE (1/DAY) .0070 RETURN FLOW STORAGE (MM) 100.
MCP3 Debug Output: Computed Daily Empirical Coefficients
EX57: EMPIRICAL COEFFICIENTS: 245 .62 September 1 EX57: EMPIRICAL COEFFICIENTS: 246 .62 EX57: EMPIRICAL COEFFICIENTS: 247 .62 EX57: EMPIRICAL COEFFICIENTS: 248 .62 EX57: EMPIRICAL COEFFICIENTS: 249 .62 EX57: EMPIRICAL COEFFICIENTS: 250 .61 EX57: EMPIRICAL COEFFICIENTS: 251 .61 EX57: EMPIRICAL COEFFICIENTS: 252 .61 EX57: EMPIRICAL COEFFICIENTS: 253 .61 EX57: EMPIRICAL COEFFICIENTS: 254 .61 EX57: EMPIRICAL COEFFICIENTS: 255 .61 EX57: EMPIRICAL COEFFICIENTS: 256 .60 EX57: EMPIRICAL COEFFICIENTS: 257 .60 EX57: EMPIRICAL COEFFICIENTS: 258 .60 EX57: EMPIRICAL COEFFICIENTS: 259 .60 September 15 EX57: EMPIRICAL COEFFICIENTS: 260 .59 EX57: EMPIRICAL COEFFICIENTS: 261 .58 EX57: EMPIRICAL COEFFICIENTS: 262 .57 EX57: EMPIRICAL COEFFICIENTS: 263 .56 EX57: EMPIRICAL COEFFICIENTS: 264 .55 EX57: EMPIRICAL COEFFICIENTS: 265 .54 EX57: EMPIRICAL COEFFICIENTS: 266 .53 EX57: EMPIRICAL COEFFICIENTS: 267 .52 EX57: EMPIRICAL COEFFICIENTS: 268 .51 EX57: EMPIRICAL COEFFICIENTS: 269 .50 EX57: EMPIRICAL COEFFICIENTS: 270 .49 EX57: EMPIRICAL COEFFICIENTS: 271 .48 EX57: EMPIRICAL COEFFICIENTS: 272 .47 EX57: EMPIRICAL COEFFICIENTS: 273 .46 EX57: EMPIRICAL COEFFICIENTS: 274 .45 September 30
Computations: Daily Empirical Coefficients
Days 245-274 = September 1-30, 1976 Leap Year From input parameters... Aug 15 Coef., Day 228 = 0.65 Sep 15 Coef., Day 259 = 0.60 Oct 15 Coef., Day 289 = 0.30 Interpolation of September 1 Coefficient: K(245) = K(228) + [K(259) - K(228)] * (245 - 228) / (259 - 228) = 0.65 + [0.60 - 0.65] * 17 / 31 = 0.62 Interpolation of September 30 Coefficient: K(274) = K(259) + [K(289) - K(259)] * (274 - 259) / (289 - 259) = 0.60 + [0.30 - 0.60] * 15 / 30 = 0.45
MCP3 Debug Output: Computed Daily Daylight Hours
EX57: DAYLIGHT HOURS: 256 12.37 EX57: DAYLIGHT HOURS: 257 12.32 EX57: DAYLIGHT HOURS: 258 12.27 EX57: DAYLIGHT HOURS: 259 12.22 September 15 EX57: DAYLIGHT HOURS: 260 12.17 EX57: DAYLIGHT HOURS: 261 12.12 EX57: DAYLIGHT HOURS: 262 12.07 EX57: ANNUAL DAYLIGHT HOURS: 4380.
Computations: Daily Daylight Hours (ASCE 1990)
Latitude (L) = 42.70 ...from input parameters Julian Day (J) = 259, September 15 Latitude (radians, o) o = L * 2 * PI / 360 = 42.70 * 2 * PI / 365 = 0.745 tan(o) = 0.01300 Declination (radians, d) d = 0.4093 sin [2 * PI * (284 + J) / 365] = 0.4093 sin [2 * PI * (284 + 259) / 365] = 0.0665 tan(d) = 0.00116 Sunset Hour Angle (radians, Ws) Ws = PI / 2 - arctan{[-tan(o) * tan(d)] / [1 - tan2(o) * tan2(d)]1/2} = PI / 2 - arctan{[-0.013*0.00116] / [1 - (0.013)2 * (0.00116)2]1/2} = PI / 2 - (- 0.000864) = 1.5717 Daylights Hours on JD 259, h(259) h(259) = Ws * 24 / PI = 1.5717 * 24 / PI = 12.22 Annual Daylight Hours = h(1) + h(2) + … + h(365) = 4380
MAT: Input Temperature Data
DATACARD MAT TEMP DEGF 6 PIHI1L PIHI1 LOWER MAT 9 1976 9 1976 6 F9.3 976 6 64.596 39.527 27.756 57.431 75.156 50.005 976 7 38.049 64.414 80.786 64.120 56.057 69.303 976 8 76.815 56.765 47.433 61.757 69.871 47.232 976 9 36.707 56.928 69.014 48.529 38.861 60.583 976 10 73.488 52.759 42.956 62.752 74.646 56.041 September 15 976 11 47.233 65.824 76.714 56.322 46.733 63.559 976 12 73.395 52.466 42.666 56.986 65.455 46.596 976 13 37.776 57.071 68.498 49.325 40.274 61.637 976 14 74.026 50.512 39.461 62.163 75.941 56.574 976 15 47.363 62.184 70.757 50.125 40.498 60.326
MCP3 Debug Output: Computed Crop Evapotranspiration
EX57: CROP ET: OPTION 0: 9 12 1976 256 8.57 16.53 21.04 8.46 13.65 56.57 .28 .60 2.45 EX57: CROP ET: OPTION 0: 9 13 1976 257 2.61 13.85 20.56 9.18 11.55 52.79 .28 .60 2.28 EX57: CROP ET: OPTION 0: 9 14 1976 258 3.81 15.88 23.05 11.53 13.57 56.42 .28 .60 2.42 EX57: CROP ET: OPTION 0: 9 15 1976 259 6.09 17.08 23.69 13.36 15.05 59.10 .28 .60 2.51 September 15 EX57: CROP ET: OPTION 0: 9 16 1976 260 8.46 18.79 24.84 13.51 16.40 61.52 .28 .59 2.56 EX57: CROP ET: OPTION 0: 9 17 1976 261 8.18 17.53 23.00 11.37 15.02 59.04 .28 .58 2.41 EX57: CROP ET: OPTION 0: 9 18 1976 262 5.93 13.88 18.59 8.11 11.63 52.93 .28 .57 2.11
Output Description: Month, Day, Year, Julian Day, 6hr MAT (deg C), 6hr MAT (deg C), 6hr MAT (deg C), 6hr MAT (deg C), Ave. MAT (deg C), Ave. MAT (deg F), % Annual Daytime Hours, Daily Empirical Coefficient, Crop Evapotranspiration (mm)
Computations: Crop Evapotranspiration
While temperatures in the input MAT file are in degrees Fahrenheit, NWSRFS stores temperatures in degrees Celsius. deg C = ( deg F - 32 ) * 5 / 9 = ( 42.956 - 32 ) * 5 / 9 = 6.09 = ( 62.752 - 32 ) * 5 / 9 = 17.08 = ( 74.646 - 32 ) * 5 / 9 = 23.69 = ( 56.041 - 32 ) * 5 / 9 = 13.36 The temperatures in the MAT correspond to the temperature input for the consumptive use operation. Ave. MAT (deg C) = ( 6.09 + 17.08 +23.69 + 13.36 ) / 4 = 15.05 The SCS Blaney-Criddle Method of evapotranspiration estimation uses English units (ASCE 1990). Ave. MAT (deg F, t) t = 9 / 5 * Ave. MAT + 32 = 9 / 5 * 15.05 + 32 = 59.10 % Annual Daytime Hours (p) p = h(259) / Annual Daytime Hours * 100 = 12.22 / 4380 * 100 = 0.28 Daily Empirical Coefficient (k) = 0.60 ...from previous computations Crop Evapotranspiration (mm, CE) CE = k * t * p / 100 * (25.4 mm / in) = 0.60 * 59.10 * 0.28 / 100 * 25.4 = 2.51
MCP3 Debug Output: Computed Diversion and Adjusted Flows
EX57: FLOWS: 9 12 1976 2.45 6.39 9.84 14.75 12.39 4.92 2.46 2.36 .98 129.29 EX57: FLOWS: 9 13 1976 2.28 5.93 9.12 14.91 12.55 5.79 2.28 2.36 .91 129.26 EX57: FLOWS: 9 14 1976 2.42 6.29 9.68 14.83 12.47 5.15 2.42 2.36 .97 129.29 EX57: FLOWS: 9 15 1976 2.51 6.55 10.07 14.57 12.22 4.50 2.52 2.36 1.01 129.35 September 15 EX57: FLOWS: 9 16 1976 2.56 6.67 10.27 14.30 11.94 4.03 2.57 2.36 1.03 129.43 EX57: FLOWS: 9 17 1976 2.41 6.27 9.65 14.06 11.70 4.41 2.41 2.36 .96 129.45 EX57: FLOWS: 9 18 1976 2.11 5.50 8.46 14.10 11.74 5.63 2.12 2.36 .85 129.36 EX57: FLOWS: 7 12 1977 1.59 4.13 6.35 6.35 5.11 .00 1.59 1.24 .64 68.09 EX57: FLOWS: 7 13 1977 1.53 3.99 6.13 6.13 4.89 .00 1.53 1.24 .61 68.20 EX57: FLOWS: 7 14 1977 1.49 3.87 5.95 5.95 4.71 .00 1.49 1.24 .60 68.30 EX57: FLOWS: 7 15 1977 1.45 3.76 5.79 5.79 4.55 .00 1.45 1.25 .58 68.38 July 15 EX57: FLOWS: 7 16 1977 1.41 3.68 5.66 5.66 4.41 .00 1.42 1.25 .57 68.44 EX57: FLOWS: 7 17 1977 1.39 3.62 5.56 5.56 4.32 .00 1.39 1.25 .56 68.50 EX57: FLOWS: 7 18 1977 1.37 3.56 5.48 5.48 4.23 .00 1.37 1.25 .55 68.54 Output Description: Month, Day, Year, Crop Evapotranspiration (mm, CE), Crop Demand (cmsd, QCD), Diversion (cmsd, QDIV), Natural + Return Flow Out (cmsd, QSUM), Natural Flow (cmsd, QNAT), Adjusted Flow (cmsd, QADJ), Return Flow In (cmsd, QRFIN), Return Flow Out (cmsd, QRFOUT), Other Losses (cmsd, QOL), Return Flow Storage (mm, RFSTOR)
Computations: Diversion and Adjusted Flows
Units conversion factor (f) 1 mm*km2 * [(1m /1000mm)*(1000m/km)*(1000m/km)*(1 day/ 86400 sec)] = 0.011574 cmsd
Crop Evapotranspiration (mm, CE) = 2.51 ...from previous computations Crop Demand (cmsd, QCD) QCD = CE * Area * f = 2.51 mm * 225 km2 * 0.011574 cmsd / mm*km2 = 6.55 Diversion Flow (cmsd, QDIV) QDIV = QCD / Irrigation Efficiency = 6.55 / 0.65 = 10.07 Return Flow Out (cmsd, QRFOUT) QRFOUT = RFSTOR (previous day) * Area * f * Decay Rate = 129.29 mm * 225 km2 * 0.011574 cmsd / mm*km2 * 0.0070 = 2.36 Natural Flow (cmsd, QNAT) = 12.22 ...from snow, soil moisture, unit hydrograph, and routing operations Natural + Return Flow Out (cmsd, QSUM) QSUM = QNAT + QRFOUT = 12.22 + 2.36 = 14.57 ...total is off by a rounding difference The maximum amount of flow available for diversions is the sum of the natural flow and the return flow out. In other words, the minimum adjusted flow is zero flow. If QDIV > QSUM, then QDIV = QSUM, QCD = QDIV * Irrigation Efficiency, CE = QCD / (Area * f) If one examines the July 1977 computations, the diversion flows are set equal to the sum of the natural flow and the return flow out. The adjusted flow is zero, and the crop demand and evapotranspiration are recomputed based on the amount of water available. If QDIV < QSUM or QDIV = QSUM, then Adjusted Flow (cmsd, QADJ) QADJ = QSUM - QDIV = 14.57 - 10.07 = 4.50 Return Flow In (cmsd, QRFIN) QRFIN = QDIV * Accumulation Rate = 10.07 * 0.25 = 2.52 Other Losses (cmsd, QOL) QOL = QDIV - QCD -QRFIN = 10.07 - 6.55 - 2.52 = 1.01 ...total is off by a rounding differenceReturn Flow Storage (mm, RFSTOR)
RFSTOR(259)= [(RFSTOR(258) * Area * f) + QRFIN - QRFOUT] / (Area * f) = [(129.29 * 225 * 0.011574) + 2.52 - 2.36] / (225 * 0.011574) = 129.35
APPENDIX B. Test Calibration Output
MCP3 Output Statistics
MULTIYEAR STATISTICAL SUMMARY PORTNEUF AT PIH AREA (SQ KM) = 3238.00 WATER YEARS 1970 TO 1993 MTHLY MAX PERC PERC MAX MTHLY PERC SIM OBS BIAS ERROR AVE DLY VOL AVG ABS PERC MEAN MEAN PERC SIM-OBS SIM-OBS ABS RMS ERR MTHLY MTHLY VOL MONTHLY (CMSD) (CMSD) BIAS (MM) (CMSD) ERR ERR (MM) VOL ERR RMS ERR .................................................................................................................... OCTOBER 7.870 6.689 17.65 .976 23.545 43.01 64.23 11.816 39.17 59.19 NOVEMBER 10.609 8.190 29.54 1.937 9.957 33.06 43.33 6.607 32.51 42.11 DECEMBER 9.730 8.345 16.59 1.146 8.340 24.23 32.64 5.188 23.16 30.96 JANUARY 9.064 8.793 3.08 .224 -21.253 22.10 32.20 4.104 17.99 23.69 FEBRUARY 9.678 9.828 -1.53 -.112 -19.655 20.95 32.55 -4.869 18.72 25.33 MARCH 13.217 13.592 -2.76 -.310 10.405 21.39 26.81 5.998 17.68 21.13 APRIL 17.121 17.317 -1.13 -.157 -15.595 23.82 31.03 -8.330 18.71 25.62 MAY 20.441 20.807 -1.76 -.303 -34.495 34.99 44.55 -14.001 32.42 39.57 JUNE 9.768 11.561 -15.51 -1.435 -29.736 45.64 67.04 -14.911 42.89 61.27 JULY 2.693 3.624 -25.68 -.770 14.020 66.47 89.10 -5.998 64.00 81.81 AUGUST 2.602 3.223 -19.29 -.514 12.778 75.61 98.19 6.748 74.31 93.28 SEPTEMBER 4.690 4.671 .39 .015 19.915 50.30 63.24 4.947 47.56 56.98 .................................................................................................................... YEAR AVG 9.783 9.711 .73 .695 -34.495 32.99 49.26 -14.911 30.01 43.75 .................................................................................................................... AVERAGE ABS MONTHLY LINE OF DAILY RMS DAILY AVERAGE MONTHLY VOL VOLUME CORRELATION BEST FIT ERROR ABS ERROR ERROR RMS ERROR COEFFICIENT OBS = A + B*SIM (CMSD) (CMSD) (MM) (MM) DAILY FLOWS A B .......... ............. ........... ........... ........... ................. 4.784 3.203 2.367 3.451 .8402 1.2083 .8692 NUMBER SIM OBS BIAS MAX PERC PERC OF MEAN MEAN PERC SIM-OBS ERROR AVG ABS RMS FLOW INTERVAL CASES (CMSD) (CMSD) BIAS (MM) (CMSD) ERROR ERROR ....................................................................................................………………………………………… .00 - 2.75 1362 1.204 1.638 -26.49 -.0116 9.457 110.45 137.04 2.75 - 5.00 1297 4.069 3.829 6.27 .0064 12.823 72.58 88.99 5.00 - 7.25 1316 7.212 6.151 17.26 .0283 15.101 41.13 55.43 7.25 - 9.00 1205 9.237 8.118 13.79 .0299 17.867 30.96 44.36 9.00 - 11.00 1226 11.086 9.878 12.23 .0322 23.545 25.74 40.78 11.00 - 17.00 1226 14.281 13.252 7.77 .0275 24.541 25.87 37.08 17.00 AND ABOVE 1134 23.911 27.954 -14.46 -.1079 -34.495 26.29 33.30 ....................................................................................................
MULTIYEAR STATISTICAL SUMMARY PORTNEUF AT PIH AREA (SQ KM) = 3238.00 WATER YEARS 1970 TO 1993 DIVERSION RETURN FLOW OUT MEAN MEAN MONTHLY (CMSD) (CMSD) ................................................... OCTOBER 4.685 1.309 NOVEMBER .487 1.247 DECEMBER .000 1.140 JANUARY .000 1.039 FEBRUARY .000 .950 MARCH .000 .869 APRIL .319 .794 MAY 3.697 .760 JUNE 10.211 .845 JULY 12.024 1.023 AUGUST 10.903 1.190 SEPTEMBER 8.231 1.299 ................................................... YEAR AVG 4.238 1.040 ...................................................
ICP Output Hydrographs
Scale: 0 - 50 cfsd, 365 days Color Key: Black Observed Flow Purple Adjusted Flow (Natural + Return Flow Out - Diversion ) Blue Natural Flow Green Diversion Flow
