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The literature review covers the past history of conveyance loss studies on perennial streams in the intermountain western region. It summarizes the computer model J349 with its associated advantages and limitations for the analysis of conveyance loss modeling.


Other States

Concerns over conveyance losses date back to the 1930's when the Twin Lakes transmountain diversion project was completed in Colorado. After completion of the diversion project, Hinderlinder (1938) began investigating conveyance losses on a 175 mile portion of the Arkansas River which extended from Leadville, Colorado to the Colorado Canal near Pueblo, Colorado. Hinderlinder encountered problems in determining conveyance loss because the reach in question experienced gains. He concluded that this gain was due to the rivers flowpath through an irrigated region.

Lacey (1941) continued the study on this river reach. The study included seven reservoir releases in which flow through the river as well as diversions along its flowpath were taken into account. Lacey too discovered that the gaining nature of this river reach made determining an accurate conveyance loss very difficult. The result of these two studies did lead the State of Colorado to assess a loss value of 0.07% on total flow per mile of stream in the Arkansas River for releases from Twin Lakes Reservoir.

Wright Water Engineers (1970) attempted to determine conveyance losses for the above 175 mile reach with data collected from a series of 30 reservoir releases performed between 1966 and 1970. The study was based upon an incremental type approach. Losses to evaporation, inadvertent diversions and bank storage were considered in this study. The study suggested that a varying conveyance loss should be assessed dependent upon the magnitude of reservoir release. Additionally, the study showed that the actual conveyance loss due to reservoir water was less than the 0.07% per mile previously suggested.

Livingston (1973) conducted another conveyance loss study on the same 175 mile reach of the Arkansas River. Livingston utilized an incremental conveyance loss approach and considered four primary losses in his study. These losses included the three previous losses (evaporation, inadvertent diversions, and bank storage) as well as channel storage. Losses were found to be dependent upon the duration and rate of reservoir release, as well as the time of year of the reservoir release. The results of this investigation yielded a conveyance loss which ranged from 0.03 % per mile to 0.16 % per mile.

Lucky and Livingston (1975) created a routing model which accounted for water wave time of travel, bank storage, channel storage and inadvertent diversions. This model was applied to the same 175 mile reach of the Arkansas River as previously mentioned. Results from the model yielded similar results to those found by Livingston in 1973. The model was found to be most accurate during relatively steady flow periods.

Livingston (1978) also modeled a different reach on the Arkansas River. The reach extended 142 miles from the Pueblo Reservoir to the John Martin reservoir. The model developed in 1975 was altered so that a greater emphasis could be placed on evaporation loss. Additionally, the portion of the model that accounted for inadvertent losses was eliminated. The results of this study showed that for a ten day release of 100 cfs, incremental conveyance losses ranged from 0.05% to 0.35% per mile. Livingston concluded from this study that 80% of the total conveyance loss could be attributed to bank storage while 10% could be accounted for in channel storage and the remaining 10% could be accounted for through evaporation.

Wright Water Engineers (1982) conducted a conveyance loss study on an 80 mile reach of the Fryingpan River between Ruedi Reservoir and Parachute, Colorado. A series of theoretical equations was used to estimate losses due to bank storage, channel storage and inadvertent diversions. Conveyance losses on this reach were estimated to range between 0.02% to 0.18% per mile.

Several models have been developed which account for conveyance loss using various relationships between flowrate and aquifer parameters. Pinder and Sauer (1971) and Zitta and Wiggert (1971) developed computer models which simulate the effect that flood waves has on bank storage. Moench (1974) developed a model that compares stream and aquifer parameters in routing reservoir releases on the North Canadian River in Oklahoma. Cunningham (1977) developed a model that correlates groundwater depth and corresponding streamflow to model conveyance losses on the Truckee River in Nevada.


Basin Electric Power Cooperative in 1975 (Wyoming State Board of Control, 1976) requested of the Board of Control a transfer of 98.73 cfs through 110 miles of river reach on the Laramie River. The route extended from the Laramie River diversion of the Boughton Ditch to Grayrocks Reservoir. The Board of Control granted a transfer of 41.86 cfs with an annual maximum of 3117 acre-feet. Conveyance loss values were estimated such that existing users were protected from loss. Conveyance losses assigned are as follows:

  1. for a maximum daily diversion greater than 35 cfs, a value of 30% of total flow is assessed;

  2. for a maximum daily diversion less than 35 cfs and greater than 22.5 cfs a value of 40% of total flow is assessed;

  3. for a maximum daily diversion less than 22.5 cfs and greater than 5 cfs a value of 50% of total flow is assessed; and

  4. for a maximum daily diversion rate less than 5 cfs, value of 100% of total flow is assessed.

These conveyance losses average out to between 0.3% to 0.9% per mile of river.

In 1978, the Green River Development Company (Wyoming State Board of Control, February 1981) requested a transfer of 28.62 cfs to be routed 130 miles from the Green River and Cottonwood Creek through the Green River Supply Canal and Cottonwood Canal respectively. The Board of Control allowed a transfer of 14.31 cfs with an annual maximum of 2000 acre-feet. The Board of Control, basing the estimate solely on experience, placed a charge of 0.2% per mile to the transfer.

In 1985, Pahl completed a conveyance loss study on three Wyoming Rivers. A form of the mass balance equation was applied to streamflow data to determine incremental conveyance losses for the stream reaches in question. The equation applied in the determination was:

L = [DI - DD] - DO
L = Incremental loss,
D I = Increase in inflow,
D D = Increase in diversion, and
D O = Increase in outflow.

The major drawback to utilizing this equation is that steady flow periods are necessary for this method to predict conveyance losses accurately. A steady flow period is needed so that the stream-aquifer relationship is in equilibrium. Assuming that this is true, when flow is increased, all conveyance loss encountered would be due to that increase in flow.

Pahl determined that incremental conveyance losses are most likely to occur as a result of:

  1. Evapotranspiration,
  2. Bank storage,
  3. Channel storage,
  4. Inadvertent diversion, and
  5. Reduction in groundwater inflow.

Research was conducted on three Wyoming rivers using the methods described. One reach modeled was Piney Creek from below Lake DeSmet to a USGS gaging station at Ucross, Wyoming. An incremental conveyance loss ranging between 0.76% to 1.66% per mile was calculated.

The second reach to be considered in this study was on the New Fork River. The reach in question ran from New Fork Lake to a point approximately eight miles downstream. The incremental conveyance loss determined for this reach was 0.85% per mile.

The third study reach was on the Laramie River. The reach extended from Wheatland Reservoirs No. 2 and No. 3 to the confluence of the Laramie River and Sybille Creek, a distance of 51 miles. A conveyance loss of 0.34% per mile was calculated for this reach.

Pahl drew several conclusions from modeling the three stream reaches. First, the amount of conveyance loss in any reach is dependent on the amount of flow as well as the length of the flow period. Secondly, water lost to bank storage is not a true loss. When water stage within the reach recedes, most of the water stored as bank storage may return to the river system. Finally, this research determined average incremental conveyance losses ranging between 0.34% to 1.66% per mile.

In 1988, Hanlin completed a conveyance loss study on five Wyoming stream reaches. This study also used a form of the mass balance equation known as the net total loss type of conveyance loss. Net total conveyance loss is a method for assessing transfer charges to insure that water rights of existing users are not harmed. The net total loss equation takes the form:


The drawback to using this method for determining conveyance losses is that a steady flow period is needed to insure that the stream-aquifer relationship is in equilibrium.

Hanlin attempted to model five stream reaches. The first reach was a 52 mile segment of the North Platte River which extended from Guernsey Reservoir to the Tri-State Dam. Conveyance losses on the reach ranged from 0.3% per mile to 4.3% per mile. This compares reasonably well with the results of Livingston's (1973) research on the Arkansas River where losses were found to range between 0.02% to 4.3% per mile.

The second reach modeled was Piney Creek from Lake DeSmet to the Clear Creek at Carlock Ranch. A conveyance loss of 1.2% per mile was calculated for this reach. This compares well with conveyance losses determined by Pahl. Pahl found losses on this river to be within the range of 0.76% to 1.66% per mile.

The third reach to be modeled was 26 miles of Horse Creek from below the Woods and Lykins Diversion to just above the diversion into the Brown and Lagrange Canal. Conveyance losses for this reach ranged from 0.05% to 4.7% per mile. The upper value is high compared to the range of 0.34% to 1.66% per mile determined in earlier studies by Pahl.

The fourth reach to be modeled was on the Bear River between the USGS gaging station near Randolph, Utah to below Pixley Dam. This study was discontinued however, due to lack of adequate streamflow data.

The fifth reach to be modeled was on the Green River from just below Fontenelle Dam to the town of Green River. This study too, was discontinued due to a lack of adequate streamflow data.

For each of the reaches modeled, Hanlin developed an equation of the form:

y = a + b/x
y = stream gains or losses expressed as percent of inflow, and
x = average inflow.

This equation shows that there is a relationship between a stream's gains and flow in the stream. These equations can only be created for stream reaches with sufficient data such that the water balance approach may be used.

Farber (1992) completed research on conveyance loss modeling for two Wyoming rivers. Farber modeled the Green River from below Fontenelle Dam to the town of Green River. Additionally 50 miles of Piney Creek from Lake DeSmet to five miles east of Leiter, Wyoming were modelled.

Conveyance loss modeling for these reaches was accomplished using the-computer model known as J349. Farber received the computer code for the J349 model from Gerhard Kuhn of the United States Geological Survey. The code was initially written for use with mainframe computers and had to be altered for use with 286 or higher personal computers.

The J349 model was then utilized to determine conveyance losses on Piney Creek. Using the model on streamflow data collected in 1984, a conveyance loss of 0.65% per mile was calculated. Streamflow data for 1985 was separated into four sub-reaches. Conveyance losses were found to range between 0.011% to 0.52% per mile. These conveyance losses compare reasonably well with results determined by both Pahl and Hanlin.

The Green River reach could not be modeled in the same manner as the Piney Creek reach due to reservoir conditions at the time of the study. Flow was decreased on the Green River reach and then increased rather than just an increase.

The study revealed several interesting conclusions. First, the percent of the reservoir release lost to bank storage decreases as the reservoir release increases. Secondly, the percent of the reservoir release to bank storage decreases as the duration of the reservoir release increases. Perhaps the most important conclusion by Farber was that the J349 conveyance loss program is capable of providing reasonable estimates of conveyance loss to bank storage.


The J349 model is a conveyance loss computer model which combines a streamflow routing component with a bank storage component to determine a total conveyance loss for a given reach. The program was published as a United States Geological Survey Computer Contribution (Land 1977). Equations inherent in the model allow for actual aquifer characteristics to be considered as part of the modelling.

Hall and Moench (1972) developed a system by which bank storage could be determined. The J349 hydrologic conveyance loss model utilizes this system in its code to calculate bank storage. Darcy's Law in combination with a one-dimensional confined aquifer equation are solved for flowrate either into or out of bank storage. Boundary conditions which can be applied to the equations are:

  1. semi-infinite aquifer,
  2. infinite aquifer, and
  3. infinite aquifer with semi-permeable confining layer between stream and aquifer.

Keefer and McQuivey (1974) developed an equation to model streamflow based on the diffusion analogy. The J349 model routing component is based on this equation. This equation may be convolved in conjunction with upstream hydrograph data to determine the response of a stream channel. A multiple linear routing technique, used in the J349 model, is also described by Keefer and McQuivey. This option allows nonlinearities in the actual system to be segmented to better approximate a linear system with the computer model. The benefit of this is that the computer model, with these equations, has physical data as part of its routine.

Assumptions to the J349 Model

There are four basic assumptions inherent to the J349 computer model. The first is that the convolution technique presented by Keefer and McQuivey (1974) assumes that the hydrologic system is linear. The J349 model allows for the actual system being modeled to be segmented into smaller sub-reaches which may better approximate a linear system.

The second assumption is that the stream fully penetrates the aquifer. This assumption is important because it assumes a conservative approach to conveyance loss to bank storage. Looking at Darcy's Law:

Q = k * i * a

where k is the aquifer hydraulic conductivity, i is the hydraulic gradient of the aquifer and a is the flow cross-sectional area. When hydraulic gradient `i' decreases, flowrate also decreases. Hydraulic gradient decreases as the length of flowpath increases. When the stream channel fully penetrates the aquifer the length of flowpath is at its smallest and the hydraulic gradient is at its largest. When the hydraulic gradient is large, the flowrate into the aquifer (by Darcy's Law) is at its greatest making loss to bank storage its greatest. The third assumption is that the stream flows through the center of the aquifer. The model has components, as described earlier, developed by Hall and Moench (1972) which account for various aquifer types. This assumption is important because the model is designed to simulate losses to bank storage based on boundary conditions that are equal on each side of the stream in the transverse direction from the river channel.

The fourth assumption is that ground water in the aquifer is level with the system at the beginning of the modeling. This assumption is critical because water lost to bank storage may not be indicative of the actual amount of water lost for an incremental increase in flow if water levels are not stable prior to simulation.

Limitations to the J349 Model

Aside from the basic assumptions to the J349 model, there are also limitations to its use. One limitation is that the model does not account for evaporation losses within a study reach. Farber (1992) thoroughly develops a method for calculating evaporation losses for river reaches which includes use of evaporation data collected at nearby National Weather Service stations.

A second limitation to the model is that the model is limited to 399 time steps. This equals approximately 33 days given a two hour time step. This is not limiting, unless the travel time for the study reach is small, because the time step is normally set at the travel time for the river reach so that changes in the upstream hydrograph can be observed in the subsequent downstream hydrograph.

The most limiting factor, in terms of input structure, is that the model is limited to twenty- five changes in diversion values. A constant diversion rate may last through the entire length of the simulation, however if a diversion rate varies, each change in rate accounts for one of the twenty-five total diversions allowed. The result of this limitation is-that if the diversion rates vary, for example, every four hours than the length of the study period could last only six days.

The model is also limited in that surface infiltration into the stream aquifer system from precipitation, irrigated lands, or from any other type of surface infiltration is not accounted for in the J349 computer model. The model also does not account for return flows from irrigation canals or introduction of water through precipitation events. The model also does not account for any flowrate in the aquifer parallel to the stream channel. The only aquifer parameter the J349 model accounts for is flow transverse from the stream directly into the aquifer.

Advantages of the J349 Model

The major advantage to the J349 computer model is that periods of steady flow are not required in order to determine conveyance losses. As discussed earlier in this paper, conveyance loss analysis generally requires a steady flow period in order to apply forms of the water budget analysis to determine conveyance loss. The results of Farber (1992), Livingston (1978), and others indicate that conveyance loss can theoretically be determined for any period of streamflow data.

A second advantage to this computer model is that a conveyance loss analysis can be accomplished with accurate streamflow data and only some physical information. For example, information on aquifer width and length of channel can be collected from USGS 7.5 minute quadrangle maps. All other data pertinent to the models operation, such as transmissivity and storativity, can be determined during the calibration process using the measured streamflow and diversion data.

A third advantage is that the J349 model consists of three hydrologic components. These components account for different aspects of conveyance loss. These aspects make the program applicable to situations where variables differ. These components are:

  1. Streamflow routing component. This feature allows the user to segment the river reach when aquifer characteristics do not remain uniform for the entire length of the reach.

  2. Bank storage component. This option allows actual aquifer characteristics, such as transmissivity, to be considered as part of the calculations.

  3. A stream depletion coefficient. This option allows the user to account for water being removed from the system through groundwater production wells.

A fourth advantage that the J349 model has over incremental or net total loss approaches is that physical properties of the aquifer are part of the J349 model.

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