Creating a Generalized Water Budget for Cache Valley, UT/ID

Introduction

For the GIS term project I have determined the annual Cache Valley groundwater storage flux by creating a basic hydrologic budget using a systems approach. It is likely that subsurface flow from the Bear River Range flows into the unconsolidated sediments that underlie Cache Valley and comprise the aquifer system. This occurs because the Bear River Range is largely made up of karsted Paleozoic limestone with a fault zone at the margin of the valley (Figure 1).

The presence of limestone in the Bear River Range is significant because it is composed of calcium carbonate, and as a result it is slowly dissolved away by the carbonic acid in rainwater. In figure 1, the limestone layers are Mississippian in age, and are therefore represented by an upper case “M”, followed by letters that designate the formation’s name. The gradual dissolution of rock results in subsurface caverns and interconnected channels through which water can flow and eventually enter the unconsolidated Cache Valley aquifer system. Unfortunately, this expected subsurface inflow is yet to be accounted for in large-scale flow models of Cache Valley.

Figure 1: Geologic Map showing Cache Valley and the Bear River Mountains

Cache Valley is contained within two watersheds; the Middle Bear Watershed and the Middle Bear-Logan Watershed (Figure 2). The Middle Bear Watershed is the northern watershed, and the Middle Bear-Logan Watershed is the southern watershed. By performing a watershed analysis within ArcGIS I found that the combined area of the watersheds is 5,872.827 km². After importing a shapefile of the valley floor into ArcGIS I found that the area of the valley floor is 3,035.737 km², and after subtracting this value from the total area of the watersheds, the remaining mountainous area is calculated to be 2,837.09 km².

Figure 2: Map of Cache Valley, showing the watersheds and the valley floor

A groundwater flow model was developed for Cache Valley using Visual MODFLOW (McDonald & Harbaugh, 1988) by Kariya et al in 1994, and was modified by Myers in 2003. In Kariya’s model, no-flow boundaries were assigned along the outer margins of the valley to achieve model calibration. The no-flow boundary condition along the margins of the valley does not accurately represent the groundwater system of the valley, as there is most likely a source of subsurface flow from the mountains surrounding the valley. As a result, it was necessary for Kariya et al to assign unreasonable boundaries and parameters to the model to achieve calibration. A groundwater flow model cannot be considered reliable unless the boundaries and parameters of the model can be reasonably justified, and this is not the case with the existing flow model for Cache Valley. Therefore, it is important to determine the subsurface inflow/outflow sources of Cache Valley, and this is possible using ArcGIS.

Methods

To calculate the annual aquifer storage flux for Cache Valley I have used the following hydrologic equation:

Storage flux (Subsurface Inflow – Subsurface Outflow) = Stream Outflow + Evapotranspiration + Well Discharge – Stream/Spring Inflow – Precipitation.

The assumption in using this equation is that the annual inputs into the Cache Valley system are equal to the annual outputs of the system. This assumption is based on the groundwater budget created by Myers (2003), where he found that the inputs of the system nearly equal the outputs of the system.

In order to calculate the annual storage flux for the valley I had to find a value for each of the variables in the hydrologic equation that I am using. Stream outflow and inflow data were retrieved from the water rights divisions for Utah and Idaho. Precipitation data was obtained from local climate stations and spatially analyzed using ArcGIS. An evapotranspiration value was calculated using reference evapotranspiration data recorded at a climate station in North Logan. Well discharge data were obtained from the water rights divisions for Utah and Idaho.

Stream Inflow/Outflow

When considering inflow and outflow from streams as a component of the hydrologic budget, only streams that enter the valley from adjacent watersheds and leave through an adjacent watershed are considered. Streams that are generated within the Cache Valley watersheds are accounted for through the precipitation and stream runoff components of the hydrologic budget, and are therefore not included in the stream inflow/outflow component of the budget.

Stream inflow from adjacent watersheds occurs in the northern portion of the Middle Bear Watershed, where the Bear River flows through the Alexander Dam, in Alexander, Idaho (Figure 3). To find the total annual inflow through the Alexander dam I retrieved data from the Idaho division of water rights website, where there was 19 years worth of daily discharge data from 1989 to 2007. After computing an annual discharge value for each year (Figure 4), I calculated an average annual discharge value at the dam of 1.469 x 10¹¹ cubic meters per year.

Figure 3: Streams within the Cache Valley watersheds

Figure 4: Annual discharge at the Alexander Dam

Water leaves the Cache Valley watersheds along the Bear River as it flows through the Cutler Dam, near Collinston, Utah. Due to problems with the gage at this location I obtained daily discharge data for the Bear River at three different gaging stations located approximately one-quarter mile downstream from the Cutler Dam. At this point there are two canals that branch off from the main channel of the river, and gages are located at all three locations. Data measured at the Collinston, Utah gages was obtained from the Utah division of water rights website.

The time period and length of recorded discharge data varied for the three Collinston, UT gaging stations. The average annual discharge value at the Bear River near Collinston, UT gage was calculated using ten years worth of data from 1989 to 2007. The average annual discharge values from both the Hammond East Side Canal near Collinston, UT gage and the West Side Canal near Collinston, UT were calculated using four years worth of data from 1987 to 2005. Overall, an average combined annual outflow of 3.022 x 10¹¹ cubic meters per year was measured at the three gages (Table 1).

Table 1: Total annual Bear River outflow near the Cutler Dam

Station	Average Annual Discharge (m^3/year)
Bear River near Collinston, UT	2.12125E+11
Hammond East Side Canal near Collinston, UT	1.55998E+10
West Side Canal near Collinston, UT	7.45700E+10
Total	3.02295E+11

Precipitation

An estimate for the annual precipitation received by Cache Valley was calculated using daily precipitation data from a number of gages throughout the valley and the mountains. The stations were either assigned as a valley floor gage station or a mountain gage station. Using this classification I calculated separate annual average precipitation values for the valley and for the mountains, and then applied these values to the final hydrologic budget.

To calculate the annual average precipitation that falls on the floor of Cache Valley I used daily precipitation data from six gages located along the valley floor. Data was obtained from the Utah State University GIS climate search website. The number of years worth of data varied from station to station, but whenever possible I took a thirty year average to determine a value at each gage. A problem that I encountered while working with the data was that anywhere from 1% to 10% of the daily precipitation data was missing for any given station. In order to correct for this I applied the following equations:

1) X = (Sum of existing values) / (Number of days worth of existing values)

2) Annual Average Precipitation = (X * Total days worth of data) / (Number of years worth of data)

At the gages where less than 1% of the data was missing the correction did not make a significant difference, but at the gages where up to 10% of the data was missing the correction increased the average annual value by up to two inches per year. For a summary of average precipitation values for the six precipitation stations located within Cache Valley see table 2.

Table 2: Summary of precipitation stations located within Cache Valley

Station Name	Station ID	Latitude	Longitude	Elevation (ft)	Data Range	Avg. Annual Precipitation (in)
LOGAN UTAH ST U	425186	41.7456	-111.803	4783	6/30/77-6/30/2007	20.4070
LOGAN RADIO KVNU	425182	41.7353	-111.856	4505	4/30/77-4/30/2007	18.1049
RICHMOND	427271	41.9064	-111.81	4524	5/31/77-5/31/2007	20.8723
LOGAN 5 SW EXP FARM	425194	41.6672	-111.891	4491	6/30/77-6/30/2007	19.2454
TRENTON	428828	41.9194	-111.909	4472	6/30/73-6/30/2003	18.2758
PRESTON	107346	42.0933	-111.868	4823	5/31/80-5/31/2007	17.7689

After having calculated the average annual precipitation value at each of the gages I added the stations as a feature dataset to my ArcGIS basemap through the “Add XY Data” function. After correctly georeferencing the layer, I performed an interpolation for the valley floor portion of the Cache Valley watersheds to create a precipitation raster (Figure 5). The interpolation method used was kriging. I then looked under the “source” tab within the raster’s properties, and found the mean precipitation value for the valley floor to be 19.4792 inches per year. I then converted this to meters and multiplied it by the area of the Cache Valley floor, giving me a total valley floor annual precipitation value of 1.502 x 10⁹ cubic meters per year.

Figure 5: Cache Valley average annual precipitation

After calculating a precipitation value for the valley floor I began calculating a precipitation value for the mountains contained within the watersheds. To do this I obtained daily snow and rain accumulation data from four SNOTEL gages located within the Bear River Range. The number of years worth of data varied from four years at the Temple Fork gage to twenty-nine years at the Tony Grove Lake gage. In order to calculate an average annual precipitation value at each of the SNOTEL stations I averaged the accumulated precipitation values recorded at the gage for each year (Table 3).

Table 3: Summary of precipitation stations located in the mountains of the Cache Valley watersheds

Station Name	Station ID	Latitude	Longitude	Elevation (ft)	Data Range	Avg. Annual Precipitation (in)
Franklin Basin	11g32s	42.5	-111.0667	8085	10/01/82-10/01/2007	46.0923
Emigrant Summit	11g06s	42.35	-111.55	7390	10/01/81-10/01/2007	39.3704
Tony Grove Lake	11h36s	41.8833	-111.6167	8474	10/01/79-10/01/2007	48.6862
Temple Fork	11h58s	41.7833	-111.5333	7406	10/01/2003-10/01/2007	28.1600

Unfortunately I was not able to create a precipitation raster via interpolation using the mountain precipitation gages. I attempted to isolate the region surrounding the valley floor and perform an interpolation, but was not able to do this. Being out of ideas on how to perform an accurate interpolation with only four gage locations on the same side of the watershed, I merely averaged the four precipitation values from the SNOTEL stations, giving an average value of 40.5772 inches per year. I then multiplied this value by 2,837.09 km², the mountainous area of the valley, to give me an annual average precipitation value for the mountains of 2.9241 x 10⁹ cubic meters per year. Although this method for calculating an average mountainous precipitation value is not ideal, I believe that it gives a better annual precipitation estimate than if I had used the value calculated at the valley floor.

After calculating both the average annual precipitation for the valley floor and the mountains, these values were added together to give a total annual precipitation value of 4.4260 x 10⁹ cubic meters per year for the entire Cache Valley watersheds. This value was used as the precipitation input in the final hydrologic budget equation.

Evapotranspiration

An evapotranspiration estimate was calculated using average monthly reference evapotranspiration values obtained at the Greenville Farm climate station in North Logan. Monthly reference evapotranspiration data from 2006 to 2007 was available, and was obtained from the Utah division of water resources website.

In order to calculate an actual evapotranspiration value from the reference evapotranspiration data I first summed the monthly data for the year. I then multiplied this value by a multiplier of 0.5, which represented the assumption that only half of the potential reference evapotranspiration was actually evapotranspired per year. Another important assumption in calculating the actual evapotranspiration was that evapotranspiration only occurred during the months of April through November. The winter months were neglected, as the snowpack would prevent any significant evapotranspiration from occurring. After averaging the 2006 and 2007 annual values I obtained an actual evapotranspiration value of 0.435483 meters per year (Table 4). After multiplying this value by the total area of the Cache Valley watersheds, an average annual evapotranspiration value in the watersheds of 2.5575 x 10⁹ cubic meters per year was calculated.

Table 4: Reference evapotranspiration data from the Greenville Farm climate station

Month	2006 Refer. ET (m)	2007 Refer. ET (m)	Average Refer. ET (m)
Jan.	0	0	0
Feb.	0	0	0
Mar	0	0	0
Apr.	0.056134	0.085852	0.070993
May	0.117856	0.125222	0.121539
June	0.197104	0.149352	0.173228
July	0.185674	0.152146	0.16891
Aug.	0.165608	0.144526	0.155067
Sep.	0.096012	0.09906	0.097536
Oct.	0.051816	0.059182	0.055499
Nov.	0.02794	0.028448	0.028194
Dec.	0	0	0
Annual Total	0.898144	0.843788	0.870966

Well Discharge

To find values for total well discharge from the Cache Valley aquifers, the final component of the hydrologic budget, I used data obtained from a USGS publication and the Idaho division of water resources website. I obtained an average annual well discharge value from the Utah portion of the valley from a study done in 2006 by Carol Burden et al, of the USGS. In her study she found that from 1994 to 2005 an average annual well discharge of 3.3304 x 10⁷ cubic meters was withdrawn from wells in the Utah portion of Cache Valley. To find the average annual well discharge withdrawn from the Idaho portion of the valley I searched the Idaho division of water resources website and found a year 2000 estimated well discharge value of 3.10628 x 10⁸ cubic meters per year. Combining the Utah and Idaho well discharge values yielded a combined annual well discharge from Cache Valley of 3.43919 x 10⁸ cubic meters per year.

Results

After calculating the necessary inputs and outputs I entered the values into the hydrologic budget equation to obtain the Cache Valley aquifer storage flux, resulting in a total storage flux of 1.539 x 10¹¹ cubic meters per year. This means that the annual subsurface inflow is approximately 1.539 x 10¹¹ cubic meters per year greater than the annual subsurface outflow (Table 5).

Table 5: Final Hydrologic Budget for Cache Valley

Storage Flux = Stream Outflow + Evapotransipration + Well Discharge - Stream Inflow - Precipitation
Parameter	Value (m^3/year)
Stream Outflow	3.022948E+11
Evapotranspiration	2.557516E+09
Well Discharge	3.439192E+08
Stream Inflow	1.468685E+11
Precipitation	4.426074E+09
Storage Flux	1.539017E+11

Conclusions

I believe that the subsurface inflow is so much greater than the subsurface outflow for a number of reasons. Primarily, I believe that the subsurface inflow value is so large because of the large volume of water recharging the aquifers in the subsurface from the western margins of the karsted Bear River Range. As suspected by Myers, such a large positive storage flux implies a significant source of subsurface contribution that must be accounted for. Also, I believe that the subsurface inflow is so much greater than the subsurface outflow because of the water lost from storage into the rivers that flow through the valley. Most of the main rivers that flow through the valley are both runoff and baseflow fed, and the baseflow component of flow results in a larger stream outflow and a lower subsurface outflow.

In addition to quantifying the volume of annual subsurface inflow and outflow, I believe that the hydrologic budget that I have created can be used to improve the Cache Valley groundwater model created by Kariya et al in 1994. In Kariya’s model the only sources of subsurface recharge are due to seepage from irrigation canals and precipitation. In 2003 Myers showed that recharge due to seepage from irrigation canals is negligible, as most of the streams are gaining streams rather than losing streams, in terms of groundwater contribution. In terms of recharge due to precipitation, I believe that Kariya has greatly overestimated this value to achieve model calibration. To show this I began by subtracting the total evapotranspiration from the total precipitation. I then assumed that 50% of the remaining precipitation is infiltrated and the rest becomes runoff. Although this is a gross over-estimation of the amount of precipitation infiltrating, a value of only 9.34279 x 10⁸ cubic meters per year would be responsible for aquifer recharge from precipitation ((Total Precipitation – Total Evapotranspiration)* 0.5). This ultimately leaves a discrepancy from my calculated storage flux of approximately 1.52967 x 10¹¹ cubic meters per year (Total Storage Flux – Total recharge due to precipitation), which is unaccounted for in Kariya’s model.

Overall, I believe that the results from my study would be best used as a basis for creating a model of Cache Valley. The values obtained cannot be assumed to be completely accurate, as it was a cursory study relative to a project of this scope, but I believe that the results can provide a good idea as to where and in what relative quantities inputs and outputs are acting on the Cache Valley watershed system. Specifically, I believe that the results of this study would be most useful as an aid for the designation of boundary conditions for a Cache Valley groundwater flow model. The budget provides a general idea as to where water is coming from and going to, and provides a good starting point for boundary condition designation.

References

Burden, C.B., et al, 2006.Ground-Water Conditions in Utah, Spring 2006: Utah Department of Natural Resources, Water Resources Division, Report 47.

Kariya, K.A., Roark, D.M., Hanson, K.K.. Hydrology of Cache Valley, Cache County, Utah, and Adjacent Part of Idaho, with Emphasis on Groundwater. USGS Technical Pub. No. 108. 1994.

McDonald, M.G., and Harbaugh, A.W., 1988, A modular three-dimensional finite-difference ground-water flow model: U.S. Geological Survey Techniques of Water Resources Investigations, Book 6, Chapter A1, 586 p.

Myers, Barry. Simulation of Groundwater Flow in Cache Valley, Utah and Idaho. Utah State University Master’s Thesis. 2003.

http://climate.usurf.usu.edu/products/data.php

http://www.conservewater.utah.gov/et/etsite/default.asp?NorthLoganGreenvilleFarm.htm

http://id.waterusgs.gov/public/water.use.2000.xls

http://www.idwr.idaho.gov/gisdata/mapserver.htm

http://www.waterrights.utah.gov/cgi-bin/gageview.exe?Startup