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Groundwater Flow between Basins Mojave River Basin Centro - Baja Hydrologic Subareas California State University, Fullerton Department of Geological Sciences

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Page 1: Groundwater Flow between Basins Mojave River Basingroundwater.fullerton.edu/Mojave_Water_Agency/...Flow between Basins Report Centro - Baja Hydrologic Subareas 1.0 Introduction The

Groundwater Flow between Basins Mojave River Basin

Centro - Baja Hydrologic Subareas

California State University, Fullerton Department of Geological Sciences

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Groundwater flow between Basins Report Mojave River Basin

Centro - Baja Hydrologic Subareas

Authored by

Nicholas Napoli W. Richard Laton, Ph.D., PG, CPG

Prepared in Cooperation with and

Submitted to

Mojave Water Agency

October 2005

California State University, Fullerton

Department of Geological Sciences

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Groundwater Flow Between Basins Report Mojave River Basin

Centro - Baja Hydrologic Subareas This report has been prepared by California State University, Fullerton; Department of Geological Sciences for the exclusive use of the Mojave Water Agency. The procedures and interpretations described in this report have been prepared in accordance with practices generally accepted by other academic institutions, engineers, geologists, hydrogeologists, environmental engineers, and environmental scientists practicing in this field. No other warranty, either expressed or implied, is made. REPORT PREPARED BY: ___________________ W. Richard Laton, Ph.D., PG, CPG Assistant Professor of Hydrogeology California State University, Fullerton ___________________ Nicholas R. Napoli, MSc. Graduate Student California State University, Fullerton

UNDER THE PRIMARY REVIEW OF: ___________________ Lance Eckhart, PG, CHG Senior Hydrogeologist Mojave Water Agency

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Contents

Contents ............................................................................................................................. 4 1.0 Introduction................................................................................................................... 6 2.0 Background................................................................................................................... 6 3.0 Methods......................................................................................................................... 6

Table 1: Source and Information on Varying Hydraulic Conductivity Values. ......... 8 Figure 1. Location map of study area. ........................................................................ 9

4.0 Data ............................................................................................................................. 10 5.0 Results/Discussion ...................................................................................................... 10

5.1 Hydrograph Analysis .............................................................................................. 10 Figure 2: Location map of wells used in this study. ................................................. 11 Figure 3a: Centro - Baja groundwater hydrographs from 1915 to present. .............. 12 Figure 3b: Baja groundwater hydrographs from 1915 to present. ............................ 13 Figure 3c: Centro groundwater hydrographs from 1915 to present.......................... 14 Figure 4a: Centro - Baja groundwater hydrographs from 1990 to present. .............. 15 Figure 4b: Baja groundwater hydrographs from 1990 to present. ............................ 16 Figure 4c: Centro groundwater hydrographs from 1990 to present.......................... 17

5.2 Gradient Analysis.................................................................................................... 18 Figure 5a: Groundwater elevation contour map for 1960........................................ 19 Figure 5b: Groundwater elevation contour map for 1993. ...................................... 20 Figure 5c: Groundwater elevation contour map for 2004........................................ 21 Figure 6: Profile of interpolated groundwater elevation grid along gradient line. ... 22 Table 2: Gradient Calculations for individual time-steps. ........................................ 23

5.3 Flow Analysis ......................................................................................................... 24 Table 3: 1960 Flow Calculations (ft3/day) (Gradient of 0.0045 ft/ft)....................... 24 Table 4: 1993 Flow Calculations (ft3/day) (Gradient of 0.0049 ft/ft)....................... 24 Table 5: 2004 Flow Calculations (ft3/day) (Gradient of 0.0050 ft/ft)....................... 24 Table 6: 1960 Flow Calculations (acre-ft/day) (Gradient of 0.0045 ft/ft). ............... 25 Table 7: 1993 Flow Calculations (acre-ft/day) (Gradient of 0.0049 ft/ft). ............... 25 Table 8: 2004 Flow Calculations (acre-ft/day) (Gradient of 0.0050 ft/ft). ............... 25 Table 9: Range of yearly discharge values (acre-ft/year). ........................................ 26

6.0 Conclusions................................................................................................................. 27 7.0 References................................................................................................................... 29

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List of Tables:

Table 1: Source and Information on Varying Hydraulic Conductivity Values. Table 2: Gradient Calculations for individual time-steps. Table 3: 1960 Flow Calculations (ft3/day) (Gradient of 0.0045 ft/ft). Table 4: 1993 Flow Calculations (ft3/day) (Gradient of 0.0049 ft/ft). Table 5: 2004 Flow Calculations (ft3/day) (Gradient of 0.0050 ft/ft). Table 6: 1960 Flow Calculations (acre-ft/day) (Gradient of 0.0045 ft/ft). Table 7: 1993 Flow Calculations (acre-ft/day) (Gradient of 0.0049 ft/ft). Table 8: 2004 Flow Calculations (acre-ft/day) (Gradient of 0.0050 ft/ft). Table 9: Range of yearly discharge values (acre-ft/year).

List of Figures:

Figure 1: Location map of study area. Figure 2: Location map of wells used in this study. Figure 3a: Centro - Baja groundwater hydrographs from 1915 to present. Figure 3b: Baja groundwater hydrographs from 1915 to present. Figure 3c: Centro groundwater hydrographs from 1915 to present. Figure 4a: Centro - Baja groundwater hydrographs from 1990 to present. Figure 4b: Baja groundwater hydrographs from 1990 to present. Figure 4c: Centro groundwater hydrographs from 1990 to present. Figure 5a: Groundwater elevation contour map for 1960. Figure 5b: Groundwater elevation contour map for 1993. Figure 5c: Groundwater elevation contour map for 2004. Figure 6: Profile of interpolated groundwater elevation grid along gradient

line.

Appendices:

Appendix A – Procedural Methodology

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Flow between Basins Report

Centro - Baja Hydrologic Subareas 1.0 Introduction The following report represents the work efforts between California State University, Fullerton – Department of Geological Sciences and the Mojave Water Agency (MWA) Water Resources Department on determining the groundwater flow across sub-basin boundaries. In order to determine what, if any, groundwater flow exists at these boundaries, a series of investigative tests were run. These tests examined the change(s) in groundwater gradients across these boundaries through a comparison of historical water level records for the region in question (Figure 1). The following discussion outlines the procedures and protocols followed in order to make these determinations. 2.0 Background Flow is from Centro to Baja! I need to insert a little background regarding the Judgment and obligations of the MWA to quantify Subarea flow. I will work with Bob Wagner on this section and this can be inserted later. A little emphasis will be made regarding focus of quantifying change in flow from ~1994 to present rather than quantifying the actual amount of flow between areas with little data regarding several key variables. ADD THAT JUDGMENT STATES CENTRO IS OBLIGATED TO PROVIDE MINIMUM ANNUAL SUBSURFACE FLOW OF 1,200 AFY TO FLOW INTO BAJA 3.0 Methods Water level data from the United States Geological Survey’s (USGS) National Water Information System (NWIS) (http://waterdata.usgs.gov/nwis) and the California’s Department of Water Resources (DWR) (http://wdl.water.ca.gov/) were compiled to create a groundwater level database for the Centro - Baja Hydrologic subarea boundary region. This database was then spatially mapped to determine a definitive boundary for the study area. Once this boundary was identified, the groundwater level data inside the boundary was used to create a series of hydrographs. The hydrographs were then used to determine which multiple time-steps contained enough spatially diverse data to create reasonable groundwater elevation contour maps for individual periods of time. Groundwater gradients are then calculated using three different methods: (1) electronically (by computer), (2) manually (by hand) from the groundwater elevation contour maps, and (3) using a gradient vector analysis. The average of the three gradients is considered the actual gradient value, and is used to calculate the change in gradient during the interval between time-steps. At the boundary between the two basins, a cross-section is drawn perpendicular to the gradient, and cross-sectional area is calculated. Using Darcy’s Law (Equation 1) discharge per day is calculated for the individual time-

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periods. Flow and discharge are used interchangeably in this report. Flow is then calculated by multiplying discharge per day by days in a given time-period. Darcy’s Law (1)

KiAQ = where:

Q = discharge in ft3/day K = hydraulic conductivity in ft/day i = gradient or slope in ft/ft A = cross sectional area in ft2

The cross-sectional area (A) was based on a range of aquifer thicknesses at the Centro - Baja Hydrologic Subarea boundary. The aquifer thickness varied from a minimum of 200 feet to a maximum of 600 feet, which constitutes the floodplain aquifer. The minimum was based on Hardt [1971] whereas, the 600 foot thickness of the aquifer is based on the deepest depth of groundwater wells within the study area [Huff, J.A., et. al., 2002, Barto, R., 1986, CDWR, 1934]. Due to the lack of depth and discrete information on both basin geometry and aquifer properties, a range of values is used. This range of values was based on previous regional and local studies and estimates using available data. The ranges in hydraulic conductivities come from a variety of sources [Hardt, 1971, Stamos, et. al., 2001, Fetter 2001, Heath, 1987, Todd Engineering, 1999 and Driscoll, 1986] (Table 1). These constitute the range of expected hydraulic conductivity values for river channel deposits (boulders, gravel, sand and silt) [Frieling, J.L., et al., 1983].

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Source Hydraulic

Conductivity (K) (ft/day)

Aquifer Thickness (ft) Notes on source

Multiple Sources 0.003 NA General References

Hardt, 1971 9 - 18 200

Transmissivity of 13,000 – 27,000 gpd/ft; Hydraulic

Conductivity based on a depth of 200 feet.

Frieling, J.L., et. al., 1983 200 CM Engineering Ass. & LeRoy

Crandall and Ass.

Stamos, et. al., 2001 250 200+

USGS Water-Resources Investigations Report 01-4002;

Estimated Transmissivity values for layer 1 are greater than

50,000 ft2/day Barto, R., 1986 400 - 500

Well Logs NA 600 Deepest wells Todd

Engineering, 1999

270

Multiple Sources 300 NA General References

Table 1: Source and Information on Varying Hydraulic Conductivity Values. Although flow between subareas can be calculated, many assumptions have to be made regarding basin geometry and the hydraulic conductivity of the aquifer material(s) through which the groundwater is flowing. Therefore, a range of values have been calculated for flow across the Centro - Baja Subarea. Data associated with depth to groundwater and groundwater gradients have been collected by the MWA and others for several decades and are readily available. These data can be used to accurately determine if:

1. Regional groundwater levels have materially changed historically and within the onset of the Judgment and

2. Regional groundwater gradients, which control the speed at which groundwater flows, have changed historically and within the onset of the Judgment.

Pursuant to the subsurface flow between subareas, the only dynamic variables which can control flow are changes in water levels and changes in hydraulic gradient. Basin geometry and the hydraulic conductivity of the aquifer materials are not prone to change. Therefore, this study will focus on changes in groundwater levels and changes in hydraulic gradient. Both of these variables can be altered via groundwater pumping and historical data exists to verify these changes, if any.

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Este Hydrologic SubareaEste Hydrologic SubareaEste Hydrologic SubareaEste Hydrologic SubareaEste Hydrologic SubareaEste Hydrologic SubareaEste Hydrologic SubareaEste Hydrologic SubareaEste Hydrologic Subarea

SubareaSubareaSubareaSubareaSubareaSubareaSubareaSubareaSubareaone)one)one)Zone)Zone)Zone)Zone)Zone)Zone)

Baja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic Subarea

Centro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic Subarea

STATE HWY 247

STATE HWY 247

STATE HWY 247

STATE HWY 247

STATE HWY 247

STATE HWY 247

STATE HWY 247

STATE HWY 247

STATE HWY 247

I- 15

I- 15

I- 15I- 15

I- 15I- 15

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I- 15

BarstowBarstowBarstowBarstowBarstowBarstowBarstowBarstowBarstowLenwoodLenwoodLenwoodLenwoodLenwoodLenwoodLenwoodLenwoodLenwood

Nebo CenterNebo CenterNebo CenterNebo CenterNebo CenterNebo CenterNebo CenterNebo CenterNebo Center

Lucerne ValleyLucerne ValleyLucerne ValleyLucerne ValleyLucerne ValleyLucerne ValleyLucerne ValleyLucerne ValleyLucerne ValleyBoundary of Contour MapsBoundary of Contour MapsBoundary of Contour MapsBoundary of Contour MapsBoundary of Contour MapsBoundary of Contour MapsBoundary of Contour MapsBoundary of Contour MapsBoundary of Contour Maps

Figure 1: Location map of study area.

5 0 5 10 15

Miles

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4.0 Data A total of 546 groundwater wells were available for this study (332 wells in Centro and 214 wells in Baja), and are shown in Figure 2. Data for all 546 wells resides in the NWIS or DWR databases (see methods). Records from these wells represent 13,737 individual data points from 1917 through 2004. Groundwater elevation ranged from a low of 844 feet above mean sea level (AMSL) to a high of 2,383 AMSL (Figure 3a). 5.0 Results/Discussion The results of this study are listed in three parts: hydrographs analysis, gradient analysis and flow analysis. The hydrograph analysis consisted of visually inspecting the respective hydrographs for trends across the period of record. The gradient analysis was conducted for specific individual time-steps; 1960, 1993 and 2004. The change in gradient was derived from the differences calculated between these three time-steps. The flow analysis determines if the change(s) in gradient constitute a significant change in flow (Q) across the subarea boundary.

5.1 Hydrograph Analysis Groundwater hydrographs were created for all 546 wells within the study area (see Figure 2). Figure 3a shows that over the long-term there has been little variation in groundwater levels in the Centro Subarea. Water levels in the Baja Subarea appear to be headed in a downward trend starting in late 1950’s to early 1960’s. Minor fluctuations can be attributed to seasonal effects. However, seasonal affects cannot solely account for this downward trend in the Baja Subarea. Figures 3b and 3c, separate the data by basin (Centro and Baja) respectively, also suggesting relative stable conditions exist in Centro and that the Baja Subarea has a downward trend. Figures 4a-c provides a record of recent water levels from 1990 to present, of which a number of wells contain records from 1994 to present (the period of the last 10 years since formal adjudication). From these figures it can be shown that water levels have been stable in the Centro Subarea with only minor (less than 10 feet) fluctuation over the past 15 years. The Baja Subarea however, does show a distinct downward trend in water levels, on the order of 20 – 40 feet over the past 15 years. This suggests that water levels are stable in the Centro Subarea and are trending downward in the Baja Subarea.

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Baja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic Subarea

Centro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic Subarea

I- 15

BAR

STO

W F

WY

I- 40

NEEDLES FWY

LAS VEGAS FWY

BARSTO

W R

D

KERSFIELD HWYIR

WIN

RD

STATE HW

Y 247

STATE HWY 58

US HIG

HWAY 58

Figure 2: Location map of wells used in this study.

4 0 4 8 12

Miles

-

Bedrock

Fault

Well

Gradient

Boundary of Contour MapBoundary of Contour MapBoundary of Contour MapBoundary of Contour MapBoundary of Contour MapBoundary of Contour MapBoundary of Contour MapBoundary of Contour MapBoundary of Contour Map

Legend

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Figure 3a: Centro-Baja groundwater hydrographs from 1915 to present.

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Figure 3b: Baja groundwater hydrographs from 1915 to present.

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Figure 3c: Centro groundwater hydrographs from 1915 to present.

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Figure 4a: Centro-Baja groundwater hydrographs from 1990 to present.

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10H30E10N90 50H30E10N90 S50H30E10N90 10K40E10N90 S10K40E10N90 S20K40E10N90 S30K40E10N90 S10L40E10N90 S20Q40E10N90 S20R40E10N90 S10E60E10N90

S20H60E10N90 S40D90E10N90 S10G90E10N90 S10A01E10N90 S10J01E10N90 S10L01E10N90 S20L01E10N90 S10Q01E10N90 20Q01E10N90 S20Q01E10N90 S30Q01E10N90

S40Q01E10N90 S10R01E10N90 S20B11E10N90 S10A21E10N90 S10B21E10N90 S10H51E10N90 S30N51E10N90 S10F61E10N90 S20F61E10N90 S30F61E10N90 S40F61E10N90

S10J91E10N90 S30B02E10N90 S60B22E10N90 S10J32E10N90 S80J40W10N90 S40M40W10N90 S50M40W10N90 S60M40W10N90 S70M40W10N90 20R40W10N90 S30R40W10N90

S40R40W10N90 S50D90W10N90 S60D90W10N90 S70D90W10N90 S80D90W10N90 S40E01W10N90 S60G01W10N90 S610J01W10N90 S21J01W10N90 S31J01W10N90 S41J01W10N90

S51J01W10N90 S40M01W10N90 S610K11W10N90 S10K11W10N90 S21K11W10N90 S31K11W10N90 S41K11W10N90 S51K11W10N90 S11M11W10N90 S80N11W10N90 S30P11W10N90

S30Q11W10N90 S40Q11W10N90 S10R11W10N90 S20R11W10N90 S20L21W10N90 S30L21W10N90 S40L21W10N90 S50L21W10N90 S40N21W10N90 S50N21W10N90 S60N21W10N90

S70N21W10N90 S80N21W10N90 S20B31W10N90 S30B31W10N90 S40B31W10N90 S10C31W10N90 S20H31W10N90 S10D41W10N90 S10E41W10N90 S10Q51W10N90 S20Q51W10N90

S10R51W10N90 S10D72W10N90 S10Q70E20N90 S30Q70E20N90 S10L90E20N90 S10E01E20N90 S20N41E20N90 S10G81E20N90 S10K02E20N90 S10D22E20N90 S10M42E20N90

S20M42E20N90 S10B72E20N90 S60F72E20N90 S20J82E20N90 S10A03E20N90 S20B03E20N90 S20A10W20N90 S10F10W20N90 S20F10W20N90 S40F10W20N90 S50B20W20N90

S10A30W20N90 S20A30W20N90 S10M02E10N01 S20M02E10N01 S10C72E10N01 S30G82E10N01 S80J82E10N01 S21F23W10N01 S40Q23W10N01 S10J33W10N01 S30L33W10N01

S30L13E20N01 S50M13E20N01 S10P23E20N01 S10N61W20N01 S20N61W20N01 S30N61W20N01

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Figure 4b: Baja groundwater hydrographs from 1990 to present.

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10H30E10N90 50H30E10N90 S50H30E10N90 10K40E10N90 S10K40E10N90 S20K40E10N90 S30K40E10N90 S10L40E10N90 S20Q40E10N90 S20R40E10N90 S10E60E10N90

S20H60E10N90 S40D90E10N90 S10G90E10N90 S10A01E10N90 S10J01E10N90 S10L01E10N90 S20L01E10N90 S10Q01E10N90 20Q01E10N90 S20Q01E10N90 S30Q01E10N90

S40Q01E10N90 S10R01E10N90 S20B11E10N90 S10A21E10N90 S10B21E10N90 S10H51E10N90 S30N51E10N90 S10F61E10N90 S20F61E10N90 S30F61E10N90 S40F61E10N90

S10J91E10N90 S30B02E10N90 S60B22E10N90 S10J32E10N90 S20L21W10N90 S30L21W10N90 S40L21W10N90 S50L21W10N90 S40N21W10N90 S50N21W10N90 S60N21W10N90

S70N21W10N90 S80N21W10N90 S20B31W10N90 S30B31W10N90 S40B31W10N90 S10C31W10N90 S20H31W10N90 S10Q70E20N90 S30Q70E20N90 S10L90E20N90 S10E01E20N90

S20N41E20N90 S10G81E20N90 S10K02E20N90 S10D22E20N90 S10M42E20N90 S20M42E20N90 S10B72E20N90 S60F72E20N90 S20J82E20N90 S10A03E20N90 S20B03E20N90

S10M02E10N01 S20M02E10N01 S10C72E10N01 S30G82E10N01 S80J82E10N01 S30L13E20N01 S50M13E20N01 S10P23E20N01

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Figure 4c: Centro groundwater hydrographs from 1990 to present.

etaD

Gro

undw

ater

Ele

vatio

n (F

eet)

(AM

SL)

1/1/

1990

1/1/

1991

1/1/

1992

1/1/

1993

1/1/

1994

1/1/

1995

1/1/

1996

1/1/

1997

1/1/

1998

1/1/

1999

1/1/

2000

1/1/

2001

1/1/

2002

1/1/

2003

1/1/

2004

1/1/

2005

5291

0591

5791

0002

5202

0502

5702

0012

5212

0512

S80J40W10N90 S40M40W10N90 S50M40W10N90 S60M40W10N90 S70M40W10N90 20R40W10N90 S30R40W10N90 S40R40W10N90 S50D90W10N90 S60D90W10N90 S70D90W10N90

S80D90W10N90 S40E01W10N90 S60G01W10N90 S610J01W10N90 S21J01W10N90 S31J01W10N90 S41J01W10N90 S51J01W10N90 S40M01W10N90 S610K11W10N90 S10K11W10N90

S21K11W10N90 S31K11W10N90 S41K11W10N90 S51K11W10N90 S11M11W10N90 S80N11W10N90 S30P11W10N90 S30Q11W10N90 S40Q11W10N90 S10R11W10N90 S20R11W10N90

S10D41W10N90 S10E41W10N90 S10Q51W10N90 S20Q51W10N90 S10R51W10N90 S10D72W10N90 S20A10W20N90 S10F10W20N90 S20F10W20N90 S40F10W20N90 S50B20W20N90

S10A30W20N90 S20A30W20N90 S21F23W10N01 S40Q23W10N01 S10J33W10N01 S30L33W10N01 S10N61W20N01 S20N61W20N01 S30N61W20N01

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5.2 Gradient Analysis In order to determine changes in the groundwater gradient (slope of the water table), three time-steps within the database containing the most abundant and spatially diverse data were chosen: 1960, 1993 and 2004. In order to avoid outlying data, wells not within the contour boundary in Figure 2 were omitted from these time-step analyses. Each time-step had sufficient data to contour across the study area. The periods of 1993 and 2004 were chosen to capture the onset of the adjudication to the present. Figures 5a-c show the results of the groundwater level contour analysis. Figure 6 shows groundwater level profiles based on the computer interpolated elevations from the GIS contour analysis.

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-------------------------------

---

--------

------------------------------------ -----

-----------------

--

----

-------------------------

----- ---

----

-

---

-

-

--------

--

1,7401,7401,7401,7401,7401,7401,7401,7401,740

Baja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic Subarea

Centro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic Subarea

LAS VEGAS FWY

I- 15

BARSTOW FWY

NEEDLES FWY

I- 40

LAS VEGAS FWY

1,7601,7601,7601,7601,7601,7601,7601,7601,760

1,8201,8201,8201,8201,8201,8201,8201,8201,820

1,8601,8601,8601,8601,8601,8601,8601,8601,8601,8601,8601,8601,8601,8601,8601,8601,8601,860

1,8601,8601,8601,8601,8601,8601,8601,8601,860

1,8601,8601,8601,8601,8601,8601,8601,8601,860

1,9001,9001,9001,9001,9001,9001,9001,9001,900

1,9001,9001,9001,9001,9001,9001,9001,9001,900

1,9201,9201,9201,9201,9201,9201,9201,9201,920

1,9601,9601,9601,9601,9601,9601,9601,9601,960

1,9801,9801,9801,9801,9801,9801,9801,9801,980

2,0002,0002,0002,0002,0002,0002,0002,0002,0002,0002,0002,0002,0002,0002,0002,0002,0002,000

2,0202,0202,0202,0202,0202,0202,0202,0202,0202,0402,0402,0402,0402,0402,0402,0402,0402,040

2,0602,0602,0602,0602,0602,0602,0602,0602,060

BARSTO

W R

D

KERSFIELD HWYIR

WIN

RD

STATE HW

Y 247

STATE HWY 58

US HIG

HW

AY 58

Figure 5a: Groundwater elevation contour map for 1960.

4 0 4 8 12

Miles

Legend

-

Bedrock

Fault

Well

Gradient

1820 to 1840

1840 to 1860

1800 to 1820

1780 to 1800

2060 to 2080

2100 to 2120

2080 to 2100

2040 to 2060

1940 to 1960

1920 to 1940

1900 to 1920

1860 to 1880

1880 to 1900

1760 to 1780

1740 to 1760

Contour Interval20 feet

2020 to 2040

2000 to 2020

1980 to 2000

1960 to 1980

0.0047 ft/ft0.0047 ft/ft0.0047 ft/ft0.0047 ft/ft0.0047 ft/ft0.0047 ft/ft0.0047 ft/ft0.0047 ft/ft0.0047 ft/ft

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---------------------------------------------------

- --

---- ---------------------------

---- -

---

-----------------------------------------------

---- --

---

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

-

- ----

--

--------

---

--------------------------------

--------------------

------- - --

----

1,7801,7801,7801,7801,7801,7801,7801,7801,780

1,78101,78101,78101,78101,78101,78101,78101,78101,7810

Baja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic Subarea

Centro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic Subarea

I- 15

LAS VEGAS FWY

1,8001,8001,8001,8001,8001,8001,8001,8001,800

1,8201,8201,8201,8201,8201,8201,8201,8201,8201,9201,9201,9201,9201,9201,9201,9201,9201,920

2,0202,0202,0202,0202,0202,0202,0202,0202,020

2,0202,0202,0202,0202,0202,0202,0202,0202,020

2,0202,0202,0202,0202,0202,0202,0202,0202,0202,0402,0402,0402,0402,0402,0402,0402,0402,0402,0602,0602,0602,0602,0602,0602,0602,0602,0602,0802,0802,0802,0802,0802,0802,0802,0802,080

2,1002,1002,1002,1002,1002,1002,1002,1002,100

BARSTOW FWY

BARSTO

W R

D

KERSFIELD HWY

I- 40

IRW

IN R

D

NEEDLES FWY

STATE HW

Y 247

STATE HWY 58

US H

IGHW

AY 5

8

Figure 5b: Groundwater elevation contour map for 1993.

4 0 4 8 12

Miles

Legend

1820 to 1840

1840 to 1860

1800 to 1820

1780 to 1800

2060 to 2080

2100 to 2120

2080 to 2100

2040 to 2060

1940 to 1960

1920 to 1940

1900 to 1920

1860 to 1880

1880 to 1900

1760 to 1780

1740 to 1760

Contour Interval20 feet

2020 to 2040

2000 to 2020

1980 to 2000

1960 to 1980

0.0052 ft/ft0.0052 ft/ft0.0052 ft/ft0.0052 ft/ft0.0052 ft/ft0.0052 ft/ft0.0052 ft/ft0.0052 ft/ft0.0052 ft/ft

-

Bedrock

Fault

Well

Gradient

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-------------------

--------------------------------------

-- --

--

------------------------------------------------------------------------------------------------------------------------------------------------------

--

-

--

-- --

---

-----

--------------

-----------------

------ -

1,7801,7801,7801,7801,7801,7801,7801,7801,780

Baja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic SubareaBaja Hydrologic Subarea

Centro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic SubareaCentro Hydrologic Subarea

LAS VEGAS FWY

BARSTOW FWY

I- 15

1,7801,7801,7801,7801,7801,7801,7801,7801,780

1,8001,8001,8001,8001,8001,8001,8001,8001,800

1,8001,8001,8001,8001,8001,8001,8001,8001,800

1,8201,8201,8201,8201,8201,8201,8201,8201,8201,9401,9401,9401,9401,9401,9401,9401,9401,940

2,0402,0402,0402,0402,0402,0402,0402,0402,040

2,0602,0602,0602,0602,0602,0602,0602,0602,060

2,0602,0602,0602,0602,0602,0602,0602,0602,060

BARSTO

W R

D

KERSFIELD HWY

I- 40

IRW

IN R

D

NEEDLES FWY

STATE HW

Y 247

STATE HWY 58

US H

IGHW

AY 5

8

Figure 5c: Groundwater elevation contour map for 2004.

4 0 4 8 12

Miles

Legend

1820 to 1840

1840 to 1860

1800 to 1820

1780 to 1800

2060 to 2080

2100 to 2120

2080 to 2100

2040 to 2060

1940 to 1960

1920 to 1940

1900 to 1920

1860 to 1880

1880 to 1900

1760 to 1780

1740 to 1760

Contour Interval20 feet

2020 to 2040

2000 to 2020

1980 to 2000

1960 to 1980

0.0052 ft/ft0.0052 ft/ft0.0052 ft/ft0.0052 ft/ft0.0052 ft/ft0.0052 ft/ft0.0052 ft/ft0.0052 ft/ft0.0052 ft/ft

-

Bedrock

Fault

Well

Gradient

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0571

0081

0581

0091

0591

0002

0502

0012

0512

00005000540000400053000030005200002000510000100050

)teef( ecnatsiD latnoziroH

Gro

undw

ater

Ele

vatio

n (A

MSL

) (Fe

et)

Figure 6: Profile of interpolated groundwater elevation grid along gradient line.

1960 1993 4002Profiles of interpolated groundwater elevation grid

)4002( )3991(

Linear regression of profiles

)0691(

Gradient1960 = 0.0051 ft/ft1993 = 0.0048 ft/ft2004 = 0.0051 ft/ft

Centro Baja

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The gradient shows an increase from 1960, 0.0045 to 0.0050 ft/ft in 2004. This change in gradient is near the error (± 0.0004 ft/ft) of the analysis. The error is based on the variation in surface elevation. Surface elevations have been calculated by a comparison of the USGS topographic map and USGS digital elevation map. The variation in these measurements is ± 8.5 feet of elevation over the study region. Over the study area this equates to a gradient variation (potential error) of ± 0.0004 ft/ft.

Gradient (sloping towards Baja Subarea) Method / Period 1960 1993 2004 Hand Calculated from contour map (ft/ft) 0.0047 0.0052 0.0052 GIS Groundwater cross-section tool (ft/ft) 0.0051 0.0048 0.0051 Vector Analysis (ft/ft) 0.0038 0.0047 0.0049 Average of all three techniques (ft/ft) 0.0045 0.0049 0.0050

Table 2: Gradient Calculations for individual time-steps.

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5.3 Flow Analysis Flow is defined as the discharge (Q) across the boundary in question. Using the ranges in values and the calculated time-step gradients as discussed earlier, the following tables represent the range in discharge or flow (ft3/day) across the subarea boundary for each time-step.

Hydraulic Conductivity (K) (ft/day) Discharge (Q) (ft3/day) 0.003 18 250 300

200 19 113,400 1,575,000 1,890,000 400 38 226,800 3,150,000 3,780,000 Thickness

(b) (ft) 600 57 340,200 4,725,000 5,670,000

Table 3: 1960 Flow Calculations (ft3/day) (Gradient of 0.0045 ft/ft).

Hydraulic Conductivity (K) (ft/day) Discharge (Q) (ft3/day) 0.003 18 250 300

200 21 123,500 1,715,000 2,000,000 400 41 247,000 3,430,000 4,116,000 Thickness

(b) (ft) 600 62 370,000 5,145,000 6,174,000

Table 4: 1993 Flow Calculations (ft3/day) (Gradient of 0.0049 ft/ft).

Hydraulic Conductivity (K) (ft/day) Discharge (Q) (ft3/day) 0.003 18 250 300

200 21 126,000 1,750,000 2,100,000 400 42 252,000 3,500,000 4,200,000 Thickness

(b) (ft) 600 63 378,000 5,250,000 6,300,000

Table 5: 2004 Flow Calculations (ft3/day) (Gradient of 0.0050 ft/ft).

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Using the same ranges in hydraulic conductivity and time-step gradients, the following tables represent the discharge or flow (acre-ft/day) across the subarea boundary for each time step.

Hydraulic Conductivity (K) (ft/day) Discharge (Q) (acre-ft/day) 0.003 18 250 300

200 < 0.001 3 36 43 400 < 0.001 5 72 87 Thickness

(b) (ft) 600 < 0.001 8 108 130

Table 6: 1960 Flow Calculations (acre-ft/day) (Gradient of 0.0045 ft/ft).

Hydraulic Conductivity (K) (ft/day) Discharge (Q) (acre-ft/day) 0.003 18 250 300

200 < 0.001 3 39 47 400 < 0.001 6 79 94 Thickness

(b) (ft) 600 < 0.002 9 118 142

Table 7: 1993 Flow Calculations (acre-ft/day) (Gradient of 0.0049 ft/ft).

Hydraulic Conductivity (K) (ft/day) Discharge (Q) (acre-ft/day) 0.003 18 250 300

200 < 0.001 3 40 48 400 < 0.001 6 80 96 Thickness

(b) (ft) 600 < 0.002 9 121 145

Table 8: 2004 Flow Calculations (acre-ft/day) (Gradient of 0.0050 ft/ft).

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Converting Tables 3 thru 8 from acre-ft/day to yearly discharge (acre-ft/year) a range in values between time steps is shown in Table 9. Regional geology based on drilling logs suggests that the lower (0.003 ft/day) and higher (300 ft/day) hydraulic conductivity values are unreasonable for study area. A range of hydraulic conductivity between 18 and less than 250 ft/day is more realistic. Typical well depths range between 200 and 600 ft, thus a yearly discharge range of at least 950 – 3,170 acre-ft per year seems to be the most reasonable. Based on the Judgment, the Centro subarea is responsible for 1,200 acre-ft/year of flow to Baja subarea [Mojave Basin Area Adjudication, 1996]. Future work will be needed in order to define these values further.

Hydraulic Conductivity (K) (ft/day) Discharge (Q) (acre-ft/year) 0.003 18 250 300

200 < 0.2 950 – 1,060 13,200 – 14,660 15,800 – 18,000 400 < 0.4 1,900 – 2,100 26,400 – 29,300 31,700 – 35,000 Thickness

(b) (ft) 600 < 0.6 2,850 – 3,170 39,500 – 44,000 47,500 – 53,000

Table 9: Range of yearly discharge values (acre-ft/year).

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6.0 Conclusions Historical groundwater flow direction for the study area is from Centro Hydrologic Subarea to Baja Hydrological Subarea. Groundwater levels have been stable across the Centro Subarea with only minor fluctuations over the past 15 years (since 1990). The Baja Subarea has seen a trend in water levels downward since the late 1950’s to early 1960’s. The two subareas are divided by the Harper Lake fault. Since, Centro has seen no substantial change in water levels then it can be said that no change in flow across the subarea boundary has occurred. The downward trend in water levels in the Baja Subarea can be attributed to excess pumping of groundwater on the downside gradient of the fault. The groundwater gradient between Centro and Baja Hydrologic Sub-basins is small, less than 0.0005 ft/ft. Using three different time-steps (1960, 1993 and 2004) within a 45 year record of water levels, we were able to evaluate the change, if any, in groundwater gradient across the boundary between the subareas. Each time-step was evaluated using three separate techniques: hand calculated from a contour map, GIS cross-section tool, and vector analysis. Even though each of these analyses looked at the same data, each applied a different approach. The range in gradients was from a low of 0.0045 ft/ft in 1960 to a high of 0.0050 ft/ft in 2004. This registered change is within the calculated error of the analysis (± 0.0004 ft/ft). Overall, the change in gradient from 1993 to 2004 is negligible, thus no major change in gradient magnitude or direction is observed. At the boundary between the two basins, a cross-section was drawn perpendicular to the gradient, and cross-sectional area was calculated. Using Darcy’s Law discharge per day is calculated for the individual time-periods. Flow was then calculated by multiplying discharge per day by days in a given time-period. Darcy’s Law: KiAQ = where:

Q = discharge in ft3/day K = hydraulic conductivity in ft/day i = gradient or slope in ft/ft A = cross sectional area in ft2

The cross-sectional area (A) was based on a range of aquifer thicknesses at the Centro - Baja Hydrologic Subarea boundary. The aquifer thickness varied from a minimum of 200 feet to a maximum of 600 feet. This range of values was based on previous regional and local studies and estimates using available data. The ranges in hydraulic conductivities come from a variety of sources [Hardt, 1971, Stamos, et. al., 2001, Fetter 2001, Heath, 1987, Todd Engineering, 1999 and Driscoll, 1986]. These constitute the range of expected hydraulic conductivity values for river channel deposits (boulders, gravel, sand and silt) [Frieling, J.L., et al., 1983].

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Based on the depth to water and gradient calculations, the flow across the Centro/Baja Subarea boundary appears to have been maintained throughout the past 10+ years. A range of discharge was calculated to be between 950 – 3,170 acre-ft per year. The quantifiable amount of flow across this boundary is questionable, due to the lack of specific basin geometry and aquifer properties, but the data indicate that the flow between these adjoining subareas does not appear to have changed since the onset of the Adjudication. To determine the actual amount of subsurface flow between subareas calculations must be used which rely on significant assumptions that cannot be further quantified without additional field investigations and years of continued consistent monitoring. The only dynamic variables which control flow are changes in water levels and changes in hydraulic gradient. Basin geometry and the hydraulic conductivity of the aquifer materials are not prone to change. Therefore, more emphasis should be towards quantifying any material change in groundwater gradients and depth to groundwater since the onset of the Adjudication to present. Future research should focus on defining the basin geometry, aquifer properties and water levels throughout the area of study. This can be accomplished with the addition of several new nested monitoring wells, aquifer testing and geophysics.

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7.0 References Barto, R., 1986. Ground Water Study for the Newberry Springs Area – Agreement No.

86-87. 148 p. California’s Department of Water Resources (DWR) (http://wdl.water.ca.gov/). Driscoll, F.G., 1986. Groundwater and Wells. Reynolds Guyar Designs, 2nd Edition.

1089 p. Fetter, C.W., 2001. Applied Hydrogeology: New Jersey, Prentice-Hall, Inc., 549 p. Frieling, J.L., Brown, G.A., Rowe, J.A., Brose, R., Cole, C., and Pleasant, S., 1983.

Mojave River Groundwater Basins Historic and Present Conditions, Helendale Fault to Calico-Newberry Fault. Report by C M Engineering Associates and LeRoy Crandall and Associates. 150 p.

Heath, R.C., 1993. Basic Ground-water Hydrology. U.S. Geological Water-Supply Paper

2220. 88 p. Huff, J.A., Clark, D.A., and Martin, P., 2002. Lithologic and Ground-Water Data for

Monitoring Sites in the Mojave River and Morongo Ground-Water Basins, San Bernardino County, California, 1992-98. USGS Open-File Report 02-354.

Izbicki, J.A., 2004. Source and Movement of Groundwater in the Western Part of the

Mojave Desert, Southern California, USA: United States Geological Survey, Water-Resources Investigations Report 03-4313, 128 p.

Stamos, C.L., Martin, P., Nishikawa, T., and Cox, B.F., 2001. Simulation of Ground-

water Flow in the Mojave River Basin, California, U.S. Geological Survey, in cooperation with the Mojave Water Agency, Water-Resources Investigations Report 01-4002, 129 p.

State of California, Department of Public Works, Division of Water Resources, 1934.

Bulletin No. 47. Mojave River Investigation. 259 p. Todd Engineering, 1999. Hydrologic Analysis of the Mojave River Basin in the Alto

Subarea. 66 p. United States Geological Survey’s (USGS) National Water Information System (NWIS)

(http://waterdata.usgs.gov/nwis).

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Appendix A – Procedural Methodology

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Table of Contents 1.0 Procedure for Determining Groundwater Flow between Basins .................................. 3

Step 1: Determine the Area to be Analyzed.................................................................... 3 Step 2: Acquiring the Data.............................................................................................. 3 Step 3: Organizing the Data............................................................................................ 4 Step 4: Basic Analysis .................................................................................................... 4 Step 5: Creating Contour Maps....................................................................................... 5

Figure 1: Contour map with Gradient......................................................................... 6 Step 6: Analysis of Contour Maps .................................................................................. 7

Figure 2: Two contour maps on top of one another with a third on below representing the change map....................................................................................... 8

Step 7: Vector Analysis .................................................................................................. 9 Figure 3: Vector Analysis ......................................................................................... 10

Step 8: Statistical Analysis............................................................................................ 11 Step 9: Calculating Discharge....................................................................................... 11

Figure 4: USGS Hydraulic Conductivity Ranges. .................................................... 12 Step 10: Change in Discharge....................................................................................... 13

Figure 5: Cross-sectional Area Diagram................................................................... 13

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1.0 Procedure for Determining Groundwater Flow between Basins

Step 1: Determine the Area to be Analyzed The amount of available data plays a central role in determining the size of the study boundaries. Questions to keep in mind when determining the area boundaries may include:

1. How much data is exists in both quantity and length of record? 2. How spatially separated is the data (wells)? 3. Is the data spatially separated to sufficiently and accurately define the change in

conditions across the area of interest? Once the above points and questions are addressed, one can begin to establish the limits of the study and the potential accuracy of the results.

Step 2: Acquiring the Data Groundwater elevation data and well location is available from several sources, including:

• The Mojave Water Agency (MWA) internal database (wells monitored specifically by MWA).

• United States Geological Survey (USGS) National Water Information System (NWIS) database (http://waterdata.usgs.gov/nwis) (up to date). Information from this source is only available for download by individual wells.

• California Department of Water Resources (DWR)* (http://wdl.water.ca.gov/). Data from this source can be downloaded through a township and range search. DWR data is not as current as NWIS data.

Data may also be available from other sources such as a county office,, but it should be noted NWIS and DWR contain a wealth of well data. *The DWR database generally contains the same data as the NWIS database. Both databases however, have some records not found in the other.

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Step 3: Organizing the Data This step is primarily concerned with creating a working database from multiple data sources. Once the desired data sets have been acquired, the data needs to be formatted into a workable database and all duplicate records must be filtered out and deleted. Problems with multiple data sources may include:

1. Formatting of the State Well Number (SWN). NWIS uses the format nnnlnnnlnnlnnn, where n = number and l = letter. DWR uses the format nnlnnlnnlnnn. Solution: Use “find” and “replace” in Microsoft Excel or Access to conform to one format or the other.

2. Latitude (lat) and longitude (long) are accurate up to four decimal places in the

DWR database. The NWIS database calculates latitude and longitude in decimal degrees. Solution: Use the “round” function in Microsoft Excel or Access to round to the nearest four decimal places.

3. Well location data from the DWR database comes in two files: one with water

level data and one with location data. These files need to be merged using a database program such as Microsoft Access.

4. Determining groundwater elevation requires ground surface elevation and depth

to water. Solution: Use the calculation: {groundwater elevation = ground surface elevation – depth to water}. In some cases the data will contain the above ground surface height of the casing (stick-up) and above ground surface height must be subtracted from depth to water. Both calculations can be performed in Microsoft Excel or Access.

Once the data is organized into one complete database and any discrepancies are addressed, the database is then ready for analysis.

Step 4: Basic Analysis Creating a complete set of hydrographs for the given well database is the next step. This provides a visual observation of groundwater level changes through time, but not space, to be analyzed. This analysis is usually done in Microsoft Excel. To examine water level changes spatially over time, contour maps should be created (Step 5). This step requires datasets to be analyzed for the most spatially complete time periods. Groundwater levels fluctuate throughout the year as the aquifer responds to seasonal variation in precipitation and recharge and thusly, timescale may become important. For example, analyzing change in storage over a three year period should not be calculated from January to March in one period, and from August to October in another period. The

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overall groundwater level change may be overestimated or underestimated due to seasonal groundwater oscillation within the aquifer system. Therefore, it is recommended that for short-term (< 5 years) analysis groundwater level data should be compared during the same yearly time periods. Additionally, where a well is sampled two or more times in a period, the conservative or lowest groundwater elevation value is used. For consistency, conventions should be applied to all periods of the analysis, not just one. Once two or more periods have been determined, contour maps can be created.

Step 5: Creating Contour Maps Groundwater elevation contour maps can be created from time periods, as described in Step 4. Contour maps can be created in two ways: (1) manually (by hand) or (2) by the appropriate computer program. Computer programs, such as most GIS based programs, allows for rapid calculation of change in storage while creating multiple contour maps quickly. Contour maps can be created by hand, but this is labor intensive and may not be as accurate as computer based contour modeling.

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Figure 1: Contour map with Gradient.

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Step 6: Analysis of Contour Maps Once groundwater contour maps have been created, difference maps or groundwater elevation maps can be completed. These refer to the groundwater elevation differences between two maps. The differences between these two maps represent a change in storage and/or change in gradient. Groundwater gradients can be determined by dividing the change in groundwater elevation (∆h) by the distance (∆x) between two wells or contour lines (GIS based programs will provide the fastest and more accurate results than manual operations). Once a gradient is calculated between two wells in the same location, but, of different time periods, the change in gradient can be calculated by subtracting the older of the two gradients from the younger. To calculate storage, subtract the volume under the older contour map from that of the younger contour map. This step can only be done within the intersected area of the two contour maps.

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Figure 2: Two contour maps on top of one another with a third on below representing the change map.

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Step 7: Vector Analysis Vector analysis consists of measuring the distance and elevation change mathematically between individual wells. Distances between wells can be calculated using Latitude and Longitude of the wells under investigation. Once all the distances have been calculated and the change in elevation between the two points determined, a gradient was calculated by dividing the elevation change by the distance. If more than one method (manual, computer program, or vector analysis) was applied to determine the gradient, an average gradient must be calculated.

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Figure 3: Vector Analysis

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Step 8: Statistical Analysis Statistical analysis consists of using the calculated values from steps 1 through 7 to determine if a significant correlation exists. The calculated gradients from the individual time-steps and the values from the three methods should be similar. A good result will typically be within one standard deviation of one another. If there is a glaring statistically difference, additional steps may be required to find any miscalculations, etc.

Step 9: Calculating Discharge Flow or discharge (Q) can be calculated for different gradients using Darcy’s Law (Equation 1):

KiAQ = (1) where:

Q = discharge in ft3/d K = hydraulic conductivity (see Figure 4) in ft/d i = gradient or slope (Step 8) in ft/ft A = cross sectional area in ft2

Hydraulic conductivity can have a wide range of values. Figure 4, from the USGS provides ranges of hydraulic conductivity for a variety of sediments and rocks.

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Figure 4: USGS Hydraulic Conductivity Ranges.

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Step 10: Change in Discharge Once Q has been calculated for two or more periods, change in Q can be calculated by subtracting the younger value from the older value (∆Q). Total discharge can be calculated by multiplying the average Q for two consecutive periods by the time between those periods. If more then two Q values have been calculated within the study area, treat each consecutive time period independently and add the discharge values together as the final step. Cross-sectional area is calculated by the distance of the boundary in feet times the average depth across the boundary (see figure 5). This assumes a rectangular shape which in most basins is not exact. However, for the purpose of general flow calculations this assumption is used until such time that better cross-sectional profiles of the aquifer system are determined.

Figure 5: Cross-sectional Area Diagram.

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Example Calculations Example: Calculate the flow between basin A to basin B between spring 1954 spring 2005; given the gradients in spring 1954, 1972, 1989, 1994, and 2005 are 0.005, 0.003, 0.002, 0.0007, and 0.0001, respectively. Hydraulic conductivity (K) is 40 ft/day and the cross-sectional area is 5,000,000 ft2. Solution: A) Calculate Q using Darcy’s Law (Q=KIA) for spring 1954, 1972, 1989, 1994, and 2005. 1954: 40 ft/day x 0.005 x 5,000,000 ft2 = 1,000,000 ft3/day 1972: 40 ft/day x 0.003 x 5,000,000 ft2 = 600,000 ft3/day 1989: 40 ft/day x 0.002 x 5,000,000 ft2 = 400,000 ft3/day 1994: 40 ft/day x 0.0007 x 5,000,000 ft2 = 140,000 ft3/day 2005: 40 ft/day x 0.0001 x 5,000,000 ft2 = 20,000 ft3/day B) Use the average between two consecutive time steps multiplied by the time between periods [(1,000,000 ft3/day + 600,000 ft3/day)/2] x (1972-1954) = 12,800,000 ft3

[(600,000 ft3/day + 400,000 ft3/day)/2] x (1989-1972) = 8,500,000 ft3

[(400,000 ft3/day + 140,000 ft3/day)/2] x (1994-1989) = 1,350,000 ft3 [(140,000 ft3/day + 20,000 ft3/day)/2] x (2005-1994) = 880,000 ft3 C) Sum all discharge values 12,800,000 ft3 + 8,500,000 ft3 + 1,350,000 ft3 + 880,000 ft3 = 23,530,000 ft3