Benito Thesis

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Investigation of Contaminant Transport over Multiple Length Scales:

From the Micro to the Macro

by

Pascual H. Benito

B.A. Geology (Amherst College, Amherst, MA) 1994,M.Sc. (U.C. Berkeley Dept. Civil and Environmental Engineering) 2001

A dissertation submitted in partial satisfaction of therequirements for the degree of

Doctor of Philosophy

in

Civil and Environmental Engineering

in the

GRADUATE DIVISION

of the

UNIVERSITY OF CALIFORNIA, BERKELEY

Committee in charge:

Prof. Tadeusz W. Patzek, Chair

Prof. Yoram N. RubinDr. Dmitriy B. SilinProf. G. Mathias Kondolf

Fall 2008


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The dissertation of Pascual H. Benito is approved:

Chair Date

Date

Date

Date

University of California, BerkeleyFall 2008


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Investigation of Contaminant Transport over Multiple Length Scales:

From the Micro to the Macro

c 2008by

Pascual H. Benito


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Abstract

Investigation of Contaminant Transport over Multiple Length Scales: From theMicro to the Macro

by

Pascual H. BenitoDoctor of Philosophy in Civil and Environmental Engineering

University of California, Berkeley

Prof. Tadeusz W. Patzek, Chair

Theses have elements. Isnt that nice?

Prof. Tadeusz W. Patzek, Chair Date


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To myself,

Perry H. Disdainful,

the only person worthy of my company.


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Contents

Acknowledgments xix

I First Part 1

1 Introduction 3

II Pore Scale 5

2 Pore network investigation of stability and scaling of two-phase immis-cible displacement fronts with buoyancy forces 7

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Research Question . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.3 Brief Introduction to Percolation Theory . . . . . . . . . . . . . . 11

2.3 Description of Invasion Percolation Model . . . . . . . . . . . . . . . . . . 132.3.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.2 Pore Filling Potential . . . . . . . . . . . . . . . . . . . . . . . . . 132.4 Model Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.5.1 Phase Distribution at Breakthrough . . . . . . . . . . . . . . . . . 16

2.5.2 Invasion Front Geometry . . . . . . . . . . . . . . . . . . . . . . . 172.5.3 Capillary Pressure Curves . . . . . . . . . . . . . . . . . . . . . . . 19

2.6 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.6.1 Capillary Pressure at Breakthrough . . . . . . . . . . . . . . . . . 21

2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.8 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.8.1 Limitations and Caveats . . . . . . . . . . . . . . . . . . . . . . . . 262.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.10 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.11 MATLAB code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28


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2.12 Results from Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.13 Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

III Multi-Scale 29

IV Regional Scale 31

3 Modeling the Impacts of the Food Processing Industry on RegionalGround Water Quality in the Lower San Joaquin River Basin 33

3.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.1.1 Salinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.2 Characteristics of Food Processing Waste Discharge . . . . . . . . 37

3.1.3 Attenuation of Salinity in the Vadose Zone . . . . . . . . . . . . . 373.2 Overview of Objectives and Methodology . . . . . . . . . . . . . . . . . . 39

3.3 Hydrogeological Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3.1 Regional Hydrology . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.4 Water Recharge and Pumping . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.5 Numerical ground water Flow Model . . . . . . . . . . . . . . . . . . . . . 48

3.5.1 Ground Water Flow Equation . . . . . . . . . . . . . . . . . . . . . 52

3.5.2 Spatial Discretization . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.5.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.5.4 Hydrogeological Parameters . . . . . . . . . . . . . . . . . . . . . . 58

3.6 Results of Flow Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.7 Salinity Transport Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.7.1 Numerical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.7.2 Solute Transport Parameters . . . . . . . . . . . . . . . . . . . . . 71

3.7.3 Initial and Recharge Concentrations . . . . . . . . . . . . . . . . . 73

3.7.4 Land Application waste water Loading Rates . . . . . . . . . . . . 74

3.7.5 Salinity Transport Modeling Results . . . . . . . . . . . . . . . . . 75

3.7.6 The Effects of Spatial Variability . . . . . . . . . . . . . . . . . . . 82

3.8 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.9 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.9.1 Monte Carlo simulation Results . . . . . . . . . . . . . . . . . . . . 95

3.9.2 An alternative Monte Carlo analysis . . . . . . . . . . . . . . . . . 110

3.10 Comparison with field measurements . . . . . . . . . . . . . . . . . . . . . 116

3 . 1 1 C o n c l u s i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 3

3.11.1 Future Improvements . . . . . . . . . . . . . . . . . . . . . . . . . 126

V Closure 127

4 Summary and Conclusions 129


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A Some Ancillary Stuff 137


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List of Figures

2.1 Fluid phase distributions at breakthrough for different values of BondNumber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Phase distribution at breakthrough for four different bond numbers (BondNumber increasing counterclockwise from upper left plot). . . . . . . . . 17

2.3 Non-wetting phase (red) displacement front at breakthrough with differentBond Numbers (Bond Number increasing clockwise from upper leftplot). The dashed blue line represents the mean position of the frontabove the inlet face. The width of the displacement front, is shownthrough the arrows measuring 2. . . . . . . . . . . . . . . . . . . . . . . 18

2.4 Capillary Pressure Curves shown for different Bond Numbers (Bond Num-ber increasing clockwise from upper left plot). . . . . . . . . . . . . . . . 19

2.5 Breakthrough Capillary Pressure Curves shown for different Bond Numbers,NBo.20

2.6 Breakthrough Capillary Pressure Curves for all simulations shown forBond Numbers increasing from NBo = 1 at left to NBo = 1 at right. . . 21

2.7 Breakthrough Capillary Pressure Curves for all simulations shown forBond Numbers increasing from NBo = 10 at left to NBo = 10 at right. 22

2.8 Non-wetting, connected-wetting, and trapped wetting phase saturationsat breakthrough versus Bond Number for all simulations. . . . . . . . . . 23

2.9 Non-wetting, connected-wetting, and trapped wetting phase saturationsat breakthrough versus Bond Number for all simulations, zoomed in view(NBo from -0.1 to +0.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.10 How do macroscopic properties of the two-phase fluid system scale withthe Bond Number? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.11 dimensionless capillary pressure at breakthrough as a function of BondNumber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.12 Non-wetting phase saturaiton at breakthrough as a function of Bond Num-ber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.13 dimensionless capillary pressure at breakthrough as a function of BondNumber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27


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3.1 Map showing the location and industrial groups of over 200 food proces-sors in Central Valley who discharge effluent to land and are currently

regulated by the Regional Water Quality Control Board. There are over300 additional processors currently discharging without official regulation.It is believed that land discharge practices have impacted ground waterquality at a majority of these sites [Central Valley Regional Water QualityControl Board, 2006]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2 Digram showing conceptual model for the transport of waste water appliedto land as irrigation [Miller et al., 2008]. . . . . . . . . . . . . . . . . . . . 39

3.3 Aerial view of regional study area (red rectangle), and the food processingfacilities in the model area (red diamonds). The area of the numericalmodel is shown by the black rectangle. Currently the model does notinclude the region to the west of the San Joaquin River. . . . . . . . . . . 43

3.4 Generalized geologic section and view of the Central Valley as seen lookingNorthwest along the axis of the valley (from Page, 1986). . . . . . . . . . 43

3.5 Map showing the structure of overlapping fan systems in the San JoaquinBasin. The study area is shown by the red dashed rectangle and includesthe overlapping fans from the Stanislaus, Tuolumne, and Merced Rivers(from Weissmann et al. [2005]). . . . . . . . . . . . . . . . . . . . . . . . . 45

3.6 The major sedimentary units in the Study Area (Source: Phillips et al.2007). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.7 Map view with conceptual diagram, of regional ground water flow (fromGronberg & Kratzer, 2006). . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.8 Cross-section with conceptual diagram of the regional ground water flowshowing regional flow and vertical components of flow due to agriculturalpumping and recharge(Source: Gronberg & Kratzer [2006]). . . . . . . . . 47

3.9 Well types and locations. Irrigation and municipal wells account for thegreatest volume of pumping. The median screened depth interval forIrrigation wells is 51 74 m below land surface, for municipal wells itis between 59-75m, and for domestic wells it is between 44-47 m [Burowet al., 2004]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.10 Recharge map. Lighter colors correspond to greater recharge per unitarea, darker colors to less. (Source: Phillips et al. [2007]). . . . . . . . . . 50

3.11 Pumpage map. Lighter colors correspond to more greater pumping perunit area, darker colors to less. (Source: Phillips et al. [2007]). . . . . . . 51

3.12 3-D view showing the active portion of the numerical model grid (vertical

exaggeration = 30). The Corcoran Clay layer is shown in blue, un-consolidated sediments in red and consolidated sediments in green. Theelevations of the top of the first layer are derived from the USGS digitalNational Elevation Model data set [USGS, 1999]. . . . . . . . . . . . . . . 53

3.13 An East-West cross-section showing the five layers of the numerical grid.The cells representing the Corcoran clay are shown in blue. The clay layerpinches out roughly midway through the model area. Vertical exaggera-tion is 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54


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3.14 Lateral boundary conditions and included surface water features. . . . . . 553.15 Map showing location of pumping wells (blue circles) in the numerical

model (base map from Phillips et al., 2007). . . . . . . . . . . . . . . . . . 563.16 Three dimensional view of the pumping well locations in the model. The

yellow circles are located in the center of each grid cell defined as a pump-ing well. Vertical exaggeration is 30. . . . . . . . . . . . . . . . . . . . . 57

3.17 Horizontal planar views through three-dimensional model of percentagecoarse-grained sediments in study area (source: Burow et al., 2004). Thered, elongated structures at the top maps suggest the presence of pale-ochannels. These structures disappear at larger depths, suggesting thepresence of channels only at shallow formations. . . . . . . . . . . . . . . . 62

3.18 3-D view showing the four different lithologic regions in the numericalmodel (green=Eastern Area, biege=Western Area above the Corcoran

Clay, blue= Corcoran Clay, yellow=Western Area below Corcoran Clay).Vertical exaggeration is 30. . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.19 Map view showing the Western and Eastern lithologic regions in the nu-merical model. The lateral extent of the the underlying Corcoran Claylayer is shown by the dashed lines. . . . . . . . . . . . . . . . . . . . . . . 64

3.20 Contour map of the water table for Spring of the Water Year 2000. Thecontour interval is 2 meters; red corresponds to areas of higher water tableelevations and blue to lower water surface elevations. . . . . . . . . . . . . 65

3.21 Location of observed water levels for Water Year 2000 from DWR onlinesource [base map from Phillips et al. [2007]]. The dashed lines show thelateral extent of the Corcoran clay layer. . . . . . . . . . . . . . . . . . . . 66

3.22 Contour map of computed water table elevations. The contour intervalis 2 meters; red corresponds to areas of higher water table elevations andblue to lower water surface elevations. . . . . . . . . . . . . . . . . . . . . 67

3.23 Plot of Computed head values versus observed head values (meters). . . . 683.24 Difference map between computed water table elevations and interpolated

observed water table elevations. The observations correspond to data fromSpring 2000. Red corresponds to areas where the computed water tableelevations are higher than the observed; and blue to where the computedvalues are lower than the observed. The color intensity scale is cut offat 5 meters. The location of the observations points are shown by thesmall circles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.25 Map showing the land discharge areas (white polygons) for each facility

in the regional study area . . . . . . . . . . . . . . . . . . . . . . . . . . . 743.26 Mass loading curves of Fixed Dissolved Solids (FDS) reaching the water

table over 30 year period due to land application of waste water from thefour primary food processing industries (wine & grape, meat, dairy, andtomato processing), as estimated by 1-D, reactive vadose zone modeling[Miller et al., 2008]. These loading curves serve as transfer functions forsalinity transport from the land surface through the vadose zone and tothe water table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75


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3.27 Concentration of FDS (mg/l) at 30 years in model Layer 1. The colorbar iscutoff at 1000 mg/l (so red indicated C 1000 mg/l FDS). The following

ratios were employed: L/T = 10 and L/V = 10, where L, T andV denote the longitudinal, transverse and vertical dispersivities. Allsimulations assumed V = T. The small yellow circles indicate pumpingwells whose screened interval intersect Layer 1. . . . . . . . . . . . . . . . 76

3.28 Map of water table depths less than evapotranspiration extinction depth(meters). Light blue regions show areas where the depth to water table isless than or equal to extinction depth. Such areas are prime candidates forincreased FDS due to accumulations of salt via evapotranspiration. Thiseffect is unrelated to food-processing related discharge, unless if takingplace in such areas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.29 A difference map of, FDS = FDS(with land discharge)FDS(without land discharge)

showing the net effect of simulated effluent land discharge at the watertable after 30 years. The color intensity scale is cutoff at 1,000 mg/l, soconcentrations greater than or equal to 1,000 mg/l appears as red. . . . . 79

3.30 A northward looking 3-D view of FDS where the blue iso-surfaces con-tain the subsurface volumes within which FDS 500 mg/l. The verticalscale is exaggerated by 30 times and the blue contour lines indicate theelevation of the water table. . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3.31 3-D view of particle tracking flow-path lines emanating from the watertable underneath the land discharge areas. (vertical exaggeration = 30) 81

3.32 Hypothetical hydraulic conductivity map for layer 1, which is used to an-alyze the effects of paleo channels on transport of FDS in the saturated

zone. Values shown on the color bar are in meters per day. The red arearepresents a hypothetical paleo-channel with a relatively high conductiv-ity, passing through a land application area in the study area. The otherfeatures on this map can be correlated with Figure 3.19. . . . . . . . . . . 83

3.33 30 year FDS concentration in Layer 1 with paleo-channel. Color bar inmg/l and cutoff at 1000 mg/l. . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.34 Differences in FDS in Layer 1 with simulated paleo-channel, showingthe FDS= FDS(with land Discharge) FDS(without Land Discharge).Color bar in mg/l and cutoff at 1000 mg/l The outline of the simulatedpaleo-channel is visible in light blue. This map cannot be used to ana-lyze the significance of the effects of the channel unless compared with a

similar one obtained assuming no channel, as shown below. . . . . . . . . 853.35 This map shows the difference between FDS= FDS(with land Discharge)

FDS(without Land Discharge), computed with the hypothetical paleo-channel, and FDS without the paleo-channel, in Layer 1. Color bar is inmg/l. This shows the effect a coarse-grained paleo-channel would have ascompared to no channel, in the form of differences in concentrations. Theplume concentrations are higher at the leading edge of the plume, but aresmaller at the tail end. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86


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3.36 This map shows a zoomed-in view of Figure 3.35 the difference betweenFDS with the paleo-channel and FDS without the hypothetical paleo-

channel, in Layer 1. Color bar in mg/l. This shows the effect a coarse-grained paleo-channel would have as compared to no channel. The plumeconcentrations are higher at the leading edge of the plume, but are smallerat the tail end. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.37 This map shows the difference of FDS with the paleo-channel and FDSwith out the paleo-channel, in Layer 2. Color bar in mg/l. This showsthe effect a coarse-grained paleo-channel would have as compared to nochannel. The plume concentrations are higher at the leading edge of theplume, but are smaller at the tail end. . . . . . . . . . . . . . . . . . . . . 88

3.38 This map shows the difference of FDS with the paleo-channel and FDSwith out the paleo-channel, in Layer 3 Color bar in mg/l. ItThis shows

the effect a coarse-grained paleo-channel would have as compared to nochannel. The effect of the channel is greatly diminished at greater depths. 89

3.39 This Figure shows a cross-section view with the color scale representingthe difference of FDS with the paleo-channel and FDS with out thepaleo-channel, in Layer 1. Color bar in mg/l. This Figure shows the effecta coarse-grained paleo-channel would have as compared to no channel.The differences in plume concentrations are positive higher at the leadingedge of the plume, and but are negative at the tail end. The verticalexaggeration is 30x. In the view below we are seeing projections of the x-and y-axes onto the East-West plane. . . . . . . . . . . . . . . . . . . . . . 90

3.40 Concentration maps showing the net effect of 30 yrs of land discharge forthe three different dispersivity ratio scenarios. For each dispersivity ratio(columns) the maps shows the net concentration difference, C between30 yrs with and without land discharge activity for each of the five modellayers (L01-L05), starting from top layer (L01) . The color intensity scaleis in mg/l and is cutoff at 1000 mg/l (all values greater than 1000 are inred). The white areas on east side the top 2 layers indicate dry cells abovewater table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.41 A close-up of the C maps for the two end points of the dispersivity ratioscenarios, for the top layer of the model. The maps show the concentrationdifference between 30 yrs with and without land discharge activity for eachof the top model layer L01. The color intensity scale is in mg/l and iscutoff at 1000 mg/l (all values greater than 1000 are in red). . . . . . . . . 94

3.42 This map shows the ensemble mean concentration, CMean of FDS for eachgrid block in layer 1 after 30 years. The color scale is in mg/l and is cutoffat 1000 mg/l (red1000 mg/l, blue = 0 mg/l). All white areas on the leftside indicate dry cell blocks that are above the water table. . . . . . . . . 98

3.43 This map shows the ensemble mean concentration, CMean of FDS for eachgrid block in layer 2 after 30 years. The color scale is in mg/l and is cutoffat 1000 mg/l (red1000 mg/l, blue = 0 mg/l). All white areas on the leftside indicate dry cell blocks that are above the water table. . . . . . . . . 99


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3.44 This map shows the ensemble mean concentration, CMean of FDS for eachgrid block in layer 3 after 30 years. The color scale is in mg/l and is cutoff

at 1000 mg/l (red1000 mg/l, blue = 0 mg/l). . . . . . . . . . . . . . . . 100

3.45 This map shows the ensemble mean concentration, CMean of FDS for eachgrid block in layer 4 after 30 years. The color scale is in mg/l and is cutoffat 1000 mg/l (red1000 mg/l, blue = 0 mg/l). . . . . . . . . . . . . . . . 101

3.46 This map shows the concentration standard deviation, CStdev for the en-semble of all realizations for each grid block in Layer 1 after 30 years. Thecolor scale is in mg/l and is cutoff at 1000 mg/l (red1000 mg/l, blue = 0mg/l). All-white areas to on the left side indicate dry cell blocks that areabove the water table. The drying out or wetting of different cells as thewater table rises and falls with different parameter realizations creates a

fringe of artificially high standard deviations along the edge of the gridsubject to drying out. This is visible as the red to green colors that followthe shores of the dried out cells. . . . . . . . . . . . . . . . . . . . . . . 102

3.47 This map shows the concentration standard deviation, CStdev for the en-semble of all realizations for each grid block in Layer 2 after 30 years. Thecolor scale is in mg/l and is cutoff at 1000 mg/l (red1000 mg/l, blue = 0mg/l). All-white areas to on the left side indicate dry cell blocks that areabove the water table. The drying out or wetting of different cells as thewater table rises and falls with different parameter realizations creates afringe of artificially high standard deviations along the edge of the grid

subject to drying out. This is visible as the red to green colors that followthe shores of the dried out cells. . . . . . . . . . . . . . . . . . . . . . . 103

3.48 This map shows the concentration standard deviation, CStdev for the en-semble of all realizations for each grid block in Layer 3 after 30 years. Thecolor scale is in mg/l and is cutoff at 1000 mg/l (red1000 mg/l, blue = 0mg/l). The standard deviation of the concentration decrease sharply within c r e as in g d e p th . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

3.49 This map shows the probability of FDS>500 mg/l in Layer 1 after 30years. The color scale represents probability with 0 (blue) indicating 0%probability of exceedence, and 1.0 (red) indicating 100% probability of

exceeding 500 mg/l. The location of the rivers and major streams areshown as white lines. In addition to the ET hot spots described in theprevious section there are a few artifacts associated with grid blocks thatborder the cells that dry out (i.e. cells that are entirely above the watertable). The large standard deviations associated with these grid cellsprone to drying out causes higher exceedence probabilities to be estimatedfor these regions. One such artifact is clearly visible in the middle of theeastern edge of the model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 105


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3.50 This map shows the probability of FDS>500 mg/l in Layer 2 after 30years. The color scale represents probability with 0 (blue) indicating 0%

probability of exceedence, and 1.0 (red) indicating 100% probability ofexceeding 500 mg/l. The location of the rivers and major streams areshown as white lines. In addition to the ET hot spots described in theprevious section there are a few artifacts associated with grid blocks thatborder the cells that dry out in (i.e. cells that are entirely above the watertable). One such artifact is clearly visible in the eastern most corner ofthe model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 06

3.51 This map shows the probability of FDS>500 mg/l in Layer 3 after 30years. The color scale represents probability with 0 (blue) indicating 0%probability of exceedence, and 1.0 (red) indicating 100% probability of

exceeding 500 mg/l. The location of the rivers and major streams areshown as white lines. In addition to the ET hot spots described in theprevious section there are a few artifacts associated with grid blocks thatborder the cells that dry out in (i.e. cells that are entirely above the watertable). The large standard deviations associated with these cells prone todrying out causes higher exceedence probabilities to be estimated for theseregions. One such artifact is clearly visible in near the eastern most cornerof the model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 07

3.52 This map shows the probability of FDS>500 mg/l in Layer 4 after 30years. The color scale represents probability with 0 (blue) indicating 0%probability of exceedence, and 1.0 (red) indicating 100% probability of ex-ceeding 500 mg/l. The location of the rivers and major streams are shownas white lines. The large hot spots that appear along the San Joaquinriver edge of the model are due to the initial background concentrationsassigned to the model, rather than to specific land application activity. . . 108

3.53 This map shows the probability of FDS>500 mg/l in Layer 5 after 30years. The color scale represents probability with 0 (blue) indicating 0%probability of exceedence, and 1.0 (red) indicating 100% probability of ex-ceeding 500 mg/l. The location of the rivers and major streams are shown

as white lines. The large hot spots that appear along the San Joaquinriver edge of the model are due to the initial background concentrationsassigned to the model, rather than to specific land application activity. . . 109

3.54 This map shows the probability of C >500 mg/l in layer 1 after 30years. The color scale represents probability with 0 (blue) indicating 0%probability of exceedence, and 1.0 (red) indicating 100% probability ofexceeding 500 mg/l. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111


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3.55 This map shows the probability of C >500 mg/l in layer 2 after 30years. The color scale represents probability with 0 (blue) indicating 0%

probability of exceedence, and 1.0 (red) indicating 100% probability ofexceeding 500 mg/l. In addition to the ET hot spots described in theprevious section there are a few artifacts associated with grid blocks thatborder the cells that dry out (i.e. cells that are entirely above the watertable,). One such artifact is clearly visible in the eastern most corner ofthe model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

3.56 This map shows the probability of C >500 mg/l in Layer 3 after 30years. The color scale represents probability with 0 (blue) indicating 0%probability of exceedence, and 1.0 (red) indicating 100% probability ofexceeding 500 mg/l. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113



3.59 Plot of measured monthly FDS concentrations in shallow groundwatermonitoring wells (Figure 3.60 at the Hilmar Cheese plant for the periodfrom May 2004 to December 2005. . . . . . . . . . . . . . . . . . . . . . . 117

3.60 Aerial photo showing the outline (yellow) of the primary land applicationarea at the Hilmar Cheese plant, shallow ground water monitoring wells(MW-1 MW-20), and agricultural tile drain (cyan) and the associatedtile drain pump stations (red symbols). . . . . . . . . . . . . . . . . . . . . 118

3.61 Satellite photo showing aerial view of a large dairy processor (cheese &whey) south of Modesto. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

3.62 This contour map shows a salinity plume under an actual large dairyprocessor in the study area. The groundwater measurements have beenaveraged over from monthly monitoring data from May 2004 to December2005. What is shown in actually a difference map of FDS above the back-ground FDS concentration in a reference well (MW-20). The color scalehas been chosen to match that of the model results, with red representingC 1000 mg/l FDS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120


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3.63 This contour map shows the simulated salinity plume in the top modellayer under a large dairy processor in the study area, after 21 years of

continuous waste discharge. The color scale shows net difference FDSabove the background FDS concentration, FDS. The upper bound of thecolor scale has been set with dark red representing C 1000 mg/l FDS.The outer yellow polygon shows the worst-case scenario land dischargearea used in the model. The inner yellow polygon shows the actual landapplication area used historically since 1985, and is about 1/8 the totalland application area on which the facility is permitted to discharge. . . . 121

3.64 Computed breakthrough curves for FDS in model layer 1 at the center ofplume for four processers from each of the main industry groups. . . . . . 122


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List of Tables

3.1 Comparison of untreated winery and domestic waste water characteristics[Central Valley Regional Water Quality Control Board, 2006] . . . . . . . 34

3.2 waste water characteristics (concentration ranges) of the four major food

processing industries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.3 Average values of the hydraulic conductivity calculated using the har-

monic (KH), geometric (KG) and arithmetic (KA) means for the fourlithologic regions shown in Figures 3.18 and 3.19, as well as the ratio ofhorizontal to vertical hydraulic conductivities (Khor/Kvert). (Check newwording.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.4 Table showing statistics of FDS for each the three dispersivity ratioscenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.5 [Table showing the parameter values used in the Monte Carlos simula-tions.] The salinity transport model is then run on each of these real-izations to get a statistical distribution of salinity concentrations at each

point in the model grid. This distribution can be characterized by meanconcentrations and standard deviations of the salt concentrations in themodel. This probability density function can be used to generate a mapwhich shows the probability of the salt concentration exceeding a giventhreshold, for example the MCL, at any given point in the model domain. 96

3.6 This table shows summary statistics for the values of the ensemble Min,Mean, Max and standard Deviation of the concentration generated in theMonte Carlo Simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.7 This table shows summary statistics for the values of the ensemble Min,Mean, Max and standard Deviation of the concentration differences (C) 110


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Acknowledgments

Here I will thank everyone that has helped me along after so many years in grad school!I would like to extend thanks to Steven Phillips of the U.S.G.S. for giving me access

to the original MODFLOW input files of their regional ground water model for the LowerSan Joaquin Basin.


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Part I

First Part


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Chapter 1

Introduction

Every dissertation should have an introduction. You might not realize it, but the intro-duction should introduce the concepts, background, and goals of the dissertation.


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Part II

Pore Scale


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Part III

Multi-Scale


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Part IV

Regional Scale


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Chapter 3

Modeling the Impacts of the Food

Processing Industry on Regional

Ground Water Quality in theLower San Joaquin River Basin

3.1 Background and Motivation

Food processing is a major economic activity in California, serving the states multi-billion dollar agriculture industry. Californias Central Valley contains over 640 food-processing plants, which consume approximately 7.9107m3 of water per year [CaliforniaLeague of Food Processors, 2007]. Solid and liquid wastes from food processing indus-tries (including canneries; meat, fruit, and vegetable packers; cheese manufacturers; andwineries) contain significant quantities of organic matter, nitrogen, and salts. Approxi-mately 80% (520) of these processors discharge their waste water to land [Central ValleyRegional Water Quality Control Board, 2005, 2006]. A large number of food processorsuse land application of their waste water as a treatment method, with little or no pre-treatment, in which ideally, the waste water serves to both irrigate and fertilize cropsgrown in the discharge area, and natural soil and plant activity attenuate the waste com-ponents before they reach the water table [Crites et al., 1974]. Postulated mechanismsfor attenuation include microbial processes such as denitrification, cation exchange, cropnutrient uptake, and mineral precipitation [California League of Food Processors, 2007].

Ground water monitoring has shown, however, that significant ground water quality im-pacts have occurred at many larger sites where these wastes have been applied [CentralValley Regional Water Quality Control Board, 2005], casting doubt on the efficacy ofland application as a mechanism for attenuation. Initial investigations found elevatedsalinity levels to be the most common form of ground water degradation near land ap-plication sites, followed by elevated levels of nitrogen compounds, mainly ammonia andnitrate.

Salt and nitrate pose significant threats to beneficial uses of ground water. The


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palatability of domestic drinking water is affected by salinity, and California drinkingwater standards include a recommended limit of 500 mg/l (ppm) total dissolved solids

(TDS) and an upper limit of 1,000 mg/l [Cal. Dept. of Public Health, 2006]. Drinkingwater delivered to consumers must meet these requirements. Furthermore, individualcomponents of salt can have adverse health affects. Sulfate levels above 500 mg/l, forexample, can cause diarrhea in sensitive individuals [Central Valley Regional WaterQuality Control Board, 2005]. Salinity can also impact the use of water for irrigationby reducing plants ability to uptake water from the soil and can cause desiccation ofleaves. Salt-sensitive crops such as strawberries, carrots, and beans can begin to sufferreduced yields when sprinkler-irrigated by water containing over 450 mg/l TDS [Rhoadeset al., 1992; Ayers & Westcot, 1994]. Nitrate in drinking water can be toxic to humans,especially infants, by limiting the ability of red blood cells to carry oxygen to the tissues ofthe body. This condition in infants can be fatal, and is known as Blue Baby Syndrome.

High nitrate levels may also affect the oxygen-carrying ability of the blood in pregnantwomen [Cal. Dept. of Public Health, 2008]. Californias primary drinking water standardare set at 45 milligrams per liter (mg/l) for nitrate as NO3 (equivalent to 10 mg/L fornitrate as nitrogen) [Cal. Dept. of Public Health, 2008].

As shown in the Table 3.1 food processing waste water is typically much higherstrength than domestic waste water, and therefore has a higher potential to adverselyimpact water quality and to create nuisance conditions.

Table 3.1: Comparison of untreated winery and domestic waste water characteristics[Central Valley Regional Water Quality Control Board, 2006]

Constituent Untreated Winerywaste water

Untreated Domesticwaste water

pH 2 11 6 8

Biochemical oxygendemand (BOD, mg/l)

300 30,000 100 400

Total dissolved solids(TDS, mg/l)

80 7,000 250 1,000

Total nitrogen (mg/l) 1 225 20 50

While California State regulations specify that the discharge of waste may not de-grade ground water quality, they do not currently specify limits on waste applicationrates or concentrations [Central Valley Regional Water Quality Control Board, 2005].Enforcement actions have been taken against multiple food processors [California EPA,

2007], and the Central Valley Regional Water Quality Control Board, who regulateswaste discharge permits in California, has begun re-examining the land-disposal permit-ting process [Central Valley Regional Water Quality Control Board, 2006]. The Stateof California, has recently passed the Porter-Cologne Act [2006], which requires thatthe economic impacts must be considered when stricter waste discharge regulations areimposed [Sunding & Zilberman, 2005]. Understanding how to manage saline waste wa-ter discharges from this industry can provide important lessons about alternatives formanagement of point source discharges of salts from other sources, and can also aid in


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the development of a comprehensive salt management policy for the entire San JoaquinValley, including salts from non-point sources. Because ground water is an important

source of agricultural and municipal water supplies, salts emanating from food processingfacilities must be analyzed in the context of regional water use and treatment systems.This circumstance calls for a multidisciplinary and comprehensive approach to salt man-agement. This study was carried out as part of a larger investigation on the water qualityand economic impacts of the food processing industry in the Central Valley, documentedin Sunding et al. [2007a]; Rubin et al. [2007]; Sunding et al. [2007b].

The portion of the study presented here aims to develop and demonstrate a frame-work for modeling the fate of chemicals of concern from land discharge of waste waterfrom multiple facilities from different food processing industries, once they have traveledthrough the vadose zone and reached the water table. The emphasis is on characterizingthe effects at a regional scale. To develop this framework, the study will focus on the fate

of the salinity component of the waste water, with the intent of expanding this analysisto nitrogen and organic compounds at a later stage.

Irrigated agriculture causes ground water impacts, even without considering the reuseof waste water. All irrigation water, with the exception of direct rainfall, contains dis-solved salts. Salts become concentrated within the soil by evaporation and by transpira-tion from crops. The addition of more irrigation water results in a build up of salts in thesoil that can harm crops if left unchecked. The arid and semi-arid climates of the CentralValley make this process more severe as rainfall rates are insufficient to naturally leachthe salts from the soil [Central Valley Regional Water Quality Control Board, 2005]. Saltaccumulation resulting from intensive irrigated agriculture is already a major problemin the the Central Valley, and the impacts from waste discharge from food processors

take place against this background. The focus of this study is limited to the net impactof the food processing waste discharge practices, and is not meant to directly addressthe broader impacts of irrigated agriculture on water quality in the Central Valley.

3.1.1 Salinity

The term salinity encompasses multiple individual ion species and is commonly rep-resented as either electrical conductivity (EC) or fixed dissolved solids (FDS). FDS isthe direct measurement of the concentration of ionic species, whereas EC representsan indirect measure of their charge. The major ions comprising salinity are: chloride(CL), calcium (Ca2+), magnesium (Mg2+), potassium (K+), sodium (Na+), ammo-

nium (NH+4 ), nitrate (NO3 ), sulfate (SO24 ), and phosphate (PO34 ). Two carbonatespecies (CO34 and HCO

3 ) are also significant contributors. The trace elements alu-minum, manganese, zinc, copper, and iron can also contribute to FDS [Hillel, 2000;Appelo & Postma, 2005]. It is useful to briefly relate FDS to the more commonly re-ported, Total Dissolved Solids (TDS). The fixed dissolved solids represents the portionof the total dissolved Solids that are not volatile under ignition, and often can be takento represent the non-organic component of the Total Dissolved Solids (although somemineral salts can also be volatilized).


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Figure 3.1: Map showing the location and industrial groups of over 200 food proces-sors in Central Valley who discharge effluent to land and are currently regulated by theRegional Water Quality Control Board. There are over 300 additional processors cur-rently discharging without official regulation. It is believed that land discharge practiceshave impacted ground water quality at a majority of these sites [Central Valley Regional

Water Quality Control Board, 2006].


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Total Dissolved Solids = Volatile Dissolved Solids + Fixed Dissolved Solids (3.1)

When the organic component is low, then TDS and FDS are approximately equal.For reference, standard seawater has a salinity of 35,000 mg/l TDS. From here on out wewill refer to salinity in terms of FDS, and for the purpose of this study will not considerthe fractions of the individual component species.

3.1.2 Characteristics of Food Processing Waste Discharge

Rubin et al. [2007] characterized the waste streams and land discharge practices fromover 200 food processors with waste discharge permits, based on their monthly dataon effluent concentrations and volumes reported to the Central Valley Regional Water

Quality Control Board (CVRWQCB) from 2003 to 2005. Four food processing indus-tries: tomato canners, dairy processors (cheese and whey), wineries (and grape juice),and meat packers, were identified as having the largest impact both in terms of thevolume of waste, and in terms of overall economic output. Representative waste streamcharacteristics were developed for each of the these four industries. The characteristicsdeveloped assumed that the processors would discharge their waste water at the maxi-mum rates and applied over the largest areas allowed by their waste discharge permits.That is to say the characteristic waste streams represent worst-case scenarios for aprocessor operating in compliance with their permits. The range of values presentativeof these scenarios for each industry is given in Table 3.2.

3.1.3 Attenuation of Salinity in the Vadose Zone

Several key biogeochemical processes in the vadose zone alter the composition of thewaste water before it reaches the water table, including microbial degradation, cropnutrient uptake, evapotranspiration, mineral precipitation, and ion exchange [CaliforniaLeague of Food Processors, 2007]. These mechanisms are shown schematically in Figure3.2. The attenuation capacity of the vadose zone above the water table and salinitymass loadings at the water table were estimated based on the results from a seriesof numerical simulations performed using the process-based, multi-component reactiveflow and transport code MIN3P [Mayer et al., 2002]. Each simulation calculated theflow rate and concentration at the water table over time using a one-dimensional, verticalvadose zone column model with detailed biogeochemical interactions. To address the high

variability in site conditions and in the waste-stream characteristics, several scenarioswere evaluated by Miller et al. [2008] for each of the four major food industry groups. Theloading rates used in this study correspond to their Case 2. This scenario representslow soil moisture saturation conditions (40-50 percent saturation), a very high ratio of soilsaturated hydraulic conductivity to waste water application rate (Ksat/qwaste 10, 000),and a waste water composition high in FDS, total ammonia, and nitrate, while low inorganic carbon. This scenario was created to show the effects of aerobic conditionsthroughout the unsaturated zone, and provides a worst case scenario for nitrate loading


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Table 3.2: waste water characteristics (concentration ranges) of the four major food prComponent FDS Organic C,

as BODAmmonium,

as TKNNitrate

(mg/l) (mg O2/l) (mg N/l)

Wineries and grapeprocessors

824300 426200 8.4200 0.153

Tomato canner 4304300 1704400 3.1520 nd2.4

Dairy Processors nd4800 5705700 1.4140 6.880

Meat packers 5303300 181700 22800 nd2.3

FDS, fixed dissolved solids; BOD, biochemical oxygen demand; TKN, totalKjehldahl nitrogen; nd, non-detect.Cheese producer data from literature [Danalewich et al., 1998]. All other dataobtained from self-reporting by individual food processors.


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Figure 3.2: Digram showing conceptual model for the transport of waste water appliedto land as irrigation [Miller et al., 2008].

to the aquifer. This scenario was also found to be most representative of conditionsfound in monitoring data in ground water wells down-gradient of waste discharge sitesin the study area [Miller et al., 2008]. The details of these vadose zone simulations aredocumented fully in Rubin et al. [2007] and Miller et al. [2008]. The results from thevadose zone model represent the transfer functions from waste loadings at the land

surface to the saturated zone ground water model.

3.2 Overview of Objectives and Methodology

The studies of Rubin et al. [2007] and Miller et al. [2008] analyzed and characterizedthe flow and transport of salts in soils underlying land application sites. An importantoutcome was the computation of the fluxes of salts at the water table under variousscenarios. This study extends their analysis to the saturated zone. Here we will analyzethe flow and transport of salts in the ground water aquifer underlying the land applicationsites. Specifically, we will analyze here the temporal and spatial evolution of the groundwater salinity plumes associated with land discharge operations.

We do not intend to explore the evolution of plumes next to each and every landapplication sites in the Central Valley. This is unattainable given the scarcity of data,on the one hand, and the large number of land application sites, on the other. Instead,we plan to assess the extent of ground water contamination under conditions typicalto the Central Valley. The analysis does not intend to replace the role of site-specificanalysis when evaluating specific sites. Rather, it intends to provide a realistic ensembleof scenarios that will then be combined to create a realistic set of expectations in termsof the extent of ground water contamination. Our scenarios intend to cover extreme con-


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ditions. They were designed as a combination of hydrologic conditions and the effluentschemical profiles that are expected to yield concentration values close to the bounds of

the concentrations. As such, the conditions and discharges constituting these worst casescenarios are not meant to be representative of actual conditions at the specific sites weconsider.

There is no guarantee that the absolute extreme values in concentrations or traveldistances from the discharge sites are captured. The range of concentrations and traveldistances expected in the field depend on local hydrologic conditions and on the scale ofthe measurement. Smaller measurement devices will yield increasingly larger concentra-tion values. The concentration values reported in our study should be viewed as averagesover the scale of the numerical grid elements (which is of the order of hundreds of meters),and considerable deviations to higher values at smaller scales. The large-scale averagesare in line with the flux-averaged concentrations, which represent the concentration of

the water pumped through wells.Although they are applied here under assumed scenarios, the methodologies devel-oped in this study could be applied using site-specific waste discharge data for individualprocessors and more detailed, site-specific hydrogeological data. The methodology couldalso be used to study other operations which impact ground water quality, such as thedisposal of biosolids, leaching from septic systems, and waste discharges from dairies andother large scale livestock operations.

To create a meaningful ensemble of scenarios, we chose to focus on a limited section ofthe Central Valley, namely the Lower San Joaquin River Basin (see 3.3). We refer to thisarea as the Representative Area (RA). This study area is relatively well-characterized interms of hydrological and hydrogeological conditions as it has been studied extensivelyby researchers from the United States Geological Survey (USGS) [Burow et al., 2004;Phillips et al., 2007]. This figure also identifies the locations of the food processorsmodeled in this study. An extended discussion of the food processors is provided inRubin et al. [2007]. Each of these facilities was studied through its periodic wastedischarge and ground water monitoring reports and the relevant documentation in itspermit for operating a land discharge site. The wide range of food-processing facilitiesin the study area (Figure 3.3) reflect the diversity of food processors operating in theCentral Valley.

Focusing on an RA was necessary since analyzing the entire Central Valley was unfea-sible given the limited budget and time available for this project. To be representative ofthe Central Valley and to allow for subsequent findings to be generalized, the RA neededto be large enough to cover a sufficient number of processors, processes and geologi-

cal conditions. It also needed to be large enough geographically to cover a wide rangeof conditions encountered in the Central Valley. A benefit of working with an RA isthat it allowed us to focus on an area whose hydrogeological conditions are much betterdocumented than in other sections of the Central Valley, thus eliminating the need tospeculate about conditions in p oorly documented regions. As will b e discussed in moredetail below, we developed a numerical model for analyzing flow and solute transportprocesses at the RA considered in this study. The model is subjected to loading of solutefluxes from a large number of food processing facilities located in the RA. These fluxes


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were computed in previous work [Rubin et al., 2007; Miller et al., 2008]. The studyarea was subjected to salinity loading at various locations (marked on Figure 3.3), from

facilities representing both small and large operations in terms of land discharge areasand flow rates. The salt loads used to simulate the land discharge are representative ofa variety of food processing industrial groups,namely, the four large-impact industrialgroups of wineries, tomato processors, meat processors and cheese makers. An extendeddiscussion of the rationale leading to salinity loads used is provided in Rubin et al. [2007];Miller et al. [2008], and is not repeated here for brevity. However, it is worth emphasiz-ing that the design loads used to simulate the salinity loading at the land dischargesites represent extreme conditions. We refer to these loads as our best and worst casescenarios, as was discussed in Rubin et al. [2007]; Miller et al. [2008]. An extreme designloadwould entail an extreme environmental impact to the ground water and would thusbe useful to identify the applicable limits and constraints. Conversely, when an extreme

design load fails to make a notable impact, this provides an indication that we shouldnot expect significant impacts for loads that are not at the extremes.

A simulation period of 30 years was chosen for modeling the transport of salt reach-ing the ground water table. A thirty year period was deemed sufficiently long to allowfor the environmental impacts to ground water to become noticeable, and at the sametime for land use changes to take place, such that the environmental impacts could pos-sibly translate into economic impacts, addressed in Sunding et al. [2007b]. Numericalsimulations over a longer period of time would require the consideration of effects suchas climate change, as well as consumer and technological trends, and all this could intro-duce significant uncertainty as well as a diversion of the discussion away from the issuesbeing addressed in this project. The 30 year simulation period is also consistent withthe planning horizon of the California State Water Plan, which extends to Year 2030.An important aspect to consider in this study is model uncertainty. Spatial viability ofhydrological conditions and hydraulic parameters, coupled with scarcity of data, makesour predictions subject to a large uncertainty. Although the study area is relativelywell documented (compared to other regions of the Central Valley), there is still largeuncertainty associated with the various model parameters that are needed. To capturethis uncertainty, we formulated our study in a probabilistic framework. We opted todo that by modeling dependent variables such as the ground water concentrations atvarious times and locations as random variables. This implies that they are modeledthrough their statistical moments such as means, variances and probability distributionfunctions. We will provide our results using, for example, quantitative assessment ofthe probability for the concentration to exceed a certain threshold value at a certain

time. An extended discussion on probabilistic methods is provided in Rubin [2003].Note that a statement such as the probability for the concentration to exceed a valueC0 is equal to 80% implies that 8 out of ten sites with similar conditions are expectedto show concentrations exceeding C0. As a way to model the effects of uncertainty inthe groundwater and contaminant transport parameters, a Monte Carlo was employedmethod, as will be described in 3.9. It is worth noting that the Monte Carlo methodwas only used for analysis of the saturated zone but not for the unsaturated zone. Rel-ative to the unsaturated zone, flow and transport processes in the saturated zone are


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less complex to model, and the needed parameters and their statistical distributions aremuch better documented in the literature; in this case a Monte Carlo analysis can be

performed relatively easily to yield meaningful results. This is unlike the unsaturatedzone, however, where knowledge of the many parameters needed for complex transportmodels is painfully scarce; in this case a Monte Carlo analysis is less useful. Anotherissue we wish to address in this introduction section is that of subsurface variability ofparameters such as the hydraulic conductivity. This subject has been explored exten-sively in recent years (see for example Kitanidis [1990] and Rubin [2003], which includesmany additional references). In general, one would like to be able to characterize theflow domain at the highest resolution possible, which is especially important for the caseof modeling point sources of contamination. Such an undertaking is very demandingin terms of field data acquisition and in terms of numerical modeling. Fortunately, theland application sites cover large areas that are much larger than the typical length

scales of heterogeneity of the relevant properties. In such situations, it is appropriateto use effective properties rather then resorting to detailed subsurface characterizationdata. Effective properties are useful for modeling the mean behavior, that is, the large-scale trends of the concentration field. While effective properties are not expected toproduce the small scale variability of the concentrationperhaps more importantlytheyare successful in their ability to estimate the flux-averaged concentration, which is theconcentration that is measurable at a pumping well.

3.3 Hydrogeological Setting

The California Central Valley is the largest ground water basin in the state, in terms ofboth total storage capacity and high utilization rate. Annual extraction rates are on theorder of 11 km3 per year ( 9,000,000 acre-feet), largely to support Californias agricultureindustry. The basin is recharged by direct precipitation and infiltration along the bedsof the San Joaquin and Sacramento river systems, whose discharge is primarily fromrainfall and snowmelt in the Sierra Nevada [Ferriz, 2001].

The San Joaquin Valley is more than 400 km long, ranging in width from 40 to 90km, and it makes up the southern two-thirds of the Central Valley. The San JoaquinValley is bordered on the east by the Sierra Nevada, which rises up to elevations of morethan 4,200 meters, and on the west by the Coast Range, which is of more moderateelevation. The San Joaquin Valley is made up of two sub-regions: the San Joaquin Basinin the north, which drains to the Sacramento-San Joaquin Delta; and at the southern

end an interior drainage called the Tulare Basin, named after a Pleistocene Lake thatoccupied most of the area [Page, 1986; Bertoldi, 1991]. The valley floor is underlainby an asymmetric structural trough filled with marine and continental sediments up to10 km thick, underlain by granitic bedrock of the Sierra Nevada batholith [Page, 1986;Bertoldi, 1991]. Figure 3.4 shows a generalized geologic section and view of the CentralValley as seen looking Northward along the axis of the valley.

Several large overlapping fluvial fans have formed along the eastern margin of theSan Joaquin Basin where their rivers exit the Sierra Nevada. Seven of these Eastern


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Figure 3.3: Aerial view of regional study area (red rectangle), and the food processingfacilities in the model area (red diamonds). The area of the numerical model is shown

by the black rectangle. Currently the model does not include the region to the west ofthe San Joaquin River.

Figure 3.4: Generalized geologic section and view of the Central Valley as seen lookingNorthwest along the axis of the valley (from Page, 1986).


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fansthe Mokelumne, Stanislaus, Tuolumne, Merced, San Joaquin, Kings and KaweahRiver fanshave drainage basins that connect to glaciated portions of the Sierra Nevada

(Figure 3.5). The fans in the northern portion are smaller due to the narrower width ofthe valley compared to the southern area [Weissmann et al., 2005]. Smaller fans haveformed along the western edge of the valley along the base of the Coast Range, referredto as the Western fans. Although no two fluvial fans are identical, they display similarsedimentary structures. They can generally be divided into three physiographic regions:the western fans, the eastern fans, and the basin deposits as illustrated in Figure 3.6[Burow et al., 2004]. The sediments on the western side are unconsolidated and haverelatively higher hydraulic conductivities. The eastern edge is more consolidated and ischaracterized by lower hydraulic conductivity. The Corcoran Clay layer underlies thewestern half of the regional study area and is present at depths of about 30 to 40 metersbelow ground surface. The Corcoran Clay layer is a member of the regionally extensive

lacustrine E-clay layer underlying a large portion of San Joaquin and Tulare basins.This pattern of repeating fans suggests that studying the transport of salinity overa single or a couple of such fans can provide insight about the transport of salinity atother locations, and that studying salinity transport over a limited section of the CentralValley seems like a reasonable means for obtaining general results.

3.3.1 Regional Hydrology

Under natural conditions prior to intensive agricultural development, ground water inthe Central Valley was primarily recharged in the upper parts of alluvial fans where thestreams enter the valley (Figure 3.7 and Figure 3.8). Ground water followed the dipof the underlying basement rock and flowed southwest towards the San Joaquin River,around which Artesian conditions existed [Page, 1986; Bertoldi, 1991].

Prior to agricultural development the Corcoran Clay is believed to have acted asan effective confining layer. Most of the ground water flowed laterally through theaquifer, with a small of amount of upward leakage through the confining layer. Theconsequent drilling of large diameter wells through the Corcoran Clay with perforationsabove and below the clay unit (see Figure 3.9 showing well types, locations, and screenedinterval depths), however, has diminished the effectiveness of the layer as a confined unit[Bertoldi, 1991], allowing the passage of water between the upper aquifers and the deeperunits. Reductions in the hydraulic head of the confined aquifer systems due to large scalepumping has resulted in a net downward movement of water through well casings. Insome places, the amount of water that flows downward through one large-diameter well

has been estimated to be equivalent to the natural leakage through the E-clay overan area of approximately 7 square miles. During the peak of the withdrawal season, thenet downward flow may be, on average, as much as 0.3 cubic foot per second per well[Planert et al., 1995].

Extensive ground water development in the valley (Figure 3.9), coupled with theincrease in effective vertical conductivity of the Corcoran Clay layer have greatly alteredthe regional flow patterns. The current flow regime is strongly affected by agriculturalpumping and irrigation, and these local effects lead to strong vertical gradients. The


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Figure 3.5: Map showing the structure of overlapping fan systems in the San JoaquinBasin. The study area is shown by the red dashed rectangle and includes the overlappingfans from the Stanislaus, Tuolumne, and Merced Rivers (from Weissmann et al. [2005]).


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Figure 3.6: The major sedimentary units in the Study Area (Source: Phillips et al.2007).


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Figure 3.7: Map view with conceptual diagram, of regional ground water flow (fromGronberg & Kratzer, 2006).

Figure 3.8: Cross-section with conceptual diagram of the regional ground water flowshowing regional flow and vertical components of flow due to agricultural pumping andrecharge(Source: Gronberg & Kratzer [2006]).


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induced gradients in the relatively high pumping zones (discussed in Section 3.4) mayoverwhelm the natural gradient by introducing a strong vertical gradient.

3.4 Water Recharge and Pumping

The surface recharge and ground water pumping rates were derived from data fromBurow et al. [2004]. Recharge includes water infiltration from irrigation and precipita-tion. It also includes leakage from reservoirs based on estimates provided in Phillipset al. [2007]. Irrigation rates were estimated based on crop type and land use data.Sixty percent of recharge is from irrigation and forty percent is from precipitation. Ofthe total irrigation, sixty percent is from surface water deliveries and the rest from pump-ing. This information is important for calculations of the chemical composition of therecharge water, which will be discussed in the next section.

Pumping includes municipal and agricultural wells. Pumping rates were determinedin Burow et al. [2004], based on data provided by water districts in the study area and byestimates determined from irrigation demands. Domestic wells make a relatively smallcontribution to the total pumping rates and were ignored, following the recommendationsof Burow et al. [2004].

Recharge and pumpage estimates were developed for irrigation districts, which werefurther broken down into 64 subregions, shown by the various regions in Figures 3.10and 3.11. Figure 3.10 shows a map of the spatially variable recharge applied at the watertable in the model. Lighter colors correspond to greater recharge, darker colors to less.Figure 3.11 shows a map of the estimated pumping per unit area,or pumpage. Lightercolors correspond to more greater pumping per area, darker colors to less. While this

map does not identify depths of the well screens interval, but this data is implementedin the model.

3.5 Numerical ground water Flow Model

This section provides an overview of the numerical model constructed for the regionalstudy area shown in Figure 3.3. The numerical model follows closely the principles andconceptual models employed in Burow et al. [2004] and Phillips et al. [2007], and usesinformation obtained directly from the USGS numerical models input files. This sectiondiscusses the numerical models spatial discretization, boundary conditions, sources andsinks, and the hydrogeologic parameters.

The model is three-dimensional, to allow for modeling the effects of vertical gradients.It is a steady-state model based on information from water-year 2000 (October 1, 1999 September 30, 2000) when the ground-water system was in a quasi-steady-state condition[Burow et al., 2004; Phillips et al., 2007]. Variables such as irrigation, precipitation andpumping rates were computed on a monthly basis, and were then averaged to yield annualrates which were assumed to be constant over time. We are using MODFLOW-2000[Harbaugh et al., 2000], a program that solves the three-dimensional ground water flowequation using a finite-difference numerical method, in combination with GMS (ground


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Figure 3.9: Well types and locations. Irrigation and municipal wells account for thegreatest volume of pumping. The median screened depth interval for Irrigation wells is51 74 m below land surface, for municipal wells it is between 59-75m, and for domesticwells it is between 44-47 m [Burow et al., 2004].


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Figure 3.10: Recharge map. Lighter colors correspond to greater recharge per unit area,darker colors to less. (Source: Phillips et al. [2007]).


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Figure 3.11: Pumpage map. Lighter colors correspond to more greater pumping per unitarea, darker colors to less. (Source: Phillips et al. [2007]).


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water Modeling System), which provides pre/post-processing capabilities and integrationwith GIS layers.

The steady-state strategy was chosen mainly for computational efficiency, and due tothe difficulty in obtaining sufficiently detailed data. The steady-state modeling strategyis an approximation to a flow regime that is in fact transient in nature. The potentialconsequences of making this approximation are as follows.

Increased recharge due to temporarily reduced pumping rates (or increased infiltra-tion rates) could raise the water table and reduce ground water contaminant concentra-tions (and vice versa). Our model provides an annually averaged concentration. Anotherimportant effect to consider is the potential for transient reversals of gradients at thelocal scale. The induced changes in the flow direction due to transients can, under somecircumstances, enhance mixing of contaminants. These reversals can lead to increasesin the area affected by contaminants, but they also lead to dilution and hence reduc-

tion in the concentration due to the larger volume of ground water that mixes with thecontaminants.

3.5.1 Ground Water Flow Equation

MODFLOW [Harbaugh et al., 2000] solves the following partial-differential equationdescribing transient ground water flow in a three-dimensional, heterogeneous, anisotropicmedium, in which the axes of the hydraulic conductivity tensor are aligned with themodel grid coordinate system:

x

Kxx

h

x

+

y

Kyy

h

y

+

z

Kzz

h

z

+ W = Ss

h

t(3.2)

where, x,y, and z are principal coordinates of the grid system, Kxx,Kyy, and Kzz arethe diagonal components of the hydraulic conductivity tensor [LT1], h is the hydraulichead [L], W is a volumetric flux per unit volume of aquifer, representing sources andsinks of water [T1], Ss is the specific storage coefficient of the porous material [L

1],and t is time [T]. Additional assumptions include constant and uniform fluid (water)density, viscosity, and temperature.

MODFLOW solves Equation 3.2 using the finite-difference method in which thegroundwater flow system is divided into a grid of cells. For each cell, there is a sin-gle point, called a node, at which they hydraulic head is calculated. The finite-differenceequation method used is documented in McDonald & Harbaugh [1988].

3.5.2 Spatial Discretization

The spatial discretization of the model was chosen to align with the USGS numericalground water model being developed for the study area (Phillips et al., 2007). Figure3.12 and 3.13 provide an areal view and a vertical cross-section view of the numericalgrid. The lateral dimensions of the grid area are 61.2054.8 kilometers. In plan view, themodel area was discretized into a grid of 153137 blocks with the individual grid blockdimensions of 400 meters by 400 meters. This block size is approximately the size of the


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Figure 3.12: 3-D view showing the active portion of the numerical model grid (verticalexaggeration = 30). The Corcoran Clay layer is shown in blue, unconsolidated sedi-ments in red and consolidated sediments in green. The elevations of the top of the first

layer are derived from the USGS digital National Elevation Model data set [USGS, 1999].

smallest land discharge area, which is important because it allows us to model accuratelythe loading of the discharge. In the vertical direction the model area was discretized intofive layers, generally of increasing thickness with depth, thus allowing greater resolutionat the depths near the water table. The layer thickeness were defined by combining layersfrom the 16-layer model of Phillips et al. [2007], resulting in a coarser vertical resolution.The Corcoran clay layer (see Figure 3.12 and Figure 3.13) is modeled as a distinct layerbecause of the large conductivity contrasts with the adjacent layers. The region of thenumerical grid to the west of the San Joaquin River was not modeled, so these grid

blocks were set as inactive. The elevation of the top layer is taken by mapping from theUSGS digital elevation model [USGS, 1999] to the grid. The total thickness of the modelranges between 220 and 430 meters, as shown in a representative cross-section in Figure3.13. With the exception of the Corcoran Clay layer whose thickness is constrained bywell logs [Page, 1986], the thickness of the layers increases from top to bottom.

The orientation of the model layers follows the dip angle of the sediments. The modelaxes are generally aligned with the geologic structures of the valley to allow modeling ofthe hydraulic conductivity and dispersivity as diagonal tensors.


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Figure 3.13: An East-West cross-section showing the five layers of the numerical grid.The cells representing the Corcoran clay are shown in blue. The clay layer pinches outroughly midway through the model area. Vertical exaggeration is 30.

3.5.3 Boundary Conditions

Boundary conditions are assigned for the lateral boundaries of our study area as well as atthe water table, as shown in Figure 3.14. The easternmost edge of the model at the baseof the Sierra foothills was defined as a no-flow boundary. This is based on the assumptionthat ground water flow from the foothills is negligible when compared to the flow throughthe other boundaries. The northern and southern edges were modeled as general-headboundaries using the MODFLOW General Head Boundary package [Harbaugh et al.,2000]. This boundary condition allows for flux into or out of the model by defining aconstant head at a known distance from the model b oundary. The western edge of themodel along the San Joaquin River was also modeled using the general-head boundarypackage. This allows for pumping induced cross-flow from under the river. Figure 3.14

shows a map of the lateral boundary conditions.The bottom of the aquifer is set at depths determined by the USGS that represent

topographic variability and the general dip of the Corcoran Clay and which is assumedto be deep enough to avoid any undesirable modeling effects on the flow regime [Phillipset al., 2007].

The water table was modeled as a flux boundary, based on the spatial distributionof recharge shown in Figure 3.10. Following the findings of Phillips et al. [2007], therecharge rate for all sub-regions shown Figure 3.10 had to be reduced by 10 percent inorder to achieve numerical convergence in the flow model.

Pumping WellsPumping wells were modeled using the MODFLOW Well Package [Harbaugh et al., 2000].The locations and pumping rates of the wells are based on the USGS model [Phillipset al., 2007], as shown in Figure 3.15 and Figure 3.16. Due to the large number of wellsconsidered in this study, no grid refinement was carried out around pumping wells. Ifwell locations were not known, then wells were evenly distributed within a sub-regionand pumping rates defined to add up to total estimated pumpage for the sub-region, asdescribed in Phillips et al. [2007].


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Figure 3.14: Lateral boundary conditions and included surface water features.


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Figure 3.15: Map showing location of pumping wells (blue circles) in the numerical model(base map from Phillips et al., 2007).

To approximate the depths of the screened intervals the pumping rates were onlyassigned to the layers of the model that most closely matched the screened intervals.The current model has only 5 layers (a decision made in order to facilitate the MonteCarlo analysis) as compared to the 16 layers in the USGS model, so the depth resolutionof the screened intervals is limited by the layer thicknesses.

Evapotranspiration

Evapotranspiration (ET) was simulated using the MODFLOW Evapotranspiration Pack-age Harbaugh et al. [2000]. The evapotranspiration package models ET with a maxi-mum rate of ET0 at the land surface, decreasing linearly to zero at extinction depth.The USGS value of ET0 = 0.043 m/day was used and is in line with the annual averagedetermined from data from the California Irrigation Management Information System(CIMIS) website for the water-year 2000 [California Dept. of Water Resources, 2007],


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Figure 3.16: Three dimensional view of the pumping well locations in the model. Theyellow circles are located in the center of each grid cell defined as a pumping well. Verticalexaggeration is 30.

ET0 = 0.0039 m/day. The extinction depth of 2.1 meters was also used based on thevalue used in the USGS model [Phillips et al., 2007].

Ground Water - Surface Water Interactions

Leakage from the three reservoirs along the eastern edge of the model was simulated byapplying additional recharge based on estimated leakage rates from the reservoirs. Theriver/ground water interactions were modeled in the same fashion as in the USGS model.The San Joaquin River and the lower reaches of its tributaries are generally taken asbeing gaining reaches, where the ground water table is above the river bottom, whereasthe upper reaches of the tributaries have been found to be under losing conditions,

with the water table below the river bottom [Jones and Stokes Associates & MussetterEngineering Inc, 2002; Corporation, 2002; Phillips et al., 2007], although this can varylocally and seasonally in some areas. Gaining reaches were modeled with General HeadBoundary conditions. The prescribed heads were based on river stage measurements,linearly interpolated between gaging stations, and the river bottom conductances weretaken from the USGS model [Phillips et al., 2007]. The losing reaches of the rivers (inthe upslope regions) were modeled by applying recharge over the losing reaches (0.005m/day). The locations of the different surface water zones are shown in Figure 3.14.


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Lithologic Subregion KH[m/day]

KG[m/day]

KA[m/day]

Khor/Kvert

Western Area (aboveCorcoran Clay)

19 40 84 300

Western Area (belowCorcoran Clay)

12 25 54 300

Eastern Area (entirethickness)

111 24 50 300

Corcoran Clay 1.3 103 1.3 103 1.3 103 1

Table 3.3: Average values of the hydraulic conductivity calculated using the harmonic(KH), geometric (KG) and arithmetic (KA) means for the four lithologic regions shown inFigures 3.18 and 3.19, as well as the ratio of horizontal to vertical hydraulic conductivities(Khor/Kvert). (Check new wording.)

Phillips et al. [2007] provide histograms showing the distribution of their calibratedhydraulic conductivities values for all the lithologic sub-regions in the model except theCorcoran clay, which they assumed to be of uniform and isotropic conductivity. Thecalibrated value from Phillips et al. [2007] of 1.3103 m/day) was used. This is aboutthree orders of magnitude larger than the conductivity values determined from core-scalesamples of the Corcoran Clay [Page, 1977], most likely due to enhanced conductivitybecause of a large number of wells drilled through and screened across the clay layer,and also possibly due to fracturing [Williamson et al., 1989; Phillips et al., 2007].

These data were used to compute effective conductivity tensors for each of the four

lithological subregions. As stated earlier, the Batchelor bounds for the effective conduc-tivity are defined by the harmonic and arithmetic averages of the conductivities, withthe geometric mean lying somewhere next to the middle of this range. Log-normal dis-tributions were fit to each of the conductivity histograms, and the harmonic, geometric,and arithmetic mean of the log of the conductivity were computed for each zone andused to assign a mean value to each subregion in the current model, using equation 5.8from Rubin [2003]. A variance was also determined for each zone. These statistics willbe used to develop different conductivity realizations for Monte Carlo simulations. Table3.3 below provides the arithmetic, geometric, and harmonic means of the four lithologicregions, as well as the ratio of horizontal to vertical hydraulic conductivities.

3.6 Results of Flow Model

Figure 3.22 shows a contour map of the water table elevations computed by the model forthe case where for each lithologic region Keff = KG. Figure 3.20 shows a contour mapgenerated from water level observations from over 500 wells for Spring 2000 obtainedfrom the Department of Water Resources online data repository [DWR, 2006]. Figure3.15 identifies the locations of these observed water surface elevations. In general, themodel captures the general features and trends of the observed water elevations, although


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not perfectly. The local ground water depression under the city of Modesto, for example,is not well captured, and while the depression in the southwestern corner of the model is

captured, the computed heads are slighly higher than the observed heads. Figure 3.23 isa scatter plot of the observed and computed water table elevations. Perfect agreementbetween the observed and computed heads would result in the points falling along astraight line of unit slope. The match between observed and computed values is notperfect, but the general trend is captured. It appears that in general the computedheads are higher than the the Spring 2000 observations.

The model error can be quantified by the average error, e, and the root mean squareerror (RMSE):

e =1

n

ni=1

(hobs,i hcomp,i) (3.3)

RMSE=

1n

ni=1

(hobs,i hcomp,i)2 (3.4)

where hobs,i and hcomp,i are the ith observed and computed hydraulic head pair,

respectively, and n is the total number of head observations.

The RMSEis a measure of the error magnitude, whereas the average error indicatesif the computed heads are overall higher (e > 0) or lower (e < 0) than the observedvalues. The RMSEwas 3.8 meters, and the average error was +1.3 meters, with n=526,indicating that in general the model is predicting water levels that are slightly higherthan the observed values.

Figure 3.24 shows a difference map between computed water table elevations and in-terpolated observed water table elevations. Red corresponds to areas where the computedwater table elevations are higher than the observed; and blue to where the computedvalues are lower than the observed. The color intensity scale is cut off at 5 meters. Thelocation of the observations points are shown by the small circles. The map shows thatthe largest model over-predictions of head generally occur in the upland eastern areaof the model and in the area below the city of Modesto. The Monte Carlo simulations(that will be discussed in more detail in Section 3.9) in which different values of Kef fwere assigned to the different regions, showed that that the standard deviation of thehead (over all generated random realizations) was largest in the up-slope Eastern Region.This indicated that the hydraulic heads in this region of the model are the most sensitive

to variations in the value of Keff.It is not unexpected

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