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ONLINE SUPPLEMENT TO :

Relationship of Salt Marsh Vegetation Zonation to

Spatial Patterns in Soil Moisture, Salinity and Topography

Kevan B. Moffett1*, David A. Robinson2 , and Steven M. Gorelick1

1 Dept. of Environmental Earth System Science, Stanford University, Stanford, California 94305,

USA

2 Centre for Ecology & Hydrology, Environment Centre Wales, Bangor, Gwynedd LL57 2UW,

UK

Contents:

I. Complete vegetation maps

II. EMI signal depth calculation

III. ECa uncertainty determination

IV. Soil sampling results and ECa relationship to edaphic conditions

V. Archie’s Law parameter estimations: f, φ, and σs

VI. Cross-correlation of geographic and edaphic metrics

VII. Literature cited in supplement

* Corresponding author. E-mail: moffett@stanford.edu. Fax: 650-498-5099.

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II. EMI signal depth calculation 1

Many portable EMI devices, like the DUALEM-1S used in this study, include two pairs 2

of electrodes in orthogonal horizontal and vertical configurations. Due to the difference in the 3

directionality of the induced and received magnetic fields, these two configurations result in 4

different signal penetration depths. In terrestrial environments, 70% of the apparent bulk soil 5

electrical conductivity signal measured with the electrodes in the horizontal configuration (ECaH) 6

by the DUALEM-1S typically originates above sH = 0.76 m depth; 70% of the vertical signal 7

(ECaV) originates above sV = 1.59 m (Abdu and Robinson 2007). In the highly conductive salt 8

marsh environment a “skin effect” due to soil currents travelling more rapidly and with less 9

resistance through highly conductive near-surface sediments reduces the effective signal depths 10

(Callegary and others 2007). We fit logarithmic curves to the data of Callegary and others (2007, 11

after correcting their reversal of their vertical and horizontal data labels) and extrapolated their 12

calculations of the skin effect to the range of bulk conductivities measured in the salt marsh 13

(Eqns. S1 and S2). The asymptotic logarithmic shape of the data by Callegary and others (2007) 14

gave us good confidence that the large extrapolation required was reasonable. The units of these 15

regressions are: depth in m and conductivity in mS/m. 16

( ) 757.0ln049.0 +−= HH ECas (R2 = 0.96) (Eqn. S1) 17

( ) 599.1ln148.0 +−= VV ECas (R2 = 0.98) (Eqn. S2) 18

Using these regressions and ECaH = 1364 mS/m and ECaV = 1453 mS/m, the medians of the 19

temperature-corrected ECa data from this study (dry and wet conditions pooled), we calculate 20

effective support depths of 0-0.40 m (sH, shallow) and 0-0.52 m (sV, deep). Only the shallow 21

data, more relevant to the root zone (of comparable depth), was presented in the paper. 22

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III. ECa uncertainty determination 24

The stated accuracy of the Electromagnetic Induction (EMI) geophysical instrument used 25

in this study (DUALEM-1S, Dualem, Inc., Milton, ON, Canada) was 0.001 dS/m. Despite this 26

very high accuracy, we took the conservative approach of determining the in situ measurement 27

uncertainty based on two types of successive field measurements of ECa obtained at multiple test 28

locations. Based on these two types of tests, described presently, we estimated the measurement 29

uncertainty for this study as 0.01 dS/m. 30

The first method we used to estimate ECa measurement uncertainty was to stand in one 31

location and collect a streaming series of 1479 ECa measurements, one measurement every one 32

to two seconds. The 95% confidence level for the mean of these measurements (horizontal 33

electrode configuration) was 0.01 dS/m. 34

The second method we used to roughly confirm this ECa measurement uncertainty was to 35

identify, from the locations of all the measurement points within each survey, pairs of points 36

nearly-overlapping measurement points created either by temporary pauses during the streaming 37

survey or by the intersection of survey traverses in different directions. To identify such pairs, 38

the distances between all points within a given survey were calculated and filtered for points 39

within 15 cm. Among a total of 5859 data pairs (2024 from dry conditions, 3835 from wet 40

conditions), the median ECa difference within the pairs was 0.015 dS/m. The result changed 41

little for a small increase in the distance filter: a distance filter of 20 cm resulted in a total of 42

85336 pairs (11910 from dry conditions, 73426 from wet conditions), and a median difference of 43

0.016 dS/m. Although this value was higher than the uncertainty determined using the first 44

method, we also award it lower overall confidence because the points in question were not 45

identical, but rather separated somewhat in space, time, and potentially in instrument orientation. 46

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Given this additional uncertainty, we felt this second method sufficiently confirmed the 47

magnitude of the uncertainty estimated by the first method to proceed with our analysis. 48

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IV. Soil sampling results and ECa relationship to edaphic conditions 50

Salt marsh soil properties were determined from 23 cores from 0-30 cm depth (Table S1). 51

Empirical relationships have shown ECa to increase with increasing clay content (Domsch and 52

Giebel 2004; Rhoades and others 1999), increasing soil water content (Malicki and Walczak 53

1999; Rhoades and others 1999), or increasing solution conductivity (Malicki and Walczak 1999, 54

Rhoades and others 1999; Sam and Ridd 1998), though not for as high values of these properties 55

as occur in salt marshes. To establish the specific relationships between ECa and edaphic 56

variables for the salt marsh environment, we conducted linear regression analyses (Figure S2). 57

The relationship between temperature-corrected (Reedy and Scanlon 2003) ECa and soil paste 58

extract conductivity (ECe) for our data was essentially an extrapolation of that reported by 59

Rhoades and others (1999) for a glacial till. The pore water conductivity (ECw) values of our 60

marsh were higher than those reported previously in the EMI literature (Friedman 2005; Rhoades 61

and others 1999) but spanned a smaller range compared to our ECa range, resulting in a 62

shallower ECw/ECa regression slope. Although soil paste extract conductivity (ECe) represents 63

the total soluble soil salinity, related to the osmotic potential in the soil, the dissolved salt 64

incident upon a plant root membrane as part of the transpiration stream is better represented by 65

the pore water solute conductivity (ECw); we defined an interstitial electrical conductivity index 66

(IECI) as the difference between these two parameters to represent the excess soil salinity above 67

the background pore water level. Variance in ECa was more closely related to variance in IECI 68

than to variance in ECw (Table S2), highlighting the importance of considering the effects of 69

interstitial salinity in clayey salt marsh soils. 70

The relationship between ECa and volumetric water content (θ) for our data was roughly 71

a linear extrapolation of that reported by Malicki and others (1999) for a silty loam with high 72

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solution conductivity (11.7 dS/m). The relationship of ECa to clay content for our data was 73

unique: the clay contents of our soils were beyond the range of those used by Domsch and 74

Giebel (2004) to compare ECa and clay fraction; our soils were likely more similar to the 75

gleysols excluded from their regression analysis than to the soils they included. The fit of the 76

linear relationship between ECa and clay fraction was strongly influenced by a few data points 77

associated with the margin of the marsh closest to the bay, which unsurprisingly contained 78

smaller clay fractions. In summary, variability in ECa values mostly reflected variability in soil 79

water content (θ) and in the total salt content of the soil (ECe). These results establish the overall 80

utility of ECa data as a proxy for these zonation-relevant edaphic variables and confirm the 81

applicability of EMI methods to the salt marsh environment. 82

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Table S1. Root Zone Soil Core and Pore Water Characteristics

Characteristic Statistic

Average Std. Dev.

Wet core bulk density (g/cm3)* 1.33 0.19

Core water fraction (g H20 / g total)* 0.60 0.09

Volumetric water content [θ] (cm3 H2O/cm3 total)* 0.83 0.15

Sand fraction* 2.64% 6.95%

Silt fraction* 35.54% 5.04%

Clay fraction* 61.82% 9.44%

Textural ClasS8 Clay

Paste extract electrical conductivity [ECe] (dS/m)* 68.94 15.01

Pore water electrical conductivity [ECw] (dS/m)** 57.2 7.0

Interstitial electrical conductivity index [IECI] (dS/m)** 14.25 12.43

* N (0-30 cm depth soil cores) = 23, ** N (ECw @ -30 cm depth) = 17

85 Table S2. ECa - Soil Properties Correlation Matrix

ECa ECe ECw† IECI† θ Clay Silt Sand

ECa 1

ECe 0.674*** 1

ECw† 0.526* 0.596* 1

IECI† 0.675** 0.891*** 0.167 1

θ 0.437* 0.413 0.286 0.400 1

Clay 0.509* 0.513* 0.631* 0.341 0.346 1

Silt -0.548* -0.644** -0.313 -0.627* -0.358 -0.695*** 1

Sand -0.293 -0.230 -0.632* -0.020 -0.210 -0.854*** 0.219 1

N = 23, † N = 17for ECw samples * significant at p < 0.05, ** significant at p < 0.005, *** significant at p < 0.0005

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Table S3. Parameters of Linear Relationships between ECa and Salt Marsh Soil Properties (Illustrated in Figure S2), with 95% Confidence Intervals

Dependent Variable Slope Intercept

R2 Lower 95% Value Upper 95% Lower 95% Value Upper 95%

ECe (dS/m) 2.11 4.21 6.30 -24.15 7.04 38.23 0.45

IECI (dS/m) 1.28 3.23 5.17 -60.72 -32.27 -3.82 0.46

ECw (dS/m) 0.16 1.42 2.69 18.12 36.66 55.20 0.28

θ (fraction) 0.00 0.03 0.05 0.04 0.42 0.80 0.19

Clay (fraction) 0.00 0.02 0.04 0.10 0.32 0.55 0.26

87 88

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Figure S2. Relationships between apparent bulk soil electrical conductivity (ECa) and related 90

soil properties for salt marsh sediment cores 0-30 cm deep and pore water samples from -30 cm. 91

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V. Archie’s Law parameter estimations: f, φ, and σs 93

Archie’s Law is an empirical model that relates temperature-corrected apparent bulk soil 94

electrical conductivity data (ECa) to the pore water fluid conductivity (ECw), a formation factor 95

(f = 1/F = φm/a, with porosity φ), soil saturation (S), and the mineral surface conductivity (σs) 96

(Kirsch 2006). 97

sn

m

sn S

aECwSfECwECa σϕσ +⋅⋅=+⋅⋅= (Eqn. S3) 98

Surface conductivity is important in soils with large clay fractions, such as our salt marsh, but 99

had not been tabulated for saline, clay, salt marsh soils. The parameters σs and f (and φ) are 100

difficult to measure but can be estimated in multiple ways. We compare three methods here and 101

test the uncertainty in the salt marsh clay soil parameter estimates. 102

Method 1 103

Rhoades and others (1989) proposed an empirical relationship between σs (dS/m) and the 104

volumetric clay content (VCC) of a soil. 105

021.031.2 −⋅= VCCsσ (Eqn. S4) 106

We calculated σs for each of 23 cores taken from 30-60 cm depth based on their clay mass 107

fraction and a clay bulk density of 1.05 g/cm3. We used cores from this depth interval because 108

they were below the water table and so were saturated, permitting the assignment of S = 1. Using 109

these values of σs, a = 1, m = 2, n = 2, and S = 1, we solved Eqn. S3 for φ for each core. 110

( ) ( )2SECwECaa s ⋅−⋅= σϕ (Eqn. S5) 111

The resulting averages were σs = 1.595 ± 0.406 dS/m (µ ± 1σ) and φ = 0.417 ± 0.036, which are 112

reasonable for clay soils. The corresponding average formation factor value was f = 0.175 ± 113

0.030. Use of a different m value yielded no difference in the saturation changes estimated by 114

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the differential EMI calculation because the values of σs and f used in evaluating equation E1 115

were not affected by (insensitive to) the value of m. 116

Method 2 117

Pore water samples were collected from below the water table (60 cm depth) at 16 118

locations concurrently with coring and ECa measurements. A simple linear regression between 119

the ECw (dS/m) of these samples and the coincident temperature-corrected ECa (dS/m) yielded 120

an equation in the form of Eqn. S3 (for S = 1). The slope of the regression was f = 0.223 (φ = 121

0.472 for f=ϕ ) with intercept σs = 2.479 dS/m. These parameter estimates were uncertain 122

because single point-samples of pore water were related to ECa measurements of an overlying 123

volume in each case, inherently assuming sediment and solution homogeneity. The simplicity of 124

the method enhanced its general utility, however. 125

Method 3 126

Sen and others (1988) proposed a complex formulation of Archie’s Law describing ECa (S/m) 127

for clay-bearing sandstones in terms of ECw (S/m), the soil cation exchange capacity (CEC, 128

meq/g), grain density (ρg = 2.65 g/ml), a formation factor (f = 1/F = φm, with porosity φ), and 129

empirical parameters m, A = 1.93*m, C = 0.7, and E ~ 0. [Note that our study uses standard units 130

of dS/m and cmolc/kg; we provide the conversion from the units used by Sen and others (1988) 131

where applicable.] 132

QEQCECw

QAECwECa m ⋅+

⋅+⋅+⋅⋅= 1ϕ (Eqn. S6a) 133

( ) ϕϕρ −⋅⋅= 1gCECQ (Eqn. S6b) 134

The parameter Q represents volume-normalized CEC. For unsaturated conditions, one would 135

replace Q with Q/S and f with nSf ⋅ (Kirsch 2006). A parameter for mineral surface 136

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conductivity (σs), analogous to that in equation E1, can be algebraically extracted from Eqn. S6b 137

(for EQ = 0). 138

⋅+⋅⋅⋅=

QCECw

QAfECwsσ (Eqn. S7) 139

Because φ, m, and CEC were unknown, there was one excess degree of freedom in Eqns. S6a 140

and S6b. We addressed this uncertainty by parameter estimation and sensitivity analysis. 141

Because measurements of CEC for the salt marsh soils were unavailable, we solved 142

equations S7 and S6b for CEC using the values for f, φ, and σs found in the above empirical 143

regression and an observed average value of ECw = 5.285 S/m (52.85 dS/m) for the marsh pore 144

water. We tested the sensitivity of the result to multiple m values (Table S4). The CEC estimates 145

were very close to the 11.14 cmolc/kg CEC of Stege Marsh, a San Francisco Bay salt marsh 146

similar to our study area and located 53 km to the north (Córdova-Kreylos and Scow 2007). 147

Table S4. Sensitivity of CEC Estimates to m Values

Parameter Test 1 Test 2 f 0.223 same φ 0.472 same σs 0.2479 S/m (2.479 dS/m) same

ECw 5.285 S/m (52.85 dS/m) same

m 2 2.34 CEC 0.1011 meq/g (10.11 cmolc/kg) 0.1068 meq/g (10.68 cmolc/kg)

148

With a CEC estimate, Eqn. S6 can be solved in terms of an φ polynomial and the 149

resulting value of φ used to calculate f and σs. 150

For gCECAa ρ⋅⋅= and gCECCc ρ⋅⋅= : 151

( ) ( ) ( )( ) ( )ECwECacECaECwECacacacECw mm ⋅−−⋅⋅++⋅+−−⋅= + ϕϕϕ 10 (Eqn. S8) 152

We tested the sensitivity of this method to uncertainty in CEC and m (Table S5) using the 153

ECa and ECw data for the same subset of cores as above. Halving CEC from 0.1 meq/g to 0.05 154

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meq/g yielded a change in the average saturation difference (∆S) calculated by the Q-DEMI 155

methodology of 0.6%, that is, only 10% of the 6.2% average saturation change estimated using 156

CEC = 0.1 meq/g. Changing m from 2 to 2.34 yielded parameter estimates that were unrealistic 157

for clay sediments, so we elected to use m = 2 in the remaining calculations. 158

Table S5. Sensitivity of φ, f, and to CEC and m Values

Parameter Test 1 Test 2 Test 3

ECa and ECw from core data same same

ρg 2.65 g/ml

(2605 kg/m3) same same

m 2 2 2.34

CEC 0.10 meq/g

(10 cmolc/kg) 0.05 meq/g

(5 cmolc/kg) 0.05 meq/g

(5 cmolc/kg)

φ (µ ± 1σ) 0.396 ± 0.037 0.422 ± 0.035 0.017 ± 0.086

f (µ ± 1σ) 0.158 ± 0.028 0.179 ± 0.028 0.006 ± 0.029

σs (µ ± 1σ) 0.2307 ± 0.0124 S/m (2.307 ± 0.124 dS/m)

0.1211 ± 0.0042 S/m (1.211 ± 0.042 dS/m)

0.0041 ± 0.0212 S/m (0.041 ± 0.212 dS/m)

159

Summary 160

The three methods, described above, for estimating the parameters in Archie’s Law are 161

compared in Table S6 (Method 3 using CEC = 0.1 meq/ml and m = 2). The results are 162

comparable from all three methods. This study used the parameters from Method 2 because the 163

simplicity of Method 2 lends it the greatest potential to be widely applied in future studies. 164

Table S6. Comparison of Archie’s Law Parameter Estimates

Parameter

Method 1 (using VCC)

Method 2 (linear regression)

Method 3 (using CEC)

average st. dev. average st. dev

φ 0.417 0.036 0.472 -- 0.396 0.037

f 0.175 0.030 0.223 r2 = 0.20

0.158 0.028

σs (dS/m) 1.595 0.406 2.479 2.307 0.124

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VI. Cross-correlation of geographic and edaphic metrics 166

One aspect of the study was the assessment of the spatial correlation between each of the 167

six metrics used to represent abiotic salt marsh ecosystem structures. Testing the correlation 168

between the metrics for all 2256 marsh locations yielded the correlation structure of Table S7. 169

Some of these correlation coefficients, when pertinent to the main scientific discussion, were 170

included in the paper; all are provided here for reference. 171

Notably, elevation was poorly correlated with any of the other metrics. ECa values were 172

slightly more strongly correlated with the distance to a main tidal channel than to the nearest 173

channel of any size. The magnitude and spatial distribution of ECa values from dry and wet 174

conditions were similar (strongly and significantly correlated). The difference in the sign of the 175

correlation between ∆ECa and dry or wet ECa values was due to the dual nature of the edaphic 176

change between these two conditions, involving both water and salt dynamics in the root zone 177

(see Q-DEMI methodology description in the paper). 178

Table S7. Geographic and Edaphic Metrics’ Correlation Matrix (N = 2256)

Elevation Dist. to main

channel Dist. to any

channel ECa dry ECa wet ∆ECa

Elevation 1

Dist. to main channel

-0.068* 1

Dist. to any channel

0.185** 0.428** 1

ECa dry -0.004 0.537** 0.440** 1

ECa wet 0.061* 0.405** 0.357** 0.831*** 1

∆ECa -0.118** 0.217** 0.134** 0.272** -0.309** 1

* significant at p < 0.005, ** significant at p < 0.0005, *** significant at p << 0.0005

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VII. Literature cited in supplement 180

Abdu H, Robinson DA, Jones SB. 2007. Comparing bulk soil electrical conductivity 181

determination using the DUALEM-1S and EM38-DD electromagnetic induction instruments. 182

Soil Science Society of America Journal 71: 189-196. 183

Callegary JB, Ferré TPA, Groom RW. 2007. Vertical spatial sensitivity and exploration depth of 184

low-induction-number electromagnetic-induction instruments. Vadose Zone Journal 6: 158-185

167. 186

Córdova-Kreylos AL, Scow KM. 2007. Effects of ciprofloxacin on salt marsh sediment 187

microbial communities. International Society for Microbial Ecology Journal 1: 585-595. 188

Domsch H, Giebel A. 2004. Estimation of soil textural features from soil electrical conductivity 189

recorded using the EM38. Precision Agriculture 5: 389-409. 190

Friedman SP. 2005. Soil properties influencing apparent electrical conductivity: a review. 191

Computers and Electronics in Agriculture 46: 45-47. 192

Kirsch R. 2006. Petrophysical properties of permeable and low-permeable rocks. Kirsch R, 193

editor. Groundwater Geophysics. New York: Springer. 194

Malicki MA, Walczak RT. 1999. Evaluating soil salinity status from bulk electrical conductivity 195

and permittivity. European Journal of Soil Science 50: 505-514. 196

Reedy RC, Scanlon BR. 2003. Soil water content monitoring using electromagnetic induction. 197

Journal of Geotechnical and Geoenvironmental Engineering 129: 1028-1039. 198

Rhoades JD, Chanduvi F, Lesch S. 1999. Soil salinity assessment: methods and interpretation of 199

electrical conductivity measurements. Irrigation and Drainage Paper 57, FAO, Rome, Italy. 200

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Rhoades JD, Manteghi NA, Shouse PJ, Alves WJ. 1989. Soil electrical conductivity and soil 201

salinity: new formulations and calibrations. Soil Science Society of America Journal 53: 433-202

439. 203

Sam R, Ridd P. 1998. Spatial variations of groundwater salinity in a mangrove-salt flat system, 204

Cocoa Creek, Australia. Mangroves and Salt Marshes 2: 121-132. 205

Sen PN, Goode PA, Sibbit A. 1988. Electrical conduction in clay bearing sandstones at low and 206

high salinities. Journal of Applied Physics 63: 4832-4840. 207