mapping soil salinity in 3‐dimensions using an em38 and...

Mapping soil salinity in 3-dimensions using an EM38 andEM4Soil inversion modelling at the reconnaissance scale incentral Morocco

H. DAKAK1, J. HUANG

2, A. ZOUAHRI1, A. DOUAIK

1 & J. TRIANTAFILIS2

1National Institute of Agricultural Research, Avenue de la Victoire, Rabat, Morocco, and 2School of Biological, Earth and

Environmental Sciences, UNSW Sydney, Kensington, NSW 2052, Australia

Abstract

Large areas of Morocco require irrigation and although good quality water is available in dams,

farmers augment river water with poorer quality ground water, resulting in salt build-up without a

sufficient leaching fraction. Implementation of management plans requires baseline reconnaissance

maps of salinity. We developed a method to map the distribution of salinity profiles by establishing a

linear regression (LR) between calculated true electrical conductivity (r, mS/m) and electrical

conductivity of the saturated soil-paste extract (ECe, dS/m). Estimates of r were obtained by

inverting the apparent electrical conductivity (ECa, mS/m) collected from a 500-m grid survey using

an EM38. Spherical variograms were developed to interpolate ECa data onto a 100 m grid using

residual maximum likelihood. Inversion was carried out on kriged ECa data using a quasi-3d model

(EM4Soil software), selecting the cumulative function (CF) forward modelling and S2 inversion

algorithm with a damping factor of 3.0. Using a ‘leave-one-out cross-validation’ (LOOCV), of one in

12 of the calibration sites, the use of the q-3d model yielded a high accuracy (RMSE = 0.42 dS/m),

small bias (ME = �0.02 dS/m) and Lin’s concordance (0.91). Slightly worse results were obtained

using individual LR established at each depth increment overall (i.e. RMSE = 0.45 dS/m; ME = 0.00

dS/m; Lin’s = 0.89) with the raw EM38 ECa. Inversion required a single LR (ECe = 0.679 +0.041 9 r), enabling efficiencies in estimating ECe at any depth across the irrigation district. Final

maps of ECe, along with information on water used for irrigation (ECw) and the characterization of

properties of the two main soil types, enabled better understanding of causes of secondary soil

salinity. The approach can be applied to problematic saline areas with saline water tables.

Keywords: Soil mapping, electrical conductivity, soil salinity, baseline data, EM inversion modelling

Introduction

Morocco is located in one of the driest regions of the world

with most of the land classified as arid (~85%). Of the

9 million hectares of arable land, irrigation is used to

supplement the meagre rainfall across 10% of this area. There

are nine irrigation districts, of which Tadla is the largest and

covers over 120 000 ha. As for many irrigated areas, the

quality and availability of water are becoming increasingly

problematic. Although water in storage dams has little

salinity, its quality diminishes downstream (Badraoui et al.,

2002). In addition, farmers augment river water with poorer

quality groundwater (Badraoui et al., 2002). Both factors are

beginning to limit sustainable soil management as salts build-

up in the absence of a sufficient leaching fraction. In addition,

the Intergovernmental Panel on Climate Change (IPCC)

climate models suggest annual rainfall will decrease over the

next few decades (MATUHE, 2001).

Given water authorities are struggling to distribute and

provide potable water for domestic and industrial use,

knowledge about the current status of soil salinity is necessary

to monitor the impacts of applying degraded water to arable

land. Collecting the necessary soil baseline information across

large irrigated areas and throughout the root-zone is costly

and time-consuming (Odeh et al., 1998). However, proximal

sensing electromagnetic (EM) induction instruments have

been used to augment limited laboratory measurements of

extracts of a saturated soil paste (i.e. ECe – dS/m). There is a

growing body of literature showing increasing research inCorrespondence: J. Triantafilis. E-mail: [email protected]

Received September 2016; accepted after revision July 2017

© 2017 British Society of Soil Science 1

Soil Use and Management doi: 10.1111/sum.12370

SoilUseandManagement

http://orcid.org/0000-0003-1561-0242

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http://orcid.org/0000-0003-1561-0242

developing countries aimed at using such an approach to

measure and map soil salinity. This includes Indonesia

(McLeod et al., 2010), Turkey (Cetin et al., 2012), Uzbekistan

(Akramkhanov et al., 2014) and China (Yao & Yang, 2010;

Guo et al., 2013) where in coastal tidelands susceptibility to

shallow water tables and saline soil conditions after

reclamation requires knowledge for monitoring and

management. In Africa, similar work has also been

undertaken including South Africa (Johnston et al., 1997),

Senegal (Ceuppens & Wopereis, 1999; Barbi�ero et al., 2001)

and Tunisia (Arag€u�es et al., 2011).

Most of the studies have been conducted at the field level. In

addition, as described by Amezketa & del Valle de Lersundi

(2008), the first step is the development of a linear regression

between the measured apparent electrical conductivity (ECa)

and average ECe (i.e. for 0–1.0 m depth). A similar approach

was used by Triantafilis & Buchanan (2010) to map subsurface

saline material (6–12 m) across an irrigated district. The

problem with these approaches is that managing the salinity

requires knowledge of whether the salt distribution is normal

(i.e. increasing salinity with depth), uniform (e.g. nonsaline

[<2 dS/m] or moderately saline [4–8 dS/m]) or inverted (i.e.

moderately saline topsoil and slightly saline subsoil). To

resolve this, various authors have developed linear regression

(LR) models at different depths (e.g. Yao & Yang, 2010).

However, this approach requires different models for mapping

soil ECe at different depths, and it is not able to predict soil

ECe at depths where soil samples are not collected. It can also

introduce uncertainty at different depths due to the use of

different input data (Huang et al., 2015a).

Another approach is first to invert ECa into estimates of true

electrical conductivity (r, mS/m) at depths of interest; whereby

r can be directly related to ECe at the same depths. Hendrickx

et al. (2002) used Tikhonov regularization to invert EM38 ECa

at different depths and to model salinity at individual sites. Li

et al. (2013) used a similar 1-d inversion at each site prior to

mapping ECe. To calibrate r and ECe using a single equation,

Goff et al. (2014) and Huang et al. (2015b) established

calibrations by inverting ECa from a single-frequency and

multiple-coil DUALEM-421 to predict salinity across

estuarine–alluvial and semi-arid gilgai clay plains, respectively.

More recently, using a quasi-3d inversion model, Davies et al.

(2015) showed how saline wedges in a swash-zone (i.e. upper

part of the beach between backbeach and surf zone) can be

discerned with Zare et al. (2015) and Huang et al. (2017a)

mapping ECe in 3-d across, respectively, irrigated and dryland

fields affected by salinity. The aim of our study was to map the

variability of ECe across an irrigated alluvial plain in the Tadla

irrigation district of central Morocco. We approached this by

producing a reconnaissance set of EM38 ECa acquired across

an area of 2000 ha. Using a quasi-3d algorithm we established

a single LR equation between r and ECe and mapped ECe for

any depth within the electromagnetic conductivity image

(EMCI) generated. We compared accuracy, bias and Lin’s

concordance with that of LR relationships established between

EM38 ECa and ECe at three depth increments (i.e. 0–0.3, 0.3–0.6 and 0.6–0.9 m). We evaluated the model uncertainty for the

inversion-based approach, and identified where improvements

in mapping might be achieved. We have discussed the results in

terms of the causes of the minor soil salinization relative to

various soil properties and briefly the implications in terms of

appropriate soil management to mitigate the problem.

Materials and methods

Study area

The study area, located ~260 km south-east of Rabat in the

Tadla irrigation district (Figure 1), consisted of two

subdistricts straddling the Oum Rabia River, including the

Beni Amir to the north and Beni Moussa to the south. The

study area was located in the northern part of the Ben Amir in

a semi-arid zone, with an annual rainfall ~250 mm, varying

between a minimum of 140 and maximum of 400 mm. The

potential evaporation was large (1800 mm). Daily temperature

(18 °C annual average) varied between a maximum of 40 °Cin August (summer) and a minimum of 3 °C in January

(winter). The study area covered 2066 hectares with the

predominant crops being wheat (40%), alfalfa (34%), olive

groves (15%), vegetables (7%) and sugar beet (4%).

The soil was predominantly of two different types

(Figure 2a). The largest area was an Isohumic (Chernozem,

FAO 2006) soil, containing medium brown subtropical soils,

saline and saline-sodic brown subtropical soils and medium

chestnut soils. This soil class, characterized by clayey and

clayey-silt textures, is deep to moderately deep with

limestone present throughout. The other class was the

Fersialitic (Chromic Luvisol, FAO 2006). A small part of the

area was characterized by calcimagnesic soil, which includes

brown limestones and ‘rendziniform’ soils. These highly

calcareous soils are generally shallow (i.e. 0.2–0.4 m).

There are two sources of water for irrigation: the primary

source of water originates from the El-Hansali dam (storage

capacity 800 million m3) and reaches the study area by canals

from the river Oum Rabia. Water quality is fair (Dakak, 2015)

with an average electrical conductivity (ECw) of 1.9 dS/m)

having slight to moderate (0.7–3.0 dS/m) degree of restriction

(Ayers & Westcot, 1985). Irrigation is gravity fed. Groundwater

also augments river water. In the northern area, ECw varies

from 0.73 to 3.8 dS/m and between 0.64 and 4.87 dS/m in the

southern half. Values of ECw >3.0 dS/m may be problematic.

EM38 data collection and interpolation

The ECa data were acquired using an EM38 instrument

(Geonics Limited, Mississauga, ON, Canada). The instrument

operates at a low frequency (14.8 kHz). The transmitter (Tx) is

located at one end with the receiver located at the other end and

© 2017 British Society of Soil Science, Soil Use and Management

2 H. Dakak et al.

1 m away. Depth of exploration (DOE) of ECa by EM38 is a

function of coil spacing (s) and array orientation. When placed

on the ground, DOE for an EM38 is 0.59s and 1.69s for

measurements made in the vertical (EM38v) and horizontal

(EM38h) positions, respectively. DOE, determined as the depth

of an array, accumulates 70% of its total sensitivity when

operating at low induction numbers (LIN) (McNeill, 1980).

The EM38 survey involved traversing the area in a

pseudo-regular grid, where sites were spaced 500 9 500 m

apart. The EM38 was placed on the ground. A total of 92

ECa measurement locations were visited (Figure 2b) with the

horizontal and vertical modes and with the data

geo-referenced in latitude and longitude using a Garmin

Dakota 20 Global Positioning System (GPS) (Garmin Ltd.,

Kansas, USA), with an accuracy of <10 m.

To understand the spatial variability of ECa across the

whole area, we fitted two variograms for EM38h and EM38v

using the residual maximum-likelihood (REML) method.

This was because when the sample size is small, REML has

been reported as a more robust approach than the

traditional ‘method-of-moments’ approach (Lark & Cullis,

2004; Lark et al., 2006; Kerry & Oliver, 2007). The fitting

was carried out using the ‘likfit’ function of the geoR

package (Ribeiro & Diggle, 2001) in R software (R Core

Team, 2016).

Once the variograms were calculated, EM38h and EM38v

ECa values were kriged onto a 100 m grid across the study

area using ordinary kriging with a maximum neighbour of 5

points. This was carried out using the gstat package

(Pebesma, 2004) available in R software. We used 5 points

as the maximum neighbour for kriging because we only had

92 ECa measurements and we did not want to over smooth

the ECa data.

Soil sampling and laboratory analysis

To calibrate the calculated estimates of ECa, a total of 36

samples were collected from 12 locations. To cover the spatial

extent, the sampling points were taken on an ~1 km grid in

the east-west orientation and on transects spaced ~2 km apart

from north to south (Figure 2c). In addition, to account for

the maximum and minimum ECa and the range, sampling

7°10’W

32°40’N

32°30’N

32°20’N

32°10’N

32°40’N

32°30’N

32°20’N

32°10’N

7°W 6°50’W 6°40’W 6°30’W 6°20’W 6°10’W

7°10’W 7°W 6°50’W 6°40’W 6°30’W 6°20’W 6°10’W

Situation map of the study area

Study zone

Tadla irrigated perimeter

Figure 1 Location of the study area in Beni Amir section of the Tadla Irrigation District in central Morocco.


3D soil salinity mapping in Morocco 3

Northing (m)217 000

N

(a)

214 000

212 000

210 000

208 000

Northing (m)217 000

214 000

212 000

210 000

208 000

370 000 372 000

Easting (m) Easting (m)

375 000 370 000 372 000 375 000

370 000

Boundary ofstudy area


Fersialitic

Undefined

Complexes

Isohumic

Calcimagnesic


EM38 surveylocation

500 m

372 000


375 000 370 000 372 000 375 000

Elevation (m)

<420

<425

<430

<435

≥435

N

N N

90

72

6084

53 46

31 10

2115

Soil samplinglocation

28

49

500 m

500 m 500 m

(b)

(c) (d)

Figure 2 (a) Map of soil types in the Ben Amir section of the Tadla Irrigation District and spatial distributions of the (b) EM38 survey

locations, (c) soil sampling points and (d) contour plot of elevation (m).


4 H. Dakak et al.

points representative of every 10 percentile in the distribution

of ECa were selected.

At each of the 12 locations, soil samples were collected at

three depths, including the topsoil (0–0.3 m), subsurface

(0.3–0.6 m) and subsoil (0.6–0.9 m). The samples were

oven-dried and ground to pass through a 2-mm sieve. A

saturated soil-paste extract was prepared, and the electrical

conductivity of the soil-paste extract (ECe) was measured

using an Orion (Model 162) conductivity instrument

(Thermo Electron Corporation, Beverly, MA, USA).

Quasi-3d inversion of EM38 data

The EM4Soil V2.02 software package (EMTOMO, 2014)

was used to invert the EM38 ECa data. EM4Soil is able to

invert 1-dimensional (1d), 2d and 3d ECa data. The quasi-3d

(q-3d) inversion was used. It assumes that below each

measured location, 1-dimensional variation of calculated soil

conductivity (r, mS/m) is constrained by variation under

neighbouring locations.

The inversion algorithm is based on Occam’s

regularization (Sasaki, 1989), with the best q-3d model of r,compared to measured soil ECe. This was achieved by

varying parameters used by EM4Soil, including; choice of

forward modelling (cumulative function [CF] and full

solution [FS]), choice of inversion algorithm (S1 or S2) and

the damping factor (k) (Triantafilis & Monteiro Santos,

2013; Triantafilis et al., 2013a,b).

With respect to the inversion algorithm to be used, there is a

choice of S1 and S2; whereby S2 (see Sasaki, 2001) has more

constraints than S1 (see Sasaki, 1989) and therefore would

produce smoother results than S1. Under low induction number

conditions, the CF model is based on the ECa cumulative

response and is used to convert depth-profile r to ECa (McNeill,

1980). FS considers the Maxwell equations of the propagation

of EM fields (Kaufman & Keller, 1983) and is not limited to the

low induction number condition (i.e. conductivity <100 mS/m).

As a result the FS can improve models calculated from ECa data

acquired over highly conductive soil.

Here, the quasi-3d inversion was carried out on the 92 ECa

measurements and on the kriged ECa locations across the

whole study area. A three-layer model with depths of layers of

0.3, 0.6 and 0.9 m and initial r of 100 mS/m was used to

estimate r, with k set from 0.07, 0.3, 0.6 and at 0.6 increments

thereafter to a maximum value of 3.0. In this study, 20

iterations were used to determine the best inversion

parameters, based on our previous experience. Generally, too

few iterations produce inversion results with abrupt changes in

r with depth while too many iterations are time-consuming.

A comparison was made between estimated r and ECe at

all depths considering the coefficient of determination (R2).

The set of parameters (CF or FS, S1 or S2 and k), whichgave the largest R2, was used to establish a linear regression

(LR) between r and ECe. Note that the process of varying

inversion parameters is equivalent to the parameters

optimization or tuning in machine learning algorithms such

as the artificial neural network (Taghizadeh-Mehrjardi et al.,

2015), support vector machine (Ji et al., 2014) and ensemble

Kalman filter (Huang et al., 2017b).

Validation and comparison with LR established using ECa

Once the optimal inversion parameters were determined, we

used the corresponding set of r generated by inverting 92 ECa

points to produce a linear regression (LR) model to predict

ECe at different depths. The LR model was also applied to the

set of r generated by inverting the kriged ECa points to obtain

the predicted ECe across the whole study area and on a 100 m

grid. To determine the robustness of the LR, a cross-

validation procedure was conducted. Here, a single sample

point was removed, and a calibration was developed from the

remaining points (i.e. 11). This leave-one-out cross-validation

(LOOCV) procedure was carried out 12 times with each one of

the sampling points excluded in turn.

This approach was compared with a traditional LR

established directly between ECe and the raw ECa data following

Yao & Yang (2010). Here, we fitted three LR models for

predicting ECe at each depth, including the topsoil (0–0.3 m),

subsurface (0.3–0.6 m) and subsoil (0.6–0.9 m), but using only

the most highly correlated EM38 ECa. The same LOOCV

procedure was used to evaluate the LR model predictions.

The accuracy of the predictions was assessed using the root

mean square error (RMSE) of prediction; whereby the closer

the value to zero the more accurate the prediction. Prediction

bias was calculated using the mean error (ME). Again the

closer to zero then the less biased is the prediction. The Lin’s

concordance correlation coefficient (qc) was calculated to

determine how close the model was to the 1:1 relationship for

the various depth increments (i.e. 0–0.3, 0.3–0.6 m and 0.6–0.9 m). We chose this because the Lin’s coefficient (Lin, 1989)

measures agreement between two variables (here the measured

and predicted ECe) and was calculated:

qc ¼2SXY

S2X þ S2Y þ ð�X � �YÞ2 ð1Þ

where �X and �Y are the means for the two variables, S2X and

S2Y are the corresponding variances, and SXY is the

covariance between the two variables:

SXY ¼ 1n

Xn

i�1Xi � �Xð Þ ðYi � �YÞ ð2Þ

Evaluation of the model uncertainty

To evaluate the model uncertainty for the inversion-based

approach, we used a LOOCV approach. That was, for each

of the 12 iterations of LOOCV process introduced in the



previous section, we predicted soil ECe onto the 100 m grid

using the LR model established with the 11 soil samples.

This process was carried out 12 times. The standard

deviation of the predicted soil ECe was calculated as the

model uncertainty.

Results and discussion

Preliminary data analysis: soil properties

Table 1 shows the average soil properties of the soil samples

obtained from the calibration sites. It is evident that the

Fersialitic profiles in the north had slightly alkaline pH

(~7.5) with increasing bulk density and what appeared to be

a texture change at a depth of 0.3 m; whereby clay increased

from the topsoil (28.1%) to subsurface (57.6%). By

comparison, the Isohumic profiles in the south had a more

alkaline pH (~8.45), which was a function of the large

amounts of calcium carbonate present, particularly in the

subsoil (i.e. 25.35%). The clay was uniform throughout

subsoil (33.41%) clay almost half of that present in the

north.

Table 2 shows that the mean EM38h ECa (87.6 mS/m)

was only slightly smaller than the average EM38v (88.4 mS/

m). This was also the case with the maximum values (i.e.

130.1 and 132.2 mS/m, respectively) with the minimum

values reversed (39.2 and 33.1 mS/m, respectively). Given

that the median for the EM38h (89.3 mS/m) and EM38v

(91.5 mS/m) was equivalent to the mean, we conclude the

EM38h and EM38v data were normally distributed. This

was reinforced by the small skewness in the EM38h (�0.4)

and EM38v (�0.8).

Table 2 also shows the summary statistics for the ECa

measured at the 12 calibration points shown in Figure 2c.

The mean EM38h (82.9 mS/m) was slightly larger than

EM38v (81.2 mS/m). This was also the case with the

maximum (i.e. 130.1 and 113.1 mS/m, respectively), with the

minimum values showing the EM38h (41.1 mS/m) was

slightly larger compared with the EM38v (33.1 mS/m). The

median values were similar with the mean with the EM38h

(81.9 mS/m), while the median of EM38v (84.3 mS/m) was

slightly larger than the mean. Again the data were

approximately normally distributed. We surmise there was a

good agreement between the sample sites selected for

calibration and the survey data.

Table 3a shows the mean ECe of the topsoil (0–0.3 m)

samples was largest (4.2 dS/m), with the largest individual

ECe (6.5 dS/m) measured in the topsoil. The salinity in the

topsoil was on average nominally of moderate (4–8 dS/m)

salinity but the largest value suggested that it did not

approach concentrations where germination might be

problematic in legumes (i.e. 2 dS/m) and some wheat

cultivars (i.e. 6 dS/m). The average ECe decreased ever so

slightly with depth with the smallest being the subsoil

(4.0 dS/m) where the minimum ECe (1.6 dS/m) was also

recorded. At these levels, which would be considered

nonsaline (<2 dS/m), most arable crops including legumes

would not be susceptible to any perceptible problems with

salinity. The decreasing ECe with depth was consistent with

the slightly larger EM38h compared with EM38v measured

at the calibration points, because DOEs were 0.75 and 1.5 m

for EM38h and EM38v, respectively.

Table 1 Soil properties for the two soil types at three depths

Soil property

Soil type

Fertialitic Isohumic

Soil depth (m) 0–0.3 0.3–0.6 0.6–0.9 0–0.3 0.3–0.6 0.6–0.9

Bulk density

(g/cm3)

1.3 1.43 1.76 1.2 1.37 1.46

Sand content

(%)

36.3 30.7 26.8 22.7 22.7 21.2

Silt content

(%)

35.6 26.9 27.9 48.3 46.82 45.4

Clay content

(%)

28.1 57.6 54.7 29.1 30.5 33.4

pH 7.6 7.4 7.6 8.4 8.4 8.5

Organic

carbon (%)

2.2 1.4 0.4 2.3 1.3 0.3

Calcium

carbonates

(%)

1.6 1.5 1.6 16.5 21.1 25.4

N-NO3

content (g/t)

22.6 15.7 11.9 19.4 16.9 14.0

Field capacity

(m3/m3)

14.8 12.2 10.9 14.1 15.0 16.6

Wilting

point (m3/m3)

18.7 19.6 20.7 22.9 23.5 21.7

Table 2 Summary statistics of apparent electrical conductivity (ECa

– mS/m) measured by an EM38 for the entire survey area and at the

12 calibration sites

N Min Mean Median Max Skewness CV

Survey data

EM38h

(mS/m)

92 39.2 87.6 89.3 130.1 �0.4 23.2%

EM38v

(mS/m)

92 33.1 88.4 91.5 132.2 �0.8 23.8%

Calibration data

EM38h

(mS/m)

12 41.1 82.9 81.9 130.1 0.22 27.0%

EM38v

(mS/m)

12 33.1 81.2 84.3 113.1 �0.9 25.6%


6 H. Dakak et al.

The constant trend in ECe with depth indicated on

average the salinity profiles was uniform at the time of

sampling. Whereas the levels of salinity varied from

nonsaline, to slightly saline and moderately saline, the

uniformity suggested accumulation of salts was occurring as

a function of irrigation with poorer quality water and that

the leaching fraction was insufficient to facilitate the removal

of the salts added.

Table 3b also shows the correlation coefficient (r) between

soil ECe and the EM38 ECa. In general, all ECa

measurements were statistically correlated with soil ECe

(P < 0.001). The most statistically significant (P < 0.001) and

largest correlation was between the EM38h ECa and topsoil

(r = 0.92) and subsurface (r = 0.93) ECe. The EM38v ECa

was statistically significant (P < 0.0001) with subsoil (0.91)

ECe.

Preliminary data analysis: ancillary data

A contour plot of elevation shows the land surface was

higher (i.e. >435 m) at the northern end with elevation

generally decreasing gradually towards the south (<420 m)

(Figure 2d). The spatial distribution of kriged EM38h shows

that small (<60 mS/m) and intermediate-small values (60–75 mS/m) of ECa characterized the southern end (Figure 3a).

At a few sites, ECa was similarly intermediate–small in the

central areas, where ECa was generally intermediate (70–90 mS/m). Intermediate–large (90–105 mS/m) and large

(>105 mS/m) values of ECa were generally found along the

western flank and north-eastern corner of the study area.

Spatial distribution of kriged EM38v shows that patterns of

ECa values were similar to those for EM38h (Figure 3b).

The spherical model parameters of the variograms, fitted

for EM38h and EM38v (Table 4), were selected according to

the log-likelihood values (�399.7 and �404.8, respectively).

The EM38h had a smaller nugget:sill ratio (74.3%)

compared with EM38v (84.7%). Within the range 1627 and

2000 m for EM38h and EM38v, respectively, the spatial

dependence values for horizontal and vertical configurations

were not strong and more ECa data need to be collected to

characterize the short-scale variation.

Figure 3c,d show the kriging variance for EM38h and

EM38v, respectively. The patterns were similar. Here, large

error occurred in the central and north-eastern margins of

the study area, where no samples were collected. However,

EM38h had smaller kriging variance (460–490 mS2/m2)

compared with EM38v (380–440 mS2/m2). This was

consistent with the larger nugget:sill ratio of EM38v.

Determination of optimal quasi-3d inversion parameters

The coefficient of determination (R2) between the calculated

true electrical conductivity (r) from the q-3d inversion and

ECe at all depths is shown in Figure 4a and when different

sets of inversion parameters were considered. This includes

forward modelling (i.e. CF and FS) and inversion (i.e. S1

and S2) algorithms versus k.The S2 performs better than the S1 given the consistently

larger R2 produced. In addition, the CF for the S2 algorithm

produces slightly larger R2 than S1. The best R2 (0.87) was

achieved when the S2 was used in concert with the CF and

when the k value of 3.0. As an increase in k after 3.0 did not

significantly increase R2 (data not shown), we therefore

selected these parameters to estimate r from a linear

regression relationship between r and ECe and to map the

latter across the field at various 0.3 m depth increments.

Model fitting was conducted using the bivariate fit tool

(JMP software, SAS Institute Inc., 2014). Figure 4b shows

the fitted lines and confidence curves (confidence limits for

the mean value) and individual confidence curves (confidence

limits for individual predicted values) between ECe and r.The significant level (a) was set to 0.05. As shown in

Table 5, the regression equation was ECe = 0.679 +0.041 9 r. Given the large coefficient of determination

Table 3 (a) Summary statistics of measured electrical conductivity of

the saturated soil-paste extract (ECe – dS/m) at the calibration sites,

(b) correlation coefficient (r) between soil ECe and the measured

apparent electrical conductivity (ECa) of each of the EM38 arrays

and (c) the calibration linear regression models with their coefficient

of determination (R2) used to predict ECe from the EM38 which was

most highly correlated with ECe and for each depth increment.

Note: *, P < 0.05; **, P < 0.001; ***, P < 0.0001

(a)

N Min Mean Median Max Skewness CV

ECe

(0–0.3 m)

12 2.3 4.2 4.3 6.5 0.4 26.7%

ECe

(0.3–0.6 m)

12 2.1 4.1 4.1 6.2 0.2 24.5%

ECe

(0.6–0.9 m)

12 1.6 4.0 4.2 5.6 �0.8 26.7%

(b)

r EM38h EM38v

ECe (0–0.3 m) 0.92*** 0.78*

ECe (0.3–0.6 m) 0.93*** 0.84**

ECe (0.6–0.9 m) 0.90** 0.91**

(c)

Equation R2

ECe (0–0.3 m) 0.4680 + 0.0447 9 EM38h 0.85***

ECe (0.3–0.6 m) 0.7153 + 0.0404 9 EM38h 0.87***

ECe (0.6–0.9 m) 0.3360 + 0.0449 9 EM38v 0.82**



Northing (m)217 000

N

214 000

212 000

210 000

208 000

500 m

370 000 372 000


375 000 370 000 372 000 375 000

Northing (m)217 000

214 000

212 000

210 000

208 000

370 000 372 000


375 000 370 000 372 000 375 000

N

N N

EM38hECa (mS/m)

<60

<75

<90

<105

≥105

EM38vECa (mS/m)

<60

<75

<90

<105

≥105

Kriging variance(mS/m)2

<460

<470

<480

<490

≥490

EM38v

Kriging variance(mS/m)2

<380

<400

<420

<440

≥440

EM38h

500 m

500 m 500 m

(a) (b)

(c) (d)

Figure 3 Contour plot of kriged apparent electrical conductivity (ECa, mS/m) collected using an EM38 in the (a) horizontal (EM38h) and

(b) vertical (EM38v) modes and the kriging variance (mS2s/m2) of (c) EM38h and (d) EM38v across the Ben Amir section of the Tadla

Irrigation District. Note: EM38 survey points were marked in black dots.


8 H. Dakak et al.

(i.e. R2 = 0.87), the use of r should yield good estimates of

ECe at all depths from this single equation.

Table 3c shows the summary statistics of the LR models

established between the raw EM38 ECa. It was evident that

the best coefficient of determination (R2 = 0.85) was

achieved for the topsoil (0–0.3 m) and using the EM38h.

This was also the case for the subsurface (0.3–0.6 m) ECe

where the correlation was a little stronger (R2 = 0.87).

Subsoil (0.6–0.9 m) ECe was best predicted using only the

EM38v ECa (R2 = 0.82), however.

Evaluation of soil salinity prediction

A leave-one-out cross-validation (LOOCV) approach was

applied on each calibration location. In the first instance, we

describe the results achieved using the q-3d calibration

approach and to predict ECe from r. Figure 4c shows that

predicted ECe at each location was in general accurate and

unbiased given the RMSE (0.42 dS/m) and small ME (-

0.02 dS/m), respectively. This was also reflected in the Lin’s

concordance (0.91), which was very large and which for the

most part showed excellent agreement between measured and

predicted ECe.

Figure 4d shows similar results from the LOOCV obtained

by establishing a LR relationship at each depth. The Lin’s

concordance was the same (0.89), RMSE higher (0.45 dS/m)

with predictions unbiased (0.00 dS/m) overall. One of the

differences between the methods was the q-3d modelling

approach better accounted for and predicted the largest

measured ECe and produced predictions with short ranges

where ECe was near the average (i.e. 4 dS/m).

In addition, the LR approach requires three models to be

established and cannot predict soil ECe at the depths below

0.75 m. This was not the case for the inversion approach as

it was designed to predict soil ECe at any depths within the

DOE of the EM38 (~1.5 m) without using any depth

functions for interpolation (Malone et al., 2009).

Nevertheless, the results achieved with the q-3d modelling

were comparable to recent investigations conducted at the

field level using more densely collected ECa data. For

example, at the field scale and in a highly saline area of

Bourke in northwest New South Wales, Australia, Zare

et al. (2015) achieved a larger Lin’s concordance (0.93)

between measured and predicted ECe; however, their q-3d

model was based on DUALEM-421 data collected along

transects spaced 50 m apart. Moghadas et al. (2016) carried

out an equivalent modelling approach but across a much

larger area with EM38 data across the Ardakan area of

central Iran. They achieved progressively smaller Lin’s

concordance with increasing depth from the topsoil (0.75) to

the subsurface (0.35). However, the reduced ability to predict

ECe was a function of the EM38 survey spacing with the

requirement to collect EM38 data on a closely spaced and

denser survey grid of <500 m.

Comparison between measured and predicted ECe profiles

To better understand the predicted ECe achieved using the q-

3d modelling approach and against the measured ECe,

Figure 5a shows the measured ECe for each of the calibration

sites with predicted ECe shown in Figure 5b. With respect to

sampling site 10, the measured ECe (2.3 dS/m) in the topsoil

was only slightly saline (2–4 dS/m) and decreased to

nonsaline levels in the subsurface (2.1 dS/m) and subsoil

(1.6 dS/m). In general, the predicted ECe at this site was

satisfactory for subsurface equivalent to measured ECe

(2.2 dS/m), with topsoil (2.7 dS/m) and subsoil (1.9 dS/m)

ECe slightly overestimated.

With respect to the slightly saline measured ECe profiles

(i.e. sites 15, 21, 49, 53 and 72) the predicted ECe was also

satisfactory. Issues arise in prediction where sites were

located near areas where ECa changes rapidly. This was the

case around site 53, where predicted subsoil ECe (4.3 dS/m)

was slightly saline, which was much greater than measured

(3.4 dS/m) ECe that was nonsaline. Figure 3b shows this

clearly and specifically where EM38v ECa increased from

intermediate (75–90 mS/m) to large (>105 mS/m) values over

a distance of <500 m either side of site 53. This was the scale

of the ECa surveying interval.

With regard to the moderately saline profiles (i.e. sites 28,

46, 60, 84 and 90), similarly good predictions were also

achieved. There was, however, an issue with underestimation

of topsoil ECe (3.9 dS/m) at site 90 which was predicted to

be slightly saline when it was moderately saline (4.6 dS/m).

Here, as with the predictions at site 53, the prediction error

was a function of site 90 being close to an area of rapid

change in ECa. This was evidenced in Figure 3b in the

northeast corner of the study area.

In terms of the most saline and inverted salinity profile of

site 31, the predicted ECe was generally satisfactorily

resolved in the topsoil and subsoil depths. However, the

measured subsurface ECe (6.2 dS/m) was slightly

under-predicted (5.7 dS/m) in terms of the salinity class.

Again, as with the other sites cited and for that matter most

Table 4 Summary statistics of the variograms fitted for apparent

electrical conductivity (ECa) data measured by the EM38 in the

horizontal (EM38h) and vertical (EM38v) modes using residual

maximum-likelihood method

Mode EM38h EM38v

Variogram model Spherical Spherical

Log-likelihood �399.7 �404.8

Nugget 302 375.4

Partial sill 104.6 68.0

Nugget/sill 74.3% 84.7%

Range (m) 1627 2000



sites where errors in salinity classification occurred, the

short-range spatial variation at less than the survey interval

of 500 m was problematic.

Another reason for the slight errors in prediction was a

function of the 100 m grid, which the ECa data needed to be

gridded onto to enable the q-3d inversion of the ECa data.

R2

0.90

0.88

0.86

0.84

0.82

0.800.07

Predicted ECe (dS/m) Predicted ECe (dS/m)

Calculated true electrical conductivity ( ) (mS/m)σ

Lin’s concordance = 0.91

RMSE = 0.45 dS/mME = 0.00 dS/mLin’s concordance = 0.89

ME = –0.02 dS/mRMSE = 0.42 dS/m

0.5 1.0 1.5 2.0 2.5 3.0

8Measured ECe (dS/m)

confidence curves fit

R 2 = 0.872confidence curves individual

fitted line

6

4

2

0

8

6

4

2

00 2 4 6 8 0 2 4 6 8

8

6

4

2

0

0 30 60 90 120 150

0.6 - 0.9 m

0.3 - 0.6 m0.0 - 0.3 m

0.6 - 0.9 m

Measured ECe (dS/m)

0.3 - 0.6 m0.0 - 0.3 m

0.6 - 0.9 m

Measured ECe (dS/m)

0.6 - 0.9 m: ECe = 0.336 + 0.045 × EM38v0.3 - 0.6 m: ECe = 0.715 + 0.040 × EM38h0.0 - 0.3 m: ECe = 0.468 + 0.045 × EM38h

0.3 - 0.6 m0.0 - 0.3 m

S1, FSS1, CF

S2, FS

λ

S2, CF

ECe = 0.679 + 0.041 × σ

ECe = 0.679 + 0.041 × σ

(a) (b)

(c) (d)

Figure 4 Plot of (a) coefficient of determination (R2) achieved between the electrical conductivity of the saturated soil-paste extract (ECe – dS/m)

and calculated true electrical conductivity (r, mS/m) generated by inverting EM38 ECa using EM4Soil quasi-3d (q-3d) inversion algorithm,

cumulative function (CF) and full solution (FS), inversion algorithm S1 or S2 versus damping factor (k), (b) measured ECe versus r when CF,

S2 were used with the k value of 3.0, and measured ECe versus predicted ECe generated by leave-one-out cross-validation at the calibration

points using (c) quasi-3d (q-3d) inversion model of the EM38 ECa (mS/m) and (d) linear regression of individual EM38 ECa at different depth

intervals.


10 H. Dakak et al.

In this regard, the collection of ECa data on a 100 m grid

would lead to less smoothing. This was not a problem with

the LR method, because the EM38 ECa data collected above

each calibration site was directly correlated with ECe at each

depth. To improve the results in q-3d modelling, we

recommend in future research that EM38 ECa data should

be collected at either 250 or 100 m apart or smaller, because

the gridded data would be less smoothed.

Interpreting ECe maps at the three depths

Figure 6 shows predicted ECe spatially distributed using the

relationship established between r and ECe with the q-3d

inversion. With respect to topsoil ECe, Figure 6a shows that

there were only a few isolated areas where soil ECe was

nonsaline (<2 dS/m). These occurred in the southern part of

the study area, associated with the sands of Isohumic soil

profiles in the lower landscape positions. Interestingly, ECe

gradually increased from slightly saline (2–4 dS/m) to

moderately saline (4–8 dS/m) in areas immediately to the

north and similarly characterized by Isohumic profiles. In

the areas to the north, soil became mostly slightly saline (2–4

dS/m) as characterised by Fersialitic profiles.

Figure 6b,c show the spatial distribution of predicted ECe

at depths of 0.3–0.6 and 0.6–0.9 m, respectively. For the

most part, the patterns in ECe distribution were equivalent.

We note, however, that the areas where predicted salinity in

subsurface and subsoil ECe was smaller in terms of being

moderately saline. This was particularly the case in the

contiguous area in the central southern part of the study

area characterized by the Isohumic profiles. Conversely, the

area to the north as characterized by the Fersialitic profiles

was predicted to have larger and moderately saline ECe (i.e.

>4 dS/m) in the subsoil in particular.

The reasons for the differences in ECe appear to be a

function of the ECw and the soil properties. In the south-

eastern half, the generally smaller ECe was most likely a

function of the uniformly siltier nature of the soil (~46%)

Table 5 Summary statistics of the linear regression model established between calculated true electrical conductivity (r) and measured electrical

conductivity of the saturated soil-paste extract (ECe)

Parameter estimates Estimate Standard error t Ratio Probability>|t| Coefficient of determination (R2)

Intercept 0.679 0.232 2.93 0.0060 0.87

r 0.041 0.003 15.23 <0.0001

Depth (m)

10 5321 7215 90604649

10 532172 15 9060 4649

Depth (m)

0(a)

0.3

0.6

0.90 1 2 3 4

2884

2884

Measured ECe (dS/m)

Predicted ECe (dS/m)

5 6

31

7 8

0 1 2 3 4 5 6 7 8

0

0.3

0.6

0.9

31(b)

Figure 5 Plot of (a) measured and (b)

predicted electrical conductivity of the

saturated soil-paste extract (ECe – dS/m)

with depth (m) at the soil sampling locations

generated using quasi-3d (q-3d) inversion

model of the EM38 ECa (mS/m), cumulative

function (CF) forward modelling and S2

inversion algorithm with a damping factor

(k) of 3.0.



and smaller bulk density (e.g. average subsoil = 1.46 g/cm3)

of the Isohumic profiles. This was despite the generally

larger ECw of ground water (i.e. 0.64 and 4.87 dS/m), which

in some cases seemed to produce moderately saline

conditions in the central and western parts of the area.

Conversely, in the areas associated with the Fersialitic

profiles to the north, whilst the ECw was slightly smaller

(0.73–3.8 dS/m) the larger subsurface (57.60%) and subsoil

(54.70%) clay and bulk density appeared to favour the

accumulation of more salts, particularly in the subsoil.

Overall, the maps of predicted ECe were generally in

accord with the measured ECe profiles (Figure 6a). The

unity of the results was therefore informative in terms of

soil use and management and as a function of the salinity

tolerance of the main agricultural crops used within the

Tadla irrigation district. In terms of olives (Olea sylvestris)

which are grown in 15% of the area, the ECe at current

levels is generally satisfactory given olives are moderately

tolerant; albeit they prefer conditions where ECe was

<4.5 dS/m.

With respect to wheat (T. turgidum L. var. durumDesf.),

which is commonly grown across 40% of the area, the levels

of ECe currently prevailing should not be overly problematic

given the threshold ECe is 5.9 dS/m (Francois et al., 1986).

This was because this was larger than most predicted topsoil

ECe; albeit that at site 31 and surrounds this may not be the

case given measured ECe (6.5 dS/m) exceeded this value

(Table 3a). However, this was not the case for alfalfa

(Medicagosativa L.), which is grown in 34% of the area and

usually in rotation with wheat. In this regard, the ECe

tolerance is 1/3 that of wheat and at 2 dS/m (Bower et al.,

1969; Bernstein & Francois, 1973) this value was exceeded

across most of the area and at all soil depths investigated.

This was therefore problematic given the role of alfalfa was

to provide carbon and nitrogen to the soil and for the

benefit of wheat cropping.

Evaluation of the model uncertainty

Figure 7 shows the standard deviation of predicted ECe at

different depths using the LOOCV approach. We note that

the model uncertainty illustrated by the standard deviation

was small (<1.2 9 10�8 dS/m). This was most likely due to

the limited soil samples (i.e. 12) used in the LOOCV

Northing (m)217 000

N

(a)

90

7260

84

46 49

31 28 10

1521

53

90

7260

84

46 49

31 28 10

1521

53

90

7260

84

46 49

31 28 10

1521

53

214 000

212 000

210 000

208 000

370 000

500 m

372 000 375 000

ECe (dS/m)<2

<3

<4

<5

≥5

ECe (dS/m)<2

<3

<4

<5

≥5

ECe (dS/m)<2

<3

<4

<5

≥5

370 000 372 000 375 000 370 000 372 000 375 000Easting (m) Easting (m) Easting (m)

500 m 500 m

N N

(b) (c)

Figure 6 Spatial distributions of predicted electrical conductivity of the saturated soil-paste extract (ECe–dS/m) at depths of (a) 0–0.3 (topsoil),

(b) 0.3–0.6 (subsurface) and (c) 0.6–0.9 m (subsoil) across the Ben Amir section of the Tadla Irrigation District using the quasi-3d (q-3d)

inversion algorithm with cumulative function (CF) forward modelling and S2 inversion algorithm with a damping factor (k) of 3.0.


12 H. Dakak et al.

approach, whereby all the iterations with the remaining 11

samples produced similar linear models. To better account

for the model uncertainty, a conditional simulation (Nelson

et al., 2011) could be carried out with more soil samples

collected.

Conclusions

A quasi-3d (q-3d) inversion algorithm was used to invert

kriged EM38 ECa data across a small part of the Beni Amir

irrigated district, in the Tadla area, central Morocco. The

true electrical conductivity (r) was strongly correlated with

ECe, when we used the q-3d and CF, S2 algorithm and

k = 3.0. We also achieved equivalent results by developing

individual LR equations at each depth increment with the

raw EM38 ECa. We conclude that the inversion approach

was more efficient as a single LR equation was needed and

to apply it to a quasi-3d electromagnetic conductivity image

(EMCI). This approach also allowed prediction of ECe at

not only the depths of sampling but at any depth within a

quasi-3d EMCI.

The final maps of the estimated ECe at various depths

allowed the causes and potential management of secondary

soil salinity to be understood and appropriate management

strategies to be initiated and with respect to the application of

poorer quality groundwater for irrigation. This was

particularly the case with respect to the larger amounts of ECe

accumulating in the northern part of the study area associated

with the Fersialitic profile, which was characterized by larger

subsoil clay and bulk density, and with Isohumic profiles in

the central and western parts of the study.

In either case, the methodology provides for baseline data,

which can be used to monitor the effect of continued use of

poorer quality groundwater for irrigation. The methods

developed also have application for extending the area

mapped to other areas where salinity is more problematic

and in areas where saline ground waters are known to exist

to the south and in other parts of the Tadla irrigation

district as well as in other parts of Morocco such as the

Skhirat region (Zouahri et al., 2015). The results also point

to where more detailed studies are needed and to better

understand the cause of the uniform and moderately saline

profiles. In this regard, the approach of Zare et al. (2015)

might be useful to measure, map, manage and monitor

salinity at the field scale and using q-3d inversion modelling

of DUALEM-421 ECa data.

Northing (m)

217 000

90

72

6084

46 49

31 28 10

15

ECe (dS/m)

<3×10–9

<6×10–9

<9×10–9

<1.2×10–8

≥1.2×10–8

<3×10–9

<6×10–9

<9×10–9

<1.2×10–8

≥1.2×10–8

<3×10–9

<6×10–9

<9×10–9

<1.2×10–8

≥1.2×10–8

21

500 m

53

90

72

6084

46 49

31 28 10

1521

53

90

72

6084

46 49

31 28 10

1521

53

214 000

212 000

210 000

208 000

370 000 372 000 375 000 370 000 372 000 375 000 370 000 372 000 375 000

Easting (m) Easting (m) Easting (m)

N N N

(a) (b) (c)

ECe (dS/m) ECe (dS/m)

500 m 500 m

Figure 7 Spatial distributions of the standard deviation of the predicted electrical conductivity of the saturated soil-paste extract (ECe–dS/m) at

depths of (a) 0–0.3 (topsoil), (b) 0.3–0.6 (subsurface) and (c) 0.6–0.9 m (subsoil) across the Ben Amir section of the Tadla Irrigation District

using the 12 iterations of leave-one-out cross-validation and the quasi-3d (q-3d) inversion results.



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