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Irrigation & Drainage Systems Engineering

Phogat et al., Irrigat Drainage Sys Eng 2016, 5:1
http://dx.doi.org/10.4172/2168-9768.1000155

ISSN: 2168-9768

Research Article

Open Access

Statistical Assessment of a Numerical Model Simulating Agro Hydrochemical Processes in Soil under Drip Fertigated Mandarin Tree
Phogat V1*, Skewes MA1, Cox JW1,2 and Simunek J3South Australian Research and Development Institute, Australia
The University of Adelaide, Australia
3
Department of Environmental Sciences, University of California, USA
1
2

Abstract
Qualitative assessment of model performance is essential because reliable statistical comparison of observed
data with simulated behaviour of a model reflects the performance and consistency of the mathematical tool under
defined conditions. In this study we compared the measured temporal and spatial distribution of water content, soil
solution salinity (ECsw), and nitrate (NO3--N) concentration in the soil beneath a drip-fertigated mandarin tree during acomplete season with corresponding HYDRUS-2D simulated values using a range of standard statistical techniques,
comprising mean error (ME), mean absolute error (MAE), root mean square error (RMSE), paired t-test (tcal), coefficientof determination (R2), Nash and Sutcliffe model efficiency (E), index of agreement (IA), relative model efficiency (Erel),relative index of agreement (IArel), modified E (E1) and IA (IA1).
Temporal and spatial values of ME, MAE, and RMSE for water content (-0.04 to 0.05 cm3.cm-3) and salinity (-0.420.93 dSm-1) were within an acceptable range. However, a relatively wider range in MAE (1.44-27.65 mg.L-1) and
RMSE (2.00-39.57 mg.L-1) values were obtained for NO3--N concentrations measured weekly or at the 25-cm depth(MAE = 21.2 and RMSE = 30.7 mg.L-1). Temporal and spatial RMSE were higher than MAE, which suggests a slightbias in RMSE due to squared differences between measured and simulated values. Similarly, the paired t-test (tcal)
showed significant differences for NO3--N during the mid-season (85-140 DOY) for temporal (weekly) comparison andat several depths for water content (10, 25, 80 and 110 cm), salinity (100 and 150 cm) and NO3--N concentration (25,
100 and 150 cm).
The R2 values varied in a narrow range (0.5 to 0.59). Similarly, values for E (0.12-0.43), IA (0.80-0.84), and E1 (0.260.32) and IA1 (0.61-0.69) suggest that the model precisely predicted water content, salinity and nitrate concentration
over the season, however, Erel (-319.25) and IArel (-71.3) values were highly negative for nitrate concentration, indicatinga mismatch. It was concluded that none of the evaluated measures described and tested the performance of the model
for water, salinity and nitrate ideally. Each criterion had its specific advantages and disadvantages, which should
be taken into account. Hence, sound model performance evaluation requires the use of a combination of different
statistical criteria, which consider both absolute and relative errors. Judicious use of statistical criteria should lead to
improvements in the modelling assessment of water, salinity and nitrate dynamics in soil under cropped conditions.

Keywords: HYDRUS-2D; Water content; Salinity; Nitrate; Statisticalerrors; Model efficiency

Introduction
The advent of high speed computers, which enable enhanced
modelling capabilities and rapid development in mathematicalsoftware, has transformed the mathematical evaluation of naturalprocesses. Models are extensively used in almost every field of sciencefor problem solving and decision making, and the vadose zone of
agricultural soils is not spared from this revolutionary change. Due tothe advancement of micro-irrigation systems such as sprinkler and/or
surface/subsurface drip irrigation, which has transformed irrigationand fertilizer practices, there is an increasing interest in evaluating andoptimizing these high frequency systems for water and fertilizer use
efficiency [1-3].
Development of mathematical tools has contributed towards
improving irrigation system design and installation, and themonitoring of water and solute movement through the soil from point
source applications. Additionally, models can save time and money
because of their ability to perform long term simulations evaluating
the effects of root zone processes and management activities onwater quality, water quantity, and soil quality. Recently, a number ofnumerical codes have been developed or improved, such as SWAP,
FEHM, HYDROBIOGEOCHEM, RZWQM, TOUGH2, APSIM,
HydroGeoSphere, and HYDRUS, to cater to the needs of soil physicists/
irrigation experts for evaluating irrigation systems and vadose zone
Irrigat Drainage Sys Eng
ISSN: 2168-9768 IDSE, an open access journal

processes for water movement, climate variability, water quality, andsolute transport in the soil [4-11]. Especially, the HYDRUS model
has been used extensively for evaluating the effects of soil hydraulicproperties, soil layering, dripper discharge rates, irrigation frequency,
water quality, and timing of nutrient applications on wetting patterns
and solute distribution [1-3,12-22]. The most significant aspect of thesestudies, which determines the utility of these models, is the evaluationof modelling outputs against field observed values. The model should
generate data which closely mirror field observations, so that reliableconclusions can be drawn about real world processes.
There are a number of reasons why there is a need to evaluate model
performance: (1) to provide a quantitative estimate of the model’sability to reproduce historic and future behaviour of agricultural/environmental systems; (2) to provide a means for evaluating*Corresponding author: Phogat V, South Australian Research and Development
Institute, Australia, Tel: +61 8 83039567; E-mail: vinod.phogat@sa.gov.au
Received January 19, 2016; Accepted January 22, 2016; Published January 25,
2016
Citation: Phogat V, Skewes MA, Cox JW, Simunek J (2016) Statistical Assessmentof a Numerical Model Simulating Agro Hydro-chemical Processes in Soil under
Drip Fertigated Mandarin Tree. Irrigat Drainage Sys Eng 5: 155. doi:10.4172/21689768.1000155
Copyright: © 2016 Phogat V, et al. This is an open-access article distributed under
the terms of the Creative Commons Attribution License, which permits unrestricted
use, distribution, and reproduction in any medium, provided the original author andsource are credited.

Volume 5 • Issue 1 • 1000155

Citation: Phogat V, Skewes MA, Cox JW, Simunek J (2016) Statistical Assessment of a Numerical Model Simulating Agro Hydro-chemical Processes
in Soil under Drip Fertigated Mandarin Tree. Irrigat Drainage Sys Eng 5: 155. doi:10.4172/2168-9768.1000155

Page 2 of 9

improvements to the modelling approach through adjustment of model
parameter values, model structural modifications, the inclusion of
additional observational information, and representation of important
spatial and temporal characteristics of the domain; (3) to compare
current modelling efforts with previous studies [23]. Field calibrationand validation of the model requires conducting tests based on statisticalmeasures, and is the most important aspect of testing the goodnessof fit of values generated by the model. This process of assessing theperformance of a model requires evaluation of the closeness of thesimulated behaviour of the model to field measurements made within
the domain.
Exhaustive evaluations and objective analyses have been carriedout for models used in various fields of hydrological and hydraulicmodelling [23-30]. Accepting the wide recognition and utility of
HYDRUS for modelling water and solute movement under irrigation
applications, there is a need to assess the performance of HYDRUS for
potential sources of deviation using appropriate and simple indicators.
Most field evaluation studies using HYDRUS either present graphicalcomparisons or subjective assessments [15,31-33], and generally
considered only limited error and correlation estimates, i.e., an
objective assessment [16,18,20,34] of the performance of the model
to evaluate water, salt and nitrate movement in soils. These criteria
may place emphasis only on a particular behaviour of the model,
and may not be able to assess the overall efficacy of the model on along term basis. Hence, there is a need to evaluate the performanceof HYDRUS more vigorously, utilizing different error analyses, testof significance, regression analyses, and efficiency testing to clearly
assess the model’s sustained performance. It is important to compare
the suitability and relative importance of each of these techniques forevaluating modelling predictions of water and solute transport underhigh efficiency irrigation systems.
In the present investigation, the performance of HYDRUS-2D
in simulating water movement, soil solution salinity, and nitrate
movement under a mandarin tree during one season was assessed,using eleven statistical measures: mean error (ME), mean absolute error(MAE), root mean square error (RMSE), paired t-test (tcal), coefficientof determination (R2), model efficiency (E), index of agreement (IA),relative model efficiency (Erel), relative index of agreement (IArel),modified E (E1) and modified IA (IA1)). The aim of this comparison was
to identify which subset of the statistical measures is most appropriate
for evaluating model performance.

Materials and Methods
The statistical tests were employed on the measured and simulated
data generated from the field experiment on mandarin and modelling
simulations illustrated in our earlier paper Phogat et al. [3]. However,a brief description of experimental details and modelling technique ispresented here.

Experimental detail
Modelling evaluation was performed on field experimental datacollected at Dareton Agricultural and Advisory Station (34.10ºS and
142.04ºE), located in the Coomealla Irrigation Area, New South Wales,
Australia for one season during 2006-2007. The field experiment
involved surface drip irrigation of mandarin, established in October
2005. The trees were planted at a spacing of 5 m x 2 m between
rows and plants, respectively. The trees were managed and fertilized
following current commercial practices. The total yearly rainfall during
the experimental period was 187 mm, which was significantly less thanannual potential evapotranspiration (1400 mm).
Irrigat Drainage Sys Eng
ISSN: 2168-9768 IDSE, an open access journal

Irrigation water was supplied through a surface drip system, withdrip lines placed at a distance of 60 cm on both sides of a tree line.
The laterals had 1.6 L.h-1 pressure compensating drippers spaced at
an interval of 40 cm. Irrigation was performed weekly, and the totalseasonal irrigation was 432.8 mm. The salinity of the irrigation water(ECw) was monitored daily, and ranged between 0.09 and 0.19 dS.m-1,
well below the ECw threshold for irrigation of orange, a close relativeof mandarin (1.1 dS.m-1). Daily water content measurements were
performed using Sentek® EnviroSCAN® capacitance soil water sensors,and soil water was sampled on a weekly basis using SoluSAMPLERs™
[35]. The extracted soil solution was analysed to determine soil solution
salinity (ECsw) and nitrate-nitrogen (NO3--N) content.

Modelling technique
The HYDRUS-2D software package was used to simulate thetransient two-dimensional movement of water and solutes in the soil[11]. Refer to the HYDRUS technical manual for a detailed descriptionof the governing equations describing variably-saturated flow using the
Richards’ equation, solute transport using the advection–dispersion
equation, and root water uptake, as well as various initial and boundary
conditions that can be implemented. In this approach, the drip tubing
was considered as a line source, because in this twin line drip irrigation
system the wetted patterns from adjacent drippers merge to form acontinuous wetted strip along both sides of the tree [36,37]. Modelledobservation nodes corresponded to the locations where EnviroSCAN
probes (at depths of 10, 25, 50, 80, and 110 cm) and SoluSAMPLERs (atdepths of 25, 50, 100, and 150 cm) were installed.
Soil hydraulic properties were described using the van GenuchtenMualem constitutive relationships [38]. The spatial root distribution isdefined in HYDRUS-2D according to Vrugt et al. [39]. We considereda simple root distribution model, in which the roots of mandarin trees
expanded horizontally into all available space between the tree lines (xm= 200 cm), were concentrated mainly below the drip emitter (x* = 60cm, z* = 20 cm) where water and nutrients were applied, and extended
to a depth of 60 cm (zm = 60 cm).
Reduction of root water uptake due to water stress was describedusing the piecewise linear relation developed by Feddes et al. [40].
The following parameters in the Feddes et al. model were used: h1 =−10, h2 = −25, h3 = −200 to −1000, h4 = −8000 cm, which were takenfrom Taylor and Ashcroft for orange. Reduction of root water uptake
due to salinity stress, α2(hϕ), was described by adopting the Maas andHoffmann salinity threshold and slope function [40,41]. The salinity
threshold (ECT) for orange (closely related to mandarin) corresponds
to a value of the electrical conductivity of the saturation extract (ECe) of
1.7 dS.m-1, and a slope (s) of 16%.
The longitudinal dispersivity (εL) was considered to be 20 cm, andthe transverse dispersivity (εT) was taken as one-tenth of εL, optimisedin similar studies involving solute transport in soils [12,20]. Since
NH4NO3 and mono-ammonium phosphate were the fertilizers used inour study, nitrification of NH4+-N to NO3−-N was assumed to be themain N process occurring in the soil. HYDRUS-2D incorporates thisprocess by means of a sequential first-order decay chain.
A time-variable flux boundary condition was applied to a 20 cm
long boundary directly below the dripper, centred on 60 cm fromthe top left corner of the soil domain. During irrigation, the drip
line boundary was held at a constant water flux, q. The atmosphericboundary condition was assumed for the remainder of the soil surface
during periods of irrigation, and for the entire soil surface during
periods between irrigation. A no-flow boundary condition was

Volume 5 • Issue 1 • 1000155

Citation: Phogat V, Skewes MA, Cox JW, Simunek J (2016) Statistical Assessment of a Numerical Model Simulating Agro Hydro-chemical Processes
in Soil under Drip Fertigated Mandarin Tree. Irrigat Drainage Sys Eng 5: 155. doi:10.4172/2168-9768.1000155

Page 3 of 9

established at the left and right edges of the soil profile, to account forflow and transport symmetry. A free drainage boundary condition was
assumed at the bottom of the soil profile. Initial conditions for water,
salinity and nitrate simulations were based on measured data which aredescribed in details in Phogat et al. [3].
HYDRUS-2D requires daily values of potential evaporation (Es)and transpiration (Tp), which were obtained using the dual crop
coefficient approach and local meteorological data [42,43].

Statistical indicators
Error estimates: The model’s performance was evaluated bycomparing measured (M) and HYDRUS-2D simulated (S) values ofwater content, electrical conductivity of the soil solution (ECsw), andnitrate concentration (NO3--N) in the soil, and calculating a rangeof error estimates, tests of significance, regression analyses, anddimensionless efficiency tests. The error estimates included meanerror (ME), mean absolute error (MAE), and root mean square error(RMSE), given by:

1=ME∑ ( M i − Si ) 			
N i =1

(1)

MAE =

1 N
∑ M i − Si 			N i =1

(2)

=
RMSE

1 N
2 		
( M i − Si )∑N i =1N

tcal =
Sm

2
1 1

(3)

2
2 2

ns +n sx1 − x2 and Sm = n + n − 2
1
2

(4)

Here, n and s are the number of comparable paired points andstandard deviation respectively; subscripts 1 and 2 are indicative
respectively of measured and predicted values; Sm is the standard
deviation of the mean, and tcal is the calculated paired t-test value.
Efficiency criteria: The coefficient of determination (R2) wasapplied for testing the proportion of variance in the measured dataexplained by the model, and is defined as the square of the coefficientof correlation (r) according to Bravais-Pearson, calculated as:

(

)(

)

)

(

)

(5)

Values of R2 can vary between 0 and 1, with higher values indicating
less variance, and values greater than 0.5 typically considered acceptable[24].
Efficiency measures for the evaluation of model performance
investigated in this study were: model efficiency (E), index of agreement(IA), relative model efficiency (Erel), and relative index of agreement(IArel).
Model efficiency (E), as proposed by Nash and Sutcliffe [44], isdefined as one minus the sum of absolute squared differences between

Irrigat Drainage Sys Eng
ISSN: 2168-9768 IDSE, an open access journal∑ (M − S )i

E = 1 − iN=1

i

2

			

∑ (M − M )

2

(6)

i

i =1

The range of E lies between − ∞ and 1.0 (perfect fit). An efficiency
value between 0 and 1 is generally viewed as an acceptable level of
performance. Efficiency lower than zero indicates that the mean valueof the observed time series would be a better predictor than the model,
and denotes unacceptable performance [45].
The index of agreement (IA) was proposed by Willmot (1981), andrepresents the ratio of the mean square error to the potential error:N∑(M − S )IA = 1 − N

i

i =1

2

i

∑( S − M + M − M )
i

2

		

(7)

i

The value of IA varies between 0 and 1. A value of 1 indicates aperfect agreement between measured and simulated values, and 0
signifies no agreement at all.
Relative efficiency criteria: Various criteria described above (R2, E,
and IA) quantify the difference between observations and predictionsin absolute values. As a result, an over- or under-prediction of larger
values has, in general, a greater influence than that of smaller values. To
counteract this, efficiency measures based on relative deviations can bederived from E and IA as:2

 M i − Si ∑
M i 
i =1 
			E rel = 1 −2N Mi − M 


∑
 M 
i =1 N

 M i − Si 


∑
M 
i =1 
N

IA rel = 1 −

2

N




∑ M i − M Si − S
2
1
i
=
 		
R =
N
N
2
2 
 ∑
Mi − M∑ Si − S i =1 i =1(Ni =1

The test of significance was conducted using the paired t-test (tcal)
and given as:d
1 1 ; d=+n1 n2

simulated and measured values, normalized by the variance ofmeasured values during the period under investigation:(8)2

 Si − M + M i − M 


∑


M
i =1


N

2

(9)

where, Erel and IArel represent the relative efficiency and a relativeindex of agreement, respectively. These parameters can also range
between the values described for E and IA, respectively.
Modified form of E and IA: The modified form of E and IA are
extensively used to overcome the problem of squared differences andoversensitivity to extreme values induced by the mean squared error in
E and IA as given below:N∑ ( Mi − Si )j

Ej =1 − iN=1, j ∈ N 		j
∑ Mi − M
i =1

(

)

(10)

Volume 5 • Issue 1 • 1000155

Citation: Phogat V, Skewes MA, Cox JW, Simunek J (2016) Statistical Assessment of a Numerical Model Simulating Agro Hydro-chemical Processes
in Soil under Drip Fertigated Mandarin Tree. Irrigat Drainage Sys Eng 5: 155. doi:10.4172/2168-9768.1000155

Page 4 of 9N

∑ ( Mi − Si )j

i =1
IA j =
1− N, j∈ N
j
Si
−
M
+
Mi
−
M
∑
i =1

(

) (

)

(11)

where j represents an arbitrary power i.e. a positive integer(N). Especially when j=1, the errors and differences are given theirappropriate weighting, not inflated by their squared values. Hence E1
and IA1 represent modified form of efficiency and index of agreement.
Squaring in statistics (E2 and IA2) is useful because squares are easier tomanipulate mathematically than are absolute values, but use of squares
forces an arbitrarily greater influence on the statistic by way of thelarger values [23]. These parameters can also range between the values
described for E and IA, respectively.
The error measures (ME, MAE and RMSE) and t-test werecomputed temporally (across all measurement/simulation depths on
weekly basis), spatially (across all weekly measurement/simulation foreach depth), and across all individual measurements/simulations forthe entire dataset. However, regression and efficiency (R2, E, IA, Erel,
IArel, E1 and IA1) measures were only evaluated on the entire dataset.

Results and Discussion

Comparing MAE and RMSE in Figure 2 reveals that the magnitudeof the inter-quartile range (IQR) was higher in RMSE as compared toMAE. IQR is the difference between the 25th and 75th percentile, andindicates the magnitude of variation in the mid-range of error values.
The magnitude of IQR in RMSE was 0.01 cm3.cm-3, 0.36 dS.m-1, and 19.05
mg.L-1, as compared to 0.01 cm3.cm-3, 0.33 Ds.m-1, and 14.98 mg.L-1 in
MAE, for water content, ECsw, and NO3--N, respectively. Similarly, theSoilParameter

Scale

Range

Water
content(cm3cm-3)

TemporalMax
Min

SpatialMax

TemporalMin

Salinity(ECsw)(dSm-1)

Nitrate(NO3--N)(mg L-1)

Data sets for error parameter comparison

Mean error (ME) is the signed measure of deviations between
measured and simulated values, indicating whether the deviations tend
to be positive or negative. The ME in temporal data ranged from -0.04
to 0.04 cm3.cm-3, -0.42 to 0.54 dS.m-1, and -11.31 to 12.38 mg.L-1 forwater contents, ECsw, and NO3--N concentrations, respectively in Table
1 and Figure 1. Similarly, spatial MEs for water contents, ECsw, andNO3--N concentrations ranged from -0.01 to 0.04 cm3.cm-3, -0.24 to
0.34 dSm-1, and -21.09 to 4.21 mg.L-1, respectively in Table 1 and Figure2). Seasonal ME values for water content, ECsw, and NO3--N for theentire data set were 0.003 cm3.cm-3, 0.12 dSm-1, and -6.7 mg.L-1 (Table2). This comparison revealed that ME was smallest for water content
and greatest for NO3--N, with ECsw in between. Although NO3--N errors
indicated the widest variability, a low value of ME may still conceal
simulation inaccuracy due to the offsetting effect of large positive andnegative errors, hence the need to also consider MAE and RMSE.
Irrigat Drainage Sys Eng
ISSN: 2168-9768 IDSE, an open access journal

Water contents (cm3 cm-3)

Numerous error estimation methods are in use for comparing
simulation results with measured data. These indices are valuable tools
because they evaluate the error in the units of the constituent of interest,
which helps in the analysis of results and describe the performance andutility of the modelling exercise. Weekly computed temporal error
indices (ME, MAE, and RMSE) on measured and simulated watercontent, soil solution salinity (ECsw) and nitrate-nitrogen content (NO3-N) are depicted in box plots in Figure 1 and range of these parameters
are shown in Table 1. Spatial values of error indices are shown in Figure
2. Seasonal values of all statistical measures are displayed in Table 2.

0.06

0.04

0.04

0.05

-0.04

0.005

0.01

0.04

0.04

0.05

Min

-0.01

0.02

0.02

Max

0.54

0.76

0.93

-0.42

0.08

0.09

Max

0.34

0.47

0.56

Min

-0.24

0.19

0.25

Temporal

Max

12.31

27.65

39.57

Min

-11.381.44

2.00

Spatial

Max

4.21

21.24

30.75

Min

-21.09

5.06

5.89

(a)

0.04
0.02
0

ME

-0.02

MAE

RMSE

MAE

RMSE

MAE

RMSE

-0.04
1
0.8

ECsw (dS m-1 )Comparison of error indices

RMSE

Table 1: Maximum and minimum values of ME, MAE, and RMSE obtained fromspatial and temporal data sets of water content, ECsw and NO3--N

0.6

(b)

0.4
0.2
0
-0.2

ME

-0.4
-0.6
45
35

NO3 --N (mg L-1)

The total data set of weekly measured (M) and HYDRUS-2D
simulated (S) water content, soil solution salinity (ECsw), and nitratenitrogen concentration (NO3--N) at different depths and their graphicalcomparisons are described in Phogat et al. [3]. These data sets provide
an ideal basis for comparing the range of error parameters, given thatthe three data sets (water content, salinity and nitrate concentration)
represent a range from good matching between simulated andmeasured data (water content) to relatively poorly matched (nitrateconcentration). This allows comparison of the various error parametersacross a range of error values and efficiency testing.

MAE

Spatial

ME

(c)

25
15
5
-5

ME

-15
Figure 1: Box plots showing the scatter of errors (mean error, ME; mean
absolute error, MAE; root mean square error, RMSE) between weekly
measured and simulated values of (a) Water contents, (b) Soil solution
salinity (ECsw) and (c) Nnitrate-nitrogen (NO3--N) contents.

Volume 5 • Issue 1 • 1000155

Citation: Phogat V, Skewes MA, Cox JW, Simunek J (2016) Statistical Assessment of a Numerical Model Simulating Agro Hydro-chemical Processes
in Soil under Drip Fertigated Mandarin Tree. Irrigat Drainage Sys Eng 5: 155. doi:10.4172/2168-9768.1000155

Page 5 of 9
Statistical
Measures#

Moisture content(cm3cm-3)

Salinity (ECsw)(dSm-1)

Nitrate (NO3--N)(mg L-1)

N#

240

188

192

ME

0.003

0.12

-6.70

MAE

0.03

0.34

24.49

RMSE

0.03

0.46

26.76

hSDm

0.023

0.28

7.35

tcal

0.84

1.79

3.42*

R2

0.50

0.59

0.56

E

0.43

0.30

0.12

Erel

0.36

0.49

-319.25

E1 (j=1)

0.26

0.32

0.28

IA

0.84

0.85

0.80

IArel

0.82

0.80

-71.3

IA1 (j=1)

0.61

0.69

0.68

Number of measured and simulated data pairs; Significant at 5% level*

Table 2: Values of ME, MAE, and RMSE, half of the standard deviation of
measured data (hSDm), and a paired t-test (tcal), coefficient of determination (R2),model efficiency (E), index of agreement (IA), relative model efficiency (Erel),relative index of agreement (IArel), modified E (E1), and modified IA (IA1) estimatedfor the entire (seasonal) dataset

spatial RMSE values were also higher than the MAE values at all depths
shown in Figure 2, but their magnitude was much wider at shallow
depths (10-25 cm) where RMSE values were 0.01 cm3.cm-3, 0.2 dS.m-1,
and 9.49 mg.L-1 higher than MAE values for water content, ECsw, andNO3--N, respectively. However, higher variations in all types of errors
at the surface depth (10-25 cm) reflect the assumption in the model ofa constant atmospheric boundary flux during daily time steps, which
deviates from actual conditions at the surface boundary, particularly
the diurnal fluctuation in evaporation, which peaks in day time anddecreases during the night [2].
Comparison of MAE and RMSE further indicated that as themagnitude of variations between measured and predicted values
increased, RMSE increased disproportionately, as is evident fromthe NO3--N values. Similar trends for NO3--N were also obtained in
the MAE and RMSE analysis of the whole data set, where the valuesof these parameters were 24.49 mg.L-1 and 26.76 mg.L-1, respectively
in Table 2. RMSE was always larger than MAE, and varied with thevariability of the error magnitude, because the errors are squared in
RMSE before they are averaged. RMSE varies with the variability within
the distribution of error magnitudes and with the square root of thenumber of errors (n1/2), as well as with the average-error magnitude (asMAE) [26]. Hence, RMSE gives a relatively high weight to large errors,
as obtained in the case of NO3--N. On the other hand, MAE is a linear
measure, which means that all individual differences are weighted
equally in the average. Hence, MAE may be preferred over RMSE asa more natural measure of the average error, and for an unambiguous
assessment of model predictions. Legates and McCabe expressedsimilar views as RMSE produces inflated values when large outliers arepresent [23].
The use of these two measures (RMSE and MAE) suffers from asignificant drawback, in that they do not indicate the direction of
the error. However, this discrepancy may be ignored where the main
focus of the comparison is the magnitude of the error rather than its
direction.
There is no universally accepted threshold limit for error magnitude
when judging the degree of accuracy of model performance. However,Singh et al. stated that RMSE and MAE values smaller than half of thestandard deviation of the measured data (hSDm) may be considered
Irrigat Drainage Sys Eng
ISSN: 2168-9768 IDSE, an open access journal

low and appropriate for model evaluation [46]. Therefore, RMSE,
MAE, and hSDm values obtained using temporal water content data arecompared in Figure 3. It can be seen that these errors (RMSE and MAE)
were higher than hSDm except on a few occasions during mid season(DOY 36 to 64) and during the terminal period (DOY 194 onward).
Similarly, MAE and RMSE values were higher than hSDm in all analysesof the complete data set shown in Table 2. Hence, model performance
was relatively poor in view of this criterion.
In the context of such definitive measures of model performance,
it is important to consider the natural variability inherent in themeasured data against which the simulations are judged [47]. Realworld variability of the natural environment, such as soil variations,as well as measurement inaccuracies can cause measured data to vary
relative to the best simulation. For example, in our study EnviroSCAN®
sensors were used to measure the profile water content. The probes were
properly calibrated during installation; however, measurements withcapacitance probes are highly variable and sensitive to bulk electricalconductivity, temperature, and change in storage estimates [48]. The
capacitance sensors used in access tubes may generate consistent errors≤ 0.05 cm3 cm-3, which is similar to the variation observed in our study
between EnvironSCAN measured and simulated values.
The error associated with simulated data and outliers in observed
data can be further minimised by optimizing the input data by complex
weighing techniques and probability distribution based uncertainty
analysis techniques like Monte Carlo simulation and Bayesian analysis
framework which deals with both random and systemic errors in thesimulations [30,49].

Test of significanceThe paired t-test was used to evaluate the level of significancebetween measured and simulated data on water content, ECsw, andNO3--N content which is shown in Figure 4. It showed non-significant
differences (p = 0.05) between mean values of temporal measured
and simulated water content. However, positive tcal values during theearly period showed that the measured values were higher than thecorresponding simulated values, and the opposite was true later in theseason shown in Figure 4a. Similarly, insignificant differences wereobserved for soil salinity, except at DOY 36 and 43, where differences
between measured and simulated mean ECsw were significant. However,significant differences were observed in NO3--N content from DOY 78
to 134, which corresponded to a period from March 2007 to early May
2007.
However, t-test showed significant differences in the spatial data set
at depths of 10, 25, 80, and 110 cm for water content, 25, 100, and 150
cm for NO3--N content and 100 and 150 cm for ECsw (data not shownhere). These revelations conform to visual observation of the dataset[3]. Additionally, the tcal values for water content and ECsw for thewhole season (Table 1) were non-significant at p = 0.05, whereas the tcal
value for NO3--N showed significant difference, indicating a relatively
poor performance of the model for nitrate simulation. However,t-test represents variation between the mean values of measured andsimulated data, and therefore a single seasonal figure may not reflect
the degree of spatial and temporal heterogeneity across the season.
Moreover, t-test assumes that the measured and simulated values arenormally distributed, and that both groups have equal variance. Theseassumptions may not be perfectly satisfied, and this calls into question
the reliability of this statistical measure.
It is also important to understand that hypothesis driven tests, suchas paired t-test, should not be relied on solely to measure reliability ofVolume 5 • Issue 1 • 1000155

Citation: Phogat V, Skewes MA, Cox JW, Simunek J (2016) Statistical Assessment of a Numerical Model Simulating Agro Hydro-chemical Processes
in Soil under Drip Fertigated Mandarin Tree. Irrigat Drainage Sys Eng 5: 155. doi:10.4172/2168-9768.1000155

Page 6 of 9

Water content (cm3cm-3)-0.02
00.02 0.04 0.06 -0.30

Depth (cm)

10
25
50

ME

ECsw (dS m-1)
0.00
0.30

0.60

-40

NO3--N (mg L-1)
-20
0
20

25

25

50

50

100

100

150

150

40

MAE
RMSE

80

110

Figure 2: Various errors (ME, MAE, and RMSE) for water contents, soil solution salinities (ECsw) and nitrate-nitrogen (NO3--N) contents at different soil depths

Figure 3: Comparison of error values (RMSE, MAE) and half of standard deviation of measured values (hSDm) for weakly measured water contents (cm3cm-3)

simulations, as the degree of random variation determines the detectionof a significant difference; significant systematic bias will be less likely
to be detected if it is accompanied by large random errors [50,51].

Regression analysis and efficiency testing
Model performance was also assessed using regression analysis[coefficient of determination (R2)] and various efficiency testing
indices [model efficiency (E), index of agreement (IA), relative model
efficiency (Erel), relative index of agreement (IArel), modified form of E
(E1), and modified form of IA (IA1)]. These measures were computed
using the complete data set of measured and corresponding simulated
values of water content (240 values), soil solution salinity (ECsw; 188values), and nitrate nitrogen content (NO3--N; 192 values) at all spatial
and temporal positions (Table 2).
The R2 value of 0.5 for water content was just at the margin of thesatisfactory level [24]. However, its values for ECsw (0.59) and the NO3Irrigat Drainage Sys Eng
ISSN: 2168-9768 IDSE, an open access journal-N content (0.56) were within the acceptable limit. Hence, R2 produced
relatively similar results across all simulated processes (water content,
ECsw, and NO3--N) (Table 2). This is contrary to our results using error
tests, where the variability in water content was comparatively smaller
than in NO3--N content (Table 2). This reveals a serious drawback in
considering R2 values alone for model performance evaluation, in thatit only quantifies dispersion among values. Krause et al. reported that amodel which systematically over- or under-predicts at all times will still
result in R2 values close to 1.0, even if all predictions are wrong, which
undermines the reliability of R2 values [25]. Similarly, Legates andMcCabe suggested that correlation based measures are inappropriate
and should not be used to evaluate the goodness-of-fit of model
simulations, as these measures are oversensitive to extreme values andare insensitive to additive and proportional differences between model
predictions and observations [23]. Hence, consideration of R2 alone formodel performance assessment sometimes leads to a flawed acceptanceof modelling results.

Volume 5 • Issue 1 • 1000155

Citation: Phogat V, Skewes MA, Cox JW, Simunek J (2016) Statistical Assessment of a Numerical Model Simulating Agro Hydro-chemical Processes
in Soil under Drip Fertigated Mandarin Tree. Irrigat Drainage Sys Eng 5: 155. doi:10.4172/2168-9768.1000155

Page 7 of 9233

water content (cm3cm-3)
-2
-1
0
1
2 -1

ECsw (dS m-1)
0
1
2

3 -6

NO3--N (mg L-1)
-4
-2
0

2

254
276
296
317
338

DOY

360
15
36
57
78
100
127
148
169
205
232
Figure 4: Temporal paired t-test (tcal) values between measured and simulated a) Water content, b) Soil solution salinity (ECsw) and c) Nitrate-nitrogen (NO3--N) content

Six efficiency tests were applied to the data set to evaluate theirrelative performance. The E, Erel, IArel, E1 and IA1 values for watercontent were 0.43, 0.84, 0.82, 0.20 and 0.59 respectively (Table 2),
suggesting a good match between measured and simulated data, as
indicated by previous parameters. On the contrary, IA (0.36) showed
relatively poor efficiency of the model for simulating water content
distribution. However, values of modified efficiency(E1) and index
of agreement (IA1) were lower than relative estimates because thesestatistics utilize absolute values rather than squared differences intheir computation which makes them more conservative measures[23]. The E value (0.43) was within the satisfactory limit reported inother studies [24,45]. Similarly, the E, IA, Erel, IArel, E1 and IA1 values
for weekly soil solution salinity (ECsw) data were 0.30, 0.49, 0.85, 0.80,
0.32 and 0.69, respectively, which are well within acceptable limits, andmatch previous indicators relatively well. Relative efficiency (Erel) forwater and relative index of agreement (IArel) for water and salinity wererelatively close to their precursors, E and IA, respectively (Table 2).
Conversely, the nitrate simulation provides a more complicatedpicture. The Nash and Sutcliffe efficiency (E = 0.12) and index ofagreement (IA = 0.80) values are within acceptable limits, and in fact
IA is quite high, in contrast to previous error parameters for nitrateconcentration. The modified estimates (E1 and IA1) fall within acceptable
range. However, large negative values of Erel (-319.25) and IArel (-71.3)
reflect the wide divergence between measured and simulated values
at certain times during the simulation. However, relative deviations
reduce the influence of absolute differences among the measures andsimulated values.
It is significant that Nash-Sutcliffe efficiency (E), the mostfrequently used indicator in hydrologic studies, is much more sensitive

Irrigat Drainage Sys Eng
ISSN: 2168-9768 IDSE, an open access journal

to errors in higher values, as the differences between measured andsimulated values are squared. As a result larger values in a data series
have a much higher weighting, whereas lower values are neglected [23].
This comparison suggests that E and/or IA may not always be suitableparameters for describing model performance. Additionally, the large
negative values of Erel and IArel for nitrate showed disproportionately
high under-prediction, as reported in Krause et al. [25]. Hence, theseparameters proved to be sensitive only to large variations in values andnot at all to small divergences because, due to the summation of theabsolute or squared errors in efficiency testing methods, emphasis isplaced on larger errors while smaller errors tend to be neglected. Hencemodified efficiency (E1) and index of agreement (IA1) could be themore appropriate measures for model’s efficiency testing than theirprecursors (E and IA) and relative statistics (Erel and IArel). Nevertheless
IA1 has advantages due to its bounds between 0.0 and 1.0 [23]. But goodmodelling efficiency shown by E1 and IA1 statistics is contradictory to
the poor modelling simulation for NO3--N revealed in error estimates.
Additionally, tests of significance and efficiency measures, similar tot-test, evaluate the mean variability in the domain and are unable tocapture the modelling divergence at a particular point.
Overall, it can be stated that none of the efficiency parameterswhich were evaluated in this study adequately described and tested thereliability of model predictions. Each has specific pros and cons, whichhave to be taken into account during model calibration and validation.
Hence, for a sound model performance evaluation, a combination ofdifferent statistical efficiency criteria, complemented by the assessmentof the absolute or relative error, may need to be included.

Volume 5 • Issue 1 • 1000155

Citation: Phogat V, Skewes MA, Cox JW, Simunek J (2016) Statistical Assessment of a Numerical Model Simulating Agro Hydro-chemical Processes
in Soil under Drip Fertigated Mandarin Tree. Irrigat Drainage Sys Eng 5: 155. doi:10.4172/2168-9768.1000155

Page 8 of 9

Conclusion
Simulation models have been increasingly used in high efficiency
drip irrigation systems to evaluate the water and solute dynamics undercropped conditions, and suggest necessary management options to
optimise the system efficiency. In this study, eleven statistical measures
were used to compare HYDRUS-2D simulated values of water content,
soil solution salinity (ECsw), and nitrate-nitrogen (NO3--N) dynamics
with field measured values obtained under drip irrigated mandarin
crop over a season. as the statistical parameters compared were meanerror (ME), mean absolute error (MAE), root mean square error(RMSE), paired t-test (tcal), coefficient of determination (R2), model
efficiency (E), index of agreement (IA), relative model efficiency (Erel),relative index of agreement (IArel), modified E (E1), and modified IA(IA1). The purpose of applying all of these parameters to the same data
sets was to evaluate the relative importance of these parameters inmodel performance testing.
The error parameters (ME, MAE and RMSE) remained within
acceptable limits when applied to measured and simulated values ofwater content and ECsw, whilst a wider range of values of MAE (1.44 to
27.65 mg.L-1) and RMSE (2.00 to 39.57 mg.L-1) obtained for nitrate (NO3-N) indicated poor agreement between simulated and measured values
for this data set. Low ME values may conceal simulation inaccuracy
due to the offsetting effect of large positive and negative errors. The
results revealed that RMSE values were consistently higher than MAE
due to squaring of the difference between measured and simulated
values. Hence, it was concluded that among the error tests, MAE may
be preferred over ME and RMSE for evaluating goodness-of-fit of thesimulated values.
Paired t-test values revealed a non-significant difference (p =0.05) between weekly measured and predicted water content andECsw distributions. However, differences were significant for the NO3-N distribution during the mid-season and at several spatial depths.
Similarly, regression analysis (R2) and efficiency testing methods(E, IA, Erel, IArel, E1 and IA1) also indicated that the model accurately
predicted seasonal changes in water and salinity distributions in thesoil. However, negative values of Erel (-319.25) and IArel (-71.3) forNO3--N reflected the relatively poor prediction of NO3--N dynamics inthe soil. However, relative deviations reduce the influence of absolutedifferences among the measures and simulated values.
It was concluded that, for reliable model performance evaluation,
a combination of different statistical efficiency criteria, along with theassessment of the absolute or relative volume error, must be included.
Taken together, these comparisons were able to provide an objective
assessment of the closeness of the simulated behaviour to the observed
measurements of water, salinity and nitrate distribution in the soil under
mandarin. It is expected that such studies would help in improving theperformance evaluation and reliability of modelling data on irrigationand fertigation programme of horticultural crops, and contribute toimproving system efficiency, and reducing environmentally harmful
agro-hydrological practices.
Acknowledgement

2. Ramos TB, Šimůnek J, Goncalves MC, Martins JC, Prazeres A, et al. (2012)
Two-dimensional modeling of water and nitrogen fate from sweet sorghum
irrigated with fresh and blended saline waters. Agric Water Manage 111: 87104.
3. Phogat V, Skewes MA, Cox JW, Sanderson G, Alam J et al. (2014) Seasonal
simulation of water, salinity and nitrate dynamics under drip irrigated mandarin(Citrus reticulata) and assessing management options for drainage and nitrateleaching. J Hydrol 513: 504-516.
4. Van Dam JC, Huygen J, Wesseling JG, Feddes RA, Kabat P, et al. (1997)
Theory of SWAP version 2.0. Simulation of water low, solute transport andplant growth in the soil-water-atmosphere-plant environment. WAGENINGEN
UR.
5. Zyvoloski GA, Robinson BA, Dash ZV, Trease LL (1997) Use’s Manual for the
FEHM application- A finite-element heat- and mass-transfer code. Geothermal.
6. Yeh GT, Salvage KM, Gwo JP, Zachara JM, Szecsody JE (1998)
HydroBioGeoChem: A coupled model of hydrologic transport and mixed
biogeochemical kinetic/equilibrium reactions in saturated-unsaturated media.
UNT digital library.
7. Ahuja LR, Hanson JD, Rojas KW, Shaffer MJ (1999) The Root zone water
quality model. Water Resources Publications LLC.
8. Pruess K, Oldenburg C, Moridis G (1999) TOUGH2 User's Guide, Version 2.0.
9. Keating BA, Carberry PS, Hammer GL, Probert ME, Robertson MJ, et al. (2003)
An overview of APSIM, a model designed for farming systems simulation. Eur
J Agron 18: 267-288.
10. Therrien R, McLarren RG, Sudicky EA, Panday SM (2010) HydroGeoSphere: A
three-dimensional numerical model describing fully-integrated subsurface andsurface flow and solute transport.
11. Šimůnek J, van Genuchten MTh, Šejna M (2008) Development and applicationsof the HYDRUS and STANMOD software packages and related codes. Vadose
Zone J 7: 587-600.
12. Cote CM, Bristow KL, Charlesworth PB, Cook FJ, Thorburn PJ (2003) Analysis
of soil wetting and solute transport in subsurface trickle irrigation. Irrig Sci 22:
143-156.
13. Lazarovitch N, Šimůnek J, Shani U (2005) System-dependent boundary
condition for water flow from subsurface source. Soil Sci Soc Am J 69: 46-50.
14. Assouline S, Moller M, Cohen S, Ben-Hur M, Grava A, et al. (2006) Soil–plantsystem response to pulsed drip irrigation and salinity: Bell pepper-Case study.
Soil Sci Soc Am J 70: 1556-1568.
15. Ajdary K, Singh DK, Singh AK, Khanna M (2007) Modelling of nitrogen leachingfrom experimental onion field under drip fertigation. Agric Water Manage 89:
15-28.
16. Patel N, Rajput TBS (2008) Dynamics and modeling of soil water undersubsurface drip irrigated onion. Agric Water Manage 95: 1335-1349.
17. Šimůnek J, Hopmans JW (2009) Modeling compensated root water andnutrient uptake. Ecol Model 220: 505-521.
18. Doltra J, Munoz P (2010) Simulation of nitrogen leaching from a fertigated crop
rotation in a Mediterranean climate using the EU-Rotate-N and Hydrus-2Dmodels. Agric Water Manage 97: 277-285.
19. Li J, Liu Y (2011) Water and nitrate distributions as affected by layered-texturalsoil and buried dripline depth under subsurface drip fertigation. Irri Sci 29: 469478.
20. Phogat V, Mahadevan M, Skewes M, Cox JW (2012) Modeling soil water andsalt dynamics under pulsed and continuous surface drip irrigation of almondand implications of system design. Irri Sci 30 : 315-333.
21. Phogat V, Skewes MA, Mahadevan M, Cox JW (2013a) Evaluation of soil plantsystem response to pulsed drip irrigation of an almond tree under sustained
stress conditions. Agric Water Manage 118: 1-11.

Dareton Agricultural Research and Advisory Station farm staff for managing
the site and plantings; and financial support of the National Program for Sustainable

22. Phogat V, Skewes M, Cox JW, Alam J, Grigson G, et al. (2013b) Evaluationof water movement and nitrate dynamics in a lysimeter planted with an orange
tree. Agric Water Manage 127: 74-84.

References

23. Legates DR, McCabe GJ (1999) Evaluating the use of goodness-of-fit
measures in hydrologic and hydroclimatic model validation. Water Resour Res
35: 233-241.

Irrigation is gratefully acknowledged.

1. Hanson BR, Šimůnek J, Hopmans JW (2006) Evaluation of urea–ammonium–
nitrate fertigation with drip irrigation using numerical modeling. Agric Water
Manage 86: 102-113.

Irrigat Drainage Sys Eng
ISSN: 2168-9768 IDSE, an open access journal

24. Van Liew MW, Arnold JG, Garbrech JD (2003) Hydrologic simulation on agricultural
watersheds: Choosing between two models. Trans ASAE 46: 1539-1551.

Volume 5 • Issue 1 • 1000155

Citation: Phogat V, Skewes MA, Cox JW, Simunek J (2016) Statistical Assessment of a Numerical Model Simulating Agro Hydro-chemical Processes
in Soil under Drip Fertigated Mandarin Tree. Irrigat Drainage Sys Eng 5: 155. doi:10.4172/2168-9768.1000155

Page 9 of 9
25. Krause P, Boyle DP, Base F (2005) Comparison of different efficiency criteria
for hydrological model assessment. Adv Geosci 5: 89-97.

37. Falivene S, Goodwin I, Williams D, Boland A (2005) Introduction to OpenHydroponics. NPSI Fact sheet.

26. Willmott CJ, Matsuura K (2005) Advantages of the mean absolute error(MAE) over the root mean square error (RMSE) in assessing average model
performance. Climate Res 30: 79-82.

38. Van Genuchten MTh (1980) A closed form equation for predicting the hydraulicconductivity of unsaturated soils. Soil Sci Soc Am J 44: 892-898.

27. Schaefli B, Gupta H (2007) Do Nash values have value? Hydrol Processes 21:
2075-2080.
28. Jain SK, Sudheer KP (2008) Fitting of hydrologic models: A close look at the
Nash-Sutcliffe index. J Hydrol Eng 13: 981-986.
29. Gupta HV, Kling H, Yilmaz KK, Martinez GF (2009) Decomposition of themean squared error and NSE performance criteria: Implications for improvinghydrological modelling. J Hydrol 377: 80-91.
30. Pechlivanidis IG, Jackson B, McIntyre N, Wheater HS (2011) Catchment
scale hydrological modelling: A review of model types, calibration approaches
and uncertainty analysis methods in the context of recent developments intechnology and applications. Global NEST J 13: 193-214.
31. Hassan G, Persaud N, Reneau RB (2005) Utility of HYDRUS-2D in modelingprofile soil moisture and salinity dynamics under saline water irrigation ofsoybean. Soil Sci 170: 28-37.
32. Goncalves MC, Šimůnek J, Ramos TB, Martins JC, Neves MJ, et al. (2006)
Multicomponent solute transport in soil lysimeters irrigated with waters ofdifferent quality. Water Resour Res.

39. Vrugt JA, Hopmans JW, Šimůnek J (2001) Calibration of a two dimensional root
water uptake model. Soil Sci Soc Am J 65: 1027-1037.
40. Feddes RAP, Kowalik J, Zaradny H (1978) Simulation of field water use andcrop yield.
41. Taylor SA, Ashcroft GM (1972) Physical Edaphology. Freeman and Co, USA.
42. Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration
guidelines for computing crop water requirements. FAO Irrigation and Drainage
Paper, Italy.
43. Allen RG, Pereira LS (2009) Estimating crop coefficients from fraction of groundcover and height. Irrig Sci 28: 17-34.
44. Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models
part I-A discussion of principles. J Hydrol 10: 282-290.
45. Moriasi DN, Arnold JG, Van Liew MW, Bingner RL, Harmel RD et al. (2007)
Model evaluation guidelines for systematic quantification of accuracy inwatershed simulations. Trans ASABE 50: 885-900.
46. Singh J, Knapp HV, Demissie M (2004) Hydrologic modelling of the Iroquois
river watershed using HSPF and SWAT.

33. Crevoisier D, Popova Z, Mailhol JC, Ruelle P (2008) Assessment andsimulation of water and nitrogen transfer under furrow irrigation. Agric Water
Manage 95: 354-366.

47. Harmel RD, Cooper RJ, Slade RM, Haney RL, Arnold JG (2006) Cumulative
uncertainty in measured stream flow and water quality data for small
watersheds. Trans ASAE 49: 689-701.

34. Roberts T, Lazarovitch N, Warrick AW, Thompson TL (2009) Modeling salt
accumulation with subsurface drip irrigation using HYDRUS-2D. Soil Sci Soc
Am J 73: 233-240.

48. Evett SR, Schwartz RC, Casanova JJ, Heng LK (2012) Soil water sensing forwater balance, ET and WUE. Agric Water Manage 104: 1-9.

35. Biswas T, Schrale G (2007) Sentek SoluSAMPLER: A tool for managing salt
and nutrient movement in the root zone, Instruction Manual Version 2.0. Sentek
Pvt Ltd, Australia.
36. Skaggs TH, Trout TJ, Šimůnek J, Shouse PJ (2004) Comparison of Hydrus2D
simulations of drip irrigation with experimental observations. J Irrig Drainage
Eng 130: 304-310.

49. Finsterle S, Najita J (1998) Robust estimation of hydrogeologic model
parameters. Water Resour Res 34: 2939-2947.
50. Altman DG (1991) Practical statistics for medical research. Chapman and Hall,
London.
51. Bland JM, Altman DG (1995) Comparing two methods of clinical measurement:a personal history. Internat J Epidemiol 24: 7-14.

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