A Fuzzy Decision Support System For Irrigation and Water Conservation in Agriculture
A Fuzzy Decision Support System For Irrigation and Water Conservation in Agriculture
A Fuzzy Decision Support System For Irrigation and Water Conservation in Agriculture
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 18 April 2014
Received in revised form
24 September 2014
Accepted 25 September 2014
Available online
Since agriculture is the major water consumer, web services have been developed to provide the farmers
with considerate irrigation suggestions. This study improves an existing irrigation web service, based on
the IRRINET model, by describing a protocol for the eld implementation of a fully automated irrigation
system. We demonstrate a Fuzzy Decision Support System to improve the irrigation, given the information on the crop and site characteristics. It combines a predictive model of soil moisture and an
inference system computing the most appropriate irrigation action to keep this above a prescribed safe
level. Three crops were used for testing the system: corn, kiwi, and potato. This Fuzzy Decision Support
System (FDSS) favourably compared with an existing agricultural model and data-base (IRRINET). The
sensitivity of the FDSS was tested with random rainfall and also in this extended case the water saving
was conrmed.
2014 Elsevier Ltd. All rights reserved.
Keywords:
Decision support systems
Irrigation management
Climate changes
Fuzzy inference systems
Fuzzy modelling
1. Introduction
Water conservation in agriculture is becoming an increasingly
important issue in the Mediterranean countries, in view of the
current changes both in climate and in the agricultural practices.
There is a great need for irrigation system modernization to cope
with the increasing value and decreasing availability of this commodity. Decision Support Systems (DSS) are now recognized as a
fundamental tool in environmental management and planning.
Since Guariso et al. (1985) rst introduced DSS many studies have
reported advances in their use for the management of water
resource. McIntosh et al. (2011) reviewed the experience of a global
group of environmental decision support systems (EDSS) developers, emphasizing the key challenges and structures in EDSS
development. The integration between large-scale models and
socio-economic and environmental issues in the EDSS context was
considered by van Delden et al. (2011) and by Lehmann and Finger
(2014), who developed a bio-economic model to optimize management decisions in potato production in the Broye catchment
(Switzerland). The importance of involving stakeholders in the
irrigation management was considered in MONIDRI (Fais et al.,
2004) advocating participatory planning, whereas the relevance
* Corresponding author.
E-mail addresses: stefano.marsililibelli@uni.it, Sig-zzig@libero.it (S. MarsiliLibelli).
http://dx.doi.org/10.1016/j.envsoft.2014.09.020
1364-8152/ 2014 Elsevier Ltd. All rights reserved.
74
DT
mi
Symbol
a,b,d
c
ETc
Irr
I
m
N
P
RI
Tsum
U
Ulow
Uhigh
vi
Abbreviations
mfs
Membership functions
CER
Canale Emiliano Romagnolo
DSS
Decision Support System
EDSS
Environmental Decision Support Systems
FCM
Fuzzy C-Means (Bezdek, 1981)
FDSS
Fuzzy Decision Support System
IPI
Irrigation Performance Index
Nmfs
Number of membership functions
PP
Phenophase
RF
Rain Forecast
RTU
Remote Terminal Unit
SCADA Supervisory Control And Data Acquisition
VAF
Variance Accounted For
IPI
Irrk;
(1)
75
Fig. 1. Development stages of the IRRISAVE project e In Step 1 an independent soil moisture model is calibrated with the IRRINET database and internal model. In Step 2 a set of
irrigation rules is designed to automate the irrigation advices and assess the water saving obtained by comparison with the IRRINET scheme. In the Step 3, yet to be implemented,
the FDSS is ported onto the eld, closing the loop from the irrigation advice back to the FDSS.
Fig. 2. Structure of the decision support system based on a predictive soil moisture model calibrated with the IRRINET-generated agricultural data, an irrigation inference system,
and a performance index to assess the effectiveness of each irrigation advice.
76
The proposed fuzzy model is shown in Fig. 3 and can be regarded as an extension of the classical Sugeno approach (Takagi and
Sugeno, 1985; Yager and Filev, 1994; Babuska, 1998a) with the antecedents being clusters representing typical crop conditions to
which local linear models are associated as consequents. The global
model response is then obtained by defuzzication, consisting of
the average of the consequent linear models weighted by their
degrees of membership. This mixed cluster/linear consequents
approach was proposed by Babuska (1998a) and Abony (2003) and
previously applied to the composting process (Giusti and MarsiliLibelli, 2010) by adapting the public-domain software developed
by Babuska (1998b).
As shown in Fig. 3 the model has three inputs, sampled at daily
intervals during the active phenophase horizon (tjjj 1,,N). The
Growth Degree Days (Tsum), the actual water applied to the crop
(RI), and the evapotraspiration (ETc) form the input vector
z(tj) [Tsum(tj), RI(tj) Rain(tj) Irr(tj), ETc(tj)] whose values are
partitioned into c relevant operating regions (clusters) according to
the Fuzzy C-Means (FCM) algorithm (Bezdek, 1981; Abony, 2003).
These clusters are identied by their labels and their centroids
i
Zi Tsum
; RIi ; ETic ji 1; ; c, dened by the coordinates of each
cluster centre. The degree of membership of a generic input vector
z(tj) to each cluster Zi determines the degree of activation (mi) of the
corresponding consequent linear model, which contains past input/
output samples, taking the form of Eq. (2)
b t
Ri : if z tj Zi then U
i j
ai;0 U tj1 bi;0 Tsum tj2 bi;1 Tsum tj3 bi;2 ETc tj2
bi;3 ETc tj3 bi;4 RI tj1 bi;5 RI tj2 di i
1; :::; c:
(2)
b t of each rule (Ri) is computed by the algebraic
The output U
i j
part of Eq. (2), whose coefcients have yet to be determined. The
b t is then obtained as the average of the individual
model output U
j
b t weighted by their respective degrees of
model outputs U
i j
membership mi
b t
U
j
Pc
b t
mi $ U
i j
:
Pc
i1 mi
i1
(3)
b arg min
P
P
N
2
X
b t
U tj U
j
(4)
j1
PN b 2 C
B
B
C
j1 U tj U tj
C
VAF 100B
2 C;
PN
B1
@
A
U
U
t
j
j1
(5)
where Uis the average soil moisture. Equation (5) compares the
b in the numerator to the
model error variability Utj Ut
j
intrinsic data variability Utj U in the denominator. The summation in Eq. (5) is extended to all the N observations in the active
time-horizon.
77
Fig. 4. Growth area of the crops used in this study, in the Ferrara province, north-eastern Italy. The dark dots indicate the location of the rain gauges, whereas the hollow dots refer
to the crop locations.
78
Fig. 5. Calibration (left) and validation (right) of the fuzzy model Eqs. (2)e(3) with the Corn data from the IRRINET database. VAF as a goodness-of-t measure is computed according to eq. (5).
Table 1
Calibration and validation results for the Corn fuzzy cluster model. VAF as a goodness-of-t measure is computed according to eq. (5).
Crop: Corn
VAFcalib 99.0608
VAFvalid 93.3315
DVAF 5.78%
Antecedents
Location: Berra
Calibration year: 2008; validation year: 2006
Label
Centroids
ao
b3
b4
b5
z1 (L)
Tsum 443.1945
RI 2.5798
ETc 3.2284
Tsum 655.5432
RI 2.4756
ETc 3.8597
Tsum 1980.5421
RI 1.9579
ETc 1.6125
0.970
1.105
1.123
3.191
1.963
0.054
0.104
6.884
1.022
0.837
0.843
2.906
1.144
2.129
0.337
7.589
0.993
0.0619
0.062
0.131
0.652
1.040
0.083
1.194
z2 (M)
z3 (H)
bo
b1
at least in the central phenological period, whereas at the beginning and at the end of the growth season, the FDSS uses a variable
threshold to better adapt the irrigation to the changing crop
phenology.
The inner structure of the FDSS is shown in Fig. 8. In addition to
the soil moisture model of Sect. 2.2. the decision process is split in
two hierarchical levels: rst the need for irrigation is checked, then
the its amount is determined.
b2
b t U t
AND Irr tj1 0 AND Irr tj2 0 ;
U
j
th j
(6)
with tj being the current simulation day. The rst condition ensures
that the soil moisture does not drop below the minimum threshold
Fig. 6. Calibration (left) and validation (right) of the fuzzy model Eqs. (2)e(3) with the Kiwi data from the IRRINET database. VAF as a goodness-of-t measure is computed according to eq. (5).
79
Table 2
Calibration and validation results for the Kiwi fuzzy cluster model. VAF as a goodness-of-t measure is computed according to eq. (5).
Crop: Kiwi
VAFcalib 97.8389
VAFvalid 92.6242
DVAF 5.33%
Location: Berra
Calibration year: 2008; validation year: 2006
Antecedents
Label
Centroids
ao
b1
b2
b4
b5
z1 (L)
Tsum 736.5458
RI 1.8308
ETc 3.6901
Tsum 1881.9935
RI 20.1291
ETc 4.3558
Tsum 2394.8524
RI 0.2053
ETc 3.6378
0.948
0.081
0.081
1.480
0.266
0.875
0.065
11.878
0.971
0.066
0.065
1.093
0.396
1.046
0.237
4.442
0.022
0.669
0.288
1.666
0.034
1.283
z2 (M)
z3 (H)
1.000
bo
0.0224
Uth, whereas the other two prevent repeated irrigation on two days
running. The soil moisture threshold value Uth is crop-specic and
is dened as a time-varying prole, depending on the crop
phenology, as follows:
if PP 3
then
if 3 < PP 4
then
if 4 < PP PPn 1
then
then
b3
Uth tj Ulow
Uhigh Ulow
Uth tj Ulow
tj t3
t4 t3
Uth tj Uhigh
Ufinal Uhigh
Uth tj Uhigh
tj tn1
tn tn1
(7)
1:
DTj Tsum tj Tsum tj1
(8)
Fig. 7. Calibration (left) and validation (right) of the fuzzy model Eqs. (2)e(3) with the potato data from the IRRINET database. VAF as a goodness-of-t measure is computed
according to eq. (5).
80
Table 3
Calibration and validation results for the Potato fuzzy cluster model. VAF as a goodness-of-t measure is computed according to eq. (5).
Crop: Potato
VAFcalib 98.6849
VAFvalid 93.7375
DVAF 5.01%
Location: Ciarle-Mirabello
Calibration year: 2008; validation year: 2006
Antecedents
Label
Centroids
ao
b1
b2
b4
b5
z1 (L)
Tsum 851.8959
RI 4.1583
ETc 2.5932
Tsum 1721.2683
RI 4.9185
ETc 0.6128
Tsum 3282.4682
RI 0.5287
ETc 1.4991
0.769
0.247
0.245
0.857
0.154
0.471
0.070
9.729
0.985
0.081
0.079
0.578
0.603
1.380
0.124
3.637
0.981
0.078
0.076
1.087
0.055
0.158
0.056
8.781
z2 (M)
z3 (H)
2:
bo
2
X
RFj
Rain tji
(9)
b3
Pn m $Irr
i
i1 i
I tj P
n
i1 mi
(12)
i0
3:
Current evapotranspiration
ETcj ETc tj
(10)
Ri : IF DTj is Ti AND RFj isRi AND ETcj is Ei THEN Irri Iri
i 1;;n;
(11)
where Ti, Ri, and Ei are time e invariant fuzzy sets whose membership
functions (mfs) will be dened later, and Iri are the possible (singleton)
irrigation values (Iri 10;30;60). The combined antecedent degree of
membership of the i-th rule (mi), obtained by AND-ing the individual
degrees, represents the relative weight of the corresponding singleton
(Iri). From Eq. (11) the actual irrigation is then obtained by
defuzzication
8
1
>
>
>
>
>
xa 2
>
>
>
12
>
<
ba
zmf x; a; b
>
>
xb 2
>
>
2
>
>
ba
>
>
>
:
0
x<a
ax
ab
2
ab
<x b
2
x>b
Fig. 8. Integration of the predictive soil moisture model of Fig. 3 in the Fuzzy Decision Support System.
(13)
81
Fig. 9. Numerical membership functions of the three antecedent variables obtained by clustering the operational data from the IRRINET database.
8
>
xm1 2
>
>
>
>
2
>
2s
>
1
x m1
>e
<
>
gauss2mf x;m1 ;s1 ;m2 ;s2
1
m1 <x m2 m1 <m2
>
>
>
>
2
> xm2
>
>
>
2
>
:e
2s
2
x>m2
(14)
High (H): S-shaped membership function, with two parameters
(a, b)
8
0
>
>
>
>
>
xa 2
>
>
>
2
>
<
ba
smf x; a; b
>
>
xb 2
>
>
1
2
>
>
ba
>
>
>
:
1
x<a
ax
ab
2
(15)
ab
<x b
2
x>b
It can be seen that the two side-functions zmf and smf are
complementary to one another, i.e. smf 1 zmf . The parameters
of the mfs Eqs. 13e15 were adjusted in two stages. In the rst stage
the parameters were chosen to minimize the sum of squared errors
with the data-generated memberships of Fig. 9. In this way the
intermediate humps of the numerical mfs, due to the constraint
P
m 1, inherent to the FCM clustering procedure, were eliminated. In the second stage, these analytical mfs were used as initial
Table 4
Optimized parameters of the nal membership functions and singleton
consequents.
Antecedents
Consequent
DT
RF
ETc
4.35
20.60
3.21
11.10
2.82
13.01
8.89
20.50
1.09
34.36
3.79 17.90
11.63 46.42
6.14
23.90
Ir
1.38
4.80
0.61 0.95
2.81 6.02
1.30
3.77
10
30
60
conditions for a further tuning where the goal was the minimization of the water quantity, given the model prediction and the soil
moisture threshold of Eq. (7) as constraints. The parameters of the
nal mfs are listed in Table 4 whereas the three groups (datagenerated, tted, nal) of mfs are shown in Fig. 10.
2.4.3. Denition of the FDSS inference rules
At each simulation day tj the irrigation logic computes the
amount of irrigation depending on the three input variables
dened by Eqs. (8e10). The FDSS decision rules were obtained by
N N
starting with the complete set of Nmfsant cons 331 81 combinations and eliminating inconsistent or contradictory rules. A
further decimation was then introduced by eliminating the rules
that during the simulations were globally activated by less than 5%.
This produced the rule set of Table 5, with the last rule being an
override option stating that when the rain forecast is High the
irrigation should be Low, irrespective of all the other conditions.
This reduced set of rules should be regarded as a preliminary
example to demonstrate the conceptual viability of the method at
this early stage of the project. They are neither denitive nor
exhaustive and are expected to be further tested and enhanced
during the eld experimentation, possibly making them cropspecic.
2.4.4. Sensitivity of the FDSS scheme to rain perturbations
To test the robustness of the FDSS scheme, a set of random
precipitations were synthesized on the basis of the rainfall
observed at the sites shown in Fig. 4 in the same calibration year
(2008). For each day we computed the rain mean and variance over
the nine gauging stations and tted a Gaussian distribution to those
data, as shown in Fig. 11. During each simulation, a random sample,
drawn from the distribution of the current day, was introduced into
the model as the perturbed rain. A total of 10,000 simulations were
performed for each crop, producing in the results of Fig. 12.
Only the amount of rainfall was randomized without introducing a corresponding time jitter by varying the timing of the rain
event. Likewise no randomization of the growing degree days
(GDD) was introduced because this would reect into the ETc and
hence into the phenophases. In fact, introducing too many degrees
of freedom into the simulations would make the results difcult to
interpret.
The comparison between IRRINET and FDSS is summarized in
Table 6, that also includes the single simulations with the observed
82
Fig. 10. Evolution of the antecedent membership functions, from their initial shape identied from the data, to the data-generated clusters of the input variables of Fig. 9, until the
nal shape is reached on the basis of the overall irrigation performance.
Table 5
FDSS Decision rules for irrigation. The qualiers L. M. H refer to the quantities and
variables of Table 4 and not to those of Tables 1e3.
n
Rule
1
2
3
4
5
6
7
8
9
10
11
12
If
If
If
If
If
If
If
If
If
If
If
If
Fig. 11. Daily precipitation distributions during 2008 at the sites of Fig. 4. The dots represent the daily spatial average value and the bars extends for 1 std. dev. The shadowed
curves represent the tted Gaussian distributions from which the daily rainfall value was sampled and used in the perturbed simulations.
83
Fig. 12. Comparison of IRRINET and FDSS irrigation schemes where the latter was applied with 10,000 independent realizations of the randomized precipitation process. (a) Corn;
(b) Kiwi; (c) Potato.
For example the rules of Table 5 could be made visible and editable
by the irrigation manager, who can adapt them to the specic crop
needs. As said, the rules listed in Table 5 are neither exhaustive nor
universal, but just an initial seed of knowledge that should be
enhanced with the experience gained through eld practice.
As the project moves forward to its eld implementation further
interactions and renements will be necessary (van Delden et al.,
2011). At this early stage, however, our goal is to test the feasibility of automating the irrigation advice on a simulation platform
(Matlab), with automatic computation of the irrigation at the
faucet. Additional efciency factors related to the type of irrigation
system (e.g. sprinkler, ridge and furrow, etc.) and crop coefcients
could be introduced only after the water distribution system has
been specied. In this sense the approach advocated by Inman et al.
(2011) of evaluating the EDSS based on the perception of groups of
end-users is not yet applicable here, given the early stage of IRRISAVE development, in which our primary goal is to demonstrate
that IRRISAVE could overcome the limitations of IRRINET
mentioned in Sect. 1.1. Following the development of Fig. 1, once the
Table 6
Comparison between IRRINET and FDSS irrigation schemes in terms of water saving, both with observed and randomized precipitations. The FDSS suggestion beats the IRRINET
advice in all cases but one (kiwi validation). The test and val labels stand for test and validation runs. The check sign in the t-test column indicates that the difference between
IRRISAVE and the average FDSS irrigation is statistically signicant.
Crop
Corn
Kiwi
Potato
Observed precipitations
Randomized precipitations
IRRINET irrigation
FDSS irrigation
% Saving
FDSS irrigation
% Average saving
One-sample t-test
test
val
test
val
test
val
226.42
234.79
413.63
4.02.81
138.17
193.15
5.65
1.13
4.24
3.26
34.55
24.61
215.19 15.61
10.33
407.26 19.41
5.71
172.87 17.84
18.12
239.97
237.48
431.93
390.09
211.12
256.20
84
Fig. 13. Comparison between the FDSS and IRRINET irrigation polices for the corn crop in both the test (a) and the validation (b) years. The numbers along the variable soil moisture
threshold (dashed line) indicate the beginning of each phenophase.
Fig. 14. Comparison between the FDSS and IRRINET irrigation polices for the Kiwi crop in both the test and the validation years. The numbers along the variable soil moisture
threshold (dashed line) indicate the beginning of each phenophase.
85
Fig. 15. Comparison between the FDSS and IRRINET irrigation polices for the Potato crop in both the test and the validation years. The numbers along the variable soil moisture
threshold (dashed line) indicate the beginning of each phenophase.
86
Guariso, G., Rinaldi, S., Soncini-Sessa, 1985. Decision support system for water
management: the Lake Como case-study. Eur. J. Oper. Res. 21, 295e306.
Inman, D., Blind, M., Ribarova, I., Krause, A., Roosenschoon, O., Kassahun, A.,
Scholten, H., Arampatzis, G., Abrami, G., McIntosh, B., Jeffrey, P., 2011. Perceived
effectiveness of environmental decision support systems in participatory
planning: evidence from small groups of end-users. Environ. Model. Softw. 26,
302e309.
Lehmann, N., Finger, R., 2014. Economic and environmental assessment of irrigation
water policies: a bioeconomic simulation study. Environ. Model. Softw. 51,
112e122.
Mannini, P., Genovesi, R., Letterio, T., 2013. IRRINET: large scale DSS application for
on-farm irrigation scheduling. Procedia Env. Sci. 19, 823e829.
Matthews, K.B., Rivington, M., Blackstock, K.L., McCrum, G., Buchan, K., Miller, D.G.,
2011. Raising the bar? The challenges of evaluating the outcomes of environmental modelling and software. Environ. Model. Softw. 26, 247e257.
McCarthy, A.C., Hancock, N.H., Raine, S.R., 2014. Simulation of irrigation control
strategies for cotton using model predictive control within the VARIwise
simulation framework. Comput. Electron. Agric. 101, 135e147.
McIntosh, B.S., Ascough II, J.C., Twery, M., Chew, J., Elmahdl, A., Haase, D.,
Harou, J.J., Hepting, D., Cuddy, S., Jakeman, A.J., Chen, S., Kassahun, A.,
Lautenbach, S., Mathews, K., Merrit, W., Quinn, N.W., Rodriguez-Roda, I.,
Sieber, S., Stavenga, M., Sulis, A., et al., 2011. Environmental decision support
systems (EDSS) development e challenges and best practices. Environ. Model.
Softw. 26, 1389e1402.
Merot, A., Bergez, J.-E., 2010. IRRIGATE: a dynamic integrated model combining a
knowledge-based model and mechanistic biophysical models for border irrigation management. Environ. Model. Softw. 25, 421e432.
Paredes, P., Rodrigues, G.C., Alves, I., Pereira, L.S., 2014. Partitioning evapotranspiration, yield prediction and economic returns of maize under various irrigation
management strategies. Agric. Water Manag. 135, 27e39.
Portoghese, I., D'Agostino, D., Giordano, R., Scardigno, A., Apollonio, C., Vurro, M., 2013.
An integrated modelling tool to evaluate the acceptability of irrigation constraint
measures for groundwater protection. Environ. Model. Softw. 46, 90e103.
Rossi, F., Nardino, M., Mannini, P., Genovesi, R., 2004. IRRINET Emilia Romagna:
online decision support on irrigation. Online agrometeological applications
with decision support on the farm level. Cost Action 2004 (718), 99e102.
Shivakumar, H.K., Ramachandrappa, B.K., Mudalagiriyappa, H.V.N., 2011. Effect of
phenophase based irrigation schedules on growth, yield and quality of baby
corn (Zea mays L.). Agric. Sci. 2, 267e272.
Stone, P.J., Wilson, D.R., Reid, J.B., Gillespie, R.N., 2001. Water decit effects on sweet
corn. I. Water use, radiation use efciency, growth, and yield. Aust. J. Agric. Res.
52, 103e113.
Takagi, T., Sugeno, M., 1985. Fuzzy identication of systems and its applications to
modeling and control. IEEE Trans. Syst. Man Cybern. 15, 116e132.
van Delden, H., Seppelt, R., White, R., Jakeman, A.J., 2011. A methodology for the
design and development of integrated models for policy support. Environ.
Model. Softw. 26, 266e279.
van Oel, P.R., Krol, M.S., Hoekstra, A.Y., Taddei, R.R., 2010. Feedback mechanisms
between water availability and water use in a semi-arid river basin: a spatially
explicit multi-agent simulation approach. Environ. Model. Softw. 25, 433e443.
Yager, R.R., Filev, D.P., 1994. Essentials of Fuzzy Modeling and Control. John Wiley &
Sons, p. 408.