Online ISSN: 2382-9931
Journal of Water and Irrigation Management
Homepage: https://jwim.ut.ac.ir/
University of Tehran Press
Evaluation of Entropy Theory Based on Random Forest in Quality Monitoring of Ground Water Network
Fatemeh Bageri1 |Keivan Khalili2 | Mohammad Nazeri Tahroudi3
1. Department of Civil Engineering, Saba Institute of Higher Education, Urmia, Iran. E-mail: [email protected] 2. Corresponding Author, Department of Water Engineering, Urmia University, Urmia, Iran. E-mail: [email protected] 3. Department of Water Engineering, Shahrekord University, Shahrekord, Iran. E-mail: [email protected]
Article Info ABSTRACT
Article type:
Research Article
Article history:
Received: August 11, 2022 Received in revised form:
October 12, 2022
Accepted: October 23, 2022 Published online: April 14, 2023
Keywords:
Entropy Theory,
Information Transformation, Quality Monitoring, Random Forest.
The quality monitoring of groundwater networks is of great importance due to its importance in different sectors of agriculture, drinking, industry, etc., and the necessity of its periodic use leads to the recognition of quality changes of water resources in different periods. In this study, the entropy theory based on random forest was used to quality monitoring of electrical conductivity (EC) and total dissolved solids (TDS) in the groundwater of 12 wells in the Tasouj plain located in south of Lake Urmia from 2002 through 2019. In order to investigate the interaction of wells in the aquifer area, the conventional method (multivariate regression) and the random forest algorithm were used. By comparing the performance of the two mentioned models in simulating EC and TDS values in a 12-variable mode, the results showed that the random forest model has a better performance and a lower error rate than the multi-variable regression model. On average, the random forest algorithm reduced the error rate by 40 percent and 56 percent in simulation EC and TDS values, respectively, in the studied aquifer. The ranking results of the studied wells showed that the Qara Tape well has the highest rank and the Amestjan well has the least important rank among the studied wells, which indicates the importance of the information extracted from the Qara Tape well. According to the zoning of the information transformation index in the aquifer area, the results showed that there is no limitation in monitoring of EC values in the aquifer, and the scattering of the wells is the best. There is no shortage of wells in terms of exchange of salinity information in the study area. Regarding the TDS values, a lack of wells was observed in the central areas and the eastern and western border areas.
Cite this article: Bageri, F., Khalili, K., & Nazeri Tahroudi, M. (2023). Evaluation of Entropy Theory Based on Random Forest in Quality Monitoring of Ground Water Network. Journal of Water and Irrigation Management, 13 (1), 123-139. DOI: https://doi.org/ 10.22059/jwim.2022.347038.1010
© The Author(s). Publisher: University of Tehran Press.
DOI: https://doi.org/ 10.22059/jwim.2022.347038.1010
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Table 1. Statistical characteristics of the investigated data in the Tasouj aquifer
Well Min Max Mean STD
Almas 435.0 799.00 659.57 84.96
Emstjan 1018.5 1400.0 1277.9 99.32
Tasouj 962.0 1523.5 1340.40 174.18
Angeshtjan 648.0 1020.5 839.68 126.03
Topchi 1177.0 2390.3 2007.94 259.39
Til 1064.5 2564.0 1754.99 478.28
Cheshmeh Konan 1280.0 3300.0 2047.31 608.55
Chehregan 563.0 2299.7 1268.31 554.05
Dizaj Sheikh Marjan 508.5 726.0 611.09 56.94
Gholmansara 1273.5 2755.0 1850.84 559.13
Qareh Tapeh 1650.0 2930.0 2144.31 410.33
Gezelcheh 2500.0 329.0 3012.90 203.74
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The degree of importance of the area
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- _# < * - =< H"I ? D
9 ! B - ) 3 ( B - _# < . - D )
3 ( & # * *
W ? @ A? B+ C ) .
D
>"D ? " &
"P< W
# * . - D @ A? B+ C &
" - # 2 )
EC
W ) . D
>"D ? 80
! " & D F * - D
"P< W
>"D ? ) SL K" ) D ! . - D
RMSE
" - @ A? B+ C & ( # 2 )
EC
" & D F
"P< W K"
D 9 ! B - ) 4 ( . BD X . - D
>"D ? _# < ) D ! T#
RMSE
B - D C ? D @ A? B+ C & - )
4 ( IN W W D n D
? . - D
B - D C ? D )
4 (
" - ) SL K"
# 2 ) ]„< EC
" & D F @ A? B+ C &
"P< W B - D C ? D .F <@ # D
) . ) 2 ( ) 3 ( ) 4 ( BD X FX ? @ A? B+ C & & X
" - )
EC
W BD 2< ] D " & D F C ) .
"P< W . * .
Figure 2. The results of investigating the error rate (RMSE) of random forest models and multivariate
regression in the simulation of electrical conductivity values in the studied stations.
Figure 3. Performance evaluation of random forest models and multivariate regression in the simulating of EC values in the studied stations using Nash-Sutcliffe statistic
Figure 4. The percentage of improvement of the simulation results of EC values due to the random forest
model compared to the multivariate regression model in the studied stations
3 . 2 .
! 3
' 4
5 6 ' 7 4 TDS *
# 2 .
EC
# 2
TDS
W ) . G S
" & =< D K"
"P< W @ A? B+ C
W BD 2< ] D F C
" - +# # D F .
" - _# < . - ) )
=< D .
RMSE
D NSE
# 2 D _# < .F@ X
" - RMSE
# 2 ) DTDS
9 ! B - ) 5 ( D . - o
B - D C ? )
5 (
" - SL K" D _# <
# 2 )
TDS
W ) . G S
9 ""P? *
RMSE
&
"
"P< W T"D
16 I"
? C ƒ"- Y +< # <" D J 509
I"
<" D J
"P< W +< #
" - _# < BD 2 . - D # 2 )
TDS
W @ A? B+ C =< D ) .
G S T"D & T# ) SL K" *
7 / 13 I"
D J ? C ƒ"- YK# W <"
72 I"
D J
"P< d< W <"
# 2 9 ""P? * D C ? D . - D & RMSE
D * _# <
" & D ) G j:<L @ A? B+ C &
"P< W
" - # 2 )
TDS
D _# < . # *
&
) . D
" - # 2 )
TDS
K"
D 9 ! B - ) 6 ( B - D C ? D . - o )
6 ( # 2 a <
NSE
W ) . G S
@ A? B+ C &
75 " & !
"P< W Z
37 ! . - D
" & I
"P< W
" - # 2 )
TDS
F# w >ED " & OX . - D
"P< W
W BD 2< ] .
D D L # 2 # 2 _# < .F D " & RMSE
"P< W B+ C &
@ A?
D 9 ! B - ) 7 ( # 2 ) D ! . - o
RMSE
D F @ A? B+ C &
" &
"P< W B -
) 7 ( D . BD X q w W ? . - D
) . G S
# 2 ) D !
RMSE
BD X . @ A? B+ C & OX . - D D
D L K" F < ?
RMSE
" & D F
"P< W . . >. *
>"D ? # 2 >. * T#
RMSE
W B"? +< # D n D D
Q"? ? Z 81 / 87
32 / 87 ! . - D D
; " & D # 2 @ A? B+ C & K" a <
"P< W
B* F ?
V G S
K"
" - - RMSE
# 2 ) Z TDS
56 . . >. * ! # 2 # 2
" - ) -
EC TDS
2S G S
" & =< D
"P< W
@ A? B+ C
" - ) SL K" F < ? @ A? B+ C & * # 2 )
EC
+< # Y ? d< h ) .
ƒ"- YK# W * W B"? y0 ? d< + IN C
X c?
y KX D
Q"? ? Z 6 / 13
5 / 45 3 / 56 30 3 / 48 8 / 42 1 / 28 82 5 / 8 7 / 62 2 / 38 1 / 18
" - ) SL K" ! # 2 )
TDS
D Q"? ? Z 4 / 28 7 / 40 4 / 76 5 / 81 9 / 9 8 / 78 5 / 20 3 / 87 8 / 14 6 / 78 1 / 73 4 / 80 ED D ! "
.F
3 . 3 . ' " # 3 EC
'8 TDS 9: 8
@ A? B+ C & ( E< D F#
D
" - " ? D &
# 2 )
EC TDS
^.
T" W &
W BD 2< ] D i AL ? D W BD 2< ] Y ? V .
) '? - D +# # D F .
C 0 <
- ? . # 2 =< D .
EC TDS
^.
T" W
" - # 2 )
B+ C & =< D -
eL - @ A?
^ - D 0 < ) . eL - T# ?
) ) .
ITI
? _# < . - o (N(i)
W ) D ) .
D eL - =< D
N(i)
D 9 ! & C ) 3 ( . - o eL -
N(i)
eL - #
" ^ ) .
" # ( - ># 0 W ? eL - T# . - D
2S F" . g . # 2 . .
N(i)
F x
. W )M D F" . F- g
? D . - D & C D C
) 3 ( W ? ? 2S C ) .
G S < 0 D C ? D
EC
W & C T# D C ? D . * . TDS
X c?
? 1 .
< 0
EC TDS
_# < T# .F * Q *
? ! * . W s# - D " *
D F- j G
9 :; & ? g
EC TDS
W - @ G 2S X
c?
#K T# < D W T# T"D n ? OX . - D
W # D 2S ) .
G S
>"D ? o _# < D C ? D . - D -
# 2 ?
EC TDS
W T#
)X c?
="* "P< . ) D K" d< W . ^" G? ED B* D (
EC TDS
>"D ? Q * ? T#
* F *
. W # D W T# H"Gw n ? .
# 2 D C ? D . - D W N(i)
d< ) .
h Y ?
^*
? # 2 D C ? D ? T#
W EC
9 :; & 2< D C ? D y KX W d< ) .
TDS
^*
?
* Q * ? T#
.
Figure 5. The results of investigating the error rate (RMSE) of random forest models and multivariate
regression in the simulation of TDS values in the studied stations.
Figure 6. Performance results of random forest models and multivariate regression (Nash-Sutcliffe statistic) in the simulating of TDS values in the studied stations.
Figure 7. The percentage of improvement of the simulation results of TDS values due to the random forest
model compared to the multivariate regression model in the studied stations
Table 3. The ranking results of the studied wells based on the quality values of EC and TDS
Well N(i)-TDS N(i)-EC Rank based on EC Rank based on TDS
Almas 0.010 -0.0242 10 4
Emstjan -0.281 -0.3294 12 12
Tasouj -0.002 -0.0334 11 8
Angeshtjan 0.018 -0.0125 7 2
Topchi -0.002 0.0000 5 7
Til 0.000 0.0001 3 5
Cheshmeh Konan 0.000 0.0001 4 6
Chehregan -0.017 -0.0230 9 11
Dizaj Sheikh Marjan -0.003 -0.0192 8 9
Gholmansara 0.011 0.0002 2 3
Qareh Tapeh 0.041 0.0002 1 1
Gezelcheh -0.008 -0.0002 12 10
eL - +# # # 9 :; & 2< eL - 0 < ) '? ^ ) .
ITI
# * eL - T# . - D
9 :; + K@
EC TDS
2S ="* # 2 ># 0 " 9 :; eL - T# . .
2S
"<L X h Z W * # <- W * 2; . . "D eL - T# a ? -
^" A? F C . - < D ) "
^.
T" W # 2 < D >#
ITI
2S G S
# 2
ITI
D n D
< 0
EC TDS
0 ) D D 9 ! B - ) . ) 8 ( ) 9 ( D Q"? ? # 2 ) D
EC TDS
. - o D C ? D
B - ) 8 ( 0 i AL # 2 ) D
EC
Y ? F- ED |S
2S B* * * . ?
G S X a < >"D a < F Z F X ? <@
* ED X - n 2 W * ) .
. ) - 9 :; & 2< g W 9 :; & 2< g g ED - )K* Z . -
D . C 2S T# W * F <@ X a < F"Gw ) - 0 g I* ;
<
EC
2S G S
W * 0 <- C ># 0 .
D D L W IG@ * 0 "W D . - D
.
2S G S
F"Gw 9 :; ?
EC
D _# < . * D 2S
* .
2S G S
# C W … Z 2S D C `; . ? w < D ># 0 F C
G S J C D
9 :; & 2< g W * K" W †Z
EC
. T" . K" 0 < ) '? ^ ) . D * # . -
d"< T# .F z w Y ? B"? T"D ) - 9 :; & 2< 2S T# W * C D .
D D L " # ( |S Z T# < .F X D D
B"
D M D " W # D # K
EC
Z T#
K"
>"D ? - Z < 0 . - D
TDS
9 =< a# - T#
B - D C ? D . - D )
9 ( ?
X - ) )K* Z < X * * .
^.
T" W & ? g Y ? ED D N ) Z
9 :;
TDS
W * W ED )K* Z . - D
G S W * 0 g a < F Z K"
.
. X
2S - ) Z
G S
^.
T" W
F C . X F Z ED X - ( C Z
2S ED " D ># 0 G S
9 :; ># 0 g Y ? F- Z # C W … Z D " TDS
u K X
" D ># 0 j . * ? ! . - D D *
- D " # ( ="* -
?
h D
C _# <
# * =Z # C ) . 9 :; & 2< * # .
^*
? . * j‚Z ^< " )
- F C W * # . W ?
- * j‚Z #M D ? * # . * # .
G?
Q W
F < D F " C .
h D
"0
Mogheir et al.
(2006)
W # * < ) .
W . * =< - ># 0 F C ( - ) .
Figure 8. Zoning of ITI index values regarding the qualitative monitoring of EC values
Figure 9. Zoning of ITI index values regarding the qualitative monitoring of TDS values
4 .
< 12
=
G S T#
*
# '?
) 0 <
? D )
># 0 2S ) Y ? ED " # ( F"="* -
# D F@ X .
# 2 i AL T#
EC TDS
" # ( 12
) W 2IZ
98 - 1382
W BD 2< ] D F C J 0 < ) '? . - =<
"P< W " +# # D F .
=<
. -
^.
T" W W BD 2< ] D @ A? B+ C ^<# + FX # *
" * .
"P< W D _# < . - D
@ A? B+ C & * . D
D L W BD 2< ] F < ? D .
" & D # 2 @ A? B+ C & # * K" *
"P< W BD 2< ] D . ED D
+< # - `@ @ A? B+ C . D
; ) SL K" a <
RMSE
" - ( +< # BD 2< ] )
.
< 0
EC TDS
D Q"? ? Z 56 40 @ A? B+ C & ( E< D . . >. * J D F !
D eL - ? D &
eL - D _# < . - D 0 < ) '? ) . ="* ># 0 D n D ITI
# 2
EC
ED IG@ F"Gw * G S
W IG@ "W D D Q * 0 g & 2< C ) .
" # ( ) - 9 :;
D D L ># 0 `"X ># 0 F C Y ? F- ED IG@ F"Gw D C ? D . -
# 2
EC
C # C W =Z D "
2 ; . # 2 i AL Q N ) D
ITI
< 0
EC
X <
W . X c?
d< W D
Q"? ? F" . D F" . ^* T# ? # 2 ># 0 i AL W T# ?
ED EC
Y ? F- # 2 ># 0 _# < . - D
TDS
eL - D C ? D Y ? F- ED
ITI
L D *
( C ) )K* n 2 h Z W * ED € - ( N
. - D g
`"X ># 0 F C ?
9 :; & 2< D
TDS
F- ED D
W =Z D "
2S # C ) . * - D
?
# 2
TDS
W # 2 . . * =< K" ( - # ? . ) .
EC
W ) . X c?
d<
D Q"? ?
F" . D
^* T# ? F" .
W T# ? ED . z w T# . - D
# 2 ^" G? ># 0 ) D * .
EC
# 2 F < D Y ? ED D TDS EC
W TDS
X c?
W . - =<
#M D ? * # .
* Q * G@
"
F d? JKI< .
# g C ) D W T# ) .
< .
^*
? L D ) . - D
W Bx # . X
c?
? *
^*
?
* Q * )
=
"
?
# - 9 :; T 0
#
? >
"
# T# ‡=Z
W ) w " # ( - . "IX 9 ""P? D C ? D . - D
^.
T" W
= F- D ># K@
># 0 .
" # ( ="* *
? D ( F"="* F" * i AL . ^< "
# ) . * * B "
^. @ T# 0 <
.F *
& " # ( ="* * 9 ""P? "IX 9 ""P? D C ? D ) .
# HI<E n 2 "L D
/#
h Z >"0 >"D " # ( ="* * ># 0 J K " W # w Z
) D * d"< . * F# # C ( OD <D |"V! F# # D ? - T#
>. /0 " D ) # o
" # ( ="* ># 0 F C +< # BD 2< ] <D * - D
. T" E? ) ?M D F"GSX FX D .
5 .
?!
* 1. Information Transfer Index
6 .
A B 9
f".
. C # T"D G@ ˆ G?
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