Online ISSN: 2382-9931
Journal of Water and Irrigation Management
Homepage: https://jwim.ut.ac.ir/
University of Tehran Press
Investigating the Efficiency of the Multi-Model Ensemble System to Improve the Forecast Skill of Numerical Precipitation Models
Mitra Tanhapour1 | Jaber Soltani2 | Bahram Malekmohammadi3 | Kamila Hlavcova4 | Mohammad Ebrahim Banihabib5
1. Department of Water Engineering, Faculty of Agricultural Technology, University College of Agriculture and Natural Resources, University of Tehran, Tehran, Iran. E-mail: [email protected]
2. Corresponding Author, Department of Water Engineering, Faculty of Agricultural Technology, University College of Agriculture and Natural Resources, University of Tehran, Tehran, Iran. E-mail: [email protected]
3. Department of Environmental Planning and Management, Graduate Faculty of Environment, University of Tehran, Tehran, Iran. E-mail: [email protected]
4. Department of Land and Water Resources Management, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia. E-mail: [email protected]
5. Department of Water Engineering, Faculty of Agricultural Technology, University College of Agriculture and Natural Resources, University of Tehran, Tehran, Iran. E-mail: [email protected]
Article Info ABSTRACT
Article type:
Research Article
Article history:
Received: October 18, 2022 Received in revised form:
January 20, 2023 Accepted: April 03, 2023 Published online: April 14, 2023
Keywords:
Ensemble precipitation forecasts, GMDH model,
Multi-model ensemble, Post-processing techniques, Regression models.
The lead-time and accuracy of the precipitation forecasts have a substantial influence on the flood forecast and warning systems. This research aims to improve the skill of numerical precipitation models using post-processing techniques. In this regard, EPFs of three meteorological models, e.g., NCEP, UKMO, and KMA, were extracted for sex precipitation events leading to flood in the Dez river basin. The statistical approaches and data-driven model were applied to post-process the EPFs. For this purpose, the raw forecast of every single model was corrected using linear and power regression models. Then, the corrected output of single models was combined using the proposed model of Group Method of Data Handling (GMDH) to construct the multi-model ensemble system. The results indicated that Power Regression Model (PRM) outperformed the mathematical linear models to correct raw forecasts. After correction of the dynamical models' output, more accurate results were obtained by NCEP and UKMO models. Moreover, the Multi-Model Ensemble (MME) system constructed by the GMDH model (MME_GMDH) had a great effect on the skill of numerical precipitation models, so that the Nash–Sutcliffe and normalized error (NRMSE) efficiency criteria for MME_GMDH respectively were improved on average 23 and 11 percent in comparison with the PRM. A comparative assessment of the discrimination capability of MME with single ensemble models using ROC curve at the thresholds of 2.5 and 10 mm represented a higher discrimination ability by MME_GMDH for both thresholds. Post-processed EPFs exert as a reliable input to the hydrological models for extreme events forecast.
Cite this article: Tanhapour, M., Soltani, J., Malekmohammadi, B., Hlavcova, K., & Banihabib, M. E. (2023).
Investigating the Efficiency of the Multi-Model Ensemble System to Improve the Forecast Skill of Numerical Precipitation Models. Journal of Water and Irrigation Management, 13 (1), 275-293.
DOI: https://doi.org/ 10.22059/jwim.2023.350086.1025
© The Author(s). Publisher: University of Tehran Press.
DOI: https://doi.org/ 10.22059/jwim.2023.350086.1025
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Homepage: https://jwim.ut.ac.ir/
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Table 1. Characteristics of precipitation events in the studied area
Precipitation depth (mm) Time (hr)
Date of end Date of start
No
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1
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Table 2. Characteristics of the numerical precipitation models used in this research
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N K ' : P!!
. *S JI M D: ;< P '% \6 R % P! ! gW
' O ! * 4
. S XO P %
P O % b!
D!< R I ' : % ' h '% O,: o J"I J, '% 0", O % !%
. *S J?O
', ? J"I ' h % *W* ' h a O P O % '7M P (No < Y % ! *" % a O . *S
fI*O
R *` P !n . *S
%
% Y* Y '%
.
D!< ? '" / (N S Y
!%
D!< ) : S !%
XO % * I % :
6 ' h
'%
0 )
Chang and Hwang, 1999
.(
D!< ? ' "S : !mO D: ;< P
!%
) 1 * E % S :
? W 6 !mO 0 NWP
% : N: . S %
P! H 70 ` '% *z4 : '% y*% E % :
"S E * % [ R *`
' 30
S UO * % ` )
Theocharides et al., 2020
( 3: . ' ' * ' "S '% ) P O6 *S
' h % ' R X P % 0 4* [ "[4 :
P!! E * '7M % 1 * '!> ? F :
' ! % ? G] *S :
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XO R *`
h % 0I "[4 ' "S ) '% 0",
'%
) ! : :
Kardan Moghaddam et al., 2021
0 W D: ;< P 074 P!3: '% .(
% b!
) ) E % 4 f7OU : .0 S XO GMDH
2 . 4 . - . /
& 0
D!< 0/` .!
!%
G< : E <
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) W S
) 3 ) 0 S % (
Fallah Kalaki et al., 2020
.(
Table 3. Evaluation metrics for verification of the post-processed precipitation forecasts
Best fit/
Poorest fit Description
Equation Evaluation metrics
1/-∞
Measure of the relative magnitude of the residual variance compared to the observed data variance
&'( ) ∑ * +,
∑ * *-, Nash-Sutcliffe Efficiency
1/-∞
A function of correlation, bias, and variability ./( ) 0 ) 1,) 2,) 3,
Kling-Gupta Efficiency
Capability of linear relationship between 1/-1 observed and forecasted data
1 ∑ * *- + +- 0 * *-, 0 + +-, Pearson coefficient
The difference between observed 0/
and forecasted data
&45'( 6)&∑ * +,
*- Normalized Root Mean Square Error
The difference between observed 0/
and forecasted data 57( )
& 8|* +|
Mean Absolute Error
Note: : and ; respectively represent the observed and forecasted precipitation data; :< and ;< denote observed mean forecasted men; N is total number of the precipitation records; = is the bias ratio ( = ;< :<⁄ ); ? is the variability between forecasted and observed values (? @AB⁄@AC); @A is the coefficient of variations.
€6 S % 84 'r :
v* ) W S 734 '[U /
)14
(ROC
* % %
F! X D!< g<
!%
'O % R : '% 0", h 3OM : %
t .% % ? ' *3 %) S
FH*
) 0 S XO (€U ' O F
D’onofrio et al., 2010; Jha et al., 2018
7 0> M .(
% ? D!%
S % €U ' O P !n .( < }*I ) 0 ƒ E % ' I 0X *
Y !>* E .( < }*I Y 4) 0 ƒ % ' I R *`
P %ROC
J ' 0 R *`
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D : :′R *`
) W) N!,?
4 .(
q %
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: Y 4 : *#
D!< E % '% y*%
.0 S !%
0 H
D!< }*I ƒ < ' : ) 0 S !%
.(0 S ` ` : ' 0 FA
.0 ƒ < 0! I *S !%MA
ƒ < '
> M :
0 ` % : '
4 < }*I Y 4 CN
` Y
: ) S %
D’onofrio et al., 2010
.(
q %
*6 % | : * g R /!V*
)15
FG
( '%
R *`
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; G ; :′⁄
.(
P % / b!
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03 '%
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Y
%ROC
E % ' O Z\
5 / 2 10 7!
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b!
E % ' O !%
P! FH* : S N! S %
) 0
Zakeri et al., 2014
.(
Table 4. Contingency table for ROC curve
Total Non-occurrence
Occurrence Observed
Forecasted
A FA
H Alarm
A' CN
MA No-Alarm
N O'
O Total
Note: H, FA, MA, and CN relatively are hit, false alarm, miss alarm, and correct no-alarm
3 . 12 % 3 -
Y D!< R *" % % : ) !%
D . *: $V 4 : XO :
F!
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G< Z!/[ '% y*% a O O%
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) XO % E % 'r \6 !n \6 *! :
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b! 0 W GMDH
% Z!/[
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: *6 % :
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Y 6 :
Z!/[
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R *`
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a O % .0 S E %NWP
q %
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.0 S Y o * E * JM : (MAE
% : ! ? ', ? ) W
: ) 5 ) ( 6 ( ) :
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% Y 6
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) '% 0", * *! : \6 V :
D!%
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Table 5. Linear regression model and efficiency criteria for post-processing the ensemble precipitation forecasts
NWP models Linear regression models
Evaluation metrics
Train Test
NSE MAE NSE MAE
NCEP C 0.184 1.191 0.531 2.838 0.651 2.108
KMA C 0.933 1.205 0.518 3.115 0.51 2.725
UKMO C 0.038 0.841 0.473 2.704 0.462 2.671
Note: C is the observed precipitation and and is the raw EPFs
Table 6. Power regression model and efficiency criteria for post-processing the ensemble precipitation forecasts
NWP models Power regression models
Evaluation metrics
Train Test
NSE MAE NSE MAE
NCEP C 1.021 . #O 0.532 2.816 0.651 2.107
KMA C 0.485 .!# 0.53 2.972 0.5 2.658
UKMO C 1.032 .O " 0.541 2.701 0.513 2.682
Note: C is the observed precipitation and and is the raw EPFs
'%
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R *" % % PRM
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7 % (
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q %
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D!< R % : ! '!7 !%
G< : E <
% '% 0", S ) P Y 6
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D % : ! ? -
f!7
R !!m ` \6 d7\ P! ! ) % :
)NCEP
'%
b!
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UKMO
) '%
b!
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d!I 'r .
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!%
:
G<
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)MAE
'%
b!
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` 20 0 † [O6 *6 '% ( ` Z!/[ G< a O *" % .! 0X *
) 1 * :
) % PRM
) '% 0", UKMO
q*,/ R !!m : '% Y h .
0 w '%
J!>
P G< '
Z!/[
% )
: d!I a O NWP
'% 0", b! J34 0 S J` M Y 6 :
% P
) ) 1 * ! : % GMDH
Z!/[ : .0 S Y o S
Table 7. Efficiency criteria for raw and corrected ensemble precipitation forecasts Evaluation metrics NCEP The percentage
of variations
KMA The percentage of variations
UKMO The percentage of variations Raw Corrected-PRM Raw Corrected-PRM Raw Corrected -PRM
NSE 0.53 0.55 +4 0.51 0.52 +2 0.51 0.54 +6
Pearson correlation 0.74 0.74 0 0.72 0.72 0 0.72 0.75 +4
NRMSE 0.82 0.8 -2 0.85 0.83 -2.3 0.81 0.71 -12
MAE 2.57 2.18 -15 2.85 2.62 -8 2.78 2.21 -20
3 . 2 .
6 '
7 ' GMDH
P D: ;<
'%
*L ) '!> 1 S 0! \I Y 4 ) 34 :
) P \6 S 0! \I Y 4 NWP
:
d!X7 ) 0 S XO
Hagedorn et al., 2005; Chen et al., 2021
.(
D!< % ' F !%
'4*3o (... E % ) 3!7I !mO )
S *: : XO
'% *S X ) F W
D!< 0I % S *:
h % !%
'%
* 4 b! % )
% ) '!7
XO S *: : S
'%
*L
G<
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XO S *: : ) ' H 3: ) '% ' *S
'OX (MME
. *S
q %
D!< F P b! J O M !%
% '4*3o
) : J` M NWP
*S
)
Krishnamurti et al., 2009; Hagedorn et al., 2005
d!X7 % D: ;< P .(
) :
GMDH
D!< b! a O .0 S XO
!%
XO % % 3: : )
* E * JM %GMDH
0 O J }*3o ) ) W E % :
8 O% % : ! 0 w '% Y h .0 S 'r (
'%
3: % z4 F : '%
R *`
J P! ! ? G] S '" / .o 20
% *z4
) W ) 8 ( 'r .0 S
Table 8. Efficiency criteria for the combination of EPFs using GMDH model Evaluation metrics Train data Test data All data
NSE 0.68 0.65 0.68
KGE 0.75 0.68 0.73
Pearson correlation 0.82 0.83 0.82
NRMSE 0.63 0.64 0.65
MAE 2.15 2.18 2.11
'r a O v* ) W S ) % :
) 734 *" % 3 D? GMDH
:
NWP
D!< %
. : % !%
N:
P! H 'r a O ', ? S
) W : ) 7 ) ( 8 ( :
.!
D!< 3O4 0!7% I R
!%
b! 1 * :
% )
: G< '% 0", NWP
X ) : E <
J% I .! '% NWP
'LM8
*# .0 'O *" % D : ! '
- ) f!7 R % P! ! gW (NSE
) \6 ) S
NRMSE
( '%
*#
1 *O 23 ` 11 ` ) '% 0", . O *" % * *! :
P D!< 0!X! *" % % y " a O ) !%
: b! XO %NWP
% ) P
a O % :
D: ;<
: ) 0?% \ J"I
Hagedorn et al., 2005; Pakdaman et al., 2022; Saedi et al., 2020;
Aminyavari and Saghafian., 2019
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Figure 4. The variations trend of the ensemble precipitation forecasts compared to the observed precipitation for all dataset using GMDH model
0 5 10 15 20 25 30 35
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Precipitation (mm)
Data sample
Obs Ens
2.5 mm (b)
Figure 5. ROC curve for the raw forecasts compared to the multi-model ensemble precipitation forecasts. (a):
2.5 mm (b): 10 mm
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3: % !%
q %
/ Z\ 0M , €6 S ROC
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Javanshiri et al.
) (2021
. 0 %
Figure 6. RSS for the raw and multi-model ensemble precipitation forecasts 0
0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
Hite rate
False alarm rate
Raw_NCEP Raw_KMA
Raw_UKMO MME_GMDH
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
Hite rate
False alarm rate
Raw_NCEP Raw_KMA
Raw_UKMO MME_GMDH
0.79 0.85
0.71 0.73
0.81 0.84 0.76 0.86
0 0.2 0.4 0.6 0.8 1
2.5 mm 10 mm
RSS
Thresholds
NCEP_RAW KMA_RAW UKMO_RAW MME_GMDH
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: * *! ) XO %NWP
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D!%
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%
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Figure 7. Box-plot of the observed precipitation compared to the posed-processed ensemble precipitation
4 . 8 -
% '%
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'[U P :
D!< % 3!7I 8! W !%
i*> !: :
P . 0!3:
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