Citation: Mimeche, O.; Aieb, A.;
Liotta, A.; Madani, K. A Novel
Interannual Rainfall Runoff Equation
Derived from Ol’Dekop’s Model
Using Artificial Neural Networks.
Sensors 2022, 22, 4349. https://
doi.org/10.3390/s22124349
Academic Editors: Daniele Giusto
and Matteo Anedda
Received: 1 May 2022
Accepted: 6 June 2022
Published: 8 June 2022
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Article
A Novel Interannual Rainfall Runoff Equation Derived from
Ol’Dekop’s Model Using Artificial Neural Networks
Omar Mimeche
1
, Amir Aieb
2
, Antonio Liotta
3,
* and Khodir Madani
2,4
1
Research Laboratory in Applied Hydraulics and Environment (LRHAE), Department of Hydraulics, Faculty
of Technology, University of Bejaia, Targa Ouzemour, Bejaia 06000, Algeria; omar.mimeche@univ-bejaia.dz
2
Laboratory of Biomathematics, Biophysics, Biochemistry, and Scientometric (BBBS), Bejaia University,
Bejaia 06000, Algeria; amir18informatique@gmail.com (A.A.); madani28dz2002@yahoo.fr (K.M.)
3
Faculty of Computer Science, Free University of Bozen-Bolzano, 39100 Bolzano, Italy
4
Research Center of Agro-Food Technologies (CRTAA), Bejaia 06000, Algeria
* Correspondence: antonio.liotta@unibz.it
Abstract:
In water resources management, modeling water balance factors is necessary to control
dams, agriculture, irrigation, and also to provide water supply for drinking and industries. Generally,
conceptual and physical models present challenges to find more hydro-climatic parameters, which
show good performance in the assessment of runoff in different climatic regions. Accordingly, a
dynamic and reliable model is proposed to estimate inter-annual rainfall-runoff in five climatic
regions of northern Algeria. This is a new improvement of Ol’Dekop’s equation, which models the
residual values obtained between real and predicted data using artificial neuron networks (ANN
s
),
namely by ANN
1
and ANN
2
sub-models. In this work, a set of climatic and geographical variables,
obtained from 16 basins, which are inter-annual rainfall (IAR), watershed area (S), and watercourse
(WC), were used as input data in the first model. Further, the ANN
1
output results and De Martonne
index (I) were classified, and were then processed by ANN
2
to further increase reliability, and make
the model more dynamic and unaffected by the climatic characteristic of the area. The final model
proved the best performance in the entire region compared to a set of parametric and non-parametric
water balance models used in this study, where the R
2
Adj
obtained from each test gave values between
0.9103 and 0.9923.
Keywords:
rainfall-runoff modeling; water balance model; ANN model; watercourse; De Martonne
index; inter-annual time scale; northern Algeria; watershed
1. Introduction
Precipitations are the origin of water resources, which undergo different quantitative
and qualitative transformations on the slopes. The losses of rainwater are almost observed
as a form of infiltration, retention in the soil, and evaporation. Some part of this quantity can
also flow into wadis until it moves into the sea. The estimation of actual evapotranspiration
is the component most required for estimating water and energy balance equations [
1
,
2
].
This resource can be accessed on the inter-annual scale, according to the history of climatic
and hydrometric measurements that could be given in the outlet of some watersheds. For
ungauged watersheds, the lack of some information posed a big problem in the estimation
of the mean annual flow, which is the main scientific challenge for many hydrologists
[3–5]
.
The water balance concept was considered to study the hydrological behavior of watersheds
and to describe the relationship between water and thermal components of the earth. This
relativity was defined by a mathematical ratio between rainfall (R), rainfall-runoff (RR),
and real evapotranspiration (Ea) [
6
]. The estimation of rainfall-runoff is necessary as the
first step to search for the best evaluation of Ea. In literature, the first attempts were
started by Schreiber [
7
] and Ol’Dekop [
8
]. Then, Budyko [
9
] proposed an average model of
both previous equations to minimize the estimation errors that were given by Schreiber
Sensors 2022, 22, 4349. https://doi.org/10.3390/s22124349 https://www.mdpi.com/journal/sensors
