
Experimental models (black box model) do not explicitly account for the physical laws
of the processes and only connect the input and output via the conversion function.
The second group consists of conceptual models, which are based on limited studies
of the existing processes in the basin hydrology system, as opposed to the
distributional physically-based models; their development has not been based on the
total number of physical processes but rather on the designer's comprehension of the
system's behavior. The third group consists of distributional physically-based models;
these models attempt to account for all the processes within the desired hydrological
system by applying physical definitions. In contrast, physically based models provide
a more realistic approach by mathematically representing the real phenomenon. Even
though physically-based models appear to be more suitable for modeling purposes,
they lack acceptability because of their fundamental uncertainty and high
computational cost.
Reports indicate that machine learning techniques such as ANN and FIS effectively
model such complexities (flow coefficient). Their simplicity and capacity for dealing
with nonlinearity without understanding the entire system distinguish them from
others. Numerous examples in the literature demonstrate that fuzzy logic (FL)-based
systems excelled at modeling different hydrological events such as precipitation,
runoff, streamflow, etc. Due to the presence of uncertainty and vagueness in these
domains, FL-based systems are well-suited for modeling.
This study proposes one of the pertinent machine learning algorithms, the Adaptive
Neuro-Fuzzy Inference System (ANFIS), for estimating the flow coefficient. The
ANFIS model employs Tagaki-Sugeno-Kang (TSK) first order [13,14]. As a flow
coefficient prediction, the hybrid learning algorithm is selected from various algorithms
for supervised learning. The widespread use of hybrid learning algorithms justifies
their selection. An advantage of ANFIS is that it is a combination of ANN and fuzzy
systems employing ANN learning capabilities to acquire fuzzy if-then rules with
suitable membership functions, which can learn something from the inaccurate data
that has been input and leads to the inference. Another benefit is that it can effectively
utilize neural networks' self-learning and memory capabilities, resulting in a more
sustainable training process [15].
These methods (ANFIS and other fuzzy systems) lack a definitive method for
determining the number of fuzzy rules and membership functions (MF) required for
each rule [13]. In addition, they have no learning algorithm for refining MF that can
minimize output error. Therefore, Toprak in 2009 [16] proposed a new method known
as the Simple Membership functions and fuzzy Rules Generation Technique
(SMRGT). This new technique takes into account the physical cause-and-effect
relationship and is designed to assist those who struggle to select the number, form,
and logic of membership functions (MFs) and fuzzy rules (FRs) in any fuzzy set.
Gaussian Process Regression (GPR) is a statistical learning theory and Bayesian
theory-based machine learning technique. It is well-suited for handling complicated
regression tasks, such as high dimensions, a small number of samples, and
https://doi.org/10.17993/3ctecno.2023.v12n2e44.125-146
nonlinearity, and it has a substantial potential for generalization. Gaussian process
regression has many favorable circumstances over neural networks, including simple
implementation, self-adaptive acquisition of hyper-parameters, flexible inference of
non-parameters, and probabilistic significance of its outcome. Results are less
affected by bias and easier to read thanks to the GPR's seamless integration of
hyperparameter estimates, model training, and security assessments. Processes with
a Gaussian (GP) distribution take it for granted that the overall distribution of the
model's probabilities is Gaussian.
The objectives of this study are to (1) compare the predictive power of the ANFIS,
SMRGT, and GPR models and (2) select the model and algorithm with the highest
degree of accuracy and the lowest error rate. This is the first attempt to compare the
abovementioned models to determine the flow coefficient.
2. MATERIALS AND METHODS
2.1. AREA OF STUDY AND DATASET
The Aksu River basin is located in the Antalya Basin, southwest of Turkey. The total
length of the Aksu River is approximately 145 km, with headwaters Akdag situated
within Isparta Province and discharges to the Mediterranean from the Antalya-Aksu
border. The southern part of the basin is narrower than the north. Two different
climatic types, Mediterranean and continental climates, are observed in the Aksu
River basin. The north part has low precipitation throughout the year, and the
northwest and northeast mountain areas are the highest areas and have lower
temperatures, intense precipitation, and snow, whereas the south plain areas are
generally warmer with intense rainfall and evaporation. Several measurement data
are collected to support the study. The primary data are obtained from TSMS (Turkish
State of Meteorological Service). The data processed for this study are precipitation,
temperature, and humidity.
2.2. CLIMATE PROPERTIES OF THE STUDY AREA
2.2.1. PRECIPITATION
The most severe effect of climate change is a rise in the frequency and intensity of
extreme weather events in some parts of the world; the most obvious manifestation of
this is the recent rise in the frequency and intensity of extreme precipitation in various
parts of the world, which is causing infrastructure systems to become completely
inadequate. Precipitation ranks among the most crucial elements of climatic
parameters and atmospheric circulation, as well as the element that provides water to
the land and is the primary flow source. In this work, the precipitation stations' data
and locations are obtained from TSMS (Turkish State of Meteorological Service). 57
https://doi.org/10.17993/3ctecno.2023.v12n2e44.125-146
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254-4143
Ed.44 | Iss.12 | N.2 April - June 2023
129