Published

2025-01-31

Neural Networks and Fuzzy Logic-Based Approaches for Precipitation Estimation: A Systematic Review

Enfoques basados en redes neuronales y lógica difusa para la estimación de la precipitación: una revisión sistemática

DOI:

https://doi.org/10.15446/ing.investig.108609

Keywords:

precipitation, river basin, neural networks, fuzzy logic, machine learning, fuzzy inference systems (en)
precipitación, cuenca hidrográfica, redes neuronales, lógica difusa, aprendizaje automático, sistemas de inferencia difusa (es)

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Precipitation estimation at the river basin level is essential for watershed management, the analysis of extreme events and weather and climate dynamics, and hydrologic modeling. In recent years, new approaches and tools such as artificial intelligence techniques have been used for precipitation estimation, offering advantages over traditional methods. Two major paradigms are artificial neural networks and fuzzy logic systems, which can be used in a wide variety of configurations, including hybrid and modular models. This work presents a literature review on hybrid metaheuristic and artificial intelligence models based on signal processes, focusing on the applications of these techniques in precipitation analysis and estimation. The selection and comparison criteria used were the model type, the input and output variables, the performance metrics, and the fields of application. An increase in the number of this type of studies was identified, mainly in applications involving neural network models, which tend to get more sophisticated according to the availability and quality of training data. On the other hand, fuzzy logic models tend to hybridize with neural models. There are still challenges related to prediction performance and spatial and temporal resolution at the basin and micro-basin levels, but, overall, these paradigms are very promising for precipitation analysis.

La estimación de la precipitación a nivel de cuenca hidrográfica es esencial para la gestión de cuencas, el análisis de eventos extremos y dinámicas meteorológicas y climáticas, y el modelado hidrológico. En los últimos años se han empleado nuevos enfoques y herramientas como las técnicas de inteligencia artificial para estimar la precipitación, ofreciendo ventajas sobre los métodos tradicionales. Dos paradigmas principales son las redes neuronales artificiales y los sistemas de lógica difusa, que pueden utilizarse en una amplia variedad de configuraciones, incluyendo modelos híbridos y modulares. Este trabajo presenta una revisión de la literatura sobre modelos híbridos metaheurísticos y de inteligencia artificial basados en procesos de señales, centrándose en las aplicaciones de estas técnicas en el análisis y la estimación de la precipitación. Los criterios de selección y comparación utilizados fueron el tipo de modelo, las variables de entrada y salida, las métricas de desempeño y los campos de aplicación. Se identificó un aumento en el número de este tipo de estudios, principalmente en aplicaciones que involucran modelos de redes neuronales, los cuales tienden a volverse más sofisticados según la disponibilidad y calidad de los datos de entrenamiento. Por otro lado, los modelos de lógica difusa tienden a hibridarse con modelos neuronales. Aún existen desafíos relacionados con el desempeño de las predicciones y la resolución espacial y temporal a nivel de cuenca y microcuenca, pero, en general, estos paradigmas son muy prometedores para el análisis de la precipitación.

Recibido: 4 de mayo de 2023; Aceptado: 11 de diciembre de 2024

ABSTRACT

Precipitation estimation at the river basin level is essential for watershed management, the analysis of extreme events and weather and climate dynamics, and hydrologic modeling. In recent years, new approaches and tools such as artificial intelligence techniques have been used for precipitation estimation, offering advantages over traditional methods. Two major paradigms are artificial neural networks and fuzzy logic systems, which can be used in a wide variety of configurations, including hybrid and modular models. This work presents a literature review on hybrid metaheuristic and artificial intelligence models based on signal processes, focusing on the applications of these techniques in precipitation analysis and estimation. The selection and comparison criteria used were the model type, the input and output variables, the performance metrics, and the fields of application. An increase in the number of this type of studies was identified, mainly in applications involving neural network models, which tend to get more sophisticated according to the availability and quality of training data. On the other hand, fuzzy logic models tend to hybridize with neural models. There are still challenges related to prediction performance and spatial and temporal resolution at the basin and micro‑basin levels, but, overall, these paradigms are very promising for precipitation analysis.

Keywords

precipitation, river basin, neural networks, fuzzy logic, machine learning, fuzzy inference systems.

RESUMEN

La estimación de la precipitación a nivel de cuenca hidrográfica es esencial para la gestión de cuencas, el análisis de eventos extremos y dinámicas meteorológicas y climáticas, y el modelado hidrológico. En los últimos años se han empleado nuevos enfoques y herramientas como las técnicas de inteligencia artificial para estimar la precipitación, ofreciendo ventajas sobre los métodos tradicionales. Dos paradigmas principales son las redes neuronales artificiales y los sistemas de lógica difusa, que pueden utilizarse en una amplia variedad de configuraciones, incluyendo modelos híbridos y modulares. Este trabajo presenta una revisión de la literatura sobre modelos híbridos metaheurísticos y de inteligencia artificial basados en procesos de señales, centrándose en las aplicaciones de estas técnicas en el análisis y la estimación de la precipitación. Los criterios de selección y comparación utilizados fueron el tipo de modelo, las variables de entrada y salida, las métricas de desempeño y los campos de aplicación. Se identificó un aumento en el número de este tipo de estudios, principalmente en aplicaciones que involucran modelos de redes neuronales, los cuales tienden a volverse más sofisticados según la disponibilidad y calidad de los datos de entrenamiento. Por otro lado, los modelos de lógica difusa tienden a hibridarse con modelos neuronales. Aún existen desafíos relacionados con el desempeño de las predicciones y la resolución espacial y temporal a nivel de cuenca y microcuenca, pero, en general, estos paradigmas son muy prometedores para el análisis de la precipitación.

Keywords

precipitation, river basin, neural networks, fuzzy logic, machine learning, fuzzy inference systems.

Introduction

Precipitation is a critical component of the global water cycle, significantly influencing both climatic and hydrological dynamics [[1]]. Variations in precipitation intensity have diverse impacts on natural and societal systems [[2]]. For instance, light rainfall, which soils readily absorb, aids in drought mitigation and boosts agricultural productivity. In contrast, intense downpours frequently result in catastrophic floods and landslides. Consequently, a thorough understanding of the precipitation intensity spectrum is vital for developing specific adaptation strategies. Estimating precipitation at the watershed level is highly valuable for environmental studies, given its role as the primary input in a hydrological system, directly contributing to the analysis of the water budget and related socio-economic and ecosystem interactions [[3]]. Therefore, accurately estimating precipitation is crucial for understanding meteorological and hydroclimatic processes and their impact on extreme events such as floods and droughts [[4]]. Various statistical, analytical, and numerical methods are employed for precipitation estimation [[5]]. The main approaches involve developing models with explanatory and response variables. Diverse meteorological and physiographical parameters have been included as explanatory variables, and, in recent years, data from remote sensing systems such as satellite images and radars have been progressively incorporated. Significant models like the Global Circulation Model (GCM) and numerical weather prediction (NWP) models are particularly relevant and extensively used on the macroscale [[6]]. However, more robust and locally adapted models are required for regional and local scales.

Monitoring precipitation enables the acquisition of data for historical analysis, facilitating the development of estimation and prediction models. Measurements are obtained through rain gauges, weather radars, or satellite products with varying spatial and temporal resolutions [[7]]. The challenges in accurately estimating precipitation on the river basin scale include improving the spatial density of gauges and addressing the coarse resolution of remote sensing products [[8]]. Furthermore, the evident impacts of climate change in recent years, such as the progressive alteration of precipitation regimes and variations in the frequency and intensity of extreme events (including heavy rain and droughts) underscore the need for more robust and precise estimation at the regional level. Another limiting factor is coupling precipitation with the chaotic behavior of atmospheric dynamics. For example, a known issue in numerical systems corresponds to the errors and significant deviations in predictions caused by even slight changes in initial conditions [[9]]. Statistically, it has been also recognized that precipitation does not necessarily follow a normal distribution and can be modeled using asymmetrical distributions [[10]]. Consequently, more effective and powerful approaches, such as the use of artificial intelligence, are being studied to better approximate the correct behavior.

As a result of technological advances in the field of artificial intelligence and related areas such as data science, new approaches for processing and analyzing data for precipitation estimation are being employed. These include machine learning techniques like neural networks and the application of expert knowledge through fuzzy logic [[11]]. Such techniques provide flexibility and facilitate the development of more robust models for estimating precipitation, given their inherent ability to model complex nonlinear behaviors [[12]]. Few studies have been found which review artificial intelligence techniques for precipitation assessment, especially in relation to neural networks and fuzzy logic. [[13]] presented a review on resilient rainfall forecasting models using artificial intelligence techniques, with an emphasis on artificial neural networks (ANNs) as well as on hybrid models including neuro-fuzzy systems.

This document presents a bibliographic review of artificial intelligence techniques used for estimating precipitation. The main objective is to compare ANNs against fuzzy logic models, focusing on the differences between machine learning and expert systems approaches. The methodology for the literature search and the criteria for selection are detailed in the next section. Afterwards, the theorical basis for each method is explained, followed by a discussion of their main applications, and the article concludes with a succinct comparison of the two types of models.

Methodology

We conducted a systematic review to identify relevant studies on rainfall forecasting using artificial intelligence (AI), specifically fuzzy logic, neural networks, and neuro-fuzzy models. A literature search was conducted in the Scopus database, utilizing strategically selected keywords to capture a comprehensive overview of the most relevant studies. With the search criteria presented below, 134 articles were selected for analysis. Each study was systematically reviewed in a specific reading sequence: abstract, conclusion, results and discussion, methodology, and, finally, the introduction. This method facilitated the identification of potential themes and categories in the information presented by each paper.

Selection criteria

The main objective of this systematic review was to analyze the use of AI for precipitation estimation at the river basin level. The main selection criterion was a focus on precipitation analysis, with a preference for river basins and limited to neural networks and fuzzy logic approaches. A secondary objective involved determining and understanding the input and output variables, the model architecture, the performance metrics, and the scope of each case.

Search equations

The set of keywords encompassed terms like river basin, precipitation, and artificial intelligence, with additional specific terms for each technique: neural networks and fuzzy logic. It should be acknowledged that these terms were consulted in several permutations, including synonyms, nomenclatures, and broader keywords, in order to enhance the search breadth. The following variations were included in the search equations:

  • River basin, catchment, watershed

  • Precipitation, rainfall, rain estimation, rain rate, precipitation estimation

  • Artificial intelligence, machine learning, soft computing

  • Artificial neural networks, neural networks, deep learning, machine learning, artificial intelligence

  • Fuzzy logic, fuzzy inference systems, expert systems, soft computing, artificial intelligence

Eq. (1) was used for the initial search in Scopus:

(1) (precipitation OR rainfall OR rain OR "precipitation estimation") AND ("river basin" OR watershed OR basin OR catchment) AND ("artificial intelligence" OR "machine learning" OR "neural network" OR "fuzzy logic" OR "soft computing")

In the preliminary search, some concepts like climate change, downscaling, forecast, drought and flood forecasting, and hydrological modeling were also highlighted. Several papers reference rainfall-runoff modeling, but precipitation dynamics is the only concept that pertains to this review.

Subsequently, a more specialized search was conducted, using several widespread databases (Elsevier, Springer, IEEE) as well as conventional search engines like Google or those oriented towards academic results (Google Scholar), in order to include non-indexed results (e.g., Arxiv). To correctly filter by AI paradigm, Search Eqs. (2) and (3) were employed.

(2) ("fuzzy logic") AND (watershed OR "river basin" OR "catchment") AND (precipitation OR "precipitation estimation" OR "rainfall") (3) ("neural network") AND (watershed OR "river basin" OR "catchment") AND (precipitation OR "precipitation estimation" OR "rainfall")

Software tools

VOSViewer [14], [15] was used for the bibliometric analysis, enabling the generation of bibliometric network plots and clustering algorithms. This software facilitates the visual inspection of relevant information from bibliographic metadata such as the authors, keywords, and important terms. Additionally, a thesaurus file was manually elaborated to organize similar concepts within the results of VOSViewer.

Results

The general search using Scopus allowed for the analysis of global concepts. A bibliographic network is shown in Fig. 1, which includes the occurrence of keywords by total count, with the maximum limit of connections set to 200 in order to facilitate visualization. The most important concept found was ANN. Other AI techniques like genetic algorithms, random forests, and support vector machines were also visible in the network, highlighting their importance in more recent studies. Fuzzy logic did not seem to be included at first glance, but, after zooming in on the network, this concept indicated a higher similarity to precipitation.

Bibliometric map of the preliminary search

Figure 1.: Bibliometric map of the preliminary search

Source: Authors

In the preliminary search, some concepts like climate change, downscaling, forecast, drought and flood forecasting, and hydrological modeling were also highlighted. Several papers reference rainfall-runoff modeling, but precipitation dynamics is the only concept that pertains to this review.

The specific search for each approach returned different results, and some representative papers were identified for both neural networks and fuzzy logic according to the selection criteria. It is noteworthy that several of these papers compared their approach against different AI techniques. We prioritized papers using rain gauges and weather stations as the primary data source, as they favor watershed-level analysis. Still, some papers that only used radar or satellite images were also included.

Each of these AI paradigms has behaved differently in recent years. Although the use of AI has generally increased and expanded in the last decades, the number of neural network-related studies has increased significantly, while research involving fuzzy logic seems to be stagnant and has even decreased, with most studies appearing between 2013 and 2016 (Fig. 2). A summary of the main references is presented in Table I.

Number of papers by year and subject

Figure 2.: Number of papers by year and subject

Source: Authors

Neural networks for precipitation estimation

Artificial neural networks

ANNs, or simply neural networks (NNs), are connectionist models used to approximate a general function through a series of non-linear transformations performed by interconnected nodes or neurons [16]. ANNs are widely used in the field of machine learning, specifically in supervised learning with known input and output data (observations). During the initial training, iterative optimization algorithms are applied to slightly update the network in each iteration. This process runs until the known input data generate a very similar value to the known output data, which implies an optimal network configuration [17]. A well-trained NN can internally generalize the relationship between input and output, correctly approaching the objective function (e.g., modeling the behavior of precipitation from historical data).

The simplest NN model is the multilayer perceptron (MLP), which has at least three layers: an input layer, a hidden layer, and an output layer (Fig. 3). Each node or perceptron is partially modeled as a biological neuron, wherein backpropagation is the usual training method. Thus, MLPs are also called backpropagation neural networks (BPNNs). In several studies, ANN, NN, and BPNN are used interchangeably, but it must be clarified that are differences in the configuration of the network and in internal parameters like the weights, the bias matrix, the transfer function, and the optimization algorithm [18]. [19] conducted a study aimed at identifying relationships between atmospheric temperature and rainfall with ANN models.

Different types of AI and machine learning models can be used for precipitation prediction and forecasting applications, such as expert systems, NNs, and deep learning. In the realm of deep learning, it is possible to find models like convolutional NNs, recurrent NNs, and generative adversarial networks. ANNs have been used to complete missing data in precipitation time series [20], as well as in autoregressive models, where precipitation is modeled from historical data, as was done by [21] for 15 min precipitation, by [22] for daily precipitation, by [23] for daily precipitation with wavelets analysis, and by [24] for monthly precipitation from rain gauge data between 1961 and 2018 in the Wujiang River Basin while using an artificial bee algorithm. Moreover, [25] performed a similar study in Greece. Simpler single-layer models like the ADALINE network have been used for monthly precipitation forecasting [26].

Neural network topology

Figure 3.: Neural network topology

Source: Adapted from [27]

Different input variables can be used besides precipitation. [28] included precipitable water vapor, pressure, temperature, relative humidity, cloud top temperature, cloud top pressure, and cloud top altitude to predict hourly precipitation. Other studies have used climate indices such as the southern oscillation index (SOI), the interdecadal pacific oscillation index (IPO), La Niña 3.4 [29], [30], and the standard precipitation index (SPI) [31] as input variables.

[32] used different types of NNs to estimate monthly mean precipitation and temperature based on data from 90 weather stations, with the purpose of elaborating a climatic cartography of Chile. Likewise, [33] delved into spatiotemporal predictions in Brazil. [34] used precipitation time series derived from stations monitoring data and radar and satellite images from different weather products, and [35] applied NNs to estimate precipitation using the WSR-88D radar in Oklahoma.

[36] were the first to describe the application of ANNs to satellite images in order to improve spatial precipitation estimation. Multiple products were derived from their studies, e.g., the PERSIANN system. Furthermore, with the advent of new weather products, precipitation databases, and new research, new studies have mostly taken interest in integrating data from various sources [12]. [37] used data from satellite products (ERA-5, CHIRPS, IMD, PERSIANN-CDR) to create a machine learning algorithm that combined different sources to achieve what they called secondary precipitation estimate merging using machine learning (SPEM2L).

Since the target variable is precipitation, most papers seek to implement regressions. However, classification processes can also be applied, as was the case with [38], who used data from the global navigation satellite system (GNSS) to identify heavy precipitation.

Recurrent neural networks

Recurrent NNs are a special type of network whose neurons include an additional connection to themselves that works as a buffer or memory element (Fig. 4). This configuration is particularly useful to approximate relations depending on previous data such as time series [39]. There are different types: the basic recurrent neural network (RNN), the gated recurrent unit (GRU), and long short-term memory (LSTM).

Recurrent neural network topology

Figure 4.: Recurrent neural network topology

Source: [40]

Deep and convolutional neural networks

Deep neural networks (DNNs) are a relatively new concept that involves ANNs containing many neurons, hidden layers, and training data. This kind of architecture has shown very good results in practice, especially with large amounts of quality data and high computational power available for training and validation [41]. The field of deep learning has gained ground for its great performance, to the point that the term neural networks is now directly associated with deep learning. [42] integrated data from different sources to predict precipitation using a deep network. Meanwhile, [43] implemented a classification model to identify heavy rain events, and [44] used bio-spectral images to predict precipitation.

The progress of DNNs also allowed developing new configurations like convolutional neural networks (CNNs). These networks use specialized nodes (Fig. 5) that work as sliding filters (i.e., they convolute) on the input data to identify the particular characteristics that activate them [45]. This behavior is suitable for image analysis aimed at object detection, instance segmentation, and image and pixel classification [46]. In precipitation analysis, this can be applied in the detection of clouds, weather fronts, and atmospheric dynamics in radar products, etc.

Convolutional neural network topology

Figure 5.: Convolutional neural network topology

Source: Adapted from [40]

[47] merged data from rain gauges, radar satellite images, and digital elevation models for precipitation estimation. They used CNNs and an additional post-processing step related to precipitation probability and intensity. The integration of radar data was improved, and the station bias was reduced in subsequent research [48]. Precipitation dynamics were analyzed in another study using both DNNs and CNNs applied to images obtained from terrestrial radars [49]. A CNN-based deep learning method was used to improve rainfall-runoff modeling in the Mekon River Basin [50]. One study explored the application of a CNN-based architecture for detecting and estimating near real-time precipitation in the USA [51].

In recent years, methods based on deep CNNs have achieved significant success, and their performance continues to improve [52]. [53] set about correcting the bias of daily satellite precipitation in tropical regions using a DNN. Most deep and convolutional models use non structured data as input (e.g., images). A specific study on precipitation presented a nowcasting method based on sparse correspondence and a DNN [49]. The necessary data can be obtained directly from remote sensing products, generated from curated data provided by multiple sources, or generated from statistical or numerical models. For example, [54] used data from the ERA5 numerical and reanalysis model and the E-OBS database to apply a U-net (deep and convolutional network). The input data included weather and physical variable maps considering temperature, wind speed, water vapor, and geopotential altitude to generate the output, in the form of an hourly precipitation map.

Another project, focused on short-term weather forecasting (i.e., nowcasting), mainly used CNNs or variants with recurrent components. Here, [55] used precipitation data from radar and satellite images provided by the Geostationary Satellite Server (GOES), together with physical weather models commonly used in meteorology. They obtained good results for 12 h forecasts. [56] applied a hybrid MLP and CNN model to predict extreme regional precipitation in central-eastern China. Similarly, [57] conducted a quantitative precipitation forecasting study for China with a multi-stream CNN. On the other hand, [58] applied CNNs in the United Kingdom. They added a generative component, wherein two modules (the generator and the discriminator) compete to generate an optimal output.

Optical flow can also be used on radar images [59] and in direct processing and detection from satellite images [60], [61]. Due to the sequential nature of precipitation data, it is possible to merge image and temporal analysis [62] using models that integrate convolutions and LSTM [63]. [64] proposed a transformer-enhanced spatiotemporal neural network called TransLSTMUNet for the post-processing of precipitation forecasts, and, using a DNN, [65] developed a forecasting model based on the global normalized difference vegetation index (NDVI), air temperature, soil moisture, and precipitation.

Thanks to the availability of precipitation data from satellite images, videos, and climate reanalysis products, a whole new wave of studies using computer vision has emerged. For instance, [66] compared several convolutional models (LSTM and U-Nets) for precipitation nowcasting within a 15 min temporal scale. Notably, a large volume of precipitation images was required.

Downscaling methods

The downscaling and regionalization of data allows improving the spatial scale of weather data or radar and optical images obtained via remote sensing in order to produce information that better captures the study area [11]. [67] applied downscaling with different machine learning models for precipitation estimation, using data from the Coupled Model Intercomparison Project Phase 5 (CMIP5). [68] and [69] used CNNs for the micro-regional monitoring of precipitation, while [70] analyzed the probability of extreme events through downscaling. [71] applied radial-basis NNs based on downscaling, integrating data from precipitation time series, global circulation models, and different climate change scenarios as inputs. Downscaling can be applied by means of different models (e.g., statistical methods) or through classical NNs [72], CNNs, and U-nets [73]. Depending on the data available, this can be done on different temporal scales (annual, monthly, or daily) [74].

Fuzzy logic for precipitation estimation

Fuzzy inference systems

Fuzzy logic is based on the concept of fuzzy sets. A fuzzy set is a set with no crisp or clear boundary. Unlike two-valued Boolean logic, fuzzy logic is multi-valued, and it deals with degrees of membership and truth. Fuzzy logic uses any logical value from the set of real numbers between 0 (completely false) and 1 (completely true). This is known as the membership value, and the function that represents such value is called a membership function [75]. Fuzzy logic takes advantage of expert knowledge and the flexibility of fuzzy sets to model complex systems [18]. It allows representing numerical variables as identifiable linguistic values through membership functions (facilitating the representation of uncertainty and vagueness) (Fig. 6). Moreover, interpretable logic rules can be applied to these linguistic variables in the inference process. The fuzzy inference system (FIS) is the common configuration, comprising three main steps: fuzzification, inference, and defuzzification (Fig. 7).

Example of a membership function

Figure 6.: Example of a membership function

Source: Adapted from [76]
Fuzzy inference system

Figure 7.: Fuzzy inference system

Source: Adapted from [77]

A special instance of this approach is the Mamdani fuzzy inference system (MFIS), which is widely accepted among the scientific community due to its interpretability. Here, the consequent of the implication rules is a single value. On the other hand, the Sugeno fuzzy inference system (SFIS) has a consequent with an arbitrary fuzzy function that considers all the variables in the antecedent [16]. The behavior of a FIS can be visualized, for two inputs and a single output, as a three-dimensional surface indicating the non-linear relation between the variables (Fig. 8) -- when more variables are added, it generates an n-dimensional hyperplane [78].

FIS output surface example for precipitation estimation from time series data

Figure 8.: FIS output surface example for precipitation estimation from time series data

Source: [78]

[79] applied triangular membership functions to a FIS for precipitation data imputation. Precipitation prediction from other weather variables is also possible: [80] implemented a FIS using maximum, minimum, and mean values for wind speed, precipitation, and temperature as input in a model with 23 inference rules. [76] only used wind speed and air temperature. [81] applied fuzzy logic to a set of geographical variables including altitude, distance to the coastline, and slope -- in addition to rain gauge data -- to improve precipitation maps from meteorological radars.

[82] incorporated atmospheric pressure, humidity, dew point, temperature, and wind speed as input variables. The membership functions for each variable were triangular, with simple linguistic categories ranging from very low to very high in a MFIS. Furthermore, [83] added a temporal variable to differentiate the current day from the day before in their accumulated daily precipitation analysis. It is also possible to use preprocessed data such as those from the meteorological aerodrome report (METAR), a very common source in aerospace applications and weather analysis for air bases [84]; or those from the National Oceanic and Atmospheric Administration (NOAA) which offers data on different weather variables [85]. The main objective of the study by [84] was to predict rainfall events using a rule-based FIS that incorporated five parameters: relative humidity, total cloud cover, wind direction, temperature, and surface pressure. Similarly, [86] analyzed the uncertainties associated with extreme rainfall in terms of return levels. They also quantified the potential risk of these events in the coastal wetlands of India using fuzzy logic. [87] worked with fuzzy rainfall-runoff models to generate predictions for claypan catchments with conservation buffers in northeastern Missouri. Finally, [88] studied the climate sensitivity of mountainous regions to natural hazards through a fuzzy logic approach, identifying alterations in the level, intensity, or type of precipitation as the main drivers, together with glacier melting and permafrost thawing.

Fuzzy clustering and interpolation

Fuzzy systems can be implemented to improve the spatial interpolation of precipitation. [89] applied fuzzy logic to inverse distance weighting (IDW) for the spatial interpolation of precipitation, aiming to reduce the estimation error at river basin level. There are similar methods exclusively based on spatial interpolation [90] or classification, as is the case of [91], who used fuzzy logic to zone monthly precipitation and improve decision-making for cacao cultivation.

On the other hand, fuzzy clustering, or fuzzy C-means (FCM), is the use of membership functions to cluster, group, or categorize elements according to a similarity criterion. For example, [92] implemented this method to estimate precipitation and generate flood maps, and [90] applied it to validate spatial precipitation estimation. Fuzzy clustering can also be applied for downscaling precipitation data [93].

Fuzzy time series

Although FIS are mainly used for a system of inputs and outputs where the temporal component is not clearly incorporated, fuzzy logic can also be used for time series analysis. In this case, the time series should be interpreted as a fuzzy set. For example, [94] used fuzzy time series and NNs to predict rainfall, and, in complementary work, [78] focused exclusively on precipitation time series.

Within a purely autoregressive approach, membership functions are created by temporally dividing the precipitation time series [96]. In said cases, the membership functions split the data according to their temporal scale, i.e., the linguistic variable can be the month of the year, and, after the fuzzification of the inputs, the inference rules can directly reference the known experimental behavior of the precipitation in certain months (Fig. 9).

Membership functions for fuzzy time series

Figure 9.: Membership functions for fuzzy time series

Source: Adapted from [97]

Hybrid models: neuro-fuzzy systems

Hybrid models refers to instances that integrate machine learning components to complement FIS, e.g., NNs and genetic algorithms. Given the high effectiveness recently shown by machine learning applied to big data applications, it is increasingly common to include it as an additional step for expert systems. For example, NNs can be used to automatically generate membership functions for FIS, or even to generate inference rules [98]. [99] used NNs to generate inference rules within a so-called neuro-fuzzy system (NFS), using coordinates and their corresponding precipitation values, in a study similar to that by [100]. [101] merged data from stations, radar, and satellite images using a neuro-fuzzy network.

Another very common architecture in the literature corresponds to the adaptive neuro-fuzzy inference system (ANFIS) (Fig. 10). Neuro-fuzzy hybridization results in a hybrid intelligent system that synergizes ANNs and fuzzy logic by combining the human-inspired reasoning of fuzzy systems with the learning and connectionist structure of NNs [75]. [102] applied ANFIS to estimate precipitation from several rain gauge stations in Serbia, reporting improved reliability against uncertainty. Using ANFIS, [103] managed to identify the most relevant meteorological variables and their influence on precipitation estimation. They included data on vapor pressure, air temperature, the monthly frequency of wet days and the percent monthly cloud cover. Meanwhile, [104] used this approach to improve precipitation estimation from radar data. Some comparative studies have implemented the ANFIS method [23], as well as others focused on predicting precipitation-related climatic indices [105] or on using historical precipitation series.

Several models can also be merged into this approach, wherein the fuzzy logic component serves as a module integrator [106]. [107] presented a self-identification neuro-fuzzy inference model (SINFIM) for modeling the relationship between rainfall and runoff on a Chilean watershed. Another work studied the trends and patterns of rainfall to conduct an analysis of the city of Mumbai via the rainfall regionalization approach coupled with fuzzy logic and clustering [108]. [109] applied an ANFIS to evaluate rainfall-runoff modeling in a sub-catchment of the Kranji Basin in Singapore, and another study used NNs and fuzzy logic in statistical downscaling to support daily precipitation forecasting [110].

Topology of an ANFIS model

Figure 10.: Topology of an ANFIS model

Source: Adapted from [103]

Hybrid metaheuristic algorithms

Hybrid metaheuristic algorithms are advanced tools in the field of AI [111]. These techniques can solve problems via prediction errors, hyperparameter determination, and feature selection using machine learning algorithms [112], which is why they are gaining popularity and are being used for the development of hybrid models for hydrological research [113], including those dealing with the prediction of reference evapotranspiration (ETo), a very important parameter for determining the availability of water resources and in hydrological studies. However, they are mainly used to predict ETo, as stated by [114]. To this effect, they studied and compared the prediction capabilities of two support vector regression (SVR) models along with three metaheuristic algorithms, i.e., particle swarm optimization (PSO), gray wolf optimization (GWO), and the gravitational search algorithm (GSA), using meteorological variables in monthly ETo prediction used meteorological variables as input.

Hybrid metaheuristic algorithms have also been used to elaborate flood susceptibility maps, and the optimization capabilities offered by different machine learning algorithms has been leveraged by means of metaheuristic algorithms [111]. In the Haraz Basin, Iran, [115] employed an ANFIS coupled with the cropping (CA), bee (BA), and invasive weed optimization (IWO) algorithms. [116] used a combination of ANFIS, the genetic algorithm (GA), ant colony optimization (ACO), and PSO to generate a flood susceptibility map for the municipality of Jahrom, Iran. [24] performed ANFIS optimization with biogeography-based optimization (BBO) and the imperialist competitive algorithm (ICA). [117] used differential evolution (DE), the GA, and PSO along with an ANFIS to elaborate a flood susceptibility map for the Ganges Plain in India. [118] also used a combination of SVR, the GWO, and the bat optimizer (Bat) to generate this type of map. [119] used GWO and the whale optimization algorithm (WOA) to optimize SVR and create a flood susceptibility map for the Ardabil province in Iran. [120] combined SVR, PSO, and the grasshopper optimization algorithm (GOA) to develop a flood susceptibility map. [121] used the group method of data management (GMDH), DE, and the GA to generate a flood susceptibility map for the Haraz-Neka Basin, Iran. Moreover, [122] conducted GMDH optimization with the help of GWO in flood modeling.

[123] explored the accurate prediction of daily rainfall via AI methods. These methods were grounded in an ANFIS. Some metaheuristic optimization algorithms were also employed: the artificial bee colony algorithm (ABC), the GA, and simulated annealing (SA). [124] presented a method for providing explainability in the integration of inductive rules, combined with fuzzy logic and data mining techniques, when dealing with meteorological predictions.

Machine learning

Machine learning (ML) is a field of AI that deals with the development and study of statistical algorithms capable of learning from data and generalizing to unseen data, allowing them to perform tasks without explicit instructions.

In this vein, there are some studies related to precipitation forecasting and ML. [125] developed a conceptual metaheuristics-based framework for improving runoff time series simulation in glacierized catchments, combining hydrological model with a series predictor model and the optimization-driven parameter tuning of the firefly algorithm. Furthermore, [126] used a MLP network -- optimized via the GA, PSO, the firefly algorithm, and teleconnection pattern indices -- for rainfall modeling in the Mediterranean Basin. In addition, nested hybrid rainfall-runoff modelling has been performed via embedding ML techniques [127]. [128] used a combination of approaches, i.e., statistical, ML, deep learning (DL), and hybrid algorithms, in order to build a precipitation forecasting system. In addition, [129] proposed a new rainfall prediction model that employs different techniques as well as indicator features like average directional movement (ADX), moving average convergence divergence (MACD), and Welles Wilder's smoothing average (WWS). [130] developed a metaheuristic evolutionary DL model based on a temporal convolutional network for rainfall-runoff simulation and multi-step runoff prediction. [131] assessed some rainfall prediction models to explore the advantages of ML and remote sensing approaches. Furthermore, an assessment of hybrid ML algorithms using TRMM rainfall data for daily inflow forecasting was carried out in eastern Brazil [132]. In China, a study on automated ML for rainfall-induced landslide hazard mapping was conducted [133]. [134] performed a comparative assessment of rainfall-based water level prediction methods using ML. [135] evaluated traditional and ML approaches to rainfall prediction, and [136] examined a combination of the ERA5 dataset and ML. Long-term rainfall prediction was performed by [137], using atmospheric synoptic patterns in semiarid climates with statistical and ML methods. [138] studied ML-based rainfall models for accurate flood mapping in Pakistan. [139] conducted specific studies on short-term rainfall forecasting using cumulative precipitation fields from station data with a probabilistic ML approach.

Comparative analysis

Input variables

Both NNs and fuzzy logic models depend on the available input variables. An initial knowledge of the objective function and the possible relationships between the explanatory and response variables is assumed in order to build the model. Fig. 11 shows the common input variables for the studied field. In general, these parameters can be classified as meteorological, physiographic, or hydrological variables; climatic indices; data derived from physical or numerical models; satellite or radar products; or other derived databases.

Input variables used in the references

Figure 11.: Input variables used in the references

Source: Authors

Output variables

As the purpose of these models is estimating it, precipitation should be the output or target variable in most cases. However, this variable can be expressed in diverse temporal scales, units, or configurations, as shown in Fig. 12. In some studies, both precipitation and temperature are included as output variables [32]. The most widely used output is monthly precipitation, mainly in the fields of weather forecasting and climate analysis. These variables also allow evaluating extreme events and return periods.

Output variables used in the references

Figure 12.: Output variables used in the references

Source: Authors

Model architectures

Fig. 13 shows the common NN architectures for precipitation estimation. ANNs and BPNN are differentiated as in the referenced literature. Although DNNs, CNNs, and convolutional-recurrent networks (CRNs) are shown separately, they could be grouped into a single category (i.e., deep networks) that is representative of the selected references.

Neural network models found in the references

Figure 13.: Neural network models found in the references

Source: Authors

Fig. 14 shows fuzzy logic models for precipitation estimation. ANFIS, FIS, and MFIS are the most commonly used. It could be said that MFIS are just a special case of FIS. On the other hand, both ANFIS and NFS integrate neural elements, so they represent the hybrid models in the references.

Fuzzy logic models found in the references

Figure 14.: Fuzzy logic models found in the references

Source: Authors

Performance metrics

To validate the techniques discussed herein, it is necessary to use certain performance metrics or criteria in order to compare actual values to those generated by the models. Some of the most common metrics include the root mean square error (RMSE), the correlation coefficient (R), the determination coefficient (R^2^), and the mean absolute error (MAE), which are mainly applied to regression models. In the case of classification models, performance evaluation should be mixed; for example, a confusion matrix can be used, as well as the F1 score or accuracy values. Among the performance metrics used in the referenced literature (Fig. 15), there are specific indicators for the field of hydrology, such as the average flood exposure risk (AFER), a specialized metric for flood analysis; Nash-Sutcliffe efficiency (NSE), widely employed in model assessment; the fractions skill score (FSS) for forecasting; and the skill score (SS) denominations, which are employed in quantitative precipitation forecasting (QPF). Apart from these, the RMSE, MAE, and R stand out as the most common parameters in fuzzy logic models implementing regression approaches.

Neural network performance metrics

Figure 15.: Neural network performance metrics

Source: Authors

Software tools and implementation

AI models can be implemented using different software tools and programming languages. A few references clearly describe the software used for implementation, but most of them do not provide clear information in this regard. The MATLAB software is notably used to implement of both NNs and fuzzy logic models [80]. In addition, the R language is applied for statistical analysis and downscaling [71], and some Python libraries are used for DL models [62]. It is important to highlight that the use of statistical software and geographical information systems is essential in this field.

Applications

For the general applications mentioned in the literature on precipitation estimation, some categories are identified. Firstly, as expected, precipitation forecasting on different temporal scales tends to be the main objective of several papers. For long-term temporal scales (30 years or more), the objective is climate analysis. Some papers emphasize the usefulness of AI techniques for issuing extreme event early warnings and in watershed management [21], [24], [78], [92].

Advantages and challenges of AI methodologies

AI methods exhibit both limitations and advantages. The fundamental aspects of the main methods are outlined below.

ML offers significant advantages regarding automation, accuracy, and scalability, but it poses challenges related to data dependence, model complexity, resource requirements, and ethical considerations. Fuzzy logic is quite advantageous in handling uncertainty, providing intuitive solutions and adaptability across various domains. However, its limitations are related to precision, rule design complexity, computational effort, and the lack of self-learning capabilities. Moreover, NNs are powerful and versatile tools capable of learning complex patterns from large datasets with good learning performance, adaptability, versatility, and the possibility of continuous improvement. However, they come with significant challenges related to data dependence, computational load, interpretability, and overfitting, all of which need to be carefully managed to ensure an effective and ethical use. NFS offer a powerful combination of the learning capabilities of NNs and the interpretability and uncertainty management of fuzzy logic. These hybrid models are particularly valuable in applications that require both adaptive learning and human-like reasoning. However, they pose challenges pertaining to complexity, computational effort, overfitting, and data quality dependence. Careful design and implementation are required to fully realize these techniques' potential while managing their limitations.

Conclusions

This work presents the results of a thorough review of the literature on prediction precipitation using AI techniques. Our findings provide academia and society in general with perspectives for future research in the field. There are various approaches for precipitation estimation using AI, even when limiting the search to two specific paradigms such as NNs and fuzzy logic. Model selection widely depends on the type, quantity, and quality of the available data, and there is no single configuration that guarantees the best results. The integration of multiple data sources holds great potential for performing regression in future studies.

Although the number of studies involving fuzzy logic has decreased, these models remain a relevant option due to their interpretability. Access to large amounts of data could benefit fuzzy logic, as achieved through the inclusion of ML components to create hybrid models, allowing for scaling while maintaining interpretability.

NN research applied to precipitation estimation has grown in recent years, with more sophisticated models like deep, recurrent, and convolutional networks being incorporated and showing significantly better results. However, among their limitations is the availability of and access to large amounts of data or high computational power, as well as the lack of interpretability and implementation issues.

There are still many challenges for precipitation estimation at the river basin level. Advances in the field of AI and access to new data sources, models, and software tools have yielded very promising results for the study of precipitation at different levels, from mere forecasting to extreme events forecasting and hydrological and environmental modeling.

Tabla I

Main references by year and category regarding artificial neural networks and fuzzy logic-based approaches

Source: Authors

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CRediT author statement All authors: conceptualization, methodology, software, validation, formal analysis, investigation, writing (original draft, review and editing), data curation, supervision. All authors contributed to the writing of the manuscript and approved its definitive version for publication.
Conflicts of interest The authors declare no conflict of interest.
How to cite Ruiz Hurtado, A. F., Vargas-Franco, V. & González-Salcedo, L. O. (2024). Neural Networks and Fuzzy Logic-Based Approaches for Precipitation Estimation: A Systematic Review. Ingeniería e Investigación, 44(3), e108609. https://doi.org/10.15446/ing.investig.108609

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How to Cite

APA

Ruiz Hurtado, A. F., Vargas-Franco, V. & González-Salcedo, L. O. (2024). Neural Networks and Fuzzy Logic-Based Approaches for Precipitation Estimation: A Systematic Review. Ingeniería e Investigación, 44(3), e108609. https://doi.org/10.15446/ing.investig.108609

ACM

[1]
Ruiz Hurtado, A.F., Vargas-Franco, V. and González-Salcedo, L.O. 2024. Neural Networks and Fuzzy Logic-Based Approaches for Precipitation Estimation: A Systematic Review. Ingeniería e Investigación. 44, 3 (Dec. 2024), e108609. DOI:https://doi.org/10.15446/ing.investig.108609.

ACS

(1)
Ruiz Hurtado, A. F.; Vargas-Franco, V.; González-Salcedo, L. O. Neural Networks and Fuzzy Logic-Based Approaches for Precipitation Estimation: A Systematic Review. Ing. Inv. 2024, 44, e108609.

ABNT

RUIZ HURTADO, A. F.; VARGAS-FRANCO, V.; GONZÁLEZ-SALCEDO, L. O. Neural Networks and Fuzzy Logic-Based Approaches for Precipitation Estimation: A Systematic Review. Ingeniería e Investigación, [S. l.], v. 44, n. 3, p. e108609, 2024. DOI: 10.15446/ing.investig.108609. Disponível em: https://revistas.unal.edu.co/index.php/ingeinv/article/view/108609. Acesso em: 10 jul. 2026.

Chicago

Ruiz Hurtado, Andres Felipe, Viviana Vargas-Franco, and Luis Octavio González-Salcedo. 2024. “Neural Networks and Fuzzy Logic-Based Approaches for Precipitation Estimation: A Systematic Review”. Ingeniería E Investigación 44 (3):e108609. https://doi.org/10.15446/ing.investig.108609.

Harvard

Ruiz Hurtado, A. F., Vargas-Franco, V. and González-Salcedo, L. O. (2024) “Neural Networks and Fuzzy Logic-Based Approaches for Precipitation Estimation: A Systematic Review”, Ingeniería e Investigación, 44(3), p. e108609. doi: 10.15446/ing.investig.108609.

IEEE

[1]
A. F. Ruiz Hurtado, V. Vargas-Franco, and L. O. González-Salcedo, “Neural Networks and Fuzzy Logic-Based Approaches for Precipitation Estimation: A Systematic Review”, Ing. Inv., vol. 44, no. 3, p. e108609, Dec. 2024.

MLA

Ruiz Hurtado, A. F., V. Vargas-Franco, and L. O. González-Salcedo. “Neural Networks and Fuzzy Logic-Based Approaches for Precipitation Estimation: A Systematic Review”. Ingeniería e Investigación, vol. 44, no. 3, Dec. 2024, p. e108609, doi:10.15446/ing.investig.108609.

Turabian

Ruiz Hurtado, Andres Felipe, Viviana Vargas-Franco, and Luis Octavio González-Salcedo. “Neural Networks and Fuzzy Logic-Based Approaches for Precipitation Estimation: A Systematic Review”. Ingeniería e Investigación 44, no. 3 (December 1, 2024): e108609. Accessed July 10, 2026. https://revistas.unal.edu.co/index.php/ingeinv/article/view/108609.

Vancouver

1.
Ruiz Hurtado AF, Vargas-Franco V, González-Salcedo LO. Neural Networks and Fuzzy Logic-Based Approaches for Precipitation Estimation: A Systematic Review. Ing. Inv. [Internet]. 2024 Dec. 1 [cited 2026 Jul. 10];44(3):e108609. Available from: https://revistas.unal.edu.co/index.php/ingeinv/article/view/108609

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