Monthly Agricultural Reservoir Storage Forecasting Using Machine Learning

Abstract

Storage rate forecasting for the agricultural reservoir is helpful for preemptive responses to disasters such as agricultural drought and planning so as to maintain a stable agricultural water supply. In this study, SVM, RF, and ANN machine learning algorithms were tested to forecast the monthly storage rate of agricultural reservoirs. The storage rate observed over 30 years (1991–2022) was set as a label, and nine datasets for a one- to three-month storage rate forecast were constructed using precipitation and evapotranspiration as features. In all, 70% of the total data was used for training and validation, and the remaining 30% was used as a test. The one-month storage rate forecasting showed that all SVM, RF, and ANN algorithms were highly reliable, with R² values ≥ 0.8. As a result of the storage rate forecast for two and three months, the ANN and SVM algorithms showed relatively reasonable explanatory power with an average R² of 0.64 to 0.69, but the RF algorithm showed a large generalization error. The results of comparing the learning time showed that the learning speed was the fastest in the order of SVM, RF, and ANN algorithms in all of the one to three months. Overall, the learning performance of SVM and ANN algorithms was better than RF. The SVM algorithm is the most credible, with the lowest error rates and the shortest training time. The results of this study are expected to provide the scientific information necessary for the decision-making regarding on-site water managers, which is expected to be possible through the connection with weather forecast data.

1. Introduction

Water is a critical input for agricultural production, and it plays an important role in human survival [1,2,3]. Agricultural irrigation constitutes almost 70% of global water consumption [2,4,5,6]. The global water consumption rate increased by six times over the past 100 years; currently, it increases by 1% each year owing to rapid changes such as population increase, economic growth, and consumption patterns [7]. Water accessibility has become increasingly uncertain in many regions across the world affected by climate change and water scarcity; this is expected to intensify competition among water users [7,8,9].

South Korea uses 41% (15.2 billion tons) of its total water resources (37.2 billion tons) as agricultural water [10]. Agricultural reservoirs continue to be the main source of agricultural water supply to secure water during periods of water abundance such as non-cropping periods or flood seasons, and to supply water during periods of cropping or water shortage. There are 17,106 agricultural reservoirs distributed throughout South Korea [11]. Most of these are small reservoirs with limitations such as weak water supply to mild droughts; furthermore, the water loss from these reservoirs has increased and become concerning (85.6% (14,644 reservoirs) of total agricultural reservoirs) because 50 years or more have passed since their construction. The growing variability in water supply such as deepened extreme climatic phenomena, changes in farming patterns, and water demand diversification hinders the stable supply and management of agricultural water.

A stable water supply is crucial for sustainable agricultural practice, and this must be preceded by the efficient operation and management of agricultural reservoirs. The stable management of the storage rate and decision-making to ensure a moderate amount of discharge are key to the operation and management of agricultural reservoirs, and they must employ continuous monitoring and reasonable decision-making. The South Korean government and Korea Rural Community Corporation have collectively decided the available storage capacity (storage rate/water level) of ~1800 agricultural reservoirs in real time since 1991; however, this applies to only ~10% of all reservoirs. The operation of reservoirs is customarily based on the experience of the water manager, and the four-stage forecast and warning criteria (interest (mild drought), warning (moderate drought), caution (severe drought), serious (extreme drought)) for agricultural water that utilizes the common year storage rate as the storage rate operation standard [12]. Thus far, various research studies have attempted to overcome this limitation by attempting to predict the storage rate and proposed operational criteria [13,14,15,16,17,18,19]. The efficient management of water quantity in irrigation reservoirs and optimal operation methods have been studied and proposed for sustainable agricultural water management by numerous research studies worldwide [20,21,22,23]. However, these methods are not applicable on-site because the climate and topographical properties differ for each reservoir, and the crops, cultivating area, cropping pattern, and water management method also differ significantly. Meanwhile, storage rate estimation technology using the water surface extracted from satellite imagery has been developing rapidly owing to the increased applicability of drones and increased satellite image data [24,25,26,27,28,29,30]. However, the scope of their application remains limited because of the low time resolution and lack of measurement value verification [31].

Machine learning (ML) is “the scientific study of algorithms and computational models on computers using experience for progressively improving the performance on a specific task or to make accurate forecasts [32].” Further, ML has been frequently used to overcome the abovementioned limitations in the era of big data. ML models that are a black box can predict the future by learning data patterns of the past, unlike hydraulic and hydrological models that demand previous knowledge of physical processes and significant input data. Further, ML models can efficiently process complex problems and a significant amount of data [33,34,35].

Seo et al. assessed the applicability of the artificial neural network (ANN), generalized regression neural network (GRNN), adaptive neuro-fuzzy inference system (ANFIS), and random forest (RF) algorithms for predicting the daily water level of Chungju dam [36]. The applicability was distinguished into eight levels based on the composition of input data. The results of ANFIS1 and ANN6 models were outstanding on day 1 of prediction, ANN1 and RF6 showed exceptional results on day 5, and ANN3 and RF1 showed prominent results on day 10. Overall, the ANN algorithm outperformed others; however, it is reasonable to apply the optimal input variable and optimal prediction model based on the time of prediction. Zhang et al. simulated the hourly, daily, and monthly reservoir outflows using a 30-year operational record of reservoirs (nine input data including amount of inflow, amount of discharge, and water level) [37]. The highest accuracy was achieved by long short-term memory (LSTM), followed by support vector regression (SVR) and backpropagation neural network (BP). The LSTM model showed the best performance under various time and flow (NSE ≥ 0.99) although the BP and SVR models showed poor applicability under conditions of data excess and a low amount of inflow. Sapitang et al. tested a machine learning technique that can predict the low-water level of the Kenyir Dam, Malaysia, from day 1 to 7, to provide accurate water level prediction data to the reservoir operator [38].

Tests with boosted decision tree regression (BDTR), decision forest regression, neural network regression, and Bayesian linear regression (BLR) models showed that the BLR algorithm performed the best (R² = 0.968–0.998) when testing with the water level and rainfall as the input data; BDTR performed the best (R² = 0.998–0.999) when testing with the water level, rainfall, and discharge as the input data. Kusudo et al. predicted the water level of the Takayama reservoir (Nara Prefecture, Japan) using the deep-learning algorithm LSTM because they considered the water level prediction to be significant for managing the operation of the agricultural reservoirs [39]. The error rate was the lowest in the single-output (SO) and encoder–decoder (ED) LSTM models when the water level, rainfall, and discharge event data were used; LSTM ED was assessed to be better for long-term predictions. Ibañez et al. reviewed the long- and short-term statistics- and machine learning-based water-level prediction performance of the Angat Dam, Philippines [40]. Meteorological data and irrigation data were used to apply six models: autoregressive integrated moving average, gradient boosting machines, deep neural networks (DNN), LSTM, univariate model, and multivariate model (DNN-M). The results showed that the DNN-M model performed the best in the 30-day, 90-day, and 180-day prediction scenarios with MAE values of 2.9 m, 5.1 m, and 6.7 m, respectively. Qie et al. simulated the daily reservoir outflow using the RF, SVM, and ANN algorithms; all three were assessed to be reliable and accurate [41]. This research indicates that the variability of the optimal algorithm depends on the training data composition and temporal, spatial, and climatic characteristics of the research subject because of the intrinsic feature of machine learning that involves reproducing empirical patterns.

According to recent climate change, social demands for stable supply and efficient use of agricultural water are increasing. Stable storage rate management of agricultural reservoirs, the primary source of agricultural water, is essential. Forecasting the storage rate helps achieve stable water management by identifying the amount of agricultural water available in advance. Forecasting storage rate, especially before the farming season, is of great help in preparing agricultural drought countermeasures. In other words, storage rate forecast is helpful for preemptive responses to disasters such as agricultural drought and planning to maintain a stable agricultural water supply. Recently, machine learning technology has been widely used to solve various problems. Water management in reservoirs has a nonlinear relationship with many variables such as climate, soil, topography, and hydrology, so a machine learning model that can effectively analyze them is being reviewed [42]. Therefore, this study uses a machine learning algorithm to learn the storage rate of agricultural reservoirs and provide data for actual on-site water management decisions through future storage rate prediction. Focusing on three machine learning models, such as SVM, RF, and ANN, the monthly storage rate prediction after 1 to 3 months of the agricultural reservoir was learned, and the performance was evaluated.

2. Methods

2.1. Target Reservoir and Data Collection

This research studied agricultural reservoirs (total storage 300,000 tons or above) in Iksan-si, Gimje-si, and Jeongeup-si in Jeollabuk-do, the center of the Honam plains, a top rice-producing area. The pumped-storage-type reservoir that artificially secures storage and reservoirs lacking data from the last 30 years are excluded. In contrast, the Heungdeok reservoir (located in Gochang-gun), the largest agricultural reservoir in the Jeollabuk-do area, supplies agricultural water to Jeongeup-si and Gimje-si, and it is included as a target reservoir. In total, 13 agricultural reservoirs are selected, as shown in Figure 1.

The daily storage rates provided by the rural agricultural water resource information system (RAWRIS) are collected as the storage rate observation data of the target reservoirs. The collected storage rate data show that the irrigating and non-irrigating periods are well distinguished, and the yearly, seasonal, and regional storage rates vary significantly (Figure 2,

Table 1. Statistics on the specifications and storage rates of studied agricultural reservoirs (1991–2021).

Reservoir	Specification			Storage Rate (%)
	Total Storage (1000 m3)	Effective Storage (1000 m3)	Irrigated Paddy Field Area (ha)	Avg.	Min.	Max.	Std.
Mireuk	1320	1270	296.7	76.0	0	100	24.1
Wonsu	602	602	169.4	83.1	16	100	20.0
Geumma	935	818	229.1	78.1	9.3	100	21.7
Dosun	560	538	154.4	79.6	11.5	100	20.7
Wanggung	1957	1941	540.6	78.3	3.0	100	21.4
Yongsan	2447	2439	390.3	73.0	0	100	22.4
Naejang	4832	4828	591.6	69.8	2.0	100	23.4
Bujeon	1752	1732	249.0	71.9	8.0	100	20.1
Jisun	620	620	122.4	74.5	0	100	23.9
Ipam	3661	3482	522.4	74.0	0	100	22.5
Sucheong	7218	7001	540.3	64.7	1.0	100	23.7
Seonam	853	853	223.6	75.4	0	100	23.6
Heungdeok	9946	9946	2739.0	65.3	0	100	20.6

Avg.: Average, Min.: Minimum, Max.: Maximum, Std.: Standard deviation.

). The storage rates were low in 1994–1995, 2001, 2012, and 2015, which are years documented to have had droughts.

The automated synoptic observation system data from January 1991 to March 2022 of two (Jeonju and Jeongeup) meteorological stations, which are nearby observatories, are collected as meteorological data. The data on rainfall, maximum temperature, minimum temperature, average wind speed, relative humidity, and duration of sunshine is collected; the average value of the observatory data is applied for the missing values. The daily reference evapotranspiration (ETo) was calculated using the Penman–Monteith equation as feature data for machine learning.

Table 2. Statistics of rainfall and reference evapotranspiration in the studied agricultural reservoirs (1991–2021).

Meteorological Station	Rainfall (mm/yr)				ETo (mm/yr)				Reservoirs
	Avg.	Min.	Max.	Std.	Avg.	Min.	Max.	Std.
Jeonju	1293.1	813.5	1860.3	271.2	911.6	833.9	979.7	40.3	Mireuk, Wonsu, Geumma, Dosun, and Wanggung
Jeongeup	1330.5	826.6	1917.3	286.4	872.2	786.8	960.2	43.4	Yongsan, Naejang, Bujeon, Jisun, Ipam, Heungdeok, Seonam, and Sucheong

Avg.: Average, Min.: Minimum, Max.: Maximum, Std.: Standard deviation.

summarizes the statistical characteristics of rainfall and evapotranspiration over the entire period of the collected data.

2.2. Machine-Learning Algorithm for Regression

Regression is a supervised learning technology that predicts continuous values based on the relationship between variables [43]. This research tested the basic regression algorithms SVM, RF, and ANN among the supervised learning ML algorithms. All three algorithms are used in classification and regression problems and frequently for prediction across various fields [44,45,46,47]. This research used Python and Scikit-Learn, Pandas, Numpy, and Seaborn libraries.

The SVM is based on the Vapnik–Chervonenkis theory [48], and it minimizes the structural risk; therefore, its overfitting tendency is lower than that of the other models [49,50]. In general, SVM is used for classification, regression, and outlier detection, etc. For regression, the ε-insensitive loss function is implemented to train the model to allow the input of as many samples as possible within a certain margin of error. Nonlinear regression is resolved by mapping from low to high dimensions using kernel tricks such as the polynomial, sigmoid, and radial basis functions (RBF) [51,52]. The SVM approximates the function as:

$$min\frac{1}{2}{w}^2+C{\displaystyle \sum }_{n=1}^N\left({\mathsf{\xi }}_i+{\mathsf{\xi }}_i{}^{*}\right) subject to \left\{\begin{array}{c}{y}_i-w^T{x}_i-b \le \epsilon +{\mathsf{\xi }}_i\\ w^T{x}_i+b-y_i \le \epsilon +{\mathsf{\xi }}_i{}^{*}\\ {\mathsf{\xi }}_i, {\mathsf{\xi }}_i{}^{*} \ge 0 \end{array}\right.$$

(1)

where $x_i$, $y_i$ are the input and output values, $y_i$ is weight vector, b is a scalar basis, T is degree, C is a penalty constant (regularization constant), ξ is slack variable (upper and lower constraint, respectively), ε is margin of tolerance.

The hyperplane function can be written as:

$$f\left(x_i\right)={\displaystyle \sum }_{n=1}^N{\alpha }_n{y}_{n}K\left(x_n, x_i\right)+b$$

(2)

${\alpha }_n$ is Lagrange multiplier, $y_n$ is membership class label, $x_n$ is support vector for nth class, $K\left(x_n, x_i\right)$ is the kernel function, and $b$ is bias.

The RF algorithm combines numerous decision-tree models. As a typical ensemble model, it uses the bagging (bootstrap aggregating) method, which refers to the resampling method that allows duplicates within a training dataset. The RF is simple, and its learning speed is fast; further, it is relatively less impacted by noise or outliers [53,54,55]. However, its performance is low for high dimensions or rare data. The regression uses the average value of each classifier as the final prediction value, and the major hyperparameters of RF include the number of decision trees, minimum number of samples of a node, and depth setting [56,57,58,59,60]. The RF regression model can be presented as:

$$f_{rf}^N \left(x\right)=\frac{1}{N}{\displaystyle \sum }_{n=1}^N{T}_{ree}\left(x\right), x=x_1, x_2, \cdots , x_p$$

(3)

where, N represents the average number of regression trees built by RF, 𝑥 is a p-dimensional vector of inputs, and $T_{ree}$ refers to decision-tree.

The ANN comprises an input layer, output layer, and one or more hidden layers. Further, it is referred to as a multilayer perceptron (MLP); its strengths include outstanding non-linear mapping and normalization capacity [61,62]. In the Scikit-Learn library, stochastic gradient descent (SGD) or limited-memory quasi-Newton methods (L-BFGS) are used to find parameters that minimize the loss function. The ANN hyperparameters include the hidden layer sizes, activation functions, learning rate, batch size, and a number of epochs [63,64]. The ANN approximates the function as:

$$y=a(w_{hd}\times a\left(w_{in}\times x+B_{in}\right)+B_{hd}$$

(4)

where, $w_{hd}$ and $w_{in}$ are weight matrices for hidden and input layers, $B_{hd}$ and $B_{in}$ are bias vectors for hidden and input layers, $x$ is an input vector, and $a$ is activation function.

The RMSE, MAE and coefficient of determination (R²) were used as indicators to evaluate the performance of the machine learning model.

$$RMSE=\sqrt{MSE}=\sqrt{\frac{1}{n} {\displaystyle \sum }_{i=1}^n{\left(x_i-y_i\right)}^2}$$

(5)

$$MAE=\frac{1}{n} {\displaystyle \sum }_{i=1}^n\left|x_i-y_i\right|$$

(6)

$$R^2=1-\frac{\frac{1}{n} {{\displaystyle \sum }}_{i=1}^n{\left(x_i-y_i\right)}^2}{\frac{1}{n} {{\displaystyle \sum }}_{i=1}^n{\left(x_i-\overline{x}\right)}^2}=1-\frac{MSE}{var\left(x\right)}$$

(7)

where $x_i$, $y_i$, $n$, and $\overline{x}$ represent the target value (actual value), predicted value, number of data, and average of the target value (actual value), respectively.

RMSE and MAE with an error value closer to 0 signifies high performance; an R² value closer to 1 indicates high performance. The possible R² value ranges between −∞ and 1 depending on the correlation between the actual and predicted values [65]. If R² is negative, it signifies an abnormal case in which the prediction performance is lower than the model predicted by the mean value. It can be negative when calculated on out-of-sample data (or for a linear regression without an intercept) [66].

2.3. Hyperparameter Optimization

This research uses random search to tune the hyperparameters. The random search searches for the best parameter based on the combination of random numbers that are possible within a set number range. This method is more efficient than grid search when the range is broad or when it is challenging to predict the range of the parameter value [67,68]. Further, five-fold cross-validations were implemented to prevent over/underfitting and utilize all training data for training and validation. The hyperparameters for the SVM, RF, and ANN algorithms and the range of set values are summarized in

Table 3. Hyperparameter settings for SVM, RF, and ANN algorithms, respectively.

Algorithm	Hyperparameter	Possible Values	Iteration	CV
SVM	kernel	rbf	200	5-fold
	gamma	scale
	C	uniform (10, 300)
	epsilon	uniform (0.0001, 1)
RF	criterion	mean squared error
	n estimators	randint (100, 500)
	Max depth	randint (5,10)
ANN	max iter	50,000
	learning rate	adaptive
	batch size	auto
	activation	tanh, relu
	solver (optimizer)	lbfgs, adam
	hidden layer size	randint (1, 30)

uniform: Return random floats from low (inclusive) to high (exclusive), randint: Return random integers from low (inclusive) to high (exclusive), CV: cross validation.

. Except for the important parameters, the default parameters provided in scikit-learn were used. For the SVM, the penalty constant (normalization constant) “C” and the “ε” value representing the allowable error are determined. Further, the default value (default = “scale”) is used for gamma because the addition of a parameter for “gamma” that determines the decision boundary curvature is required because “rbf’ is selected as the kernel function. For the RF, MSE is set as the criteria for distinguishing trees, and the values are determined for “n_estimators” that represents the number of decision-making trees and “min_samples_split” that represents the minimum number of node samples. For the ANN, the values are determined for “max_iter (epoch),” “activation,” “solver,” and “hidden layer size” which represent the maximum frequency of repetition, activation function, method of weight optimization, and the number of neurons and hidden layers, respectively. In this research, a single-layer neural network with one hidden layer is constructed; the remaining batch size and learning rate are configured as per the basic parameters of “auto” and “adaptive,”, respectively. The maximum frequency of repetition is limited to 1000 times, and the training proceeds at the adaptive learning rate.

The regulation intensity is lowered for the hyperparameter range in case of concerns related to underfitting, and it is raised in case of concerns related to overfitting. The optimal parameters are searched for by randomly creating 200 parameter combinations within the set range.

2.4. Learning Model and Training Dataset Setting

Irrigation facilities for agricultural water supply are artificially manipulated by water managers. Therefore, it is known that 10-day or monthly data reflect actual values better than daily data [69,70]. All collected daily data are transformed into monthly data for use in training. The label for constituting the learning model is set to the average storage rate (AS); a total of nine learning models are formed by altering the meteorological conditions depending on the extent of time (

Table 4. Setup of nine dataset models for forecasting reservoir storage rates using machine learning algorithms.

Models	Algorithms	Label	Features
SVM1	SVM	AS(m + 1)	ESm, CPm+1, CEm+1
RF1	RF
ANN1	ANN
SVM2	SVM	AS(m + 2)	ESm, CPm+1, CPm+2, CEm+1, CEm+2
RF2	RF
ANN2	ANN
SVM3	SVM	AS(m + 3)	ESm, CPm+1, CPm+2, CPm+3, CEm+1, CEm+2, CEm+3
RF3	RF
ANN3	ANN

AS: Average storage rate, ES: storage rate on the last day of the month, CP: monthly cumulative rainfall, CE: monthly cumulative standard evapotranspiration, and m: current period (month), m + 1: after one month, m + 2: after two months, and m + 3: after three months.

). The extent of time is set to one to three months, considering the cultivating period of paddy rice and the applicability of the meteorological forecast data. The input data, as the previous storage rates, are combined based on three criteria: storage rate on the last day of the month (ES), monthly cumulative rainfall (CP), and monthly cumulative standard evapotranspiration (CE).

All data are randomly shuffled to prevent a sampling bias; training and validation data are configured to 70% and 30% of the total data, respectively. Thus, 262 (70%) among 375 monthly data are used as training data for each reservoir, and the remaining 113 (30%) are used as test data to assess the test performance. Further, the average and standard deviation are standardized to 0 and 1, respectively, to manage the features on a different scale. The SVM that uses the RBF kernel assumes a Gaussian distribution, wherein data standardization must proceed. Further, employing optimization algorithms such as gradient descent after standardization can help reduce the learning time for weight values and the possibility of falling into the local optimum (local minimum). The methodology employed in this research for predicting the average storage rate using ML is illustrated in Figure 3.

3. Results and Discussion

3.1. Performance in One-Month Forecasting Models

Performance evaluation, best parameters, and learning time results were compared for three models for one-month forecasting. The results from all 13 reservoirs were highly reliable because they showed R² values of 0.8 or above (

Table 5. Performance of applied models in the training and test phases for one-month forecasting.

Reservoir	SVM1						RF1						ANN1
	Training			Test			Training			Test			Training			Test
	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2
Mireuk	6.4	3.60	0.93	7.7	4.75	0.88	3.4	2.26	0.98	8.1	4.91	0.87	5.8	3.64	0.94	7.8	4.96	0.88
Wonsu	5.7	3.14	0.91	6.8	3.96	0.87	2.6	1.63	0.98	6.6	4.27	0.88	5.6	3.46	0.92	7.2	4.63	0.85
Geumma	5.0	2.94	0.95	7.2	4.42	0.87	2.4	1.53	0.99	7.5	4.71	0.86	4.6	2.89	0.96	6.9	4.42	0.88
Dosun	5.1	2.86	0.94	7.4	4.29	0.85	2.8	1.83	0.98	7.3	4.57	0.85	5.6	3.60	0.93	7.0	4.32	0.87
Wanggung	5.1	2.73	0.94	6.5	4.12	0.89	2.4	1.55	0.99	7.2	4.62	0.86	4.8	2.97	0.95	6.6	4.39	0.88
Yongsan	5.6	3.25	0.93	8.9	5.69	0.83	2.9	2.02	0.98	9.5	6.32	0.81	6.4	4.36	0.91	9.0	6.11	0.83
Naejang	6.9	4.47	0.90	8.5	5.77	0.87	3.7	2.66	0.97	9.2	6.33	0.85	7.4	5.21	0.88	8.3	5.96	0.88
Bujeon	6.1	3.87	0.90	6.5	3.97	0.89	4.0	2.87	0.96	8.0	5.17	0.84	5.6	3.88	0.91	6.7	4.19	0.89
Jisun	7.2	3.93	0.90	9.0	5.35	0.83	3.4	2.2	0.98	9.5	5.41	0.81	7.7	4.61	0.89	7.9	4.80	0.86
Ipam	5.4	3.36	0.94	7.8	4.68	0.86	3.1	2.22	0.98	8.1	5.35	0.84	4.5	3.22	0.96	7.7	5.10	0.86
Sucheong	5.6	3.11	0.94	8.1	4.82	0.89	2.8	1.89	0.98	8.2	5.46	0.88	5.7	3.74	0.94	7.0	4.42	0.91
Seonam	6.7	4.12	0.91	7.2	4.56	0.89	3.1	2.09	0.98	7.5	5.04	0.89	6.2	4.18	0.92	7.5	4.83	0.88
Heungdeok	5.7	3.53	0.92	6.6	4.55	0.88	2.7	1.84	0.98	7.2	5.09	0.86	5.9	4.18	0.91	6.6	4.75	0.88

and Figure 4). The RMSE and MAE were also excellent. The best model has a small generalization error; i.e., training and test performances must be good, and the difference between the training and test performance must be slight. A high training performance but a significantly low learning performance implies overfitting to training data, whereas a significantly higher learning performance most likely signifies underfitting. Generalization error showed good performance in the order of ANN1, SVM1, and RF1. Considering the learning performance and generalization error, the SVM1 and ANN1 models were relatively superior to the RF1 model, but the difference was insignificant. Hyperparameter optimization results show that the parameters that give the best performance for a given dataset are different for each agricultural reservoir (

Table 6. Results of best parameters and learning time of models for one-month forecasting.

Reservoir	Hyperparameter Optimization							Learning Time (sec.)
	SVM1		RF1		ANN1			SVM1	RF1	ANN1
	C	ε	D	n	A	S	H
Mireuk	24.2	0.14	7	214	relu	lbfgs	14	0.004	0.572	4.161
Wonsu	22.9	0.13	8	145	relu	lbfgs	15	0.004	0.629	3.584
Geumma	24.9	0.76	9	484	relu	lbfgs	23	0.004	0.588	4.352
Dosun	91.5	0.06	7	109	relu	lbfgs	7	0.004	0.649	3.928
Wanggung	63.9	0.05	9	182	relu	lbfgs	17	0.005	0.630	3.594
Yongsan	108.1	0.25	8	235	relu	lbfgs	12	0.005	0.626	4.173
Naejang	105.6	0.98	9	467	relu	lbfgs	13	0.004	0.610	3.906
Bujeon	19.3	0.96	6	485	relu	lbfgs	8	0.004	0.636	4.215
Jisun	99.4	0.06	9	332	relu	lbfgs	6	0.004	0.643	4.876
Ipam	45.7	0.75	7	101	relu	lbfgs	26	0.005	0.644	4.263
Sucheong	108.3	0.04	9	140	relu	lbfgs	6	0.005	0.643	3.598
Seonam	29.8	0.31	9	436	relu	lbfgs	8	0.004	0.641	4.371
Heungdeok	51.7	0.74	9	114	relu	lbfgs	12	0.005	0.669	4.429

C: penalty constant, ε: epsilon, D: max depth, n: n estimators, A: activation, S: solver, and H: hidden layer size.

). As such, the proper values of the parameters depend on the data, so it is necessary to optimize the parameters to obtain a generalizable model. This means that the data should not be over- or underfitting [71,72]. Learning time represents the average learning time (total learning time/number of parameter combinations). The learning time of each model was 0.004, 0.629, and 4.111 s for SVM1, RF1, and ANN1, respectively. The learning time was the training time for one parameter combination, and the computation time across 200 combinations showed a much more significant difference. Regarding learning time, the performance was good in the order of SVM1, RF1, and ANN1 models. The SVM algorithm involves repetitive/iterative computations involving the multiplication of large dimensional matrices, which demand substantial computational time and storage space to define the best hyperplanes [73]. The SVM algorithm provides excellent results but has limitations that apply to problems with large datasets (more than 100 K) due to significant learning times [74,75]. The RBF kernel of the SVM algorithm in particular was expected to have poor learning time performance due to relatively high temporal and spatial complexity compared to other kernels. However, a high-speed performance was observed in this study because the number of training data samples was low at 262 units. The SVM1 and ANN1 models slightly outperformed the RF1 model in learning performance, but the ANN1 model is the most inefficient regarding learning time. Therefore, the one-month forecast model is judged to be a model optimized in the order of SVM1, RF1, and ANN1 when considering everything up to the learning time.

3.2. Performance in the Two-Month Forecasting Models

The training and test performance results of the model forecast of two-month storage rates are summarized in

Table 7. Performance of applied models in the training and test phases for two-month forecasting.

Reservoir	SVM2						RF2						ANN2
	Training			Test			Training			Test			Training			Test
	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2
Mireuk	11.1	6.27	0.79	11.5	7.75	0.73	5.1	3.33	0.95	12.6	8.74	0.67	10.3	6.80	0.81	11.8	8.40	0.71
Wonsu	11.0	5.74	0.69	10.3	6.30	0.66	4.8	3.14	0.94	11.0	7.52	0.61	10.7	7.06	0.71	10.3	7.26	0.66
Geumma	9.9	5.74	0.80	11.3	7.32	0.68	4.2	2.8	0.96	10.7	7.31	0.71	9.5	6.52	0.81	11.3	7.91	0.67
Dosun	8.8	5.57	0.81	12.6	7.57	0.57	4.0	2.76	0.96	12.2	7.99	0.6	8.4	6.02	0.83	12.6	7.97	0.57
Wanggung	8.7	5.31	0.84	8.7	5.64	0.79	3.9	2.5	0.97	8.7	5.84	0.8	8.4	5.97	0.85	9.3	7.02	0.77
Yongsan	10.3	6.78	0.77	13.0	9.08	0.61	5.1	3.66	0.94	13.6	10.13	0.58	9.5	6.72	0.81	14.7	9.94	0.50
Naejang	10.5	7.10	0.78	12.3	9.33	0.69	5.6	4.37	0.94	13.7	10.96	0.61	10.6	7.81	0.78	13.6	10.78	0.62
Bujeon	8.4	5.78	0.81	10.9	7.42	0.70	7.0	5.48	0.87	11.1	7.79	0.68	7.2	5.41	0.86	10.7	7.50	0.71
Jisun	12.0	7.59	0.74	13.2	8.84	0.59	5.2	3.61	0.95	13.0	9.53	0.6	11.9	8.37	0.75	12.6	9.22	0.62
Ipam	7.8	4.80	0.88	10.5	7.34	0.71	4.4	3.27	0.96	11.0	8.05	0.68	7.8	5.44	0.88	9.4	6.90	0.77
Sucheong	8.2	5.41	0.88	10.2	7.30	0.79	4.2	3.2	0.97	11.0	7.75	0.76	7.7	5.58	0.89	9.9	7.01	0.81
Seonam	10.0	6.83	0.80	11.0	7.29	0.76	4.9	3.65	0.95	10.5	7.31	0.78	9.3	6.88	0.83	11.7	8.01	0.72
Heungdeok	9.2	6.03	0.80	10.8	7.91	0.64	4.5	3.36	0.95	11.0	7.99	0.63	9.7	7.27	0.77	9.8	7.46	0.70

and Figure 5. Although not better than the one-month forecast, the lowest R² value was 0.5. The average R² values of SVM2, RF2, and ANN2 were 0.69, 0.65, and 0.68, respectively, and therefore, they were significantly reliable. The difference in the training and test performances was similar in the SVM2 and ANN2 models; comparatively, the SVM2 model showed a smaller generalization error. In contrast, the RF2 model showed a significant difference in performance between the training and test phases. In the training phase, the RF2 model has an MAE of 2.70–5.52 and an RMSE of 3.9–7.0, significantly outperforming the other models. However, in the test phase, the MAE was 6.30–11.98, and the RMSE was 8.7–13.7, higher than the other two models.

Table 8. Results of best parameters and learning time of models for two-month forecasting.

Reservoir	Hyperparameter Optimization							Learning Time (sec.)
	SVM2		RF2		ANN2			SVM2	RF2	ANN2
	C	ε	D	n	A	S	H
Mireuk	17.7	0.04	9	106	tanh	adam	28	0.005	0.688	4.269
Wonsu	26.6	0.02	9	105	tanh	adam	25	0.005	0.699	3.856
Geumma	18.6	0.09	9	186	tanh	adam	23	0.004	0.671	4.441
Dosun	14	0.09	9	159	tanh	adam	17	0.005	0.695	4.803
Wanggung	14	0.09	9	329	tanh	adam	16	0.005	0.669	4.365
Yongsan	21.2	0.01	8	228	relu	lbfgs	9	0.004	0.704	3.590
Naejang	49.8	0.05	9	432	relu	lbfgs	10	0.007	0.691	3.827
Bujeon	14.8	0.08	5	434	relu	lbfgs	10	0.004	0.702	4.376
Jisun	24.2	0.08	9	491	tanh	adam	25	0.004	0.675	4.141
Ipam	106	0.01	8	257	relu	lbfgs	12	0.004	0.667	3.916
Sucheong	16	0.1	8	119	relu	lbfgs	5	0.005	0.690	3.550
Seonam	28.9	0.07	9	125	tanh	adam	28	0.004	0.676	4.320
Heungdeok	47.5	0.09	9	288	relu	adam	17	0.004	0.675	3.892

C: penalty constant, ε: epsilon, D: max depth, n: n estimators, A: activation, S: solver, and H: hidden layer size.

shows the hyperparameter optimization results and learning time results. The hyperparameters were the combination of parameters that showed the best performance by optimization, and the values for all reservoirs appeared different. The learning time was 0.005, 0.042, and 4.104 s for SVM2, RF2, and ANN2, respectively. The RF algorithm is computationally less expensive and faster in training the model and performing predictions [76]. The RF algorithm in particular is more effective in handling large datasets [73]. However, an increase in computation time was observed when a high number of trees was considered, as in the study by Rodriguez-Galiano et al. [72]. In this study, RF2 showed a large generalization error. The RF algorithm is significantly impacted by the number of data to a greater extent than other models, and thus, the number of data needs to be increased to overcome test accuracy and overfitting issues [77]. The RF2 model was relatively more straightforward to implement than the other two models, but there were limits when the data were limited. As with the one-month forecast, the SVM2 and ANN2 models did not differ significantly in learning performance, but the learning time of the SVM2 model was overwhelmingly better. Considering only the training time, the RF2 model was superior to the ANN2 model, but due to the high generalization error, the two-month storage rate forecast model was judged to be superior in the order of SVM2, ANN2, and RF2 model.

3.3. Performance in the Three-Month Forecasting Models

The three-month storage rate forecast performances demonstrated that all three models are reliable; the R² values, MAE, and RMSE values for SVM3, RF3, and ANN3 are presented in

Table 9. Performance of applied models in the training and test phases for three-month forecasting.

Reservoir	SVM3						RF3						ANN3
	Training			Test			Training			Test			Training			Test
	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2
Mireuk	11.9	6.72	0.75	12.2	8.74	0.71	9.3	6.56	0.85	13.9	9.97	0.62	12.0	8.11	0.74	11.8	8.62	0.73
Wonsu	11.7	6.11	0.65	10.9	6.69	0.64	6.1	4.36	0.90	11.1	7.59	0.63	11.0	7.42	0.69	12.0	8.81	0.56
Geumma	11.4	6.15	0.73	14.4	9.56	0.50	5.5	3.70	0.94	13.7	9.18	0.55	11.2	7.29	0.74	13.4	9.04	0.57
Dosun	9.2	5.50	0.79	14.5	9.41	0.50	4.7	3.38	0.94	14.6	9.47	0.49	10.0	7.01	0.75	15.5	10.50	0.43
Wanggung	8.8	5.16	0.82	10.1	7.24	0.76	5.7	4.02	0.93	10.5	7.42	0.74	9.1	6.32	0.81	9.4	7.01	0.79
Yongsan	10.7	7.05	0.74	14.3	10.32	0.57	6.2	4.64	0.91	15.1	11.24	0.52	11.5	8.60	0.70	14.7	10.89	0.55
Naejang	11.8	8.30	0.71	13.3	10.00	0.67	6.9	5.68	0.90	15.1	12.01	0.57	12.9	10.44	0.66	13.4	10.73	0.66
Bujeon	8.9	5.81	0.79	10.1	7.38	0.73	5.8	4.59	0.91	11.5	8.51	0.65	8.6	6.49	0.80	12.0	9.06	0.62
Jisun	11.9	7.71	0.74	14.0	10.11	0.57	6.1	4.51	0.93	14.9	11.25	0.52	12.9	9.82	0.69	13.6	10.29	0.60
Ipam	8.4	5.17	0.85	10.2	7.43	0.77	4.9	3.64	0.95	12.6	9.28	0.65	8.5	6.30	0.85	10.7	7.95	0.75
Sucheong	8.4	5.55	0.87	10.3	7.22	0.80	5.3	4.28	0.95	11.8	8.77	0.73	8.1	6.22	0.88	10.4	7.54	0.79
Seonam	10.2	6.59	0.80	12.4	8.94	0.69	7.8	5.86	0.88	14.0	10.08	0.60	11.7	8.57	0.73	12.3	9.22	0.69
Heungdeok	8.8	5.63	0.81	13.2	9.88	0.52	5.4	4.23	0.93	13.7	10.37	0.48	10.0	7.82	0.76	12.7	10.08	0.55

and Figure 6. SVM, RF, and ANN models for the three-month storage rate forecast showed reliable results. The MAE shows an error within 10%, and the average R² values of SVM3, RF3, and ANN3 were 0.65, 0.60, and 0.64, respectively, all of which have explanatory power. In the case of the generalization error, the RF3 model showed relatively large errors, similar to the two-month forecast. The performance of the SVM3 and ANN3 models were similar, as were the storage rate forecast for two months. However, this study configured the hidden layer to 1 for the ANN algorithm. The hidden layer in the neural network impacts the model performance; considerable research on the method for determining the appropriate number of hidden layers is in progress [50,78,79]. Nguyen et al. recommended ANN with 2–3 hidden layers for simple regression [80], and Heaton argued that two hidden layers showed high accuracy when using a reasonable activation function [81]. Generally, the largest and most complex networks are more practical for defining a training dataset. However, these types of networks perform less accurate generalizations than smaller and simpler networks [72]. Considering these points, we should try to extend the hidden layers and number of neurons in the future and confirm the improvement of the ANN algorithm learning performance. The optimal parameters appear differently, and the learning times of SVM3, RF3, and ANN3 are 0.007, 0.732, and 4.372 s, respectively (

Table 10. Results of best parameters and learning time of models for three-month forecasting.

Reservoir	Hyperparameter Optimization							Learning Time (sec.)
	SVM3		RF3		ANN3			SVM3	RF3	ANN3
	C	ε	D	n	A	S	H
Mireuk	105.1	0.81	5	431	tanh	adam	26	0.007	0.745	4.722
Wonsu	109.4	0.24	7	199	relu	lbfgs	9	0.008	0.742	2.606
Geumma	104.7	0.83	8	123	tanh	adam	24	0.008	0.708	4.685
Dosun	111.1	0.11	8	203	relu	lbfgs	7	0.008	0.741	4.548
Wanggung	100.9	0.36	6	491	tanh	adam	28	0.008	0.703	4.664
Yongsan	100.2	1.01	7	320	tanh	adam	19	0.007	0.751	4.716
Naejang	101.6	0.37	8	121	tanh	adam	29	0.006	0.724	4.138
Bujeon	100.5	0.84	7	301	relu	lbfgs	11	0.007	0.760	3.878
Jisun	113.5	1.00	9	147	tanh	adam	17	0.006	0.736	4.537
Ipam	122.6	0.95	9	111	tanh	adam	13	0.008	0.732	4.670
Sucheong	104.4	0.87	7	443	relu	lbfgs	7	0.008	0.753	4.656
Seonam	249.7	1.06	6	100	relu	lbfgs	6	0.007	0.697	4.822
Heungdeok	248.8	0.88	8	128	relu	lbfgs	6	0.007	0.718	4.200

C: penalty constant, ε: epsilon, D: max depth, n: n estimators, A: activation, S: solver, and H: hidden layer size.

). The learning time for ANN3 is significantly longer than SVM3 and RF3 models. The ANN algorithm uses the time-consuming backpropagation algorithm to update the weight values, which requires more time for learning than the other models. ANN has the potential to become a more widely used regression algorithm, but because of their time-consuming parameter tuning procedure, the numerous types of neural network architectures to choose from, and the high number of algorithms used for training ANN, some researchers recommend SVM or RF algorithm [82]. Considering all aspects, such as learning outcome and learning time, the SVM3 is determined to be relatively more efficient than the ANN3.

4. Conclusions

In this study, the ML algorithms such as SVM, RF, and ANN were used to forecast the monthly storage rates after 1–3 months, and their applicability was verified. To this end, the storage rate data for 13 agricultural reservoirs collected over about 30 years (1981 to March 2022) and two sources of meteorological data from nearby observatories were used as training data. Nine learning models were tested based on the algorithm type and label, and the test performances of each learning model were assessed using two performance indices, RMSE, MAE, and R².

The one-month storage rate forecasting showed that all SVM, RF, and ANN algorithms were highly reliable, with R² values of 0.8 or above. In the results of the storage rate prediction test for two and three months, the ANN and SVM algorithms showed relatively good explanatory power with an average R² ranging from 0.64 to 0.69. In contrast, the RF algorithm showed high generalization error. Although the SVM and ANN algorithms were superior to the RF algorithm in terms of learning performance, it was found that the learning speed was faster in the order of the SVM, RF, and ANN algorithms in terms of learning time. Overall, the SVM algorithm is the most reasonable model for storage rate forecast by showing the best performance in all evaluations, such as learning performance and learning time.

This research investigated the regression ML algorithms for the storage rate forecasting of agricultural reservoirs; they were sufficiently applicable. In the case of limited data, the SVM algorithm was more valuable than the RF and ANN algorithms. However, this could differ based on the data’s amount, characteristics, and complexity. Therefore, a comparison of several learning algorithms is suggested before selecting the optimal model for a certain issue.

In the future, a more accurate prediction of storage rates is expected because storage rate data continue to accumulate. In addition, the provision of scientific information necessary for the decision-making of on-site water managers is expected to be possible through the connection with highly reliable meteorological forecast data. Further, subsequent research studies that focus on the optimal model for storage rate forecasting by testing various learning data and learning models relevant to the storage rate, such as the previous rainfall and deviations in rainfall, are necessary.