Front. Environ. Sci. Frontiers in Environmental Science Front. Environ. Sci. 2296-665X Frontiers Media S.A. 1659521 10.3389/fenvs.2026.1659521 Original Research On WRF hybrid-dynamic regression approach in heavy rainfall forecasting over the Northern of Thailand Sirisombat et al. 10.3389/fenvs.2026.1659521 Sirisombat Nattawadee 1 Conceptualization Data curation Formal Analysis Funding acquisition Investigation Methodology Project administration Resources Software Supervision Validation Visualization Writing - original draft Writing - review and editing Chinram Ronnason 1 Conceptualization Data curation Formal Analysis Funding acquisition Investigation Methodology Project administration Resources Software Supervision Validation Visualization Writing - original draft Writing - review and editing Panityakul Thammarat 1 * Conceptualization Data curation Formal Analysis Methodology Project administration Resources Supervision Validation Visualization Writing - original draft Writing - review and editing Thinnukool Orawit 2 * Formal Analysis Supervision Visualization Writing - review and editing Division of Computational Science, Faculty of Science, Prince of Songkla University, Songkhla, Thailand Innovative Research and Computational Science Lab, College of Arts, Media and Technology, Chiang Mai University, Chiang Mai, Thailand Correspondence: Thammarat Panityakul, thammarat.p@psu.ac.th; Orawit Thinnukool, orawit.t@cmu.ac.th 26 02 2026 2026 14 1659521 08 07 2025 04 11 2025 09 01 2026 Copyright © 2026 Sirisombat, Chinram, Panityakul and Thinnukool. 2026 Sirisombat, Chinram, Panityakul and Thinnukool https://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Rainfall forecasting in Northern Thailand presents considerable challenges due to the complex topography of the region and its highly variable climatic conditions, particularly during periods of heavy rainfall in August. This is compounded by limitations in ground-based observation data, such as missing data and sparse station coverage. This study has two primary objectives. First, it examines the sensitivity of rainfall simulations using the weather research and forecasting (WRF) model to different configurations of microphysics and cumulus parameterization schemes. Second, it evaluates the performance of four different approaches in forecasting models including autoregressive integrated moving average (ARIMA), artificial neural network (ANN), dynamic exponential regression and autoregressive integrated moving average (DER–ARIMA), and dynamic quadratic regression and autoregressive integrated moving average (DQR–ARIMA). The period was focused on 1–31 August from 2009 to 2023. The performance of both components is assessed using three statistical metrics: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Symmetric Mean Absolute Percentage Error (SMAPE). The results showed that the most accurate configurations in WRF model were Kessler–New Tiedtke for the Salween (RMSE = 9.85) River Basin, WSM5–New Tiedtke for the Ping (RMSE = 8.43) and Yom (RMSE = 10.41) River Basins, and WSM6–New Tiedtke for the Upper Mekong (RMSE = 13.73), Wang (RMSE = 11.10), and Nan (RMSE = 11.08) River Basins. For forecasting models, the ANN model demonstrated the highest accuracy in the Salween (RMSE = 10.66), Upper Mekong (RMSE = 15.09), and Nan (RMSE = 16.30) River Basins, while the DER–ARIMA model performed best in the Wang (RMSE = 15.63) and Yom (RMSE = 12.08) River Basins. The DQR–ARIMA model was found to be the most suitable for the Ping (RMSE = 12.04) River Basin.

 heavy rainfall WRF model microphysics cumulus parameterization dynamic model Faculty of Science, Prince of Songkla University 10.13039/501100022536 1-2565-02-010. The author(s) declared that financial support was received for this work and/or its publication. Research Assistantship for the Academic Year 2022, Contract No. 1-2565-02-010. This research work was partially supported by Chiang Mai University. section-at-acceptance Environmental Informatics and Remote Sensing Introduction

Northern Thailand is characterized by a complex and diverse topography, featuring high mountain ranges that alternate with foothills. This topography directly influences precipitation processes, particularly where orographic lift, the forced uplift of air masses by mountains, thereby inducing localized rainfall. Moreover, local valleys and basins can retain moisture, resulting in significant spatial variability in precipitation (Climatological Center, 2016). Furthermore, this region is influenced by highly variable climatic systems, notably the Southwest Monsoon (May-October) and the El Niño-Southern Oscillation (ENSO), which increase the complexity of forecasting precipitation (Singhrattna et al., 2005). Thus, the accurate forecasting of precipitation is essential for both effective water resource management and disaster preparedness.

However, the use of data from rain gauge stations as input data for rainfall forecasting can have limitations, such as missing data or inadequate coverage over remote mountainous areas. Therefore, the Weather Research and Forecasting (WRF) model (Skamarock et al., 2008) is an essential tool for addressing the data gap. International studies in regions such as the central Himalaya (Tiwari and Bush, 2025) and central Korea (Kim et al., 2012), which have geography and rainfall similar to Northern Thailand, have consistently shown that it is very important to select the appropriate microphysics and cumulus parameterization schemes. Chotamonsak et al. (2012) demonstrated that selecting a suitable cumulus parameterization scheme is critical for accurately simulating monthly rainfall in Thailand with the WRF model. Specifically, the use of the Betts–Miller–Janjic (BMJ) scheme combined with nudging significantly enhanced the accuracy of the model’s rainfall simulations. Studies by Kaewmesri et al. (2017a), Kaewmesri et al. (2017b) identified that selecting an appropriate microphysics parameterization, such as the WSM6 or Thompson schemes. This was a critical factor in enhancing the WRF model’s performance when simulating heavy rainfall from the Southwest Monsoon in Thailand. Torsri et al. (2023) studied the impact of various microphysics and cumulus schemes on simulating heavy rainfall in Thailand using the coupled WRF-ROMS model. They found that the combination of the Thompson microphysics and Kain–Fritsch cumulus schemes yielded the most accurate results. Kirtsaeng and Kreasuwan (2010) found that configuring the WRF model with the WSM5 microphysics scheme and the Kain–Fritsch cumulus parameterization yielded effective results in simulating heavy precipitation over the southeast coast of Thailand.

Several studies have shown that choosing suitable microphysics and cumulus parameterization schemes can improve the accuracy of WRF model rainfall simulations in Thailand. Chotamonsak et al. (2012) and Kaewmesri et al. (2017a), Kaewmesri et al. (2017b) found that the WSM6 and Thompson microphysics schemes performed well during the Southwest Monsoon, while Torsri et al. (2023) showed that the combination of Thompson microphysics and Kain–Fritsch cumulus schemes produced the best results for heavy rainfall events. Recently, researchers have extended the use of the WRF model by combining it with data-driven and hybrid regression techniques to improve rainfall forecasting. For example, Pathak et al. (2023) discussed multi-observation uncertainty in model evaluation, and Ghimire et al. (2022), Hossain et al. (2023), and Zhang et al. (2024) demonstrated that hybrid AI and deep-regression frameworks can significantly enhance precipitation prediction accuracy. Building upon these advances, this study evaluated the sensitivity of rainfall simulations to different microphysics and cumulus schemes across six major river basins in Northern Thailand (Salween, Upper Mekong, Ping, Wang, Yom, and Nan) and applied hybrid forecasting models (ARIMA, ANN, DER–ARIMA, and DQR–ARIMA) to assess their performance in predicting heavy rainfall events.

After simulating the daily average rainfall for each river basin during 1–31 August from 2009 to 2023 using a suitable WRF model, this study proceeded to evaluate the performance of various forecasting models. The efficiency of this forecasting model was evaluated through comparison with four different approaches including autoregressive integrated moving average (ARIMA), artificial neural network (ANN), dynamic exponential regression and autoregressive integrated moving average (DER–ARIMA), and dynamic quadratic regression and autoregressive integrated moving average (DQR–ARIMA) (Sirisombat and Panityakul, 2025), which has been developed from previous work. Lakshminarayana et al. (2020) presented a comprehensive literature review on rainfall forecasting using ANN models from 1997 to 2019. Their work evaluated commonly used ANN architectures and highlighted their advantages in terms of flexibility and predictive accuracy, revealing that ANN models generally outperform traditional regression and numerical methods. However, a study by Kişi (2007) highlighted several limitations of ANN models in hydrologic forecasting, noting that they are prone to overfitting, can function as black-box models, and lack interpretability. Syed et al. (2022) showed that the ARIMA model is effective for short and medium terms rainfall prediction in Southeast Asia, especially in tropical monsoon regions with strong seasonal cycles. This finding supports the idea that the model could be useful for Northern Thailand’s climate. Furthermore, other studies indicate that the ARIMA model can accurately forecast rainfall in specific environments. For instance, it has proven effective in regions with complex mountainous terrain (Swagatam Bora and Abhilash Hazarika, 2023) and in areas with tropical monsoon climates (Mohd Zain et al., 2023). In previous work, Sirisombat and Panityakul (2025) developed two dynamic regression (DR) models, namely the DER–ARIMA and DQR–ARIMA models. These models are characterized by a dynamic structure, dynamic dates, and dynamic modeling capabilities. The DER–ARIMA model is suitable for time series data exhibiting an exponential trend. In contrast, the DQR–ARIMA model is effective at capturing non-linear relationships, specifically a quadratic trend.

 Methodology Observed data

Daily rainfall from August 1-31 for the period 2009-2023 were obtained from 27 rain gauge stations of the Thai Meteorological Department (TMD) in Northern Thailand. These stations are distributed across the six river basins including Salween, Mekong, Ping, Wang, Yom and Nan. Given the varying number of stations in each river basin, the daily average rainfall for each river basin was calculated using the arithmetic mean of the daily rainfall from all stations located within that specific river basin. To effectively manage and reduce the influence of seasonality in rainfall data, the daily average rainfall time series for each river basin was reorganized by day across the years. Therefore, the dataset for each river basin consists of daily rainfall values recorded on the same calendar day (e.g., August 1) from 2009 to 2023. However, the observed rainfall data from the Thai Meteorological Department (TMD) stations were used as the reference dataset to evaluate model performance. These observations may contain uncertainties due to limited station coverage and measurement errors, particularly in mountainous basins. As noted by Pathak et al. (2023), such observational uncertainties can be comparable to or even greater than model uncertainties.

 Weather research and forecasting (WRF) model

The Weather Research and Forecasting (WRF) model was developed by the National Center for Atmospheric Research (NCAR) and was one of the Numerical Weather Prediction (NWP) model. The WRF model was a famous dynamical atmospheric model because can be applied high resolution from meters to thousands of kilometers (Skamarock et al., 2008). In this study, two nested domains were configured as shown in Figure 1. The outer domain (Domain 1) covered Thailand, and the resolution was 27 km (68 × 78 grid points). This domain is located between 92°15′18″E and 109°14′42″E longitudes and 4°3′29″N and 22°56′53″N latitudes. The sub-domain (Domain 2) covered Northern Thailand, and the resolution was 9 km (73 × 76 grid points). This domain is located between 96°18′43″E and 102°23′53″E longitudes and 15°2′35″N and 21°4′1″N latitudes in the vertical direction with a maximum of 50 hPa. Initial and boundary conditions were generated by the NCEP FNL data on 1 ° × 1 ° global grids every 6 h. The physics parameterization schemes are available in the model to represent processes, including cumulus convection, microphysics, radiative transfer, planetary boundary layer (PBL) and the land surface. All the sensitivity experiments used the same physical options, except for the different microphysics and cumulus parameterization schemes. The 15 experiments employed three different microphysics schemes: Kessler (Kessler, 1969), the WRF single Moment 5-class (WSM5) (Hong et al., 2004) and the WRF single Moment 6-class (WSM6) (Hong and Lim, 2006) and five different cumulus parameterization schemes: Kain-Fritsch (KF) (Kain, 2004), Betts–Miller–Janjic (BMJ) (Betts and Miller, 1986; Janjic, 1994; Janjic, 2000), Multi–scale Kain–Fritsch (Multi–scale KF) (Zheng et al., 2016), New Simplified Arakawa–Schubert (NSAS) (Han and Pan, 2011) and New Tiedtke (NT) (Zhang et al., 2017). Tables 1, 2 summarized comparisons of microphysics and cumulus parameterization schemes in WRF model, respectively. The fixed physics options used in this study including Dudhia (Dudhia, 1989) for shortwave radiation and Rapid Radiative Transfer Model (RRTM) (Mlawer et al., 1997) for long-wave radiation, the Yonsei University (YSU) (Hong et al., 2006) for planetary boundary layer, Revised MM5 (Jiménez et al., 2012) for surface layer and Noah Land-Surface Model (Chen and Dudhia, 2001) for surface physics. Table 3 is summarized the simulations in this study.

The two domains used in WRF model.

Map showing Southeast Asia with two defined regions labeled as Domain 1 and Domain 2. Domain 1 covers a broader geographic area while Domain 2, a smaller region, is outlined within Domain 1. Longitude and latitude lines are included.

Comparisons of microphysics schemes in WRF model.

Scheme Suitable area types Advantages Disadvantages
Kessler Tropical regions with dominant convective rainfall Computationally simple and efficient Neglects ice-phase processes, limiting applicability in mixed-phase environments
WSM5 Areas with complex topography and varied terrain Accounts for mixed-phase processes, improving realism in diverse climates Requires higher computational resources compared to simpler schemes
WSM6 Tropical monsoon regions experiencingIntense precipitation Provides detailed cloud microphysics and includes graupel processes Increased complexity and slower performance relative to WSM5

Comparisons of cumulus parameterization schemes in WRF model.

Scheme Suitable area types Advantages Disadvantages
Kain–Fritsch Tropical regions with dominant convective rainfall Computationally simple and efficient Poor performance in stratiform or weak convection situations
Betts–Miller–Janjic Tropical regions with large-scale precipitation systems Simple structure; effectively adjusts thermodynamic profiles Poor performance in dry conditions
Multi–scaleKain–Fritsch Tropical and subtropical regions Simple structure; effectively adjusts thermodynamic profiles Computationally demanding and requires careful tuning
New SimplifiedArakawa–Schubert Tropical deep convective zones Mass flux–based; includes entrainment/detrainment; applicable to global model Less effective for high-resolution nested domains
New Tiedtke Coastal and tropical regions Represents both shallow and deep convection; improved moist process treatment Limited validation in mid-latitude or arid inland regions

List of experiments with different parameterization schemes.

Simulation Microphysics Cumulus parameterization
1 Kessler Kain-Fritsch
2 Kessler Betts–Miller–Janjic
3 Kessler Multi–scale Kain–Fritsch
4 Kessler New Simplified Arakawa–Schubert
5 Kessler New Tiedtke
6 WSM5 Kain-Fritsch
7 WSM5 Betts–Miller–Janjic
8 WSM5 Multi–scale Kain–Fritsch
9 WSM5 New Simplified Arakawa–Schubert
10 WSM5 New Tiedtke
11 WSM6 Kain-Fritsch
12 WSM6 Betts–Miller–Janjic
13 WSM6 Multi–scale Kain–Fritsch
14 WSM6 New Simplified Arakawa–Schubert
15 WSM6 New Tiedtke

The WRF model was utilized to simulate daily rainfall during 1–31 August from 2009 to 2023 by 15 different physics parameterizations. The simulated daily rainfall was extracted at the exact latitude and longitude coordinates of 27 rain gauge stations. For each river basin, the daily average rainfall was calculated using the arithmetic mean of the daily rainfall from all stations within that river basin, as shown in Equation 1. The daily average rainfall time series for each river basin was reorganized by calendar day across the years. Consequently, each dataset was represented daily rainfall data corresponding to the same date over the 15-year period. The resulting daily average rainfall simulated by the WRF model was then compared against the observed daily average rainfall derived from the TMD stations. The optimal physical parameterizations for each of the six river basins in Northern Thailand was identified based on the minimum values of mean absolute error (MAE), root mean square error (RMSE), and symmetric mean absolute percentage error (SMAPE).

In this study, the daily average rainfall simulated by the optimal WRF configurations for each river basin during 1–31 August 2009–2023 was used as the input dataset for forecasting models. The dataset was divided into two parts including training data and test data. For training data, the period from 1 to 31 August 2009–2020 was used to train the ARIMA, ANN, DER–ARIMA, and DQR–ARIMA models. After the models were developed, testing data was applied to forecast daily average rainfall for 1–31 August 2021–2023 as shown in Figure 2.

Training and test data.

Table titled "Upper Mekong" with years 2009 to 2023 in rows. Columns are labeled Date 1 to Date 31. Green sections indicate training data. Pink sections for 2022 and 2023 indicate test data. Data series range from N2_1 to N2_31. Forecasting models Autoregressive integrated moving average (ARIMA) model

The autoregressive integrated moving average (ARIMA) model was developed by Box and Jenkins (Box et al., 2015) and is widely used in the field of hydrology. It consists of three main components: autoregressive (AR), integrated (I), and moving average (MA), represented by the notation ARIMA p , d , q .

 Artificial neural network (ANN) model

An artificial neural network (ANN) is a fundamental component of both artificial intelligence (AI) and machine Learning. The two primary characteristics of ANN (Baboo and Shereef, 2010) are its ability to learn from data and subsequently recall that knowledge to new information. A feed-forward neural network (FNN) is utilized in this study. The FNN is a foundational architecture of ANN where information moves unidirectionally from the input layer to the output layer via one or more hidden layers. This means the network contains no recurrent connections or feedback loops (Rojas, 1996). In this study, we used FFN model with five ( n ) hidden layers, as shown in Figure 3. The sigmoid function was used as the activation function, and the number of training epochs was set to 200. The mathematical equations for hidden and output node can be written as Equations 1, 2 respectively. h n = φ ∑ n = 1 5 ω n t + b n where,

A feed-forward neural network in this study.

Diagram of a neural network structure with three layers: input, hidden, and output. The input layer contains node \( t \), connected via colored lines (representing different weights) to five hidden nodes (\( h_1 \) through \( h_5 \)). Each hidden node is connected to an output node \( \hat{y}_{i\_jt} \), with thresholds noted above the connections.

h n is the value of hidden node n ;   n = 1 , 2 , … , 5

ω n is the weight from the input node to hidden node n

t is the year index; t = 1,2,3, … ,15

φ · is sigmoid function

b n is the bias of hidden node n y ^ i _ j t = ∑ n = 1 5 v n h n + c where,

y ^ i _ j t is the forecasted value of daily average rainfall in river basin i ;

i = 1,2, 3, … ,6, j is a day; j = 1, 2, 3, … ,31, t is a year;

t = 1,2,3, … ,15

v n is the weight from hidden node n to outer node

c is the bias of output node

Although the ANN model employed in this study was relatively simple, its interpretability can be explained by the relationships between the input and output variables. The input neurons represented the 31-day rainfall time series simulated by the WRF model, while the output neuron corresponded to the predicted daily average rainfall for each basin. The connection weights implicitly indicated the relative importance of each input day to the forecasted rainfall value. Higher absolute weights suggested that specific days contributed more strongly to the prediction, often corresponding to periods of convective or heavy rainfall. This structure allowed the ANN to capture short-term temporal dependencies and smoothed rainfall variability without relying on complex deep-learning architectures such as LSTM or CNN. Similar findings were also reported by Baboo and Shereef (2010) and Bora and Hazarika (2023), who demonstrated that shallow ANN architectures could effectively capture nonlinear rainfall relationships while remaining interpretable and computationally efficient. Therefore, even though the ANN used here was basic, it remained suitable for regional rainfall forecasting under data-limited conditions in Northern Thailand.

 Dynamic exponential regression and autoregressive integrated moving average (DER-ARIMA) model

The dynamic exponential regression and autoregressive integrated moving average (DER–ARIMA) model Sirisombat and Panityakul (2025) is a hybrid model that combines the exponential regression (ER) and ARIMA model. The DER–ARIMA model is based on the fundamental concept of ER model but enhances it by adding flexibility to the random error component. An appropriate ARIMA model is then fitted to the residuals of the ER model, making this hybrid approach suitable for analyzing time series data that exhibits both a trend and stochastic variance. The process for DER–ARIMA model consists of the following three steps:

Step 1: Fit the ER model to the time series data, as shown in Equation 3.

y ^ i _ j t = β 0 e β 1 t + γ t where,

y ^ i _ j t is the forecasted value of daily average rainfall in river basin i ;

i = 1,2, 3, … ,6, j is a day; j = 1, 2, 3, … ,31, t is a year;

t = 1,2,3, … ,15

β 0 is a constant term (intercept).

β 1 is growth rate parameter

e is Euler’s number

γ t is the random error component of ER model at time t

Step 2: The series of the random error component generated by the ER model in the first step is treated as a new time series. The Box-Jenkins methodology is then applied to this random error component to identify and fit the most suitable ARIMA model, as shown in Equation 4.

Φ p B 1 − B d γ t = Θ q B ε t where,

γ t is the random error component of ER model at time t

B is the backward shift operator B y ^ N i j t = y N i j t − 1

Φ p B is the autoregressive (AR) polynomial,

i.e., Φ p B = 1 − ϕ 1 B − ϕ 2 B 2 − … − ϕ p B p

Θ q B is the moving average (MA) polynomial,

i.e., Θ q B = 1 + θ 1 B + θ 2 B 2 + … + θ q B q

ε t is the residual of ARIMA model at time t

Step 3: The DER–ARIMA model is formed by combining the trend component from the ER model (Step 1) and the ARIMA model for the random error component (Step 2), as shown in Equation 5.

y ^ i _ j t = β 0 e β 1 t + Θ q B ε t Φ p B 1 − B d

Dynamic quadratic regression and autoregressive integrated moving average (DQR-ARIMA) model

The dynamic quadratic regression and autoregressive integrated moving average (DQR–ARIMA) model Sirisombat and Panityakul (2025) is a hybrid model that combines the quadratic regression (QR) and ARIMA model. The process for DQR–ARIMA model consists of the following three steps:

Step 1: Fit the QR model to the time series data, as shown in Equation 6.

y ^ i _ j t = β 0 + β 1 t + β 2 t 2 + γ t where,

y ^ i _ j t is the forecasted value of daily average rainfall in river basin i ;

i = 1,2, 3, … ,6, j is a day; j = 1, 2, 3, … ,31, t is a year;

t = 1,2,3, … ,15

β 0 is a constant term (intercept).

β 1 is coefficient for the linear term

β 2 is coefficient for the quadratic term

γ t is the random error component of QR model at time t

Step 2: The series of the random error component generated by the QR model in the first step is treated as a new time series. The Box-Jenkins methodology is then applied to this random error component to identify and fit the most suitable ARIMA model, as shown in Equation 4.

Step 3: The DQR–ARIMA model is formed by combining the trend component from the QR model (Step 1) and the ARIMA model for the random error component (Step 2), as shown in Equation 7.

 y ^ i _ j t = β 0 + β 1 t + β 2 t 2 + Θ q B ε t Φ p B 1 − B d

Accuracy

The performance of both the WRF and the subsequent forecasting models is evaluated using three standard metrics: mean absolute error (MAE) as shown in Equation 8, root mean square error (RMSE) as shown in Equation 9 and symmetric mean absolute percentage error (SMAPE) as shown in Equation 10 (Hyndman and Athanasopoulos, 2018). For both models, lower values of these metrics signify higher accuracy, indicating that the model outputs (simulated or forecasted) are in close agreement with the observed data. M A E = 1 n ∑ t = 1 n x ¯ i _ j t − y ^ i _ j t R M S E = 1 n ∑ t = 1 n x ¯ i _ j t − y ^ i _ j t 2 S M A P E = 100 % n ∑ t = 1 n x ¯ i _ j t − y ^ i _ j t x ¯ i _ j t + y ^ i _ j t / 2 where,

y ^ i _ j t is the forecasted value of daily average rainfall

x ¯ i _ j t is the observed daily average rainfall from rain gauge stations

i is the specific river basin; i = 1,2, 3, … ,6

j is the day in August; j = 1, 2, 3, … ,31

t is the year; t = 1,2,3, … ,15

n is the number of rain gauge stations in river basin

 Novelty and contributions

This study provides several novel contributions to the field of rainfall forecasting in complex topographic regions such as Northern Thailand. This study presents several novel aspects and meaningful contributions to rainfall forecasting in complex topographic regions of Northern Thailand. The main novelty of this research lies in the integration of high-resolution WRF model outputs with dynamic regression models, namely DER–ARIMA and DQR–ARIMA. This hybrid approach combines the strengths of numerical weather prediction and time-series analysis, which has not been previously applied to rainfall forecasting in Northern Thailand. The study also focuses on solving data limitations by using WRF-simulated rainfall as a substitute for missing or sparse observational data.

In addition, the study contributes to the field by identifying the most suitable microphysics–cumulus combinations of the WRF model for each major river basin. These findings provide new insights into how model physics influence rainfall simulation accuracy under complex terrain and monsoon conditions. The hybrid dynamic regression models further demonstrate improved forecasting accuracy, especially during heavy rainfall events, compared with conventional ARIMA models. Overall, this work provides a practical and adaptable framework that can be applied to other data-scarce regions and can support early warning systems and flood management planning in Northern Thailand.

 Results Descriptive statistics

Figure 3 shows the boxplots of daily average rainfall (mm/day) from rain gauge stations during 1–31 August from 2009 to 2023. The data is presented for six river basins: the Salween, Mekong, Ping, Wang, Yom, and Nan River Basin. Within this dataset, a heavy rainfall day can be identified using two metrics derived from the daily average rainfall data: the maximum daily rainfall (MAX) and the third quartile of daily average rainfall ( Q 3 ). The analysis identified the day with the heaviest rainfall for each basin. For the Salween River Basin, this occurred on 8 August (MAX = 40.10, Q 3 = 24.74), as shown in Figure 4a. The day with the heaviest rainfall in the Upper Mekong River Basin on 25 August (MAX = 62.63, Q 3 = 21.67), as shown in Figure 4b. For the Ping River Basin, this occurred on 11 August (MAX = 46.03, Q 3 = 16.18), as shown in Figure 4c. The day with the heaviest rainfall in the Wang River Basin on 20 August (MAX = 38.37, Q 3 = 20.50), as shown in Figure 4d. For Yom River Basin this occurred on 21 August (MAX = 83.2, Q 3 = 16.72), as shown in Figure 4e. The day with the heaviest rainfall in the Nan River Basin on 8 August (MAX = 27.46, Q 3 = 19.37) as shown in Figure 4f.

The boxplots of the observed daily average rainfall for six river basins. (a) The observed daily average rainfall for Salween River Basin. (b) The observed daily average rainfall for Upper Mekong River Basin. (c) The observed daily average rainfall for Ping River Basin. (d) The observed daily average rainfall for Wang River Basin. (e) The observed daily average rainfall for Yom River Basin. (f) The observed daily average rainfall for Nan River Basin.

Three box plot graphs labeled (a), (b), and (c) display data distributions over 31 days, with outliers marked as dots. Each graph shows variations in medians, interquartile ranges, and whiskers, suggesting different trends or data variability for each dataset. Three box plot graphs labeled (d), (e), and (f) show data distributions over 31 days. Each plot has a vertical axis ranging from 0 to 90 and a horizontal axis labeled with days 1 to 31. The plots depict median lines, interquartile ranges, and outliers marked by dots. Weather research and forecasting (WRF) model

The daily average rainfall for each river basin was simulated using the WRF model with 15 different physics parameterization schemes to identify the optimal configuration for simulating August rainfall in Northern Thailand, classified by river basin. The accuracy was evaluated by comparing its results to the daily average rainfall from rain gauge stations, as shown in Figure 5. In summary, the most suitable parameterization schemes for each of the six river basins are presented in Table 4. The results show that the Kessler microphysics and New Tiedtke cumulus schemes provided the most accurate simulation of daily average rainfall in the Salween River Basin (MAE = 6.80, RMSE = 9.85, SMAPE = 11.96). The WSM5 microphysics and New Tiedtke cumulus schemes provided the most accurate simulation of daily average rainfall in the Ping (MAE = 5.21, RMSE = 8.43, SMAPE = 12.02) and Yom (MAE = 6.68, RMSE = 10.41, SMAPE = 19.16) River Basins. For the Upper Mekong (MAE = 8.70, RMSE = 13.73, SMAPE = 23.89), Wang (MAE = 6.78, RMSE = 11.10, SMAPE = 14.70) and Nan (MAE = 7.61, RMSE = 11.08, SMAPE = 13.67) River Basins were best simulated using the WSM6 microphysics scheme, also combined with the New Tiedtke cumulus scheme.

The accuracy between all experiments in WRF model for six river basins. (a) The MAE, RMSE and SMAPE values between all experiments in WRF model for Salween River Basin. (b) The MAE, RMSE and SMAPE values between all experiments in WRF model for Upper Mekong River Basin. (c) The MAE, RMSE and SMAPE values between all experiments in WRF model for Ping River Basin. (d) The MAE, RMSE and SMAPE values between all experiments in WRF model for Wang River Basin. (e) The MAE, RMSE and SMAPE values between all experiments in WRF model for Yom River Basin. (f) The MAE, RMSE and SMAPE values between all experiments in WRF model for Nan River Basin.

Six line graphs labeled (a) to (f) compare MAE, RMSE, and SMAPE metrics across values 1 to 15. Each graph shows three lines, with trends varying in height and fluctuations. The x-axis represents values 1 to 15, and the y-axis ranges from 0 to 100.

The suitable parameterization schemes for six river basins.

River basin Simulation Microphysics Cumulusparameterization
Salween 5 Kessler New Tiedtke
Upper Mekong 15 WSM6 New Tiedtke
Ping 10 WSM5 New Tiedtke
Wang 15 WSM6 New Tiedtke
Yom 10 WSM5 New Tiedtke
Nan 15 WSM6 New Tiedtke

Figure 6 is presented the spatial distribution of heavy rainfall events simulated by the optimal WRF configurations. In the Salween River Basin, the combination of the Kessler microphysics and New Tiedtke cumulus schemes produced moderate to very heavy rainfall (>10 mm to >110 mm) as shown in Figure 6a. Figure 6b showed the trend of daily average rainfall in the Upper Mekong River Basin, indicating light to heavy rainfall (>5 mm to >60 mm) when using the combination of the WSM6 microphysics and New Tiedtke cumulus schemes. For the Ping Basin, the WSM5–New Tiedtke configuration generated mostly trace to light rainfall (>0 mm to >10 mm) as shown in Figure 6c. The Wang Basin showed light to moderate rainfall (>5 mm to >35 mm), under the WSM6–New Tiedtke scheme as shown in Figure 6d. Similarly, the Yom Basin exhibited light to moderate rainfall amounts (>5 mm to >20 mm) when simulated with the WSM5–New Tiedtke configuration as shown in Figure 6e. Finally, Figure 6f displayed trace to moderate rainfall (>0 mm to >20 mm) in the Nan River Basin when using the combination of the WSM6 microphysics and New Tiedtke cumulus schemes.

Daily average rainfall simulated by the suitable parameterization schemes for the six river basins. (a) Rain 24 h BAUGUST2023_Kessler + New Tiedtke Salween. (b) Rain 24 h 25AUGUST2023 WSM6+ New Tiedtke Upper Mekong. (c) Rain 24 h 11AUGUST2023_WSM5+ New Tiedtke Ping. (d) Rain 24 h 20AUGUST2023 WSM6+ New Tiedtke Wang. (e) Rain 24 h 21AUGUST2023 WSM5+ New Tiedtke Yom. (f) Rain 24 h 8AUGUST2023 WSM6+ New Tiedtke Nan.

Six panels labeled (a) shows Rain 24 h 8AUGUST2023_Kessler + New Tiedtke and (b) to (f) show weather maps with varying precipitation levels. Each map uses a color gradient, ranging from white for low precipitation to purple for high precipitation. Geographical features like borders are visible, indicating regional variations. Forecasting models

The accuracy of the four forecasting approaches was interpreted from the MAE, RMSE, and SMAPE values shown in Figure 4. For this comparison, the simulated daily average rainfall from the optimal WRF model was used as the data for the forecasting models. The results of this study indicate that the ANN model is most suitable for forecasting daily average rainfall in the Salween (MAE = 6.98, RMSE = 10.66, SMAPE = 10.37), Upper Mekong (MAE = 10.34, RMSE = 15.09, SMAPE = 14.19), and Nan (MAE = 12.38, RMSE = 16.30, SMAPE = 16.98) River Basins. In contrast, the DER-ARIMA model performs best for the Wang (MAE = 9.83, RMSE = 15.63, SMAPE = 29.73) and Yom (MAE = 8.74, RMSE = 12.08, SMAPE = 20.64) River Basins, while the DQR-ARIMA is the optimal model for the Ping River Basin (MAE = 8.73, RMSE = 12.04, SMAPE = 10.81), as shown in Table 5.

The accuracy between all approaches in forecasting model for six river basins.

Model Salween Upper Mekong
MAE RMSE SMAPE MAE RMSE SMAPE
ARIMA 7.44 11.17 12.29% 16.07 23.43 22.03%
ANN 6.98 10.66 10.37% 10.34 15.09 14.19%
DER-ARIMA 7.63 11.33 11.61% 16.58 24.61 24.95%
DQR-ARIMA 8.92 12.83 14.35% 21.89 33.84 32.11%
Model Ping Wang
MAE RMSE SMAPE MAE RMSE SMAPE
ARIMA 16.15 14.66 18.02% 13.22 22.33 35.66%
ANN 11.63 7.61 8.30% 11.73 17.84 33.81%
DER-ARIMA 12.71 9.19 11.65% 9.83 15.63 29.73%
DQR-ARIMA 8.73 12.04 10.81% 16.94 26.97 38.50%
Model Yom Nan
MAE RMSE SMAPE MAE RMSE SMAPE
ARIMA 16.78 23.70 40.73% 13.70 21.56 16.30%
ANN 11.87 16.21 26.92% 12.38 16.30 16.98%
DER-ARIMA 8.74 12.08 20.64% 14.57 21.02 16.21%
DQR-ARIMA 16.78 23.70 40.73% 16.53 25.59 24.96%

Tables 6–8 present the forecast results for daily average rainfall on heavy rainfall days in river basins where the DER-ARIMA model was most suitable, such as the Wang River Basin on 20 August (N4_20) and the Yom River Basin on 21 August (N5_21). The methodology was developed in three main steps. First, the coefficients for the initial exponential regression (ER) models were determined (Table 6). Next, the residuals from these ER models were used to fit appropriate ARIMA models, with their coefficients shown in Table 7. Finally, Table 8 details the complete equations for the final DER-ARIMA models, which combine the initial ER and residual ARIMA components.

Coefficient of ER model of the daily average rainfall for river basin on heavy rainfall day.

Series data Estimate Std. Error t–value p–value sig
N4_20
Intercept 2.377 0.454 5.231 0.000 ***
Time −0.142 0.061 −2.305 0.043 *
N5_21
Intercept 2.081 0.575 3.616 0.004 **
Time −0.086 0.078 1.096 0.298 ​

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’

Coefficients of the ARIMA model of the random error from ER model.

Series data ​ Estimate p–value sig
N4_20
ARIMA (1,2,0) ar1 −0.662 0.001 **
N5_21
ARIMA (2,2,0) ar1 −1.030 0.000 ***
ar2 −0.681 0.000 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’

The equation of fitting DER-ARIMA model of the daily average rainfall amount for river basin on heavy rainfall day.

Series data Equation of the DER–ARIMA model
N4_20 y ^ N 4 _ 20 t = e 2.377 − 0.142 y N 4 _ 20 t + 1.338 γ N 4 _ 20 t − 1 + 0.324 γ N 4 _ 20 t − 2 − 0.662 γ N 4 _ 20 t − 3
N5_21 y ^ N 5 _ 21 t = e 2.081 + 0.970 γ N 5 _ 21 t − 1 + 0.379 γ N 5 _ 21 t − 2 + 0.332 γ N 5 _ 21 t − 3 − 1.030 γ N 5 _ 21 t − 4

Similarly, Tables 9–11 present the results for the DQR-ARIMA model, which followed a parallel three-step process. This process began by fitting an initial quadratic regression (QR) model, with its coefficients detailed in Table 9. Subsequently, the residuals from this QR fit were modeled using a suitable ARIMA model, for which the coefficients are presented in Table 10. The final, complete equations for the DQR-ARIMA model are shown in Table 11, which also includes forecasts for important events, for example, in the Ping River Basin on 11 August (N3_11).

Coefficient of QR model of the daily average rainfall amount for river basin on heavy rainfall day.

Series data Estimate Std. Error t–value p–value sig
N3_11
Intercept 13.893 9.899 5.330 0.000 ***
Time −3.977 4.522 2.912 0.013 *
T i m e 2 0.505 0.275 −2.905 0.013 *

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’

Coefficients of the ARIMA model of the random error from QR model.

Series data ​ Estimate p–value sig
N3_11
ARIMA (1,1,0) ar1 −0.652 0.000 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’

The equation of fitting DQR–ARIMA model of the daily average rainfall amount for river basin on heavy rainfall day.

Series data Equation of the DQR–ARIMA model
N3_11 y ^ N 3 _ 11 t = 13.893 − 3.977 t − 0.505 t 2 + 0.348 γ N 3 _ 11 t − 1 + 0.652 γ N 3 _ 11 t − 2
Conclusion

In conclusion, this study established high-resolution rainfall simulations for Northern Thailand for the August period between 2009 and 2023. The research identified optimal WRF model configurations by evaluating 15 different physics parameterization schemes and comparing the results to observed data from rain gauge stations using MAE, RMSE, and SMAPE metrics. The 15 experiments in this study were designed by combining three microphysics schemes (Kessler, WSM5, and WSM6) with five different cumulus parameterization schemes (Kain-Fritsch, Betts–Miller–Janjic, Multi–scale Kain–Fritsch, New Simplified Arakawa–Schubert, and New Tiedtke) in every possible pairing. The results identified suitable schemes for different river basins. The combination of the Kessler microphysics and New Tiedtke cumulus schemes provided the most accurate simulation of daily average rainfall in the Salween River Basin. The WSM5 microphysics and New Tiedtke cumulus schemes provided the most accurate simulation of daily average rainfall in the Ping and Yom River Basins. The WSM6 microphysics and New Tiedtke cumulus schemes provided the most accurate simulation of daily average rainfall in the Upper Mekong, Wang and Nan River Basins. Following the generation of daily average rainfall simulations for each river basin with an optimized WRF model, these outputs served as the input dataset for the development and evaluation of four forecasting models: ARIMA, ANN, DER-ARIMA, and DQR-ARIMA. The ANN model demonstrated the highest accuracy for the Salween, Upper Mekong, and Nan River Basins. In contrast, the DER-ARIMA model was the best performer for the Wang and Yom River Basins, while the DQR-ARIMA model proved optimal for the Ping River Basin. The accuracy of each approach was determined using MAE, RMSE, and SMAPE metrics.

 Data availability statement

Publicly available datasets were analyzed in this study. This data can be found here: https://rda.ucar.edu/datasets/d083002/dataaccess/.

 Author contributions

NS: Conceptualization, Data curation, Formal Analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review and editing. RC: Conceptualization, Data curation, Formal Analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review and editing. TP: Conceptualization, Data curation, Formal Analysis, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing – original draft, Writing – review and editing. OT: Formal Analysis, Supervision, Visualization, Writing – review and editing.

 Acknowledgements

This research was developed at collaboration between Division of Computational Science, Faculty of Science, Prince of Songkla University and Innovative research and Computational Science Lab, College of Arts, Media and Technology, Chiang Mai University.

 Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

 Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

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Edited by: Karumuri Ashok, University of Hyderabad, India

Reviewed by: Raju Pathak, Indian Institutes of Technology (IIT), India

Rosnalini Mansor, Universiti Utara Malaysia, Malaysia

Siba Udgata, University of Hyderabad, India