Application of MIDAS Model in Flood Forecasting (Case Study: Bahramjoo Basin, Lorestan Province)

Introduction
In recent decades, the increasing frequency and intensity of flood events have become a major concern in water resources management and environmental planning. Floods are among the most destructive natural hazards, causing substantial economic damage, loss of life, and disruption to ecosystems. The challenge of accurately predicting runoff is particularly significant in mountainous watersheds, where complex terrain, heterogeneous precipitation patterns, and rapid hydrological responses increase uncertainty in modeling processes. Seasonal variability of rainfall further complicates the prediction of runoff, making it essential to adopt advanced modeling techniques capable of capturing these dynamics.
The Bahramjoo watershed in Lorestan Province represents a typical mountainous basin characterized by seasonal precipitation and considerable variability in hydrological behavior. Traditional time series models often face limitations when dealing with such variability, especially when input data are available at different temporal frequencies. In recent years, data-driven approaches have gained increasing attention due to their flexibility and ability to model complex relationships without requiring detailed physical assumptions. Among these, the Mixed Data Sampling (MIDAS) model has emerged as a promising approach for handling mixed-frequency data, although its application in hydrology remains relatively limited compared to fields such as economics.
Objectives
The primary objective of this study is to evaluate and compare the performance of three time series models-MIDAS, Autoregressive Distributed Lag (ARDL), and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) in predicting seasonal runoff in the Bahramjoo watershed. Specifically, the study aims to assess the capability of these models in handling mixed-frequency data, improving prediction accuracy, and preserving the inherent structure of hydrological time series. Another key objective is to investigate whether the MIDAS model can provide a methodological advantage over conventional models by directly incorporating high-frequency precipitation data into seasonal runoff forecasting.
Materials and Methods
The dataset used in this study consists of seasonal streamflow data and monthly precipitation records collected from hydrometric and meteorological stations within the study area over the period 2006 to 2023. A major challenge in the analysis arises from the mismatch in temporal frequency between the dependent variable (seasonal runoff) and the independent variable (monthly precipitation). To address this issue, three modeling approaches were implemented. In the ARDL and GARCH models, monthly precipitation data were aggregated into seasonal values to match the temporal scale of the runoff data. However, this aggregation process may result in the loss of valuable information embedded in high-frequency data. In contrast, the MIDAS model allows for the direct integration of mixed-frequency variables without the need for aggregation, thereby preserving the original temporal resolution of the data. Each model was calibrated using historical data and evaluated based on statistical performance metrics, including the coefficient of determination (R²) and the root mean square error (RMSE). Additionally, cross-validation techniques were employed to ensure the robustness and reliability of the results. These evaluation criteria provide a comprehensive assessment of the models’ ability to capture both the variability and magnitude of runoff.
Results and Discussion
The results indicate that all three models are capable of capturing the general trend of seasonal runoff variations in the study area. However, significant differences are observed in their predictive performance. Among the models, the MIDAS approach demonstrates the highest level of accuracy, with an R² value of 0.82 and an RMSE of 0.61 m³/s. In comparison, the ARDL model achieves an R² of 0.66 and an RMSE of 0.93 m³/s, while the GARCH model yields an R² of 0.52 and an RMSE of 0.71 m³/s. The superior performance of the MIDAS model can be attributed to its ability to incorporate high-frequency precipitation data directly into the modeling framework. By avoiding temporal aggregation, the model preserves important information that would otherwise be lost in conventional approaches. Furthermore, the flexible weighting structure of the MIDAS model allows it to assign different levels of importance to lagged values of precipitation, thereby capturing delayed hydrological responses more effectively. The analysis also reveals that the runoff dynamics in the Bahramjoo watershed exhibit relatively stable behavior with characteristics of long-term memory. Runoff tends to increase during wet seasons and decrease during dry periods, reflecting the strong influence of precipitation patterns. The MIDAS model is particularly effective in capturing these seasonal fluctuations due to its ability to model interactions between variables with different temporal frequencies.
Overall, the findings highlight the limitations of traditional models such as ARDL and GARCH when applied to mixed-frequency hydrological data. While these models remain useful in certain contexts, their reliance on aggregated data reduces their ability to capture fine-scale temporal variations. In contrast, the MIDAS model provides a more comprehensive representation of the underlying processes, leading to improved predictive performance.
Conclusion
This study demonstrates that the MIDAS model offers a significant improvement over conventional time series models in predicting seasonal runoff in mountainous watersheds. Its ability to integrate mixed-frequency data without aggregation allows for better preservation of temporal information and enhances model accuracy. The results suggest that MIDAS is a robust and efficient tool for hydrological forecasting, particularly in cases where input data are available at different temporal scales.From a practical perspective, the application of the MIDAS model can contribute to more accurate flood forecasting, improved water resources management, and more effective mitigation of flood-related risks. The findings of this research provide valuable insights for hydrologists, engineers, and decision-makers seeking to enhance predictive capabilities in complex hydrological systems.Future research may focus on extending the application of the MIDAS framework to other regions and temporal scales, as well as integrating it with advanced techniques such as machine learning models. Such efforts could further improve the accuracy and reliability of hydrological predictions and support sustainable water resources management in the face of increasing climate variability.