Accurate short-term rainfall–runoff prediction is essential for flood mitigation and safety of hydraulic structures and infrastructures. This study investigates the capability of four machine learning methods (MLM), optimal pruning extreme learning machine (OPELM), multivariate adaptive regression spline (MARS), M5 model tree (M5Tree, and hybridized MARS and Kmeans algorithm (MARS-Kmeans), in hourly rainfall–runoff modeling (considering 1-, 6- and 12-h horizons). Their results are compared with a conceptual method, Event-Based Approach for Small and Ungauged Basins (EBA4SUB) and multi-linear regression (MLR). Hourly rainfall and runoff data gathered from Ilme River watershed, Germany, were divided into two equal parts, and MLM were validated considering each part by swapping training and testing datasets. MLM were compared with EBA4SUB using four events and with respect to three statistics, root-mean-square errors (RMSE), mean absolute error (MAE) and Nash–Sutcliffe efficiency (NSE). Comparison results revealed that the newly developed hybridized MARS-Kmeans method performed superior to the OPELM, MARS, M5Tree and MLR methods in prediction of 1-, 6- and 12-h ahead runoff. Comparison with conceptual method showed that all the machine learning models outperformed the EBA4SUB and OPELM provided slightly better performance than the other three alternatives in event-based rainfall–runoff modeling.

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中文翻译：

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降雨-径流建模不同方法的比较：机器学习与概念方法

准确的短期降雨-径流预报对于缓解洪水和水力结构及基础设施的安全至关重要。这项研究调查了以下四种机器学习方法（MLM），最佳修剪极限学习机（OPELM），多元自适应回归样条（MARS），M5模型树（M5Tree）和混合MARS和Kmeans算法（MARS-Kmeans）的功能。每小时降雨-径流模拟（考虑1、6和12小时的地平线），并将其结果与概念方法，基于事件的小型无约束盆地方法（EBA4SUB）和多元线性回归（MLR）进行比较。从德国伊尔梅河流域收集的降雨和径流数据被分为两个相等的部分，并且通过交换训练和测试数据集对传销进行了验证以考虑每个部分。使用四个事件将MLM与EBA4SUB进行了比较，并针对三个统计数据进行了比较（均方根误差（RMSE），平均绝对误差（MAE）和纳什-舒特克里夫效率（NSE））。比较结果表明，新开发的混合MARS-Kmeans方法在预测1、6和12小时提前径流方面表现优于OPELM，MARS，M5Tree和MLR方法。与概念方法的比较表明，在基于事件的降雨－径流建模中，所有机器学习模型都优于EBA4SUB和OPELM，其性能比其他三个替代方法略好。M5Tree和MLR方法可预测1、6和12小时提前径流。与概念方法的比较表明，在基于事件的降雨－径流建模中，所有机器学习模型都优于EBA4SUB和OPELM，其性能比其他三个替代方法要好。M5Tree和MLR方法可预测1、6和12小时提前径流。与概念方法的比较表明，在基于事件的降雨－径流建模中，所有机器学习模型都优于EBA4SUB和OPELM，其性能比其他三个替代方法要好。

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