Abstract Prediction of rivers and lakes water temperature plays an important role in hydrology, ecology, and water resources planning and management. Recently, machines learning approaches have been widely used for modelling water temperature, and the obtained results vary depending on the kind of models and the selections of the appropriates predictors. In the present paper, a new family of machines learning are proposed and compared to the famous air2stream model, using a large data set collected at 25 lakes in the northern part of Poland. The proposed models were: (i) the extremely randomized trees (ERT), (ii) the multivariate adaptive regression splines (MARS), (iii) the M5 Model tree (M5Tree), (iv) the random forest (RF), and (v) the multilayer perceptron neural network (MLPNN). The models were developed using the air temperature as input variables and the component of the Gregorian calendar (year, month and day) number. Results obtained were evaluated using several statistical indices: the root mean square error (RMSE), the mean absolute error (MAE), correlation coefficient (R) and Nash-Sutcliffe efficiency coefficient (NSE). Obtained results reveals that the air2stream model outperformed all other machines learning models and worked best with high accuracy at all the 25 lakes, and none of the ERT, MARS, M5Tree, RF and MLPNN models was able to provides an improvement of the water temperature prediction compared to the air2stream.

中文翻译：

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从气温模拟每日湖面水温：极端随机树 (ERT) 与 Air2Water、MARS、M5Tree、RF 和 MLPNN

摘要 江河湖泊水温预测在水文、生态、水资源规划与管理中具有重要作用。最近，机器学习方法已广泛用于水温建模，所获得的结果因模型类型和适当预测变量的选择而异。在本文中，使用在波兰北部 25 个湖泊收集的大型数据集，提出了一个新的机器学习系列，并与著名的 air2stream 模型进行了比较。提出的模型是：(i) 极度随机化树 (ERT)，(ii) 多元自适应回归样条 (MARS)，(iii) M5 模型树 (M5Tree)，(iv) 随机森林 (RF)，以及(v) 多层感知器神经网络 (MLPNN)。这些模型是使用气温作为输入变量和公历（年、月和日）数字的组成部分开发的。使用几个统计指标评估获得的结果：均方根误差 (RMSE)、平均绝对误差 (MAE)、相关系数 (R) 和 Nash-Sutcliffe 效率系数 (NSE)。获得的结果表明，air2stream 模型优于所有其他机器学习模型，并且在所有 25 个湖泊中都以高精度运行最佳，并且 ERT、MARS、M5Tree、RF 和 MLPNN 模型都无法提供水温预测的改进与 air2stream 相比。平均绝对误差 (MAE)、相关系数 (R) 和 Nash-Sutcliffe 效率系数 (NSE)。获得的结果表明，air2stream 模型优于所有其他机器学习模型，并且在所有 25 个湖泊中都以高精度运行最佳，并且 ERT、MARS、M5Tree、RF 和 MLPNN 模型都无法提供水温预测的改进与 air2stream 相比。平均绝对误差 (MAE)、相关系数 (R) 和 Nash-Sutcliffe 效率系数 (NSE)。获得的结果表明，air2stream 模型优于所有其他机器学习模型，并且在所有 25 个湖泊中都以高精度运行最佳，并且 ERT、MARS、M5Tree、RF 和 MLPNN 模型都无法提供水温预测的改进与 air2stream 相比。