The Eckhardt’s filter, a recursive digital filter widely used in hydrology to separate baseflow, relies on two parameters: the recession constant (a) and the maximum allowable long-term ratio of baseflow to streamflow (BFImax). While a can be determined through regression analyses, BFImax is often assigned an arbitrary value because of limited catchment information for a more objective determination. This study aimed to assess and calibrate BFImax for a 1.2 km2 rural catchment in southern Brazil using dissolved silica data. Calibration involved minimizing differences between filter-generated baseflow hydrographs and those derived from dissolved silica measurements and mass balance across 13 monitored rainfall-runoff events. The calibrated model was compared to three established models: a modified graphical method based on local minima, a backward filter model, and a one-parameter filter. The results yielded an optimal BFImax of 0.653 with high model performance (PBias ≈ 0, NSE = 0.85, KGE = 0.74, and NRMSD = 13 %) against silica-derived baseflow. Applying the calibrated filter to a six-year streamflow dataset yielded a long-term baseflow index (BFI) value of 54 %, aligned with regional and global averages. Comparisons with other models showed that the backward filter model produced unrealistic baseflow values nearly identical to streamflow values; the local minima method overestimated baseflow by +19 % and failed to accurately represent the smoothness and peaks of the baseflow hydrographs; and the one-parameter filter represented the shape and timing of the baseflow hydrographs well, but underestimated magnitude by −19 %. These findings validate the effectiveness of the Eckhardt’s filter in generating accurate baseflow hydrographs and confirm the importance of calibrating BFImax for optimal performance. The research also endorses the use of dissolved silica measurements and the mass balance method as a reliable approach for calibrating BFImax for long-term assessment of baseflows.

中文翻译：

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校准埃克哈特过滤器与替代基流分离方法的对比：巴西流域中基于二氧化硅的方法


Eckhardt 滤波器是水文学中广泛用于分离基流的递归数字滤波器，它依赖于两个参数：衰退常数 (a) 和基流与径流的最大允许长期比率 (BFImax)。虽然 a 可以通过回归分析确定，但由于流域信息有限，无法更客观地确定，BFImax 通常被指定为任意值。本研究旨在使用溶解二氧化硅数据评估和校准巴西南部 1.2 平方公里农村流域的 BFImax。校准涉及最大限度地减少过滤器生成的基流过程线与来自溶解二氧化硅测量值和 13 个监测降雨径流事件的质量平衡之间的差异。将校准模型与三个已建立的模型进行比较：基于局部最小值的修改图形方法、后向滤波器模型和单参数滤波器。结果得出最佳 BFImax 为 0.653，与二氧化硅基流相比具有较高的模型性能（PBias ≈ 0、NSE = 0.85、KGE = 0.74 和 NRMSD = 13 %）。将校准过滤器应用于六年的水流数据集产生了 54% 的长期基流指数 (BFI) 值，与区域和全球平均水平一致。与其他模型的比较表明，后向过滤模型产生的基流值与水流值几乎相同，不切实际；局部极小值方法高估了基流 +19%，并且无法准确表示基流过程线的平滑度和峰值；单参数滤波器很好地代表了基流过程线的形状和时间，但低估了幅度 -19%。 这些发现验证了 Eckhardt 过滤器在生成准确的基流过程线方面的有效性，并证实了校准 BFImax 以获得最佳性能的重要性。该研究还认可使用溶解二氧化硅测量和质量平衡方法作为校准 BFImax 以进行基流长期评估的可靠方法。