Song Jung-Hun, Her Younggu, Park Youn Shik, Yoon Kwangsik, Kim Hakkwan
Institute of Green Bio Science and Technology, Seoul National University, Pyeongchang 25354, Republic of Korea.
Department of Integrated Major in Global Smart Farm, Seoul National University, Seoul 08826, Republic of Korea.
Heliyon. 2023 Dec 19;10(1):e23603. doi: 10.1016/j.heliyon.2023.e23603. eCollection 2024 Jan 15.
The regression relationship between water discharge rates and nutrient concentrations can provide a quick and straightforward way to estimate nutrient loads. However, recent studies indicated that the relationship might produce large biases in load estimates and, therefore, may not be applicable in certain types of cases. The goal of this study is to explore the theoretical reasons behind the selective applicability of the regression relationship between flow rates and nitrate + nitrite concentrations. For this study, we examined daily flow and nitrate + nitrite concentration observations made at the outlets of 22 watersheds monitored by the Heidelberg Tributary Loading Program (HTLP). The statistical relationship between the flow rates and concentrations was explored using regression equations offered by the LOAD ESTimator (LOADEST). Results demonstrated that the use of the regression equations provided nitrate + nitrite load estimates at acceptable accuracy levels ( and %) in 14 watersheds (64 % of 22 study watersheds). The regression relationships provided highly biased results at eight watersheds (36 %), implying their limited applicability. The heteroscedasticity of the residuals led to the high bias and resulting inaccurate regression, which was commonly found in watersheds where low flow had high nitrate + nitrite concentration variations. Conversely, the regression relationships provided acceptable accuracy for watersheds that had a relatively constant variance of the nitrate + nitrite concentrations. The results indicate that the homoscedasticity of residuals is the key assumption to be satisfied to estimate nitrate + nitrite loads from a statistical regression between flow discharge and nitrate + nitrite concentrations. The transport capacity (capacity-limited) concept implicitly assumed in the regression relationship between flow discharge and nitrate + nitrite concentrations is not always applicable, especially to agricultural areas in which nitrate + nitrite loads are highly variable depending on management practices (supply-limited). The findings suggest that the regression relationship should be carefully applied to areas in which intensive agricultural activities, including crop management and conservation practices, are implemented. Thus, the transport capacity concept is reasonably regarded to contribute to the homoscedasticity of residuals.
流量与养分浓度之间的回归关系可为估算养分负荷提供一种快速且直接的方法。然而，近期研究表明，这种关系在负荷估算中可能会产生较大偏差，因此可能不适用于某些类型的情况。本研究的目的是探究流量与硝酸盐+亚硝酸盐浓度之间回归关系的选择性适用性背后的理论原因。在本研究中，我们考察了由海德堡支流负荷项目（HTLP）监测的22个流域出口处的日流量和硝酸盐+亚硝酸盐浓度观测值。利用负荷估算器（LOAD ESTimator，LOADEST）提供的回归方程探究了流量与浓度之间的统计关系。结果表明，在14个流域（占22个研究流域的64%）中，使用回归方程可在可接受的准确度水平（[具体准确度水平1]和[具体准确度水平2]）下估算硝酸盐+亚硝酸盐负荷。在8个流域（36%）中，回归关系给出了偏差极大的结果，这意味着其适用性有限。残差的异方差性导致了高偏差以及由此产生的不准确回归，这在低流量时硝酸盐+亚硝酸盐浓度变化较大的流域中很常见。相反，对于硝酸盐+亚硝酸盐浓度方差相对恒定的流域，回归关系提供了可接受的准确度。结果表明，残差的同方差性是通过流量与硝酸盐+亚硝酸盐浓度之间的统计回归来估算硝酸盐+亚硝酸盐负荷时需要满足的关键假设。流量与硝酸盐+亚硝酸盐浓度之间的回归关系中隐含假设的输送能力（容量受限）概念并不总是适用，特别是对于硝酸盐+亚硝酸盐负荷因管理措施（供应受限）而高度可变的农业地区。研究结果表明，回归关系应谨慎应用于实施了包括作物管理和保护措施在内的集约农业活动的地区。因此，合理认为输送能力概念有助于残差的同方差性。
