Stream Distance-Based Geographically Weighted Regression for Exploring Watershed Characteristics and Water Quality Relationships

Abstract

We developed a novel spatial stream network geographically weighted regression (SSN-GWR) by incorporating stream-distance metrics into GWR. The model was tested for predicting seasonal total nitrogen (TN) and total suspended solids (TSS) concentrations in relation to watershed characteristics for 108 sites in the Han River Basin, South Korea. The SSN-GWR model was run with the average seasonal water quality parameters from 2012 through 2016 and was validated with the data from 2017 through 2021. The model fit among ordinary least square regression, standard GWR (STD-GWR), and stream distance weighted SSN-GWR were compared based on their ability to explain the variation of seasonal water quality parameters. We also compared residual spatial autocorrelations as well as various error parameters from these models. Compared to the STD-GWR model, the SSN-GWR model generally provided better model fit, reduced residual spatial autocorrelation, and lessened overall modeling errors. Results show that the spatial patterns of model fit, as well as various coefficients from the upstream distance weighted regressions, capture local patterns as a product of upstream–downstream relations. We demonstrate that a successful model could be developed by integrating stream distance into the GWR, which not only improves model fit but also reveals realistic hydrological processes that relate watershed characteristics to water quality along with the stream network. The local variations in model fit derived from this work can be used to devise fine-scale interventions for water quality improvements in a spatially heterogeneous complex river basin.

通过在地理加权回归（GWR）中考虑河流距离, 我们开发了一种新的河流空间网络地理加权回归（SSN-GWR）方法。通过预测韩国汉江流域108个点位的代表流域特征的季节性氮总量（TN）和总悬浮固体（TSS）浓度, 本文对模型进行了测试。利用2012至2016年平均季节水质参数和2017至2021年数据, 进行了SSN-GWR模型的验证。以季节水质参数变化的解释能力为衡量标准, 本文对比了普通最小二乘回归、标准GWR（STD-GWR）和河流距离加权SSN-GW的模型拟合度。我们还比较了这些模型的剩余空间自相关以及各种误差参数。与STD-GWR模型相比, SSN-GWR模型普遍能提供更优模型拟合、更少剩余空间自相关、更小总体建模误差。结果表明, 模型拟合的空间模式和上游距离加权回归的各个参数, 能捕获上下游关系的局部模式。我们证明, 结合河流距离与GWR, 能够开发出成功的模型。这不仅可以提高模型的拟合度, 还可以揭示现实的水文过程, 并将流域特征与水质和河网关联起来。模型拟合的局部变化, 可用于设计精细的干预措施, 改善空间异质的复杂流域的水质。

Desarrollamos una nueva regresión geográficamente ponderada de la red espacial de corrientes (SSN-GWR), incorporando métricas de la distancia de las corrientes en la GWR. El modelo se probó para predecir las concentraciones estacionales de nitrógeno total (TN) y de sólidos totales en suspensión (TSS) en relación con las características de la cuenca para 108 sitios en la Cuenca del Río Han, Corea del Sur. El modelo SSN-GWR se ejecutó con los parámetros de calidad del agua en promedio estacional de 2012 a 2016 y se validó con los datos de 2017 a 2021. El ajuste del modelo entre la regresión mínima cuadrática ordinaria, la GWR estándar (STD-GWR) y la SSN-GWR ponderada para la distancia de la corriente fueron comparados a partir de su capacidad de explicar la variación de los parámetros estacionales de la calidad del agua. También comparamos las autocorrelaciones espaciales residuales, lo mismo que varios parámetros de error de estos modelos. Comparado con el modelo STD-GWR, el modelo SSN-GWR rindió, en general, un mejor ajuste del modelo, una autocorrelación espacial residual reducida y disminuyó los errores del modelado, en general. Los resultados muestran que los patrones espaciales de ajuste del modelo, lo mismo que varios coeficientes de las regresiones ponderadas por distancia aguas arriba, capturan los patrones locales como un producto de las relaciones de la parte alta de la corriente con la baja. Demostramos que podría desarrollarse un modelo exitoso integrando la distancia de la corriente en la GWR, que no solo mejore el ajuste del modelo, sino que revele también los procesos hidrológicos realistas que relacionen las características de la cuenca con la calidad del agua junto con la red de corrientes. Las variaciones locales en el ajuste del modelo derivadas de este trabajo pueden usarse para diseñar intervenciones a escala fina para mejorar la calidad del agua en una cuenca fluvial compleja, espacialmente heterogénea.

Key Words:

• hydrological processes
• scale
• spatial network
• stream distance
• water quality

关键词:

• 水文过程
• 尺度
• 空间网络
• 河流距离
• 水质。

Palabras clave:

• calidad del agua
• distancia entre corrientes
• escala
• procesos hidrológicos
• red espacial

Acknowledgments

We thank four anonymous reviewers whose comments helped clarify many points of the article. We thank Dr. Jennifer Morse, Dr. Daniel Taylor Rodriguez, and Dr. Jeremy Spoon for their inputs to the previous version of this article. We also owe gratitude to Dr. Jay M. ver Hoef; a brief discussion with him led to materializing of the idea of this article.

Supplemental Material

Supplemental data for this article can be accessed on the publisher’s site at: 10.1080/24694452.2022.2107478. The supplemental materials contain additional statistics related to models, the map of the coefficients, and R codes use to run the standard and stream distance weighted regression.

Additional information

Funding

This material is based on work supported by the U.S. National Science Foundation NSF-GSS Grant #1560907. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Notes on contributors

Janardan Mainali

JANARDAN MAINALI is a Teacher-Scholar Fellow at the Institute for Water and Environmental Resilience, Stetson University, Deland, FL 32723. E-mail: [email protected]. His primary research interest is spatial statistical applications in environmental problems. He has broad experience in vegetation ecology, watershed hydrology, water quality, climate vulnerability mapping, and environmental resilience studies.

Heejun Chang

HEEJUN CHANG is a Professor of Geography and Interim Associate Dean for Research and Graduate Programs in the College of Liberal Arts and Sciences, Portland State University, Portland, OR 97201. E-mail: [email protected]. His research interests focus on geographical hydrology and spatial analysis including climate change and urban development impacts on runoff, water quality, floods, and water-related ecosystem services.

Rabindra Parajuli

RABINDRA PARAJULI is a PhD Candidate in the Department of Geosciences, Florida Atlantic University, Boca Raton, FL 33431. E-mail: [email protected]. His research interests focus on ecological biogeography, including forest ecosystem management, geospatial and ecological modeling applications, and biodiversity and climate change.