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Prediction of the subsurface flow of hillslopes using a subsurface time-area model

  • H. Fariborzi
  • T. SabzevariEmail author
  • S. Noroozpour
  • R. Mohammadpour
Paper
  • 37 Downloads

Abstract

Prediction of subsurface flow (SF) in hillslopes is more complicated than prediction of surface flow; hence, a simple and practical SF model would interest hydrogeologists. For the first time, the time-area method is employed to estimate the SF of hillslopes. The locations of the isochrone curves for complex hillslopes were determined using SF travel-time equations. Some equations were developed to delineate the isochrones and the subsurface time area (STA). The analytic equations suggested by the characteristics method of solving a hillslope-storage kinematic wave were used for validation of the STA method results in complex hillslopes. The average values of the coefficient of efficiency (CE), correlation coefficient (R), error of peak flow (EPF) and root-mean-square error (RMSE) of the STA method for the nine defined hillslopes are, respectively, 0.96, 0.96, 1.35, and 0.076. To further verify the results, a laboratory rainfall simulator with sandy loam soil was employed, which was conditioned under artificial rainfall intensities of 31.7, 4.6 and 63.46 mm/hr, and slopes of 3°, 6° and 9°. The STA model results were compared with those of a laboratory model of subsurface flow. The average values of CE, R, EPF and RMSE of the STA method for the nine events are, respectively, 0.81, 0.85, 0.98, and 0.017, which are regarded as good values. For the final evaluation of the STA model, the subsurface flow rates obtained from the Richards’ equation using HYDRUS were also used. The proposed STA model has good agreement with the results of the laboratory and HYDRUS models.

Keywords

Subsurface time area Isochrone curves Hillslope geomorphology Analytical solutions Laboratory experiments/measurements 

Prévision de l’écoulement souterrain de pentes en utilisant un modèle de zones temporelles de surface souterraine

Résumé

La prévision de l’écoulement souterrain (ES) dans les pentes est plus complexe que la prévision des écoulements de surface; ainsi, un modèle simple et pratique dédié aux ES intéresserait les hydrogéologues. Pour la première fois, la méthode des surfaces temporelles est employée pour estimer l’ES des pentes. Les emplacements des courbes isochrones pour les pentes complexes ont été déterminées à l’aide des équations de temps de transit d’ES. Certaines équations ont été développées pour délimiter le isochrones et les surfaces temporelles souterraines (STS). Les équations analytiques suggérées par la méthode des caractéristiques pour résoudre l’onde cinématique du stockage dans les pentes ont été utilisées pour valider les résultats de la méthode STS dans des pentes complexes. Les valeurs moyennes du coefficient d’efficacité (CE), du coefficient de corrélation (R), de l’erreur au pic de l’écoulement (EPE) et de l’erreur quadratique moyenne (RMSE) de la méthode STS pour les neuf pentes définies sont, respectivement, 0.96, 0.96, 1.35, et 0.076. Pour vérifier davantage les résultats, un simulateur de pluie de laboratoire avec un sol sablonneux limoneux a été utilisé, qui a été conditionne sous des intensités de pluie artificielle de 31.7, 4.6 et 63.46 mm/hr, et pentes de 3°, 6° et 9°. Les résultats du modèle STS ont été comparés à ceux d’un modèle de laboratoire d’écoulement souterrain. Les valeurs moyennes de CE, R, EPE et RMSE de la méthode STS pour les neufs événements sont, respectivement, 0.81, 0.85, 0.98 et 0.017, qui sont considérées comme de bonnes valeurs. Pour l’évaluation finale du modèle STS, les débits d’écoulement souterrain obtenus à partir de l’équation de Richards’ utilisant HYDRUS ont aussi été utilisés. Le modèle STS proposé est en accord avec les résultats des modèles de laboratoire et HYDRUS.

Predicción del flujo subsuperficial en pendientes utilizando un modelo área–tiempo

Resumen

La predicción del flujo subsuperficial (SF) en las laderas es más complicada que la predicción del flujo superficial; por lo tanto, un modelo simple y práctico de SF interesaría a los hidrogeólogos. Por primera vez, el método de área - tiempo se emplea para estimar el SF en una ladera. Las ubicaciones de las curvas isócronas para las laderas complejas se determinaron utilizando las ecuaciones de tiempo de tránsito de SF. Se desarrollaron algunas ecuaciones para delinear las isócronas y el área - tiempo subsuperficial (STA). Las ecuaciones analíticas sugeridas por el método de características para resolver una onda cinemática de almacenamiento en pendiente se utilizaron para validar los resultados del método STA en laderas complejas. Los valores promedio del coeficiente de eficiencia (CE), el coeficiente de correlación (R), el error máximo de flujo (EPF) y el error cuadrático medio (RMSE) del método STA para las nueve pendientes definidas son, respectivamente, 0.96, 0.96, 1.35 y 0.076. Para verificar aún más los resultados, se empleó un simulador de lluvia de laboratorio con suelo franco arenoso, que se acondicionó con intensidades de lluvia artificial de 31.7, 4.6 y 63.46 mm/h, y pendientes de 3°, 6° y 9°. Los resultados del modelo STA se compararon con los de un modelo de laboratorio de flujo subsuperficial. Los valores promedio de CE, R, EPF y RMSE del método STA para los nueve eventos son, respectivamente, 0.81, 0.85, 0.98 y 0.017, que se consideran valores buenos. Para la evaluación final del modelo STA, también se usaron las tasas de flujo subsuperficial obtenidas de la ecuación de Richards’ utilizando HYDRUS. El modelo STA propuesto tiene un buen acuerdo con los resultados del laboratorio y los modelos HYDRUS.

采用地面之下时区模型预测山坡地面之下的水流

摘要

预测山坡地面之下的水流比预测地表水流要复杂;因此,水文地质工作者对简单和实用的地面之下水流模型更感兴趣。第一次采用时区模型估算山坡地面之下的水流。利用地面之下水流行程时间方程式确定了复杂山坡等时线曲线的位置。开发了一些方程式描述等时线和地面之下时间区。利用求解山坡储存动态波浪的特征方法提出的解析方程验证复杂山坡地面之下时间区法结果。九个界定的山坡地面之下时区效率系数、相关系数、峰值水流误差以及均方根误差平均值分别为0.96、0.96、1.35 和 0.076。为进一步核实结果,采用了室内砂质土壤降雨模拟装置,人工降雨强度分别为31.7、4.6 和63.46 mm/hr,坡度分别为3°、6°和9°。地面之下时区模型结果与地面之下水流实验室模型结果进行了对比。地面之下时区方法的九种情景下的效率系数、相关系数、峰值水流误差以及均方根误差平均值分别为0.81、0.85、0.98和0.017,被视为是很好的值。在地面之下时区模型最后的评估中,还采用了根据HYDRUS从Richards’方程式得到的地面之下水流量。提出的地面之下时区模型与实验室结果和HYDRUS模型非常吻合。

Predição do fluxo subsuperficial de encostas usando um modelo de área de tempo subsuperficial

Resumo

A predição do fluxo subsuperficial (FS) em encostas é mais complicada do que a predição do fluxo superficial; portanto, um modelo simples e prático de FS interessaria aos hidrogeólogos. Pela primeira vez, o método da área de tempo é empregado para estimar o SF de encostas. As localizações das curvas isócronas para encostas complexas foram determinadas usando equações de tempo de viagem do FS. Algumas equações foram desenvolvidas para delinear as isócronas e a área de tempo subsuperficial (ATS). As equações analíticas sugeridas pelo método das características de resolução de uma onda cinemática de armazenamento de encosta foram utilizadas para a validação dos resultados do método ATS em encostas complexas. Os valores médios do coeficiente de eficiência (CE), coeficiente de correlação (R), erro de pico de fluxo (EPF) e erro quadrático médio (EQM) do método ATS para os nove taludes definidos são, respectivamente, 0.96, 0.96, 1.35 e 0.076. Para verificar os resultados, empregou-se um simulador de chuva laboratorial com solo franco-arenoso, que foi condicionado sob intensidades artificiais de precipitação de 31.7, 4.6 e 63.46 mm/hr, e declives de 3°, 6° e 9°. Os resultados do modelo ATS foram comparados com os de um modelo de laboratório de fluxo subsuperficial. Os valores médios de CE, R, EPF e EQM do método ATS para os nove eventos são, respectivamente, 0.81, 0.85, 0.98 e 0.017, os quais são considerados bons valores. Para a avaliação final do modelo ATS, também foram utilizadas as vazões subsuperficiais obtidas a partir da equação de Richards’ usando HYDRUS. O modelo de ATS proposto tem boa concordância com os resultados dos modelos de laboratório e HYDRUS.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • H. Fariborzi
    • 1
  • T. Sabzevari
    • 1
    Email author
  • S. Noroozpour
    • 1
  • R. Mohammadpour
    • 1
  1. 1.Department of civil engineering, Estahban BranchIslamic Azad UniversityEstahbanIran

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