Abstract
This study evaluates the applicability of the chloride mass balance (CMB) method for groundwater recharge estimation in a semi-arid region in Canada, where recharge largely occurs under topographic depressions. The CMB applicability was tested at three scales: point-scale recharge rates at different topographical positions; average recharge rates incorporating multiple topographical positions on a local scale; and an identification of spatial trends of recharge on a regional scale. Agricultural chloride inputs were shown to be a major factor affecting chloride concentrations at all three scales, where elevated chloride concentrations in the shallow subsurface affected by agricultural inputs surpassed background concentrations by an order of magnitude. The propagation depth of elevated concentrations varied among study sites from being largely confined to the unsaturated zone to extending well into the saturated zone. Lateral chloride redistribution further affected the CMB applicability for point-scale recharge rates. Specific solutions enabling the CMB application in these conditions are presented, including runoff concentration measurements for point-scale estimates, using groundwater age tracers on a local scale, and using the harmonic mean concentration of a large number of samples on a regional scale.
Résumé
Cette étude évalue l’applicabilité de la méthode du bilan massique en chlorures (BMC) pour l’estimation de la recharge des eaux souterraines dans une région semi-aride du Canada, où la recharge se produit en grande partie dans des dépressions topographiques. L’applicabilité du BMC a été testée à trois échelles: taux de recharge ponctuel à différents niveaux topographiques; taux de recharge moyens incorporant plusieurs niveaux topographiques à une échelle locale; et identification des tendances spatiales de recharge à l’échelle régionale. Les apports en chlorures agricoles se sont révélés être un facteur majeur affectant les concentrations en chlorures aux trois échelles, en effet les concentrations élevées en chlorures dans le sous-sol peu profond, touché par les intrants agricoles, dépassent les concentrations naturelles d’un ordre de grandeur. La profondeur de propagation des concentrations élevées varie d’un site d’étude à l’autre, de la zone non saturée à la zone saturée. La redistribution latérale des chlorures a une incidence supplémentaire sur l’applicabilité du BMC aux taux de recharge à l’échelle ponctuelle. Des solutions spécifiques permettant l’application du BMC dans ces conditions sont présentées et comprennent des mesures de concentrations du ruissellement pour des estimations à l’échelle ponctuelle, l’utilisation des traceurs de datation des eaux souterraines à l’échelle locale, et l’utilisation de la moyenne harmonique des concentrations d’un grand nombre d’échantillons à l’échelle régionale.
Resumen
Este estudio evalúa la aplicabilidad del método de balance de masa de cloruros (CMB) para la estimación de la recarga de aguas subterráneas en una región semiárida de Canadá, donde la recarga ocurre principalmente en depresiones topográficas. La aplicabilidad del CMB se probó a tres escalas: tasa de recarga a escala del sitio en diferentes posiciones topográficas; tasa de recarga promedio que incorporan múltiples posiciones topográficas a escala local; y una identificación de las tendencias espaciales de recarga a escala regional. Las entradas de cloruro de origen agrícola demostraron ser un factor importante que afecta las concentraciones de cloruro en las tres escalas, donde las concentraciones elevadas de cloruro en el subsuelo poco profundo afectado por las entradas debido a la agricultura superaron las concentraciones de fondo en un orden de magnitud. La profundidad de la propagación de las concentraciones elevadas varió entre los sitios de estudio, desde estar confinada en gran medida a la zona no saturada hasta extenderse hasta bien adentro de la zona saturada. La redistribución lateral de cloruro afectó aún más la aplicabilidad del CMB para las tasas de recarga a escala del sitio. Se presentan soluciones específicas que permiten la aplicación del CMB en estas condiciones, incluyendo mediciones de la concentración de escorrentía para estimaciones a escala del sitio, utilizando trazadores de la edad de aguas subterráneas a escala local, y utilizando la concentración media armónica de un gran número de muestras a escala regional.
摘要
本研究评估了氯质量平衡(CMB)方法应用于加拿大半干旱地区地下水补给量估算的适用性,其中地下水补给主要在地面洼地。在三个尺度上进行了CMB方法的适用性测试,包括:不同地形的点尺度补给率;局部地段考虑多个地形的平均补给率;区域尺度补给量空间变化趋势识别。研究表明农业氯来源是影响三个尺度氯化物浓度的主要因素,其中受农业氯来源影响的浅层地下水氯化物浓度增加值超过了背景浓度的一个数量级。高浓度氯的扩散深度随地点不同发生变化,主要在不饱和区,并且很好地扩散到饱和区。侧向氯质量的再分配进一步影响了CMB在点尺度进行地下水补给率估算的适用性。论文提出了在三种尺度下CMB方法应用的具体解决方案,包括点尺度估算时径流浓度测量,局部尺度时采用地下水年龄示踪剂,以及区域尺度上使用大量样本的调和平均浓度。
Resumo
Este estudo avalia a aplicabilidade do método do balanço de massa de cloreto (BMC) para estimativa de recarga de águas subterrâneas em uma região semiárida do Canadá, onde a recarga ocorre em grande parte em depressões topográficas. A aplicabilidade do BMC foi testada em três escalas: taxas de recarga em escala pontual em diferentes posições topográficas; taxas médias de recarga incorporando múltiplas posições topográficas em escala local; e uma identificação das tendências espaciais de recarga em escala regional. A contribuição das atividades agrícola mostrou-se o fator mais importante que afeta as concentrações de cloreto em todas as três escalas, onde concentrações elevadas do íon na parte rasa da subsuperfície superaram as concentrações de fundo em uma ordem de magnitude. A profundidade de propagação de concentrações elevadas variou entre os locais de estudo, sendo confinada em grande parte à zona não saturada, estendendo-se até a zona saturada. A redistribuição lateral de cloreto afetou ainda mais a aplicabilidade do BMC para taxas de recarga em escala pontual. Soluções específicas que possibilitam a aplicação do BMC nestas condições são apresentadas, incluindo medidas de concentração de escoamento para estimativas de escala de pontos, usando traçadores de idade das águas subterrâneas em escala local e usando a média harmônica da concentração de um grande número de amostras em escala regional.
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Acknowledgements
The authors thank the Christensen and Stauffer families for allowing the installation of research equipment and sample collection on their lands; Brandon Hill, Jesse He, Laura Morgan and other members of the Groundwater Recharge in the Prairies (GRIP) project for assistance with fieldwork; Larry Bentley for helpful discussion; Farzin Malekani for assistance in sample analysis; Alberta Innovates, Alberta Agriculture and Forestry, Alberta Environment and Parks, and Alberta Energy Regulator - Alberta Geological Survey for supporting the GRIP project; and NSERC CREATE for Water Security and the Canadian Geophysical Union for providing scholarships to the lead author. Constructive suggestions by the editor and reviewers improved the clarity of the paper.
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Appendix
Appendix
The following describes the derivation of Eqs. (6) from (5). First, a new variable yn is defined as:
Using the Reynolds decomposition, An and yn are expressed in terms of their means and perturbations:
The summation in the right hand side of Eq. (5) can now be written as:
where \( {\sum}_{n=1}^N{A}_n^{\prime}\cdotp \overline{y} \) vanishes according to the definition of perturbation (i.e. deviation from the mean). The last term in Eq. (9) also vanishes when there is no correlation between An and yn (and cn). Noting that \( \overline{A}={A}_{\mathrm{tot}}/N \),
Therefore, Eq. (5) can be approximated as:
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Pavlovskii, I., Hayashi, M. & Cey, E.E. Estimation of depression-focussed groundwater recharge using chloride mass balance: problems and solutions across scales. Hydrogeol J 27, 2263–2278 (2019). https://doi.org/10.1007/s10040-019-01993-2
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DOI: https://doi.org/10.1007/s10040-019-01993-2