Abstract
Variable-density groundwater models require extensive computational resources, particularly for simulations representing short-term hydrologic variability such as tidal fluctuations. Saltwater-intrusion models usually neglect tidal fluctuations and this may introduce errors in simulated concentrations. The effects of tides on simulated concentrations in a coastal aquifer were assessed. Three analyses are reported: in the first, simulations with and without tides were compared for three different dispersivity values. Tides do not significantly affect the transfer of a hypothetical contaminant into the ocean; however, the concentration difference between tidal and non-tidal simulations could be as much as 15%. In the second analysis, the dispersivity value for the model without tides was increased in a zone near the ocean boundary. By slightly increasing dispersivity in this zone, the maximum concentration difference between the simulations with and without tides was reduced to as low as 7%. In the last analysis, an apparent dispersivity value was calculated for each model cell using the simulated velocity variations from the model with tides. Use of apparent dispersivity values in models with a constant ocean boundary seems to provide a reasonable approach for approximating tidal effects in simulations where explicit representation of tidal fluctuations is not feasible.
Résumé
Les modèles de nappe à maille variable requièrent des moyens de calcul importants, en particulier pour les simulations représentant une variabilité hydrologique de court terme, telles que les fluctuations de la marée. Les modèles d’intrusion d’eau salée négligent habituellement les fluctuations de la marée et ceci peut introduire des erreurs dans les concentrations simulées. Les effets des marées sur les concentrations simulées dans un aquifère côtier ont été évalués. Trois analyses sont présentées : dans la première, des simulations avec et sans marées ont été comparées pour trois valeurs différentes de la dispersivité. Les marées n’affectent pas significativement le transfert d’un contaminant supposé vers l’océan ; cependant, la différence de concentration entre les simulations avec et sans marées pourrait atteindre 15 %. Dans la seconde analyse, la valeur de la dispersivité pour le modèle sans marées a été augmentée dans une zone limitrophe de l’océan. En accroissant légèrement la dispersivité dans cette zone, la différence de concentration maximale entre les simulations avec et sans marées a été réduite jusqu’à 7 %. Dans la dernière analyse, une valeur de dispersivité apparente a été calculée pour chaque maille du modèle, en utilisant les variations simulées de la vitesse du modèle avec marées. L’utilisation des valeurs de dispersivité apparente dans les modèles à limite océanique fixe semble fournir une approche acceptable pour évaluer les effets de la marée dans les simulations où une représentation formelle de ses fluctuations n’est pas possible.
Resumen
Los modelos de aguas subterráneas de densidad variable requieren amplios recursos computacionales, particularmente para simulaciones que representan variabilidad hidrológica en cortos tiempos tales como las fluctuaciones de las mareas. Los modelos de intrusión de agua salada usualmente desprecian las fluctuaciones de las mareas y estas pueden introducir errores en las concentraciones simuladas. Se evaluaron los efectos de las mareas sobre concentraciones simuladas en acuíferos costeros. Se han reportado tres análisis: en el primero, se compararon las simulaciones con y sin mareas para tres valores de dispersividad diferentes. Las mareas no afectan significativamente la transferencia del contaminante hipotético hacia el océano; sin embargo, la diferencia de concentración entre las simulaciones con y sin mareas podrían ser de hasta 15%. En el segundo análisis, el valor de dispersividad para el modelo sin mareas fue incrementado en una zona cercana al límite del océano. Mediante un leve incremento de la dispersividad en esta zona, la diferencia máxima entre la simulación con y sin mareas se redujo hasta un 7%. En el último análisis, se calculó un valor de aparente dispersividad para cada celda del modelo usando las variaciones simuladas de velocidad a partir de un modelo con mareas. El uso de valores de aparente dispersividad en modelos con un límite océanico constante parece proveer un enfoque razonable para aproximar los efectos de las mareas en las simulaciones donde la representación explícita de los fluctuaciones de la marea no es factible.
Riassunto
I modelli di flusso idrico sotterraneo densità-dipendente richiedono solitamente importanti risorse computazionali, specie per quelle simulazioni che includono variazioni di breve periodo delle condizioni al contorno, come le fluttuazioni di marea. Generalmente i modelli di intrusione salina trascurano le oscillazioni mareali e questo può portare ad errori nelle concentrazioni simulate, sia per l’intrusione salina sia per il trasporto di inquinanti. In questo articolo vengono valutati gli effetti della marea sulle concentrazioni simulate in un acquifero costiero attraverso tre analisi. Nella prima, vengono paragonate simulazioni con e senza marea per tre differenti valori di dispersività: la marea non influenza significativamente, in termini di massa, il flusso di un ipotetico contaminante che arriva al mare ma le differenze tra le distribuzioni di contaminazione simulate con e senza marea arrivano ad essere maggiori del 15%. Nella seconda analisi, il valore di dispersività nelle simulazioni senza marea è stato incrementato in una zona in prossimità della costa: aumentando leggermente il valore della dispersività in questa zona, la massima differenza di concentrazione tra le simulazioni con e senza la marea si riduce fino al 7%. Nell’ultima analisi infine, è stato calcolato un valore di dispersività apparente per ogni cella del modello utilizzando le variazioni di velocità simulate nel modello con la marea. Attraverso l’utilizzo dei valori di dispersività apparente, in un modello con una condizione di carico costante sul mare, si è giunti alla conclusione che sia possibile raggiungere una ragionevole approssimazione degli effetti di marea, in simulazioni in cui la rappresentazione esplicita delle oscillazioni di carico non è fattibile con tempi di calcolo accettabili.
Resumo
Modelos de águas subterrâneas com densidade variável exigem vastos recursos computacionais, principalmente para as simulações que representam variabilidade hidrológica de curto prazo, como flutuações de maré. Modelos de intrusão salina negligenciam normalmente as flutuações das marés, e isso podem introduzir erros nas concentrações simuladas. Os efeitos de maré sobre as concentrações simuladas num aquífero costeiro foram avaliados. São relatadas três análises: na primeira, as simulações com e sem marés foram comparadas para três valores diferentes de dispersividade. As marés não afectam significativamente a transferência de um contaminante hipotético para o oceano; no entanto, a diferença de concentração entre as simulações, considerando ou não considerando, as marés, pode atingir 15%. Numa segunda análise, o valor da dispersividade para o modelo sem marés foi aumentado, numa zona perto da fronteira com o oceano. Aumentando ligeiramente a dispersividade nesta zona, a diferença de concentração máxima entre as simulações, com e sem marés, foi reduzida para o valor mínimo de 7%. Na última análise, um valor de dispersividade aparente foi calculado para cada célula do modelo, usando as variações de velocidade simulada do modelo com as marés. A utilização de valores de dispersividade aparente nos modelos com uma fronteira constante em relação ao oceano parecem fornecer uma abordagem razoável para aproximar os efeitos das marés nas simulações em que a representação explícita das flutuações de maré não é viável.
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Acknowledgements
The authors are grateful to Politecnico di Milano (DIIAR.), Italy, for supporting collaboration with the US Geological Survey. The authors also thank colleagues at the US Geological Survey for thoughtful reviews of an earlier manuscript. Support for Christian Langevin was provided by US Geological Survey through the Groundwater Resources Program.
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Appendix: Longitudinal and transverse apparent dispersivity calculation
Appendix: Longitudinal and transverse apparent dispersivity calculation
Mass transport of non-reactive chemicals in transient flow fields has been studied previously. Ackerer and Kinzelbach (1986) define the apparent longitudinal and transverse dispersivity (α La and α Ta respectively) resulting from fluctuations in groundwater flow direction as:
where α L and α T are the true longitudinal and transverse dispersivities [L] respectively, V is the groundwater velocity [LT–1], and V L and V T [LT–1] are its components in the mean flow and transverse directions, respectively, with overbars indicating time averages. In this study, velocities of one tidal cycle simulation along the x and z directions were taken from each cell of the domain in the tide model.
The following calculations were applied to each cell to calculate apparent longitudinal and transverse dispersivity values that characterize the velocity variation in that cell during one tidal cycle (n stress periods). Subscript i in the calculations refers to stress periods (1, … n).
From the extracted \( V{x_i} \) and \( V{z_i} \) [LT–1] velocities, the mean flow velocity V [LT–1] was calculated for the whole tidal cycle:
where
is the velocity [LT–1] for the ith stress period.
Then for each stress period, the flow direction \( {\vartheta_i} \) [°] (i.e. the angle relative to the horizontal) was determined:
and the mean flow direction \( \vartheta \) [°] was calculated as:
The component of velocity in the mean flow direction (V Li) and the component of velocity transverse to the mean flow direction (V Ti) were calculated for each stress period:
where
and represents the deviation of the ith velocity from the mean flow direction [°].
Apparent longitudinal and transverse dispersivity values, α La and α Ta [L], were finally calculated from Eq. 1, where:
and
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La Licata, I., Langevin, C.D., Dausman, A.M. et al. Effect of tidal fluctuations on transient dispersion of simulated contaminant concentrations in coastal aquifers. Hydrogeol J 19, 1313–1322 (2011). https://doi.org/10.1007/s10040-011-0763-9
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DOI: https://doi.org/10.1007/s10040-011-0763-9