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jonasthu

Dry cells in steep mountain terrain

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Hi, 

I'm having some difficulties with my current model and would love som help/feedback. I'm currently doing a SS model of a mountain terrain. The model is constructed with 10x10 m cells and 1 layer where the topography is from a 1x1m DEM and the bedrock (bottom of cells) are interpolated from borehole data. The thickness of the cells are around 10 - 25 m, and the model domain is relatively steep. Boundary conditions are a river (river packaged) and specified flux (calculated through water balance). Water flows to the river.

So the problem i'm facing is dry cells. The steep topography and the relatively thin thickness of the aquifer leads to dry cells. However, this is actually not completely wrong as our field measurements show that during some periodes some of our wells are dry. However, MODFLOW don't like this, so I'm having problem constructing my model..

So does anyone have som experience with these kinds of problems, and could spare some time helping me out? Or maybe recommend me som literature/studies?

Thanks!

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Hi, MODFLOW assumes flat continuous aquifer. You could probably overcome the drying/wetting problem by using Newton linearization implemented in MODFLOW-NWT. However, if there are large not negligible differences in elevation between two horizontaly adjacent cells MODFLOW results will be incorrect. Fortunately the finite volume formulation in MODFLOW-USG adressed this issue - it involves true interface area into the calculation. If I remember it right, this is supplied for each cell connection in the DISU file somewhere. If you use GMS, this should be done automaticaly for you. You could use the upstream weighting (LPF package) and newton linearization (SMS package) for a more robust solution. With this setup the model should converge to a correct solution.

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Thanks for the replay. I'm using GMS, however I'm not familiar with MODFLOW-USG. Is it alot different from regular MODFLOW? How difficult would you say it is to learn (maybe hard to answere?)?

Also, would you care to explain why cells become dry when the layers are steep? Is it because of a high hydraulic gradient between cells?

I would love to see some studies and or litterature addressing this issue, if you have some.

Thanks!

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I would say that MF-USG is very different in terms of how the solution to the flow equation is aproached compared to the traditional structured modflow. However it is usually not too difficult to set up a MF-USG simulation in GMS. There are some tutorials out there that could help. I would recommend reading the MF-USG manual as well to grasp the internal differences.

Regarding your second question. I believe there are other people here that could provide more accurate answer. The problem comes from the way MODFLOW solves the groundwater flow equation, that is by numerical approximation. During these approximations (in MF-2005) if head in a cell falls bellow the cell bottom the cell is assumed dry and is inactivated (becomes no-flow cell). However in subsequent approximation the cell could become wet and active again if certain criteria are met. For instace if head in the cell below (i,j,k-1) is 0.1 m above the cell (ijk) bottom. The 0.1 m would be the user specified threshold for conversion from dry to wet. This whole process brings instability into the solution and may cause convergence problems especialy if poor initial head values and low threshold values are specified.

However MF-NWT adressed this issue in a brilliant way. It does not deactivate dry cells, but instead it uses upstream weighting approach to limit flow from dry cell to a neighboring partialy saturated cell. It also uses additional smoothing for conductance and storage functions which allows the use of newton numerical method for outer iterations. It therefore provides a continuous solution for all unconfined groundwater flow conditions and is very robust.

However if you have steep aquifer your problem is different. Consider two neighboring cells of 10 m thickness. Lets say, under extremely steep conditions they share only 1 m thickness. However structured modflow will assume 10 m anyway and would not modify transmissivity accordingly. Such a solution would be incorrect. That is why I recommend using MF-USG in your case as mentioned earlier in my previous post.

For literature I suggest reading the manuals published by USGS for modflow 2000, 2005, NWT and USG. There are plenty of further references there too.

 

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