Best practice to calculate observed heads within a cell

[Groundwater-modeler]

Hi,

After a discussion with a colleague regarding the functionality of the drain boundary condition (BC), I decided to conduct some experiments to understand its behavior better. To my understanding the drain BC is independent of its position within a cell and is influenced only by the drain elevation and the specific cell in which it is applied.

To clarify, the position of the drain is relevant only to the extent that it determines the cell it resides in. The x, y, z coordinates within that cell should not affect the results.

To verify this hypothesis, I placed a drain at various locations within a single cell and applied drain elevations both above and below the drain's z elevation, ensuring that all positions assigned in ModelMuse fell within the same cell's bounds. The results supported my hypothesis. However, I encountered something concerning during my tests.

In these experiments, I placed a drain at the center of my model domain. At the model's outer boundary, I set a constant head at the surface elevation. Additionally, I added an observation point at the center-BC to monitor the resulting head without having to import head results after each test run.

Upon running the model, I was surprised to find that the observed head did not reach the elevation of the drain, despite setting a very high conductance value. Increasing the conductance further yielded the same result. Suspecting an issue with the model, I tried applying a constant head boundary condition (CHD) to force the heads to the defined elevation of -9. The results remained unchanged.

When I imported the heads and checked, the cell head was indeed -9, but the observed head was -7.4. This discrepancy reminded me that the observed head is calculated from adjacent cells (the nearest four cells). While this method is beneficial for accounting for head variations within the cell, it can be misleading in certain situations, such as this one.

I am unsure how the code is intended to function or the best way to handle this scenario. Does anyone have any thoughts or ideas on this matter?

Is it best that head is calculated only based on the cell or with the adjacent cells taken into account? I lean towards the second option but still cant shake the feeling that cases such as this one can get a quite severe misrepresentation.

Best regards

[emorway-usgs]

@Groundwater-modeler, would you mind zipping up the model input and sharing here? I'd like to explore this a bit more.

[Groundwater-modeler]

Hi Eric,

Sure. I'll attach a zipped model in this message. However, I have gained some clarity in the matter and it seems to work as intended and in a desirable manner for the purpose.

What I initially missed was the fact that the observation points placement in the cell had a significant impact on the calculated head. The head is thus influenced by both the cell in which it is present and its adjacent cells.

I find this approach to be desirable (for most applications at least) but not necessarily applicable for all situations. I don't know what you (or others) think. But to me this is reasonable for cases where the observations are situated in cells that are not directly influenced by a boundary condition as there can (and should) be an internal variation of the head within a cell, especially when cells are large.
However, it might be the other way around in situations where a cell is directly influenced by a drain or constant head and the idea is that the entire cell is covered by some draining structure that should lower the heads to a defined elevation. Then you may want the head elevation to be static inside the whole cell.

Perhaps you could enlighten me in how the observation package is intended to work in this matter what you believe is the "right" way to utilize it? So far I am bent towards how it is implemented in the attached model.

PS Move CHD/OBS within the cell to study how it affects the level in the observation.

OBS_Test 2025_05_14.zip

Best regards

[emorway-usgs]

Then you may want the head elevation to be static inside the whole cell.
When you say "static inside the whole cell," I'm interpreting that as you what the calculated head for a cell to be constant over the entire area of a cell, though that head value may change with time (and not necessarily be "static" with respect to time). Keep in mind that only a single head value is calculated for the computational node location within each cell (most commonly the cell center). The focus for MODFLOW is to give users the freedom to leverage that head value any way they like. That is, it's on the user to apply some sort of interpolation with neighboring cell heads if needed, or not.

Another option is to use the unstructured grid discretization packages (DISV, DISU) to add spatial refinement to cells in an area of interest (i.e., around a well) but continue to use coarse discretization elsewhere.