I thought I would pass along some information about a useful, relatively new MODFLOW development, the Layer Variable Direction horizontal Anisotropy (LVDA) package. Modeling the effect of anisotropy on flow has interested me for a long time, so I thought I would share some background on where things were when I wrote a paper on the subject in 2003 (previous post), and what LVDA can do now.
MODFLOW's LVDA package is mainly used for implementing generalized anisotropy in a horizontal plane, i.e. as it would change on a map. Speaking with Ken Kipp and Mary Hill circa 2002, I learned that they (and others) were working on this code for the USGS Death Valley Regional Flow project, where they were interested in simulating the effect of jointing that was changing direction spatially.
At the time of my article (2003), I cited the Kladias and Ruskauf (1997) paper “Implementing spatially variable anisotropy in Modflow” in Ground Water 35, and noted that they, “…outline how to incorporate spatially variable (heterogeneous) anisotropy within the plane of the layer in Modflow. Their modification generalizes the column-to-row anisotropy factor into an array, prescribing a unique value for each cell in the model. This approach does not allow for the orientation of the principal axes to change spatially.” I then mentioned, “The U.S. Geological Survey is currently researching ways to incorporate generalized heterogeneous anisotropy within the plane of the layer in MODFLOW, where both the anisotropic factor and orientation of principal axes can change spatially,” a personal communication at the time from Mary Hill (cited) and Ken Kipp. They were referring to the LVDA package in development at the time.
Kipp's and Hill's (and others) work made it to press as a 2002 OFR. It was not available, at least not printed, at the time of my article, but is now incorporated in MODFLOW 2000
with this reference:
Anderman, Evan R.; Kipp, K. L.; Hill, Mary C.; Valstar, Johan; Neupauer, R. M., 2002. Documentation of the Model-Layer Variable-Direction Horizontal Anisotropy (LVDA) capability of the Hydrogeologic-Unit Flow (HUF) package. USGS Open-File-Report 02-409.
Generalized anisotropy within a layer is a very exciting development for MODFLOW, however the next two sentences from my 2003 article still apply: “Cross-sectional models constructed within a single layer would thus be able to handle structural dip. However two or three-dimensional, multiple layered models exploiting the boundary-matching method [still will not] handle structural dip until a correction for generalized heterogeneous anisotropy is implemented in the vertical plane.”
Though the LVDA package is a significant advancement, MODFLOW is still not capable of handling dipping anisotropy in a vertical plane when using multiple layers, thus cannot accurately model the effect of dip unless the model is a 2D-single-layer, LVDA, cross sectional model with the layer “flipped up.” As far as I know, Cliff Voss’ Sutra is the only USGS model that can handle generalized anisotropy in 3D.