Preferential Flow Mapping Tool (PF Map)

Preferential Flow Mapping Tool (PF Map)

Taber Midgley

My main thesis research objective is to observe the effects of subsurface flow on seepage erosion on an actual streambank using a unique trench injection system. Basically, a trench was dug into the soil profile approximately 4 meters from the streambank. The trench was installed 2.8 m from the nearest point on the bank with a length of 2.4 m, a width of 0.6 m, and depth of 2 m. A tensiometer network was installed between the trench and the bank (figure 1). This network contains tensiometers in rows and columns at various depths and records data every 10 minutes. It was hypothesized from observations of the tensiometer readings that much of the water was moving from the trench towards the bank at an[OT1] the angle indicated in figure 1. The water movement was trended downward (by observation). The use of tensiometers is common in soil-water research and I would like to create a tool in MATLAB which can easily map the general direction of water movement based on the data collected by the tensiometer network.

Figure 1: Location of tensiometers relative to trench (black box) and bank edge location (green line). Tensiometers beyond bank edge 10 cm pen tensiometers installed horizontally into the side of the bank.

The location of each tensiometer would need to be entered into the tool using 3 dimensional Cartesian coordinates using a standard reference location (to set as 0,0,0). For example in my situation I would use the corner of the trench marked by a red circle in figure 1. The matric potential data for the tensiometers would then be entered. [OT2]Using this data, the program would calculate a hydraulic head for each tensiometer based on the matric potential and elevation relative to the reference point. Flow direction and magnitude from each tensiometer other tensiometers would be calculated. For example, the program would calculate flow direction and magnitude from TR2 (see figure 1- trench right 2 m) to TR1.5, MR1, MR 2, TM2.5, and TM1.5. It would only consider the five or six tensiometers closest to the tensiometer in question[OT3]. The magnitude would be calculated from the difference in hydraulic head [OT4]calculated as

whereH is the hydraulic head (m), ψ is the matric potential (m), and z is the elevation (m). The magnitude of the flow vector would be the difference between the hydraulic head of the tensiometer in question and one of the other tensiometers. The angle of the vector would be calculated by the line between the tensiometer in question and the terminal tensiometer.

After these calculations are computed for each tensiometer (using the 5 closest tensiometers) and program would have five flow vectors originating from each tensiometer. These could easily be plotted, but most likely would still be too dense to easily visualize the prevalent flow patterns. [OT5]The vectors from each tensiometer could be averaged, resulting in a resultant vector the represents the major flow direction from each tensiometer with the magnitude represented by the length of the vector. Using these vectors, the program could interpolate between the points to create a vector field which could represent the entire soil block. This of course would be an estimation of the flow field because the interpolation would not accurately represent the entire flow field, but could indicate the general flow direction and magnitude of that flow in the entire soil block.

There is literature which addresses the interpolation of vector fields such as Optimal Vector Interpolation of Wind Fields by Feliks et al. (1996). I will use these methods to interpolate the vector field in MATLAB. I found a very useful paper on tensiometers called Tensiometers-Theory, Construction, and Use by David Stannard (1990) but there are plentiful literature resources that could be utilized.

The tool would be able to easy[OT6] show 2D and 3D plots of the flow and would be helpful in supporting conclusions of this research and other similar research projects. I am not aware of another tool to assist with these computations, but they could be done by hand. The process of doing this work by hand (or calculator) would be time consuming and mistakes could easily be made.The overall purpose for this tool is to simplify the analysis of this type of data. End users could be any researchers who utilize observation wells and tensiometers for data collection.

Stannard, D.I., “Tensiometers-Theory, Construction, and Use,” Ground Water and Vandose Zone Monitoring, ASTM STP 1053, D. M. Nielsen and A. I. Johnson, Eds., American Society for Testing and Materials, Philadelphia, 1990, pp. 34-51

Feliks, Y., E. Gavze, and R. Givati.“Optimal Vector Interpolation of Wind Fields,” American Meteorological Society, 1996.1153-1165.

[OT1]delete

[OT2]Consider making an Excel template where users would enter the data, then Matlab can import the Excel file.

[OT3]Why? Seems like it would be better to consider all the data

[OT4]Assuming homogeneous and isotropic K, the magnitude would be proportional to the gradient in hydraulic head, not the difference alone.

[OT5]I think you may get better results if you first fit a surface to the hydraulic head, then you can calculate and map the slope of the surface at each point.

Problems may arise at the edges of your observation network where the slope of the hydraulic head surface may be hard to define with confidence.

[OT6]easily