# Calculating proportional change in surface volume

I am using the Surface Volume tool (3D Analyst/Functional Surface) in ArcGIS 10.1 to calculate the volume between a reference plane and two water table surfaces (year 1 and year 2) that I interpolated from monitoring data (i.e., water table elevation points).

I specified that the tool should calculate the volume ABOVE the plane (up to the surface). My x,y, and z units are all in meters, so Z-factor = 1. I used the same reference plane height for both surfaces (it was set to a height that would not intersect either surface).

I am interested in calculating the proportional (percent) change in surface volume between years, not in the raw volume numbers per se. After running the tool, I did the following to calculate percent change: ((Year 2 vol - Year 1 vol)/ Year 1 vol)*100

I ran the Surface Volume tool multiple times using the same two surfaces (year 1 and year 2), but changed the height of the reference plane (the plane never intersected either surface). I expected the percent change to remain the same, regardless of the reference plane height. However, the percent change in volume between the two years changes each time I alter the reference plane height.

Here is an example of my data:

Percent change in volume between year 1 and 2:

``````-0.31% (ref plane at 725 m)
-2.10% (ref plane at 760 m)
-5.46% (ref plane at 763.7 m)
``````

As I raise the plane, it gets closer to my surfaces, and the raw volume numbers decline.

Why does the percent change differ as I change the reference plane height?

Perhaps it is related to the overall downhill trend in my water table data.

If I understand you correctly, this makes perfect sense. The Surface Volume tool is explicitly calculating a volume between the reference plane and your surface(s). As you move the reference plane, your volumes will change correspondingly. What doesn't change is the volume between your two surfaces (Year 1 and Year 2). This volume will always be the same, but as you increase or decrease the total volume by changing your reference plane, the constant difference between Y1 and Y2 constitutes a different percentage of that total volume. It may be easier to strip your actual values out of the problem and look at it conceptually:

Y1 = 1; Y2 = 2; Plane=0

In this situation your volume difference is 100% ((2-1)/1)*100

Y1 = 1; Y2 = 2; Plane = 0.5

Now ((1.5-0.5)/0.5)*100 = 200%

To solve this, you either need to pick a single reference plane (that ostensibly has some meaning to your analysis) and calculate your proportional change as you have already done, OR forget about proportions and simply take the total volume change between your two surfaces (which should be constant no matter your reference plane height).

This is to support JWallace answer: Please note decrease in volume with level rise equal (760-725) and (763.7-760) I bet that your (depth decrease)/(41.029-40.902) will result in some number with almost nothing after decimal point