Vector calculus: Finding a model fit from a 2D grid

First of all, I am a biologist. My knowledge of math is very limited. Therefore, I come here for help, but please take into consideration that I may not be very good at asking the question in a good way, and you may need to explain it like I'm five years old.

I have a number of water flow measurements that I use as an input to Wolfram Mathematica for ListStreamPlot to show how water flows through a transect of the river. It looks really nice, but I would like to get some statistics from this. I'm sure Mathematica uses some sort of model that my measurements are fitted to. I would like to reproduce this model and get something like R^2 statistic or similar to measure the goodness of fit. So what I need to do is fit a model to the 2D grid of velocity vectors, and then plot that model (but now using the StreamPlot function, if you're into Mathematica).

Here are some example measurement values {x,y,xvel,yvel}:

xy1 = {{0.75, 0.6, 0.2432214285714285714, -0.0032285714285714286}, {2.25,
1.2, -0.0130909090909090909, 0.1693969696969696970}, {2.25, 0.2,
0.0051228571428571429, 0.16554571428571428571}, {1.5, 1.8,
0.2067933333333333333, -0.1746966666666666667}, {2.25, 0.6,
0.0738333333333333333, 0.0093393939393939394}, {1.5, 1.2,
0.2102258064516129032, -0.0555451612903225807}, {1.5, 0.2,
0.1615791666666666667, -0.02004583333333333333}, {0.75, 1.2,
0.2198725000000000000, -0.0172975000000000000}, {0.75, 0.2,
0.1580366666666666667, 0.0221100000000000000}, {2.25,
1.8, -0.0058160000000000000, -0.08341200000000000000}, {1.5, 0.6,
0.20290344827586206897, -0.04414827586206896552}, {0.75, 1.8,
0.0030500000000000000, -0.01323846153846153846}, {0, 0, 0, 0}, {0,
0.6, 0, 0}, {0, 1.2, 0, 0}, {0, 1.8, 0, 0}, {0, 2, 0, 0}, {3, 0, 0,
0}, {3, 0.6, 0, 0}, {3, 1.2, 0, 0}, {3, 1.8, 0, 0}, {3, 2, 0,
0}, {1.5, 0, 0, 0}, {1.5, 2, 0, 0}}


I use those values in Mathematica like this:

ListStreamPlot[xy1, StreamScale -> 0.11, StreamStyle -> Black,
PlotRange -> {{0, 3}, {0, 2}},
PlotLabel -> "0.75 m from upstream wall"]


I tried searching for methods, and I see words like "vector calculus" or "partial differential equations", but I don't know how to work with these things. I also tried asking in the Mathematica StackExchange subsection, but I didn't get a single reply there. So I hope you math people are more up for the task. :)

So what I'm asking is, how do I find a model that describes the vectors that I have data for? If the answer is going to be really long and complicated, maybe you could just recommend a book that will give me an answer? I tried searching Amazon, but it's not easy because I'm not exactly sure what I'm looking for.