I have some data which I would like to fit a surface to. More specifically, I am conducting a project on hydrology investigating velocity and flow rate. I collected data from a stream and would like to know I can could fit a surface to it. To find discharge, we multiply velocity by the area that the water is crossing. However, in a stream, the velocity is constantly changing. Therefore, the following formula gives us the total discharge $Q$: $$Q=\iint\limits_Rv(x,y)\,dA$$ where $v(x,y)$ is the velocity at the point $(x,y)$ and the region $R$ is the area of water we are integrating over. On the x-axis, I would have the depth of the water, and on the y-axis, the distance from the bank. This integral would then give us the total discharge. Do you know of any free software that fits a surface to 3D data?
Thank you.