I can create a linear blend like the following by using an empty alpha channel:

And I can create a non-linear blend like the following by using a modified alpha channel:

But with the non-linear blend the grass never completley fades away, like you see with the linear blend. So is there a way to combine the two?
Where initialy it will blend with the modified alpha channel, giving a more natural looking transition, but then eventualy having the grass fade away completley.