Averaging and Quantifying a Dependent Variable in a 2D Domain along One Axis

I am solving a pde problem in a 2D domain, the dependent variable is phi. My goal is to determine quantitatively the region in the 2D domain that the average of phi along the vertical direction reaches a particular value. Mathematically,

phi_bar (x) = 1/L*integrate(phi(x,y), 0, L) >= 0.8;

I will appreciate any assistance. Thanks