Qiangbing

To do the average you need to integrate ln(z(r))*exp(-r/R)* d(r/R) from zero to infinity, which in your case (3 zones)the result is: average = log(z1)*(1.-exp(-r1/R)) + log(z2)*(exp(-r1/R)-exp(-r2/R)) + log(z3)*exp(-r2/R)

Hi, The slope gird is calculated straightforwardly from the terrain inclination grid. For terrain inclination (dx, dy) the slope in percentage is s = sqrt(dx^2 + dy^2), which is the length of the inclination vector, while the aspect is just the direction of the vector, a = atan(dy/dx). Qiangbing

The sector-wise reference roughness are calculated by weightedly averaging over distance the logarithmic of roughness of the sector in question, and then taking the exponential of the average. The weight of the roughness at distance r is taken to be exp(-r/R), where R is the decay length for roughness area size, which in our case is taken to be 10,000 meters.

The tilt angle is calculated as the arctan of the ratio of the z-component of wind speed over the horizontal wind speed: tilt = atan2(u_z, sqrt(u_x^2 + u_y^2)).