DARCIAN WEIGHTED INTERBLOCK CONDUCTIVITY MEANS FOR VERTICAL UNSATURATED FLOW

The true Darcian interblock conductivity mean for vertical unsaturated flow, Ky, is derived from Darcy's law, q/Ks = Kv (dH/dx), and the assumption that flow is constant between grid centers. It can be expressed as Kv = (Delta x Kx - Delta p Kh)/(Delta x - Delta p), where Kx is the gravity flow mean, Kh is the capillary flow mean, and H = x - p (total head = elevation - matric suction). Plotting contours of Kx, Kh, and Kv in the plane of adjacent grid center conductivities, (kr1, kr2), shows that a component of Kx behaves like a simple weighted mean, Kw = w kr2 + (1 - w) kr1, where w is a nonlinear, monotonic function of the grid separation, Delta x. Results from a mass-conservative model of infiltration into dry sand are compared for substituting:(1) the arithmetic mean, Ka = (kr1 + kr2)/2, for Kv,(2) Kw for Kv,(3) Ka for Kx in Kv (called Km), and (4) Kw for Kx in Kv (called Kmw), over a range of the ratio of Delta x to the conductivity displacement pressure, pk, from 0.01 to 1.6. The simulation for Delta x/pk = 0.002 is taken to be the exact solution. Kw and Kmw reduce the gross cumulative net inflow error generated with Ka and Km from 3.84 to 8.84 times. Kmw performs consistently better in terms of gross water content distribution error by up to a factor of three.