An algorithm for calculating the time to equilibrium of complex waters
heds is developed for spatially varied watershed characteristics and e
xcess rainfall intensity. The wave travel time through the flow path o
riginating from the hydraulically most remote point in the basin essen
tially determines the equilibrium time of the system. The wave travel
time is computed for two distinct phases: overland flow and channel fl
ow. The hydraulically most remote point is stationary for all spatiall
y uniform rainstorms but may vary for spatially distributed storms. Th
e time to equilibrium varies inversely with rainfall intensity raised
to the power 0.4. Using a raster-based approach, algorithms were devel
oped to determine the distance-drainage area relationship and to perfo
rm the numerical integration of the time to equilibrium. Although appr
oximate, the algorithm provides maps showing the isochromes of surface
runoff and travel time to the outlet, along with time-area histograms
for uniform or spatially distributed rainstorms. Isochrones determine
the response time required for water, dilute suspensions and pollutan
ts to reach the watershed outlet under complete equilibrium. The effec
ts of infiltration in delaying the time to equilibrium are significant
only when delta/K is large.