How does slope influence runoff

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Runoff is the precipitation excess or the water leaving a drainage area regarded as rainfall minus loss by evaporation or infiltration.Runoff volume is the total volume of runoff water occuring over a period of time where Q(t) is the discharge at time t and the expression is :-

Total runoff is the sum of the overland flow,ground water flow and through flow.The reason why water flow down hill over a sloping land surface is because of the following of the Bernoulli's equation.However,other opinion says the reason is decrease in potential energy rather than Bernoulli's equation .Steep slope will provoke speedy movement of water towards the outlet while gentle slope will result in slow movement allowing evapotranspiration.If the soil is porous then there will be infiltration and downflow in the form of throughflow or it may enter the ground water flow.Surface runoff or infiltration excess overland flow can only occur on the catchment slope if :-
a)Rainfall rate is greater than infiltration rate or capacity of that region;
b)The soil is saturated so no infiltration can't occur.Runoff may take the form of return flow which is caused by an impermeable barrier in the path of moving water like for instance,a saturated soil layer, and emerges at the surface.If the water passes through an unsaturated soil on the catchment slope in the form of unsaturated throughflow then it's movement would be slow due to low hydraulic conductivity of unsaturated soil.However,saturated thoroughflow is faster than it's unsaturated counterpart.In cold climates where catchments are situated ,have their slopes  covered with snow/ice for a major part of the year there role of slope o runoff is negligible and overlooked.
In conclusion,it can be pointed out that  runof generation in a catchment area depends on the physical properties,time and climate.

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