Hydrology I

Jozsef Szilagyi, Professor of Hydrology Department of Hydraulic and Water

Resources Engineering Budapest University of Technology and

Economics

Lecture #8: Determination of the watershed unit-pulse response function and runoff components separation

Watershed runoff response to a constant intensity rain of infinite duration is proportional to the runoff contributing area, A(t), through time.

The time of concentration (Tc) is the time-interval required for the water to travel from the most remote part of the watershed to the outlet (design point). By this time the entire watershed

delivers water to the outlet. The A(t)/A(Tc) function is the unit-step response, g(t), of the watershed. An isochrone connects those pointsof the catchment that are separated from the outlet by the same travel time (t). t is

proportional to L / S1/2, where L is path-length of the raindrop, S is path slope. [Chezy: v ~ CS1/2, t=L/v]. With discrete data one must determine the UPR [u(t)=g(t)-g(t-Δt)].

Watershed

1h2h

3h

Isochrones

9h

Tc=10h

A1

A2

A3

1

A(t)/Ac

tTc

A(Tc)=Ac

Δtg(t)-g(t-Δt)

The UPR ordinates, u(t), can be plotted

Watershed response to precipitation can now be obtained by the discrete convolution:

Q(iΔt)=∑ij=1Pe(jΔt)u[(i-j+1)Δt]

where Pe is the effective precipitation (the part of the precipitation that contributes to runoff).

This approach can be best used on small watersheds (A<10 km2).

The only parameter needed to be estimated is Tc. There are several empirical equations for it.

Linearity (if such exists) can be best expected between Pe and Qq, i.e., the quick storm response.

How to separate Pe and Qq from the observed precipitation and flow?

t

u(t)

• The Φ-index method: Pe=P-Φ, where the constant Φ value must be chosen so that V(Pe)=V(Qq) (i.e. the two volumes must be equal).

• Runoff component separation:

runoff

surface subsurface baseflow

(interflow) (gw contr.)

quick-storm delayed-storm

response

All existing base-flow separation methods are empirical only.

Fixed-base method: Nd=0.82A0.2

where A is the watershed area in km2, Nd is the watershed-specific time delay in days.

P

t

Φ

t

Pe

t

Q

Qp

t(Qp)

Nd

Assumed baseflow (Qb)

Qq(t)=Q(t)-Qb(t),

Automation of the fixed-base graphical separation method:

Digital filter algorithm

Qb(i)=pQb(i-1)+0.5(1-p)[Q(i)+Q(i-1)]

If Qb(i) > Q(i) → Qb(i) = Q(i)

The filter parameter, p (0.85-0.99), must be chosen so that the resulting Nd be close to that of the fixed-base method!

HW#1: Apply the the digital filter on a watershed of your choice with different p values and show the measured flow and estimated baseflow time-series.

Lab#6: Estimate the unit-pulse response function of Karola Creek and calculate the runoff over the 1-6 h interval for Pe values of 5, 2, 1 mm/h.

Elevation (m) above mean sea level