HYDROGRAPH COMPONENTS
5.1 HYDROGRAPH COMPONENTS
A hydrograph is a graph showing discharge (i.e., stream flow at the concentration point) versus time. The various components of a natural hydrograph are shown in Fig. 5.1. At the beginning, there is only base flow (i.e., the ground water contribution to the stream) gradually depleting in an exponential form. After the storm commences, the initial losses like intercep- tion and infiltration are met and then the surface flow begins. The hydrograph gradually rises
Effective duration of net rain
Rainfall, P all i (cm/hr)
Hyetograph Net rain, P net
Rainf
net C.g of P
P net = P – Losses
intensity Infil- Infil-
f-curve
tration loss tration loss
(loss rate) Time t (hr or min) Time t (hr or min)
Basin lag Basin lag
N days after peak N days after peak
Peak flow
N(days) = Crest A 1.21 (empirical) A = Area of basin (km 2 )
Time of Time of
Inflection
concentration concentration
point
(cumec)
Total runoff hydrograph (TRH) Total runoff hydrograph (TRH)
of stream-flow = of stream-flow =
1 Recession limb or Recession limb or
Direct surface
curve (or falling limb) curve (or falling limb)
Discharge
runoff volume =P net ×A
Ground water Ground water depletion curve extrapolated depletion curve extrapolated
Point Point of rise of rise
Ground water
N days after peak
depletion curve
B.F. Separation line
GW depletion curve
2 Ground water contribution
Elevated
of stream flow (base flow B.F.)
ground water table contributes more
Time t (hr or days) Fig. 5.1 Components of streamflow hydrograph
HYDROLOGY
and reaches its peak value after a time t p (called lag time or basin lag) meaured from the controid of the hyetograph of net rain. Thereafter it declines and there is a change of slope at the inflection point, i.e., there has been, inflow of the rain up to this point and after this there
is gradual withdrawal of catchment storage. By this time the ground water table has been built up by the infiltrating and percolating water, and now the ground water contributes more into the stream flow than at the beginning of storm, but thereafter the GWT declines and the hydrograph again goes on depleting in the exponential form called the ground water depletion curve or the recession curve. If a second storm occurs now, again the hydrograph starts rising till it reaches the new peak and then falls and the ground water recession begins, Fig. 5.2.
Intensity (cm/hr)
3 peaks due to 3-storms in succession
(cumec) Recession Q
lines
Discharge
Estimated base flow Time t (hr or days)
Fig. 5.2 Hydrograph with multiple peaks
Thus, in actual streams gauged, the hydrograph may have a single peak or multiple peaks according to the complexity of storms. For flood analysis and derivation of unit hydrograph, a single peaked hydrograph is preferred. A complex hydrograph, however, can be resolved into simple hydrographs by drawing hypothetical recession lines as shown in Fig. 5.2.
It has been found from many hydrographs that the ground water depletion curves for a given drainage basin are nearly the same and hence it is termed as the normal ground water depletion curve. It has been found that such curves, or at least their segments, follow a simple inverse exponential function of the elapsed time of the form.
...(5.1) where Q 0 = discharge at start of period Q t = discharge at end of time t K r = recession constant As Q t is the derivations of storage with respect to time,
Q t =Q 0 K –t r
–dS t =Q t dt –dS t =Q t dt
log e K r
Hence, the discharge at any time is proportional to the water remaining in storage i.e.,
...(5.2 a)
Taking logarithms on both sides of Eq. (5.1)
log Q t = log Q 0 – t log K r
which is in the straight line form y = mx + c with y = log Q t ,x = t, and m = – log K r . The value of K r can be determined by plotting the recession data i.e., Q t vs. t on a semi-log paper, taking care to select periods of little or no direct runoff; see Example 17.3.
a. Semi-log plot of continuous a discharge hydrograph
(cumec) scale
Q Log
Discharge
Time t (hr or days) (natural scale)
a b. Semi-log plot of c master depletion curve e
b g d Lower ends of curves
Master
are tangential to a
Log
depletion curve f
h common line
(semi-log plot)
Time t (hr or days) (natural scale)
Master depletion curve (natural scale)
(cumec) Q
c. Master depletion curve drawn to linear scale
Discharge
Time t (hr or days)
Fig. 5.3 Composite ground water depletion curve
HYDROLOGY
If a continuous stream flow record is available for a number of years, the hydrograph can be plotted on a semi-log paper, i.e., log Q vs. t, Fig. 5.3. Starting with the lowest recession flow line, a line is drawn tangential to the lower portion on a tracing paper. This tangent line is progressively extended by moving the tracing-paper towards the origin with the abscissae coincident, such that the line is tangential to the lower portion of the successive depletion curves of increasing magnitude. This common line is the log plot of the master depletion curve, which is then converted to linear vertical scale and is called the composite ground water depletion curve.
A composite ground water depletion curve can be constructed from the recession graphs resulting from a number of storms. The various segments of the recession graphs are shifted with respect to the time axis until they appear to match and then, an average or composite curve is drawn through them as shown in Fig. 5.4.
Master depletion curve
or 14 10 12 Storm recession curves
10 moved (to match) w.r.t.
3 6 9 12 15 18 21 24 27 Time t (hr or days)
Fig. 5.4 Composite depletion curve