Chapter 3 Hydrograph Analysis

Chapter 3

Hydrograph Analysis

Components of Runoff

Hydrograph Characteristics Unit Hydrograph Theory

Synthetic Unit Hydrographs

q (m3_/s)

t (hr)

The major characteristics of streamflow are:

its volume for a certain duration (month or year) different uses & storage

its extreme values

Hydrograph Analysis

i (mm/hr) q (m3/s)

t (hr) input

(Rainfall) system _(Basin)

t (hr) output (Runoff)

Components of Runoff

Channel Precipitation Surface Runoff Interflow Groundwater Flow Interception, depression storage, soil moisture are LOSSES for streamflow. The other portions of

precipitation reach streams sooner or later.

In a rainfall block interception Loss for streamflow storage (mm/hr) depression moisture i soil _ater groundw_interflow streamflow infiltration surface runoff channel precipitation

COMPONENTS OF RUNOFF

In a rainfall block

In the channel channel precipitation _{surface flow}

interflow groundwater flow groundwater table GW flow interception

Loss for streamflow

streamflow surface runoff channel precipitation i (mm/ h r)

Hydrograph

Hydrograph  discharge vs time

(m3_{/s, lt/s) (min, hr, day, month, yr)}

Sometimes plotted as stage vs time.

The comparison of hydrographs with the corresponding

rainfall hyetographs provides a lot of information about the

rainfall-runoff relation of the basin.

Q (m3_{/s, lt/s)}

HYDROGRAPH

t (min, hr, day, week, month, year)

Shape of the rising limb = f(rainfall intensity & basin

characteristics s.a. infiltration capacity, shape, slope, etc.)

Shape of falling limb = f(basin characteristics s.a. depression, surface & subsurface storages)

Characteristics of the rainfall do not impact the falling limb

since recession starts after the end of the rainfall.

t_L

r

Hydrograph

peak rate crest

inflection points

The crest of the hydrograph is governed by the duration of rainfall. rising limb (concentration curve) surface runoff (direct runoff) falling limb (recession curve) (depletion curve) A GW recession base flow t_p t (hr) t_b q (m 3/s )

Hydrograph shapes

for different

conditions

The shape of the

hydrograph varies with the orientation of the storm in

surface flow channel precipitation interflow i f F : rainfall rate : infiltration rate : total amount of infiltrated water SMD : soil moisture deficiency Case 2 i<f F>SMD  t₁ t₂ t (hr) t₁ t₂ t (hr) Case 4 i>f F>SMD  t₁ t₂ t (hr) no rain t (hr) groundwater flow groundwater GW table flow Case 3 i>f F<SMD q (m 3 /s) q (m 3 /s) q (m 3 /s ) q (m 3 /s ) q (m 3 /s) Case 1 i<f F<SMD t₁ t₂ t (hr) q (m3_/s) B A Basin A Basin B _{t (hr)}

Hydrograph Separation Techniques

Separation line between surface runoff & baseflow is not

definite & varies widely depending on the existing conditions.

Inaccuracies in separation are not very important for many

storms, since the max. rate of discharge is only slightly

affected by the base flow.

Methods for seperation:

Simple Method

Approximate Method

Seperation Methods

1. Barnes (Semi-log) Method

1 Total flow (SF+SSF+BF) q  q0 e α₁t 4 _{Base flow (BF)} 2 (SF+SSF) (1) – (4) q  q _{0 e}α2t 5 Subsurface flow (SSF) 3 Surface flow (SF) _{(2) – (5)} Q 1 9 (m3/s) 8 7 6 5 4 3 2 1 3 1 9 8 7 6 5 4 _ 4 2 3 5 2  1 E (linear) t (hr) q (m3_/s) q (m3_/s) q (m3_/s) q (m3_/s)

Master depletion curve (representative depletion curve)

Slope is related to storage coefficient

of the basin

q = q₀e-αt

log q = log q₀ - t α log e y a b x

y = a + bx (straight line on semi-log paper)

log q (m3/s)

master depletion line

Unit Hydrograph (UH) Theory

Hydrograph of surface runoff (direct runoff) resulting from

1 cm of excess rainfall which is uniformly distributed over

basin area at a uniform rate during a specified period of time.

Depth = 1 mm for arid or semi-arid regions or if basin is small.

Given by Sherman in 1932.

It is assumed that the UH is representative for the runoff

process of a basin.

Baseflow should be separated from total flow to find direct

runoff, and all the losses should be subtracted from total precipitation before any analysis.

Unit Hydrograph (UH) Theory

UH assumptions:

1.

Excess rainfall is

uniformly distributed within a

specified period of time.

2.

Excess rainfall is

uniformly distributed over the

basin area.

3.

Base time of direct runoff is constant

for a

specified duration of rainfall.

4.

Ordinates of direct runoff hydrograph are directly

proportional to the total amount (depth) of direct

runoff ( = depth of excess rainfall) for the same

duration rainfalls.

1. Linearity assumption

(Principle of superposition, Principle of proportionality)

2. Principle of time-invariance

When basin characteristics change  UH changes

i (mm/hr) i ni t (hr) t_r q (m3_/s) nq _i hydrograph for ni mm/hr rain q_i hydrograph for i mm/hr rain t (hr) t_b (same base time)

Unit Hydrograph

The unit hydrograph is denoted as dUH_t ( d in cm, t in hr)

The depth of flow for a hydrograph  the area under the

hydrograph. q (m3_/s) a q3 3 q 4 a q2 1 1 t t 2 a q qn a _n+1 t t t (hr)

...

V = q*t

Figure 7.18 Determination of volume of runoff

d = V A 



= A q dt  _{q * Δt} A

∑q = sum of ordinates of the hydrograph (m3_/s)

d_t = time interval (s) A = basin area (m2₎

Unit Hydrographs of Different Durations

There are 2 methods to obtain UHs of different durations for a basin when a UH of certain duration is known

The lagging method S-curve method The Lagging Method

A UH of certain duration can easily be obtained by using the lagging method if a UH of different duration is known for the basin.

The only condition is that the durations be multiples of each other.

HYDROGRAPH ANALYSIS –

lagging method

i (mm/hr) 1 cm 1 cm t (hr) t_r t_r q (m3_/s) UH_tr [UH₂]

t_r hour lagged UH_tr [UH₂]

t (hr) t_b t_r i (mm/hr) _{1 cm} tr q (m3/s) t (hr) UHtr [UH2] t (hr) tb 1 cm i (mm/hr) _{1 cm} tr t (hr) tr q (m3/s)

addition of two hydrographs = 2UH2tr [2UH4] tb UHtr [UH2] tr hour lagged UHtr [UH2] t (hr) tr UH₂ + (2 hr lagged) UH₂ = 2UH₄ i (mm/hr) 1 cm 1 cm t (hr) t_r t_r q

(m3_/s) addition of two hydrographs = 2UH2tr [2UH4]

UH_2tr [UH₄] UH_tr [UH₂]

t_r hour lagged UH_tr [UH₂]

t (hr)

HYDROGRAPH ANALYSIS –

lagging method

q_p es As t_r _{es tp} t_b _es es i (mm/hr) 1 cm 1 cm 1 cm t (hr) tr tr tr q (m3_/s) tb UHtr tr hour lagged UHtr 2 tr hour lagged UHtr t (hr) tr tr i (mm/hr) 1 cm 1 cm t (hr) tr tr q (m3_/s) UHtr tr hour lagged UHtr t (hr) tb tr i (mm/hr) 1 cm tr t (hr) q (m3_/s) UHtr t (hr) tb

UH_t + (t hr. lag) UH_t + (2t hr.lag) UH_t =3UH_3t i (mm/hr) 1 cm t_r 1 cm 1 cm t_r t_r t (hr) q (m3_/s)

addition of 3 hydrographs = 3UH_3tr

UH_3tr UH_tr t_r hour lagged UH_tr 2 t_r hour lagged UH_tr t (hr) t_b t_r t_r

The S-Curve Method

It is used to obtain UHs of different durations that are

not multiples of each other.

S-curve is the hydrograph that would result from an

infinite series of UHs of t_r durations, each delayed t_r hours

wrt the preceding one.

In other words, it is the hydrograph of the runoff of

continuous rainfall with an intensity of 1/t_r.

S-curve has the form of a mass curve, the discharge of the basin becoming constant after the time of concentration. Thus each S-curve is unique for a specified UH duration, in a particular drainage basin.

S - Curve

i (mm/hr) tr q (m3/s) tr tr tr t (hr)

S - curve

Qe UHt _r tr tb t_r t (hr) tr tb i (mm/hr) t (hr) t tr tr r q (m3_/s) t (hr) tr tr tb i (mm/hr) t (hr) t tr r q (m3_/s) t (hr) tr i (mm/hr) t (hr) tr q (m3_/s) t (hr) tb

n = t

_b

/t

_r Q_e = i * A (mm/hr * km2₎ Q_e = d/t_r * A = 1/t_r * A (d= 1 cm) Q_e = constant outflow (m3_/s) A = area of basin (km2₎ tr = duratio of UH (hr) Q  2.78 A e t _r

S - Curve

There may be fluctuations around the constant flow Q_e

due to a number of reasons.

One of them may be the duration of effective

precipitation, t_r.

It may be shorter or longer than the actual effective precipitation duration with uniform intensity.

Another one may be the uneven distribution of rainfall in the basin or nonlinearities in the system.

Obtaining UH using S-curve (t

₂

< t

₁

)

i (mm/hr) t (hr) t1 t1 q (m3/s) t1 St₁ t (hr) i (mm/hr) q (m3/s) t1 t1 t2 t (hr) t1 St1 (t2 hr. lag) St₁ t2 t (hr) i (mm/hr) t (hr) q (m3/s) t1 t2 t1 t1 St₁ (t2 hr. lag) St₁ UHt ₂ = t1 Diff. t2 Diff. = t2 UH t1 t 2 t2 tb t (hr) i (mm/hr) t (hr) q (m3/s) t1 t2 t1 t1 St₁ (t2 hr. lag) St₁ Diff. = t2 UH t1 t 2 t2 tb t (hr) UH  t1 [s t 2 _t t1  (t 2 hr. lag) s t1 ] 2 Diff. = S_t1 - (t₂ h.l.) S_t1 Diff. = (t₂ . 1/t₁) UH_t2= t₂/t₁ UH_t2

7. Determine the representative UH for the basin by

averaging

the peak flows, times to peak, and

time bases of the UHs.

The average UH is then sketched following the shapes of the individual hydrographs.

8. Adjust the area under the curve to unit depth.

q (m3_/s) q_p2 q_p3 q_p1

.

average peak ( p1 p2 p3 q + q + q _, t _{p1 + t + t} 3 p2 3 p3 ) average unit hydrograph

average base time t_b1 + t_b2 + t_b3 ) t_p3 t_p2 t_p1 ( t_b2 t_b3 3 t_{b1 t (hr)}

Example

UH₁ of a basin is given.

Determine UH₂ , UH₃ and area of this basin by lagging method Time (hr) UHm3_/1 s 1 hr.lag UH1 2UH 2 UH2 2 hr.lag UH1 3UH3 UH 3 0 0 0 0 0 0 1 12 12 6 0 12 4 2 36 48 24 3 24 12 60 30 0 48 16 4 18 ₃₆ 42 21 _{12 72 24} 5 12 30 15 24 3 6 78 26 6 6 18 9 18 2 4 54 18 7 0 6 3 8 12 0 0 18 36 12 9 ₆ 12 _{18 6} 0 6 6 2 0 _{0 0} q 108 108 108 Σq* Δt Σq* Δt UH₁ + (1 hr. lag) UH₁ = 2 UH₂ d   A  A d UH₁ + (1 hr. lag) UH₁ + (2 hr. lag) UH₁ = 3 UH₃ A  108*1*3600 _0.01  38.88*106 m2  38.88 km2

1

Example

UH of a basin is given.

Determine UH₂ and UH₃ of this basin by S-curve method

UH 



















₁ [S  _{(2 hr.lag) S ]} UH 



















₁ [S  _{(3 hr.lag) S ]} N = t_b / t_r = 7/1 = 7 2 2 1 1 3 3 1 1 UH _t 2  [s t₁ t t1  (t hr. lag) s ] 2 t1 2 t (hr) UH1 1 h.l _UH 1 2 h.l UH1 3 h.l UH1 4 h.l UH1 5 h.l UH1 6 h.l UH1 S₁ 2 h.l S1 dif f UH 2 3 h.l S1 dif f UH3 0 0 0 0 0 0 0 1 12 _{0 12 12 6 12 4} 2 36 ₁₂ 0 48 0 48 24 48 16 3 24 3 6 12 ₀ 72 12 60 30 0 72 24 4 18 2 4 36 _{12 0 90 48 42 21 12 78 26} 5 12 18 24 36 12 0 102 72 30 15 48 54 18 6 6 12 18 24 36 12 0 108 90 18 9 72 36 12 7 0 6 12 18 24 36 12 108 102 6 3 90 18 6 8 0 6 12 18 24 36 108 108 0 0 10 2 6 2 9 0 6 12 18 24 108 108 10 8 0 0

Synthetic Unit Hydrograph

Snyder Method

SCS Method

(developed by Soil Conservation Services, 1957)

Espey Method Mockus Method

DSİ Synthetic Unit Hydrograph Method Time Area Method