UH

Synthetic Unit Hydrographs

• All the methods of deriving a UH discussed previously require observations of rainfall and runoff. However, for some drainage basins rain gages and/ or streams flow gages are not, therefore, rainfall – runoff data are not available. For those basins, some kind of techniques to generate UH (without using rainfall – runoff records) is needed. The UH so derived is called synthetic UH.

• Three types of synthetic UHs:

(1) those relate hydrograph characteristics (peak discharge, time base,

time-to-peak, etc.) to basin characteristics;

(2) those based on dimensionless UH; and those based on models of

watershed storage.

UH

Snyder’s Method - 1

• Study area: US Appalachian highlands. 10 ~ 10,000 mi2 (30 ~30,000 km2)

• Properties characterizes the response of watershed under various rainfall inputs:

(a)   Duration of rainfall excess;

(b)   Lag time;

(c)   Time base of UH;

(d)   Time to peak;

(e)   Peak discharge of UH;

(f) Shape of UH.

UH

Snyder’s Method - 2

Snyder’s method allows the computations of

(a) lag time (tL);

(b) UH duration (tr);

(c) UH peak discharge (qp);

(d) Hydrograph time width at 50% and 75% (W50, W75) of peak flow

UH

Snyder’s Method - 3

1. Lag time (tL): time from the center of rainfall – excess to the UH peak 

tL = C1Ct (LLc)0.3

where tL = Time [hrs]; C1 = 0.75 for SI unit; 1.0 for English unit; Ct =

Coefficient which is a function of watershed slope and shape, 1.8~2.2

(for steeper slope, Ct is smaller); L = length of the main channel [mi,

km]; Lc = length along the main channel to the point nearest to the

watershed centroid

UH

Snyder’s Method - 4 2. UH Duration (tr): 

tr = tL / 5.5

where tr and tL are in [hrs]. If the duration of UH is other than tr, then the lag time

needs to be adjusted as 

tpL = tL + 0.25 (tR - tr)

where tLR = adjusted lag time; tR = desired UH duration.

3. UH Peak Discharge (qp):

  or

 

where C2 = 2.75 for SI unit; 640 for English unit; Cp = coefficient accounting for

flood wave and storage condition, 0.4 ~ 0.8; qp = specific discharge,

[m3/s/km2] or [ft3/s/mi2]

To compute actual discharge, Qp = Aqp

pt

pC

2C

pq

pRt

pC

2C

pq

UH

Snyder’s Method - 54. Time Base (tb):

  Assuming triangular UH,

tb = C3 / qp

where tb – [hrs]; C3 = 5.56 for SI unit, 1290 for English unit.

 

5. UH Widths: or

where

CW, 75 = 1.22 for SI unit; 440 for English unit;

CW, 50 = 2.14 for SI unit; 770 for English unit;.

W50, W75 are in hours; Usually, 1/3 of the width is distributed before UH

peak and 2/3 after the peak

Remember to check that the volume of UH is close to 1 cm or 1 inch

1.08p

q

w,75C

75W

1.08p

q

w,50C

50W

UH

Snyder’s Method - Example

UH

SCS Dimensionless UH

UH

SCS Dimensionless UH

UH

Instantaneous Unit Hydrograph (IUH) - L e t t h e d u r a t io n o f a t - h r U H g o t o in fin it e s im a lly s m a ll, t h a t is , t 0 , t h e

r e s u lt in g U H is c a lle d t h e I U H . - I U H o f a d r a in a g e b a s in r e s u lt s fr o m 1 u n it ( 1 c m o r 1 “ ) o f e ffe c t iv e r a in fa ll

a p p lie d t o t h e w a t e r s h e d in z e r o t im e .

1 . T h e a d v a n t a g e o f I U H is t h a t n o r e fe r e n c e w it h r e s p e c t t o d u r a t io n is n e e d e d .

2 . S u p p o s e w e h a v e a 1 - h r S - c u r v e , t h e d t - h r U H c a n b e o b t a in e d b y

dt

dt)S(tS(t)

B y le t t in g d t 0 , t h e r e s u lt in g U H is c a lle d I U H . I n o t h e r w o r d s , I U H c a n b e o b t a in e d fr o m fin d t h e s lo p e o f 1 - h r S - c u r v e , i. e . ,

I U H ( t ) = d S ( t ) / d t

w h e r e S ( t ) = 1 - h r S - c u r v e

UH

HK WSD 15-min Dimensionless UH• Dimensionless discharge: Q’ = Q(Lag+tr/2)/V

Dimensionless time: t’= 100 t / (Lag+tr/2)

• where V = surface runoff from 1” of rainfall excess (in ft3);

Lag = basin lag time (min)

= time between the centroids of rainfall excess

and runoff hydrograph

=1.47 A0.54 with A = basin area (acres);

tr = 15min

15 min

1”Lag

t

u

UH

HK WSD 15-min Dimensionless UH

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32.437648'006547.0'38.6376.80393

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6.44'0,'0001078.0'00758409.4exp['

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tfort

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ttt

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HK Dimensionless 15-min UH

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