Watershed Hydrology

Lesson 27 Synthetic Unit Hydrograph

These methods being based on empirical correlations are applicable only to the specific regions in which they were developed and should not be considered as general relationships for use in all regions.

 

27.2 Snyder’s Method

Snyder (1938), based on a study of a large number of catchments in the Appalachian Highlands of eastern United States developed a set of empirical equations for synthetic-unit hydrographs in those areas.

 

These equations are in use in the USA, and with some modifications in many other countries, and constitute what is known as Snyder’s synthetic-unit hydrograph.The most important characteristic of a basin affecting a hydrograph due to a storm is basin lag. Basin lag (also known as lag time) is the time difference between the centroid of the input (rainfall excess) and the output (direct runoff hydrograph). However, difficulty in determining the centroid of the direct runoff hydrograph (DRH), lag time is defined for practical purposes as the elapsed time between the centroid of rainfall excess and peak of DRH. Physically, lag time represents the mean time of travel of water from all parts of the watershed to the outlet during a given storm. Its value is determined essentially on the topographical features, such as the size, shape, stream density, length of main stream, slope, land use and land cover. The modified definition of basin time is very commonly adopted in the derivation of synthetic unit hydrographs for a given watershed.

 

The first of the Snyder’s equation relate the basin lag t_p,defined as the time interval from the mid-point of rainfall excess to the peak of the unit hydrograph (Fig. 27.1) to the basin characteristics as

 (27.1)

where t_p is basin lag in hours, L is basin length measured along the water course from the basin divide to the gauging station in km, L_ca distance along the main water course from the gauging station to a point opposite to the watershed centroid in km, C_t is a regional constant representing watershed slope and storage effects (1.3 to 1.65).

 

Snyder adopted a standard duration t_rhours of effective rainfall given by

 (27.2)

 

The peak discharge Q_ps(m³/s)of a unit hydrograph of Standard duration t_rh is given by Snyder as

 (27.3)

WhereA is catchment area km², C_p is a regional constant (0.56-0.69).

 

This equation is based on the assumption that the peak discharge is proportional to the average discharge of  

Lf a non-standard rainfall duration t_Rh is adopted, instead of the standard value t_rto derive a unit hydrograph the value of the basin lag is affected. The modified basin lag is given by

 (27.4)

Where= basin lag in hours for an effective duration oft_Rhand t_pis as given by Eq.  (27.1).The value of must be used instead of t_pin Eq. (27.2). Thus the peak discharge for a nonstandard ER of duration t_Ris in m³/s.

 (27.3a)

When t_R = t_r

Q_p = Q_ps

The time base of a unit hydrograph (Fig. 27.1) is given by Snyder as

 (27.5)

Witht_b(given in h) taken as the next larger integer value divisible by t_R, i.e. T_bis about five times the time-to-peak.

 

To assist in the sketching the unit hydrographs, the widths of unit hydrographs at 50 and 75% of the peak are given by

 (27.6)

 (27.7)

WhereW₅₀ is width of UH in h at 50% peak discharge, W₇₅ is width of UH in h at 75% peak discharge

q = Q_p/A = peak discharge per unit catchment area in m³/s/km²

 

Example 1

Characteristics of two catchments M and N measured from a map are given below:

Item	Catchment M	Catchment N
Lca	76 km	52 km
L	148 km	106 km
A	2718 km2	1400 km2

 

For the 6-h unit hydrograph in catchment M, the peak discharge is at 200 m³/s and occurs at 37 h from the start of the rainfall excess. Assuming the catchments M and N are meteorologically similar; determine the elements of the 6-h synthetic unit hydrograph for catchment N by using Snyder’s method.

 

Answer

 

1. a.  For catchment M

t_r = 6 h

Time to peak from beginning of ER

t^'_p = 34h

From equation

tp = 34.047

ct = 2.073

C_p = 0.899 ≈ 0.9

b.  For catchment N

Using

References

Subramanya, K. (2008). Engineering Hydrology.Third edition, Tata McGraw Hill, 225-229.

Suggested Reading

Singh, V. P. (1994). Elementary Hydrology.Prentice Hall of India Private Limited,New Delhi.

Suresh R. (2007). Soil and Water Conservation Engineering. Fourth edition, Standard Publishers Distributors, New Delhi.

Murty, V.V.N. and Jha, M.K. (2009).Land and Water Management Engineering.Fifth edition, Kalyani Publishers, Ludhiana.