UNIVERSITY OF SOUTH AFRICA
College of Agriculture and Environmental Sciences
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
Hydrology and Water Supply
Assignment Solutions — Semester 1, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
Hydrology and Water Supply
Module:
WSE3701
Module Code:
01
Assignment Number:
Submitted in partial fulfilment of the requirements
for Hydrology and Water Supply — UNISA 2026
, UNISA | Hydrology & Water Supply Assignment Solutions
Question 1: Rainfall Losses, Index Estimation and Hyetograph [24 Marks]
Rainfall-runoff analysis forms the basis of flood estimation and catchment management. The
phi-index (ϕ) method separates total rainfall into abstraction losses and excess (effective)
rainfall, which directly produces direct surface runoff (Chow, Maidment and Mays, 1988).
1.1 Estimation of the ϕ-Index and Direct Surface Runoff [14 Marks]
Given Data
The storm has a total recorded rainfall of 35.0 cm and produces an equivalent excess rainfall
of 27.5 cm. The hourly incremental rainfall is given in Table 1.
Table 1: Hourly Incremental Rainfall Distribution
Time from start 1 2 3 4 5 6 7 8 9 10
(hr)
Incremental rainfall 0.60 1.70 3.10 5.80 9.70 6.30 4.00 2.20 1.20 0.40
(cm)
Total rainfall confirmed: 0.60 + 1.70 + 3.10 + 5.80 + 9.70 + 6.30 + 4.00 + 2.20 + 1.20 + 0.40 = 35.0
cm.
Step 1: Establish the Loss Volume
Total losses = Total rainfall − Excess rainfall = 35.0 − 27.5 = 7.5 cm
Step 2: Determine the ϕ-Index by Trial and Error
The ϕ-index is defined as the constant infiltration rate (cm/hr) above which all rainfall con-
tributes to excess runoff. For any hour i:
Excessi = max(Pi − ϕ, 0)
and the sum of all excess must equal 27.5 cm.
Trial: ϕ = 0.80 cm/hr
Hours where Pi < ϕ: Hour 1 (P = 0.60) and Hour 10 (P = 0.40) – both fall entirely below ϕ
Page 2 of 15
College of Agriculture and Environmental Sciences
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
Hydrology and Water Supply
Assignment Solutions — Semester 1, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
Hydrology and Water Supply
Module:
WSE3701
Module Code:
01
Assignment Number:
Submitted in partial fulfilment of the requirements
for Hydrology and Water Supply — UNISA 2026
, UNISA | Hydrology & Water Supply Assignment Solutions
Question 1: Rainfall Losses, Index Estimation and Hyetograph [24 Marks]
Rainfall-runoff analysis forms the basis of flood estimation and catchment management. The
phi-index (ϕ) method separates total rainfall into abstraction losses and excess (effective)
rainfall, which directly produces direct surface runoff (Chow, Maidment and Mays, 1988).
1.1 Estimation of the ϕ-Index and Direct Surface Runoff [14 Marks]
Given Data
The storm has a total recorded rainfall of 35.0 cm and produces an equivalent excess rainfall
of 27.5 cm. The hourly incremental rainfall is given in Table 1.
Table 1: Hourly Incremental Rainfall Distribution
Time from start 1 2 3 4 5 6 7 8 9 10
(hr)
Incremental rainfall 0.60 1.70 3.10 5.80 9.70 6.30 4.00 2.20 1.20 0.40
(cm)
Total rainfall confirmed: 0.60 + 1.70 + 3.10 + 5.80 + 9.70 + 6.30 + 4.00 + 2.20 + 1.20 + 0.40 = 35.0
cm.
Step 1: Establish the Loss Volume
Total losses = Total rainfall − Excess rainfall = 35.0 − 27.5 = 7.5 cm
Step 2: Determine the ϕ-Index by Trial and Error
The ϕ-index is defined as the constant infiltration rate (cm/hr) above which all rainfall con-
tributes to excess runoff. For any hour i:
Excessi = max(Pi − ϕ, 0)
and the sum of all excess must equal 27.5 cm.
Trial: ϕ = 0.80 cm/hr
Hours where Pi < ϕ: Hour 1 (P = 0.60) and Hour 10 (P = 0.40) – both fall entirely below ϕ
Page 2 of 15
