1. Worcester Polytechnic Institute Civil and Environmental Engineering
Hydrology
Lecture # 3
Paul P. Mathisen
Worcester Polytechnic Institute Civil and Environmental Engineering

2. CE 590 Hydrology Hydrologic principles Rainfall and runoff
Surface water &
ground water flow
Watersheds and
terrestrial inputs to
surface water bodies
Examples developed
from Wachusett
Reservoir
Web site:
Instructor: Paul Mathisen (with some assistance from others)

3. Last time ... Brief review Some clarifications on definitions
Quantitative analysis of rainfall
Rainfall measurement

4. Today ...
Review
Abstractions
Catchments
Runoff
Intro to infiltration

5. Water Budget E P I T R G

6. Rainfall / runoff
rainfall
depression
storage
overland flow
streamflow

7. Abstractions
Processes acting to reduce total ppt into effective ppt., which ultimately produces runoff
Interception
surface or depression storage
infiltration
evaporation
evapotranspiration

8. Interception Abstraction by vegitation or other surface cover
throughfall - part of ppt that reaches the ground
fx of storm, vegatative cover, season
amounts
light storms - 25 percent
moderate storms - 7 to 36 % in growing seas.
heavy & longer storms - small

9. Interception Components Interception storage - retained by foliage
evaporation loss
Where ..
L=interception loss (mm)
S = interception storage depth (mm)
K= evap.foliage surf/its horiz projection
E= evap. Rate (mm/hr)
t= storm duration
L= S + K E t

10. Surface/depression storage
Abstracted ppt is retained in puddles, ditches , and other depressions in surface
milder the relief, greater the depression storage
ex -
sand - 5mm - pervious urban mm
loam mm - paved areas mm
clay mm

11. Depression storage Quantification
lump in with other components such as infiltration
Peak flow correction factor (SCS TR55)
Vs = Sd (1 - e-kPe) where Vs is the equiv depth of depress storage (mm), Pe is precip excess, Sd is depression storage capacity (mm) [typically 10 to 50 mm], and k is a const

12. Infiltration Infiltration - seepage of rainfall into the ground
(contribution to groundwater) R
(in)
t (hrs)

13. Antecedent moisture
Infiltration has an important effect on abstracted ppt.
Infiltration is dependent on initial level of soil moisture, or antecedent moisture
Antecedent ppt index (API)
typical depletion rate
Ii = K I I-1
where Ii is index for day, Ii-1 is index for preceding day, and K= recession factor ( )

14. Antecedent Precipitation Index
High API, greater runoff
Alternative definitions
Antecedent moisture condition (AMC)
by SCS .. I(dry), II(avg), or III(wet)
SSARR - soil moisture index (SMI) - relates runoff to SMI and ppt. intensity
Runoff percent (R/P)*100

15. Surface runoff runoff depends on the antecedent ppt index
water flowing on earth’s surface
overland flow
flow in rills, gullies and streams

16. 3 components contribute to runoff
surface flow
interflow
groundwater flow

17. Surface runoff in catchments
Overland flow - sheet flow over land surf.
rill flow - small rivulets (conc of overland)
gully flow - runoff with erosive cabability
streamflow - concentrated runoff
river flow - confluence of streams

18. Catchment characteristics
area
Slope
Shape
Flow length
streams (location, density, nature)

19. Catchment area Drainage area catchment divide Estimate: Q peak=Can
leads to potential runoff volume
catchment divide
may differ from groundwater divide
Estimate: Q peak=Can
divide A

20. Catchment shape Form Compactness
Kf=A/L2 where Kf is form ratio, and L is catchment length
Compactness
Kc=0.282P/A1/2 where Kc is a compactness ratio, and P is the perimeter
Catchment response - conc. & timing of runoff
If Kf high, or Kc~1, then rapid runoff
Factors: relieve, veg. cover, drainage density, ..

21. Flow length - approximate equations
Approximate estimate
Lo=1/(2D)
where D=drainage density since overland flow length is approx 1/2 of mean distance between channels
More precise estimate
Lo=1/[2D{1-(Sc/Ss)}1/2]
where Sc is the mean channel slope and Ss is the mean surface slope

22. Linear measures Catchment length -length along principle watercourse
length to centroid (often est. as point to 2 or more bisecting straight lines
Order
0 = overland flow
1 = gets flow from 0 orders
2 = gets flow when 2 1st order streams combine
etc. G L Lc

23. Estimating the overland flow length
collector
collector
collector

24. Slope/catchment relief
Relief - an elevation difference
max relief = max elev diff between highest & lowest points
Relief ratio=max relief/longest straight lgth

25. Land surface slopes Often use grid methods to get slopes
hypsometric analysis = curve showning elevation of catchment above this elevation
Ei-Emin
Emax-Emin
Ai/Ac

26. Stream channels Slope S1 - from max and min elev’s
mountains
some tidal rivers
S1 - from max and min elev’s
S2 - const slope that makes shaded area above equal to shaded area below
S3 - equivalent slope -
break channel into subreaches & obtain slope E 2
Li up
Down
S3=
Distance
 (Li/Si 1/2)

27. Stream-types and baseflow
perennial
(always flowing)
flow maintained by “base flow” during dry weather
ephemeral
(only in response to ppt)
intermittent
(only in certain times of the year)

28. Hydrographs Characteristics of the hydrograph
Distribution of uniform rainfall

29. Runoff Volume or flow rate varies with timeQ
(cfs)
Volume or flow rate
varies with time
may express in flow per unit drainage area, per unit runoff depth, or per both
surface flow - direct runoff
also get indirect runoff
T (hr)

30. Runoff coefficients R=k P surface k urban residential: single 0.3
apts 0.5
commerial and industrial 0.9
forests
parks; farms
asphalt and pavement

31. First part of class ...
Review
Abstractions
Catchments
Runoff

32. Next ... Infiltration Definitions Physical aspects Simple models
Physically based models
measurement

33. 3 components contribute to runoff
surface flow
interflow
groundwater flow

34. Infiltration
Infiltration - process by which ppt is abstracted by seeping into soil below ground surface
define it by
an instantaneous infiltration rate (mm/hr)
an average infiltration rate (mm/hr)
Function of rainfall intensity, soil properties and soil type, surface conditions, vegitative cover, and water quality

35. Physical problem unsaturated Close-up flow view on next slide

36. Moisture in the unsaturated zone
air
water
water
moisture content
=Vwater/Vtot
porosity
n=Vw /Vt=Vvoid/Vtot

37. Capillarity & capillary fringe
capillary forces result in rise of fluid 2R  hc
(2 cos )
hc =
rwgR
In subsurface, we get a capillary fringe
Vadose/unsaturated zone
capillary fringe

38. Conditions in unsaturated zone
total potential or head
h = z +  where z is the elevation head and  is the pressure head (or moisture potential)
is a function of 
Darcy’s law applies:
q=K( dh/dz  

39. Controls on the Range of moisture content
Field capacity
maximum amount of moisture the soil structure can hold agains the force of gravity
upper level of moisture before rapid drainage
Wilting point
soil mosture at which permanent wilting of plants starts to occur

40. [NEXT TIME] Infiltration - quantitative approaches
Estimation from water balances
Horton Equation
Philip’s Equation
 Index
Green-Ampt model
Measurement