Runoff and Streamflow
Runoff/streamflow major focus in hydrology due to relation to:
 Floods: high runoff events --> flooding (need flood protection)
 Water supply: runoff can be captured in storage reservoirs for water
supply
P
Q
 Runoff in streams is the integration of several upstream processes in a
watershed (can be thought of as integrated “response” to storm events)
Recall: Watershed (or river basin) is defined based on topography, e.g.:
Based on a chosen
outlet point, can
trace out all points
that would ultimately
flow to the outlet.
Stream Network
Similarly, the stream network (within a basin) is defined as those points
where flow accumulation area is large, where accumulated flow area (Ac) is
the upstream area flowing to a certain point.
Map of log(Ac)
Note: Topographic
ridges have low Ac
(blue) and main
stream channel has
high Ac (red/yellow)
Together, the watershed consists of a well-defined area with interconnected
hillslopes and a channel network.
Runoff and Streamflow
The collection of hillslopes and channels generate runoff
from a given pixel and ultimately contribute to streamflow
Questions:
 What are mechanisms that generate runoff?
 When/why/where do they occur?
 How do they contribute to the overall flow in stream?
Two main classes of runoff:
 surface (overland) runoff (two mechanisms)
 subsurface runoff (two mechanisms)
Surface (overland) Runoff
Mechanism 1: Infiltration Excess Runoff (“Hortonian” runoff)
 Occurs when precipitation rate (P) exceeds infiltration rate (f) of soil
hillslope
P >f
*Saw this when
discussing
infiltration models
Occurs only during storm; often in localized low conductivity soils (P>K)
where ponding at surface occurs
Mechanism 2: Saturation excess overland flow (“Dunne” runoff)
 Occurs when groundwater table saturates soil from below (rising water
table); precipitation falls on saturated surface
Water table moves
up/down in response
to storm/inter-storm
periods
 Dynamics of water table leads to expanding/contracting “variable
contributing areas”
During/after big storm
1 week after storm
 Runoff occurs only during storm; in lowland areas near streams (i.e.
where shallow GW exists)
Subsurface Runoff
Mechanism 1: Interflow (perched stormflow)
 Lateral movement of water through unsaturated zone; often resulting
from temporary perched water table on low conductivity soil lens
 Generally small component of total runoff; due to unsaturated flow
velocities water may reach storm after storm ends
Mechanism 2: Baseflow (GW flow)
 Flux of water into streams from unconfined/confined aquifers; baseflow
responsible for perennial streams where flow exists during interstorm
periods
 Recharge and aquifer flow time scales such that flow reaching stream
occurs during interstorm period
interflow
baseflow
Snowmelt
Note: Snowmelt is an important contributor to runoff in many regions
(including ours). For snow, the melt output acts the same as a precipitation
input to the surface.
Hence snowmelt can ultimately lead directly to runoff via the following
mechanisms:
 Infiltration excess runoff (if soil beneath snowpack has low conductivity)
Saturation excess runoff (if soil beneath snowpack is saturated)
The subsurface mechanisms may also ultimately contribute snowmelt to
streamflow
The key point is that runoff generation may occur for long periods in the
absence of precipitation when snowmelt is involved.
Hydrographs
Streamflow at basin outlet is often measured; distribution vs. time
is called a “hydrograph”, e.g.:
Note: Time delay between precip.
onset and streamflow peak allows for
potential prediction
How much each mechanism contributes to overall streamflow depends on:
Individual storm (intensity/location/etc.)
 basin characteristics (topography, soil types, vegetation types, etc.)
For flood forecasting/estimating design flows, generally most interested in
“stormflow”= immediate runoff response to storm (baseflow generally does
not contribute much to stormflow
Goal: Build models for representing runoff processes in basin (i.e., given
measured P  predict Q).
[Note: The subject of hydraulics of flow once water is in channel is one of
the main topics of CEE 151.]
Figure 8.1.3a (p. 249)
(a) Separation of sources of streamflow on an idealized
hydrograph (from Mosley and McKerchan (1993)).
Basin-scale Rainfall-Runoff Modeling
Modeling approaches:
Empirical/Conceptual Models for Estimating Design Floods/Forecasting:
 usually treat basin as lumped unit
 use historical data to develop predictive tool
 systems (“black-box”) response approach
 make simplifying assumptions
 computationally efficient
Examples: SCS method, unit hydrograph method, etc.
Physically-based Distributed Hydrologic Modeling:
 account for physical processes distributed throughout basin
 explicitly model states/fluxes as function of space/time
 integrates hydrologic processes via mass/energy balance
 require distributed (in space) inputs
 computationally demanding
Examples: “Topmodel”, “tRIBS”, “Mike SHE”, etc.
Figure 8.2.1 (p. 252)
Concept of rainfall excess. The difference between the total
rainfall hyetograph on the left and the total rainfall excess
hyetograph on the right is the abstraction (infiltration).
Figure 8.2.3 (p. 253)
Storm runoff hydrographs. (a) Rainfall-runoff modeling; (b)
Steps to define storm runoff.
Unit H yd ro g raph E xamp le
2
A s torm of du ra ti o n D = 6 hr o cc urring u n ifor m ly o v er a 65 km wa ter sh ed y ield s
th e o u tlet h y drog rap h tabu la ted b elow (e. g. in h yd ro g raph .dat ).
3 -1
Ti m e
(hours)
Flo w (m s )
0
3
6
9
12
15
18
21
24
27
30
33
36
39
42
13. 3 1
33. 9 8
63. 7 1
82. 6 8
75. 6 1
58. 5 5
40. 4 9
31. 1 5
25. 7 7
22. 0 9
19. 2 6
16. 9 9
15. 2 9
14. 4 4
14. 1 6
1. D etermi n e the 6-hr U H fo r th is sto rm ev ent.
2. A 6 -hou r st o rm with an eff ect iv e ra infall of 7.5 cm oc cu rs. Pr ed ict th e
sto rmfl o w usi n g the UH m ethod. W h at is p eak fl o w and ti m e-to -p eak?
3. Pr ed ict th e st o rm flow from a 1 2-hou r st o rm, w h ic h can b e co nc eptual iz ed
as tw o con se cuti v e 6 -hr st o rm s that con tribu te 5 cm and 10 cm of d ir ect
runoff. What is p ea k flow and tim e-to -peak?
UH C ons truc tion
1. I d entify D -hour storm and esti
m at e b a sef low:
2. R em o v e ba sef low to de termi n e storm flow hy d rog raph:
3. In teg ra te und er cur v e to iden tify eff ecti v e r a infa ll fo r th is st o rm:
4. N o rm al iz e st o rm flow hy d rog raph by eff ect ive rainf a ll to get D -h r U H:
Stormf low Pr ed ict io n: 6 -hour st o rm w ith 7.5 cm of ef fe cti v e r a infal l.
Note: By construction the response time of
the hydrograph (e.g. 42 hours in this case)
remains unchanged for a D-hr event
Stormf low Pr ed ict io n: A 12 -ho u r sto rm (co n ceptu a liz ed a s two con se cuti v e 6 hr st o rm s w ith 5 cm and 10 cm of eff ect ive r a infa ll).
Note: As more complex responses are
“built-up” from multiple UHs, the
response time may change (e.g. in this
case 48 hours for a 2*D-hr storm)
Effective Rainfall
Being able to apply the UH method requires a mechanism for
estimating the effective rainfall (Peff).
This can be done using a physical model (i.e. attempting to predict
the infiltration/runoff partitioning).
Alternatively, it is often done empirically. One example is using
the Soil Conservation Service (SCS) method:
Peff 
( P  0.2V m ax )
2
P  0.8V m ax
where Peff in this equation is given in units of inches (as is the
measured rainfall P) and Vmax is the watershed storage capacity
(also in inches) which is estimated via:
V m ax 
1000
 10
CN
where CN is the so-called SCS curve number and can be
determined from tabulated values for different soil or land-use
types. The single curve number for a basin is often determined
from a weighted average of the curve numbers for different
soil/land-use types in the basin based on their relative areas.
Note: This type of method is highly empirical and will generally
introduce some error in the estimate of effective rainfall.
Figure 8.6.1 (p. 262)
Variables in the SCS method of rainfall abstractions; Ia = initial
abstraction, Pe = rainfall excess, Fa = continuing abstraction,
and P = total rainfall.
Figure 8.6.2 (p. 263)
Solution of the SCS runoff equations (from U.S. Department of
Agriculture Soil Conservation Service (1972)).
Table 8.7.3a (pp. 265-267)
Runoff Curve Numbers