LUMPED HYDROLOGIC MODELS Before GEO3280! BLACK BOX U N IT H YD R O G RAPH THEO RY Input,I Output,O Transfer Function O t = f{I t ,I t-1 ,I t-1 , ...... ,I t-n } R ainfall H yetograph D rainage Basin Discharge H ydrograph Time R ainfall 0 10 20 Time Discharge 0 10 20 I O
LUMPED HYDROLOGIC MODELS. BLACK BOX. Before GEO3280!. UNIT HYDROGRAPH THEORY. Sherman - 1932 Horton - 1933 Wisler & Brater - 1949 - “the hydrograph of surface runoff resulting from a relatively short, intense rain, called a unit storm.” - PowerPoint PPT Presentation
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UNIT HYDROGRAPH THEORY
Input, I Output, OTransferFunction
Ot = f{It,It-1,It-1, ......, It-n}
RainfallHyetograph
DrainageBasin
DischargeHydrograph
Time
Rai
nfal
l
0
10
20
TimeD
isch
arge
0
10
20 IO
LUMPED HYDROLOGIC MODELS
Before GEO3280!
BLACK BOX
UNIT HYDROGRAPH THEORY
Sherman - 1932Horton - 1933Wisler & Brater - 1949 - “the hydrograph of
surface runoff resulting from a relatively short, intense rain, called a unit storm.”
The runoff hydrograph may be “made up” of runoff that is generated as flow through the soil (Black, 1990).
THE TIME BASE OF EACHRESPONSE REMAINS AT 7MINUTES, REGARDLESS OF WHETHER THE IMPUT IS 0.22 OR 1 mm/minutes AS IN THIS MORE COMPLEX EVENT
HOW CAN A UNIT HYDROGRAPHBE DERIVED IN REALITY?
Days since April 30, 1969
0 30 60 90 120 150 180 210 240 270 300 330 360
Mea
n D
aily
Dis
char
ge (m
3 s-1
)
0
20
40
60
80
100
120
140
May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr
DAILY DISCHARGE AT ELECTRIONA
1. Select fairly clearly defined single events from available records
Avoid this sort of complex response where it is hard to separate one storm from the next
Days since April 30, 1969.
205 210 215 220 225
Mea
n D
aily
Dis
char
ge (m
3 s-1
)
0
20
40
60
80
100
120
140Dec. 1Nov 25 Dec. 13
2. Extract observed hydrograph
Days since April 30, 1969.
205 210 215 220 225
Mea
n D
aily
Dis
char
ge (m
3 s-1
)
0
20
40
60
80
100
120
140Dec. 1Nov 25 Dec. 13
3. Separate out the “Direct Runoff” response from the groundwater or baseflow.
GROUNDWATER?
Direct RunoffHydrograph
1. Define point at which flood hydrograph rises2. Superimpose Master Recession curve of declining limb.3. Identify “Inflection Point” at which baseflow is dominant process4. Join Time of Rise to Inflection Point with straight line5. Graphically separate Direct Runoff Hydrograph from Base Flow
HYDROGRAPH SEPARATION
Time (T)
0 10 20 30 40 50
Sta
ge (L
)
0
20
40
60
80
100
120
140
160
Time ofRise
InflectionPoint
MasterRecession
Straight Line
DRH
BASE FLOW
Days since April 30, 1969
0 30 60 90 120 150 180 210 240 270 300 330 360
Mea
n D
aily
Dis
char
ge (m
3 s-1
)
0
20
40
60
80
100
120
140
May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr
DAILY DISCHARGE AT ELECTRIONAHOW TO COMPUTE MASTER RECESSION CURVE
CREATING MASTER RECESSION CURVE
Time (T)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sta
ge (L
)
15
20
25
30
35
40
Master Recession
IndividualRecession
Curves
4. Determine the quantity and temporal distribution of “Effective Rainfall” that gave rise to that Direct Runoff Hydrograph
As is assignments and lectures, this involves consideration of water lost to interception, depression storage and infiltration.
• This S-curve showing the response to a very large number of sequential 37.6mmm in 90 events would be the same no matter what time we actually started the sequence, at time 0, or after 5 minutes, or 60 minutes.
• Imagine that we set such a sequence running at time 0, and a second identical sequence running at time 60 minutes.
• We have two s-curves offset by 60 minutes.• The difference in discharges between the two S-
curves, measured at any time, represents the response of the first S-curve, that the second one hasn’t yet experienced because of the 60 minute shift.
• This difference therefore represents the “missing” rainfall in that 60 minute period, or the 37.6mm for 60 minutes hydrograph.
60 HERE IS OUR BASIC “BUILDING BLOCK”, DERIVED WITHOUT HAVING TO GO THROUGH THE EXERCISE OF ISOCHRONES ETC., BUT WHICH CAN BE USED TO FORECAST RESPONSES TO STORM DELIVERING VARYING QUANTITIES OF WATER IN DIVERSE PATTERNS OVER TIME.