ENVI 412ENVI 412Hydrologic Losses and Hydrologic Losses and

Radar MeasurementRadar MeasurementDr. Philip B. BedientDr. Philip B. Bedient

Rice UniversityRice University

Qe = energy used for evaporation

Qh = sensible heat

Q = stored energy

Qv = advected energy

QN = net radiation absorbed by water body

Lake Energy BudgetLake Energy Budget

• Function of wind speed, T, and      humidity gradient

•  Energy source - solar energy

• Mass transfer, energy budget,     and pan evaporation

• Penman’s combined (1948)

Lake EvaporationLake Evaporation

E = es - ea (a + bu)

Where E = evaporation (cm/day)

es = Sat vapor pressure (T)

ea = Vapor pres at fixed z

u = wind speed in m/sec

a,b = constants

Mass TransferMass Transfer

Shallow Lake Evap Shallow Lake Evap (Kohler, 1955(Kohler, 1955))

Evaporation PansEvaporation Pans

• Anemometer - wind

• Rain Gage - precip.

• Pan for water - evap

• Level measured daily

• Refilled as necessary

Soil Moisture CycleSoil Moisture Cycle Very Complex Soil Physics

• Autumn - rainfall recharge

• Winter - max soil storage

• Spring - some evap loss

• Summer - most depleted                     condition

Surface Flow Surface Flow DistributionDistribution

Horton’s Infiltration ConceptHorton’s Infiltration Conceptf(t) = Rate of water loss into soilf(t) = Rate of water loss into soil

f = fc + (fo - fc) exp (-kt)

fc = final rate value

fo = initial rate value

K = decay rate

Can integrate to get

F(t) = Vol of infiltration

Horton’s EqnHorton’s Eqn

index Methodindex Method• Assumes constant rate   over time of rainfall

• Volume above line is   DRO

• Volume below line is F(t)

• Trial and error computed

Example of Example of IndexIndex

DRO

VOL Infiltration F(t)

DRO

Example of Example of IndexIndexAssume 4.9 in of DRO from a 560 acre BasinSet up a general Eqn for indexindex

2(1.4 - +3(0.7-

Find by trial and error by assuming a value and solving - try = 1.5 in/hrAnd it only accounts for 0.8 x 3 = 2.4 in of DRO0.5 in/hr yields 9.0 in of DRO - too much DRO

Try 1.0 in/hr or 2(.4) +3(1.3)+2(.1) = 4.9 inches

Harris Gully drainsRice/TMC Area

Brays Bayou and Harris Brays Bayou and Harris GullyGully

Harris Gully: Harris Gully: 4.5 sq. mi.4.5 sq. mi.Study Area: Study Area: 8 sq. mi.8 sq. mi.Brays Bayou: Brays Bayou: 129 sq. mi.129 sq. mi.

TMC

Existing Minor Drainage NetworkExisting Minor Drainage Network

2-15’x15’

2-11.5’x15’

7.5’x11’

90”

60”

72”

6.5’

x10’

66”

60”

60”

72”

60”6.

5’x1

0’

66”

72”

96”

114”

54”

84”

Hermann Park

TMC

Rice

High Water Inundation in Rice/TMC Basin Area

Brays Bayou at Main Brays Bayou at Main St BridgeSt Bridge

• Measure v at 0.2 and 0.8 of depth

• Average v and multiply by W*D

• Sum up across stream to get total Q

Stream Cross-Section for QStream Cross-Section for Q

• Plot of z vs. Q

• Determined from stream    measurements of V

• Unique for each stream

• Changes with development

• Available for all USGS gages

Typical Rating Curve for StreamTypical Rating Curve for Stream