Basic HydrologyBasic Hydrology

Precipitation - Runoff RelationsPrecipitation - Runoff Relations

Watershed MorphologyWatershed Morphology

Watershed morphologyWatershed morphology

Morphological properties of a watershed Morphological properties of a watershed can affect the shape of the storm can affect the shape of the storm hydrograph and the delivery of sediment to hydrograph and the delivery of sediment to the main channelthe main channel

Various parameters can be calculated to Various parameters can be calculated to describe the channel network and the describe the channel network and the physical characteristics of the watershedphysical characteristics of the watershed– these all affect hydrograph shapethese all affect hydrograph shape

Basin sizeBasin size Delineate watershed according to the height of Delineate watershed according to the height of

land that separates water draining to the point of land that separates water draining to the point of interest from water that drains to adjacent basinsinterest from water that drains to adjacent basins

Watershed area (kmWatershed area (km22, ha), ha)– smaller watersheds tend to have a more peaked smaller watersheds tend to have a more peaked

hydrograph, more intermittent water supplyhydrograph, more intermittent water supply– larger watersheds have flatter hydrographs because larger watersheds have flatter hydrographs because

larger channel network can store more waterlarger channel network can store more water

Watershed land slopeWatershed land slope The slope of the sides of a watershed govern how The slope of the sides of a watershed govern how

fast water will drain to the channelfast water will drain to the channel– steep slopes - peaked hydrographsteep slopes - peaked hydrograph

– gentle slopes - flat hydrographgentle slopes - flat hydrograph

This is simply the average gradient of hillslopes - This is simply the average gradient of hillslopes - slope is vertical over horizontal distance, derived slope is vertical over horizontal distance, derived from topographic mapsfrom topographic maps

An objective repeatable formula for land slope:An objective repeatable formula for land slope:

SL C I

A

( )( . .) where L is the total length of contours, C.I. is the contour interval and A is the watershed area.

Area - elevation curveArea - elevation curve Area - elevation is critical for modeling snowmeltArea - elevation is critical for modeling snowmelt Can be useful in determining precipitation Can be useful in determining precipitation

distribution from a ppt. - elevation relationshipdistribution from a ppt. - elevation relationship

1620 1680 1740 1800 1860 1920 1980 2040Elevation (metres above sea level)

0

50

100

Per

cen

t o

f A

rea

At

Or

Ab

ove

G

iven

Ele

vati

on

240 Creek

median elevation

Matching area- and ppt- elevation Matching area- and ppt- elevation relationships can be used to compute relationships can be used to compute

basin average precipitationbasin average precipitation

1620 1680 1740 1800 1860 1920 1980 2040Elevation (metres above sea level)

0

50

100

Per

cen

t o

f A

rea

At

Or

Bel

ow

G

iven

Ele

vati

on

700

750

800

Mea

n A

nn

ual

Pp

t. (

mm

)

Precipitation-elevation relationship

Area - elevationrelationship

Indices of basin shapeIndices of basin shape

Form factorForm factor

– elongated - F.F. is low, flatter hydrographelongated - F.F. is low, flatter hydrograph– squatty - F.F. is high, peaked hydrographsquatty - F.F. is high, peaked hydrograph

F FAverage Width

Axial Length. .

.

.

Strahler’s order of streamsStrahler’s order of streams

A headwater stream with no A headwater stream with no tributaries is a first order tributaries is a first order streamstream

When two first order When two first order streams join they form a streams join they form a second order streamsecond order stream

Two second order streams Two second order streams form a third order streamform a third order stream

etc.etc.

1

12

21

1 1

2 1

123

31

Bifurcation ratioBifurcation ratio BBii = ratio of # first order to # second order streams = ratio of # first order to # second order streams

If watershed is > 2nd order:If watershed is > 2nd order:

1 2 3Stream Order u

0.5

1.0

1.5

2.0

2.5

log

(#

Str

eam

s o

f O

rder

u)

log (Nu) = 2.77 -0.693 (u)

Plot log Nu vs. u as shown, Bi is the anti-logof the slope of the regression line. For the example given, Bi = anti-log(0.693) = 4.93

Effect of BEffect of Bii on hydrograph shape on hydrograph shape

Elongated basinBi is high (=13)flat hydrograph due to even supply of water to channel

Rounder basinBi is low (= 4.9)peaked hydrograph becauseflow is concentrated

Assuming uniform ppt.distribution,all other factorsbeing equal...

Channel slope and profileChannel slope and profile Channel slope plays a role in the shape of the Channel slope plays a role in the shape of the

hydrographhydrograph– the steeper the slope, the more peaked the hydrograph the steeper the slope, the more peaked the hydrograph

0 500 1000 1500 2000 2500 3000Distance from the W eir (m )

1600

1650

1700

1750

Ele

vati

on

Ab

ove

Sea

Lev

el (

m)

240 Creek channel profile

mean channel slope

Determining mean channel slopeDetermining mean channel slope Each tributary channel in a watershed has its own Each tributary channel in a watershed has its own

profileprofile– commonly done only for the main channelcommonly done only for the main channel

Calculate the slope of a line drawn such that the area Calculate the slope of a line drawn such that the area under the line = the area under the main channel profileunder the line = the area under the main channel profile

An index of channel slope An index of channel slope

can be calculated from the can be calculated from the

slopes of n equal channel slopes of n equal channel

segments:segments: Ss

nc

ii

n

1

2

Drainage densityDrainage density Drainage density is determined by measuring the Drainage density is determined by measuring the

total length of all streams on a map and dividing total length of all streams on a map and dividing by the watershed areaby the watershed area– units of km/kmunits of km/km22

– for comparative purposes, you must use maps with the for comparative purposes, you must use maps with the same level of detail for all basins of interestsame level of detail for all basins of interest

Effect on hydrograph shape:Effect on hydrograph shape:– high Dhigh Ddd - peaked hydrograph - peaked hydrograph

– low Dlow Ddd - flat hydrograph - flat hydrograph

Valley flatValley flat

Area adjacent to stream or river floodplain Area adjacent to stream or river floodplain where the slope is < 8%where the slope is < 8%

Buffers the stream channel from landslides Buffers the stream channel from landslides which may run out on the valley flat before which may run out on the valley flat before depositing sediment in the channel.depositing sediment in the channel.

Calculate the length of mainstem channel Calculate the length of mainstem channel that has a valley flat, express as a proportion that has a valley flat, express as a proportion of the length of the mainstem channel.of the length of the mainstem channel.

Other factorsOther factors

LithologyLithology– importance: can govern slope stability, bedrock importance: can govern slope stability, bedrock

leakage, permeabilityleakage, permeability Presence or absence of glaciersPresence or absence of glaciers

– will govern timing and mangitude of peak will govern timing and mangitude of peak runoffrunoff

Land use...Land use...

Precipitation - runoffPrecipitation - runoff Methods have been developed to predict Methods have been developed to predict

characteristics of runoff as a function of precipitation characteristics of runoff as a function of precipitation characteristicscharacteristics– volume of runoffvolume of runoff

» seasonalseasonal» annualannual» based on seasonal or annual total precipitationbased on seasonal or annual total precipitation

– peak flowpeak flow» annual peak flow - e.g., snowmelt peak (interior), a function of annual peak flow - e.g., snowmelt peak (interior), a function of

peak snow accumulationpeak snow accumulation» storm peaks - a function of rainfall intensitystorm peaks - a function of rainfall intensity

Runoff coefficientRunoff coefficient

Simplest form of ppt - runoff relationSimplest form of ppt - runoff relation– ratio of total streamflowratio of total streamflow

over total precipitationover total precipitation Runoff coefficient can be assessed Runoff coefficient can be assessed

annually, seasonally or monthly depending annually, seasonally or monthly depending on purposeon purpose

Should be a characteristic quantity of a Should be a characteristic quantity of a watershed assuming no change in land usewatershed assuming no change in land use

RQ

P

Calculating rainfall - runoff ratioCalculating rainfall - runoff ratioExample: 240 Creek, UPCExample: 240 Creek, UPC

Water year Sept - AugWater year Sept - Aug

Q P R1987-88 236 640 0.371988-89 283 713 0.401989-90 522 859 0.611990-91 425 738 0.58

Since R is related to P or Q, a better way to get the ralationshipis to plot Q vs. P and fit a regression line.

Runoff coefficient 240 CreekRunoff coefficient 240 Creek

0 200 400 600 800 1000Total Annual Precipitation (m m)

0

200

400

600

To

tal A

nn

ual

Str

eam

flo

w (

mm

)

Q = 1.163 (P) - 474R squared = 83.5%

Runoff threshold: water loss to ET

Runoff coefficientincreases withtotal precip.

Spring-summer runoff vs snowpackSpring-summer runoff vs snowpack This can be more meaningful than a runoff This can be more meaningful than a runoff

coefficient - e.g., 240 Creek, 1985-91coefficient - e.g., 240 Creek, 1985-91

120 160 200 240 280 320Snowpack, April 1 (m m)

100

200

300

400

500

To

tal A

pri

l - J

uly

Str

eam

flo

w (

mm

)

Q = 1.355 (S)R squared = 99.6%

1990 - rain on snow late May

Predicting spring runoff in Predicting spring runoff in interior watershedsinterior watersheds

Unlike runoff coefficient relationship, relationship Unlike runoff coefficient relationship, relationship between spring - summer runoff and peak between spring - summer runoff and peak snowpack passes through the originsnowpack passes through the origin– this shows that virtually all the snowpack contributes to this shows that virtually all the snowpack contributes to

spring - summer runoffspring - summer runoff

Slope > 1: relationship is a very good predictor of Slope > 1: relationship is a very good predictor of snowmelt runoff but doesn’t account for snowmelt runoff but doesn’t account for precipitation that occurs after April 1 - doesn’t precipitation that occurs after April 1 - doesn’t work for unusual conditions such as rain-on-snowwork for unusual conditions such as rain-on-snow

Precipitation & temperaturePrecipitation & temperature

Jan Feb M ar Apr M ay Jun Jul Aug Sep O ct N ov D ec

0

40

80

120

To

tal M

on

thly

Pre

cip

itat

ion

(m

m)

-20

-10

0

10

20

Mea

n M

on

thly

Tem

per

atu

re (

deg

C)

Total M onthly P recip itationM ean M onthly M ax Tem peratureM ean M onthly M in Tem perature

Use of snow course data to Use of snow course data to predict runoffpredict runoff

For an interior watershed, snow course data should For an interior watershed, snow course data should provide a better measure of runoffprovide a better measure of runoff

Used to predict inflows to reservoirs, potential floodsUsed to predict inflows to reservoirs, potential floods For a coastal watershed, rainfall data is needed, but For a coastal watershed, rainfall data is needed, but

annual runoff coefficient is probably relatively annual runoff coefficient is probably relatively meaninglessmeaningless– monthly runoff ratio, averaged over several years monthly runoff ratio, averaged over several years

may be usefulmay be useful– expected to be much higher than for interior w/sexpected to be much higher than for interior w/s

Effect of antecedent conditions Effect of antecedent conditions on rainfall - runoff relationon rainfall - runoff relation

The amount of soil moisture prior to a storm will The amount of soil moisture prior to a storm will affect the runoff ratio for that storm, and will affect affect the runoff ratio for that storm, and will affect the shape of the hydrographthe shape of the hydrograph– wet antecedent conditions lead to more runoff wet antecedent conditions lead to more runoff

per unit ppt., dry antecedent conditions result in per unit ppt., dry antecedent conditions result in more of the input water going to basin rechargemore of the input water going to basin recharge

– antecedent conditions are a function of ET and antecedent conditions are a function of ET and soil/groundwater drainage.soil/groundwater drainage.

Not always possible to quantify these factors...Not always possible to quantify these factors...

Antecedent Precipitation IndexAntecedent Precipitation Index API is a method of accounting for daily API is a method of accounting for daily

changes in water balance.changes in water balance.– API is a decay factor - each days API is a fixed API is a decay factor - each days API is a fixed

percentage of the previous day’s API (e.g., percentage of the previous day’s API (e.g., 90%), plus daily rainfall and/or snowmelt90%), plus daily rainfall and/or snowmelt

– runoff coefficient will vary according to the runoff coefficient will vary according to the API:API:

» the higher the API, the higher the runoff coefficientthe higher the API, the higher the runoff coefficient

API for Russell Creek Jan 1992API for Russell Creek Jan 1992

0 10 20 30

0

40

80

Dai

ly R

ain

fall

(mm

)

0

100

200A

PI (

mm

)

API for Russell Creek Jul 1992API for Russell Creek Jul 1992

0 10 20 30

0

4

8

Dai

ly R

ain

fall

(mm

)

0

20

40A

PI (

mm

)

Synthetic unit hydrographSynthetic unit hydrograph It has been determined empirically that the It has been determined empirically that the

parameters of the unit hydrograph - lag parameters of the unit hydrograph - lag time, peak and time base - can be time, peak and time base - can be determined from basin morphologydetermined from basin morphology

lag time: (hours)lag time: (hours)

t C LLp t C0 3.

LC

L = length of mainchannelCt range 1.8 to 2.2

Time base: (in days)Time base: (in days)

Peak flow: various formulae have been advanced to Peak flow: various formulae have been advanced to predict peak flowpredict peak flow– Rational formula: QRational formula: Qpp = RIA = RIA

where R = runoff coefficient, I = rainfall intensity and A where R = runoff coefficient, I = rainfall intensity and A = basin area= basin area

– Other formulae: Other formulae:

Tt p 3

3

24

QC A

tp

p

p

Cp range 0.15 to 0.19 per mmwith Q in m3/s, A in km2

Russell Creek 1991 - 92Russell Creek 1991 - 92

0 20 40 60 80 100Max 24-hour Storm Intensity (m m)

0

10

20

30

40

Pea

k F

low

(m

3/s)

R2 = 83.8%

Peak = 0.342 (24hr) + 1.17 BaseR2 = 92 %