Eagelson, P.S, 1991.

ATMOSPHERE

OCEANS CONTINENTS

1,338,000

12.9

47,660

97% 2.999%

0.001%

ANNUALGLOBAL

FLUX577

Precip.

Evap.

84%16%

77% 23%

-7% +7%

Global Runoff 7%

All Blue figuresin thousands ofkm3.

ATMOSPHERE

OCEANS CONTINENTS

1,338,000

12.9

47,660

484.7 92.3

444.3 132.7

40.4

WATER BALANCE APPROACH

Input = Output +/- Change in Storage

List List List

Volume of Store = 10 balls

Input = 1 ballper timeperiod

Output = 1ball per time

period

??

Input = Output ………. No change in Storage

WHAT ARE RESIDENCE TIMES?

Average number of samplings required

Volume of Store = 20 balls

Input = 1 ballper timeperiod

Output = 1ball per time

period

??

CHANGE VOLUME OF STORE

Volume of Store = 10 balls

Input = 2 ballsper timeperiod

Output = 2balls per time

period

????

CHANGE RATES OF INPUT AND OUTPUT

Oceans:

STORE

Precipitation

Runoff

Evaporation

Avg. Residence Time = Volume of Store/Average Flux [T] = [L3] / [L3T-1]

2760 yr = 1,338,000,000 (km3)/ 484,680 (km3 yr-1)

Basic time step over which we are completing the accounting.

Avg. Residence Time = Volume of Store/Average Flux [T] = [L3] / [L3T-1]

Volume = 47,659,600 km3

Input rate = Precipitation (23%)Output rate = Evaporation (16%) + Runoff (7%)

Average rate = (23 + (16+7))/2 = 23% of 577,000132,710 km3 per year

Avg. Residence = 47,659,600 / 132,710 = 359 years

Continents:

STORE

Precipitation

Runoff

Evaporation

Atmosphere:

STORE

Precipitation

Evaporation

Precipitation

Evaporation

ContinentsOceans

Avg. Residence Time = Volume of Store/Average Flux [T] = [L3] / [L3T-1]

Volume = 12,900 km3

Input rate = Evap (oceans) (84%) + Evap (continents) (16%)Output rate = Prec. (oceans) (77%) + Prec. (continent) (23%)Average rate = ((84+16) + (77 +23))/2 = 100% of 577,000

577,000 km3 per year

Avg. Residence = 12,900 / 577,000 = 0.02 yrs (7.3 days)

1. Evaporation driven by energy from the Sun, raises water vapor into the atmosphere, renewing the potential energy of the water, and removing most of the dissolved materials inn the water

2. Rising air cools and vapor condenses, releasing energy to atmosphere and forming clouds. Under the correct conditions, the water drops formed will descend under the influence of gravity (kinetic energy) onto the landscape.

3. Water moving over and through the landscape uses both its kinetic energy and propensity to dissolves chemicals, to shape the landscape. Rivers, glaciers, caves, groundwater etc.

4. This kinetic and chemical energy given to the water by the Sun, through the process of evaporation is lost once it reaches sea level or some local “datum”, like a lake.

GLOBAL SIGNIFICANCE OF RESIDENCE TIMES

CHANGING THE TIME SCALE OF THE STUDY

Annual S = 0 (No huge lakes or ice sheets in Florida)

Monthly S ~ Groundwater

Weekly S ~ Lakes, Swamps

Daily S ~ Rivers

Hourly S ~ Soil Moisture

Volume

(km3x103)

Average Residence

Times STORES Oceans Land Snow and ice Groundwater Freshwater lakes Inland Seas Soil moisture Rivers Atmosphere Biosphere

1,338,000.0 24,064.0 23,400.0 91.0 85.0 17.5 2.1 12.9 1.1

~ 4000 years days -10,000 yrs2 weeks-10,000 yrs~ 10 yrs days- year~ 2 weeks ~ 10 days ~ 1 week

The shorter the smaller the time step (hour, day, month, year) over which you are accounting, the more stores need to be considered

Time and Space scales of studies usually related. Small area , short time step, large area, along time step

WHICH STORES CONSIDERED WHEN?

Unless huge lakes or glaciers present

ST. MARY’S RIVER, SW. PIER, MICHIGANIMPACT OF LONG-LASTING STORE

Stow, Lamon, Kratz and Sellinger, 2008. Eos, 89, 41, p. 389-390

Continent

Precipitation (mm)

Evaporation(mm)

Runoff (mm)

Europe

790

507

283

Asia

740

416

324

Africa

740

587

153

North America

756

418

339

South America

1600

910

685

Australasia

791

511

280

Antarctica

165

0

165

Source: Shiklomanov (1990)

WATER BALANCE EQUATIONON A CONTINENTAL SCALE

Input = Output +/- Change in StoragePrecipitation = { Evaporation + Runoff } +/ Change in Storage

Assume ΔS 0 in Long Run

Source: Shiklomanov (1990)

Data provided by Mario Mighty

REGION

Mean AnnualRunoff (mm)

Average Coefficient

Of Variation

World 610 0.43North Africa 200 0.31South Africa 210 0.78Asia 620 0.38N. America 1050 0.35S. America 670 0.35Europe 460 0.29South Pacific 1290 0.25Australia 420 0.70

MEASURES OF GLOBAL VARIABILITY IN FLOW

.

Source: McMahon, T. A., B. L. Finlayson, A. T. Haines, and R. Srikanthan,1992: Global Runoff—Continental Comparisons of AnnualFlows and Peak Discharges. Catena Verlag Paperback, 166 pp

Coefficient of Variation = standard deviation/mean

Big value represents relatively high variability from year to year (inter-annual variability)

REGION

Mean AnnualRunoff (mm)

Average Coefficient

Of Variation

Average ratio of largest annual

flow to the annual mean

World 610 0.43 2.2North Africa 200 0.31 1.8South Africa 210 0.78 3.5Asia 620 0.38 2.0N. America 1050 0.35 2.0S. America 670 0.35 2.1Europe 460 0.29 1.7South Pacific 1290 0.25 1.5Australia 420 0.70 3.1

MEASURES OF GLOBAL VARIABILITY IN FLOW

.

Source: McMahon, T. A., B. L. Finlayson, A. T. Haines, and R. Srikanthan,1992: Global Runoff—Continental Comparisons of AnnualFlows and Peak Discharges. Catena Verlag Paperback, 166 pp

Ratio of the discharge of the biggest flow in a year to the average flow in the entire year.

Big values mean that the biggest flow with in a year (intra-annual) tend to be extremely large in comparison to the other flow

REGION

Mean AnnualRunoff (mm)

Average Coefficient

Of Variation

Average ratio of largest annual

flow to the annual mean

Mean Annual Flood

(m3s-1km-2)

Coefficient of variation of log

of annual floods

World 610 0.43 2.2 0.44 0.28North Africa 200 0.31 1.8 0.05 0.18South Africa 210 0.78 3.5 0.34 0.46Asia 620 0.38 2.0 0.30 0.24N. America 1050 0.35 2.0 0.85 0.25S. America 670 0.35 2.1 0.16 0.14Europe 460 0.29 1.7 0.12 0.17South Pacific 1290 0.25 1.5 1.21 0.22Australia 420 0.70 3.1 0.45 0.45

MEASURES OF GLOBAL VARIABILITY IN FLOW

.

Source: McMahon, T. A., B. L. Finlayson, A. T. Haines, and R. Srikanthan,1992: Global Runoff—Continental Comparisons of AnnualFlows and Peak Discharges. Catena Verlag Paperback, 166 pp

Year0 20 40 60 80 100 120 140 160 180 200

Annual Precipitation

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120 140 160 180 200

Annual Evaporation (m

m)

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120 140 160 180 200

Annual Hydrologic Flux (m

m)

0

200

400

600

800

1000

1200

1400

PrecipitationEvaporation

P - E = R

P

E

0 20 40 60 80 100 120 140 160 180 200

Annual Runoff (m

m)

0

200

400

600

800

1000

1200

1400

Higher Mean; Higher Variability

Lower Mean; Lower Variability Lower Mean; High Variability

R = P - E

P

E R

Land Use Land Cover

Simulated Year0 50 100 150 200

Sim

ulated Annual F

lux (mm

)

0

200

400

600

800

1000

1200

1400

1600

1800

PrecipitationRunoff

Evergreen ScenarioMean = 800mm; St. Dev. = 150mm; C. of V. = 18.75%ET = 500mmMean = 300mm; St. Dev. = 150mm; C. of V. = 50.00%

POTENTIAL ROLE OF VEGETATION TYPE

C. of. V. = (St. Dev./ Mean)*100Figures based on Australian conditions

Higher ET as trees do not lose leaves

Simulated Year

0 50 100 150 2000

200

400

600

800

1000

1200

1400

1600

1800Deciduous ScenarioMean = 800mm; St. Dev. = 150mm; C. of V. = 18.75%ET = 320 mmMean = 480mm; St. Dev. = 150mm; C. of V. = 31.25%

Sim

ulated Annual Flux (mm

)

Lower ET as trees lose

leaves

JONGLEI CANAL

JONGLEI = DRAINING THE EVERGLADES?

Pielke 2001

BIOTIC PUMP

Condensation

Water as liquid

Water as vapor

Upward motionCooling

Decline in atmosphericPressure as Water Vapor leaves column of gasses

INLAND

Precipitation Declining Exponentially

BIOTIC PUMP

Condensation

Water as liquid

Upward motionCooling

Decline in atmosphericPressure as Water Vapor leaves column of gasses

PressureGradient

BIOTIC PUMP

Condensation

Water as liquid

Water as vapor

Upward motionCooling

Decline in atmosphericPressure as Water Vapor leaves column of gasses