ce 394k.2 hydrology, lecture 3 water and energy flow

CE 394K.2 Hydrology, Lecture 3Water and Energy Flow

• Literary quote for today:

“If I should die, think only this of me; That there's some corner of a foreign field That is for ever England. ”

Rupert Brooke, English poet, “The Soldier”(he died in WWI and is buried on the island of Skyros in Greece)

Watershed system

Hydrologic System

Take a watershed and extrude it vertically into the atmosphereand subsurface, Applied Hydrology, p.7- 8

A hydrologic system is “a structure or volume in space surrounded by a boundary, that accepts water and other inputs, operates on them internally, and produces them as outputs”

System Transformation

Transformation EquationQ(t) = I(t)

Inputs, I(t) Outputs, Q(t)

A hydrologic system transforms inputs to outputs

Hydrologic Processes

Physical environment

Hydrologic conditions

I(t), Q(t)

I(t) (Precip)

Q(t) (Streamflow)

NWISNWIS

ArcGISArcGIS

ExcelExcel

NCARNCAR

UnidataUnidata

NASANASAStoretStoret

NCDCNCDC

AmerifluxAmeriflux

MatlabMatlabAccessAccess JavaJava

FortranFortran

Visual BasicVisual Basic

C/C++C/C++

Some operational services

CUAHSI Web ServicesCUAHSI Web Services

Data SourcesData Sources

ApplicationsApplications

Extract

Transform

Load

http://www.cuahsi.org/his/

http://www.cuahsi.org/his



Concept of Transformation

• In hydrology, we associate transformation with the connection between inflow and outflow of water, mass, energy

• In web services, we associate transformation with flow of data (extract, transform, load)

• Can we link these two ideas?

Stochastic transformation

System transformationf(randomness, space, time)

Inputs, I(t) Outputs, Q(t)

Ref: Figure 1.4.1 Applied Hydrology

How do we characterizeuncertain inputs, outputsand system transformations?

Hydrologic Processes

Physical environment

Hydrologic conditions

I(t), Q(t)

Questions for discussion on Tuesday (from Chapters 1 and 2 of Text)

• How is precipitation partitioned into evaporation, groundwater recharge and runoff and how does this partitioning vary with location on the earth?

• Can a closed water balance be developed using discrete time rainfall and streamflow data for a watershed?

• How do the equations for velocity of water flow in streams and aquifers differ, and why is this so?

• How is net radiation to the earth’s surface partitioned into latent heat, sensible heat and ground heat flux and how does this partitioning vary with location on the earth?

Global water balance (volumetric)

Land (148.7 km2)(29% of earth area)

Ocean (361.3 km2)(71% of earth area)

Precipitation100

Evaporation61

Surface Outflow38

Subsurface Outflow1

Precipitation385

Evaporation424

Atmospheric moisture flow 39

Units are in volume per year relative to precipitation on land (119,000 km3/yr) which is 100 units

Global water balance (mm/yr)

Land (148.7 km2)(29% of earth area)

Ocean (361.3 km2)(71% of earth area)

Precipitation800

Evaporation484

Outflow316

Precipitation1270

Evaporation1400

Atmospheric moisture flow 316

What conclusions can we draw from these data?

Applied Hydrology, Table 1.1.2, p.5

Digital Atlas of the World Water Balance(Precipitation)

http://www.crwr.utexas.edu/gis/gishyd98/atlas/Atlas.htm

Continuity equation for a watershed

I(t) (Precip)

Q(t) (Streamflow)dS/dt = I(t) – Q(t)

dttQdttI )()(Closed system if

Hydrologic systems are nearly alwaysopen systems, which means that it isdifficult to do material balances on them

What time period do we chooseto do material balances for?

Continuous and Discrete time data

Continuous time representation

Sampled or Instantaneous data(streamflow)truthful for rate, volume is interpolated

Pulse or Interval data(precipitation)truthful for depth, rate is interpolated

Figure 2.3.1, p. 28 Applied Hydrology

Can we close a discrete-time water balance?

Surface and Groundwater Flow Levels are related to Mean Sea Level

Earth surface

EllipsoidSea surface

Geoid

Mean Sea Level is a surface of constant gravitational potential called the Geoid

http://www.csr.utexas.edu/ocean/mss.html

Vertical Earth Datums

• A vertical datum defines elevation, z• NGVD29 (National Geodetic Vertical

Datum of 1929)• NAVD88 (North American Vertical

Datum of 1988)• takes into account a map of gravity

anomalies between the ellipsoid and the geoid

Energy equation of fluid mechanics

gV2

21

fhgVyz

gVyz

22

22

22

21

11

Datum

z1

y1

bed

water surface

energy grade line

hf

z2

y2

gV2

22

L

How do we relate friction slope, Lh

S ff to the velocity of flow?

Open channel flowManning’s equation

2/13/249.1fSR

nV

Channel Roughness

Channel Geometry

Hydrologic Processes(Open channel flow)

Physical environment(Channel n, R)

Hydrologic conditions(V, Sf)

Subsurface flowDarcy’s equation

fKSAQq

Hydraulic conductivity

Hydrologic Processes(Porous medium flow)

Physical environment(Medium K)

Hydrologic conditions(q, Sf)

Aq q

Comparison of flow equations

2/13/249.1fSR

nAQV

fKSAQq

Open Channel Flow

Porous medium flow

Why is there a different power of Sf?

Heat energy

• Energy– Potential, Kinetic, Internal (Eu)

• Internal energy– Sensible heat – heat content that can be

measured and is proportional to temperature– Latent heat – “hidden” heat content that is

related to phase changes

fhgVyz

gVyz

22

22

22

21

11

Energy Units

• In SI units, the basic unit of energy is Joule (J), where 1 J = 1 kg x 1 m/s2

• Energy can also be measured in calories where 1 calorie = heat required to raise 1 gm of water by 1°C and 1 kilocalorie (C) = 1000 calories (1 calorie = 4.19 Joules)

• We will use the SI system of units

Energy fluxes and flows

• Water Volume [L3] (acre-ft, m3)

• Water flow [L3/T] (cfs or m3/s)

• Water flux [L/T] (in/day, mm/day)

• Energy amount [E] (Joules)

• Energy “flow” in Watts [E/T] (1W = 1 J/s)

• Energy flux [E/L2T] in Watts/m2

Energy flow of1 Joule/sec

Area = 1 m2

MegaJoules

• When working with evaporation, its more convenient to use MegaJoules, MJ (J x 106)

• So units are– Energy amount (MJ)– Energy flow (MJ/day, MJ/month)– Energy flux (MJ/m2-day, MJ/m2-month)

Internal Energy of Water

0

1

2

3

4

-40 -20 0 20 40 60 80 100 120 140

Temperature (Deg. C)

Inte

rnal

Ene

rgy

(MJ)

Heat Capacity (J/kg-K) Latent Heat (MJ/kg)Ice 2220 0.33Water 4190 2.5

Ice

Water

Water vapor

Water may evaporate at any temperature in range 0 – 100°CLatent heat of vaporization consumes 7.6 times the latent heat of fusion (melting)

2.5/0.33 = 7.6

Water Mass Fluxes and Flows

• Water Volume, V [L3] (acre-ft, m3)

• Water flow, Q [L3/T] (cfs or m3/s)

• Water flux, q [L/T] (in/day, mm/day)

• Water mass [m = V] (Kg)

• Water mass flow rate [m/T = Q] (kg/s or kg/day)

• Water mass flux [M/L2T = q] in kg/m2-day

Water flux

Area = 1 m2

Latent heat flux

• Water flux– Evaporation rate, E

(mm/day)

• Energy flux – Latent heat flux

(W/m2), Hl

Area = 1 m2

ElH vl = 1000 kg/m3

lv = 2.5 MJ/kg)/)(1000/1(*)/)(86400/1(*/1)/(105.2)/(1000/ 632 mmmsdaydaymmkgJmkgmW

28.94 W/m2 = 1 mm/day

Radiation

• Two basic laws– Stefan-Boltzman Law

• R = emitted radiation (W/m2)

= emissivity (0-1) = 5.67x10-8W/m2-K4

• T = absolute temperature (K)

– Wiens Law = wavelength of

emitted radiation (m)

4TR

T

310*90.2

Hot bodies (sun) emit short wave radiationCool bodies (earth) emit long wave radiation

All bodies emit radiation

Net Radiation, Rn

Ri Incoming Radiation

Ro =Ri Reflected radiation

albedo (0 – 1)

Rn Net Radiation

Re

ein RRR )1(

Average value of Rn over the earth and over the year is 105 W/m2

Net Radiation, Rn

Rn Net Radiation

GLEHRn

Average value of Rn over the earth and over the year is 105 W/m2

G – Ground Heat Flux

LE – EvaporationH – Sensible Heat

http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/energy/radiation_balance.html

Energy Balance of Earth

6

4

10070

51

21

26

38

6

20

15

Sensible heat flux 7Latent heat flux 23

19

Energy balance at earth’s surfaceDownward short-wave radiation, Jan 2003

600Z


900Z


1200Z


1500Z


1800Z


2100Z

Latent heat flux, Jan 2003, 1500z

Digital Atlas of the World Water Balance(Temperature)


Digital Atlas of the World Water Balance(Net Radiation)


Why is the net radiation largeover the oceans and small over the Sahara?

GLEHRn

ce 394k.2 hydrology, lecture 3 water and energy flow

Documents

velocity of water flow

outflow of water

closed water balance

earth areaocean

flow of data extract

streamflow data

qta hydrologic system

transformationin hydrology