atm 301 lecture #2 (sections 1.3-1.8) some basics 1.conservation laws and units 2.properties of...

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ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

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Page 1: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

ATM 301 Lecture #2 (sections 1.3-1.8)

Some Basics1.Conservation Laws and Units

2.Properties of Water

3. Watershed

4. Regional Water Balance

Page 2: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Basic Laws Applied in Hydrology• Conservation of Mass: Mass (e.g., of water) is neither created or destroyed. It can only be

converted into different forms (e.g., ice, liquid water, or vapor). • Conservation of Energy:

Energy (e.g., heat in water) is neither created or destroyed. It can only be converted into different forms (e.g., latent, sensible, kinetic, or radiative).

• Conservation of Momentum:- The momentum of a body remains constant unless a net force acts on the

body; - The rate of momentum change of a body is proportional to the net force

acting on the body (F = m x a)• Fick’s First Law of Diffusion:

A diffusing substance moves from regions with high concentration to regions with low concentration at a rate proportional to the concentration gradient: x

CDFx

Page 3: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Dimensions and Units• The fundamental physical dimensions: Force (F), Mass (M), Length (L), Time (T), and temperature () Force and Mass are related: [F] = [M L T-2] ; [M] = [F L-1 T2] The dimensions of energy (E) is [F L] • Units: any standards in which the magnitude of quantities are expressed.

• The Système International (SI) The international standard of units for all sciences.The SI units: Length: m; Mass: kg; Time: s; Temperature: K

• Unit Conversion: Example 1: miles per hr to m/s: 1 mi/hr = 1 x 1600m /(3600s) = 0.4444m/s

100mi/hr = 44.44m/s, 50mi/hr = 22.22m/s Example 2: km3/yr to m3/s: 1 km3/yr = 1 x (1000m)3/(1yr x 365 day/yr x

24hr/day x 3600s/hr) = 109 m3/ (3.1536x107 s) = 31.71 m3/s

40,000km3/yr = 40,000 x 31.71 m3/s =1.2684 x 106 m/s

Page 4: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Properties of Water

• Determined by water atomic and molecular structures

• Affects the behavior of water in the soil, at the surface, and in the atmosphere

Page 5: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance
Page 6: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Phase Transition of Water

Page 7: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Phase Transition of Water

Page 8: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Water Density (w)(mass per unit volume)

Weight density = weight per unit volume = g

Page 9: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Surface Tension• Molecules near the surface of liquid water are pulled inward by

hydrogen bonding with the molecules below;

• Surface tension () is that inward force per unit distance over which it acts (in units of F L-1 or N m-1);

• Surface tension for water is comparatively high;

• It decreases rapidly as temperature increases.

Page 10: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

The Bond Number (Bo)• Surface tension is important where the flow scale is less than a

few mm (e.g., in soils),

• It helps soil hold water against gravity;

• The relative importance of surface tension and gravity depends on the Bond Number:

2L

B wo

where w = w g is weight density, L is the length scale of the flow (e.g., soil-pore diameter or flow depth).

In flows with Bo < 1, surface tension forces exceed gravitational forces

Page 11: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Viscosity () of Liquid Water• Viscosity is the internal intermolecular friction that resists motion

of a fluid. You can think of viscosity as “the resistance to flow”.• Water has a comparatively low viscosity due to the rapidity with

which the intermolecular hydrogen bonds break and reform.• No-slip condition: the flow velocity at a stationary boundary is

always zero (e.g., on the bottom of oceans). • Viscosity is important at small scales (cm or less) and slow velocity

(less than a few cm/s).

Page 12: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Turbulence & Reynolds Number (Re)• As the scale and velocity increase, the flow becomes chaotic due

to eddies, forming turbulence.

• Viscosity often dominates the flow in soil pores.

• Turbulent resistance often dominates surface water flows.

• The relative importance depends on the Reynolds Number:

w

e

LUR

where U is average velocity, L is the length scale.• In subsurface flow, L = the soil-pore diameter, and flows with Re < 1 are dominated by viscosity; • In open channel flow, L = flow depth, and flows with Re < 500 are dominated by viscosity

Page 13: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Latent Heat• Latent heat is the energy released or absorbed during a phase

change per unit mass;

• No temperature change is associated with this “latent” heat;

• Water’s latent heats are comparatively large due to the strong hydrogen bonds in water molecules.

• Latent heat of fusion (f): the heat added or released when a unit mass of substance melts or freezes. f = 3340 J/kg for water.

• Latent heat of vaporization (v): the heat added or released when a unit mass of substance vaporizes or condense.

• v = 2.471x106 J/kg for water at 10oC, one of the highest known, more than six times of f and more than five times of the energy to warm the water from the melting point to the boiling point!

• v decreases with temperature.

Page 14: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Specific Heat • Specific heat (or heat capacity), cw, is the amount of energy

needed to raise a unit mass of a substance by one unit temperature. In units of J kg-1 K-1.

• cw = 4.191 x 103 J kg-1 K-1 at 10oC for water, highest of any liquid except ammonia.

• The specific heat is high for water because most of added energy is used to break down the hydrogen bonds, rather than to increase the rate of molecular vibrations, the measure of temperature.

• The heat capacity of water help stabilize the temperature of warm-blooded organisms and water bodies (e.g., the oceans).

Page 15: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance
Page 16: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Projected Temperature Changes

Page 17: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

The Watershed(a.k.a., drainage basin, river basin, catchment )

“The area that topographically appears to contribute all the water that passes through a specified cross section of a stream” -Dingman, 2015

Requires:1. Topographic map (higher resolution

is better)2. Specified outlet point (city, lake,

fork, ocean)3. Changes with the outlet point!

http://techalive.mtu.edu/meec/module01/whatiswatershed.htm

Most fundamental hydrological landscape unit.

Divide: boundary of watershed

Page 19: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

http://www.usbr.gov/lc/region/pao/lawofrvr.htmlhttp://en.wikipedia.org/wiki/Colorado_River_Compact

Law of the RiverColorado River Watershed

http://www.usbr.gov/

http://www.nasa.gov/topics/earth/features/colorado20100920a.html

Page 20: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

• Civil war veteran (lost an arm)• Lead expedition in 1869 to explore Colorado

River (in wooden boats)• Founder of Illinois Museum of Natural History

Major John Wesley Powell

Page 21: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Powell’s vision for the West

Western Ag can only be limited:“When all the water running in the streams found in the region are conducted on the land, there will be but a small portion of the country redeemed…one to three percent”

Homestead Act was flawed

Unused water rights should revert to public trust (use it or loose it!)

(1876, USGS)

Watersheds as political boundaries!

Page 22: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

http://water.usgs.gov/GIS/huc.htmlhttp://www.nrcs.usda.gov/wps/portal/nrcs/detail/national/water/watersheds/dataset/?cid=nrcs143_021617

regions (2 digit) sub-regions (4 digit)basins (6 digit) subbasins (8 digit)watersheds (10 digit)subwatersheds (12 digit)

US Geological Survey (USGS) divides US by Hydrological Unit Codes (HUCs)• Largely separated on watershed boundaries• Often used to group hydro and environmental data

regions (2 digit) sub-regions (4 digit)

Page 23: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Delineation (determining watershed boundaries)

Manual:1. Pick an outlet (usually on a stream/river) on a

topographic map. Your map needs to cover entire basin.

2. Starting at outlet, draw lines away from L or R bank. Keeping perpendicular to contour lines.

3. Continue up to headwaters (highest point on divide).

4. Draw from the other side and connect.5. Check:

a. A divide should never cross a stream (can cross a lake or wetland)

b. Lowest point should be the outlet (unless it is a closed basin)

http://learn.genetics.utah.edu/content/gsl/physical_char/

Page 24: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

http://www.udel.edu/FREC/spatlab/basins/

Automated (Using Geographic Information System software):• Computer starts from a Digital Elevation Model (DEM): a 3D digital

representation of a terrain surface• DEM’s can be raster or vector representation.• Must first create a “depression-less DEM” by eliminating artificial

closed basins• Next find terrain slope and flow direction at all points• Next find flow accumulation at all points to get stream network• Pick outlet(s) and computer uses above info to delineate.

http://proceedings.esri.com/library/userconf/proc97/proc97/to200/pap198/p198.htm

Delineation (determining watershed boundaries)

Page 25: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Regional Water Balance• The Water-Balance Equation for a Watershed:

• All the quantities are watershed-averaged values

• Water storage change rate (S) is equal to water input (P+GWin) minus water output (ET+Q+ GWout) --- mass conservation

)( outin GWQETGWPS

Page 26: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Regional Water Balance• For most watersheds, groundwater inflow

GWin is negligible

• When averaged over a long period (e.g., 30yrs), the storage change S is small compared with P and ET, so that

where R Q + GWout is the total Runoff, which is the rate at which liquid water leaves a region. R represents the potential water resource in a region.

• Both P and ET are mostly meteorology- or climate-driven variables• Thus, runoff is the difference between two climate-driven

quantities.

ETPR

Page 27: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Estimates of the Balance Terms• A major task of Hydrology

• Runoff R: streamflow (Q) is the main part, GWout is small for most cases

• Q is often measured by stream gauges

• Precipitation P: watershed-mean P is estimated using raingauge point measurements, or satellite estimates,

often contain large errors • Evapotranspiration ET: not directly measured, a function of surface

net radiation Rnet, Ta, RH, U, soil water content , vegetation height zveg, and leaf area index LAI:

• ET = P – R is often used to estimate regional mean ET.

),,,,,,( LAIzURHTRfET veganet

Page 28: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

US Precip.

Page 29: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

May-Sept. 2007

https://www2.ucar.edu/atmosnews/water-futures/splash-of-reality

US ET

Page 30: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance
Page 31: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Estimates of the Balance Terms

• Subsurface Runoff GWout: not directly measured, can be significant for some cases

• Water Storage Change Rate S:

• Storage S includes groundwater and soil water, both are not well measured regionally.

• Recent GRACE satellite estimates since 2002 make it possible to derive S over large regions.

T

SSS T 0

Page 32: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

32

Monitoring Water Storage Change from Space• GRACE satellites measure changes in water storage over land by measuring changes in gravity. Launched in March 2002.

GRACE=Gravity Recovery and Climate Experiment

Page 33: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

33

GRACE Satellite Measurements(~7min.)

Page 34: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

(for 8/2002 – 2/2011)

Page 35: ATM 301 Lecture #2 (sections 1.3-1.8) Some Basics 1.Conservation Laws and Units 2.Properties of Water 3. Watershed 4. Regional Water Balance

Homework #1: Due on Tue., Sep. 8.

1. Ex.#7 on p.44 (30%),

2. Ex.#3 on p. 107 (15%), and

3. #5 on p.108 (30%) of Dingman (2015).

4. Briefly describe the global hydrologic cycle and its major water fluxes and storages, and how it is coupled to the global energy cycle. (25%)