Lecture 14, Water, Humidity, Pressure and Trace Gases, Part 1

• Physical and chemical properties of water • Gas Laws • Chemical Potential of Water • Rainfall/Drought

10/6/2014 Biometeorology, ESPM 129 Atmospheric Gas Composition

constitue percent by percent by molecular nt volume mass weight (g mole-1)

N2 78.091 75.5 28.02

O2 20.95 23.1 32.00 Ar 0.930 1.3 39.94

CO2 0.036 0.05 44.01 H2O ? 18

Biometeorology, ESPM 129 Water

•Gas • Liquid • Solid

Biometeorology, ESPM 129 Soil-Plant-Atmosphere-Water Continuum

-50 MPa

atmosphere

R boundary Layer

R stomata

leaf -0.7 MPa

Xylem Water Moves UPWARD because it flows DOWNHILL Energetically

R xylem -0.2 MPa

Root

R root/soil -0.05 MPa Soil ESPM 129 Biometeorology Triple Point for Water

http://chemwiki.ucdavis.edu/@api/deki/files/7399/=f_copy.png

Biometeorology, ESPM 129 Phase Changes of Water

How can we Exploit the Triple Point Curve to prevent water from condensing on our air sampling tube? http://www.laetusinpraesens.org/musings/images/climate_files/phase1.jpg Biometeorology, ESPM 129 Properties of Water

Property Value molecular weight 18 g mole‐1 melting point 273.15 K boiling point 373.15 K latent heat of 2.442 MJ kg‐1 or 44.00 kJ mol‐1 vaporization at 20 C latent heat of 2.826 MJ kg‐1 or 51.00 kJ mol‐ sublimation 1at 0 C dialectric constant 80 thermal conductivity 0.599 W m‐1 at 20 C heat capacity of water 4182 J kg‐1 at 20 C molecular diffusivity, 2.42 10‐5 m2 s‐1 at 20 C water in air Density 1.000 kg m‐3 at 4 C

Biometeorology, ESPM 129 Properties of Water, f(T)

temperature density latent heat of kinematic viscosity evaporation oCMg m-3 kJ mol-1 mm2 s-1 0 0.99987 45.0 1.79 4 1.0000 44.8 1.57 10 0.99973 44.6 1.31 20 0.99823 44.1 1.01 30 0.99568 43.7 0.80 40 0.99225 42.8 0.66

Biometeorology, ESPM 129 Measures of Atmospheric Moisture

• Water Potential, Pa • Relative Humidity, unitless • Dew Point Temperature, C • Wet Bulb Temperature, C • Vapor Pressure, Pa • Vapor Pressure Deficit, Pa • Density, mole m-3 • Mixing Ratio, unitless

Biometeorology, ESPM 129 Charles Law and Boyle's Law pressure, volume and temperature are inter-related.

PV nRT

R is the universal gas constant, 8.3144 J mol-1 K-1, T is absolute temperature (K), P is pressure (Pa, N m-2), V is volume n is the number of moles

Biometeorology, ESPM 129 the molar volume of air (volume occupied by one mole of air, n=1) for standard pressure (0.1013 MPa, 101.3 kPa, 1013 mb) and temperature (273.15 K),

nRT V P

22.41 liters mole-1 or 0.02241 m3 mol-1.

Biometeorology, ESPM 129 Gas Law used by Meteorologists

RT RT P P m m

m is the molecular weight of a gas (g mol-1) is the mass density (g m-3) is 1/.

Biometeorology, ESPM 129 Partial Pressure Law

Pp p p p p... NOArCOHO22 2 2 R p T m

p a v c ... mmma v c RT

Biometeorology, ESPM 129 Air Density

TdrySaturated oCKg m‐3 kg m‐3 0 1.292 1.289 ()P em em 5 1.269 1.265 av RT RT 10 1.246 1.240 15 1.225 1.217 20 1.204 1.194 25 1.183 1.169 30 1.164 1.145 40 1.128 1.096

Does a baseball fly Less far on a humid day?

Biometeorology, ESPM 129 Water Potential of atmospheric humidity is function of its mole fraction

-40

RT ea -30 p ln( )

VeTws() -20 MPa

-10

R: Universal gas constant, J K-1 mol-1 0 T: absolute temperature 0.0 0.2 0.4 0.6 0.8 1.0 1.2 ea: vapor pressure RH P: pressure -6 3 -1 Vw: molal volume of water, 18.05 10 m mole

What is the water potential of boiling water?

Biometeorology, ESPM 129 mass gas density (grams of a gas molecule per unit volume)

nm pm cc cc c V RT

nc is the number of moles V is volume R is universal gas constant

-1 mc is the molecular mass (g mole ) of the compound.

Biometeorology, ESPM 129 molar gas density (moles of a gas molecule per unit volume)

n p c ccc V RT mc

nc is the number of moles V is volume

-1 mc is the molecular mass (g mole ) of the compound.

Biometeorology, ESPM 129 Mass fraction (mass per unit mass of air)

c ccm Mc a ma

-1 ma is the molecular weight of dry air (g mol ) mc is molecular weight of trace gas -3 a is the mass density of dry air (g m ) -3 c is the mass density of trace gas air (g m )

Biometeorology, ESPM 129 Mole fraction, the number of moles of a trace gas divided by the total number of moles present in the mixture

Moist air

ncam ccp Cc n mc p

Dry air

n p p C c c c c n p pp d d aHO2

Biometeorology, ESPM 129 Mixing Ratio of Water Vapor, Saturated Atmosphere

Saturation Mixing Tdryvapor Ratio pressure o -3 CKg mg m-3 mmol m‐3 ppt 0 1.292 4.85 269 6.02 5 1.269 6.8 377 8.60 10 1.246 9.4 522 12.1 15 1.225 12.07 670 15.8 20 1.204 17.31 961 23.1 25 1.183 23.06 1281 31.3 30 1.164 30.4 1688 41.9 40 1.128 51.2 2844 72.9

Biometeorology, ESPM 129 Saturation Vapor Pressure

• When a pool of water is at constant temperature in a closed container, some water molecules are leaving the liquid and others are condensing and returning to the liquid. Molecules in the head space exert a partial pressure on the system. • The equilibrium vapor pressure that occurs is called the saturation vapor pressure. • It is a function of temperature and is independent of pressure.

Biometeorology, ESPM 129 Saturation Vapor Pressure-Temperature Function

Over Water Over Ice bTc a=0.611 a=0.611 kPa eTsc( ) a exp( ) b= 17.502 b= 21.87 cT c c=240.97 c=265.5

14

12

10

8

(T) (kPa) 6 s e

4

2

0 0 102030405060

T (oC) Biometeorology, ESPM 129 Boiling Point: Pressure equals Saturation Vapor Pressure

Saturation Vapor Pressure-Temperature

120 Sea Level 100

80

60 Mountains

40

20 Saturation Vapor Pressure, kPa Pressure, Vapor Saturation 0

0 20406080100120 Temperature, C

Biometeorology, ESPM 129 Slope of Saturation Vapor Pressure-Temperature Curve

17.502T 0.611 17.502 240.97 exp( ) de() T s s 240.97 T dT(240.97 T )2

es, saturation vapor pressure, kPa ea, vapor pressure hr, relative humidity s, slope of es vs T relation T, temperature, C

Ta, air temperature Ts, surface temperature

Biometeorology ESPM 129 Relative Humidity, hr,

the ratio between the actual (ea) and saturation vapor pressures (es(T).

It ranges between zero and 1.0, with one indicating saturation.

1.0

0.9

ea hr 0.8 eTs ()

0.7 Relative Humidity

0.6 ea=pH2O 0.5 0 400 800 1200 1600 2000 2400

Time (hours)

Biometeorology, ESPM 129 Absolute humidity or vapor density (g m-3):

em av 3 2165.()ekPaa v ()gm RT v k Tk

-1 -1 -1 (R=8.3143 J mol K mv=18 g mol )

12.0 Boardman, OR D158, 1991 11.5

11.0

10.5 ) -3 10.0 (gm v 9.5

9.0

8.5

8.0 0 400 800 1200 1600 2000 2400 Time (hours)

Biometeorology, ESPM 129 3

es

ea

2 vapor pressure (kPa) 1

0 500 1000 1500 2000

Time (hours)

Biometeorology, ESPM 129 Humidity vs Temperature

60

50 e =1.0 kPa

es(T) 40 RH=0.5 )

-3 30 (g m v 20

10

0

270 280 290 300 310 320

Temperature (K)

Biometeorology, ESPM 129 Virtual Temperature. is the temperature dry air would have if it had the same density as moist air at the same pressure

it is related to the speed of sound Cp P Cp RTv vsound and Cv Cv mair

buoyancy of the air.

' () parcel ' T ag v parcel Tv

Acceleration, a

Biometeorology, ESPM 129 Air Temperature and Virtual Temperature

305

300

295

290

285 dry air 0.005 g/g 280 0.010 g/g temperature

275

270

265 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 1.30

air density (g m-3)

Biometeorology, ESPM 129 Virtual Temperature is the Temperature Dry air would have if its Pressure and specific volume were equal to those of a sample of moist air

Derivation: Virtual Temperature

RTav av RT PPe()||dry e moist RT ( ) mmmmav a

T T v em 1(1)v Pma

Biometeorology, ESPM 129 Biometeorology, ESPM 129 Chemical Potential of Water

Chemical potential quantifies the driving force for movement of water between two locations

The chemical potential of water is related to the amount of change in the Gibbs free energy of the system, subjected by pressure, temperature and minor constituents , e,g., salts, . It relates to the free energy needed for a transition from State A to B

It is a function of its chemical concentration, pressure, electrical potential and gravity

The chemical potential has units of energy (J mol-1).

Biometeorology, ESPM 129 Water Potential

The potential energy of water is related to the difference between its chemical potential

(w) and a reference state (wo):

o ww Vw

By convention, Water potential is normalized by Vw, the partial molal volume of water (18.05 10-6 m3 mol-1), giving it units of Pressure.

Biometeorology, ESPM 129 Chemical Potential is a function of:

Chemical activity: RT ln(a); a = vC Pressure: (VP) Electrical Potential: (zPE) Gravity: (mgh)

0 RTaVPzFEmghln( )

Biometeorology, ESPM 129 The total water potential of a system consists of the sum of water potentials associated with

Turgor (pressure), osmotic, matrix and gravitational forces

pmg

Units, Pressure: Pa

Biometeorology, ESPM 129 • Turgor (pressure) potential – is related to the hydrostatic pressure, as when someone is blow on or sucking on straw that is inserted in a reservoir of water. Its sign can be positive or negative. • osmotic potential – The presence of solutes reduces the activity of water. • matric potential – interactions between water and solid surfaces act to reduce the activity of water. • gravity Potential – gravitational force is a function of the density of water, the acceleration due to gravity and the height of the water reservoir above or below a reference height:

gw gh

Biometeorology, ESPM 129 Water Potential of atmospheric humidity is function of its mole fraction

-400

-450 RT e a -500

p ln( ) -550 V P MPa

w

-600

-650

-700 R: Universal gas constant 0 5 10 15 20 25 30 35 40 e (hPa) T: absolute temperature a

ea: vapor pressure P: pressure -6 3 -1 Vw: molal volume of water, 18.05 10 m mole

Biometeorology, ESPM 129 Probability of Time between Storms Probability of amount of rain per storm

1 h f ( ) exp( ) fh() exp( )

is the rate of rain (units of rain events 1/ is the depth of the rain. is computed per day). It is computed by summing by summing the amount of rain per year the number of rain days per year and and dividing by the number of rainy days. dividing by 365

Stochastic Rain Fall

5

4

3

rain (cm) rain 2

1

0 0 100 200 300 day

Biometeorology, ESPM 129 Drought

• Meteorological – Periods when precipitation is significantly below the long-term average • Hydrological – When water level in lakes and rivers fall significantly below normal conditions • Agricultural – Occurrence of low levels of plant available water • Sociological – When drought disrupts societies and/or societies disrupt supplies of water, eg via civil war, famine, political decisions

Biometeorology, ESPM 129 Drought Metrics

• Palmer Drought Index • Budyko Aridity Index • Thornthwaite Index – Ratio of between potential and actual evaporation – Ratio between precipitation and available energy

Biometeorology, ESPM 129 Summary

• The concept of chemical potential energy quantifies the driving force for movement

• of water between two locations, such as in the soil, in a plant and between the soil, plant and atmosphere.

• Matrix, pressure, osmotic, gravitational potential sum to determine the chemical potential of water.

• Saturation vapor pressure is an exponential function of temperature

• The probability of rainfall events and its amount can be computed with a Poisson probability distribution

Biometeorology, ESPM 129