Atmospheric Sciences 321. Science of Climate. Lecture 14: Surface Energy Balance Chapter 4

Transcription

1 Atmospheric Sciences 321 Science of Climate Lecture 14: Surface Energy Balance Chapter 4

2 Community Business Check the assignments HW #4 due Today, HW#5 is posted Quiz Today on Chapter 3, too. Mid Term is Wednesday May 7 Practice exams on homework assignment page We re now on Chapter 4: Surface Energy Balance Questions?

3 Drag Laws Aerodynamic Formulas Vertical fluxes of heat and moisture in the boundary layer are accomplished by small-scale high-frequency turbulence that is not measured by the normal climate observations. SH = c p ρ w T, LE = Lρ w q So we have come up with formulas that allow us to estimate the fluxes from time mean observations SH = c p ρ C DH U ( r T s T ( a z )) r LE = Lρ C DE U ( r q s q ( a z )) r

4 Equilibrium Bowen Ratio The Bowen ratio is the ratio of the sensible heat flux to the latent heat flux B o = SH LE We can estimate the Equilibrium Bowen Ratio, which is the Bowen ratio under equilibrium conditions when the air is staturated.

5 Equilibrium Bowen Ratio - II Go back to our bulk aerodynamic formula and put in our approximation for q a where LE = Lρ C DE U ( r q s q ( a z )) r LE ρ LC DE U q * 1 s (1 RH) + RH B c p e L (T T ) s a B e 1 L c p q * T Is the inverse equilibrium Bowen Ratio

6 Equilibrium Bowen Ratio - II Take our estimate of LE, assume the air is saturated, then compute the Bowen ratio LE ρ LC DE U q * 1 s (1 RH) + RH B c p e L (T T ) s a For RH = 1 this is LE ρ LC DE U B c 1 p e L (T T ) s a and c p ρ C DH U ( r T s T a ( z r )) B o = ρ LC DE U B c B e 1 p e L (T s T a ) with the proviso that the drag coefficients for heat and vapor are equal

7 Equilibrium Bowen Ratio III The dependence of saturation mixing ratio on temperature is approximately exponential q * T L q *(T ) R v T 2 lnq * T L R v T

8 Equilibrium Bowen Ratio III Equilibrium Bowen Ratio is large at low temperatures, like high latitudes and would be very low in the tropics, assuming the surface is wet and the air not too dry, like over the ocean. 0.3

9 Surface Energy Balance Zonal, Annual Mean Radiation and Evaporative cooling are big in the tropics and the biggest terms almost everywhere except poleward of about 60 degrees.

10 The Diurnal Variation The sun rising and setting every day is a big deal The radiative driving from this is huge. The solar part goes from zero to a big value. The longwave part does not vary quite as much, because of the strong infrared opacity of the atmosphere

11 The Diurnal Variation Over a dry lake bed in the CA desert The radiative driving is huge First the surface stores heat G by warming up Then sensible cooling, turbulent transfer of sensible heat c p T Takes over

12 The Diurnal Variation Over a cornfield in Wisconsin in September The radiative driving is huge First the evaporation starts Then storage and sensible cooling, kick in later.

13 The Diurnal Variation Over a alfalfa field in Wisconsin in July Something weird The evaporation is bigger than the radiation The sensible heat flux is downward and the storage is mostly negative. Why? Dry air, irrigated field

14 Seasonal 200 West Palm Beach, Florida a) 200 San Antonio, Texas b) Variations W m R s LE SH R s LE SH Discuss among yourselves. Difference between West Palm Beach and San Antonio Difference between Yuma and Flagstaff Difference between Astoria and Madison W m -2 W m G J F M A M J J A S O N D Yuma, Arizona c) R s SH LE G J F M A M J J A S O N D Astoria, Oregon e) R s LE SH G J F M A M J J A S O N D Flagstaff, AZ d) R s SH LE G J F M A M J J A S O N D Madison, Wisconsin f) R s LE SH 0 G 0 G -50 J F M A M J J A S O N D -50 J F M A M J J A S O N D

15 Seasonal Variations The ocean, especially in the Gulf Stream region, is different. Horizontal transport and storage are the biggest terms. Radiation is smaller than LE

16 Global Maps of Annual Means Net Surface Radiation

17 Global Maps of Annual Means Evaporation Cooling

18 Global Maps of Annual Means Sensible Heat Cooling

19 Global Maps of Annual Means Surface Heat Storage, or flux into the ocean

20 Summary Chapter 4 Basic surface balance is net radiation, mostly solar, is balanced by mostly evaporative cooling Over land sensible heat is important locally Over ocean heat flux into (in equatorial region, mostly) and out of (mostly in western boundary current regions) is important. On land diurnal and seasonal variations depend on land moisture, very different in deserts and rain forests.

21 Chapter 5: Hydrologic Cycle The water valance of the Surface g w = P + D E f Combine P=precipitation and D=dewfall, assume no storage of water, and get that runoff equals P-E f = P E Water balance for atmosphere g = ( P + D E) f wa a

22 Where s the Water? It s Salty and in the Ocean!

23 Where s the Fresh Water? It s Frozen!

24 World Water Balance Vapor moves from ocean to land, rivers flow back Units are centimeters of water per year, averaged over area of land or ocean. Areas are different.

25 Continental Water Balances Old data

26 Old data Ocean Water Balances

27 Water Balance: Zonal-Annual Means P, E and runoff as functions of latitude Equator and midlatitudes wet, subtropics dry.

28 Precipitation Maps Global from gauges and satellites

29 Precipitation Maps: Seasonal Global from gauges and satellites

30 Formulas: Penman s Equation Remember the Bowen Ratio B o = SH LE c p L ( T s T ) a (q s q a ) Make the following approximation (q * s q * a ) (T s T a ) dq * dt and assume the surface air is saturated, whence B o = B e 1 (q * q a a ) (q * s q a )

31 Penman s Equation We can write the surface energy balance as ( ) = E en E 1 + B o where, E en = 1 L (R s ΔF eo G) is the energy available at the surface to evaporate water or balance sensible cooling. Next,

32 Penman s Equation Next take the equation below doe the surface energy balance And put in our formula for Bowen Ratio To get the following. E 1+ B e E( 1 + B ) o = E en B o = B e 1 (q * q a a ) (q * s q a ) q * ( ) a q a = E en + E B e ( ) ( q * s q ) a

33 Penman s Equation Next take what we had And put in our bulk aerodynamic formula for Evaporation from a wet surface To get the following. E = ( ) = E en + E B e q a E 1+ B e LE = Lρ C DE U r ( q * s q ) a 1 (1+ B e ) E en + B e (1+ B e ) E air ( * q ) a ( q * s q ) a E air = ρ C DE U (q a * q a ) = ρ C DE U q a * (1 RH)

34 Penman s Equation E = 1 (1+ B e ) E en + B e (1+ B e ) E air where E air = ρ C DE U (q a * q a ) = ρ C DE U q a * (1 RH) is the capacity of the air to take on water because the air is unsaturated. So Penman s equation divides the evaporation into two parts that depend on the availability of energy to evaporate water at the surface and dryness in the air to absorb more water

35 Penman s Equation E = 1 ( (1+ B e ) E + B E ) en e air E en = 1 L (R s ΔF eo G) E air = ρ C DE U (q a * q a ) = ρ C DE U q a * (1 RH) So Evaporation gets smaller for large B e cold temperatures, as more of the heat goes into SH The relative importance of relative humidity being less than saturated becomes less important at tropical temperatures where Be is small.

36 Evapotranspiration On land, a lot of the evaporation is mediated by the roots of plants moving moisture from the soil and the vapor comes out through the stomata of plant leaves = Transpiration.

37 Potential Evapotranspiration E = 1 ( (1+ B e ) E + B E ) en e air Since Penman s equation assumes a wet surface, it is in a sense the maximum evaporation that could occur, which we can call the Potential Evapotranspiration or PET. E en = 1 L (R s ΔF eo G) E air = ρ C DE U (q a * q a ) = ρ C DE U q a * (1 RH) ( ) PET = ρ a C DE U q *(T s ) q a All else being equal, it increases rapidly with temperature

38 Annual Variation of Water Balance for Selected Regions

39 Annual Variation of Water Balance for Selected Regions - II

40 Thanks!