HEAT BALANCE

Energy and Temperature

• When an object absorbs short‐wave energy its• When an object absorbs short‐wave energy, its temperature increases

A th t t i it it• As the temperature increases, it emits more long‐wave radiation out to space

• This process will continue until the rate of absorption of short‐wave radiation equals the emission rate of long‐wave radiation

Daily/Seasonal Radiation Patterns

•• insolationinsolation peak vs. temperaturepeak vs. temperature•• daily lagdaily lag•• seasonal lagseasonal lagL i f ti f t fL i f ti f t f••Lag is function of type of Lag is function of type of

surface, wetness, wind, etcsurface, wetness, wind, etc

•• Temperature increases whenTemperature increases whenppinput > outputinput > output

•• Temperature decreases whenTemperature decreases wheninput < outputinput < outputinput < outputinput < output

The Surface Energy Budget

• Determines amount of energy available for evaporation of surface water and to change the surface temperature

• Contributes to overall energy balance of Earth

• More complex than top of the atmosphere energy budget– Latent and Sensible heat fluxes

• Depends on insolation (incoming solar), surface h h hcharacteristics, atmosphere characteristics

Surface differences …..

No two places on Earth have exactlyNo two places on Earth have exactly the same surface

Differences in surfaces will result in diff i l l li tdifferences in local climate

Surface Energy Budget

There is an imbalance in the energy budget with just the radiation fluxes present (R )radiation fluxes present (RN)

Non-radiative fluxes (transfer of energy other thanNon-radiative fluxes (transfer of energy other than radiation) need to be included:

S ibl H t Fl (H)Sensible Heat Flux (H)

Latent Heat Flux (LE)( )

Ground Heat Flux (G)

Surface Energy Budget

∆ = RN - ( H + LE + G)

The RN term involves only radiation

H + LE + G represents the nonradiative fluxes

On the globally averaged scale, ∆ = 0, which represents a planetary energy balance

RN = H + LE + GN G

Seasonal variation of surface energy budget

Net radiometer (measure net radiation Rn)

Piranometer (measure shorwave radiation (sun))

1200

Net Radiation z = 2.5 m

W/m2

800

1000

400

600

Net Radiation z = 2.5 m

0

200

‐400

‐200

SENSIBLE HEAT FLUXSENSIBLE HEAT FLUX

Estimation of energy components …

• Sensible heat flow (H) is a diffusive process driven by turbulence (eddies) inprocess driven by turbulence (eddies) in the wind

s aa p H

T TH c Kh

ρ −⎛ ⎞= ⎜ ⎟Δ⎝ ⎠u Ta a p H h

ρ ⎜ ⎟Δ⎝ ⎠

ρa = air density (kg m–3)

a

cp = specific heat of air (1005 J kg–1deg–1)u = wind speed (m s–1)Ta = air temperature at height ∆hu = 0 Ts

a p gKH = eddy diffusivity of heat

Depends on wind speed, roughness, atmospheric stability

Sometimes written as KHu

Sensible Heat flux Bulk Aerodynamic FormulaAerodynamic Formula

wind speed atwind speed atreference level Surface temperature

( )( )rasrDHp zTTUCcQ −= ρ ( )( )rasrDHpHQ ρ

Temperature of air atf h i ht

specific heat (const. p)Transfer Coeff. (temperature)

reference height z

C.C. Hennon, UNC Asheville

SENSIBLE HEAT FLUX a) Inundated tidal flats (Zaker, 2003)

)(CQ )( −= TawThCVpcHQ ρ

)º(c

)(d11

3

−−

−

=

=

CJkgapacityheatspecificc

kgmensityairρ

)/(

)(c

=

=p

smV

CJkgapacityheatspecificc

1976) Smitt, and (Friehe1091.0 3−=hC

SENSIBLE HEAT FLUX b) Exposured tidal flats (Evett 1994 2002)b) Exposured tidal flats (Evett, 1994, 2002)

)( TTDcQ −=ρ )( aTsThDpcHQ ρ3 )(kgmdensity 3−= airρ

)º(c 11p

−−= CJkgcapacityheatspecificp

2

2 ln ⎥⎤

⎢⎡

⎟⎟⎞

⎜⎜⎛ zVkD

)/( smV =

KVkln ⎥⎦

⎢⎣

⎟⎟⎠

⎜⎜⎝

=oh

h zVkD cteKarmanVon =k

heightreference=z heightreference=zDh = heat exchange coefficient [m s–1]

LATENT HEAT FLUX

Latent Heat flux Bulk Aerodynamic Formula

Latent Heat of VaporizationSpecific Humidity

wind speed atreference level

( )( )zqqUCLLE −= ρ ( )( )rasrDE zqqUCLLE −= ρ

Transfer Coeff. (humidity)

Vapor Pressure (e)• Vapor pressure (e) is simply the amount of pressure exerted only by the water vapor in the air

• The pressures exerted by all the other gases are not considered

• The unit for vapor pressure will be in units of pressure (millibars and hectoPascals are the same value with a(millibars and hectoPascals are the same value with a different name) 

Saturation water vapor pressure

es = 0.6108 [exp(17.27 Ta) ⁄ (Ta + 237.3)][kPa]

e = (RH es) ⁄ 100Water vapor pressure

Specific humidity

(Allen et al.1998, Evett 2002)

SOIL HEATSOIL HEAT FLUXFLUXSOIL HEAT SOIL HEAT FLUXFLUX

Ground Thermal VariationsVariations

Ground Temperatures Variations• exponential decrease of diurnal wave 

amplitude (A) with depth

• phase shift of wave with depth• phase shift of wave with depth

• For typical soil, A becomes insignificant below 1 m.

Source: The Hydrology Technical Group Pacific Northwest NationalGroup, Pacific Northwest National

Laboratory (PNNL), Richland, Washington

Soil heat fluxP i il b d ti i ti• Primarily by conduction, i.e. no convection

• Found to be proportional to temperature gradient and thermal conductivity (λ) ( )thermal conductivity (λ).

• λ ‐ the thermal conductivity, is the amount of heat

( )dzdTG λ−=

λ the thermal conductivity,  is the amount of heat transferred through a unit area in unit time under a unit temperature gradient. For soil it depends upon its mineral 

iti d OM t t ll th lcomposition and OM content, as well as on the volume fractions of water and air.

• For same porosity, λ increases with an increase in volume wetness for a given soil.  However, for same porosity and g , p ywetness: λ(sand) > λ (clay).

Thermal diffusivity (κ)

C = heat capacity = specific heat density = c ρ

κ – thermal diffusivity (change in temperature produced in a unit volume by the quantity of heat flowing through th l i it ti d it t tthe volume in unit time under a unit temperature gradient)