GEOG 402. Soil Temperature and Soil Heat Conduction. Summit of Haleakalā. Surface Temperature. 20 Soil Temperature at 5.0 cm.

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1 GEOG 40 Soil Temperature and Soil Heat Conduction Summit of Haleakalā Surface Temperature Soil Temperature at.5 cm 0 Soil Temperature at 5.0 cm 5 0 Air Temp 5 0 0:00 3:00 6:00 9:00 :00 5:00 8:00 :00 0:00 Bare cinder substrate Tsoil & Tair: Mean diurnal cycle Oct 996 Tir: Mean diurnal cycle Oct 00

2 Sensible Heat Transfer to and from Soil Soil Heat Conduction or Soil Heat Flux (G) Soil is major storage location for heat Acts as an energy sink during the day Acts as an energy source at night 3 Definitions Heat capacity: ratio of heat absorbed to the temperature increase (J K - ). Mass specific heat: the amount of energy needed to raise the temperature of kg of a substance by degree (J kg - K - ). Volume specific heat: the amount of energy needed to raise the temperature of m 3 of a substance by degree (J m -3 K - ). 4

Ohm s Law Georg Ohm (87) I = V R I = electrical current (amperes) V = potential difference (volts) R = resistance (ohms) Solution: I = V R = V 3Ω = 4A 5 http://www.allaboutcircuits.com/vol_/chpt_/.

3 Ohm s Law Georg Ohm (87) I = V R I = electrical current (amperes) V = potential difference (volts) R = resistance (ohms) Solution: I = V R = V 3Ω = 4A 5 Soil Heat Flux and Thermal Conductivity I = V R = R V = KV where K = ; conductivity (K) is the inverse of resistance R S = K dt dz where: K = thermal conductivity of the soil (W m - K - ) dt dz Ohm s Law Analogy = the vertical temperature gradient in the soil Note: energy fluxes toward surface are positive; fluxes away 6 from surface are negative. 3

4 α = K C s = K ρ c s where: Thermal Diffusivity α = thermal diffusivity of the soil (m s - ) C s = heat capacity of the soil (Jm 3 K ) ρ = soil density (kg m 3 ) c s = specific heat of soil (J kg K ) 7 Influences on Soil Thermal Properties Soil Texture Soil Moisture Content Thermal conductivity and specific heat of soil both increase with water content Rosenberg et al. (983, Fig..a) 8 4

5 Temperature Profile Temperature cycle at greater depth lags behind temperature cycle at shallower depth Temperature cycle at greater depth has lower amplitude than temperature cycle at shallower depth Penetration of Heat into the Ground ( " π % z = s exp* z$ ' )* # α p& where: z = temperature ranges at depth z ( C) s = temperature ranges at the surface ( C) z = depth (m) α = thermal diffusivity (m s - ) ,- p = period of oscillation (s) 0 5

6 Lag in Heat Penetration t t = where : t t z z p απ 0.5 = time at which maxima or minima occur at depth z = time at which maxima or minima occur at depth z Examples For light soil with roots, get the relative diurnal and annual soil heat flux wave amplitudes at depths of 0.5 and 0. m. z = e s ( " z π % * $ ' ) * # α p& , - α = 3.0 x 0-7 m s - for light soil with roots p = 86,400 s for the diurnal cycle p = 3.6 x 0 7 s for the annual cycle 6

7 Examples Solution for light soil with roots: z s = for diurnal cycle at z = 0. m z s = for diurnal cycle at z = 0.5 m z s = for annual cycle at z = 0. m z s = for annual cycle at z = 0.5 m 3 Examples For wet sandy soil, get the relative diurnal and annual soil heat flux wave amplitudes at depths of 0. and 0.5 m. α =.0 x 0-6 m s - for wet sandy soil 4 7

8 z s z s z s z s = = Examples Solutions for wet sandy soil: for diurnal cycle at z for diurnal cycle at z = 0.m = 0.5 m = for annual cycle at z = 0.m = 0.854for annual cycle at z = 0.5 m 5 Summary Relative amplitude Light soil with roots z Diurnal Annual Wet sandy soil z Diurnal Annual

9 Examples For light soil with roots, get the lag time for the diurnal and annual soil heat flux waves at depths of 0., 0.5, and 5 m. = t where : t = lag time between occurence of at depth z = α = 3.0 x 0 p = 86,400 s for thediurnal cycle p = 3.6 x 0 z compared with z -7 z 7 m s - p απ 0.5 for light soil with roots s for theannual cycle maxima or minima 7 Examples Solutions for light soil with roots: = 4 hr min for diurnal cycleat z = 0.m = 3 days 8 hours for annual cycle at z = 0.m = hours for diurnal cycle at z = 0.5 m = 6 days8 hours for annual cycle at z = 0.5 m = 8 days8 hours for diurnal cycle at z = 68 days for annual cycle at z = 5 m = 5 m 8 9

Summary Lag times for light soil with roots z Diurnal Annual 0. 4 hrs min 3 days 8 hrs 0.5 hrs 6 days 8 hrs 5.

10 Summary Lag times for light soil with roots z Diurnal Annual 0. 4 hrs min 3 days 8 hrs 0.5 hrs 6 days 8 hrs days 8 hrs 68 days 9 Measurement To get soil heat flux in the field, we need to take measurements with three types of instruments. 0 0

11 Field set up: Measurement G 8cm ΔT = G 8cm + S Data Analysis ΔTsCsd S = t G = soil heat flux at the surface(w m G C sfc sfc s s = soil heat flux measured at 8 cm depth (W m = change in soil temperature (K) = heat capacity of the moist soil d = depth of soil layer (m) t = time interval (s) - ) - )

C s = ρ b θ m = ρ w ρ b θ v Data Analysis ( C d +θ m C w ) C s = heat capacity of moist soil C d = heat capacity of dry mineral soil C w = heat capacity of water ρ b = soil bulk density ρ w =

12 C s = ρ b θ m = ρ w ρ b θ v Data Analysis ( C d +θ m C w ) C s = heat capacity of moist soil C d = heat capacity of dry mineral soil C w = heat capacity of water ρ b = soil bulk density ρ w = density of water θ m = mass soil water content (kg 3 kg -3 ) θ v = volume soil water content (m 3 m -3 ) 3 Data Analysis Example Measurements from two soil HFT3 sensors give us samples of G at 8 cm depth. 4

5 Data Analysis Example Adding the smoothed values of change in stored sensible heat

13 Data Analysis Example Temperature change in the upper 8-cm layer is used to estimate change in stored sensible energy in that layer. These data need to be smoothed. 5 Data Analysis Example Adding the smoothed values of change in stored sensible heat in the 0- to 8-cm layer to the average of the two HFT3s gives us our estimate of G sfc. 6 3

Lecture 10. Surface Energy Balance (Garratt )

Lecture 10. Surface Energy Balance (Garratt 5.1-5.2) The balance of energy at the earth s surface is inextricably linked to the overlying atmospheric boundary layer. In this lecture, we consider the energy