Heat Pulse Measurements to determine: soil thermal properties soil water content infiltrating liquid water flux sensible heat flux in soil latent heat flux (vaporization or fusion) upward liquid water flux Agron 405/505

Soil heat and water dynamics Impact biological, chemical, and physical, processes Modeling coupled heat and water dynamics is difficult and requires many hard to measure parameters Measuring in situ coupled heat and water dynamics has improved recently

Jackson SSSA Spec. Publ., 5, 37–55 Diurnal soil water content change 5, 6, and 7 days after irrigation Sun rise Sun set

Coupled Heat and Water Transfer Thermal gradients cause water to move in unsaturated soil. When water moves in soil, it carries heat. Because heat transfer and water movement affect one another they are coupled.

Theory Water Flow Heat Transfer

Some heat pulse probe possibilities Measure soil thermal properties Measure soil water content Measure infiltrating liquid water flux Measure sensible heat flux in soil Measure latent heat flux (vaporization or fusion) Measure upward liquid water flux

Heat Pulse Probe

40 mm 6 mm 1.3 Stainless steel tubing Thermocouple Resistanceheater Sketch of a heat pulse sensor Heat pulse probe

t(s)  T ( o C) (t m, T m ) A V Datalogger DC power r Heat Pulse Method For a cylindrical coordinate, heat conduction Eq. and solution:

Temperature response after applied t 0 =8 s heat pulse on the central heater needle Time (s) Temperature increase (K) t m =30 s ΔT m =1.23 K Determining of soil thermal properties by heat pulse sensor

Soil thermal conductivity (W/m  C): Soil heat capacity C (J/m 3  C): Soil thermal diffusivity (J/m 3  C)                 r ttt t tt mm m m () ln ()

Example of heat pulse data By fitting a heat transfer model to the heat pulse data we determine the soil thermal properties. Time (s) Temperature increase (K)

Thermal properties

Soil thermal properties

Influences of soil texture,  b and  on bb

Calculation of Volumetric Heat Capacity This equation can be used to estimate soil  b or  with the heat-pulse technique.

Factors Influencing Soil  c For mineral soils,  c increases linearly with 

Thermo-TDR Water Content

Upstream needle Heater Downstream needle 1 cm  Heat pulse measurements for estimating soil liquid Water Flux

Heat transfer equations The governing heat transfer equation is where J is the water flux [volume / (time x area)]

A solution to heat transfer equation (Ren et al., 2000)

The relationship between water flux and the temperature ratio is very simple (Wang et al., 2002) The ratio of downstream and upstream T increase When

Temperature ratio is constant

Sand Measured heat pulse signals

Sand Heat pulse signals converted to T d /T u

Heat pulse flux estimates versus imposed unsaturated fluxes

A Heat Pulse Technique for Estimating Soil Water Evaporation

Basic theory of HP method: Sensible heat balance provides a means to determine latent heat (LE) used for evaporation. Sensible heat balance provides a means to determine latent heat (LE) used for evaporation. LE = (H 1 – H 2 ) –  S LE = (H 1 – H 2 ) –  S condensation nevaporatio n no    LE Sensible heat flux out, H 2 Sensible heat flux in, H 1 Sensible heat storage change  S

Determining the dynamic soil water evaporation H1H1 H2H2 Sensible soil heat flux: H =- (dT/dz) 1, C 1, 2, C 2, dT/dz 1, dT/dz 2, LE = (H 1 – H 2 ) –  S T3T3 T2T2 T1T1 Soil layer SS Change in sensible heat storage: ΔS = C (ΔZ) (dT/dt) Heat-pulse sensor12 3

Heat-pulse sensors arrangement. Six sensors were installed within the top 7 cm of the soil profile. 7cm

Temperature (T ); Heat capacity (C) and thermal conductivity(λ) C (MJ/m 3 C) T ( C) C Day of year 2007 λ ( W/ mC )

Heat fluxes at 3 and 9 mm (H1,H2); heat storage change ( ∆S) at soil layer (3~9 mm) Day of year 2007 H and ∆S (W/m 2 )

Evaporation dynamics measured by heat pulse method Evaporation (mm/hr) Day of year ~9 mm 1st depth 9~15 mm 2nd 15~21 mm 3rd 21~27 mm 4th

Comparison of daily soil water evaporation (mm) from heat pulse with micro-lysimeters and Bowen ratio methods HP daily evaporation (mm)Micro-lysimeters daily evaporation (mm)

Latent Heat in Soil Heat Flux Measurements

Better Energy Balance Closure When the latent heat flux (LE) includes evaporation from soil, the depth at which we measure soil heat flux (G) is critical to accurately representing the surface energy balance. Objective: Characterize variations in G with depth near the soil surface.

Materials and Methods Soil heat flux (G) measured via heat-pulse sensors installed at 3 depths: 1, 3, and 6 cm G = - (  T/  z)

cutaway view soil surface heat-pulse sensor side view 1 cm 3 cm 6 cm

Materials and Methods Evaporation (LE) determined via microlysimeters (per 24 h)

Cumulative Soil Heat Flux at 1-cm Depth

‘G’ measured above the drying front isn’t really G – its G + LE.

Accumulated Energy

Conclusions Shallow soil heat flux measurements may capture G + (soil- originating) LE Leads to ‘double accounting’ for LE in energy balance closure based on above-ground measurements Recommendation: G must be measured at a depth below the expected penetration of the drying front (here, possibly as deep as 6 cm) in order to treat the surface energy balance as R n – G = LE + H

HP sensors installed in a corn field in 2009 Bare soil In-row Between-rows with roots Between-rows without roots

Soil temperature at different locations Temperature ( ˚ C) Day of year

Evaporation (mm) Day of year 2009 Soil water evaporation dynamics

Day of year 2009 Cumulative soil water evaporation at 3-mm soil depth Cumulative Evaporation (mm)

For a soil layer, ΔE is the evaporation rate (cm/h), F t and F b are the liquid water flux (cm/h) at top and bottom boundaries, and ΔS is the change in water storage (cm/h). E Water storage change  S FdFd FuFu

Liquid water flux at the 7.5 mm soil depth from the model simulation.

Conclusions The heat pulse method is able to provide a wide range of soil heat and water measurements. This is an important time period to advance coupled heat and water experiments and models.

References Ren, T., G.J. Kluitenberg, and R. Horton Determining soil water flux and pore water velocity by a heat pulse technique. Soil Sci. Soc. Am. J. 64:552–560. Wang, Q., T.E. Ochsner, and R. Horton Mathematical analysis of heat pulse signals for soil water fl ux determination. Water Resour. Res. 38, DOI /2001WR Heitman, J.L., R. Horton, T.J. Sauer, and T.M. DeSutter, Sensible heat observations reveal soil water evaporation dynamics, J. Hydrometeor., 9: Heitman, J.L., X. Xiao, R. Horton, and T. J. Sauer, Sensible heat measurements indicating depth and magnitude of subsurface soil water evaporation. Water Resour. Res., 44, W00D05, doi: /2008WR Xiao X., R. Horton, T.J. Sauer, J.L. Heitman and T. Ren, Cumulative soil water evaporation as a function of depth and time. Vadose Zone J. (in press).