1. A heat pulse technique for measuring water flow in soil Tyson Ochsner USDA-ARS Soil and Water Management Research Unit St. Paul, MN

2. Application of the heat pulse technique Upstream sensor Heater Downstream sensor 1 cm The heat transfer occurs by conduction and convection.

3. Heat transfer equations where J w is the water flux. The governing heat transfer equation is The solution of this governing equation leads to a simple relationship between water flux and the temperature increase ratio.

4. We tested the technique in the lab using packed columns of sand, sandy loam, and silt loam soil. Laboratory experiments

5. Heat pulse signals converted to T d /T u The temperature increase ratio increases with flow rate. Sand Flux (cm h -1 )

6. Resulting water flux estimates Strong linear relationship between flux measured by the sensor and that measured at the column outlet.

7. Soil type Slope (S) Intercept Std. Err. r2r2 cm hr -1 Sand0.7650.6050.3900.998 Sandy loam0.2320.4520.1250.998 Silt loam0.4002.880.0710.999 Linear regression results Regression results indicate good precision and linearity, but the slopes are less than one.

8. Linking theory and measurements Choosing a = 1/S and b = 1 leads to an enhanced conduction model. Choosing a = 1 and b = S leads to a reduced convection model.

10. Results The smallest flux detected with the heat pulse technique was 0.12 cm hr -1. The relationship between heat pulse flux estimates and the outflow flux was linear up to 40 cm hr -1. The standard heat transfer model over- predicted the sensitivity of the heat pulse sensor to water flux. A reduced convection model accounted for the discrepancies between the measured data and the standard model.

11. Closing statements Uncorrected heat pulse measurements are fairly accurate in sand. Theoretical over-predictions of instrument response to convective heat transfer are common. A reliable procedure for correcting heat pulse measurements is needed. The heat pulse approach for measuring soil water flux warrants further development.

12. Acknowledgements Collaborators are Robert Horton, Gerard J. Kluitenberg, and Quanjiu Wang. This work was conducted at Iowa State University.