Error Analysis of the Heat Pulse Method for Measuring Soil Volumetric Heat Capacity

Abstract

Abstract A recently developed heat pulse method allows rapid, automated measurements of the volumetric heat capacity (ρ c ) of soil. Estimation of ρ c is accomplished by using a model for the conduction of heat away from an instantaneously heated infinite line source (IHILS). This study was conducted to examine possible errors in the use of the IHILS theory by comparing the IHILS model with three other models that account for the following characteristics of the heat pulse apparatus: finite probe length, cylindrical heater geometry, and short‐duration (noninstantaneous) heating. For typical probe geometry and heating times, estimates of ρ c obtained from the IHILS theory were within 1% of the estimates obtained by using the more rigorous models. The most significant error resulted from approximating short‐duration heating with instantaneous heating in the IHILS model. A generalized error analysis is presented that permits direct graphical estimation of errors for different probe geometries, different heating times, and different soil thermal properties. First‐order error analysis was also used to examine potential error in ρ c as a result of errors in probe spacing ( r ), temperature maximum ( T m ), and heat input ( q ), the measured quantities that are used in the IHILS model to estimate ρ c . Relative errors of 1% in measuring q and T m lead to relative errors of 1% in ρ c , whereas a relative error of 1% in r resulted in a 2% error. Measurement error in r and T m limits the precision achievable with this method.