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Errors of Dual Thermal Probes Due to Soil Heterogeneity across a Plane Interface

^a CSIRO Land and Water, G.P.O. Box 1666, Canberra, ACT 2601, Australia
^b Dep. of Agronomy, Kansas State University, Manhattan, KS 66506 USA

View larger version (60K): [in a new window]   Fig. 1 The heating probe H at (x,z) = (0,0) on the interface between soil in z > 0 with = +, C = C+ and z < 0 with = -, C = C-. The sensor is at (x,z) = (0,)

View larger version (40K): [in a new window]   Fig. 2 Dual probes near the soil surface or wetting front. Configurations (a), (b), and (c) of heating probe H and sensor S are presented. For each configuration H is at (x,z) = (0,0)

View larger version (18K): [in a new window]   Fig. 3 Dependence of the ratio tmh/tm on z0/ for dual probes near a surface or front. In the heterogeneous system the sensor maximum temperature occurs at t = tmh. For a homogeneous system it occurs at t = tm. Here is the distance between probes, z0 the distance between the surface or front and the probes (Configuration [a]) or the nearer probe (Configurations [b] and [c]). The near-surface curves apply also behind a wetting front

View larger version (16K): [in a new window]   Fig. 4 Dependence of the ratio Tmh/Tm on z0/ for dual probes near a surface or front. Tmh is the sensor maximum temperature in the heterogeneous system. For a homogeneous system it is Tm. Other symbols are the same as in Fig. 3

View larger version (24K): [in a new window]   Fig. 5 Bounds on fractional errors in thermal diffusivity , thermal conductivity , and volumetric heat capacity C for dual probes near a surface when heterogeneity is ignored. The label on each curve indicates , , or C, together with the configuration. The curves apply also to probes behind a wetting front

View larger version (22K): [in a new window]   Fig. 6 The same as for Fig. 5 for dual probes near a wetting front. Bounds on fractional errors in , , and C are 1, , and respectively as z0/ 0