In many practical applications the state of field soils is monitored
by recording the evolution of temperature and soil moisture at discrete
depths. We theoretically investigate the systematic errors that arise
when mass and energy balances are computed directly from these measurements.
We show that, even with no measurement or model errors, large residuals
might result when finite difference approximations are used to compute
fluxes and storage term. To calculate the limits set by the use of
spatially discrete measurements on the accuracy of balance closure,
we derive an analytical solution to estimate the residual on the
basis of the two key parameters: the penetration depth and the distance
between the measurements. When the thickness of the control layer
for which the balance is computed is comparable to the penetration
depth of the forcing (which depends on the thermal diffusivity and
on the forcing period) large residuals arise. The residual is also
very sensitive to the distance between the measurements, which requires
accurately controlling the position of the sensors in field experiments.
We also demonstrate that, for the same experimental setup, mass residuals
are sensitively larger than the energy residuals due to the nonlinearity
of the moisture transport equation. Our analysis suggests that a
careful assessment of the systematic mass error introduced by the
use of spatially discrete data is required before using fluxes and
residuals computed directly from field measurements.