Analysis of the dynamic response of the thermometric net radiometer

Several authors have considered the possibility that the net radiation measurement may be the seat of the widely perceived energy balance closure problem, but apparently in all cases presupposing that time variation of the radiative fluxes on turbulence timescales need not be considered. However by virtue of the flux boundary conditions on its upper and lower planes, the equations governing the response of a thermometric radiometer are non-linear, raising the possibility that if the long wave flux densities vary in time on frequencies that are rapid compared to the reciprocal of the inertial time constant of the device, a mean signal might be produced even in the absence of a mean net longwave flux density: such a bias would not be detected in steady state calibrations. By adopting an elementary non-linear description of the thermometric sensor and solving for the temperature as function of time and position under sinusoidal radiative forcing, it is proven that apparently such a bias {\em does not} exist.