Time-Sampling Errors of Earth Radiation From Satellites: Theory for Outgoing Longwave Radiation

The measurements of radiation budget by satellites in low Earth orbit provide limited sampling of the diurnal cycle. Thus, maps of monthly mean radiation fluxes contain errors due to this limitation. The Earth Radiation Budget Experiment reduced these errors in the data products by using a half-sine fit to account for regional diurnal cycles. An algorithm is presented to compute errors that are created when one computes the average value of outgoing longwave radiative flux (OLR) for a month based on the half-sine fit. Details of the temporal sampling are described by a sampling matrix that gives the number of OLR measurements in each local hour and each day of the month. The error analysis must take into account the correlation in time between irregularly spaced data due to synoptic variations, the weighting of measurements to accommodate the half-sine fit and deviations of the regional diurnal cycle from the half-sine. Using these ingredients, a closed-form expression is presented for the standard deviation of the temporal-sampling errors of the monthly mean OLR as computed from satellite measurements. The method is demonstrated for a well-sampled case and a poorly sampled case. This approach can be used to evaluate data products for existing measurements and for future mission design, or evaluating measurements of other atmospheric parameters.