Sampling error of observation impact statistics

An observation impact is an estimate of the forecast error reduction by assimilating observations with numerical model forecasts. This study compares the sampling errors of the observation impact statistics (OBIS) of July 2011 and January 2012 using two methods. One method uses the random error under the assumption that the samples are independent, and the other method uses the error with lag correlation under the assumption that the samples are correlated with each other. The OBIS are obtained using the forecast sensitivity to observation (FSO) tool in the Korea Meteorological Administration (KMA) unified model (UM). To verify the self-correlation of the observation impact data, the lag correlations of the observation impact data at 00 UTC in the Northern Hemisphere (NH) summer months (June, July and August 2011) and winter months (December 2011 and January and February 2012) are calculated. The self-correlation approaches zero at 6 days for the summer, whereas it approaches zero at 4 days for the winter, which implies that the observation impact data are serially correlated. The sampling error considering lag correlation is larger than the random error for NH summer and winter. While the random sampling error is approximately 12–13% of the approximation error, the sampling error considering the lag correlation is approximately half of the approximation error of the OBIS. The sampling error that considers the lag correlation of the OBIS is more appropriate for representing the uncertainty in the OBIS because the OBIS at different times are correlated.