This code is for a project to correct misreported observation times in data assimilation. Paper in preparation. Draft abstract:
Data assimilation, the joining of computer models with measurements, is applied in a variety of scientific fields involving forecasting of dynamical systems, most prominently in atmospheric and ocean sciences. The existence of misreported observation times (time error) poses a unique and interesting problem for data assimilation. Mapping observations to incorrect times causes bias in the prior state and affects assimilation. We find that the presence of normally distributed time error well within the error bounds of NWS radiosonde launch intervals has a significant negative impact on forecast skill in low-order models. We propose a numerical method to determine the probability distribution of time error, then show analytically that the method returns the correct time error with an overdispersive estimate of variance in a simplified case. We also propose a method to use the inferred time error distribution to update the observation likelihood distribution when using a Kalman filter, then test the methods on a low-order chaotic dynamical system. We find that implementing this method, both with a known distribution for time error and with the inferred distribution, is associated with significant increases in forecast skill. Moreover, we find that the inferred time error distribution may be applied to achieve generally more accurate estimates of observation time for individual observations. Examination of inferred time error for the treatments suggests that the bias we calculate in variance is less significant a contributor to the error in the inference than is error introduced by chaos in certain dynamical systems. The results suggest that the proposed method may be useful and applicable to assimilation in time-sensitive environments.