Understanding past climate variability and predicting future climate changes requires long records of observed climate fields. However, observations from the past are typically noisy and irregularly sampled in time and space, with large spatial gaps. Improved representations of the uncertainty in analyzed fields would be extremely useful in climatological research. To help meet this need, this project will pursue research into a systematic and robust method of producing an analyzed field from gappy climate data. The approach to be taken is to attempt to fuse two computationally efficient approaches that address variability at different scales. The first of the two methods was developed in climate research and uses a low-rank approximation to the system error covariance matrix. The method reconstructs mainly large-scale features of a climate field and hence misses most of small-scale variability. The second approach stems from Bayesian estimation in geostatistics that combines the strength of a globally estimated covariance with nonstationary local estimates; it represents the uncertainty not only due to the observational noise and sampling deficiencies, but also uncertainty due to unknown covariance relationships. The methods have been developed independently and their coupling for a practical climatological application or representing uncertainty in a historical analysis by ensemble has yet to be accomplished. To make this approach work for realistic climate problems requires the theoretical research proposed
If successful, the result of the project will the development of an efficient numerical algorithm suitable for very large, disparate, irregularly spaced climatological data sets that a) reconstructs variability on different scales, b) produces an average analysis field over a regular spatio-temporal grid and, c) yields a method to produce a collection of equally likely analysis fields (an ensemble) which reflects the uncertainty in the average analysis field. The method will then be applied to data sets of marine and land climate important to current climatological research. The results will also provide a better technique for creating the initial conditions for climate simulation ensembles, permitting better estimation of uncertainty in predictions of climate variation. Software implementing the new approach and the climate data sets derived from it will be made publicly available.
