Typical approaches to climate signal estimation from data are susceptible to biases if the instrument records are incomplete, cover differing periods, if instruments change over time, or if coverage is poor. Here a method (Iterative Universal Kriging, or IUK) is presented for obtaining unbiased, maximum-likelihood (ML) estimates of the climatology, trends, and/or other desired climatic quantities given the available data from an array of fixed observing stations that report sporadically. The conceptually straightforward method follows a mixed-model approach, making use of well-known data analysis concepts, and avoids gridding the data. It is resistant to missing data problems, including selection bias, and should also be helpful in dealing with common data heterogeneity issues and gross errors. Perhaps most importantly, the method facilitates quantitative error analysis of the signal being sought, assessing variability directly from the data without the need for any auxiliary model. The method is applied to rawinsonde data to examine weak meridional winds in the equatorial lower stratosphere, providing some improvements on existing climatologies. ¿ 2000 American Geophysical Union