A gridded monthly upper-air data set from 1918 to 1957

Abstract

Significant efforts have been devoted in recent years towards extending observation-based three-dimensional atmospheric data sets back in time. Such data sets form an important basis for a better understanding of the climate system. Here we present a new monthly three-dimensional global data set that is based on historical upper-air data and surface data. We use statistical reconstruction techniques, calibrated using ERA-40 data, to obtain gridded data from the numerous, but scattered and heterogeneous historical upper-air observations. In contrast to previous work, in which we used hemispheric principal components on both the predictor and the predictand side to reconstruct spatially complete fields back to 1880, we restrict the procedure to places and times where upper-air observations are available. Each grid column (consisting of four variables at six levels) is then reconstructed independently using only predictor variables in the vicinity (i.e., only local stationarity is required rather than stationary large-scale patterns). The product, termed REC2, is a gridded, global monthly data set of geopotential height, temperature, and u and v wind from 850 to 100 hPa back to 1918. The data set is sparse (i.e., many grid cells are empty), but provides an alternative to large-scale reconstructions as it allows for non-stationary teleconnections. We show the results of several validation experiments, compare our new data set with a number of existing data sets, and demonstrate that it is suitable for analysing large-scale climate variability on interannual time-scales.

Appendix: Addition of noise to the ERA-40 predictors

Gaps in the predictor data (i.e., the observations) during the calibration period were filled with ERA-40 data. In order to account for the differences between reanalysis and observations, we perturbed the interpolated reanalysis data (i.e., all filled gaps) by a stochastic error model with three components: a constant bias, an error in each monthly profile, and a random error. Except for the last error, the errors within a profile are dependent. Therefore, we first defined error profiles which in a later step were scaled with random numbers. The error is 0.75°C for temperature, 1 m/s for wind (constant with altitude), and 12.3, 14.8, 16.8, 19.2, 22.1, 25.9, 31.1, 35.1, and 40.1 gpm, respectively, for GPH at 850, 700, 600, 500, 400, 300, 250, 200, and 100 hPa.

The introduced bias is a step inhomogeneity with random start date (sampled from an equal distribution) and random length (between 5 and 30 years) that affects each station independently. Note that if the ending date is still within the period, there will be two steps. The bias is thought to describe step inhomogeneities that may arise due to changes in instruments, for instance. The bias is vertically coherent, i.e., we sampled one number from a random normal distribution with a mean of 0 and a standard deviation of 1, N(0,1), to scale the error profiles of both variables (i.e., either u and v or GPH and temperature; there is no record with all four variables). Large temperature errors (constant with altitude) are accompanied by large GPH errors (increasing in magnitude with height) of the same sign. This is a very typical error for radiosonde data (although other errors are possible). Large u-wind anomalies are accompanied by large v-wind anomalies of the same sign, which is also an error that can occur (e.g., due to unit errors or errors in the reduction process), although there is no such thing as a typical wind error profile.

The profile error also is vertically coherent (as described above), but applies to each individual monthly mean independent of the previous month. It was also generated by sampling from N(0,1). Errors of that sort may arise from sampling, but also from instrumental errors. Finally, the random error is completely random, i.e., has no vertical, spatial, or temporal structure. This part of the error measures the random error of the instrument reading. It was also generated by sampling from N(0,1), but in this case for each variable and level individually.

The contributions of the three sources of error to the total variance of the error were chosen as 25, 37.5, and 37.5%. Note that these fractions as well as the timing of biases (see above) are somewhat arbitrarily chosen. Real observational series may have more complex step inhomogeneities (or network-wide biases), they may also have trend inhomogeneities, and u and v wind errors may have different relations. Also, possible undercorrection or overcorrection of radiation errors could lead to errors that are dependent on the altitude, the time of day, and the month of the year. However, the assumptions required for modeling such errors are increasingly difficult to justify. In any case, the disturbances resulting from our process have the desired magnitudes (see Brönnimann 2003; Grant et al. 2009a, b, and Stickler et al. 2010 for approximate errors in the historical upper-air data) and appear reasonable.

Note that these errors adjust for the differences between ERA-40 and upper-air observations and hence they also represent (partly unknown) errors and uncertainties in ERA-40 (although at locations where upper-air data was assimilated into ERA-40, the two are normally very close).