Techniques for analyses of trends in GRUAN data

Abstract. The Global Climate Observing System (GCOS) Reference Upper Air Network (GRUAN) provides reference quality RS92 radiosonde measurements of temperature, pressure and humidity. A key attribute of reference quality measurements, and hence GRUAN data, is that each datum has a well characterized and traceable estimate of the measurement uncertainty. The long-term homogeneity of the measurement records, and their well characterized uncertainties, make these data suitable for reliably detecting changes in global and regional climate on decadal time scales. Considerable effort is invested in GRUAN operations to (i) describe and analyse all sources of measurement uncertainty to the extent possible, (ii) quantify and synthesize the contribution of each source of uncertainty to the total measurement uncertainty, and (iii) verify that the evaluated net uncertainty is within the required target uncertainty. However, if the climate science community is not sufficiently well informed on how to capitalize on this added value, the significant investment in estimating meaningful measurement uncertainties is largely wasted. This paper presents and discusses the techniques that will need to be employed to reliably quantify long-term trends in GRUAN data records. A pedagogical approach is taken whereby numerical recipes for key parts of the trend analysis process are explored. The paper discusses the construction of linear least squares regression models for trend analysis, boot-strapping approaches to determine uncertainties in trends, dealing with the combined effects of autocorrelation in the data and measurement uncertainties in calculating the uncertainty on trends, best practice for determining seasonality in trends, how to deal with co-linear basis functions, and interpreting derived trends. Synthetic data sets are used to demonstrate these concepts which are then applied to a first analysis of temperature trends in RS92 radiosonde upper air soundings at the GRUAN site at Lindenberg, Germany (52.21° N, 14.12° E).