Soil moisture variability is analysed in the re-analysis data ERA-40 of the European Centre for Medium-Range Weather Forecasts (ECMWF) which includes four layers within 189 cm depth. Short-term correlations are characterised by an e-folding time scale assuming an exponential decay, whilst long-term memory is described by power law decays with exponents determined by detrended fluctuation analysis. On a global scale, the short-term variability varies congruently with long-term memory in the surface layer. Key climatic regions (Europe, Amazon and Sahara) reveal that soil moisture time series are non-stationary in arid regions and in deep layers within the time horizon of ERA-40. The physical processes leading to soil moisture variability are linear according to an analysis of volatility (the absolute differences), which is substantiated by surrogate data analysis preserving the long-term memory.