In environmental radiation monitoring, the time-variable natural gamma radiation background complicates the nuclide identification and analysis of a gamma spectrum. A full spectrum analysis based on the noise adjusted singular value decomposition method for the description of the time-variable background and adjustment calculations is a possible analysis method, which may provide advantages compared with a peak-based analysis, if applied to a time series of gamma spectra. An analysis example is shown and discussed with a measured time series of gamma spectra obtained from a spectroscopic gamma detector with a NaI(Tl) scintillator as it is used in the environmental radiation monitoring.