This work introduces a new climate description scheme based on a long range statistical model fitted to local daily temperature anomaly series. The appropriate model can be considered as a sum of two processes, namely, stationary white noise (WN) and nonstationary random walk (RW). In the case of local series, the variance of the WN component appears to be much larger than that for the generator of RW (also a WN, but independent on the first one). Such a situation enables us to approximate the range of variability for local temperature anomalies by means of the standard deviation of the stationary WN component of the model. This means that the climate description splits into two parts; one describes ordinary and the other extreme weather events. This paper presents a detailed description of that approach using the air temperature series from Stockholm (1756–2011) as an example. The scheme produced here enables us to see that large weather variability does not always mean climate variability. It separates climate and weather scale variability, which is important for precise determination of climate variability and does not confuse the weather and climate time scales in climate description.