Record occurrence and record values in daily and monthly temperatures

We analyze the occurrence and the values of record-breaking temperatures in daily and monthly temperature observations. Our aim is to better understand and quantify the statistics of temperature records in the context of global warming. Similar to earlier work we employ a simple mathematical model of independent and identically distributed random variables with a linearly growing expectation value. This model proved to be useful in predicting the increase (decrease) in upper (lower) temperature records in a warming climate. Using both station and re-analysis data from Europe and the United States we further investigate the statistics of temperature records and the validity of this model. The most important new contribution in this article is an analysis of the statistics of record values for our simple model and European reanalysis data. We estimate how much the mean values and the distributions of record temperatures are affected by the large scale warming trend. In this context we consider both the values of records that occur at a certain time and the values of records that have a certain record number in the series of record events. We compare the observational data both to simple analytical computations and numerical simulations. We find that it is more difficult to describe the values of record breaking temperatures within the framework of our linear drift model. Observations from the summer months fit well into the model with Gaussian random variables under the observed linear warming, in the sense that record breaking temperatures are more extreme in the summer. In winter however a significant asymmetry of the daily temperature distribution hides the effect of the slow warming trends. Therefore very extreme cold records are still possible in winter. This effect is even more pronounced if one considers only data from subpolar regions.