of hemispheric or global average temperatures. This is complemented by Climate Field Reconstruction (CFR) methods which show how climate patterns have developed over large spatial areas. Considerable care must be taken in the averaging process; for example, if a certain region has a large number of tree ring records, a simple average of all the data would strongly over-weight that region, and statistical techniques are used to avoid such over-weighting. In the and CFR reconstructions, principal components analysis was used to combine some of these regional records before they were globally combined. An important distinction is between so-called 'multi-proxy' reconstructions, which attempt to obtain a global temperature reconstruction by using multiple proxy records distributed over the globe and more regional reconstructions. Usually, the various proxy records are combined arithmetically, in some weighted average. More recently, Osborn and Briffa used a simpler technique, counting the proportion of records that are positive, negative or neutral in any time period. This produces a result in general agreement with the conventional multi-proxy studies. The 2007 IPCC Fourth Assessment Report cited 14 reconstructions, 10 of which covered 1,000 years or longer, to support its conclusion that "Average Northern Hemisphere temperatures during the second half of the 20th century were very likely higher than during any other 50-year period in the last 500 years and likely the highest in at least the past 1,300 years". Qualitative reconstruction using historical records It is also possible to use historical data such as times of grape harvests, sea-ice-free periods in harbours and diary entries of frost or heatwaves to produce indications of when it was warm or cold in particular regions. These records are harder to calibrate, are often only available sparsely through time, may be available only from developed regions, and are unlikely to come with good error estimates. These historical observations of the same time period show periods of both warming and cooling. Limitations The apparent differences between the quantitative and qualitative approaches are not fully reconciled. The reconstructions mentioned above rely on various assumptions to generate their results. If these assumptions do not hold, the reconstructions would be unreliable. For quantitative reconstructions, the most fundamental assumptions are that proxy records vary with temperature and that non-temperature factors do not confound the results. In the historical records temperature fluctuations may be regional rather than hemispheric in scale. In a letter to Nature pointed at the original title