A simple framework to quantitatively describe monthly precipitation and temperature climatology

Climate descriptors and classifications are vital for ordering past, current and future climatic conditions. Yet, these parsimonious descriptors of climatic conditions only capture specific aspects of this climate signal, and lose all other information available in the observations. As a result, climate descriptions are often not physically insightful when they are applied in other studies. In this study, we show that a sinusoidal function with an annual period can adequately describe the vast majority of monthly precipitation and temperature climates around the world. This finding allows us to synthesize intra-annual monthly precipitation and temperature climatology using five indices that are easy to interpret. The indices describe (1) the mean precipitation rate ((P) over bar), (2) the mean temperature ((T) over bar), (3) the seasonal precipitation amplitude (delta(P)), (4) the seasonal temperature amplitude (Delta T) and (5) the phase difference between the precipitation and temperature regimes (s(d)). The combination of the five indices describes the relative time series of precipitation and temperature climatology, in contrast to earlier proposed similarity indices that only capture specific aspects of these time series. We demonstrate how the framework can reproduce many earlier proposed indices and classifications, and provide an example how the framework can be used to classify regions. We argue that the framework provides comprehensive insight into global climatology and can function as a quantitative conceptual basis for climate descriptions among different sciences.