Supplementary material to "Calendar effects on surface air temperature and precipitation based on model-ensemble equilibrium and transient simulations from PMIP4 and PACMEDY"

Numerical modeling enables a comprehensive understanding not only of the Earth's system today, but also of the past. To date, a significant amount of time and effort has been devoted to paleoclimate modeling and analysis, which involves the latest and most advanced Paleoclimate Modelling Intercomparison Project phase 4 (PMIP4). The definition of seasonality, which is influenced by slow variations in the Earth's orbital parameters, plays a key role in determining the calculated seasonal cycle of the climate. In contrast to the classical calendar used today, where the lengths of the months and seasons are fixed, the angular calendar calculates the lengths of the months and seasons according to a fixed number of degrees along the Earth's orbit. When comparing simulation results for different time intervals, it is essential to account for the angular calendar to ensure that the data for comparison are from the same position along the Earth's orbit. Most models use the classical calendar, which can lead to strong distortions of the monthly and seasonal values, especially for the climate of the past. Here, by analyzing daily outputs from multiple PMIP4 model simulations, we examine calendar effects on surface air temperature and precipitation under mid-Holocene, Last Interglacial, and pre-industrial climate conditions. We came to the following conclusions. (a) The largest cooling bias occurs in boreal autumn when the classical calendar is applied for the mid-Holocene and Last Interglacial, due to the fact that the vernal equinox is fixed on 21 March. (b) The sign of the temperature anomalies between the Last Interglacial and pre-industrial in boreal autumn can be reversed after the switch from the classical to angular calendar, particularly over the Northern Hemisphere continents. (c) Precipitation over West Africa is overestimated in boreal summer and underestimated in boreal autumn when the classical seasonal cycle is applied. (d) Finally, month-length adjusted values for surface air temperature and precipitation are very similar to the day-length adjusted values, and therefore correcting the calendar based on the monthly model results can largely reduce the artificial bias. In addition, we examine the calendar effects in three transient simulations for 6-0 ka by AWIESM, MPI-ESM, and IPSL-CM. We find significant discrepancies between adjusted and unadjusted temperature values over continents for both hemispheres in boreal autumn, while for other seasons the deviations are relatively small. A drying bias can be found in the summer monsoon precipitation in Africa (in the classical calendar), whereby the magnitude of bias becomes smaller over time. Overall, our study underlines the importance of the application of calendar transformation in the analysis of climate simulations. Neglecting the calendar effects could lead to a profound artificial distortion of the calculated seasonal cycle of surface air temperature and precipitation.