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

Abstract. Numerical modelling 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 is from the same position along the Earth's orbit. Most models use the classical "fixed-length" 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 conclude that: (a) The largest cooling bias occurs in autumn when the classical calendar is applied for the mid-Holocene and last interglacial. (b) The sign of the temperature anomalies between the Last Interglacial and pre-industrial in boreal autumn can be reversed after the switch from 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 "fixed-length" seasonal cycle is applied. (d) Finally, correcting the calendar based on the monthly model results can reduce the biases to a large extent, but not completely eliminate them. In addition, we examine the calendar effects in 3 transient simulations for 6–0 ka by AWI-ESM, MPI-ESM, and IPSL. We find significant discrepancies between adjusted and unadjusted temperature values over ice-free 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 "fixed-length" 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. One important fact to be noted here is that the discrepancy in seasonality under different calendars is an analysis bias and is highly depends on the choice of the reference position/date (usually the vernal equinox, which is set to 31th March) on the Earth's ellipse around the sun. Different model groups may apply different reference dates, so ensuring a consistent reference date and seasonal definition is key when we compare results across multiple models.