Model-based changes in global annual mean surface temperature change (Delta T_g) and radiative forcing due to land ice albedo changes (Delta R_[LI]) over the last 5 Myr, supplementary material

It is still an open question how equilibrium warming in response to increasing radiative forcing - the specific equilibrium climate sensitivity S - depends on background climate. We here present palaeodata-based evidence on the state dependency of S, by using CO2 proxy data together with a 3-D ice-sheet-model-based reconstruction of land ice albedo over the last 5 million years (Myr). We find that the land ice albedo forcing depends non-linearly on the background climate, while any non-linearity of CO2 radiative forcing depends on the CO2 data set used. This non-linearity has not, so far, been accounted for in similar approaches due to previously more simplistic approximations, in which land ice albedo radiative forcing was a linear function of sea level change. The latitudinal dependency of ice-sheet area changes is important for the non-linearity between land ice albedo and sea level. In our set-up, in which the radiative forcing of CO2 and of the land ice albedo (LI) is combined, we find a state dependence in the calculated specific equilibrium climate sensitivity, S[CO2,LI], for most of the Pleistocene (last 2.1 Myr). During Pleistocene intermediate glaciated climates and interglacial periods, S[CO2,LI] is on average ~ 45 % larger than during Pleistocene full glacial conditions. In the Pliocene part of our analysis (2.6-5 Myr BP) the CO2 data uncertainties prevent a well-supported calculation for S[CO2,LI], but our analysis suggests that during times without a large land ice area in the Northern Hemisphere (e.g. before 2.82 Myr BP), the specific equilibrium climate sensitivity, S[CO2,LI], was smaller than during interglacials of the Pleistocene. We thus find support for a previously proposed state change in the climate system with the widespread appearance of northern hemispheric ice sheets. This study points for the first time to a so far overlooked non-linearity in the land ice albedo radiative forcing, which is important for similar palaeodata-based approaches to calculate climate sensitivity. However, the implications of this study for a suggested warming under CO2 doubling are not yet entirely clear since the details of necessary corrections for other slow feedbacks are not fully known and the uncertainties that exist in the ice-sheet simulations and global temperature reconstructions are large.

The albedo of junipers measured in summer 2009 at the Niederhorn, Switzerland

This field study was performed to obtain a defensible value for the surface reflectivity (albedo) of Juniper shrublands that could be used by Brigitta Ammann to quantitatively assess the role of Juniper shrublands in surface energy balance feedbacks to climate after the last glaciation. Measurements were carried out over a Juniper shrubland at mount Niederhorn, Switzerland (North of the Lake of Thun) during summer 2009 over a Juniper shrubland that was considered to present the most representative surface cover to estimate albedo for a modeling exercise that addresses biotic responses to the rapid warming around 14.685 ka BP at Gerzensee (Central Europe). For a detailed description of this data set see "Further details:"

(Table 4) Daily mean spectral snow albedo at different wavelengths measured at Neumayer, Antarctica

Spectral albedo in high resolution, from 290 to 1050 nm, has been measured at Neumayer, Antarctica, (70°39' S, 8°15' W) during the austral summer 2003/2004. At 500 nm, the spectral albedo nearly reaches unity, with slightly lower values below and above 500 nm. Above 600 nm, the spectral albedo decreases to values between 0.45 and 0.75 at 1000 nm. For one cloudless case an albedo up to 1.01 at 500 nm could be determined. This can be explained by the larger directional component of the snow reflectivity for direct incidence, combined with a slightly mislevelled sensor and the snow surface not being perfectly horizontal. A possible explanation for an observed decline in albedo is an increase in snow grain size. The theoretically predicted increase in albedo with increasing solar zenith angle (SZA) could not be observed. This is explained by the small range of SZA during albedo measurements, combined with the effect of changing snow conditions outweighing the effect of changing SZA. The measured spectral albedo serves as input for radiative transfer models, describing radiation conditions in Antarctica.

Time-series of snow spectral albedo and superficial snow specific surface area at Dome C in Antarctica, 2012-2015

Spectral albedo has been measured at Dome C since December 2012 in the visible and near infrared (400 - 1050 nm) at sub-hourly resolution using a home-made spectral radiometer. Superficial specific surface area (SSA) has been estimated by fitting the observed albedo spectra to the analytical Asymptotic Approximation Radiative Transfer theory (AART). The dataset includes fully-calibrated albedo and SSA that pass several quality checks as described in the companion article. Only data for solar zenith angles less than 75° have been included, which theoretically spans the period October-March. In addition, to correct for residual errors still affecting data after the calibration, especially at the solar zenith angles higher than 60°, we produced a higher quality albedo time-series as follows: In the SSA estimation process described in the companion paper, a scaling coefficient A between the observed albedo and the theoretical model predictions was introduced to cope with these errors. This coefficient thus provides a first order estimate of the residual error. By dividing the albedo by this coefficient, we produced the "scaled fully-calibrated albedo". We strongly recommend to use the latter for most applications because it generally remains in the physical range 0-1. The former albedo is provided for reference to the companion paper and because it does not depend on the SSA estimation process and its underlying assumptions.