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An empirical estimate for the snow albedo feedback effect

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Abstract   

We estimate snow albedo feedback effects of anthropogenic increases in global radiative forcing, which includes carbon dioxide, methane, nitrous oxide, CFC11, CFC12, black carbon, anthropogenic sulfur emissions, total solar irradiance, and local sulfur emissions by compiling annual observations (1972–2008) for radiative forcing, temperature, snow cover, sulfur emissions, and various teleconnections for 255 \({5}^{^\circ }\times {5}^{^\circ }\) grid cells in the Northern Hemisphere. Panel DOLS estimates of the long-run relations indicate that the effect of radiative forcing on temperature increases with latitude (consistent with polar amplification), eliminating snow cover increases local temperature by about 2.8 °C, and a 1 °C temperature increase reduces snow cover by about 1%. These values create a snow albedo feedback (SAF) that amplifies the temperature increase of higher forcing by about 3.4% relative to its direct effect while an increase in sulfur emissions increases the temperature reduction by about 0.4% relative to its direct effect. The 3.4% SAF is smaller than values generated by process-based climate models and may be associated with the empirical estimates for snowmelt sensitivity \({\Delta S}_{c}/\Delta {T}_{s}\). To narrow estimates for the SAF from climate models, we conclude with suggestions for a new experimental design that controls for the simultaneous relation between temperature and snow cover.

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Data availability

The data and code used to estimate the results reported here will be made available through a public data repository.

Notes

  1. Log values approximate the formulae that converts sulfur emissions to radiative forcing.

  2. Concerns about simultaneous equation bias may be alleviated by test statistics (Pedroni 1999) that suggest variables in Eqs. (2) and (3) cointegrate. Cointegration implies that the residuals are stationary while Snow and Temp are nonstationary, which reduces any correlation between the variables and the residuals, which is the source for simultaneous equation bias.

  3. The error correction model for Snow includes NHEM in y on the right-hand side of Eq. (7).

  4. Stationary variables cannot account for nonstationary movements in temperature and snow cover and so are not included in (5) and (6).

  5. Although the error correction term is statistically more negative than − 1.0 (t = 4.33, p < 0.0001), the top panel in Fig. 2 indicates that temperature (and snow cover bottom panel) adjust towards equilibrium quickly.

  6. The North Atlantic Oscillation is measured by differences in sea level pressure in December, January, and February and largely affects winter conditions.

  7. Both cointegrating relations and the error correction models, but zeros out the effects of NAO, SOI, and Vol.

  8. Results generated by the block bootstrap generate an SAF multiplier of 3% \(\pm 0.06\)% (standard error).

  9. This likely overstates the size of the SAF because the TCR includes the SAF, which enhances the increase in temperature beyond the direct effect of an increase in radiative forcing.

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Acknowledgements

We thank Chen Xi for compiling the data on snow cover and Glenn Rudebusch for his suggestions regarding solar insolation. We also thank Francis X. Diebold and the attendees of the climate econometrics seminar at the University of Pennsylvania for their comments. Any errors that remain are solely our responsibility.

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Significance statement

We analyze the relation among real-world measurements of temperature, snow, radiative forcing, sulfur emissions, and teleconnections to test ideas about anthropogenic climate change and the degree to which melting snow raises temperature beyond the initial increase in temperature. Results indicate that human emissions increase temperature, with the greatest rise at high latitudes and that eliminating snow cover would raise temperature by about 0.7 °C. Melting snow raises temperature by an additional 3%, which is smaller than the 40% indicated by climate models. This difference is likely caused by the uncertainty about the effect of higher temperatures on snow cover. To resolve this difference, we suggest experiments to be run by climate models.

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Kaufmann, R.K., Pretis, F. An empirical estimate for the snow albedo feedback effect. Climatic Change 176, 107 (2023). https://doi.org/10.1007/s10584-023-03572-7

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