Teaching Slides: Ice albedo and ice-albedo instability

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7.2: The radiative balance equation: Earth’s radiating surface temperature self-adjusts to balance incoming Solar (short-wavelength) radiation with outgoing (long-wavelength) radiation.

7.3: Ice-line latitude on an all-ocean planet as a function of Solar flux or equivalent pCO2, based on a simple energy-balance model of the Budyko-Sellers type. Under the present Solar flux (1.0), three stable climate states are possible, all ice (blue), no ice (red) and small ice (yellow). Large ice (open circle) is unstable and spontaneously falls to all ice. Black arrows indicate jumps in the CO2 hysteresis loop of a snowball earth cycle.

7.4: Joseph L. Kirschvink, originator of the snowball earth concept, a self-reversing climate instability driven by ice-albedo feedback.

7.5: Ice albedo is a critical variable in snowball earth climate models: snow-covered ice has a high albedo (~0.9), bubble-free (mature) marine ice has relatively low albedo (~0.4) and bubble-rich glacial ice (compacted snow) has intermediate albedo (~0.65).

7.6: Ice-line latitude on an all-ocean planet as a function of CO2 radiative forcing in an energy-balance model with fully-coupled sea-ice dynamics (Pollard & Kasting, 2005). Solution shown assumes bubble-free ice in the ablative zone, where thin ice (<2 m thick) occupies a ~2200-km-wide equatorial band, permitting “healthy” rates of photosynthesis to occur. If the ablative ice is bubble-rich, equatorial ice is thick and the CO2 hysteresis is magnified.

7.7: Atmospheric general circulation model (AGCM) with reduced solar luminosity and paleogeography appropriate for 750 Ma, in which a snowball earth (equatorial surface temperature <0C) occurs with CO2 set to (pre-industrial) 300 ppm (Donnadieu et al., 2003). Net sublimation is widespread on sea ice, most strongly in the subtropics, implying significant snowfall on land-based (elevated) tropical ice sheets.

7.8: Simulations using an AGCM for 750 Ma with coupled sea-ice and ice-sheet dynamics (Donnadieu et al., 2003): (A) with 900 ppm CO2, land-based ice sheets build up but the ocean remains open; (B) with 300 ppm CO2, ocean is completely ice covered but land-based ice sheets continue to grow, covering most global land area by 400 kyr after snowball onset; (C) same as (B) showing basal temperature of land-based ice sheets; (D) same as (B) showing basal sliding velocities of land-based ice sheets. Note the narrow corridors of fast-flowing wet-base ice (ice streams) near the margins of the tropical ice sheets.

7.9: Simulation using an AGCM with coupled ice-sheet dynamics (no sea-ice dynamics) and a ca 575 Ma paleogeography in which a loose supercontinent stretches from pole to equator (Hyde et al., 2000). Within a prescribed range of CO2, equatorial margins of the supercontinent are glaciated, as a result of ice-sheet flowage, while the tropical ocean remains above the freezing point.