3. (14 points) Sedimentary deposits in rocks show that liquid water was present on Earth as early as 3.8 billion years ago, when solar radiation intensity was only 70% of today's value. Consider the simple greenhouse model described in this course where the atmosphere is represented as a thin layer transparent to solar radiation and absorbing a fraction f of terrestrial radiation. Assume throughout this problem a constant planetary albedo A = 0.3 for the Earth. Today's solar constant is F=1360 W m2. The Stefan- Boltzmann constant o = 5.67x108 Wm K. 1) (4 points) If the greenhouse effect 3.8 billion years ago were the same as today (f= 0.77), what would be the surface temperature of the Earth? Would liquid water be present? 2) (2 points) Current thinking is that a stronger greenhouse effect offset the weaker Sun. Let us try to simulate this stronger greenhouse effect by keeping our l-layer model for the atmosphere but assuming that the atmospheric layer absorbs 100% of terrestrial radiation. Calculate the resulting surface temperature. 3) (5 points) We can modify our model to produce a warmer surface temperature by representing the atmosphere as two superimposed layers, both transparent to solar radiation and both absorbing 100% of terrestrial and atmospheric radiation. Calculate the resulting surface temperature. 4) (3 points) It has been proposed that the strong greenhouse effect in the early Earth could have resulted from accumulation in the atmosphere of CO2 emitted by volcanoes. Imagine an Earth initially covered by ice. Explain how volcanic CO2 would accumulate in the atmosphere under such conditions, eventually thawing the Earth