Module Contact: Dr Mark Claire, ENV Copyright of the University of East Anglia Version 1

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1 UNIVERSITY O EAST ANGLIA School of Environmental Sciences Main Series Postgraduate Examination EARTH AND LIE ENV-MA38 Time allowed: 2 hours. Answer TWO questions, ONE from EACH section. Write EACH answer in a SEPARATE answer book. ALL questions carry equal marks Notes are not permitted in this examination. Do not turn over until you are told to do so by the Invigilator. ENV-MA38 Module Contact: Dr Mark Claire, ENV Copyright of the University of East Anglia Version 1

2 2 SECTION A 1. Describe the major features of the carbonate-silicate feedback cycle on atmospheric CO 2 concentrations, including a feedback diagram. Describe how catastrophic breakdowns of the carbonate-silicate cycle lead to the boundaries of the classical circumstellar habitable zone. 2. Is the Gaia hypothesis consistent with the theory of evolution by natural selection? Is the Gaia hypothesis testable? If so, how? If not, why not? Your answer should start with a definition of the Gaia hypothesis, address the main biological criticisms of it, and describe evidence and models that attempt to answer the criticisms. Your answer should also draw on examples of postulated feedback mechanisms and evidence from Earth history. 3. Discuss how atmospheric oxygen concentrations have changed over Earth history, focusing on evaluating the evidence for step changes at the Great Oxidation and Cambrian Explosion events. What evidence is there that the major changes were caused by evolutionary innovations, and what evidence is there that the changes in oxygen in turn influenced the evolution of life? SECTION B 4. The Critical Step model of Carter (1983) assumes that evolution towards complex, and ultimately intelligent, observer species is governed by the necessity to pass a number of critical steps. Each step is assumed to occur with a uniform, but low probability, and cannot occur until previous steps in the sequence have occurred. Considering only the subset of planets on which observer species do evolve, the probability distribution for the evolution of such a species, that requires n critical steps, is found to be: nt Pnn / () t t n 1 n h per unit time, where t is time, measured from the point where life first becomes possible on the planet, t h is the habitable lifetime of the planet, and 0 < t < t h. a) Sketch the shape of this probability distribution as a function of t, for the cases n = 1, n = 2, and n = 3.

3 b) The expectation time <t n > (the mean time averaged over many realizations) at which the observer species evolves is given by the integral 3 t h tn tpn / n() t dt 0 Show that the solution of the integral is: t n n 1 n t h c) Assuming Earth has been habitable since the end of the late heavy bombardment 3.9 Ga ago, give estimates for the number of critical steps required for the evolution of ourselves as observer species on Earth, under each of the following two assumptions: (1) the habitable period of the Earth is 10 Ga, as Carter (1983) assumed ; and (2) the habitable period of Earth is 5 Ga, as Watson (2008) assumed. [15%] d) It has been suggested that because life became established on Earth soon after the planet became continuously habitable is evidence that the origin of life must be a common event, so that prokaryotic life should be found frequently in the universe. Comment on and contrast the implications for the likelihood of life evolving if (1) the evidence of the Isua formation rocks (3.8 Ga old) is accepted as evidence for life, and (2) if the evidence of the Swaziland formations (3.5 Ga old) is accepted as evidence for life. Assume that the end of the late heavy bombardment marks the earliest time from which the Earth could be continuously habitable. [25%] PLEASE TURN OVER

4 5. a) Briefly describe (with a chemical equation if appropriate) the effect of the following processes as sources or sinks for atmospheric oxygen, on geological time scales: 4 i) Organic carbon burial in sediments ii) Oxidative weathering of continental rock iii) Hydrogen escape iv) Reduced gases emanating from volcanoes To a first approximation, the equation for the rate of change of oxygen in the atmosphere due to geologic sources and sinks can be written. do cb oxw dt (1) where o is a non-dimensional oxygen content of the atmosphere, equal to 1 in the presentday, cb is the molar flux of carbon buried in sediments and oxw the flux of oxygen consumed by oxidative weathering of continental rocks. A similar equation for phosphorus in the oceans can be written dp dt (2) pw pb where pw is the molar flux of phosphorus released by continental weathering, ε is the fraction of pw that is biogeochemically available, and pb is the rate of burial of this material in the oceans. We further assume the following relationships: Carbon and phosphorus are buried in a constant ratio, R c/p cb pb R (3) c / p Phosphorus weathering and oxidative weathering take place in a constant ratio, R ox/p oxw pw R (4) ox/ p

5 b) Show by assuming steady state of the phosphorus equation that there can be no steady state for oxygen according to the system of equations (1) (4), unless either (a) continental weathering is zero, or (b) if R c/ p Rox/ p 5 (5) c) Van Cappellen and Ingall (1994) proposed that the main feedback that stabilizes oxygen concentration is that R c/p increases with decreasing oxygen concentration. They suggest that R c/p is not constant but is a function of atmospheric oxygen, for example: R / p o 0.05 c (6) Taking R ox/p = 150, show that this function implies that steady state oxygen has the following linear dependence on ε: o (7) [20%] d) Lenton and Watson (2000) proposed that a tendency of land vegetation to increase the value of ε has been important in determining the history of atmospheric oxygen. What range of values of ε does equation (7) suggest would be appropriate to: i) The Proterozoic, before land vegetation evolved, and ii) The Phanerozoic during the period since vascular land plants evolved? [20%] PLEASE TURN OVER

6 6.a) The following circuit diagram with input, i, contains a system, with output, o, which is the linear sum of its inputs. It also contains a feedback loop with an amplifier (amp.), which multiplies the incoming signal by a gain factor, G. 6 i) Write down an expression balancing the inputs and outputs of the system and rearrange it to get the ratio of output to input (the amplification factor ) in terms of the gain. ii) iii) iv) What range of values for the gain factor gives negative feedback? What range of values for the gain factor gives positive feedback? What is the condition for runaway positive feedback? b) One postulated state for the Earth system is that an organic haze would form in the atmosphere if the CH 4 :CO 2 ratio were to reach a value of approximately 1:10. Assuming that the CH 4 flux is due to methanogenic bacteria, and that the haze regulates the temperature due to an anti-greenhouse effect leads to a biologically-modulated feedback cycle. At a fixed CO 2 concentration (5%), the surface temperature (T S ) in Celsius as a function of methane concentration (in ppm) as computed by an Archean climate model that includes the effect of organic haze (Haqq-Misra et al. 2008) is: T S (CH 4 ) = CH CH (1) Methanogens are thermophilic bacteria whose growth rate increases with temperature. Assume a linear growth rate such that CH 4 concentrations (in ppm) increase with surface temperature as: CH 4 (T S ) = (T S ) / ( ) (2)

7 7 i) Show that a temperature of 12º C forms a steady state solution to the set of equations (1) and (2). ii) The gain factor of this system is given by: G dt S dch 4 dch 4 dt S (3) where dt S /dch 4 comes from differentiating equation (1) and dch 4 /dt S from differentiating equation (2). Compute these derivatives and simplify the resulting expression for the gain factor. iii) What is the value of the gain factor at the steady state found in part (i)? What does this tell us about the sign and strength of the feedback and hence the stability of this state? iv) ind the alternate steady state solution of the system (by inserting (1) into (2), rearranging, and solving). v) What is the value of the gain factor at the state in part (iv)? What does this tell us about the sign of the feedback and the stability of this state? vi) At what temperature does the feedback change sign? [60%] c) Sketch a graph of equations (1) and (2), with annotations indicating important numbers and stability regions calculated in part b) [10%] END O PAPER