How would the mean annual temperature of the Earth change if theaverage albedo of the Earth were 1) raised to 0.5 from its present value ofabout 0.3, and 2) lowered to 0.1?

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Learning Goal: I’m working on a discrete math multi-part question and need an explanation and answer to help me learn.Directions: Please answer all portions of the questions, providing appropriateexamples and evidence as needed. Please label the questions you’re trying toanswer. Describe the answers you get in words as well as provide all yourcalculations. If you use any symbols in your answer sheet, please state in wordswhat each symbol stands for, and indicate the units of the answers whereverapplicable.1. How would the mean annual temperature of the Earth change if theaverage albedo of the Earth were 1) raised to 0.5 from its present value ofabout 0.3, and 2) lowered to 0.1? Please provide a percentage ofchange in Earth’s temperature for both these cases. (20 Points)2. What is the soil production function? Sketch the two main forms of soilproduction function and describe the key differences between them.Specifically, why do we expect the soil production rate to be different atlow soil depths? (15 Points)3. On a hillslope with a weathering rate of 20 microns/yr and an effectivehillslope diffusivity of 0.02 m2/yr, what is the expected curvature of thehillslope at steady-state? Plot the full profile if the summit of the hillslope,at x=0, is 1000 m. The channels at the edge of the hillslope are 200 m fromthe hillcrest. (20 Points)4. Consider a long linear hillslope with a slope angle of 25°. It has soil that is1 m thick, and a shear test on the soil reveals its internal angle of friction is31°, a cohesion (including roots) of 5000 Pa, and a porosity of 35%.Perform a stability analysis on this slope for the worst case scenario of fullsaturation. If you find that it is indeed unstable under full saturation, assessthe water table height that is required to cause failure. (20 Points)5. Explain as simply as you can why a compacted granular material is lesslikely to fail catastrophically on a slope than is a loosely packed material.(15 Points)6. Calculate steady state water discharge at the base of a hillslope. Thehillslope is 150 m long, the rainfall rate is 7 mm/hr and the rain has beenfalling for long enough that the hydrology of the slope may be taken assteady, with a uniform steady infiltration rate of 1.5 mm/hr. Provide theanswer both in m3/s per m length of the bounding stream, and in cubic ftper second (cfs) per linear foot of channel. (20 Points)7. In the above question, calculate the thickness of the steady stateoverland flow at the base of the slope if the slope is uniform at 8° and theDarcy-Weisbach friction coefficient Cf = 0.04. Recall the equation thatdescribes the mean flow velocity in terms of Generalized Darcy-Weisbachfriction coefficient. (20 points)8. Consider a steep-walled river channel with a width of 50 m, a bankfulldepth of 3 m (to the levee tops), and a slope of 0.5 m/km (i.e., note thatthis is the tangent of the slope, which for small angles is equivalent to theslope, in radians: 0.0005). The bed of the river is made of coarse sand,organized into ripples that result in an effective roughness height (zo) of 3mm. The river at the moment is flooding at a stage of 0.5 m abovebankfull. In the calculations below you will again need to recall that theshear velocity is defined asu*= gHS .What is the water discharge in the channel, in m3/sa) at bankfull? (15 Points)b) at 0.5 m above bankfull (i.e., at present)? (15 Points)(Note that in both cases you may ignore the effects of the banks, whichwill be small relative to the bottom in imposing friction on the flow.) In thelatter calculation, ignore the contribution from that flow that escapes overthe floodplain.9. Discuss how rivers might differ if the fluid being transported were of adifferent density or viscosity or both. (20 Points)10.Discuss how a bedrock river should respond to glacial-interglacialfluctuations in base level of order 120 m. What legacy of the glacial sealevel low stand might be seen in the present profile, and what mightgovern the magnitude of these effects? (20 Points)


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