Add time stepping naked planet model

Time-Stepping Naked Planet Model/Grading/GWmod1.py

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+#My first tijme making a plot for climate modeling.
+#Hopefully, this works.
+#Note that using spreadsheets for this course is optional;
+#the only way to get credit is with Python3!
+
+"""The background for this material can be found in Sections 2 and 3 of Part I
+of this class. Joules are units of energy; Watts are energy flow (J/s).
+The temperature of a planet is determined by balancing energy fluxes in and out of a planet.
+Incoming solar heat is determined by L*(1-albedo)/4,
+and outgoing infrared is calculated as epsilon * sigma * T^4."""
+
+"""The heat capacity of the surface planet depends on the water thickness.
+Using the fact that 1 gram of water warms by 1 K with a 4.2J (1 cal) of heat,
+and the density of water, to calculate how many Joules of energy it takes
+to raise the temperature of 1 m2 of the surface, given some water depth
+in meters."""
+
+"""The goal is to numerically simulate how the planetary temperature of a
+naked planet would change through time as it approaches equilibrium
+(the state at which it stops changing, which we calculated before).
+The planet starts with some initial temperature.
+The “heat capacity” (units of Joules / m2 K) of the planet is set by
+a layer of water which absorbs heat and changes its temperature.
+If the layer is very thick, it takes a lot more heat (Joules) to change the temperature.
+The differential equation you are going to solve is:"""
+#d(HeatContent)/dt = L*(1-alpha)/4 - epsilon * sigma * T^4
+"where the heat content is related to the temperature by the heat capacity:"
+#T[K] = HeatContent [J/m2] / HeatCapacity [J/m2 K]
+"""The numerical method is to take time steps, extrapolating the heat content
+from one step to the next using the incoming and outgoing heat fluxes,
+same as you would balance a bank account by adding all the income and subtracting all the expenditures
+over some time interval like a month.
+The heat content "jumps" from the value at the beginning of the time step,
+to the value at the end, by following the equation:"""
+#HeatContent(t+1) = HeatContent(t) + dHeatContent/dT * TimeStep
+"""This scheme only works if the time step is short enough so that
+nothing too huge happens through the course of the time step.
+Set the model up with the following constants:"""
+timeStep = 40           # years; convert to seconds.
+time = 0                 # years; this shall denote how much time has passed in total.
+T = 0                    # Kelvin, according to question demands.
+waterDepth = 2000        # meters; multiply by cH2O and water density.
+L = 1350                 # W m-2, same as J s-1 m-2 (Solar Constant) -> multiply by no. of seconds in each timestep
+albedo = 0.3             # alpha
+epsilon = 1
+sigma = 5.67E-8          # W m-2 K-4
+cH2O = 4200              # specific heat capacity of water (units of 4200 J kg-1 K-1).
+rhoH2O = 1000            # Density is 1000 kg m-3.
+energy_per_m2 = waterDepth * cH2O * rhoH2O #in J m-2 K-1
+#heat influx and outflux must be calculated along the way.
+import numpy
+import matplotlib.pyplot
+#Getting our lists needed with the very first variables already in:
+nSteps = input("Please use 20 or more")
+#apparently the autograder that the MOOC uses also mistakes strings for operators.
+nSteps = int(nSteps)
+time_list = [time]
+temperature_list = [T]
+HeatContent = 0 #only true when T = 0 Kelvin, this is the heat content of the Earth.
+difference = 0
+outflux = 0
+for x in range(nSteps):
+    time = time + timeStep
+    time_list.append(time)
+    difference = (L * (1 - albedo) / 4 - (epsilon * sigma * T**4)) #W m-2
+    HeatContent = HeatContent + difference * 365 * 24 * 60 * 60 * timeStep #J m-2
+    T = (HeatContent / energy_per_m2) #Kelvin
+    outflux = epsilon * sigma * T**4 # as per instructions
+    temperature_list.append(T)
+#derive answers and end with:
+matplotlib.pyplot.plot(time_list, temperature_list)
+matplotlib.pyplot.show()
+#Give the last temperature derived by the model:
+#print(temperature_list[-1], outflux)
+#The tolerances in the grader for temperatures are 2-3 degrees C,
+#and for the heat fluxes, +- 0.1 W/m2.