Climate Change Economics Lab Assignment 1 UC Berkeley | Summer 2024 The model that you have to build this week has two components: a climate dynamics model (Section 1) and a simple carbon cycle model (Section 2). Section 1 Overview This section has two parts: 1) you will build a very simple physical climate model in Excel and 2) analyze some very simple CO2 concentration scenarios with that model. 1.1: Modeling Overview The input (or forcing) to the climate dynamics model is yearly atmospheric CO2 concentrations, measured in ppm. The output of the climate dynamics model is the yearly average temperature increase over pre-industrial temperatures in °C. The forcing to the climate dynamics model is provided to you in the Excel file "CCE Assignment 1 - Forcings.xlsx". Your model will run in yearly time steps, and will start in the year 2010 and run to the year 2300, Climate Dynamics Model The climate dynamics model you will build has two parts: the first part computes how much extra energy is warming the atmosphere due to climate change and what the long term temperature effect of that extra energy would be. The second part computes the predicted yearly global average temperature increase over time. The amount of extra energy caused by rising CO2 concentrations is called the radiative forcing and is measured in W/m2. The equation to compute this variable is (1) rfcº2= 5.35ln- Cpre Ct rf.CO2 is the radiative forcing at time t caused by CO2 in W/m2. Ct is the atmospheric CO2 concentration at point t in ppm, as provided in the forcing file. Cpre is the pre-industrial level of 1 atmospheric CO2 concentrations, and you should use 275 ppm for this. In(x) is the natural logarithm, the Excel function name for it is "=LN(x)". Other greenhouse gases also contribute to global warming, and they further increase radiative forcing. You are not going to model the effect of these other greenhouse gases explicitly for this exercise, but our model should nevertheless account for them. Consequently, we will integrate the forcing caused by other greenhouse gases as a forcing that is supplied to you as part of this exercise in the file "CCE Assignment 1 - Forcings.xlsx". For the remainder of this assignment, I will refer to the radiative forcing of other greenhouse gases as r ft fother The total effect of global warming, that is all greenhouse gases, is computed as rft = rft f.C02 +rfother (2) for time t. The next step in the model is to compute the warming that would occur if a given level of radiative forcing would be sustained for a very long time. The equation for that is (3) Te = 1 x rft Here Te is the increase in global average surface temperature over pre-industrial levels if the radiative forcing of rft were to be held constant for a very long time. 1 is called the climate sensitivity and you should set it to 0.8 for this exercise. The final step is to compute the actual temperature for each time step. We will use a very simple delay formulation. For each time step we will first compute the difference between the temperature in the previous year and the temperature that the system would reach if radiative forcing were to be held constant for a very long time (Te - Tt-1). We then assume that the actual temperature will warm by a very small fraction of this computed difference. The equation for this process is (4) Tt =Tt-1 + u(Te -Tt-1) Tt is the quantity we are really interested in, the global average temperature increase above pre- industrial times in °C at time t. u is the parameter that controls the delay of the warming, and you should set it equal to -. As this equation relies on the temperature in the previous time period we cannot use it to compute Tt for the first time period of our model. For the first time period you should set T2010 to 0.8, roughly today's observed warming over pre-industrial temperatures in °C. 1.2: Policy Analysis Question 1a: What happens to projected temperature if CO2 concentrations were held constant at 2010 levels in the model? You should copy the Excel sheet that contains your model for this exercise. The new sheet should have the model output with constant concentrations. 2 Question 1b: Create two graphs, one for CO2 concentrations and one for temperature. The x- axis should have years on it for both graphs. Then plot each of the two cases analyzed (base case and constant concentrations) as one line. You should create a new empty sheet in Excel, and then reference the values in all the other sheets as data for your chart. Section 2 Overview This section has two parts: 1) you will add a very simple carbon cycle model to Section 1; 2) analyze some very simple CO2 emission scenarios with that new model. 2.2: Modeling Overview You will now build a carbon cycle model and couple it with the climate dynamics model you built in Section 1. The input (or forcing) to the carbon cycle model are yearly emissions of CO2, measured in Mt C (megatonne carbon = 1 million tonne carbon). The output of the carbon cycle model is atmospheric concentrations of CO2, measured in ppm (parts per million). The two components are coupled via the atmospheric concentration of CO2, i.e. the output of the carbon cycle model is an input to the climate dynamics model. The forcing to the carbon cycle model (CO2 emissions) is provided to you in the Excel file "CCE - Assignment 1 Forcings.xlsx". Carbon Cycle model The carbon cycle model you will implement is a simple five-box model. The five boxes don't correspond to anything in the physical world; they are purely an abstraction that as a whole mimics the results from much more complicated models. In this model, all atmospheric CO2 concentrations live in one of five boxes. If one wants to compute the total atmospheric CO2 concentration at a point in time, one simply adds the amount of CO2 in each of the five boxes up. Over time, CO2 disappears from each of these boxes, at different rates for each individual box. On the other hand, new anthropogenic CO2 emissions are added each year into the atmosphere. In the five-box model these yearly influxes of new CO2 into the atmosphere are distributed by fixed shares into the five boxes: 13% percent go into the first box, 20% into the second, 32% into the third, 25% into the fourth and the remaining 10% into the fifth box. There are consequently five variables that represent the five boxes and each of these variables takes on a different value in each year. The equation that is used to compute the amount of CO2 in box i (which takes values from 1 to 5) at time t (which takes on value from 2010 to 2300) is: (5) Boxi,t = ai X Boxi,t-1 + YißEt 3 Boxit is the amount of CO2 in box i at time t, measured in ppm. ai is the share of CO2 in box i that stays in the atmosphere until the next time period (so 1 - ai is the share of CO2 that disappears each year from box i). Yi is the share of emissions that goes into box i. ß is a unit conversion factor: CO2 emissions in our model are measured in Mt C, but atmospheric CO2 concentrations are measured in ppm; ß converts from the unit Mt C to CO2 ppm. Et are world total emissions of CO2 in year t, measured in Mt C. You cannot use this equation to compute the values for each box in the first time period, i.e. in the year 2010: the equation for that year would rely on the values for this box in the previous year, but our model only starts in 2010. Therefore, for the first year only, you should not use equation (5) but instead use initial values for each of the five boxes that are provided below as Boxi,2010- The values for the forcing Et are provided to you as an Excel file. You should use the following values for ai, Yi, Boxi,2010 and ß: @1 =1 Y1 = 0.13 Box1,2010 = 301.099 ₿ = 0.00047 a2 = exp - 363 1 Y2 = 0.2 Box2,2010 = 30.098 a3 = exp - 74 1 Y3 = 0.32 BOX3,2010 = 34.878 1 a4 = exp - 17 14 = 0.25 Box4,2010 = 12.357 112 Y5 = 0.1 BOX5,2010 = 0.897 The values for some of the ai are little equations themselves, you can enter them directly in Excel as a formula, e.g. for a2 you would enter "=EXP(-1/363)" as the Excel formula. The final step in the carbon cycle model is to compute atmospheric CO2 concentrations at each point in time: (6) Ct = >Boxit = Box1,t + Box2,t + Box3,t + Box4,t + Box5,t i=1 5 Ct is the atmospheric concentration of CO2 at time t, it is simply the sum of the five boxes at that time. Coupling To couple the climate dynamics model with the carbon cycle model you need to make a change to the climate dynamics model you built in Section 1: you should replace the values in the row 4 that had the CO2 concentration forcing in the climate dynamics model with a formula that references the output from the carbon cycle model. 2.2: Policy Analysis Question 2a: What happens to projected temperature if CO2 emissions were held constant at 2010 levels in the model? You should copy the Excel sheet that contains your model for this exercise. The new sheet should have the model output with constant emissions. Question 2b: By how much % would we need to reduce emissions in each year to keep global warming below 2° over the next 300 years? First, copy the model sheet and do all your analysis in the new sheet. The easiest approach is to modify the line that has emissions in such a way that starting with the second time step you use an equation to compute emissions. Assuming that the cell for emissions in the year 2011 is C24, the Excel formula might look like "=B23*(1-$B$20)". In this case the cell B20 would have the percent reduction in emission per year in it and you could quickly change the emissions profile by changing the value in cell B20. Finally, you might want to have one cell that displays the maximum temperature increase over the model time horizon. Assuming the predicted temperatures are in cells B48 to KF48, you might add a cell that has the equation "=MAX(B48:KF48)" in it to help you. Question 2c: If emissions stay as they are specified in base case until the year 2049, and are then reduced by a fixed percent each year, how much would they have to be reduced in percent in each year to keep global warming below 2° over the next 300 years? Again, copy the model sheet and do your analysis on the new sheet. The steps for this exercise are similar to the steps for the previous question. Question 2d: Create three graphs, one for CO2 emissions, one for CO2 concentrations and one for temperature. The x-axis should have years on it for all three graphs. Then plot each of the four cases analyzed (base case, constant emissions, reduction in emissions starting now, reduction in emissions starting in 2050) as one line. You should create a new empty sheet in Excel, and then reference the values in all the other sheets as data for your chart. 5