HW_Temp Proxies go to the Movies

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0836

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Electrical Engineering

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Jan 9, 2024

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EES 0836 Temperature Proxies go to the Movies Disasters: Geology vs. Hollywood Introduction "Everyone talks about the weather, but no one ever does anything about it." --Mark Twain Mark Twain's famous quip no longer rings true. Apparently, humans are doing a great deal to influence the weather. At least that is what the "hockey stick" plot shows, published by Mann et al. in 1999 in an issue of Nature (inset image). The plot shows time on the x- axis and global average temperature relative to 1995 in degrees Celsius on the y-axis. Notice the rise of approximately half of a degree coinciding with the industrial revolution. Why is the plot disputed? Doesn't it clearly show that the temperature was stable for hundreds of years, and then suddenly shot up? Well, the catch is that we cannot go back in time and record the actual temperatures hundreds of years ago, so the plot is based on "proxy" data. A temperature proxy is something we can measure that is not temperature but is related to temperature "well enough" to be used as a substitute. Mann et al. (1999) used combinations of paleoclimate data – tree rings, coral growth, stable isotope data, etc. – to deduce historic temperatures. For example, the amount a tree grows each year can be seen in the rings, and trees tend to grow more in warmer years. The interpretation of the proxy data is at the heart of the dispute over this famous plot. Learning Objectives ● Understand how proxies can be used to help make predictions. (1, 2, a, b) ● Explain the limitations with proxies relative to their use in climate science. (1, 2, c)

EES 0836 Part 1: A Hollywood Analogy Let's get the flavor of proxies by investigating a different type of data set. Suppose we want to predict the first- year box office receipts of a new movie that is based on a best-selling book. Hollywood has made movies based on books many times before, so we have earnings data for previous movies spun off from books compared with three things that might be related (proxies). Three possible proxies: 1. The movie's production costs (big budget films tend to make more money) 2. The amount of money spent on promotion (more ads, more sales) 3. Total book sales (movies are usually based on best-sellers) Here is our data set (all numbers are in millions of dollars ): Box Office Receipts Production Costs Promotion Costs Book Sales 85.1 8.5 5.1 4.7 106.3 12.9 5.8 8.8 50.2 5.2 2.1 15.1 130.6 10.7 8.4 12.2 54.8 3.1 2.9 10.6 30.3 3.5 1.2 3.5 79.4 9.2 3.7 9.7 91.0 9.0 7.6 5.9 135.4 15.1 7.7 20.8 89.3 10.2 4.5 7.9 On the graph below, one of the proxies in the table above has been plotted against the Box Office Receipts (y- axis). A best fit line (thin red line) has been fit to the data. This line represents the relationship between the proxy and Box Office Receipts, which would be used for predicting Box Office Receipts for future movies.

EES 0836 Questions 1. Which proxy (dataset from the table above) is plotted against the Box Office Receipts? i.e. what should the x-axis label read? Production costs 2. Do you think it is reasonable to use production costs to predict box office receipts even though the line does not fit the data perfectly? Why or why not? Yes, it is a pretty good fit and trend here – close to 1:1 trend. 3. If you were a Hollywood producer, would you rather your new movie plotted above or below the line? Why? I would rather my movie plotting above the line -- spending less on production and earning more at the box office. 4. Plotted below are the two other proxies for box office receipts. Of all three proxies plotted, which do you think is the best predictor? Explain your reasoning. It is close bet between production and promotion as a predictor of box office success, but promotion has a tighter fit with less outliers, so is a better proxy to use.

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EES 0836 Clearly, all three proxies hold some predictive value (there is at least some correlation between all three proxies and the box office receipts). Is it possible to combine the information from all three to come up with an even better predictor? The easy answer is: Yes . This can be accomplished using a method called "multiple linear regression," which tells us what weighted combination of our three predictors yields the best proxy. For this data set, it turns out the best predictor is the combination shown in the last column of the table on the next page. (As before, all numbers are in millions of dollars.) Finish filling in the values for the combined proxy in the last column of the table using the equation below. Please give answers to one decimal place. NOTE: there is an order of operations issue here. You need to do the multiplication of the values in the parentheses first , then add the four terms together to get the final answer. Combined Proxy = 7.7 + ( 3.7 ×ProductionCost ) + ( 7.6 ×Promotion Costs ) + ( 0.8 ×Book Sales )

EES 0836 Box Office Receipts Production Costs Promotion Costs Book Sales Combined Proxy 85.1 8.5 5.1 4.7 81.7 106.3 12.9 5.8 8.8 106.6 50.2 5.2 2.1 15.1 55.0 130.6 10.7 8.4 12.2 120.9 54.8 3.1 2.9 10.6 49.7 30.3 3.5 1.2 3.5 32.6 79.4 9.2 3.7 9.7 77.6 91.0 9.0 7.6 5.9 103.5 135.4 15.1 7.7 20.8 138.7 89.3 10.2 4.5 7.9 86.0 Once you have calculated the values in the table above, they should match the values plotted on the graph below. Draw a “best fit” line by eye using the Insert > Shapes > Line feature in Word. This is not connect-the-dots , but more like an average of all the dots. Just try your best with this line.

EES 0836 1. Why is there a significant benefit to using this combined proxy over any one of the individual proxies? Yes, you gave more data, so you should have a higher resolution when it comes use as a proxy. 2. Is the new combined proxy as good or better than individual measurements? Why or why not? Yes, more data is better, you have a better understanding of the relationship using multiple proxies. 3. Our data is limited in that it only accounts for a couple of unidentified recent movies. If we were to expand our data set to reflect the past 50 years worth of information, would you expect the same trends (how the data fits with each other) to continue, or would you expect the data to become more uncertain? I would expect it to have a better fit with more years-worth of data.

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EES 0836 Part 2: Back to Climate In this unit’s reaction video, Atsuhiro Muto, PhD, watched a clip from the movie The Day After Tomorrow (2004) and noted the value of proxies in reconstructing past climates. In reference to the Mann et al. (1999) plot at the beginning of this assignment, the plot includes “uncertainty limits” (fine dashed lines that surround the main curve). The degree of uncertainty is not constant throughout the plot. I know this might be difficult to see, but trust me, the “uncertainty” gets wider as you go back in time (to the left on the graph). 1. Think about what we have seen in this activity about the predictive value of individual vs. combined proxies and the different types of climate/temperature proxy data Dr. Muto discussed in the video we watched. Why does the uncertainty about temperature increase the farther back in time you go? The data becomes much more limited the further back you go, there is less preserved record the further back. 2. If there is “uncertainty” with reconstructing past climate, why is it still important to reconstruct past climates? To try and understand out current and future climate. 3. What function does proxy data and understanding past climate serve when trying to predict future trends in climate? We want to understand how things will be affected and/or change. 4. What role do you think climate science should play in driving the U.S. government to structure policy associated with curbing climate change? Yes, we should probably be prepared, adaptation and mitigation would help us into the future. 5. What role do you think climate science should play in driving international governments to structure international agreements associated with curbing climate change? Yes the worse thing it does is make a better world? We’re all in this together, so why not try and help each other out.