ANSWER KEY. Part I: Weather and Climate. Lab 16 Answer Key. Explorations in Meteorology 72

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1 ANSWER KEY Part I: Weather and Climate Table 2 lists the maximum and minimum temperatures (in F) and precipitation (in inches) for every day during April 2003 at Fairbanks, Alaska. You will compare your calculations of several climate statistics with the daily values. 1. Calculate the mean, median, mode, and standard deviation of the daily data for each of the variables in Table 2. Maximum Temperature Minimum Temperature Precipitation Mean 46 F Mean 21 F Mean 0.00 in Median 48 F Median 27 F Median 0 in Mode 48 F & 50 F Mode 27 F Mode 0 in Std. Dev F Std. Dev F Std. Dev in 2. How many times did the daily observations in Table 2 match the means that you calculated in question 1? Max. Temp. zero Min. Temp. 1 Precip How many times did the daily observations in Table 2 match the modes that you calculated in question 1? Max. Temp. 3 Min. Temp. 4 Precip How many times did the daily observations in Table 2 lie within one standard deviation of the means that you calculated in question 1? Max. Temp. 19 Min. Temp. 23 Precip Using your answers from questions 2 to 4, discuss how well the various types of climate statistics characterize the weather of April 2003 in Fairbanks, as represented by the data in Table 2. The maximum and minimum temperature data were highly variable, as indicated by their large standard deviations. Hence, using a monthly mean or a mode to forecast the high or low temperature for a given day would not work well. A forecast of a range centered on the mean would provide better results. Because the standard deviation for precipitation was quite small, the climate statistics (mean, mode, median) represent the precipitation data set well. Hence, a forecast of zero precipitation for a given day would do quite well. Explorations in Meteorology 72

2 Part II: Climate Variability Table 3 lists the annual average temperatures (in F) and annual average precipitation (in inches) from 1881 to 2000 for Philadelphia, Pennsylvania. Table 4 presents the mean, median, and standard deviation of the average temperatures for the periods of and To examine the variability of the climate, you will compare climate statistics for the period from 1881 to 2000 with those for the period from 1971 to Using Tables 3 and 4, describe how the 30-year average differs from the long-term average? What accounts for these differences? The 30-year means of both precipitation and temperature are greater than the long-term means. This fact suggests that there was a period of warmer, wetter weather during the 1970s to 1990s. The standard deviation of temperature remained constant, suggesting that annual variations in temperature about the mean have not changed. The standard deviation for precipitation increased for the 30-year period, indicating that inter-annual precipitation is more variable. Factors that may have affected recent observations include global climate change, urbanization, and land-use patterns. Explorations in Meteorology 73

3 7. Calculate a trendline for annual average temperature from 1971 to 2000 using the data in Table 5. To compute the trendline, fill in the blank boxes that are highlighted in Table 5. Then use your calculated variance and covariance to complete the equations on the next page. Table 5 Values of Annual Average Temperature for Philadelphia, PA from 1971 to 2000 Used to Calculate a Trendline X Y ( ) 2 ( )( ) Sum Average = 15.5 = The final equation for the trendline is Y = mx + b = 0.056X Explorations in Meteorology 74

4 8. Examine your results from question 7. Did the climate change during the 30-year period at the Philadelphia station? How does the trend compare to the variability measured by the standard deviation (Table 4)? The trendline indicates that the climate warmed over the 30-year period. The increase of 1.62 degrees in the trend is greater than the standard deviation of 1.3 degrees. 9. Figures 5 and 6 show the distributions of annual average temperature and annual average precipitation, respectively, for Philadelphia, PA from 1881 to What factors account for differences in the shapes of the distributions? Precipitation is more variable than temperature, as shown by the standard deviations in Table Compare trendlines on the graphs of annual average temperature from downtown Baltimore, MD (Figure 7), and from Woodstock, MD (Figure 8), located near but outside the Baltimore metropolitan area. What difference, if any, exists between the intercepts on these graphs? Also, compare the long-term trends of the two sites. What conclusions can you draw about climate trends in the Baltimore Woodstock area based on the 100 year datasets? Speculate on any causes of the climate trends. The intercept at X (Year) = 1901 is 1.5 F warmer at Baltimore, but the intercept at X (Year) = 2000 is about 5.0 F warmer at Baltimore than Woodstock. Hence, the data indicate that the climate has warmed significantly at Baltimore, but has stayed fairly stead at Woodstock. Most likely, these results signal an urbanization in the vicinity of the Baltimore observing site. If global warming were the cause, the Woodstock station should have shown a similar increase. 11. Compare the annual means and standard deviations for the cities listed in Table 6. What two cities have the means closest to each other? What two cities have the greatest variation in their means? Describe the factors that might cause El Paso, TX, to have greater climate variability than Key West, FL. Two cities with closest means Spokane and Burlington Two cities with greatest variance in their means El Paso and Spokane El Paso is subject to more temperature variability because of its geography. It has a higher elevation and is drier than Key West. In addition, more frontal systems affect El Paso because Key West is far enough south that the warm, moist air that typically persists across South Florida is rarely disturbed by frontal systems. Part III: Return Periods 12. (Advanced Students/Meteorology Majors) If a 25-year rainfall event occurs this year, how likely is a similar event to occur next year as compared to 20 years from now? Briefly explain your answer. The likelihood of an event the following year is the same as an event 20 years later. Return periods are statements of probability; hence, there is no guarantee of a longer recurrence period. Explorations in Meteorology 75

5 13. (Advanced Students/Meteorology Majors) Using the dataset of annual precipitation for Savannah, GA in Table 7 and the probablility of exceedence graph in Figure 9, calculate the value of precipitation for return periods of 5, 10, 25, and 100 years. That is, what is the maximum amount of precipitation that Savannah could expect during a 5-year period, 10-year period, etc.? Using the table (by sorting), students likely will obtain the following answers: Max. Precip. for a 5-year Return Period is inches Max. Precip. for a 10-year Return Period is inches Max. Precip. for a 25-year Return Period is inches Max. Precip. for a 100-year Return Period is inches Using the graph, students likely will obtain the following answers: Max. Precip. for a 5-year Return Period is 55 inches (finding the 20% value) Max. Precip. for a 10-year Return Period is 61 inches (finding the 20% value) Max. Precip. for a 25-year Return Period is 67 inches (finding the 20% value) Max. Precip. for a 100-year Return Period is 69 inches (finding the 20% value) 14. (Advanced Students/Meteorology Majors) Using Table 7, how often does the annual precipitation for Savannah exceed 60 inches? What is the least and greatest number of years between occurrences of this threshold? The annual precipitation exceeds 60 inches every 7.7 years. (100 years / 13 events = 7.7 years per event) Least number of years between 60-inch events 0 (zero years between 1947 and 1948) Greatest number of years between 60-inch events 31 (31 years between 1912 and 1944) Explorations in Meteorology 76