C2 t. ^0^ : / A> ' ^ OF ^ ^rts o* Climatic Degree Days for Energy Demand Assessment U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration Environmental Data and Information Service Digitized by the Internet Archive in 2012 with funding from LYRASIS Members and Sloan Foundation http://www.archive.org/details/climaticdegreedaOOwarr .^qAJMOSp^ ■?/, ^tTuft^ ^ I 1* Climatic Degree Days for Energy Demand Assessment Henry E. Warren, Economist; Sharon K. LeDuc, Senior Statistician; Mary S. Joshua, Computer Programmer Center for Environmental Assessment Services (CEAS), CIAD/Models Branch, Columbia, Mo. November 1 980 U.S. DEPARTMENT OF COMMERCE Philip M. Klutznick, Secretary National Oceanic and Atmospheric Administration Richard A. Frank, Administrator Environmental Data and Information Service Si Thomas D. Potter, Director O 11 ABSTRACT This publication presents the development and procedures for the use of real-time heating and cooling degree days information for States. These State data are determined by population weighting heating and cooling degree days data from major National Weather Service stations. The concept of a degree day index is a result of the need to monitor temperature sen- sitive energy consumption on a disaggregated basis. Climatological normals and ranges of heating and cooling degree days are calculated for each State and presented in tabular and graphical form to facilitate the use of opera- tional information. Ill CONTENTS Introduction 1 Development and design of the degree day graphs & tables 2 Operational use of the graphs and tables 22 Other uses of the graphs and tables 35 References 39 Appendix 1 - Formulas and derivations . 40 Appendix 2 - State graphs and tables of degree days 44 TABLES 1 - Weekly normal accumulated heating degree days for Indiana,.... 7 2 - Station annual normal accumulated degree days 14 3 - State annual normal degree days 20 4 - Illustration of weekly data published on State degree days.... 23 5 - Illustration of weekly degree day summary and forecast 27 6 - Illustration of one-month degree day summary and outlook 32 7 - Illustration of three-month degree day summary and outlook. .. .33 8 - Illustration of one-month natural gas summary and outlook 36 9 - Illustration of three-month natural gas summary and outlook... 37 FIGURES 1 - Indiana Weather Stations and population weights 3 2 - Indiana climatic divisions and population weights 4 3 - Plot of cumulative heating degree days 6 4 - Annual U.S. heating degree days 10 5 - Annual State heating degree days 11 6 - Annual U.S. cooling degree days. 12 7 - Annual State cooling degree days 13 8 - Illustration of weekly map published on degree days 25 9 - Example of plotting weekly data on normal curve 28 10 - Illustration of average monthly weather outlook 30 11 - Illustration of experimental 90-day outlook 31 12 - Illustration of plotting monthly data on normal curve 34 13 - Missouri natural gas sendout and heating degree days 38 IV ACKNOWLEDGMENTS The authors wish to thank Jan Hagan for the cover design and drafting of several figures, Royce Kirk for typing the manuscript, Clarence Sakamoto for his review and comments, Rita Terry for editing the manuscript and Leanne Gregg for composition of the text. Introduction This publication describes products which fill information needs of energy planners and policy makers at the State and national level in the public and private sectors. These products were developed by two agencies of the U.S. Department of Commerce, National Oceanic and Atmospheric Administration: the Climate Analysis Center of the National Weather Service (NWS-CAC) and the Climatic Impact Assessment Division of the Environmental Data and Information Service's Center for Environmental Assessment Services (EDIS-CEAS). The increasing scarcity and price of natural gas, heating oil, electricity, and other energy sources used for space heating makes it crucial to closely monitor energy requirements for space heating during the winter. The first product developed to aid in monitoring energy requirements was the weekly State heating degree day summary and forecast which was initiated by the CAC in the fall of 1975. Concurrently, the CEAS-Climatic Impact Assessment Division developed and designed the cumulative State heating degree day graphs and tables to provide statistical interpretation of successive heating degree day accumulations during the winter. In addition, for a few States, rela- tionships were derived to relate weekly heating degree day numbers to natural gas consumption in the State 1 . The heating degree day (HHD) was developed by heating engineers in the 1920 f s as a measure of energy requirements for space heating. It was subsequently adopted as a cumulative index of cold weather and energy require- ments for space heating. In the 1960's, when electrical air conditioning came into wide use in homes and offices, an index of warm weather was needed that would indicate the amount of energy consumed for air conditioning, and the cooling degree day (CCD) was developed 2 . The heating degree day was originally derived with the base 65°F and, for consistency and symmetry, the cooling degree day base was also chosen at 65°F; (See appendix I). There has been some investigation and discussion as to whether heating and cooling degree days based on 65 °F are an adequate and accurate index of energy use for space heating and cooling with current improved construction and insulation standards. The base 65 °F may be too high for heating degree days and cooling degree days. Cross-sectional com- parisons of degree days may not directly reflect energy requirements between different areas due to differences in climate and construction methods. 1 See Warren, H.E., "A Regression Model for Estimating Weekly Natural Gas Sendout in the State of Missouri," USDOC, NOAA, EDIS, CCEA Technical Note 76-9 Columbia, MO, June 1976. Also see Lehman, R.L., and H.E. Warren, "Residential Natural Gas Consumption: Evidence That Conservation Efforts Have Failed," Science , Vol. 199: 879-882, February 1978. 2 A catalogue of information available on degree days from the National Climatic Center and other sources is Heating and Cooling Degree Day Data , U.S. Dept. of Commerce, Nat. Oceanic and Atmos. Adm., Env. Data and Info. Div., "Environmental Information Summaries C-14," National Climatic Center, Asheville, N.C., April 1978. It is important to note that station weighted State degree days are a set of unique values that do not necessarily correspond to the State heating and cooling degree days published by the NOAA/EDIS National Climatic Center. The latter are based on the climatic division degree days from about 7,000 stations across the Nation which are calculated after the CAC statistics have been published (1, 2). Although both the station weighted State degree days are the climatic division weighted State degree days are calculated through population weighting, the difference in the number and location of the stations makes the two sets significantly different in several States. Each set works equally well in indicating the relative energy consumption for space heating. However, the operational values of the station weighted state heating degree days cannot be compared to either the climatic division weighted State degree day normal or values for previous years. Unless otherwise noted in this publication, "State heating degree days" and "State cooling degree days" will refer to station weighted heating and cooling degree days; the term "degree day(s)" will be used for brevity 3, 4. Development and Design of the Degree Day Graphs and Tables The degee day graphs and tables were produced from historical normals of the stations used to calculate the operational State degree day values. The 204 major weather stations selected for calculating operational State degree day values were chosen by the CAC on the basis of consistent and reliable reporting. Given this set of stations, the Climate Analysis Division of the EDIS National Climatic Center selected stations in and around each State and partitioned the State along county boundaries such that the counties would be allocated among the available stations with climatic similarities. The boundaries were drawn along county lines so that the population in the area to be associated with each station could easily be determined. The results of this proccedure for the State of Indiana are presented in figure 1 ; note that these areas are not the same as the climatic divisions of the State. As can be seen, the weight a sta- tion receives in the calculation of the State degree days is determined by the proportion of the population in the area of the State associated with the station. It can also be seen that stations near State borders that are climati- cally representative of large areas may be used in the calculations of degree days in adjoining States. For example, referring to figure 1, the counties in the 3 Nail, Daniel and Edward Arens, "The Influence of Degree Day Base Temperature on Building Energy Prediction," National Bureau of Standards Washington, D.C., Presented at January 1979 ASHRAE Weather Data Symposium. 4 For other weighting processes and additional information see Mitchell J.M. , R.E. Felch, D.E. Gilman, F.T. Quinlan, R.M. Rotty, "Variability of Seasonal Total Heating Fuel Demand in the U.S.," Special Task Group, USDOC, NOAA, Washington, D.C., September, 1973. Figure 1. - Indiana weather stations, associated areas, population, and weights for calculating station weighted State degree days. SOUTH BEND .1351 (702) FT. WAYNE .0949 (493) INDIANAPOLIS .4823 (2505) CINCINNATI, OH. .0420, LOUISVILLE, KY. 0-198 Station weight Population in area in thousands Figure 2. - Indiana Climatic Divisions Northwest .1607 North Central .1165* r West Central .0730 Northeast .0949 Central .3009 East Central .0697 Population weight northwestern corner of Indiana are climatically similar to the weather station at Chicago (Midway Airport). The population in those counties is 738,000. The total population of Indiana is 5,194,000. Thus, the weight that Chicago receives in the calculation of the degree days for Indiana is 738,000 = 0.1421. The station weighted State heating degree days are calculated for any period of time by summing products of the station weight times the degree days at the station for that period. Indiana degree days = (.1421 x Chicago degree days) + (.1351 x South Bend degree days) + (.0949 x Fort Wayne degree days ) + (.4823 x Indianapolis degree days) + (.0838 x Evansville degree days) + (.0198 x Louisville degree days) + (.0420 x Cincinnati degree days). The algebraic formulations that are used to calculate the degree day accumu- lations are presented in appendix 1. The graphs and tables of cumulative State degree days are designed to facilitate the use of operational weather infor- mation by providing a depiction of the accumulated severity of the current heating or cooling season. The normal State degree day accumulations are calculated by the same formula using the normals (1941-1970) for each of the stations and their associated weights. The normal heating degree day accumula- tion for Indiana is the middle curve presented in the graph in figure 3. The two curves symmetrical to the central curve are the upper and lower bounds of a 90 percent confidence interval around the curve. On any day during the year the accumulation of heating degree days should be contained between the two curves 9 years out of 10. The interval is symmetric so the chances of being above the upper or below the lower curve are each 5 percent. The statistical formulations that are used to calculate these bounds are presented in appendix 1. In figure 3 the accumulation of heating degree days for the entire year (July 1 - June 30) is presented. The heating year was chosen as July 1 through June 30 of the following year so a single winter would be contained in the 12-month period. There is no significant accumulation of heating degree days in the United States before September 1 (day 63) or after May 31 (day 335). Consequently, in the graphs in appendix 2, only the portion of the curve between September 1 and May 31 is presented. Similarly, for State cooling degree days only the portion of the cooling degree day accumulation curve bet- ween May 1 and September 30 is depicted; the cooling year coincides with the calendar year. In figure 3 and the graphs in appendix 2 note that the numbers labeling the vertical axis, i.e., 80.00, 160.00..., 720.00, are scaled down by a factor of 10 and thus represent 800., 1600., ..., 7200. (In States where the upper bound of HDD approaches 10,000 the scale factor is 100). In conjunction with each State's graph there is a table containing the numerical value of the points plotted on the graph of the normal, the upper bound, and the lower bound of cumulative degree day numbers for days during the heating season. The table also contains the standard deviation of normal cumu- lative degree days during the heating season. As is explained in appendix 1 , the standard deviation is the parameter used to calculate the upper and lower bounds around the the normal. Table 1 corresponds to the graph in figure 3 and contains normal values for the entire 1978-1979 heating season from the first week in July 1978 to the last week in June 1979. This is designed to correspond i'igure 3. - Indiana Cumulative Heating Degree Days xlO 1 o o INDIANA 0.00 50.00 100.00 150.00 200.00 DAYS PAST JUNE 30 250.00 300.00 350.00 Table 1 . - Indiana weekly normal accumulated heating degree days and 90% confidence interval Days past Week Lower Upper 1978-79 June 30 ending bound Normal bound Observations St. dev. 9 7/9 0.0 0.0 2.25 1.37 16 7/16 0.0 0.0 3.00 2.43 23 7/23 0.0 0.0 5.72 3.49 30 7/30 0.0 0.0 7.48 4.56 37 8/6 0.0 1.00 10.71 5.92 44 8/20 0.0 2.00 14.04 7.34 51 8/20 0.0 3.00 17.35 8.75 58 8/27 0.0 6.00 22.66 10.16 65 9/3 0.0 12.00 34.83 13.92 72 9/10 0.0 19.00 53.11 20.80 79 9/17 0.0 31.00 76.38 27.67 86 9/24 0.0 50.00 106.66 34.55 93 10/1 10.86 80.00 149.14 119 42.16 100 10/8 33.16 122.00 210.84 54.17 107 10/15 71.46 180.00 288.54 66.18 114 10/22 127.77 256.00 384.23 78.19 121 10/29 206.07 354.00 501.93 460 90.20 128 11/5 307.21 474.00 640.79 101.70 135 11/12 432.71 618.00 803.29 112.98 142 11/19 581.20 785.00 988.80 124.27 149 11/26 750.68 973.00 1195.32 135.56 156 12/3 937.82 1182.00 1426.18 1115 148.89 163 12/10 1136.51 1407.00 1677.49 164.93 170 12/17 1350.19 1647.00 1943.81 180.98 177 12/24 1575.89 1899.00 2222.11 197.02 184 12/31 1808.57 2158.00 2507.43 213.07 191 1/7 2043.59 2421.00 2798.41 230.07 193 1/14 2281.61 2687.00 3092.39 247.19 205 1/21 2518.61 2952.00 3385.39 264.26 212 1/28 2754.64 3216.00 3677.36 281.32 219 2/4 2991.41 3476.00 3960.59 3704 295.48 226 2/11 3226.75 3731.00 4235.25 307.47 233 2/18 3453.10 3977.00 4500.89 319.45 240 2/25 3668.44 4212.00 4755.56 331.44 247 3/4 3879.17 4433.00 4986.82 4886 337.70 254 3/11 4080.94 4683.00 5195.06 339.67 261 3/18 4264.71 4825.00 5385.29 341.64 Table 1. - (continued) Days past Week Lower Upper 1978-79 June 30 ending bound Normal bound Observations St. dev. 261 3/18 4264.71 4825.00 5385.29 341.64 268 3/25 4428.48 4992.00 5555.52 343.61 275 4/1 4569.10 5136.00 5702.90 5530 345.67 282 4/8 4687.88 5259.00 5830.11 348.24 289 4/15 4784.65 5360.00 5935.34 350.82 296 4/22 4864.42 5444.00 6023.57 353.40 303 4/29 4930.21 5514.00 6097.79 5972 355.97 310 5/6 4989.03 5573.00 6156.97 356.08 317 5/13 5038.52 5622.00 6205.48 355.78 324 5/20 5076.00 5659.00 6241.97 355.47 331 5/27 5104.52 5687.00 6269.48 355.17 338 6/3 5122.44 5705.00 6287.56 355.22 345 6/10 5129.55 5713.00 6296.45 355.76 352 6/17 5130.68 5715.00 6299.31 356.29 359 6/24 5129.81 5715.00 6300.18 356.82 365 6/30 5129.06 5715.00 6300.94 6189 357.28 to the weekly heating degree day summaries and outlooks produced by NWS. The additional column contains degree day accumulations during 1978-79 for selected weeks throughout the season. These values are plotted in figure 3 as the dashed line. The heating degree day accumulation nearly reached the upper bound in February and March 1979, then fell later in the season. The tables accompanying the heating and cooling degree day graphs in appendix 2 are truncated in the same manner as the graphs and contain the normal accumulation for the main part of the season. The geographic pattern of annual degree days for stations and the pattern of annual State degree days, derived from weighting station data across the contiguous United States, may be determined from inspection of figures 4 and 5 for heating degree days and figures 6 and 7 for cooling degree days. Table 2 contains an alphabetical list by States of the sta- tions used in the calculation of the State degree days and their normal annual heating and cooling degree days. 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OO'OhS OCT09S 00*06h OO'OOTi 00*02£ 00*0h2 00*091 00*06 ,01* SJ.y0 33yQ30 9NI1B3H 3Aiiuinwm 00'0° u. > UI w V\ D >- -o < 1- o ui V) v> UJ < ui-iiD a< > o> > < ao UIO: Z. uz DUiZ Q.D l-O • ao OZH Dm Zm-a M 0 z HhZffl H r Z v> a o D o << o •~ii-iocoifirM<0'*om4>-<>-4coi'iaNi')*-»~»iinW i^i-*rii')«gM P H^K)N«ioN»'ir\iflrx«MHll'»MI'l>*»*'»in>'»l/tlOIO<'llO'0 ^Or-)l^«OI')Oi-l^*rN.-IIOO"HCJK|l<1<0»H^rsO>»IAO>*r^O«Ml'l-0r^<00-O«-l«Mt'>-*ui-0MN HHHHHi-IHHHHNNnolNNNNN X riOOO^rtH l-l •* H «t <0 O- <0 ►*) UI H00004H 3 vx XO W _» » * l-l MUIMUI -IO Jh-mioz « -j < -j Z a in z OhZhXBj o o>zxz M HZO o UjOU)ilhm 29 The first week issue of each month contains information on projected accu- mulations of degree days for the coming month, for three months and the pro- jected degree day accumulation for the season for the States. These degree day outlooks are derived from the 30-day (fig. 10), 90-day seasonal, and 90-day experimental (fig. 11) temperature outlooks of the NWS-CAC using an algorithm presented in appendix 1 (4). Examples of the outlook are presented in tables 6 and 7. The use of these outlooks in conjunction with the graph is similar to the use of the weekly projection. This is illustrated in figure 12. From table 6, the initial value, 2029, of the acccumulated degree days from July 1 through December 31 , 1978 is in the first row. This amount is plotted on the graph in figure 12 at day 122 because December 31 is 122 days past August 31 • This is below the normal amount as shown in the graph and also in column 3 of figure 12. The percentile of the accumulations is 30.55 (normal is 50). The expected accumulation of heating degree days in January is computed from the outlook for average temperature in figure 10 as shown in table 6. Tne expected accumulation at the end of January is the sura, 2029 + 1170 = 3199. Based on the uncertainty of the temperature outlook, the upper and lower bounds of a confidence interval on the outlook are calculated and given in row 5, table 6 — the lower bound is 876 and the upper 1463. Using these values the bounds on the expected accumulation at the end of January are 2905 and 3492. These bounds are plotted at day 153 and bracket the expected amount, 3199. As can be seen on the graph, the forecast amount for January was near the upper bound of the confidence interval; the expected amount and the total accumulation were above the normal line. (The other rows in table 6 contain a comparison of the current totals to last year and a seasonal projection based on the one month outlook and climatology. ) This projection is not plotted on the graph of figure 8 but would be very close to the normal line. Table 7 contains the heating degree day projection based on the Experimental 90-day outlook for average temperatures in figure 1 1 . Table 7 gives the same initial value at the end of December, 2029. In line 4 the outlook for January through March is 3020, in line 5 the lower bound is 2564 and the upper 3442. When added to the initial value these values give an expected accumulation at the end of March of a near normal amount of 5049 ; a lower bound on the expectation is 4593 and an upper bound 5471. These three values are plotted at day 212 or March 31, which is 212 days past August 31. The observed heating degree days for January through March were 3476, just beyond the upper bound of the confidence interval. This brought the seasonal accumulation through March to 5505 which is well above normal. Row 7 of table 7 contains the projected heating degree day total for the season (July-June) (5634). This is calculated using the observed data from July - December (2029), the projected amount for January - March (3020), and the climatological normal amount for April - June (585). Because the seasonal projection is based on two projections, the confidence interval has an approximate value of 80 percent between the lower bound 5006 and the upper bound 6228. These values are plotted at day 273, May 31, at the end of the graph. Thus, the degree day accumulation for the season was expected to be slightly less than normal. The actual accumulation observed was 5994. As shown on the graph this amount is above normal but within the range of the confidence interval around the projected amount. This exercise demonstrated the use of the tables and graphs in conjunction with operational products and the potential range of the forecast variability. 30 — • o o r— ! 4-3 o SL, a- r— : s: c Q CD hO L CD > I 3 a' 31 C en •"3 CO CD 4-3 CT5 S-. 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The natural gas summaries and outlooks corresponding to the degree day summaries and outlooks are reproduced in tables 8 and 9. These are published monthly in the E/RAI-ECS with the degree summary and outlooks. It is also possible to develop State weekly models of natural gas or other energy consumption that can be used on a shorter time and space scale than a monthly or quarterly basis. As a demonstration, one such model developed by CEAS is illustrated in figure 13. On this graph, weekly total natural gas sendout for Missouri is plotted on the vertical and weekly station weighted state heating degree days on the horizontal for weeks in 1973 and 1974. Assuming the rela- tion is valid, current Missouri weekly degree day totals can be used to esti- mate the current weekly sendout of natural gas. Other Uses of the Graphs and Tables Although the graphs and tables are designed for operational use, they have potential use in contingency planning and simulation. Data on energy and eco- nomic variables are collected by political sub-divisions i.e., station regions. Station weighted State degree days provide a good index of weather sensitive energy consumption. The confidence interval bounds provide good estimates of the range of variability of the accumulated degree days at any point in a season. The stan- dard deviation can be used in determining the probability of occurrence of other degree day amounts through standard statistical calculations. 36 Table 8. - Summary and outlook for natural gas demand by residential and commercial customers by division one month outlook (trillions of BTU) Season: September 1978 - May 1979 NOAA-EDIS-Center for Environment Assessment Services WAT TW "MAT W 1. EST CONSUMPTION TO DATE: (12/31/78) 2550.32 2. EST CONSUMPTION TO DATE L YR: (12/31/77) 2501.09 3. EST CONS TO DATE/ EST CONS TO DATE L YR 1.02 4. PREDICTED DEMAND FOR PERIOD 1/79 1153.03 5. 90% CONF LNTERVAL FOR PREDICTION 926.40 1377.27 6. EST CONS FOR PERIOD 1/78 1277.15 7. PRED CONS/ EST CONS LAST YR 0.90 8. LOWER BOUND/ EST CONS LAST YR 0.73 UPPER BOUND/ EST CONS LAST YR 1.08 9. PRED CONSUMPTION FOR SEASON 1978-1979 6479.17 10. Q0% CONF INTERVAL FOR SEASON 5950.20 7005.76 11. EST CONSUMPTION FOR SEASON 1977-1978 6727.45 12. SEASON PRED CONS/ EST CONS LAST YR 0.96 13. LOWER BOUND/ EST CONS LAST YR 0.88 UPPER BOUND/ EST CONS LAST YR 1.04 71.78 310.49 828.07 66.15 318.03 850.55 1.09 0.96 0.81 1.12 1.01 0.94 1.07 0.98 0.90 0.73 1.09 0.93 0.86 1.01 0.97 30.37 141.30 373.55 25.56 114.71 306.28 35.57 170.02 440.81 31.74 156.40 426.72 0.88 0.72 1.03 182.48 811.38 2120.54 170.63 749.31 1969.45 194.72 875.58 2271.64 181.49 870.53 2306.37 0.92 0.85 0.98 MEM - New England, MAT - Mid Atlanta, EUC - East Worth (Central Other divisions not shown due to space limitations; West North Central, South Atlanta, East South Central, Mountain, Pacific 37 Table 9. - Summary and outlook for natural gas demand by residential and commercial customers by division three month outlook (trillions of BTU) Season: September 1978 - May 1979 NOAA-EDIS-CENTER FOR ENVIRONMENTAL AS SESSMENT SERVICES NEN MAT "TUTC 71.78 310.49 828.07 66.15 318.03 850.55 1. EST CONSUMPTION TO DATE: (12/31/78) TOTAL 2550.32 2. EST CONSUMPTION TO DATE L YR: (12/31/77) 2501.09 3. EST CONS TO DATE/ EST CONS TO DATE L YR 1.02 4. PREDICTED DEMAND FOR PERIOD 1/79-3/79 3031.42 5. 90% CONF INTERVAL FOR PREDICTION 2668.78 3374.75 6. EST CONS FOR PERIOD 1/78-3/78 3305.65 7. PRED CONS/ EST CONS LAST YR 0.92 8. LOWER BOUND/ EST CONS LAST YR 0.81 UPPER BOUND/ EST CONS LAST YR 1.02 9. PRED CONSUMPTION FOR SEASON 1978-1979 6510.91 10. S0% CONF INTERVAL FOR SEASON 6010.02 6992.50 11. EST CONSUMPTION FOR SEASON 1977-1978 6727.45 12. SEASON PRED CONS/ EST CONS LAST YR 0.97 13. LOWER BOUND/ EST CONS LAST YR 0.89 UPPER BOUND/ EST CONS LAST YR 1.04 1.09 0.95 0.87 1.03 1.01 0.95 1.07 0.98 0.91 0.82 0.99 0.94 0.87 1.00 0.97 83.68 388.64 1001.00 76.85 350.20 901.21 90.51 427.08 1093.41 87.88 429.28 1143.63 0.88 0.79 0.96' 183.20 815.36 2134.38 172.67 759.27 1990.30 193.74 871.46 2271.08 •181.49 870.53 2306.37 0.93 0.86 0.98 NEN - Mew England, MAT - Mid Atlanta, ENC - East North Central Other divisions not shown due to space limitations; West North Central, South Atlanta, East South Central, Mountain, Pacific 38 Figure 13. - Missouri weekly natural gas sendout and heating degree days, (Sept. 1973-May 1974 & Sept. 1974-Dec. 1974) o> o ? U S U) >- , Jg Q is. o u -J u H «* a a, Sou 3 y ^ <0 * Z Z r>- UJ O CO rs. ■ Q. u ID -in CO in — i— • en in - r^ - < Q UJ ID U -en OC Csi O u Q %D C3 . o> z T-H H < UJ X ID . in Q i—i uj H- X o ■■B ID UJ . T-t 1—1 5 z o i^v h- < (/> vo to in ro in m CO in o CM O Ort in in ^no'ijiu ±nOQN3S SVO 39 REFERENCES 1 . United States Department of Commerce , National Oceanic and Atmospheric Administration, Environmental Data and Information Service; State, Regional, and Monthly and Seasonal Heating Degree Days Weighted by Population . (July 1931 -June 197b). National Climatic Center, Asheville, N.C., March 1977. 2. United States Department of Commerce, National Oceanic and Atmospheric Administration, Environmental Data and Information Services; State, Regional and National Monthly and Seasonal Cooling Degree Days Weighted by Population (January 1931 December 1977). National Climatic Center, Asheville, N.C. April 1978. 3. United States Department of Commerce, National Oceanic and Atmospheric Administration, Environmental Data and Information Service; "Environmental/Resource Assessment and Information, U.S. Energy/Climate Section," published weekly since November 1978. Center for Environmenal Assessment Services, Washington, D.C. 4. United States Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service; "Average Monthly Weather Outlook," published monthly. Climatic Analysis Center, Washington, D.C. 40 Appendix 1 - Formulas and Derivations As is explained in the text, both heating and cooling degree days are calculatd as the difference between daily average temperature, T in °F, and the base 65 °F. Daily average temperature is calculated for the maximum and minimum temperatures in the day at each station. Tmax + Tmin T = where Tmax - station maximum temperature in the day (°F), Tmin - station minimum temperature in the day (°F), T - station average temperature in the day (°F). Define h = station heating degree days for the day c = station cooling degree days for the day If T < 65° , then h = 65° -T c = If T >65°, then h = c = T-65° If T = 65° , then h = c = For a State the number of degree days in a day is the population weighted sum of the degree days at the stations in and around the State. n h s = E w i h i (1) i= 1 n c s = Z w iCi (2) i=l where h.^ = heating degree days at station i, Ci = cooling degree days at station i, 41 w± = population weight of station i, h s = heating degree days for State s, c s = cooling degree days for State s, n = number of stations used. Cumulative degree days are the sum of degree days from the start of the season. k H, = £ hgjj , h s ^j is h s for jth day of season (3) j = l k C, = £ c . , c . is c for i th day of season, (4) k sj' sj s where Hr= cumulative State heating degree days to day k, C k = cumulative State ccooling degree days to day k. Normal cumulative State degree days are obtained by using the daily station normal values in equations (1) and (2) and then summing over the days in the period using equation (3) and (4). The period used for calculating normal values is 1941-1970. Let H nk = normal cumulative State heating degree days to day k, C nk = normal cumulative State cooling degree days to day k. The values of the normal cumulative degree days are presented in the tables for 10-day intervals and plotted in the graphs as the central curve. The value of the upper and lower bounds of the 90 percent confidence interval around the normal cumulative degree days are determined by assuming that the distribution of the accumulated degree days on any day has a normal distribution. The mean and standard deviation of the accumulated degree days are estimated and the confidence interval established. Cumulative degree days have been found to be normally distributed. The standard deviation of cumulative heating degree days (H k or C k ) at day k is estimated by S hk = y (H k -H ki ) 2 E i=i y- 1 2 42 y = number of years in the data set, k = day of season through which the degree days have been accumulated, H k = mean of the data series of heating degree days from July 1 to day k or H, = £ k H ki i y Data on State degree days have been compiled on a monthly basis by the National Climatic Center back to 1931 (1, 2). The most current year used was 1977 so y = 45. Using this data the standard deviations are estimated for the accumulated degree day at the end of each month, i.e., Shk for k = 31 (end of July), 62 (end of August), 92 (end of September), . .., 365 (end of June). The intermediate value of accumulations standard deviations were interpolated from the monthly accumulated values. The standard deviation of cooling degree days is defined the same as heating degree days and the values were estimated in the same way over the same years. < c k " c ki) 2 S = E Ck i=1 y-1 where y = years in the data set = 46, k = days in the accumulation (accumulations by month are k = 31 , January; k = 59, February; k = 90, March; ...; k = 365, December; for other values of k, Shk was determined by interpolation) , T k = mean of the data series of cooling degree days from January 1 y c to day k or C v = z K1 . i=l y Having calculated the necessary parameter to determine the bounds of a con- fidence interval we find from a table of the normal distribution that a 90% confidence interval has bounds of 1.645 standard deviation around the mean. In order to be consistent with the NWS data, H n k, normal heating degree days (1941-1970) were chosen as the center of the interval rather than Hk, the mean of all years in the data set. The bounds at day k are the following: 43 for heating degree days, upper bound, U hk = H nk + 1.645 S hk , lower bound, L hk = H nk - 1.645 S hk ; for cooling degree days, upper bound, U ck = C nk + 1.645 S ck , lower bound, L ck = C nk - 1.645 S ck ; . Degree days are defined only as positive numbers; if the values of L hk or L ck early in the season are less than zero they are set equal to zero. 44 Appendix 2 - Graphs and Tables of State Heating and Cooling Degree Dcrya DQ'OSe 00"Q2£ t 0l« -i r 1 1 1 r 0D - QTl2 OO'OOS 0D'Q9t 00^021 D0'06 DO'Or. SXHQ 33y03Q DNI1QQD 3A I lyinwm 00 "0 V> ir\ O > o < (- Q 111 i uj a o UJ tk OQ UJZ QiuZE 0-D HOIU D.O OZHh Dm ZHt-1 M < UJ _IUJ_J(/> a - z z H r z MO Or O < ui-oi^^o-oiHfMrosfioorNajcj-cj- i-lt-Jr-lf-lr-tr-l.-11-J.-Ji-liH OOfNvO-oh--*r < 0: X UJ z O £ o ZUJO H M_l(D »- EHH < atfjz h HOO ID O Ul Q >- -o < H Q Ul (/) to ID < id -no 0:< >- U>> > < ao uia £ UJZ QUIZ aD HO • 0.O OZH Dtfl ZHhtt H - W z < OO O HIU -j(D Z3 -■< < V) H £ z to a. 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QUIZ l-O > OZH ZHhlt M <1U i-uj-iin ooo» D UJZ Z.XHO 30IW 0<0 K O D << o f)0'IMII|<0Orm/iio<0 •-« < tlst^l0l0l'l-O-O-O(^ISh->>IN<0<0 ■^a-wr'»MOKlNO^(OI<1^f4IOONI> rl>--lt-lf-lf-lr-lfH>Hs» o o » > I- M Ml Z z o z < o azuQ M OU1UIUIM I- MCD-ODf < auuzui I- < ttOO->0 * U. S. GOVERNMENT PRINTING OFFICE : 1980 340-997/1319 PENN STATE UNIVERSITY LIBRARIES ADQQD7D c mD77D NOAA^-S/T 80-162