D-i APPENDIX D. TYPICAL METEOROLOGICAL YE AR (TMY2) ASSIGNMENTS

TABLE OF CONTENTS

D.1 INTRODUCTION .......................................................................................................... D-1 D.1.1 Purpose and Intent............................................................................................... D-1 D.1.2 Issues................................................................................................................... D-1 D.2 APPROACH ................................................................................................................... D-1 D.2.1 Additional Data Sets ........................................................................................... D-1 D.2.2 Mapping Approach ............................................................................................. D-4 D.2.2.1 Mapping Populated Places Locations to NOAA Stations................ D-4 D.2.3 Mapping NOAA Stations to TMY2 Stations...................................................... D-6 D.2.4 Calculating State-by-State Weighting Factors.................................................... D-8

LIST OF TABLES

Figure D.2.1 Locations of TMY2 Stations Superimposed on Heating Degree-Day Contours .............................................................................................................. D-2

Figure D.2.2 Locations of 4775 NOAA Stations ..................................................................... D-3

Figure D.2.3 Locations of Populated Places (PPL) .................................................................. D-4

Figure D.2.4 PPL → NOAA Mappings for Iowa Showi ng a Predominance of NearestLocation Mappings ............................................................................................. D-5

Figure D.2.5 PPL → NOAA Mappings for Washingt on Showing Some Distant Mappings in Mountainous Regions .................................................................... D-6

Figure D.2.6 NOAA → TMY2 Mappings ................................................................................. D-8D-iiAPPENDIX D. TYPICAL METEOROLOGICAL YEAR (TMY2) ASSIGNMENTS

D.1 INTRODUCTION

D.1.1 Purpose and Intent
This appendix describes the me thodology by which weighting factors were developed to scale the influence of each TMY2 weather station on each state's resu lts. The intent is to ensure that the cost-effectiveness calculations properly re flect the geographic distri bution of buildings in which the beverage vending machines will be used. State-level aggregate results need to be most heavily influenced by the climates having the most buildings.

D.1.2 Issues
TMY2 stations, of which there are 239 in th e U.S., are distributed throughout the country so as to give good coverage of the climatic vari ation in the United States. Unfortunately for this study, the T MY2 stations are not distributed so as to match the distributio n of buildings. It is therefore necessary to identify a reasonabl e mapping between the climate-based (TMY2) simulation results and the geographical distributi on of buildings in each state. Although TMY2 data give good climatic coverage, they do not give sufficient geographical coverage. Detailed data on the geographical/climatic distribution of buildings were not readily available for this task. However, data on the geographical distribution of persons (population data) can serve as a reasonable surrogate for build ings data, and are available from a number of sources. The problem facing this study was to match up population data, which are available in great geographical detail but not matched to climate indicators, with TMY2 data, which characterize climate quite well but are not connected to any population indicators.

D.2 APPROACH
Figure Error! No text of specified style in document. .1 shows the locations of the 239 TMY2 stations superimposed on a contour m ap s howing heating degree-days (HDD). It is clear that the geographic distribution of the TMY2 stati ons is too sparse to capture many of the climate variations that occur ove r relatively short distances, especi ally in mountainous regions. It is therefore not feasible to devel op weighting factors based solely on the TMY2 stations within a state. Therefore, two additional data sets are us ed to map TMY2 stations to detailed population distribution as discussed below.

D.2.1 Additional Data Sets
To develop weighting factors, we identified tw o data sets (in addition to the TMY2 data set) that provide a connection between detail ed population distributi on and TMY2 stations. These are:

 National Oceanic and Atmospheri c Admin istration (NOAA) Climate Stations – The National Climatic Data Center's (NCDC's) “CLI M81” database contains summary statistics from a large number of climate stations in the United States. We used the 1961–1990 period of record (POR), which corresponds to the POR used to define the TMY2 weather tapes, for which 4775 climate stations are represented (see http://lwf.ncdc.noaa.gov/oa/docum entlibrary/clim81supp3/clim81.htm l ). Each NOAA station

D-1is characterized by its location (latitude/longitude), annual hea ting and cooling degree-days, elevation, and various other metrics.

Figure Error! No text of specified style in document. .1 Locations of TMY2 Stations Superimposed on Heating Degree-Day Contours

 USGS Populated Places – The United States Geological Su rvey (USGS), in its Geographic Names Information System, maintains a detaile d database of cities, towns, and other important features. (For the latest version of this data set, see http://geonames.usgs.gov/ stategaz/00README.htm l . Our analysis used a version of this data set from the early 1990s, making it contemporane ous with the TMY2 and NOAA data sets.) Of interest to this task are the “populated places” (PPL), which are generally cities and towns, but also include large housing subdivisions, trailer parks, a nd other places where people may live. For many of these populated places, the USGS has a population estimate. The populated places data give ex cellent geographical coverage. The version of the data set used here has over 22,000 entries that include a population estimate out of more than 164,000 total. a Each PPL location is characterized by its location (latitude/longitude), elevation, population, and various other metrics.

The NOAA data are important because they contain climate summary information that can be mapped to the TMY2 stations, gr eatly increasing our ge ographical coverage. Figure Error! No text of spec ified style in document. .2 shows the locations of the 4775 NOAA

a Locations without USGS population estimates tend to be those with very little population. We have kept these smaller sites in our mapping analysis by assigning each a population estimate of one. Th is gives them negligible influence against the more populous locations but allows the mapping procedure to work even in very sparsely populated regions of some states.

D-2stations. The PPL database is used to make the final link between the climate information in the mapped NOAA/TMY2 stations and the ge ographical distribution of population. Figure Error! No text of specified style in document. .3 shows the PPL locations.

Figure Error! No text of specified style in document. .2 Locations of 4775 NOAA Stations

D-3Figure Error! No text of specified style in document. .3 Locations of Populated Places (PPL)

D.2.2 Mapping Approach

Our approach to generating TMY2 weight ing factors involves three major steps:

1. Map each PPL location in the United States to a best-representative NOAA station. This gives each location some summary climate me trics (chiefly, heating and cooling degreedays) that facilitate further mapping.

2. Map each NOAA station to a best-representat ive TMY2 station. This completes the link between the geographic population estimates (PPL data) and the TMY2 stations.

3. For each state, compute the fraction of the total PPL population that “points” (via its PPL → NOAA → TMY2 mappings) to each TMY2 station.

These three steps are described in order below.

D.2.2.1 Mapping Populated Places Locations to NOAA Stations

Mapping each of the 164,000+ PPL locations to a best-representat ive NOAA station is a mostly straightforward process. Because there is no climate infor mation in the PPL database, the only metrics available to asso ciate each PPL location with a NOAA station are location (latitude/longitude) and elevation (although eleva tion is not known for all PPL locations). The mapping algorithm is as follows.

D-41. For each PPL location, identify the near est NOAA station. Distances between PPL/NOAA pairs are calculated using the lati tudes and longitudes of the two locations and simple spherical geometry. If the eleva tion of the nearest NOAA station is within 300 feet of the PPL location or if the eleva tion of the PPL location is unknown, then the nearest NOAA station is the final mapping.

2. If the nearest NOAA station differs in elev ation from the PPL location by more than 300 feet: a) Identify the 20 closest NOAA stations to the PPL location. b) Choose, from among the 20, the NOAA station that is nearest in elevation to the PPL location.

This algorithm is imperfect in many situations , but was designed by trial and error to give reasonable mappings in a large majority of cases. In locations with relatively flat terrain and fairly dense population, the algorithm almost always maps to the closest NOAA station. Figure Error! No text of specified style in document. .4 shows the m appings in the state of Iowa as an example. Each plotted point on th e g raphic is one NOAA station; the “hairs” are drawn outward to the various PPL locations mapped to that station. In m ountainous terrain or in locations with large distances between PPL locations (e.g., Alas ka), the second part of the algorithm does a reasonable job of identifying a representative NOAA station, even if that station is some distance from the PPL location. Figure Error! No text of spec ified style in document. .5 shows the mappings for Washington as an example. Note that m any of th e PPL locations (the ends of the hairs) are mapped to distant NOAA stations.

Figure Error! No text of specified style in document. .4 PPL → NOAA Mappings for Iowa Showing a Predominance of Nearest-Location Mappings

D-5Figure Error! No text of specified style in document. .5 PPL → NOAA Mappings for Washington Showing Some Distant Mappings in Mountainous Regions

D.2.3 Mapping NOAA Stations to TMY2 Stations

Having ma pped each PPL location to a best-rep resentative NOAA station, the next step is to map each NOAA station to a best repres entative TMY2 station. Because the NOAA and TMY2 data sets provide less dense geographical coverage and because both data sets contain climate information, this mapping pr ocess relies less on spatial proxi mity and more on similarity of climate. Proximity remains important, t hough. In finding a best TMY2 mapping for a NOAA station, we hope for similarity in a number of climate variables: te mperature (HDD and CDD), solar and wind characteristics, rainfall and humid ity characteristics, snowfall, etc. The NOAA data set supports direct comp arison only of heating and cooling degree-days, but we rely on spatial proximity to ensure similarity in the other variables.

The NOAA-to-TMY2 mapping algorithm is as follows.

1. For each NOAA station, identify the nearest TMY2 station. If the elevation of the nearest TMY2 station is within 300 feet of the NOAA station, then the nearest TMY2 station is the final mapping.

2. If the nearest TMY2 station differs in elev ation from the NOAA station by more than 300 feet, select instead the TMY2 station that has the minimum “combined distance” from the NOAA station. The combined distan ce is defined as the sum of the literal distance (miles) between the two stations and an “equivalent latitude miles” value that

D-6accounts for known differences in heating and cooling degree-days and elevation. This latter metric requires some explanation (see below).

The equivalent latitude miles metric was developed as a means to characterize temperature (HDD and CDD) and elev ation in the same units as literal distance (i.e., miles). By casting HDD, CDD, and elevation effects into units of miles, we are able to simply sum the literal distance between two loca tions with the equivalent HDD/C DD/elevation distance to give the two values equal weight in assigning a best-representativ e TMY2 station to each NOAA station.

The equivalent latitude miles values are ba sed on several related observations. First, differences in both heating and cooling degree-d ays correlate with differences in latitude. Second, those same degree-day di fferences also correlate with differences in elevation. Combining these observations, we discovered th at differences in north-south distances (i.e., latitude miles) can be ch aracterized in terms of differences in HDD, CDD, and elevation. That is, as one moves northward (increasing latitude) and upward (inc reasing elevation), HDD tends to increase and CDD tends to decrease. A re gression analysis of thes e correlations allows us to cast HDD, CDD, and elevation differences into units of distance (miles). A linear regression on NOAA/TMY2 station pairs within 300 miles of each other gives the following result. Elev CDD HDD Id

equiv            Eq. D.1

Where: d equiv = equivalent latitude distance (miles), Δ HDD = difference in heating degree-days (base-65F) Δ CDD = difference in cooling degree-days (base-65F)

Δ Elev = difference in elevation (feet) I = -6.8938 (latitude distance in miles)

α = 0.1061 (latitude distance per Δ HDD) β

= -0.0149 (latitude distance per Δ CDD)
γ = -0.0718 (latitude distance per diffe rence in elevation in miles/feet)

The best representative TMY2 station for each NOAA station was selected as the one with the minimum sum of actual distan ce and equivalent latitude distance. Figure Error! No text of specified style in document. .6 shows the final NOAA → TMY2 mappings for the continental United States. Each plotted point is a TMY2 station, from which lines are drawn outward to the NOAA stations mapped to it.

D-7D-8 Figure Error! No text of specified style in document. .6 NOAA → TMY2 Mappings

D.2.4 Calculating State-by-State Weighting Factors

Weighting factors were developed for each U.S. state that ex press the fraction of that state’s population that is represented by each TM Y2 station. These weighting factors are based directly on the PPL → NOAA → TMY2 mappings described above. The weighting factor for a TMY2 station is defined as the summed population of all PPL locations in the state that point to that TMY2 station divided by the summed population of all PPL locations in the state. Thus, the sum of all the TMY2 weighting factors for a state is 1.0.