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APPENDIX D. TYPICAL METEOROLOGICAL YEAR (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 Showing a Predominance of NearestLocation Mappings............................................................................................. D-5

Figure D.2.5 PPL→NOAA Mappings for Washington Showing Some Distant 

Mappings in Mountainous Regions.................................................................... D-6

Figure D.2.6 NOAA→TMY2 Mappings................................................................................. D-8

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APPENDIX D. TYPICAL METEOROLOGICAL YEAR (TMY2) ASSIGNMENTS 

D.1 INTRODUCTION 

D.1.1 Purpose and Intent 

This appendix describes the methodology by which weighting factors were developed to 

scale the influence of each TMY2 weather station on each state's results. The intent is to ensure 

that the cost-effectiveness calculations properly reflect the geographic distribution 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 the U.S., are distributed throughout the country 

so as to give good coverage of the climatic variation in the United States. Unfortunately for this 

study, the TMY2 stations are not distributed so as to match the distribution of buildings. It is 

therefore necessary to identify a reasonable mapping between the climate-based (TMY2) 

simulation results and the geographical distribution 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 buildings 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 map showing heating degree-days (HDD). It is clear 

that the geographic distribution of the TMY2 stations is too sparse to capture many of the climate 

variations that occur over relatively short distances, especially in mountainous regions. It is 

therefore not feasible to develop weighting factors based solely on the TMY2 stations within a 

state. Therefore, two additional data sets are used to map TMY2 stations to detailed population 

distribution as discussed below. 

D.2.1 Additional Data Sets 

To develop weighting factors, we identified two data sets (in addition to the TMY2 data 

set) that provide a connection between detailed population distribution and TMY2 stations. 

These are: 

 National Oceanic and Atmospheric Administration (NOAA) Climate Stations – The 

National Climatic Data Center's (NCDC's) “CLIM81” 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/documentlibrary/clim81supp3/clim81.html). Each NOAA station 

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is characterized by its location (latitude/longitude), annual heating 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 Survey (USGS), in its Geographic 

Names Information System, maintains a detailed database of cities, towns, and other 

important features. (For the latest version of this data set, see 

http://geonames.usgs.gov/stategaz/00README.html. Our analysis used a version of this data 

set from the early 1990s, making it contemporaneous 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, and other places where 

people may live. For many of these populated places, the USGS has a population estimate. 

The populated places data give excellent 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, greatly increasing our geographical coverage. Figure 

Error! No text of specified 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. This 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. 

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stations. The PPL database is used to make the final link between the climate information in the 

mapped NOAA/TMY2 stations and the geographical 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 

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Figure Error! No text of specified style in document..3 Locations of Populated Places 

(PPL) 

D.2.2 Mapping Approach 

Our approach to generating TMY2 weighting 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 metrics (chiefly, heating and cooling degreedays) that facilitate further mapping. 

2. Map each NOAA station to a best-representative 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-representative NOAA station is a 

mostly straightforward process. Because there is no climate information in the PPL database, the 

only metrics available to associate each PPL location with a NOAA station are location 

(latitude/longitude) and elevation (although elevation is not known for all PPL locations). The 

mapping algorithm is as follows. 

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 1. For each PPL location, identify the nearest NOAA station. Distances between 

PPL/NOAA pairs are calculated using the latitudes and longitudes of the two locations 

and simple spherical geometry. If the elevation of the nearest NOAA station is within 

300 feet of the PPL location or if the elevation of the PPL location is unknown, then the 

nearest NOAA station is the final mapping. 

 2. If the nearest NOAA station differs in elevation 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 mappings in the state of 

Iowa as an example. Each plotted point on the graphic is one NOAA station; the “hairs” are 

drawn outward to the various PPL locations mapped to that station. In mountainous terrain or in 

locations with large distances between PPL locations (e.g., Alaska), 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 specified style in document..5

shows the mappings for Washington as an example. Note that many of the 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 

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Figure 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 mapped each PPL location to a best-representative NOAA station, the next step is 

to map each NOAA station to a best representative TMY2 station. Because the NOAA and 

TMY2 data sets provide less dense geographical coverage and because both data sets contain 

climate information, this mapping process relies less on spatial proximity and more on similarity 

of climate. Proximity remains important, though. In finding a best TMY2 mapping for a NOAA 

station, we hope for similarity in a number of climate variables: temperature (HDD and CDD), 

solar and wind characteristics, rainfall and humidity characteristics, snowfall, etc. The NOAA 

data set supports direct comparison 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 elevation 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 distance is defined as the sum of the literal 

distance (miles) between the two stations and an “equivalent latitude miles” value that 

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accounts 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 elevation 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 locations with the equivalent HDD/CDD/elevation distance to give 

the two values equal weight in assigning a best-representative TMY2 station to each NOAA 

station. 

The equivalent latitude miles values are based on several related observations. First, 

differences in both heating and cooling degree-days correlate with differences in latitude. 

Second, those same degree-day differences also correlate with differences in elevation. 

Combining these observations, we discovered that differences in north-south distances 

(i.e., latitude miles) can be characterized in terms of differences in HDD, CDD, and elevation. 

That is, as one moves northward (increasing latitude) and upward (increasing elevation), HDD 

tends to increase and CDD tends to decrease. A regression analysis of these 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. 

Id HDD CDD Elev equiv          Eq. D.1

Where: 

 dequiv = equivalent latitude distance (miles), 

ΔHDD = difference in heating degree-days (base-65F) 

ΔCDD = difference in cooling degree-days (base-65F) 

ΔElev = difference in elevation (feet) 

 I = -6.8938 (latitude distance in miles) 

α = 0.1061 (latitude distance per ΔHDD)

β = -0.0149 (latitude distance per ΔCDD)

γ = -0.0718 (latitude distance per difference 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 distance 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. 

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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 express the fraction of that 

state’s population that is represented by each TMY2 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. 

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