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HOME > Outlooks > Monthly to Seasonal Outlooks > Probability of Exceedance Forecast > Temperature to Degree Day File
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This experimental outlook product gives the probability that a temperature or precipitation quantity will be exceeded at the location in question, for the given season at the given lead time. The locations are one of 102 forecast divisions in the mainland U.S., or an individual station in other regions.
CPC Outlooks for Major U.S. Cities

Temperature to Degree Day File

Degree days are estimated from the climatological correspondence between the seasonal mean temperature, and the heating or cooling degree days for that season. The distribution of degree days can be found from the temperature distribution by applying a temperature - to - degree day (T-to-DD) correspondence file.

File Explanation

Filename: cityt_to_dd.dat
Description: Gives the information required to compute heating or cooling degree days from the seasonal mean temperatures for individual cities.
Derivation: Relationships were derived from rate of change in seasonal degree day totals at specified temperatures derived empirically from 1951-1997.
Column 1: City number
Column 2: Half year to which data apply. The climatological average relationship between degree days and 3-mo seasonal mean temperature is different in the spring and fall, so separate relationships are provided the first and last half of the year. If the value in column 2 is 1 then the relationship is valid for the seasons: DJF, JFM, FMA, MAM, AMJ, MJJ, or JJA. A value in column 2 of 2 indicates that the relationship is valid for JAS, ASO, SON, OND, or NDJ.
Column 3-15: Exact values at five degree increments.There are five rows dedicated to each city and half-year,
First row: gives the 3-month mean temperature (t5) at which the data in the following 4 rows apply.
Second row: denotes the mean number of heating degree days per day within the period (hdd(t5)).
Third row: denotes the mean number of cooling degree days per day within the period (cdd(t5)).
Fourth row: dhdd(t5), denotes the change in hdd(t) per degree of change of the seasonal mean temperature valid at temperature t5 (first derivative of heating degree day with respect to change in mean seasonal temperature).
Fifth row: d2hdd(t5) denotes the change in dhdd(t) per degree change in seasonal mean temperature at temperature t5 (second derivative of heating degree day with respect to change in mean seasonal temperature).

Data Set Usage

This file contains the information needed to translate a given seasonal mean temperature into its expected mean heating and cooling degree days per day. The table contains the average number of heating or cooling degree days (Rows 2 and 3, respectively) that accumulate for each day within the period for specific values of mean temperatures. These values are only valid for entire 3-month period averages, and must be applied evenly throughout the period (That is the expected accumulation rate varies within the period, so the mean values can only be applied to the entire 3-month period which they represent). Rows 4 and 5 contain information required for accurate interpolation to temperatures between the specific temperature values presented in the table.

When the seasonal mean temperature falls in between the values provide, then the seasonal estimates need to be interpolated. This can be done most accurately by a quadratic formula.

Variable Definition:
hdd(t),cdd(t) - The mean daily values of heating or cooling degree days expected at mean seasonal temperature, t. (Quantity solved for)
hdd(t5),cdd(t5) - The values of heating or cooling degree days for the nearest temperature exactly divisible by 5 degree (i.e, 50, 55, 60, etc.). These values are provided in the t-to-dd correspondence table.
dhdd, d2hdd - The first and second derivative of the relationship between mean temperature and heating degree days at temperature (t5). These values are also given in the table. These values are provided in the t-to-dd correspondence table.

Formula: (FORTRAN syntax used for formula), the **2 symbol indicates squaring the preceeding quantity.

hdd(t) = hdd(t5) + dhdd(t5)* (t-t5) + .5*d2hdd(t5) * (t-t5)**2
cdd(t) = cdd(t5) + (1.+ dhdd(t5))* (t-t5) + .5*d2hdd(t5)* (t-t5)**2

EXAMPLE: The following segment is from the T-to-DD file. City 35 pertains to LaGuardia Airport in New York City.
35 1 ..... 50.00 55.00 60.00 65.00 ..... New York City, LGA
35 1 ..... 15.31 11.33 7.23 4.29 .....
35 1 ..... 0.27 1.32 2.19 4.28 .....
35 1 ..... -0.868 -0.788 -0.677 -0.545 .....
35 1 ..... 0.038 0.000 0.041 0.013 .....
35 2 ..... 50.00 55.00 60.00 65.00 .....
35 2 ..... 15.43 11.26 7.34 4.24 .....
35 2 ..... 0.42 1.24 2.30 4.22 .....
35 2 ..... -0.891 -0.816 -0.710 -0.567 .....
35 2 ..... 0.020 0.010 0.033 0.024 .....

If, the seasonal mean temperature in, say, March-April-May (first half of the year) is exactly 50 degrees F, Then an average of 15.31 heating degree days and 0.27 cooling degree days accumulates for each of the N days in the season. There are a total of 92 days in that season so: 15.31*92 days = 1408 heating degree days.
The cooling degree days can be calculated by a similar method to yield a forecast for 25 cooling degree days expected in MAM.
For a seasonal mean temperature that falls in between the table values, the expected number of heating and cooling must be calculated by interpolation. The degree days for a seasonal mean temperature of 52.2 degrees in MAM, for example, would be calculated by interpolation as follows:

hdd(52.2) = hdd(50) + dhdd(50)* (52.2 - 50) + .5*d2hdd(50) * (52.2-50)**2
cdd(52.2) = cdd(50) +[1+ dhdd(50)]* (52.2 - 50) - .5*d2hdd(50)* (52.2 - 50)**2

hdd(52.2) = 15.31 - .868*(2.2)+.5*.038*(4.84)
cdd(52.2) = .27 + (1 - .868)*(2.2) + .5 * .038*(4.84)

Noting that 2.2 squared = 4.84


hdd(52.2) = 13.49, HDD= 92*hdd = 1241.


cdd(52.2) = .652 and CDD = 92*cdd = 60.

If the same mean temperatures were to occur in the fall (typically SON) the corresponding values would be: hdd= 13.52, HDD=1230, cdd=.708, and CDD=64, Note that there are 91 days in SON.
The degree day forecast distribution can be calculated by application of the above formula to the temperature distribution. Whenever the distribution of heating or cooling degree days is not normally distributed the expected value of the heating degree days should be computed to obtain the best estimate of the forecast heating or cooling degree days for the season (See below), although the 50 percentile value can be used as an approximation.

Degree Day Forecasts for Periods Longer than 3 Months:

Many users require an estimate of the heating and cooling degree days for periods of time greater than 3 months. The expected value for the total heating degree days spanning more than a single 3-month period is simply sum of the expected value of heating or cooling degree days for consecutive non-overlapping seasons. Computing the forecast distribution is a bit more complicated. Because the expected error about the FORECAST should be independent from one non-overlapping season to another (Any seasonal persistence is already accounted for by the forecasters), the variance of the total should be approximately equal to the sum of the variance of the individual seasons. If the shape of the distribution doesn't change much (it actually approaches a normal distribution, but not so rapidly for relatively small number of cases encountered here), then the a reasonable approximation to the percentile of the multi-seasonal total exceedence percentile (%) can be found by the following formula.

Variable Definition:
PT(n%) - The degree day value expected to be exceeded by n% of the time (solved for).
pt(xx) - The exceedence values for degree day at the xx percentage level. The Median is pt(50). The lower case label indicates distribution for an individual 3-month period within the period of interest.
m - The expected value of degree days for the individual 3-month seasons within the combined period.
M - The sum of the expected values (Means) of the individual non-overlapping seasons involved.

m = .035*pt(2) + .04*pt(5) + .075*pt(10) + .1*pt(20) + .1*pt(30) + .1*pt(40) + .1*pt(50) + .1*pt(60) + .1*pt(70) + .1*pt(80) + .075*pt(90) + .04*pt(95) + .035*pt(98)
M = m1 + m2+ ....+ mn (The sum of n non-overlapping seasons.)

formula1.gif (2998 bytes)
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The upper case symbols refer to the seasonal total, and lower case refers to the percentiles for individual seasons prior to summing. When individual months are non-skewed, the sum of the medians can be substituted for M. (Sum of pt(50)).
The degree day to temperature translation is non-linear, so the mean degree days cannot be found by applying the formula in the temperature-to-degree day files to the mean temperature.

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Page last modified: December 12, 2002
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