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Temperature to Degree Day File




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 (TtoDD) 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 19511997.

Contents:

Column 1:

City number

Column 2:

Half year to which data
apply. The climatological average relationship between degree days and 3mo 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 315:

Exact values at five degree increments.There are
five rows dedicated to each city and halfyear,

First row:

gives the 3month 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 3month 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 3month 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 ttodd 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 ttodd correspondence table.

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

hdd(t) =
hdd(t5) + dhdd(t5)* (tt5) + .5*d2hdd(t5) * (tt5)**2

cdd(t) =
cdd(t5) + (1.+ dhdd(t5))* (tt5) + .5*d2hdd(t5)* (tt5)**2


EXAMPLE:
The following segment is from the TtoDD 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, MarchAprilMay (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) * (52.250)**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
So:
hdd(52.2) = 13.49, HDD= 92*hdd = 1241.
and,
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 3month period is simply sum of the expected value of
heating or cooling degree days for consecutive nonoverlapping seasons. Computing the
forecast distribution is a bit more complicated. Because the expected error about the
FORECAST should be independent from one nonoverlapping 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 multiseasonal 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 3month period within the period of interest.

m

 The expected value of
degree days for the individual 3month seasons within the combined period.

M

 The sum of the
expected values (Means) of the individual nonoverlapping seasons involved.

Formula:

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 nonoverlapping seasons.)




Notes:
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
nonskewed, the sum of the medians can be substituted for M. (Sum of pt(50)).

The degree day to temperature
translation is nonlinear, so the mean degree days cannot be found by applying the formula
in the temperaturetodegree day files to the mean temperature.

