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Degree days: the different types
S e
r
TH1I332
no.
f38
DonaldW.
Boyd 5 . - - - -- .- - - . . - - - --Meteorologist seconded to the Division of
Building
Research,National Research ComciT of Canada
from the Atmospheric Environment Service
Department of F i s h e r i e s and Environment I
I
DEGREE DAYS: THE DIFFERENT
TYPES
!
Im
-1 by I Ottawa, January 1979 1.
PEGREE DAYS: THE DIFFERENT TYPES
by
Donald W . Boyd
Some energy requirements such a s the amount of fucl uscd f o r heating
and several n a t u r a l phenomena such as the growth of p l a n t s and tElc t h i c k n e s s of lake ice are correlated more or less c l o s e l y with t h e
accumulated a i r temperature below or above some s t a n d a r d or base temper:^- t u r c . When computed from daily mean temperatures, thcsc temperature differences a r e called degree days. There are two main c l a s s e s of d c g r r c days, differing in the method of calculation. T h i s Note will d e f i n e degree d a y s , distinguish between t h e two classes, and comment on a fcw exnmplcs from each c l a s s .
In g e n e r a l , a degree day is d e f i n e d as a measure of t h e departure
of t h e mean temperature f o r a day f r o m a g i v e n base temperature. TIE accumulation o f such departures o v e r a season o r up to any day can I,e uscd a s an indication of past temperature e f f e c t on some quantity.
Negative departures (or positive departures, if one is primarily c o n c c m c ~ l w i t h t h e negative ones) are treated in two d i f f e r e n t ways f o r different
purposes: t h e y may b e considered as zero, t h a t i s , contributing n o t h i n g
to t h e accumulated t o t a l , or t h e y may be considered as having a negative value w h i c h reduces t h e accumulated t o t a l . Heating, coaling and growing
degree-days belong t o the former class; freezing and thawing to t h e l a t t c r .
The fuel o r cncrgy required t o maintain a temperature of about 21°C
in a small building when outsidc a i r tcmpcraturc is below 1 8 " ~ i s rougl11y proportional to t h c d j fference between 1 8 ' ~ a n d t h c o u t s i d e t c m p c r a t u r c . The energy I-equirements also depend on o t h e r f a c t o r s including wind spccd, s o l a r r a d i a t i o n , and internal heat sources. There is no
convenient way of combining these effects, but f o r average c o ~ ~ d i t i o n s o f
wind, r a d i a t i o n , and internal sources the proportional ity w i t h tempcrnt 11re still h o l d s . Ileating d e g r e e - d a y s based on temperature alone a r c rhcrefclrc
u s e f u l when more complex methods of calculating fuel requirc~i~ents a r c n o t f e a s i h l e .
I f t i s the mean o u t s i d e a i r temperature f o r a particular day, t h c n
p r o v i d i n g t
is
less t h a n 1 8 . For mean air temperatures greater t h a n 1 8 , no energy is r e q u i r e d to keep t h e building s u f f i c i e n t l y w a r m and t h e r e - f o r e the heating degree-days a r e zero.Heating degree-days H
f o r
a few days, a month, o r a season are simply t h e sum of the d a i l y values for that periodH =
C
(18 - t] for a31 days when t < 1 8 , H = O for a l l days when t > 1 8 .In Figure 1 t h e 1977 d a i l y mean temperatures at O t t a w a International Airport have been plotted. The cross-hatched area represents f a i r l y
accurately the number of heating degree-days below 1 8 " ~ .
U n t i l recently, the published heating degree-days i n Canada w e r e
Fahrenheit degree-days beIow 65°F ( 1 ) . If the base temperature in C e l s i u s had been exactly equal to 6 S a F , then conversion of degree days would have been simply a m a t t e r o f multiplying b y 5 / 9 . The new base temperature, however, is 18°C er 6 4 . 4 O F , so that t h e accumulated d e g r e e
days are 0 . 6 Fahrenheit degree-days l e s s f o r each day t h a t the tempera- ture is below 64.4'F. This adjustment i s usually less t h a n 18 Fahrenheit degree-days per month, b u t
if
accuracyis
important a conversionprocedure f o r monthly values
has
been prepared b y Boyd (2).
Annual totals in Fahrenheit degree-days should b e reduced (by a v a l u e depending
on
t h e l e n g t h of t h e h e a t i n g season) before multiplyingby 5 J 9 to convert t o C e l s i u s degree-days. This reduction ranges from about 150 F degree-days f o r annual t o t a l s near 7500 t o about 215 F degree-days f o r annual t o t a l s of 1 2 S O 0 or over.
Normal ( i . e . 30-year average) Celsius degree-days below 18°C f o r
each month a r e available from t h e Atmospheric Environment S e r v i c e ( 3 1 .
C u r r e n t daily v a l u e s are published in t h e Monthly Meteorological
Summaries issued each month by over 50 weather s t a t i o n s
in
Canada.COOLING DEGREE-DAYS
J u s t as t h e energy required f o r h e a t i n g is roughly proportianal t o
t h e temperature d e p a r t u r e be low some base temperature, so t h e energy required f o r cooling is roughly proportional t o t h e temperature d e p a r t u r e above some b a s e . This required energy is also i n f l u e n c e d b y sun, wind, i n t e r n a l heat sources, and the humidity of t h e outside a i r . Dependence on h u m i d i t y (or, more correctly, on wet-bulb temperature) makes cooling degree days somewhat less reliable than heating degree-days, but t h e y are s t i 1 l c l o se enough f o r some app l i c a r i o n s
.
I f 1 8 O C is selected as the base temperature, t h e n the c o o l i n g degrcc-
C = C (t - 18) f o r all d a y s when t > 18,
C =
0' for a l l days when t < 18.Thc d a r k stippled a r e a in F i g u r e 1 represents f a i r l y accurately the number of cooling degree-days above 18°C.
Cooling degrcc-days for l o c a t i o n s in Canada are not readily a v a i l a h l c . Thcy can be computed, however, f r o m h e a t i n g degree-days, provided the b n s c temperature i s t h e same and the mean temperature f a r the period-conccrncd is known. The e q u a t i o n s above can h e rewritten f o r any p e r i o d of Na d a y s
ahovc and Nb d a y s helow 18°C
For Na days when t is e q u a l to or above 1 8 " ~ ,
For the r e m a i n i n g Nb d a y s when t i s below 1 6 ° C
Adding gives
C - H = Et - 18 [Na + Nb), C = I 1 + N
(t
-
l a ) ,r%~hcre
t
is the mean temperature for t h eN
d a y s . T h i s equation is cxnc t ,b u t any rounding-off error in
s
w i l l b e m u l t i p l i e d b y N.GROIVINC DEGREE-DAYS
The rate o f growth of p l a n t s is roughly proportional t o t11c dcpastul-c o f t h c a i r temperature above about 5"C, p r o v i d i n g o t h e r conditions arc sat i s f a c t o r y , Below 5°C there i s no apprec i a b l e grorlrth. Growing clegrcr- days are therefore d e f i n e d in t h e same way a s c o o l i n g degrcc-days, c x c c l ~ t
t h a t t h e base temperature is 5°C. In 1:igure I t h e l i g h t and dark stippled
areas together r e p r e s e n t f a i r l y accurately t h e number of growing d e g r e c -
days above 5 ' ~ . Normal [i. e
.
30-year average) C c l s i u s d e ~ r c c - d a y s ahovc 5°C f o r each month have been t a b u l a t e d 1 3 ) .Whcn t h e a i r tempcraturc is abavc 5°C f o r o n l y a p a r t o f t11e d a y , i t may he more approprintc to u s e degree hours or even somc more c o a p l c x
function o f temperature. 7Ilc r e s u l t s I l o u l d nevcr b c referrcrl to ns
dcgree days, Ilowcvcr, hccause, 1,y d e f j n i t io n , Jcgrec clsl)ls n rc b n s c d o n t I ~ c d a i l y mean temperature.
I:RI'I:ZIN(; AN11 TtIhWIMC; DECREE-DAYS
I k p t h of freezing o f t h e ground and t h i c k n e s s o f i c e 0 1 1 lakcs dcpcnc!
on many f a c t o r s , h u t t h e y can he cstimatcd r o u g h l y from t l ~ c dcgrcc rlays below and nhovc freezing. I n t h e s e cases, I-towcvcr, thc days w i t h inc;ul
temperature above the !lase temperature of O"C cannot h e i g n o r e d a s was done f o r h e a t i n g degree-days. On a day w i t h mean ternperatuse above 0°C
t h e r e w i l l be a tendency for some lake ice to melt
o r
ground to thaw.The temperature d e p a r t u r e s above freezing must t h e r e f o r e b e s u b t r a c t e d fmm the accumulation of temperatures below freezing. S i n c e t h e base
tcmpcraturc i s zero, t h e freezing degree-days are
for a l l days i n the period, whether t is p o s i t i v e ox negative.
T h e time required t o melt lake ice or thaw ground in thc s p r i n g i s
sornctimes estimated u s i n g thawing degree-days. As w i t h f r e e z i n g degsee-
d a y s , both positive and n e g a t i v e departures must b e accumulated and l ~ c n c c
t h e t h a w i n g degree-days are
f o r a3 1 days i n the p e r i o d .
T h e thawing i n d e x o r thawing degree-days f o r a whole thawing season
a r c represented f a i r l y accurately in Figure 1 b y tlae Arcs between tlac
g r a p h and t h e zero temperature line for the season whcn ternperaturc i s
gcncrally above z e r o , decreased h y the area below z e r o f o r sliort periods
s u c h a s t l ~ o s c in early April and mid-November, i n d i c a t e d by arrows, This
i s a poor method of representing t h e t h a w i n g index because it r e q u i r e s
t h c visualization of the d i f f e r e n c e of areas. A much b e t t e r method is
shown in IYigure 2, where degree days above and below z e r o laave been
accumulated day by day, s t a r t i n g w i t h 1000 degree days in 1976 at the
f i r s t of October, t o i l l u s e a t e both f r e e z i n g and t h a w i n g indices. The areas above and belaw O"C in Figure 1 are represented by v c r t i c a l
d i s t a n c e s in Figure 2.
?he freezing index for winter is defined as t h e number of cIegrce days (below and above freezing) between t h e h i g h e s t p o i n t i n t h e autumn
and t h e lowest point t h e following spring on the cumulative degrcc-day timc curve. Similarly, t h e t h a w i n g i r~dcx i s thc n u n ~ b c r of degree d a y s
from t h c l o w e s t p o i n t i n the s p r i n g to thc h i g h c s t po i n t t h e following autumn (Pigurc 2 ) . Because o n l y degrcc-day d i f f c r c n c c s a r c o f concern, thc zero p o i n t on the dcgree-day s c a l e is q u i t e arbitrary. Tt was starrcd at 1000 to avoid negative v s l u c s .
hriy s p r i n g or autumn month t h a t i n c l u d e s a scasonr;l inirlirnu~n or
rnaxim~m of t h e c u m u l a t i v e degree-days above freezing c u r v e will bc c a l l c ~ l
3 "chatlge-svcrrl month. In a1 I other months the Ccl s j 11s dcgrcc-days ahovc freezing a r e
w l ~ c r e
F
i s t h e monthly mean tcrnperaturc and cach t j s n d a i l y ncantemperature. These valucs a r e p o s i t i v e i n sumnicr a n d a r c c a l l e d thowi ng d c g ~ e e - d a y s . Days below f r e e z i n g will decrease t h e thawing degree-day t o t a l f o r the month, h u t t h e r e w i l l b e no f ~ e e z i n g degree-days. I n w i n t e r monrhs t h e v a l u e s w i l l be n e g a t i v e . Their a11r;olutc v a l u c s a r c
c a l I c d freezing degrce-days and the thawing degree-days are z e r o .
I n a change-over month b o t h fseezing and thawing d e g r e e - d a y s have
non-zero v a l u e s , one o c c u r r i n g o n l y before the changeover d a t e a n d t h c
o t h e r only a f t e r . I t can b e shown t h a t i f T is the thawing dcgrcc-days and T: t h e freezing d e g r e e - d a y s , t h e n
u h c r c 'I' and F a r e nevcr n c g a t j vc hut o n c of t h c n is zero i n cilch nmntl~
unless i t i s a chnngc-ovcr ~iionth ( 4 ) . hbnr.21 m o n t h l y frcrzing :rncl
thawing dcgrcc-days and annun1 t o t a l s for ovcr ROO weathcr stations hrwc
been computed from normal monthly mean t e m p e r a t u r e s 3s cxplaincd i n ( . I ) , and pub1 i s h e d b y t h e Atmospheric Environment Servicc (5)
.
C o ~ ~ v c r s i o n from Fahrenheit degrec-days to Celsius i s s i m p l y a m a t t e r of multiplying by S / Y , s i n c e the base temperatures are e x a c t l y equivalent.As i n d i c a t e d , Reference [ 3 ) i n c l u d e s t a l l u l a t i a n s o f the normal
degree days below 1 8 ' ~ and above
5"C,
calculated according t o the acceptcrlmethod f o r t h a t c l a s s of degree day. Unfortunately, it also includcs degrcc d a y s above and below 0°C calculated
in
the same w a y . T h i s meanst h a t s h o r t freezing p e r i o d s during t h e thawing season and s h o r t thawing
periods during the freezing s e a s o n a r e i g n o r e d i n s t e a d of d e c r e a s i n g t l l c
accumulated degree d a y s . The d e g r e e days above and helow 0 ° C in Rcfcrcncc
( 3 ) a r c t h e r e f o r e not t h e same as the f r e e z i n g and thawing degree-days u n d c r d i scussion.
' l l ~ e r e seems t o b c a good d e a l o f confusion a n d i n i s u t i d c r s t n n d i n g connected w i t h d e g r e e days, caused p a r t l y b y the d i f f ~ r c n t methods o f calcuIation f o r d i f f e r e n t p u r p o s e s , and p a r t l y l ~ y the difficulty o f canvcrting from F a h ~ e n h c i t to Celsius. T h i s r 2 i s c u s s i o n shoultl l e a d to 3
b e t t e r understanding o f the different k i n d s of d e g r e e d a y s and t l r c i r
rerationship. REFERENCES
1 , bleating dcgrcc-day normals below 65°F - nascd on t h c p c r i o d I ! ) J I - I P 1 , O .
C l imatology D i v i s i o n , Metcorological U r a n c l ~ , Toron t o (now Atmo sphcr i c linviror~inent S e r v i c e , Downsvicw)
,
CDS 15-64, O c t ~ h e r 1 9 6 4 .2 . Royd, I)onal d W . C o n v e r t i n g h e a t i n g dcgrce-days from llclow 65°F t o Rclow 1 8 " ~ . National Rescarch C o u n c i l of C a n a d a , I l i v i s i o n o f
3 . Aston, 0 . Dcgree Days 1 9 4 1 - 1 9 7 0 :
CDS # 7-77 A t l a n t i c Provinces, June 19 77
CUS HX1-77 Ontario, October 1977
CDS 1112-77 The North-YT and
NWT,
Deceniber 1977 C D S # 1 3 - 7 7 Quebcc, Dccember 1977CDS # 2-78 Manitoba, May 1978
CDS # 3-78 Saskatchewan, June 1978
CDS 4 - 7 8 A l b e r t a , August 1978 B . C . to b e p u b l i s h e d
Atmospheric Environment S e r v i c e , Downsview,
4 . Boyd, Ijonald 1V. Cornput i n g freezing and t h a w i n g ilcgrce- Jays from
m o n t l ~ l y temperatures. National Research Counci l of Can:!d;l, nivision of Building Research, NRCC 14791, J u l y 1975.
5. Royd, Donald IV. Normal f r e e z i n g and t h a w i n g degree-days f o r Canada
1931-1960. Atmospheric Environment S e r v i c e , Downsview, Canada, CLT 4 - 7 3 , 1973.
-30 J T M A M J J A S O N D F I G U R E 1 D b l L Y M E A N T E M P E R A T U R E S . S H A D E D A R E A S I L L U S T R A T E : - ' H E A T I N G D E G R E E D A Y S
