Determining snowpack accumulation at snow course sites in southwestern Montana using climatic
station data and meteorological parameters--an assessment
by W Bruce Tremper
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in
Earth Science
Montana State University
© Copyright by W Bruce Tremper (1984)
Abstract:
This study tests the feasibility of adequately estimating snowpack water equivalent at snow course sites
in southwest Montana using meteorological parameters along with precipitation and temperature data
from local climate stations in an inexpensive statistical model. The model was developed using a
sample period of 200 days. Meteorological and climate station parameters were entered as independent
variables in a statistical stepwise multiple regression equation. Daily snowfall at snow courses and
SNOTEL sites were used as dependent variables. The equations generated were then run with data
from a 17 year period to estimate monthly snow accumulation at nearby monthly snow course sites.
These estimated values were then compared to actual monthly totals to determine the success of the
model. Using this methodology, the results show that estimates of monthly snow accumulation
correlate with actual values with correlation coefficients of 0.90 and above for six of the twelve snow
course sites tested (highest, 0.98) and 0.84 and above for 11 of the 12 sites.
This technique could augment snow course measurements or, in some cases, replace snow courses.
This method can easily be used in other locations to. estimate mountain snowpack in a cost effective
manner as long as the area in question has representative records of daily mountain snowfall and
corresponding local climate station records. DETERMINING SNOWPACK ACCUMULATION AT SNOW COURSE SITES
IN SOUTHWESTERN MONTANA USING CLIMATIC STATION DATA
AND METEOROLOGICAL PARAMETERS—AN ASSESSMENT
by
W» Bruce Tremper
A t h e s i s submitted in p a r t i a l f u l f i l l m e n t
o f t h e r e q u i r e m e n t s f o r t h e d eg r ee
of
M as te r o f S c i e n c e
n,
E arth Science
\ X X: ' T .
MONTANA STATE UNIVERSITY
Bozeman, Montana
March 1984
MAIN
us.
N3%
ii
C o p -S
APPROVAL
o f a t h e s i s s u b m i t t e d by
W. Bruce Tremper
Th is t h e s i s has been r e a d by each member of t h e t h e s i s committee
and h a s b e e n f o u n d t o be s a t i s f a c t o r y r e g a r d i n g c o n t e n t , E n g l i s h
u s a g e , format c i t a t i o n s , b i b l i o g r a p h i c s t y l e , and c o n s i s t e n c y , and i s
r e a d y f o r s u b m is s io n t o t h e C o ll e g e o f G r ad ua te S t u d i e s .
^0 VUftvd ISkV
Date
C h a i r p e r s o n , G r ad ua te Committee
Approved f o r t h e Major Department
Date
Head, Major Department
Approved f o r t h e C o ll e g e f o r G r ad ua te S t u d i e s
Date
G ra d u a te Dean
iii
STATEMENT OF PERMISSION TO USE
In
p resenting
th is
th esis
in
p artial
fu lfillm en t
of
the
r e q u i r e m e n t s f o r a m a s t e r ’s d e g r e e a t M o n t a n a S t a t e U n i v e r s i t y ,
I
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s o u r c e i s made.
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D i r e c t o r o f L i b r a r i e s when, i n t h e o p i n i o n o f e i t h e r , t h e p r opo se d use
of the m a t e r i a l is for s c h o l a r l y purposes.
m aterial
in th i s
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Signature
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for fin a n c ia l
Any copyi ng o r use of t h e
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V
ACKNOWLEDGMENTS
I w i s h t o , t h a n k R o b e r t Yaw a n d e s p e c i a l l y P a u l Dawson ( s t u d y
a d v i s o r ) f o r t h e i r i n s p i r a t i o n , s u g g e s t i o n s and e n d l e s s hours spe nt in
c o n s u l t a t i o n w ith m e te o r o lo g i c a l problems.
S p e c i a l t h a n k s t o Georgia
Ziemba f o r h e r i n v a l u a b l e h e l p w i t h s t a t i s t i c a l and computer pro ble ms .
-_I w i s h t o
give
my d e e p e s t
thanks
to
Dr.
Stephan C u ste r ( t h e s i s
a d v i s o r ) f o r h is v e ry thorough e d i t i n g of the t e x t ,
inspiration.
Also,
g a v e many h e l p f u l
Dr. John Montagne and t h e
h i s d i r e c t i o n and
l a t e Dr. Donald Smith
s u g g e s t i o n s an d m o s t o f a l l ,
in sp iratio n .
My
a p p r e c i a t i o n t o Dr. Ro b er t Brown who p r o v i d e d a d d i t i o n a l computer time
and Bob Motch and C h r i s G r o f f f o r t h e i r ! v e r y v a l u a b l e computer a d v i c e
an d
services.
I
esp ecially
want
to
thank
P hil
Fam es,
S oil
C o n s e r v a t i o n S e r v i c e , Snow S u r v e y f o r h i s c o o p e r a t i o n and h e l p f u l
advice.
T h i s r e s e a r c h was s u p p o r t e d by a g r a n t f r o m t h e o f f i c e o f W a t e r
R e s e a r c h and T e c h n o lo g y ,
a u t h o r i z e d u n d e r t h e W a t e r R e s o u r c e an d
D e v e l o p m e n t A c t o f 1 97 8, P. I . 9 5 - 4 6 7 .
The g r a n t was a w a r d e d by t h e
M ontana W ater R e s o u r c e s R e s e a rc h C e n t e r .
w ithout
possible.
th e ir
fin an cial
support,
th is
I w ish to
t h a n k the m ;
stu d y w ould n o t have been
vi
TABLE OF CONTENTS
Page
LIST OF TABLES.............................................................. ............................. ..................
. LIST OF FIGURES............................................ .................................... ............ . . . . . .
■.^ i l i
ix
ABSTRACT...........................................
x
.FORWARD..............................................
I
The G e n e r a l P r o b le m ............ ........................................... ............................. ..
R e s e a r c h C o n t r i b u t i o n t o t h e P r o b l e m . . . . ......... ...............
I
3
1. INTRODUCTION..................... .....................................................................................
4
2. EXPERIMENTAL DESIGN......................
Ove rview ................................
S t a t i s t i c a l M eth od s................................................
Data Used.........................
Snow Course D a t a ............ ............................................................
C li m a t e S t a t i o n D a t a . . . . . . .............
M e t e o r o l o g i c D a t a ................................................
P a r a m e t e r s Used ............ .................................................................
M e t e o r o l o g i c P a r a m e t e r s .....................................................................
Thermal A d v e c t i o n ..........TT...........................................
H o r i z o n t a l Tem p er at u re and P r e s s u r e G r a d i e n t a t
Mandatory L e v e l s .........................................................
Rawinsonde Da ta From Mandatory L e v e l s ......................... ..
V o r t i c i t y Advect i o n . ....................................
. D i v e r g e n c e ................................
A tm o s p he ri c I n s t a b i l i t y ....................
G e n e r a l i z e d Dynamic and O r o g r a p h i c P a r a m e t e r s ............
850 mb Dew P o i n t S p r e a d . ..............................................................
P r e c i p i t a b l e W a t e r ..............................................................
Cl i m at e P a r a m e t e r s ..................
P r e c i p i t a t i o n a t Cli m at e S t a t i o n s ..........................................
24 -h ou r S u r f a c e Te m p er at u re Change........................................
A cc o u n ti n g f o r Snowmelt...............................................................................
< • CO (Ti
B a c k g r o u n d . ...................
Related R e s e a r c h ....
P u r p o se o f t h e Study
12
12
13
15
16
17
17
18
22
22
24
24
25
28 .
30
30
32
33
34
34
34
35
vii
TABLE OF CONTENTS— Continued
Page
3 . RESULTS........................................................................................................................
39
4 . DISCUSSION OF RESULTS........................................................................................
44
S uc ce s s of t h e S t u d y ............ ...................... ............................................. ..
I m p o r t a n t P a r a m e t e r s ..................................................
Cost A s s e s s m e n t ............ .................................................
44
45
48
SUMMARY AND CONCLUSIONS........ .....................................................................
50
REFERENCES CITED........... ................................. .................................................. ...........
53
APPENDIX.......................
56
Program L i s t i n g ..................................
57
t
v iii
LIST OF TABLES
Table
'
Page
I.
A L i s t o f Weather and Cli m at e P a r a m e t e r s
...................................
21
2.
A L i s t o f Snow Melt E q u a t i o n C o e f f i c i e n t s ......... ............................
38
3.
R e s u l t s o f C o r r e l a t i o n s Between Monthly Model Snow
Ac cu m ul at io n E s t i m a t e s and A c t u a l Monthly T o t a l s ............
40
R e s u l t s o f C o r r e l a t i o n s Between D a il y . Model S n o w f a ll
E s t i m a t e s and A c t u a l D a i l y S n o w f a l l Am ou nts «. . . . . . . . . . . . . . . .
41
L i s t o f Expenses f o r t h e S t u d y .................................................................
49
4.
5.
ix
LIST OF FIGURES
Figure
Page
1.
Map o f Stu dy A r e a .................................
6
2.
E l e v a t i o n s o f Cli m at e S t a t i o n s and SnowC o u r s e s ..........................
7
3.
Average Accumulated Snow Amount P l o t t e d by Month. . . . . . . . . . ' 1 11
- 4.
Map o f Rawinsonde S t a t i o n L o c a t i o n s . . . . . ........................................
19
5.
C a l c u l a t i o n o f Thermal A d v e c t i o n ..................................................
23
6.
C a l c u l a t i o n o f V o r t i c i t y ..................
27
7.
S h ear Component o f V o r t i c i t y ................................ ..................................
27
8.
C u r v a t u r e Component of V o r t i c i t y ..........................................................
28
9.
C a l c u l a t i o n o f D i v e r g e n c e .............................................
29
10.
P l o t o f Snowmelt Ve rs us T i m e . . . . . ...................
......................
36
11.
P l o t o f Snowmelt Versus T e m p e r a t u r e ...................................................
37
/
X
ABSTRACT
This study t e s t s the f e a s i b i l i t y of a d e q u a te ly e s tim a tin g
snowpack w a t e r e q u i v a l e n t a t . snow c o u r s e s i t e s i n so u th w es t Montana
using m e te o r o lo g ic a l param eters alo n g , w ith p r e c i p i t a t i o n and
t e m p e r a t u r e d a t a from l o c a l c l i m a t e s t a t i o n s i n an i n e x p e n s i v e
s t a t i s t i c a l model. The model was d e v e l o p e d u s i n g a samp le p e r i o d o f
200 days. M e t e o r o l o g i c a l and c l i m a t e s t a t i o n p a r a m e t e r s were e n t e r e d
as in d e p e n d e n t v a r i a b l e s i n a s t a t i s t i c a l s t e p w i s e m u l t i p l e r e g r e s s i o n
e q u a t i o n . D a i l y s n o w f a l l a t snow c o u r s e s and SNOTEL s i t e s were used as
dep en de nt v a r i a b l e s . The e q u a t i o n s g e n e r a t e d were t h e n r u n w i t h d a t a
from a 17 y e a r p e r i o d t o e s t i m a t e m o n t h l y snow a c c u m u l a t i o n a t n ea r b y
m o n t h l y snow c o u r s e s i t e s .
These e s t i m a t e d v a l u e s were t h e n compared
t o a c t u a l m o n t h l y t o t a l s t o d e t e r m i n e tihe s u c c e s s o f t h e model. Using
t h i s m e t h o d o l o g y , the, r e s u l t s show t h a t e s t i m a t e s o f m o n t h l y snow
a c c u m u la tio n c o r r e l a t e w ith a c t u a l v a lu e s w ith c o r r e l a t i o n
c o e f f i c i e n t s o f 0.90 and abov e f o r s i x o f t h e t w e l v e snow c o u r s e s i t e s
t e s t e d ( h i g h e s t , 0 . 9 8 ) a n d 0 .8 4 a n d a b o v e f o r 11 o f t h e 12 s i t e s .
Th is t e c h n i q u e c o u l d augment snow c o u r s e measurements o r , i n some
c a s e s , r e p l a c e snow c o u r s e s .
T h i s . m e t h o d can e a s i l y be used i n o t h e r
l o c a t i o n s to. e s t i m a t e mo un ta in .sn o w pa c k i n a c o s t e f f e c t i v e manner a s
long as th e a re a in q u e s tio n has r e p r e s e n t a t i v e r e c o r d s of d a i l y
m o u n t a in s n o w f a l l and c o r r e s p o n d i n g , l o c a l c l i m a t e s t a t i o n r e c o r d s .
I
FORWARD
The G e n e r a l P ro b le m
K n o w l e d g e o f t h e amo un t o f a c c u m u l a t e d snow ( s n o w p a c k ) i n t h e
m o u n t a in s i n f l u e n c e s o ur l i v e s i n many ways. The f r e s h w a t e r produced
from m e l t i n g
m ountain
s no w
is
a v alu ab le
resource
used
for
a g r i c u l t u r a l i r r i g a t i o n , m u n i c i p a l w a t e r s u p p l i e s and f o r w i l d l i f e and
fish habitat.
Data on d a i l y and s e a s o n a l a c c u m u l a t i o n o f s n o w f a l l as
w e l l as snowpack d e p t h s a r e us ed i n w i l d l i f e b i o l o g y , f o r e s t r y , w i n t e r
r e c r e a t i o n and a v a l a n c h e f o r e c a s t i n g .
s t r e a m f l o w a m o u n t s and t h e
tim ing
Also,
i n f o r m a t i o n on p r o j e c t e d
of the m elt
w ater
release
is
i m p o r t a n t i n f l o o d and d r o u g h t f o r e c a s t i n g , waterway d e s i g n and w a t e r
supply fo re c a s ts for i r r i g a t i o n .
E l l i o t (1977) e s t i m a t e s t h e mone tary
worth of a c c u ra te w ater supply f o r e c a s t s
for irrig a te d
agricultural
l a n d s o f t h e w e s t e r n U.S. t o be $22 m i l l i o n p e r y e a r . Snow i s a l s o a
g e o l o g i c m a t e r i a l . Knowledge o f snowpack a c c u m u l a t i o n amounts a r e
i m p o r t a n t t o g e o l o g i c d i s i p l i n e s ""such as geomorphology, g l a c i o l o g y and
h y d r o l o g y . I c e — m e t a m o r p h o s e d snow— a f f e c t s much o f t h e e a r t h ' s
s u r f a c e t h r o u g h geomorphic p r o c e s s e s s u c h a s p h y s i c a l w e a t h e r i n g o f
r o c k s , e r o s i o n from m e l t w a t e r and g l a c i a t i o n .
I n s h o r t , knowledge of
m ou nt ai n snowpack amount i s v e r y i m p o r t a n t i n p l a n n i n g and p r o t e c t i o n
o f l i f e and p r o p e r t y as w e l l as g e o l o g i c r e s e a r c h and a p p l i c a t i o n .
C u r r e n t l y , t h e S o i l C o n s e r v a t i o n S e r v i c e Snow S u r v e y h a s t h e
resp o n sib ility
of
m onitoring
the
m ountain
snowpack
amount
and
2
fo recastin g
runoff.
technicians
or
Th ey
remote
do
th is
telem etry
through
in stru m en ts
(U.S.D.A. S o i l C o n s e r v a t i o n S e r v i c e , . 197 0 ) .
disadvantages:
first,
d irect
sam pling
in sta lle d
by
o n -site
T h e s e m e t h o d s h a v e two
s i n c e snow i n t h e mo u nt ai n s r a r e l y e x i s t s
in a
u n i f o r m t h i c k n e s s , , m e a s u r i n g s n o w p a c k i n o n l y one l o c a t i o n o f t e n
m i s r e p r e s e n t s t h e b a s i n i n q u e s t i o n ( L e t t e n m a i e r , 1 97 8; G o o d i s o n ,
1981).
The s e c o n d d i s a d v a n t a g e
is
the cost
invo lv ed
due t o t h e
expense o f p e r s o n n e l , m e a s u r i n g equipment and t e l e m e t r y a p p a r a t u s .
I n r e c e n t y e a r s , tw o a l t e r n a t i v e m e th o d s of e s t i m a t i n g moun ta in
snowpack amount h a v e been d e v e l o p e d which a r e e i t h e r l e s s e x p e n s i v e o r
do n o t depend on p o i n t s o u r c e measurements.
The f i r s t method i n v o l v e s
u s i n g t e m p e r a t u r e and p r e c i p i t a t i o n measurements r o u t i n e l y
at
l o c a l , c o o p e r a t i v e c l i m a t e s t a t i o n s a f f i l i a t e d w ith the N ational
W eather S e r v i c e
an d e x t r a p o l a t i o n
of
that
snowpack amount i n t h e mo un ta in s (Tangborn,
and Rasmussen, 1977, 1976).
it
collected
suffers
data
1 980,
to
1977,
estim ate
the
and Tangborn
A l t h o u g h t h i s method i s v e r y ec o n o m ic a l,
from l a c k o f a c c u r a c y i n a r e a s such as Montana b ec a u se o f
t h e c o m p l e x i t y . o f t h e w e a t h e r and t e r r a i n and t h e s c a r c i t y o f c l i m a t e
statio n s
rep resen tativ e
of m ountain w eath e r.
The s e c o n d m e th o d
u t i l i z e s one. o f s e v e r a l computer m od el s which c o n s i d e r . t h e i n t e r a c t i o n
o f i m p o r t a n t m e t e o r o l o g i c a l v a r i a b l e s w i t h l o c a l and r e g i o n a l t e r r a i n
features
(orographic
p recip itatio n )
thereby
estim ating
m ountain
p r e c i p i t a t i o n ( R h e a , 1 9 7 8 ; C o l t o n , 1 9 7 6 ; Young, 1 9 7 4 ) . . T h i s m e th o d
has p r o v e n s u c c e s s f u l i n many mount aino us a r e a s , how eve r, i t i n v o l v e s
t h e expen se o f d i g i t i z i n g
l a r g e a r e a s o f t e r r a i n i n a f i n e mesh g r i d
( a s s m a l l a s 2.5 k i l o m e t e r s ) c o m p u t e r s o f t w a r e p u r c h a s e ,
com puter
3
r e n t a l o r d e s i g n o f a s i m i l a r l y s o p h i s t i c a t e d computer program.
t h e s e m o d e ls o f t e n f a i l
in estim ating p r e c i p i t a t i o n
Also,
from some sto rm
t y p e s e s p e c i a l l y i n complex t e r r a i n (Armstrong and W i l l i a m s , 1981).
R e s e a r c h C o n t r i b u t i o n t o t h e P ro b le m
The o b j e c t i v e o f t h i s s t u d y was t o t e s t t h e f e a s i b i l i t y o f u s i n g
p r e c i p i t a t i o n and t e m p e r a t u r e d a t a a t l o c a l c l i m a t e s t a t i o n s as w e l l
as
a sim plified
set of m e teo ro lo g ical
param eters
to
adequetely
e s t i m a t e m o n t h l y s n o w f a l l w a t e r e q u i v a l e n t t o t a l s a t snow c o u r s e s i t e s
i n s o u t h w e s t e r n Montana i n an i n e x p e n s i v e manner.
' technique u t i l i z e s
S pecifically,
this
t e m p e r a t u r e and p r e c i p i t a t i o n d a t a f r o m l o c a l
c l i m a t e s t a t i o n s as w e l l as a s i m p l i f i e d s e t of d e r i v e d m e t e o r o l o g i c a l
param eters
as
input
to
an
inexpensive
statistic al
e s t i m a t e s mo un ta in snowpack amount a t snow c o u r s e s i t e s .
model
which
Th is method
c o s ts l e s s because e x i s t i n g agencies r o u t i n e l y p ro v id e c lim a te s t a t i o n
and m e t e o r o l o g i c a l d a t a .
Because o f t h e s i m p l i c i t y o f t h e p r o c e d u r e a
u s e r c a n e a s i l y a d a p t i t t o an a r e a o f i n t e r e s t w i t h o u t p r o h i b i t i v e
ti m e and expense.
4
CHAPTER I
INTRODUCTION
Background
P recip itatio n
in th e m ountains
originates
f r o m two g e n e r a l
m e t e o r o l o g i c p r o c e s s e s , dynamic arid o r o g r a p h i c (B err y, 1981).
Dynamic
p r o c e s s e s i n c l u d e r e g i o n a l - s c a l e a t m o s p h e r i c m o ti o ns such as f r o n t s ,
low
pressure
system s
and
atm ospheric
in sta b ility .
■ O rographic
p r e c i p i t a t i o n , on t h e o t h e r hand, o c c u r s as s a t u r a t e d a i r r i s e s ,
cools
and th u s p r e c i p i t a t e s in r e s p o n s e to c r o s s i n g a to p o g r a p h i c b a r r i e r
such as a m o u n ta in ra n g e .
In o th e r words,
d y n a m ic p r o c e s s e s
are
g o v e r n e d - by f o r c e s c o n t a i n e d w i t h i n t h e at mosphere w h i l e o r o g r a p h i c
p r o c e s s e s o c c u r due t o t h e i n t e r a c t i o n b e t w e e n t o p o g r a p h y and t h e
atm osphere.
W hile
both
dynam ic
and o ro g ra p h ic p ro c e s s e s
are
i m p o r t a n t , between two and - one hu ndred t i m e s more p r e c i p i t a t i o n i n t h e
m ountains f a l l s
1981).
from o r o g r a p h i c s o u r c e s t h a n dynamic o nes (B e rry ,
Because of- t h e im po rta nc e o f o r o g r a p h i c p r e c i p i t a t i o n
m ountains,
the
amo un t
of
lo cal
relief
is
the
dominant
in the
factor
c o n t r o l l i n g t h e amount o f p r e c i p i t a t i o n t h a t f a l l s on t h e a r e a i n
question.
Since
most
orographic
p recip itatio n
falls
w ithin
15
k i l o m e t e r s o f a to p o g r a p h i c b a r r i e r ( B e r r y , 1981), l o c a l r e l i e f i s
d e f i n e d h e r e a s t h e amount o f t o p o g r a p h i c r i s e w i t h i n a r a d i u s o f
a b o u t 15 k i l o m e t e r s f r o m t h e a r e a o f i n t e r e s t . T o p o g r a p h i c f e a t u r e s
i
i n f l u e n c e m o u n t a i n snow amo un t d i s t r i b u t i o n i n a v a r i e t y o f w ay s .
5
G e n e r a l l y , t h e snowpack d e p t h i n c r e a s e s w i t h e l e v a t i o n , b e c a u s e o f two
factors.
F irst,
o r o g r a p h i c p r e c i p i t a t i o n o c c u r s more o f t e n
e l e v a t i o n s because a i r
rising
in response to crossing
at higher
a topographic
b a r r i e r > c o o l s by a d i a b a t i c e x p a n s i o n and t h u s has a g r e a t e r chance o f
being
satu rated ,
elevations,
and
second,
because
l e s s m e ltin g occurs (Berry,
of
cooler
1981).
air
at
higher
Slope a sp e c t is a l s o
i m p o r t a n t i n th e d i s t r i b u t i o n of p r e c i p i t a t i o n b ec a u se s o l a r r a d i a t i o n
m e l t s m or e snow on s o u t h - f a c i n g s l o p e s t h a n n o r t h - f a c i n g o n e s , and
more i m p o r t a n t ,
th e p r e v a i l i n g winds in th e stu d y a r e a scour th e
w i n d w a r d w e s t s i d e s o f m o u n t a i n s a n d r i d g e s and d e p o s i t t h e snow on
t h e downwind s i d e s .
M c P a r t l a n d and o t h e r s ,
(1971), A l f o r d (1979) and
T a b l e r ( 1 9 7 5 ) p o i n t o u t t h e i m p o r t a n c e o f r e d i s t r i b u t i o n o f snow by
wind i n Montana and Wyoming.
For r e a s o n s o u t l i n e d a b o v e, t h e l o c a t i o n
of those s t a t i o n w ith re s p e c t to l o c a l r e l i e f ,
is
critically
a s p e c t and top o g rap h y
i m p o r t a n t when e s t i m a t i n g m o un ta in p r e c i p i t a t i o n based
on c l i m a t e s t a t i o n s o r snow c o u r s e s .
S pecifically,
in t h i s study.
F i g u r e I shows t h e l o c a t i o n of t h e
snow c o u r s e s and c l i m a t e s t a t i o n s u s e d i n t h i s s t u d y i n r e l a t i o n t o
the
local
t o p og r ap h y,
F i g u r e 2 "shows t h e d i s t r i b u t i o n by e l e v a t i o n .
N otice th a t c lim a te s ta t io n s are lo c a te d at
e a s i l y a c c e s sib le areas.
low er e l e v a t i o n s ,
in
However, snow c o u r s e s u s u a l l y a r e l o c a t e d a t
higher e le v a tio n s
i n a r e a s more r e p r e s e n t a t i v e o f m o u n ta in snowpack
amount.
study
In
the
area,
several
clim ate
statio n s
exist
at
e l e v a t i o n s e q u i v a l e n t t o t h e lower e l e v a t i o n snow c o u r s e s and i n a r e a s
w ith s im i la r lo c a l r e l i e f .
T h e r e f o r e , one w ould e x p e c t t h a t th e s e
c l i m a t e s t a t i o n s wo uld c o r r e l a t e w e l l w i t h t h e amount and t i m i n g o f
6
SNOW COURSES
BRIDGER BOWL
MAYNARD CREEK
NEW WORLD
LICK CREEK
HOOD MEADOWS
ARCH FALLS
SHOWER FALLS
BEAR BASIN
LITTLE PARK
TAYLOR PE AKS
CARROT BASIN
T WENTY- ONE MILE
M
N
O
P
O
R
S
T
U
V
W
X
CLI MATE S T ATI ONS
BOZEMAN 1 2 N E
BELGRADE AP
BOZEMAN MSU
LI VINGSTON AP
LI VI NGSTON I 2 S
NORRIS MADISON PH
A
B
C
D
E
F
ENNIS
VIRGINIA CITY
GALLATIN GATEWAY 9 S
GALLATIN GATEWAY 2 6 S
WE S T YELLOWSTONE
HEBGEN DAM
G
H
I
J
K
L
STUDY AREA
-JP
0
5
10
15
20
25
30
Ml
KM
ELEVATION:
ABOVE 1 0 ,0 0 0 '
9 ,0 0 0 '-1 0 ,0 0 0 '
8 ,0 0 0 -9 ,0 0 0 '
6,000 '-8 ,0 0 0 ' I
I
CLIMATE STATIONS
DAILY SNOW COURSES
MONTHLY SNOW COURSES
Figure I .
Map o f t h e s t u d y a r e a showing top o g rap h y and l o c a t i o n s of
t h e c l i m a t e s t a t i o n s and snow c o u r s e s .
7
ELEVATION
SNOW COURSES
CLIMATE STATIONS
Carrot Basin
9 ,0 0 0 '
Taylor Peaks •
Bear Basin
Shower Falls
- - 8 ,0 0 0 '
Little Park
Arch Falls
Bridger Bowl
Twenty-one Mile
Lick Creek
New World
Hood Meadow
z.ooo'-r
West Yellowstone
Hebgen Dam
Maynard Creek
G a lla tin G a t e w a y 26 S
- 1-
6 ,0 0 0 '
Bozeman 12NE
Virginia City
Gallatin Gateway 9S
5,000'--
Ennis
M.S.U.
Norris
Livingston 12S
Livingston AP
Belgrade AP
4 , 0 0 0 ' -L
F i g u r e 2.
The d i s t r i b u t i o n o f snow c o u r s e s and c l i m a t e s t a t i o n s by
elevation.
8
p r e c i p i t a t i o n a t snow c o u r s e s i t e s l o c a t e d i n a r e a s o f s i m i l a r a s p e c t ,
e l e v a t i o n and l o c a l r e l i e f .
R e la te d Research
Th ere a r e two b a s i c ap p r o a c h e s u s ed t o d e t e r m i n e snow amounts i n
the
m ountains.
The f i r s t ,
is
a statistical/em p irical
approach
r e l a t i n g m ou nt ai n snow amounts t o a c c u m u l a t e d p r e c i p i t a t i o n amounts a t
l o c a l c l i m a t e s t a t i o n s and snow c o u r s e s l o c a t e d w i t h i n t h e mo u n ta in s.
For exam ple ,
t h e S o i l C o n s e r v a t i o n S e r v i c e Snow S u r v e y u s e s moun ta in
snow c o u r s e
readings
as
in d icato rs
(U.S.D.A. S o i l C o n s e r v a t i o n S e r v i c e ,
o f m ountain
1970).
s n o w p a c k amount
Tangborn (1977;
1980) and
Tangborn and Rasmussen (1976; 1977) u se d p r e c i p i t a t i o n and t e m p e r a t u r e
d a t a from l o c a l r e p r e s e n t a t i v e c l i m a t e s t a t i o n s t o e s t i m a t e mount ain
snowpack amount.
Th is method works s u c c e s s f u l l y on t h e w es t c o a s t of
t h e U.S. where w e a t h e r p a t t e r n s a r e more p r e d i c t a b l e and l e s s complex.
H o w e v e r , t h e a c c u r a c y o f t h i s a p p r o a c h d i m i n i s h e s when a p p l i e d t o
c o n t i n e n t a l c l i m a t e s c h a r a c t e r i z e d by complex and f i c k l e w e a t h e r such
as found i n t h e mo un ta in s o f s o u th w e s t Montana.
Fo r exam ple , Tangborn
( 1 9 8 0 ) f o u n d t h a t e s t i m a t e s o f s e a s o n a l a c c u m u l a t e d sn o w p a ck u s i n g
t h i s m e t h o d a c c o u n t e d f o r o n l y 53 p e r c e n t o f t h e v a r i a n c e b e t w e e n
s e a s o n a l r u n o f f amounts o r i g i n a t i n g from snowmelt i n t h e So uth Fork o f
t h e F l a t h e a d r i v e r o f w e s t e r n Montana.
A s e c o n d a p p r o a c h when d e t e r m i n i n g m o u n t a i n snow a m o u n ts i s
computer m o d e l i n g o f o r o g r a p h i c p r e c i p i t a t i o n .
Rhea
(1 9 7 8 ) ,
C o lto n
(1 9 7 6 )
and
Young
R e s e a r c h e r s such as
(1 9 7 4 )
have
developed
s o p h i s t i c a t e d computer m o d e ls which e s t i m a t e m o u n ta in p r e c i p i t a t i o n a t
9
points
on
elevations.
a
fine
mesh
grid
(as
sm all
as
2.5 km) o f
d ig itized
For exam ple , Rhea's model i s b e i n g used s u c c e s s f u l l y by
t h e C o lo r a d o A v a l a n c h e Warning C e n t e r t o f o r e c a s t d a i l y s n o w f a l l f o r
th e m ountains of w e s te r n Colorado.
The.m odel
accounts
for
such
f a c t o r s as i n t e r c e p t i o n o f m o i s t u r e by u p s t r e a m t o p o g r a p h i c b a r r i e r s ,
s u b l i m a t i o n of. s n o w f l a k e s as . t h e y f a l l
snowflake t r a j e c t o r i e s
through u n s a tu r a te d
air,
from t h e time o f c r y s t a l l i z a t i o n t o im p ac ti n g
t h e g r o u n d , r e t a r d a t i o n o r e n h a n c e m e n t o f v e r t i c a l m o t i o n due t o
atm ospheric s t a b i l i t y
st o r m p r o c e s s e s .
and a c c o u n t i n g f o r p r e c i p i t a t i o n from dynamic
Because o f t h e s o p h i s t i c a t i o n o f t h e s e m o d e l s ,
th e y
have the d is a d v a n ta g e of the expense in v o lv e d in d i g i t i z i n g la rg e
a r e a s of t e r r a i n , p u r c h a s in g th e com puter s o f tw a r e , or d e s ig n i n g a
sim ilarly
s o p h i s t i c a t e d c o m p u t e r program.
A l s o , t h e s e m od el s o f t e n
f a i l i n e s t i m a t i n g p r e c i p i t a t i o n from some t y p e s o f s to rm s e s p e c i a l l y '
i n complex t e r r a i n (Armstrong and W i l l i a m s ,
1 981).
Purp ose o f t h e Study
This
study a tte m p ts
t o c o m b in e t h e s e two. a p p r o a c h e s
into
an
i n e x p e n s i v e m e th o d ol o g y i n o r d e r t o e s t i m a t e mo u n ta in snowpack amount
a t snow c o u r s e s i t e s .
i.e.
The f i r s t a p p r o a c h i s t h a t u s e d by T a n g b o r n ,
using p r e c i p i t a t i o n
and t e m p e r a t u r e
at
e s t i m a t e m o u n t a i n p r e c i p i t a t i o n an d snowmelt.
clim ate
stations
to
Because t h e N a t i o n a l
Weather S e r v i c e r o u t i n e l y c o l l e c t s and p u b l i s h e s c l i m a t e s t a t i o n d a t a ,
t h i s method c o s t s
little.
The second ap pr oac h i n v o l v e s m o d e li n g of
b o t h o r o g r a p h i c and dynamic p r e c i p i t a t i o n , however, t h i s s t u d y d i f f e r s
i n t h a t i t u s e s a s i m p l i f i e d s e t o f w e a t h e r p a r a m e t e r s combined i n an
10
i n e x p e n s i v e s t a t i s t i c a l model.
using
Th is s t u d y e x p l o r e s t h e f e a s i b i l i t y of
w e a t h e r p a r a m e t e r s a s w e l l a s p r e c i p i t a t i o n and t e m p e r a t u r e
)
d a t a from l o c a l r e p r e s e n t a t i v e c l i m a t e s t a t i o n s t o a d e q u a t l y e s t i m a t e
m o n t h l y snow w a t e r e q u i v a l e n t t o t a l s
a t mo u n ta in snow c o u r s e s i n an
i n e x p e n s i v e manner.
T h i s s t u d y a d d r e s s e s o n l y t h e snow a c c u m u l a t i o n p e r i o d o f w i n t e r
and d o es n o t
Therefore,
attem pt
this
A p r i l —the usual
to model
runoff
from m e l t i n g
snowpack.
s t u d y c o v e r s t h e p e r i o d o f time from O cto be r th ro ug h
snow a c c u m u l a t i o n p e r i o d
3).
! /
in the
s t u d y a r e a ( F ig u r e
inches
of
water
In s n o w p a c k
11
mo n t h
Figure 3.
P l o t o f 1 9 6 3 - 1 9 7 7 a v e r a g e sn o wp ac k w a t e r e q u i v a l e n t
a c c u m u l a t i o n t h r o u g h t h e s e a s o n f o r Shower F a l l s snow
c o u r s e — a t y p i c a l snow c o u r s e i n th e s t u d y a r e a (USDA S o i l
Conservation S e rv ic e , 1983).
12
CHAPTER 2
EXPERIMENTAL DESIGN
Overview
T h i s s t u d y u s e s 54 w e a t h e r a n d c l i m a t e p a r a m e t e r s t o p r e d i c t
d aily
a nd m o n t h l y a c c u m u l a t i o n o f
s o u t h w e s t Montana.
accom plished.
th at
This
F irst,
two k i n d s
of
snow a t
section b r ie f l y
snow c o u r s e
in
s u m m a r i z e s how t h i s was
i t i s i m p o r t a n t t h a t t h e r e a d e r k e e p i n mind
snow c o u r s e s
exist.
The f i r s t
s n o w f a l l v a l u e s . The second p r o v i d e s m o n t h l y t o t a l s
snow.
sites
provides
daily
of accum ulated
D a i l y s n o w f a l l must f i r s t be p r e d i c t e d u s i n g d a i l y m e t e o r o l o g i c
a n d c l i m a t e s t a t i o n p a r a m e t e r s . C o m p u t e r p r o g r a m s w e r e w r i t t e n an d
e x e c u t e d t o c a l c u l a t e m e t e o r o l o g i c an d c l i m a t e s t a t i o n p a r a m e t e r s
(Appendix).
Then,
in o rd er to c r e a te p r e d i c t i v e eq u atio n s,
a sample
o f 2 0 0 . days o f d a i l y m e t e o r o l o g i c and c l i m a t e s t a t i o n p a r a m e t e r s were
e n t e r e d as in d e p e n d e n t v a r i a b l e s i n a s t e p w i s e m u l t i p l e r e g r e s s i o n
c o m p u t e r p r o g r a m w i t h d a i l y s n o w f a l l a t snow c o u r s e s i t e s a s t h e
dep en de nt v a r i a b l e .
snow fall best
The program d e t e r m i n e s which p a r a m e t e r s p r e d i c t
and b u i l d s them i n t o an e q u a t i o n which p r e d i c t s d a i l y
snowfall.
The 200 days o f d a i l y d a t a were t a k e n from th e months o f F e b r u a r y
from 1 970 t h r o u g h 1 976.
The d a t a span s e v e n y e a r s i n o r d e r t o es c a p e
m i s r e p r e s e n t a t i o n o f an odd y e a r ; t h e m o n t h o f F e b r u a r y was c h o s e n
13
b e c a u s e i t s t r a d d l e s t h e . u s u a l snow a c c u m u l a t i o n p e r i o d o f w i n t e r
( O ct ob er t h r o u g h A p r i l ) and i t e x p e r i e n c e s b o t h c o l d w i n t e r storms and
warmer s p r i n g - l i k e o n e s.
Since
the
p u rp o se.o f
th is
study
is
to
e s t i m a t e m o n t h l y snow a c c u m u l a t i o n , t o t e s t t h e model, d a i l y e s t i m a t e s
w e r e summed t o p r o v i d e m o n t h l y t o t a l s
o f snow a c c u m u l a t i o n f o r a
p e r i o d o f 17 y e a r s .
In
order
to
estim ate
the
s n o w p a c k a t m o n t h l y snow c o u r s e s ,
e q u a t i o n s f r o m o ne o f t h e d a i l y snow c o u r s e s w e r e a p p l i e d .
This is
n e c e s s a r y b e c a u s e c o r r e l a t i o n s b e t w e e n m o n t h l y snow a c c u m u l a t i o n
t o t a l s and d a i l y c l i m a t e s t a t i o n and m e t e o r o l o g i c a l p a r a m e t e r s i s an
"ap p les
and
accom plished.
oranges"
c o m p a r i s i o n •an d c a n n o t be r e a l i s t i c a l l y
The m o n t h l y e s t i m a t e s w e r e g e n e r a t e d a s
T a k i n g t h e m o n t h l y snow c o u r s e .
L ittle
follow s.
P a r k , . a s an exam ple,
the
m o n t h l y snow a c c u m u l a t i o n t o t a l s w e r e c o m p a r e d t o t h e m o n t h l y sums
f r o m e a c h o f t h e s i x d a i l y e q u a t i o n s u s i n g 17 y e a r s o f d a t a t o s e e
w hich c o r r e l a t e d b e s t .
Then, t h e a p p r o p r i a t e d a i l y
e q u a t i o n was
a d j u s t e d f o r t h e d i f f e r e n c e i n a v e r a g e s n o w f a l l amount between t h e two
locations.
As w i t h t h e d a i l y snow c o u r s e s , t h e s e e s t i m a t e s were t h e n
compared to th e a c t u a l m o n th ly t o t a l s to provide f i n a l c o r r e l a t i o n
coefficients.
' S t a t i s t i c a l Methods
I n a n a l y z i n g t h e p a r a m e t e r s , t h e r e were two o b j e c t i v e s :
first,
to
f i n d w h i c h p a r a m e t e r s c o r r e l a t e w e l l w i t h s n o w f a l l an d s e c o n d , t o
deriv e
e q u a tio n s w hich
p aram eters.
p red ict
S tepw ise m u l t i p l e
sn o w fall
am ounts
u sing
these
r e g r e s s i o n was c h o s e n a s
the
/
14
appropriate
statistic al
technique
because
it
accom plishes
o b j e c t i v e s and i s a l s o i n e x p e n s i v e a n d s t r a i g h t f o r w a r d .
m u ltip le
both
S tepw ise
r e g r e s s i o n was a c c o m p l i s h e d u s i n g t h e SPSS s t a t i s t i c a l
com puter package (N ie, 1975)— a commonly-used com puter s t a t i s t i c a l
p a c k a g e a v a i l a b l e on d i s c s t o r a g e a t t h e M o n ta n a S t a t e U n i v e r s i t y
computer.
For r e a d e r s n o t f a m i l i a r w i t h s t e p w i s e m u l t i p l e r e g r e s s i o n ,
a b r i e f summary i s i n c l u d e d below.
For f u r t h e r i n f o r m a t i o n , r e f e r t o
D r a p e r and Smith (1981).
'■
,„ .
Stepwise m u l t i p l e r e g r e s s io n i s a s t a t i s t i c a l
develop
an e q u a t i o n w h ich b e s t p r e d i c t s
the
t e c h n i q u e used to
dependent
( s n o w f a l l ) u s i n g two o r more in d e p e n d e n t v a r i a b l e s
variab le,
( m e t e o r o l o g i c and
c l i m a t e s t a t i o n p a r a m e t e r s ) . The program w i l l g e n e r a t e an e q u a t i o n of
t h e f o l l o w i n g form:
n
~i = I
where:
Y
n
i
= t h e dep en d en t v a r i a b l e ( s n o w f a l l )
= t h e t o t a l number o f in d e p e n d e n t v a r i a b l e s
= th e number a s s i g n e d to one of th e n in d e p e n d e n t
variables
= v a l u e s of t h e in d e p e n d e n t v a r i a b l e s ( w e a th e r
and c l i m a t e p a r a m e t e r s )
a^ = the non-standardized c o e f f i c ie n t , i.e. the
number o f u n i t s e x p e c t e d change i n Y w i t h a u n i t
change i n x
C = a c o n s t a n t te rm
15
When g e n e r a t i n g t h e e q u a t i o n , t h e p r o g r a m w i l l f i r s t , e n t e r t h e
most s t a t i s t i c a l l y
s i g n i f i c a n t parameter i d e n t i f i e d using the F - t e s t ,
i .e . th e p a ra m e te r added f i r s t to t h e p r e d i c t i v e e q u a t i o n has the
least
c h a n c e o f h a v i n g no c o r r e l a t i o n w i t h
snow fall.
T hen ,
the
p r o g r a m w i l l e n t e r t h e s e c o n d m o s t s i g n i f i c a n t p a r a m e t e r and so on
u n t i l t h e p a r a m e t e r s a d d e d no l o n g e r m e a n i n g f u l l y add t o t h e t o t a l
accuracy of the re g r e s s io n equation.
p ro g ra m !t e s t s
relatio n sh ip
Because t h e m u l t i p l e r e g r e s s i o n
only fo r a li n e a r f i t
such as
as opposed to a c u r v i l i n e a r
an e x p o n e n t i a l p a t t e r n ,
e a c h p a r a m e t e r was
a n a ly z e d to see i f i t e s ti m a t e s s n o w f a ll in a l i n e a r r e l a t i o n s h i p .
Th is was done by p l o t t i n g each p a r a m e t e r a g a i n s t s n o w f a l l and v i s u a l l y
examining t h e r e s u l t i n g p l o t p a t t e r n .
None o f t h e p a r a m e t e r s app ea re d
to ex h ib it c u r v il in e a r p a tte rn s.
;
;
■ Data Used
. Th is s t u d y u s e s t h r e e k i n d s o f d a t a — snow c o u r s e , c l i m a t e s t a t i o n
a nd w e a t h e r d a t a .
Snow c o u r s e d a t a r e p r e s e n t s t h e m e a s u r e m e n t s o f
snow w a t e r e q u i v a l e n t a t t w e l v e snow c o u r s e s i t e s
m ountains of the study are a .
lo c a te d in the
C lim ate d a ta in c l u d e s measurements of
p r e c i p i t a t i o n and te m pe ra tu re , t a k e n d a i l y a t t w e l v e c l i m a t e s t a t i o n s
lo cated
in
easily
acc essib le
M e t e o r o l o g i c d a t a comes from
from t h e t h r e e
w ith in
the
study
r aw ins ond e ( w ea th e r b a l l o o n )
c l o s e s t raw insonde s t a t i o n s .
Lander Wyoming, and Bo ise Idaho.
contains,
areas
soundings
G reat F a l l s
For e ac h k i n d o f d a t a ,
area.
this
M o n ta n a ,
section
I ) a d i s c u s s i o n and j u s t i f i c a t i o n o f t h e c h o i c e o f t h e t y p e
o f d a t a used and 2) a d e t a i l e d d e s c r i p t i o n o f t h e d a t a .
16
Snow Course Data
This
s t u d y u s e s snow c o u r s e d a t a a s an i n d i c a t o r o f m o u n t a i n
s n o w p a c k am o un t f o r t h e f o l l o w i n g r e a s o n s :
Snow c o u r s e d a t a : I ) i s
t h e o n l y e x i s t i n g d a t a b a s e f o r m o u n ta in snowpack mea sur em ent s, 2) i s
a s t a n d a r d and commonly u se d measure o f mo u n ta in snowpack amount, 3)
s p a n s a l o n g p e r i o d o f r e c o r d an d h a s go od q u a l i t y c o n t r o l and 4) i s
r o u t i n e l y c o l l e c t e d and p u b l i s h e d b y t h e S o i l C o n s e r v a t i o n S e r v i c e
!
Snow S u r v e y making i t an i n e x p e n s i v e s o u r c e o f d a t a f o r t h i s s tu d y .
In th e stu d y a re a ,
snow c o u r s e s a r e s a m p l e d e i t h e r b y t h e U.S.
S o i l C o n s e r v a t i o n S e r v i c e Snow S u r v ey o r by t h e U.S. F o r e s t S e r v i c e .
For m o n t h l y snow c o u r s e s ,
t e c h n i c i a n s v i s i t t h e s i t e as c l o s e t o t h e
f i r s t o f t h e m o n t h a s p o s s i b l e and u s e a Mt. R o s e snow s a m p l i n g t u b e
t o t a k e a c o r e o f t h e snowpack; t h e w e i g h t o f t h e c o r e i n d i c a t e s t h e
w a t e r c o n t e n t o f t h e snow.
For d a i l y snow c o u r s e s ,
a w e ig h i n g s c a l e
(snow p i l l o w ) b e n e a t h t h e snowpack c o n t i n u o u s l y weighs t h e snow above
a nd r e c o r d s
the
i n f o r m a t i o n w ith an o n - s i t e
changed once a month.
For remote s i t e s ,
strip
c h a r t w hich i s
an o n - s i t e t e l e m e t r y sy stem
r a d i o s t h e i n f o r m a t i o n to a r e c e i v i n g s t a t i o n where t h e i n f o r m a t i o n i s
r e c o r d e d (SNOTEL s i t e s ;
U.S.D.A. S o i l C o n s e r v a t i o n S e r v i c e ,
1970).
The Show S u r v e y s t a t e o f f i c e i n Bozeman Montana p r o v i d e d b o t h d a i l y
and m o n t h l y snow c o u r s e d a t a .
M o nt h ly d a t a was p r o v i d e d on computer
c a r d s and s t u d e n t s were h i r e d t o keypunch t h e d a i l y d a t a from c o p i e s
o f Snow S u r v e y r e c o r d s .
17
C l i m a t e S t a t i o n Data
C l i m a t e s t a t i o n s a r e l o c a t e d t h r o u g h o u t t h e w o r l d an d p r o v i d e
d a i l y measurements o f p r e c i p i t a t i o n an d t e m p e r a t u r e .
States,
In th e U nited
t h e s t a t i o n s a r e a f f i l i a t e d w i t h t h e N a t i o n a l Weathef S e r v i c e ,
a r e l o c a t e d i n a c c e s s i b l e a r e a s and samp led d a i l y , o f t e n by v o l u n t e e r
caretakers.
Al I a v a i l a b l e
stations
in the v i c i n i t y of the G a l l a t i n
d r a i n a g e were used which c o u l d p r o v i d e r e l i a b l e
and c o n t i n u o u s d a t a
for
A to tal
t h e p e r i o d o f t i m e c o v e r e d by t h e
s t a t i o n s were used.
study.
of tw elv e
M e a s u r e m e n t s made a t t h e s e c l i m a t e
stations
i n c l u d e : maximum and minimum t e m p e r a t u r e , 24-hour p r e c i p i t a t i o n and
24 -h ou r snow d ep t h .
Measurements a r e t a k e n around 6:00 PM d a i l y .
M e t e o r o l o g i c Data
W e a t h e r f o r e c a s t s t h r o u g h o u t t h e w o r l d a r e b a s e d p r i m a r i l y on
.. : I d a t a c o l l e c t e d from r a w in s o n d e s ( w e a th e r b a l l o o n s ) .
The ra w in s o n d es
a r e r e l e a s e d t w i c e d a i l y a t m i d n i g h t a n d no on G r e e n w i c h mean t i m e
( 5 : 0 0 AM a nd
5 :0 0
PM m o u n t a i n
standard
tim e)
at
predeterm ined
l o c a t i o n s th ro u g h o u t th e w o rld c re a tin g a r e l a t i v e l y evenly-spaced
netw ork of atm o sp h eric
soundings.
From t h i s
data,
W e a t h e r S e r v i c e c o m p u t e r g e n e r a t e s w e a t h e r maps.
exist
the N atio n al
T h u s , two s o u r c e s
f o r w e a t h e r d a t a — rawin so nd e d a t a and w e a th e r maps.
w e a t h e r p a r a m e t e r s used i n t h i s
Sin ce a l l
■:
s t u d y can be c a l c u l a t e d u s i n g e i t h e r
d a t a s o u r c e and a l s o , b o t h s o u r c e s a r e a v a i l a b l e f o r s u f f i c i e n t l y lo n g
peroids
of
Rawinsonde
tim e,
data
a d e c i s i o n had
was
chosen
for
to
the
be made a s t o w h i c h t o u s e .
follow ing
reasons:
F irst,
ra w in s o n d e d a t a i s n o t s u b j e c t t o i n t e r p r e t a t i o n by N a t i o n a l Weather
S e r v i c e co m pu ter s;
by u s i n g r aw ins ond e d a t a ,
w e a t h e r p a r a m e t e r s can
18
be c a l c u l a t e d u s i n g a c o n s i s t e n t m e t h o d t h r o u g h o u t
c o v e r e d by t h i s
s tu d y .
Second,
the
17 y e a r s
c a l c u l a t i n g w e a t h e r p a r a m e t e r s from
w e a t h e r maps i s a t e d i o u s and time consuming p r o c e s s w h i l e rawinsonde
d a t a can be used as i n p u t t o computer programs which r a p i d l y c a l c u l a t e
w eather p aram eters.
tap es
making
A l s o , r a w i n s o n d e d a t a i s a v a i l a b l e on d i g i t a l
it. easily
accessible
and s a v e s
the
expense of key
punching.
The N a t i o n a l O c e a n i c and A t m o s p h e r i c A d m i n i s t r a t i o n , N a t i o n a l
C l i m a t i c C e n t e r i n A s h e v i l l e , No rth C a r o l i n a p r o v i d e d b o t h w ea th e r and
c l i m a t e d a t a on d i g i t a l t a p e s .
. W e a th e r d a t a i n c l u d e s t w i c e - d a i l y
u p p e r : a i r rawin so nd e so u nd in g s from t h e t h r e e c l o s e s t s t a t i o n s —Great
F alls
M ontana,
L a n d e r Wyoming a n d B o i s e
Idaho ( F ig u re
soun din g p r o v i d e s i n f o r m a t i o n from ma n d at or y l e v e l s (850,
m illibars
(mb)) . and s i g n i f i c a n t , l e v e l s
(pressure h eight),
wind v e l o c i t y .
Eac h
700 and 500
( l e v e l s where t h e atmosphere'
e x i b i t s a s i g n i f i c a n t change i n c o n d i t i o n s ) .
a t each of th e s e l e v e l s
4).
A tm os phe ri c measurements
in c lu d e : the h e ig h t of the p re s s u re l e v e l
tem perature,
r e l a t i v e h u m i d i t y , wind d i r e c t i o n and
The d a t a span l e v e l s from 850 mb t o 500 mb; t h e 850 mb
l e v e l c o rresp o n d s w ith th e e l e v a t i o n of th e G a l a t i n V a lle y (about
5,000
feet).
. The u p p e r b o u n d a r y was
ch o sen b e c a u s e most w i n t e r
w e a t h e r o c c u r s b e l o w t h e a v e r a g e 500 mb h e i g h t o f a b o u t 1 8 , 0 0 0 f e e t
(H je r m s ta d ,
1970; Rhea,
1978).
P a r a m e t e r s Used
R e c a l l t h a t m o u n t a in w i n t e r t i m e p r e c i p i t a t i o n comes p r i m a r i l y
from two p r o c e s s e s , dynamic and o r o g r a p h i c .
Dynamic p r o c e s s e s i n c l u d e
19
Great Falls
study area
Boise
Lander #
F i g u r e 4.
Map s h o w i n g t h e l o c a t i o n o f t h e s t u d y a r e a an d t h e t h r e e
c l o s e s t raw insonde s t a t i o n s used in the stu d y to p ro v id e
m eteorological data.
20
f o u r d i f f e r e n t m e c h a n i s m s : F i r s t , snow c a n be c a u s e d by r e l a t i v e l y
warmer o r c o l d e r a i r m oving h o r i z o n t a l l y
advection).
in to the area (therm al
Second, v e r t i c a l m o t i o n s a s s o c i a t e d w i t h l o w - p r e s s u r e
system s cause a i r to r i s e ,
approach of upper
le v el
c o o l and t h u s p r e c i p i t a t e .
air
T hird, the
spinning counterclo ck w ise ( p o s itiv e
v o r t i c i t y a d v e c t i o n ) c a u s e s a i r t o r i s e and p r e c i p i t a t e .
F ourth,
atm ospheric i n s t a b i l i t y causes c o n v e c t i v e p r e c i p i t a t i o n .
Including
orographic
differen t
precip itatio n ,
there
are
a to tal
m e t e o r o l o g i c a l p r o c e s s e s which ca u s e s n o w f a l l .
m eteorological
processes,
p a r a m e te r s w hich a c c o u n t
for
of
fiv e
Thi s s t u d y c a l c u l a t e s
each of th e s e
fiv e
p l u s some g e n e r a l i z e d p a r a m e t e r s w h i c h a r e u s e d i n t h e
c a l c u l a t i o n of o th e r parameters.
T able I p resen ts
a l i s t o f p a r a m e t e r s f o l l o w e d by a s e c t i o n
c o n t a i n i n g a b r i e f l a y d e s c r i p t i o n o f e a c h p a r a m e t e r and d e t a i l s of
the
calcu latio n
m eteo ro lo cical
of each p a ra m e te r.
sig n ifican ce
introductory te x ts
of
each
Readers u n f a m i l i a r w ith th e
param eter
such as Byers (1974).
L
are
refered
to
21
Table I .
A l i s t o f w e a t h e r and c l i m a t e p a r a m e t e r s o r g a n i z e d ac c o r d in g
t o t h e p r o c e s s t o which each c o n t r i b u t e s .
M eteorologic param eters:
1) F r o n t a l a c t i v i t y
-therm al advection
- h o r i z o n t a l te m p e r a t u r e g r a d i e n t a t mandatory
levels
2) Low p r e s s u r e syst ems :
- p r e s s u r e h e i g h t o f mand ato ry l e v e l s
3) V o r t i c i t y a d v e c t i o n :
- v o r t i c i t y a d v e c tio n parameter
-500 mb d i v e r g e n c e
4) A tm o s p he ri c i n s t a b i l i t y :
-K i n d e x
. 5) O ro g r ap h ic p r o c e s s e s :
- v a r io u s orographic parameters ( l i s t provided in
G e n e r a l i z e d O r o g r a p h i c P a r a m e t e r s s e c t i o n s , p.
32)
.
G e n e r a l i z e d dynamic and o r o g r a p h i c p a r a m e t e r s :
. - c o m b i n a t i o n s o f o r o g r a p h i c and dynam ic
p a r a m e t e r s w i t h a t m o s p h e r i c m o i s t u r e and
s t a b i l i t y f a c t o r s added.
G eneralized param eters:
-850 mb dew p o i n t s p r e a d
- p r e c i p i t a b l e water
-m an d a to ry l e v e l t e m p e r a t u r e , r e l a t i v e h u m i d it y
and wind v e l o c i t y
-m andatory l e v e l h o r i z o n t a l p r e s s u r e h e ig h t
gradient
Climate param eters:
- p r e c ip ita tio n at clim ate statio n s
- 2 4 - h o u r s u r f a c e t e m p e r a t u r e change
- sn ow m elt p a r a m e t e r s
22
M e teo ro lo g ica l Parameters
ThermaI A d v e c ti o n .
Thermal
a d v e c t i o n means
the h o r iz o n t a l
m o ve m en t o f w a r m e r o r c o l d e r a i r i n t o t h e s t u d y a r e a (warm o r c o l d
fronts).
wind
T h i s p a r a m e t e r u s e s an upwind r aw ins ond e soun din g t o f i n d i f
d irectio n
turns
clockw ise
or
counterclockw ise w ith
i n d i c a t i n g warm o r c o l d a d v e c t i o n , r e s p e c t i v e l y .
height
Thermal a d v e c t i o n i s
c a l c u l a t e d u s i n g wind v e c t o r s and a hodo gr aph as d es cr ib e d , i n Byers
(1974).
The method i s summarized below.
C o n s i d e r a l a y e r o f a i r w i t h v e c t o r CA, t h e w i n d v e c t o r f o r t h e .
l o w e r s u r f a c e and v e c t o r OB, t h e w i n d v e c t o r f o r t h e u p p e r s u r f a c e
( t h e 850 mb a nd 500 mb s u r f a c e s
r e s p e c t i v e l y ; F i g u r e 5).
lo w e r and u p p e r s u r f a c e s
I n t h i s c a s e , t h e w in d t u r n s c l o c k w i s e w i t h .
h e i g h t i n d i c a t i n g warm a d v e c t i o n .
t h e wind which i s
are the
V e c t o r AB i s t h e s h e a r component of.
c a l c u l a t e d on t h e computer u s i n g t h e law o f s i n e s .
L i n e OC i s t h e c r o s s - i s o t h e r m c o m p o n e n t ( i s o t h e r m s w i l l a l w a y s be
p a r a l l e l t o AB).
Thermal a d v e c t i o n can be c a l c u l a t e d u s i n g a f o r m u l a
d e r i v e d from S a u c i e r ( 1 9 7 2 ) .
, Thermal a d v e c t i o n
=
V f T t C
, __________
Hg
Deg./Time
.
.
Where: V = ma g ni tu d e of t h e s h e a r v e c t o r ( F ig u r e 5; v e c t o r AB)
f = c o r i o l i s a c c e l e r a t i o n f o r t h e s tu d y a r e a = 10.3 x IO*"'1
p e r second
T = average temperature of the la y er in degrees K e lv in
t = ti m e i n t e r v a l between r aw ins ond e so un d in g s (12 h o u r s )
C = c r o s s i s o t h e r m component ( F i g u r e 5; v e c t o r OC)
H = t h i c k n e s s of th e l a y e r c o n s id e r e d (from p r e s s u r e
heights)
g = a c c e le ra tio n of g ra v ity
)
.
23
O
F i g u r e 5.
A d i a g r a m s h o w i n g t h e m e th o d o f c a l c u l a t i o n o f t h e r m a l
a d v e c t i o n ( se e t e x t f o r d i s c u s s i o n ) .
24
H o r i z o n t a l t e m p e r a t u r e and p r e s s u r e h e i g h t g r a d i e n t a t ma ndatory
le v els.
front
The h o r i z o n t a l t e m p e r a t u r e g r a d i e n t i s an i n d i c a t o r o f a
i n t h e a r e a b o u n d e d by t h e t h r e e r a w i n w s o n d e s t a t i o n s .
The
h o r i z o n t a l p r e s s u r e h e i g h t g r a d i e n t i s an i n d i c a t o r o f wind v e l o c i t y .
I n t h e f r ee , at mo sp her e ( g e n e r a l l y 700 mb o r h i g h e r i n t h i s r e g i o n ) t h e
b a la n c e between h o r i z o n t a l
p r e s s u r e d i f f e r e n c e and th e
c o r i b l is
a c c e l e r a t i o n c r e a t e s g e o s t r o p i c w in d s which flow counter clockwise
I
around a lo w -p re s s u re c e n te r .
tow ard
low
pressure
because
At t h e e a r t h ' s s u r f a c e , w i n d s b l o w
frictio n al
forces
ov er po w er t h e e f f e c t s o f t h e C o r i o l i s x a c c e l e r a t i o n .
w ith
the
ground
These p a r a m e t e r s
a r e c a l c u l a t e d s i m p l y b y t a k i n g t h e maximum d i f f e r e n c e b e t w e e n t h e
t h r e e r aw ins on de s t a t i o n r e a d i n g s .
tem perature
gradient
A param eter fo r both h o r i z o n t a l
and h o r i z o n t a l
pressure height
gradient
is
g e n e r a t e d for* each o f t h e t h r e e m an dat or y l e v e l s o f 850, ' 700, and 500
mb.
Rawinsonde d a t a from ma ndatory l e v e l s ;
These p a r a m e t e r s a r e t h e
raw d a t a c o l l e c t e d d u r i n g a rawin so nd e sounding which i n c l u d e p r e s s u r e
height,
tem perature,
r e l a t i v e humidity,
and wind v e l o c i t y .
Pressure
h e i g h t i s t h e h e i g h t o f one o f the ~m an da to ry p r e s s u r e ■l e v e l s g e n e r a l l y
i n d i c a t i n g f a i r o r f o u l w e a t h e r w i t h h i g h o r low v a l u e s r e s p e c t i v e l y .
The o t h e r p a r a m e t e r s
n e e d no e x p l a n a t i o n .
These p a r a m e te r s
are
c a l c u l a t e d u s i n g t h e v a l u e s from each o f t h e t h r e e raw in so n d e s t a t i o n s
an d u s i n g
a. w e i g h t e d
average
based
ra w in s o n d e s t a t i o n and t h e s t u d y a r e a .
(Davis,
1973):
on t h e
distance
between th e
The f o l l o w i n g e q u a t i o n i s used
25
Vl . V2
V3
__ + _ _ + _ _
Dl
Average
D2
D3
=
I
I
I
__ + __ + __
Dl
Where:
Vl
V2
V3
Dl
D2
D3
=
=
=
=
=
=
the
the
the
the
the
the
D2
D3
v a l u e from t h e G r e a t F a l l s s t a t i o n
v a l u e from t h e Lander s t a t i o n
v a l u e from t h e Bo ise s t a t i o n
d i s t a n c e from Bozeman t o G r e a t f a l l s (230 km)
d i s t a n c e from Bozeman t o Lander (350 km)
d i s t a n c e from Bozeman t o Boise (445 km)
V o r t i c i t v a d v e c t i o n . V o r t i c i t y is a measure of th e r o t a t i o n of the
h o r i z o n t a l p la n e of the a i r .
The i n c r e a s e o f v o r t i c i t y ( p o s i t i v e
v o r t i c i t y a d v e c tio n ) im p lie s v e r t i c a l atm o sp h eric m otions.
natural
coordinates,
the fo llo w in g
U si n g
equation d e sc rib e s v o r t i c i t y
( B y e r s , I 9 74 ) .
dv
V
v o r t i c i t y = __; + __ + C
dn
Where:
r
dv = c h a n g e i n h o r i z o n t a l d i s t a n c e o v e r d i s t a n c e ' 'dn
( F i g u r e 6)
dn = d i s t a n c e o v e r which v e l o c i t y change i s measured
V = h o riz o n ta l v e l o c i t y of a i r at a sp e c ifie d point
r = ra d iu s of c u r v a tu r e of the a i r stream a t the poin t
s p e c i f i e d by V
C = c o n s t a n t f o r t h e c o r i o l i s a c c e l e r a t i o n @ 45 d eg r ee s
l a t i t u d e o f 10.3 x IO- p e r second
V o r t i c i t y comes f r o m t h r e e c o m p o n e n t s : f i r s t , f r o m t h e s h e a r i n t h e
a i r p r o d u c i n g a te rm d e s c r i b i n g t h e change i n v e l o c i t y o f t h e a i r o v e r
26
a s p e c i f i e d h o r i z o n t a l d i s t a n c e (dv / dn) ( F i g u r e 7 ) ;
seco nd ,
from t h e
c u r v a t u r e o f t h e a i r s t r e a m y i e l d i n g t h e t e r m V / r ; ( F i g u r e 8) t h i r d ,
f r o m t h e i n h e r e n t c u r v a t u r e o f t h e a i r s t r e a m due t o t h e r o t a t i o n o f
the e a rth ( c o r i o l i s a c c e le ra tio n ).
I f t h e wind blows from t h e w e s t,
v o r t i c i t y i s c a l c u l a t e d in the
f o l l o w i n g m a n n e r . F i g u r e 8 shows t h e r e l a t i v e p o s i t i o n o f t h e t h r e e
raw in so nd e s t a t i o n s w i t h winds r e p r e s e n t e d as v e c t o r s .
Thus:
i
v
+ v
I
2
V = _________
2
and
dv = V - v 1
I
The r a d i u s o f c u r v a t u r e o f t h e a i r s t r e a m i s c a l c u l a t e d n o t i n g t h a t :
.r =
I
______
a
Notice t h a t i f . V is g r e a t e r than
(counterclockw ise r o ta tio n ).
o n l y when t h e
airstream
v o r t i c i t y advection,
(1 2 h o u r s
before)
, t h e f i r s t te rm i s p o s i t i v e
The t e r m r i s d e f i n e d t o be p o s i t i v e
curves
counterclockw ise.
To c a l c u l a t e
t h e v o r t i c i t y v a l u e from t h e p r e v i o u s
is
subtracted
from th e v o r t i c i t y
sounding
v a l u e of the
p r e s e n t soun din g y i e l d i n g t h e change i n v o r t i c i t y o v e r t i m e ( v o r t i c i t y
advection).
,
27
F i g u r e 6.
Shows t h e method of c a l c u l a t i n g
See t e x t f o r d i s c u s s i o n .
Vi
T
v orticity
study.
*
dv
dn
I _________ Va
F i g u r e 7.
for th is
The s h e a r component o f v o r t i c i t y .
dn
*
28
V
F i g u r e 8.
The c u r v a t u r e component o f v o r t i c i t y .
D ivergence.
div erg in g
D ivergence r e f e r s
of the
air
at
upper
c o n v e c t i o n c a u s e d by e i t h e r
t o t h e h o r i z o n t a l s p r e a d i n g and
lev els
in d icatin g
a
large
scale
low p r e s s u r e o r v o r t i c i t y a d v e c t i o n .
D iv e r g e n c e i s c a l c u l a t e d u s i n g t h e 500 mb wind v e c t o r s f o r th e t h r e e
raw in so n d e s t a t i o n s .
The p o i n t s of t h e wind v e c t o r s d e f i n e a t r i a n g l e
( F i g u r e 9) and d i v e r g e n c e ,
then,
i s th e change of th e a r e a of th e
t r i a n g l e between each rawin so nde sounding as i n t h e e q u a t i o n ( S a u c i e r ,
19 72 ).
29
Boise
F i g u r e 9.
La n d e r
The method o f c a l c u l a t i o n o f t h e p a r a m e te r d i v e r g e n c e ( s e e
te x t for discussion).
30
I
AA
D ive rg en c e = __; __ _
A
Where:
At
A = the area of the t r i a n g l e
t = time i n t e r v a l o v e r which a r e a change i s measured
A tm os phe ri c i n s t a b i l i t y .
The at m o sp h er e n a t u r a l l y becomes c o l d e r
w i t h h e i g h t due t o a d i a b a t i c e x p a n s i o n .
colder
than
one w o u l d
expect
due
When u p p e r l e v e l
to
adiab atic
a ir is
expansion,
the
a t m o s p h e r e i s u n s t a b l e b e c a u s e warm a i r r i s i n g f r o m l o w e r l e v e l s
becomes bu oy an t i n t h e c o l d e r up p er l a y e r s and forms c o n v e c t i v e c e l l s .
Precipitation
solely
from a t m o s p h e r i c
i n s t a b i l i t y , is
rare
in w inter
months b u t becomes more i m p o r t a n t w i t h t h e appro ac h o f s p r i n g .
atm ospheric
orographic
in sta b ility
processes.
in sta b ility
precipitation,
not
o n ly
enhances p r e c i p i t a t i o n
Therefore,
as
th is
study
an in d e p e n d e n t
b u t more i m p o r t a n t ,
it
is
Also,
f r o m d y n a m i c and
tests
atm ospheric
in d icato r
of w in te r
combined w i t h o t h e r dynamic
a nd o r o g r a p h i c p a r a m e t e r s t o make th e m more a c c u r a t e i n d i c a t o r s o f
p recip itatio n .
T he K i n d e x
is
a com m only u s e d
in d icato r
of
atmospheric i n s t a b i l i t y :
K i n d e x = 850 mb t e m p e r a t u r e - 500 mb t e m p e r a t u r e + 850 mb dew
p o i n t - 700 mb dew p o i n t s p r e a d .
Genera I iz ed
dynamic
and
orographic
param eters.
This
study
a t t e m p t s to keep c a l c u l a t i o n s i m p l e so t h a t t h e model r em a in s s i m p l e
an d i n e x p e n s i v e .
An e x a m p l e i s t h e d e v e l o p m e n t o f t h e o r o g r a p h i c
p r e c i p i t a t i o n parameters d e s c r i b e d in t h i s
section.
Wind d i r e c t i o n
31
affects
the
snowpack amounts and d i s t r i b u t i o n b e c a u s e t h e a n g l e a t which
wind
strik es
v ertical
a to p o g rap h ic
v elo city ,
p recip itatio n .
thus
b arrier
affectin g
affects
the
the
atm ospheric
of
oro g rap h ic
rate
M ost o r o g r a p h i c m o d e l s a c c o u n t f o r t h e i n t e r a c t i o n .
b e tw ee n wind d i r e c t i o n
an d t o p o g r a p h y by d i g i t i z i n g
topographic
e l e v a t i o n s and m o d e l i n g t h e v e r t i c a l v e l o c i t y o f t h e a i r as i t c r o s s e s
a to p o g ra p h ic b a r r i e r . This study, however,
does n o t c o n s i d e r th e
i n t e r a c t i o n b etw e e n wind d i r e c t i o n and to p o g r a p h y b e c a u s e o f t h e
expense
of
sophisticated
fu tu re
d ig itizin g
terrain
computer model.
stu d ies
may h a v e
an d
developing
If this
g reater
or
purchasing
a
study proves s u c c e s s f u l , then
success
by d e v e l o p i n g
more
s o p h i s t i c a t e d parameters.
The am oun t o f p r e c i p i t a t i o n o c c u r r i n g d u e b o t h t o d y n a m i c , a n d .
o r o g r a p h i c p r o c e s s e s i s t h e sum of t h r e e components:
vertical
liftin g
The f i r s t i s t h e
o f t h e a i r produced from t h e dynamic o r o r o g r a p h i c
mechanism i n v o l v e d
orographic, l i f t i n g .
such as d i v e r g e n c e ,
therm al ad v e c tio n an d /o r
S e c o n d , i s t h e am ou n t o f w a t e r a v a i l a b l e f o r
p r e c i p i t a t i o n ( p r e c i p ita b I e w ater).
T h i r d , v e r t i c a l m o t i o n c a n be
e i t h e r enhanced o r r e t a r d e d by t h e a t m o s p h e r i c s t a b i l i t y .
t h i s , t h e v a r i o u s d y n a m i c an d o r o g r a p h i c
liftin g
Because, of
mechanisms a r e
combined w i t h p r e c i p i t a b l e w a t e r a n d / o r a t m o s p h e r i c s t a b i l i t y
i n d e x ) t o make a t h e o r e t i c a l l y more c o n s i s t e n t p a r a m e t e r .
d y n a m i c a nd o r o g r a p h i c p r o c e s s e s ,
one
of
the
liftin g
For both
f o u r p a r a m e t e r s a r e c r e a t e d which
r e p r e s e n t v a r i o u s s i m p l e co m b in a ti o n s o f p r e c i p i t a b l e w a t e r ,
and
(K
mechanisms.
In
th is
way ,
four
K in d e x
sim ple
32
. .p ar am et er s were c r e a t e d which g e n e r a l l y i n d i c a t e p r e c i p i t a t i o n f r o m
dynamic p r o c e s s e s .
Dynamic
Dynamic
Dynamic
Dynamic
I
2
3
4
=
=
=
=
Four dynamic p a r a m e t e r s a r e d e f i n e d as f o l l o w s :
co ld a d v e c tio n x p r e c i p i t a b l e water
K index x p r e c i p i t a b l e w ater
divergence x p r e c i p i t a b l e water
v o r t i c i t y a d v e c t i o n x p r e c i p i t a b l e w a t e r x K in d e x
Four o r o g r a p h i c p a r a m e t e r s were d e r i v e d i n a s i m i l a r manner.
The
amount o f o r o g r a p h i c p r e c i p i t a t i o n o c c u r r i n g depends on t h e amount of
- p r e c i p i t a b l e w ater,
am oun t o f v e r t i c a l
the th ic k n e s s of the s a tu r a te d
liftin g
of th e a i r (B erry 1981).
l a y e r and t h e
The l i f t i n g
mechanism o c c u r s when h o r i z o n t a l l y moving a i r r i s e s o v e r a t o p o g r a p h i c
b a r r i e r such as a m o u n tain ra n g e .
T h e r e f o r e , t h e 700 mb h o r i z o n t a l
wind v e l o c i t y (ab out 10,000 f e e t ) i s u se d as an i n d i c a t o r o f v e r t i c a l
a ir velocity.
The 850 mb ( ab o u t 5,000 f e e t ) dew p o i n t s p r e a d ( d e f i n e d
b e l o w ) i s u s e d a s an - i n d i c a t o r o f t h e e l e v a t i o n a t w h i c h s a t u r a t i o n
occurs
as
the
parcel
of
air
p a r a m e t e r s , t h e K in d ex i s added
them more a c c u r a t e .
spread,
is
l i f t e d . As w i t h
the
dynam ic
t o some o f t h e s e p a r a m e t e r s t o make
Four s i m p l e c o m b i n a t i o n s o f t h e 850 mb dew p o i n t
p r e c i p i t a b l e water,
K in d e x and t h e 700 mb wind v e l o c i t y a r e
c r e a t e d as f o l l o w s :
O r o g r a p h ic
O r o g r a p h ic
O r o g r a p h ic
Orographic
I
2
3
4
=
=
=
=
700 mb
700 mb
700 mb
700 mb
mb dew
wind x 1/8 5 0 mb dew
wind x p r e c i p i t a b l e
wind x p r e c i p i t a b l e
wind x p r e c i p i t a b l e
p o in t spread
850 mb dew p o i n t s p r e a d .
p o in t spread
water
w a t e r x K in d e x
w a t e r x K i n d e x x 1/850
The d i f f e r e n c e between t h e t e m p e r a t u r e
a n d t h e dew p o i n t i s t h e dew p o i n t s p r e a d , i n d i c a t i n g t h e d e g r e e o f
33
s a tu r a t io n of the a i r .
For example, a dew p o i n t s p r e a d o f 0 means 100
p e r c e n t h u m i d it y .
P re c ip ita b le w ater.
P r e c i p i t a b I e w a t e r i s d e f i n e d t o be t h e
amount o f w a t e r a v a i l a b l e f o r p r e c i p i t a t i o n .
The f o l l o w i n g e q u a t i o n s
a r e us ed t o c a l c u l a t e p r e c i p i t a b l e w a t e r ( S a u c i e r , 1972):
n
-I
W=
r (-
P )
g
i=l ■
Where:
W
g
P
r
i
= p r e c i p i t a b l e water in centim eters of depth
= a c c e l e r a t i o n of g r a v i t y
= p re s s u re of the su rface
= mix ing r a t i o ( d e f i n e d below)
= t h e nu m b e r r e p r e s e n t i n g t h e a t m o s p h e r i c s u r f a c e
being considered
n
= t h e l a r g e s t number o f s u r f a c e s c o n s i d e r e d
P^ = t h e change i n p r e s s u r e between P^ and P ^ - I
Mixing r a t i o i s a d i m e n s i o n l e s s number d e f i n e d t o be t h e r a t i o o f
w a t e r v a p o r t o t h e mass o f t h e d ry a i r w i t h w hich t h e w a t e r i s mixed.
The commonly-used e q u a t i o n i s :
r
=
0 .6 2 2 e
_______
(By ers , 1974)
P - e
Where:
r = mi x in g r a t i o
P = atmospheric p re s s u re in m i l l i b a r s
e = v a p o r p r e s s u r e i n m i l l i b a r s ( d e f i n e d bel ow )
)
34
To o b t a i n v a p o r p r e s s u r e from t h e s a t u r a t i o n v a p o r p r e s s u r e :
e = e
(RH / 100)
( B y e r s , 1 974)
s
Where:
e g = s a t u r a t i o n v a p o r p r e s s u r e ( d e f i n e d bel ow)
RH = r e l a t i v e h u m i d i t y i n p e r c e n t
The s a t u r a t i o n v a p o r p r e s s u r e i s c a l c u l a t e d :
aT/ [T + b]
6
Where:
= 6.11 x 10
(Saucier,
197 2)
T = temperature in degrees centigrade
a and b a r e c o n s t a n t s where:
o v e r w a t e r ( a b o v e 0 d e g . C) a = 7 . 5 ; b = 237.3
degrees K e lv in
o v e r i c e ( b e l o w 0 d e g . C)
a = 9.5 ; b = 265.5
degrees K elv in
Climate Parameters
Precipitation
at
cIim ate s ta tio n s .
P r e c ip ita tio n is
24-hour t o t a l of p r e c i p i t a t i o n a t c lim a te s t a t i o n s .
simply the
The c l i m a t e
me asurements a r e t a k e n d a i l y a t ar ou nd 6:00 p.m.
2 4 - h ou r s u r f a c e t e m p e r a t u r e change.
in d ic a te the passage of a cold fro n t.
Th is p a r a m e t e r a t t e m p t s t o
I t c o n s is ts of the n e g a tiv e
( g e t t i n g c o l d e r ) c h a n g e i n minimum t e m p e r a t u r e v a l u e i n a 2 4 - h o u r
period
at
in d icato r
clim ate
statio n s.
of a co ld
front
However,
th is
is
not
an a b s o l u t e
p a s s a g e b e c a u s e h i g h v a l u e s may a l s o
i n d i c a t e a c o l d n i g h t c a u s e d by c l e a r s k i e s f o l l o w i n g a warm n i g h t
ca u se d by c l o u d c o v e r .
35
Ac co u n ti n g f o r Snowme11
T h i s s t u d y c o v e r s o n l y t h e snow a c c u m u l a t i o n p e r i o d o f w i n t e r
( O c t o b e r t h r o u g h A p r i l ) and d o e s n o t a t t e m p t t o e s t i m a t e s n o w m e l t
during the sp rin g m e lt season.
H o w e v e r , s i n c e some f a l l and w i n t e r
m e l t i n g o c c u r s , by a c c o u n t i n g f o r t h i s m e l t , t h e m o d e l c a n e s t i m a t e
snowpack amount more a c c u r a t e l y .
A l t h o u g h snowmelt i s a v e r y complex
p r o c e s s d e p e n d i n g . on many v a r i a b l e s ,
in d icato r
a nd
can
p r o v i d e ' an
a i r t e m p e r a t u r e i s an im p o r ta n t
estim ate
of
snowm elt.
T herefore,
t e m p e r a t u r e s a t c l i m a t e s t a t i o n s - a r e u sed to e s t i m a t e snowm elt.
A
d e s c r i p t i o n o f how t h i s was a c c o m p l i s h e d f o l l o w s .
In o rd e r
to g a in
some u n d e r s t a n d i n g
o f how a i r
tem perature
a f f e c t s snowmelt, a comparison was made between snowmelt ( 24-hour l o s s
o f snow w a t e r e q u i v a l e n t ) a t e a c h snow c o u r s e and,, t h e maximum and
minimum t e m p e r a t u r e s a t e a c h o f t h e c l i m a t e . s t a t i o n s t o s e e w h i c h
c lim a te s t a t i o n te m p e ra tu re s c o r r e l a t e d b e s t w i t h snowm elt ( F ig u r e
10).
A l t h o u g h . t h e s e p l o t s show a c o m p l e x r e l a t i o n s h i p , o n e c a n s e e
t h a t i n g e n e r a l , t h e r e e x i s t s a c r i t i c a l maximum t e m p e r a t u r e a b o v e
which m e l t o c c u r s .
is
For t h e p l o t p r e s e n t e d ^
a r o u n d 50 d e g r e e s F.
ma xim um
tem p eratu re
In a l l
b etter
cases,
than
the c r i t i c a l temperature
s n o w m e lt.c o rre la te d w ith
minimum t e m p e r a t u r e s .
A lso,
t e m p e r a t u r e s a t t h r e e c l i m a t e s t a t i o n s c o r r e l a t e d w i t h snowmelt b e t t e r
than o th e r
clim ate
Y ellow stone.
statio n s:
Bozeman 12 NE,
W i th many snow c o u r s e s ,
H eb g en Dam and West
an a v e r a g e o f two c l i m a t e
s t a t i o n s c o r r e l a t e d b e t t e r t h a n an i n d i v i d u a l c l i m a t e s t a t i o n .
Thus,
36
maximum t e m p e r a t u r e a t one o r an a v e r a g e o f two o f t h e s e
clim ate
s t a t i o n s was used t o e s t i m a t e m e l t ( T a b l e 2).
BRIDGER b o w l
APRIL 1977
D A Y S OF M O N T H
F i g u r e 10.
A p l o t o f snowmelt ( 2 4 - h o u r l o s s o f snow w a t e r e q u i v i l e n t )
a t t h e B r i d g e r Bowl snow c o u r s e p l o t t e d a g a i n s t minimum
and maximum t e m p e r a t u r e s a t t h e n e a r b y Bozeman 12 NE
c l i m a t e s t a t i o n f o r A p r i l , 19 7 7 .
M e l t seems t o o c c u r
a b o v e 50 d e g r e e s F a h r e n h e i t and c o r r e l a t e s w i t h maximum
tem perature.
I n a more a c c u r a t e
determ ining m elt r a te ,
test
of c r i t i c a l
t e m p e r a t u r e as w e l l as
d a i l y m e l t a m o u n t was p l o t t e d
a g a in st the
t e m p e r a t u r e abov e 50 d e g r e e s F a h r e n h e i t ( F i g u r e 11). N o t i c e t h a t t h e X
i n t e r c e p t ( t e m p e r a t u r e w h e r e m e l t i s z e r o ) f a l l s a t 50 d e g r e e s , and
and m e l t r a t e i s 0 . 0 4 i n c h e s p e r d e g r e e a b o v e 50 d e g r e e s .
From t h e
e m p i r i c a l r e l a t i o n s h i p s seen i n t h e s e p l o t s , p r e d i c t i v e m e l t e q u a t i o n
w e r e c o n s t r u c t e d b a s e d on t e m p e r a t u r e a t one o r an a v e r a g e o f two
37
m e l t in
Z
d e g r e e s a b o v e 50 F
F i g u r e 11.
P l o t of snowmelt ( 2 4 - ho u r l o s s i n snow w a t e r e q u i v i l e n t )
a t t h e B r i d g e r Bowl snow c o u r s e a g a i n s t t e m p e r a t u r e above
t h e c r i t i c a l t e m p e r a t u r e o f 50 d e g r e e s F a h r e n h e i t a t t h e
Bozeman 12 NE c l i m a t e s t a t i o n .
D as h ed l i n e s a r e one
s t a n d a r d d e v i a t i o n of m e l t v a l u e s from t h e l i n e .
clim ate s ta tio n s .
An a n a l y s i s o f t h e p l o t s f o r t h e s i x d a i l y snow
c o u r s e s y i e l d e d t h e e m p i r i c a l r e l a t i o n s h i p s shown i n T a b l e 2.
38
T a b l e 2.
C r i t i c a l t e m p e r a t u r e ^ m e l t r a t e and which c l i m a t e s t a t i o n s
were used t o p r o v i d e t e m p e r a t u r e d a t a f o r each snow c o u r s e
m e lt equation.
Snow Course
C ritical
Temp era tu re
B r i d g e r Bowl
Maynard Creek
Shower F a l l s
L i c k Creek
C a r r o t Ba sin
T a y l o r Peaks
B = Bozeman 12 NE
H = Hebgen Dam
W = West Y e l l o w s t o n e
50
50
50
45
55
50
Melt r a t e i n
inches of water
eq u iv alen t per
d e g r e e above
c r i t i c a l temp.
I 0.04
1 0 .0 3
0.0 3
0 .0 5
0.02
0.04
* Av er ag ed v a l u e s
Cli m at e
stations
providing
temperature
data.
B
B
H
H
H
H
and
and
and
and
B *
B *
W*
W*
39
CHAPTER 3
RESULTS
R e s u l t s a r e p r e s e n t e d as f o l l o w s .
results
T a b l e 3 shows t h e c o r r e l a t i o n
between e s t i m a t e s a n d - a c t u a l m o n t h l y snow a c c u m u l a t i o n .
In
t h e f i r s t c o l u m n , snow c o u r s e s a r e s e p a r a t e d i n t o d a i l y a n d m o n t h l y
I
categories.
The s e c o n d c o l u m n shows t h e c o r r e l a t i o n c o e f f i c i e n t
b e t w e e n m o n t h l y e s t i m a t e s an d a c t u a l
column, r
m onthly t o t a l s .
The t h i r d
, i s t h e v a r i a n c e ; t h i s c a n be t h o u g h t o f a s t h e amou nt o f
v a r i a n c e " e x p l a i n e d " - by t h e r e g r e s s i o n e q u a t i o n .
The. f o u r t h column,
N, i s t h e n um b er o f c a s e s , , i . e . t h e n u m b e r o f m o n t h s o f d a t a e n t e r e d
in to the re g re s s io n equation.
The s t a n d a r d e r r o r column means t h a t 68
p e rc e n t of th e tim e, th e d i f f e r e n c e between th e e s tim a te d m onthly
s n o w f a l l t o t a l and t h e a c t u a l t o t a l w i l l be l e s s t h a n o r e q u a l t o th e
standard e rro r.
The l a s t c o l u m n i n d i c a t e s w h i c h d a i l y snow c o u r s e
e q u a t i o n was used as a p r e d i c t o r f o r e ac h m o n t h l y snow c o u r s e ( r e c a l l
t h a t t h e e q u a t i o n d e v e l o p e d f o r each d a i l y snow c o u r s e was summed t o
pr o du ce m ont hly t o t a l s ) .
T able
4 shows t h e d a i l y
equations
used to g e n e r a te m onthly
t o t a l s , t h e p a r a m e t e r s u s ed and t h e i r im p o r ta n c e i n a c c o u n t i n g f o r t h e
p r e d ic tiv e a b i l i t y of the equation.
above.
The p a r a m e t e r s
column is
The f i r s t f o u r c o l u m n s a r e a s
the m eteo ro lo g ical
s t a t i o n p ara m e te rs used in the r e g r e s s i o n e q u atio n .
and c l i m a t e
The p e r c e n t r %
change column i s t h e p e r c e n t o f th e t o t a l e x p l a i n e d v a r i a n c e a c c o u n te d
40
Table 3.
C o r r e l a t i o n r e s u l t s betw een e s tim a te s of m onthly
a c c u m u l a t i o n and a c t u a l m o n t h l y snow a c c u m u l a t i o n f o r b o th
d a i l y and m o n t h l y snow c o u r s e s .
Snow Course
r
r2
N
Standard
Error (inches)
D a i l y snow c o u r s e
whose e q u a t i o n was
summed t o e s t i m a t e
m o n t h l y snow co u r s e
values.
I
D a i l y Snow C o ur s es :
B r i d g e r Bowl
C a r r o t B as in
L i ck Creek
Maynard Creek
Shower F a l l s
T a y l o r Peaks
.9 4
.91
.71
.87
.92
.86
.89
.83
.51
.76
.85
.74
66
30
44
54
43
24
1.72
4.15
1 .27
1.50
2.5 6
0.89
*
Monthly Snow C o u r s e s :
Arch F a l l s
Bear B a s in
Hood Meadows
L i t t l e P ark
New World
Twenty^One Mile
.91
.97
.89
.98
.88
.85
.82
.95
.79
.95
.76
.71
43
31
24
29
31
50
1.05
1.9 7
1 .47
1 .40
2.10
1.82
Shower
Shower
Shower
Shower
Shower
Carrot
Falls
Falls
Falls
Falls ,
Falls
Ba sin
*The e q u a t i o n d e v e l o p e d f o r ea ch d a i l y snow c o u r s e was i n t e g r a t e d t o
p r od u ce m ont hly t o t a l s .
r
N
correlation coefficient
variance
number o f c a s e s (months i n t h e r e g r e s s i o n )
T a b l e 4.
R e s u l t s o f s t e p w i s e m u l t i p l e r e g r e s s i o n w i t h d a i l y m e t e o r o l o g i c and c l i m a t e s t a t i o n
p a r a m e t e r s as in d e p e n d e n t v a r i a b l e s and d a i l y snow a c c u m u l a t i o n a t snow co u r s e s i t e s as
t h e dep endent v a r i a b l e .
The e q u a t i o n s c o n s t r u c t e d from t h e s e p a r a m e t e r s and c o e f f i c i e n t s
were i n t e g r a t e d t o p r o v i d e m o n t h l y e s t i m a t e s .
SNOW COURSE
r
r2
N
B r i d g e r Bowl
.81
.67
163
STANDARD
ERROR ( i n c h e s )
.16
I
METEOROLOGICAL
AND CLIMATIC
STATION
PARAMETERS
Zr?
CHANGE*
Bozeman 12 NE
O ro gr aph ic
Temp, change
Temp. g r a d . 850
Temp. 500
Co n sta n t
86
5
3
3
3
1 .5 2
1.04
- I ;09
-7.40
-9.80
- .126
COEFFICIENTS
E-4
E-4
E-3
E-3
Maynard Creek
.59
.35
145
.1 4
Bozeman 12 NE
Spread 850
West Yello wston e
Temp, g r ad 700
O ro g rap h ic 4
C o n s ta n t
67
9
9
8
7
.564
- 9 . 5 0 E-3
.460
- 9 . 3 0 E-3
- 5 . 5 0 E-5
.130
Shower F a l l s
.57
.32
157
.19
Bozeman 12 NE
West Yell ows ton e
Co n sta n t
84
16
.806
.586
4.70 E-2
L i ck Creek
.64
.42
135
.19
Ennis
Norris
West Y ellow stone
Dynamic 4
Di vergence
Cons tan t
62
17
6
10
5
5.23
-3.25
.679
- 3 . 3 3 E-4
6 .2 8 E-3
-1.12
T ab le 4 ( c o n t i n u e d )
C a r r o t Bas in
.6 4
.41
122
.21
Dynamic I .
Hebgen Dam
West Y ellow stone
O ro gr aph ic I
Co n sta n t
68
20
6
5
2.30 E-2
.440
.610
- 2 . 3 0 E-3
- 5 . 6 0 E-3
T a y l o r Peaks
.50
.26
127
.1 4
Hebgen
P r e s , grad 700
West Yellowstone
Co n sta n t
68
19
13
.330
1.0 0 E-3
.310
-5.60
* P e r c e n t change o f r z o f t h e r e g r e s s i o n e q u a t i o n as each p a r a m e t e r i s added.
PARAMETER DEFINITIONS:
Cli m at e S t a t i o n s :
- Bozeman 12 NE j
- West Y el lo ws ton e
- Hebgan Dam
- Ennis
- N orris
Weather P a r a m e t e r s :
O r o g r ap h ic I
O r og r ap h ic 4
Dynamic I
Dynamic 4
Temp, change
Temp. grad 850
Temp, g r a d 700
Temp. 500
Spread 850
P r e s s grad 700
D iv erg enc e
24 -hour
24-hour
24-hour
24- ho ur
24-hour
precipitation
precipitation
precipitation
precipitation
precipitation
to tal
total
total
total
total
700 mb wind speed x 1/850 mb dew p o i n t sp re ad
700 mb wind speed x p r e c i p i t a b l e w a t e r x K -in d ex x I / 850 mb dew
p o i n t s p r ea d
co l d a d v e c t i o n x p r e c i p i t a b l e w a t e r
v o r t i c i t y a d v e c t i o n x p r e c i p i t a b l e w a t e r x K-index
24-hour t e m p e r a t u r e change a t Bozeman 12 NE
850 mb h o r i z o n t a l t e m p e r a t u r e g r a d i e n t
700 mb h o r i z o n t a l t e m p e r a t u r e g r a d i e n t
500 mb t e m p e r a t u r e
850 mb dew p o i n t sp re ad
700 mb h o r i z o n t a l p r e s s u r e g r a d i e n t
500 mb d i v e r g e n c e
■
r
fo r as
each p aram eter
numbers can a l s o
is
added to
the
regression
equation.
The
be t h o u g h t o f a s t h e p e r c e n t a g e e a c h p a r a m e t e r
accounts f o r th e t o t a l p r e d i c t i v e a b i l i t y . o f the r e g r e s s io n equation.
The c o e f f i c i e n t s column r e p r e s e n t s t h e c o e f f i c i e n t s f o r t h e a s s o c i a t e d
parameters.
The s i g n i f i c a n c e o f t h e s e r e s u l t s w i l l
the following chapter.
be d i s c u s s e d
in
I
44
CHAPTER 4
DISCUSSION OF RESULTS
Su cc es s o f t h e Study
The o b j e c t i v e o f t h i s
s t u d y was t o t e s t t h e f e a s i b i l i t y o f u s i n g
!
p r e c i p i t a t i o n and t e m p e r a t u r e d a t a a t . l o c a l c l i m a t e s t a t i o n s a s w e l l
as
a sim plified
set
of m e te o r o lo g ic a l
param eters to
adequately
e s t i m a t e m o n t h l y s n o w f a l l w a t e r e q u i v a l e n t t o t a l s a t snow c o u r s e s i t e s
i n s o u t h w e s t e r n M o n t a n a i n an i n e x p e n s i v e m a n n e r .
o b j e c t i v e s o f t h e s t u d y , how w e l l do t h e . r e s u l t s
of t h i s procedure?
C onsidering the
support the success
C o r r e l a t i o n c o e f f i c i e n t s between mo nt hI y e s t i m a t e s
a n d . a c t u a l m o n t h l y s n o w . a c c u m u la t io n t o t a l s a r e 0.90 and above f o r s i x
o f t h e t w e l v e s i t e s t e s t e d ( h i g h e s t , 0 . 9 8 ) and 0 .8 4 and a b o v e f o r 11
o f t h e 12 s i t e s ( T a b l e 2).
P a r k and Bear B a s in ,
F o r e x a m p l e , a t two snow c o u r s e s . L i t t l e
t h e model a c c o u n t s f o r 95 p e r c e n t o f t h e m o n t h ly
v a r i a n c e in. snow w a t e r e q u i v a l e n t amounts; f o r s i x o f t h e t w e l v e s i t e s
tested,
t h e model a c c o u n t s f o r 80 p e r c e n t o r more o f t h e v a r i a n c e and
f o r .11 o f
the
12 s i t e s
variance.
C learly,
accuracy re q u ire d ,
it
accounts
for
over
70 p e r c e n t
f o r many snow c o u r s e s i t e s ,
of
the
d e p e n d i n g on t h e
t h i s m e t h o d o l o g y may r e p r e s e n t a n i n e x p e n s i v e
a l t e r n a t i v e t o snow c o u r s e measurements once t h e p r e d i c t i v e e q u a t i o n s
a r e e s t a b l i s h e d u s i n g snow c o u r s e d a t a .
Sou thwe st Montana r e p r e s e n t s a c h a l l e n g i n g l o c a t i o n t o t e s t t h i s
m e th o d o lo g y f o r a number o f r e a s o n s : F i r s t , w e a t h e r p a t t e r n s i n t h e
45
s t u d y a r e a a r e v e r y complex;
t h e s t u d y a r e a s t r a d d l e s two,
th re e , d if f e r e n t w intertim e airm asses.
s t u d y a r e a i s s i m i l a r l y complex.
sometimes
Second, th e t e r r a i n in th e
High mo u n ta in r a n g e s a b r u p t l y b o r d e r
b r o a d , f l a t v a l l e y s ; t h e 16,000 s q u a r e k i l o m e t e r Yel I o w s t o n e - B e a r t o o t h
p la teau
stands
consequently,
at
an e I e v a t io n
c r e a t e s much o f i t s
of
8,000
to
own w e a t h e r .
12,000
Third,
feet
and
a distance of
n e a r l y 300. k i l o m e t e r s s e p a r a t e s t h e s t u d y a r e a from t h e - c l o s e s t upwind
raw in s on d e s t a t i o n s o f Bo ise Idaho and G r e a t F a l l s Montana.
storm s p ass th e s e s t a t i o n s ,
they o f te n t r a v e l
ranges, b e fo re reaching th e study area..
t h e raw in s o nd e l o c a t i o n s
w eather,
over'm any m ountain
S in c e t h e w e a t h e r ,
create disadvantages
A f t e r th e
t e r r a i n and
i n e s t i m a t i n g mo untain
a nd s i n c e . t h i s m e t h o d o l o g y w o r k s f o r t h i s
area,
it w ill
a l m o s t c e r t a i n l y work as w e l l i n most o t h e r l o c a t i o n s .
One i s tempted t o compare t h e s u c c e s s o f t h e m e th o d o lo g y d e v e l o p e d
i n t h i s s t u d y t o t h e o t h e r methods such a s t h e Tangborn method and t h e
computer m o d e l i n g method.
However, n e i t h e r method has been t r i e d
in
s o u t h w e s t e r n Montana and a comparison would be i n a p p r o p r i a t e b ec a u se
o f t h e d i f f e r e n c e s i n t e r r a i n and l o c a t i o n s o f c l i m a t e s t a t i o n s and
r a w in s o nd e s t a t i o n s .
~
■ Im p o rta n t.Parameters
In t h i s
section,
th e p a r a m e te r s w hich a c c o u n t f o r most of th e
p r e d i c t i v e a b i l i t y o f t h e e q u a t i o n s a r e examined.
R ecall that d aily
m u l t i p l e r e g r e s s i o n e q u a t i o n s were i n t e g r a t e d to p r o v i d e m o n th ly
e s t i m a t e s o f snow amounts a t snow c o u r s e s i t e s ( T a b l e 3).
Notice th a t
t h e c o r r e l a t i o n c o e f f i c i e n t s f o r d a i l y e s t i m a t e s a r e much low er t h a n
46
the
correlation
coefficients
f o r m o n t h l y e s t i m a t e s ( T a b l e s 3 and 4).
T h i s i s b e c a u s e when summing t h e d a i l y e s t i m a t e s t o p r o d u c e m o n t h l y
to tals,
t h e e r r o r s t e n d t o be " s m o o t h e d o v e r " , i . e . a h i g h e s t i m a t e
f o r one day may be b a l a n c e d by a low e s t i m a t e f o r t h e n e x t day.
Also
n o t e ( T a b l e 4) t h a t each p a r a m e t e r a c c o u n t s f o r v a r y i n g amounts o f t h e
p r e d i c t i v e a b i l i t y o f t h e e q u a t i o n a c c o r d i n g t o t h e p e r c e n t a g e change
of, r
o f th e r e g r e s s i o n e q u a t i o n as each p a r a m e te r i s added to th e
equation.
Based on t h e s e v a l u e s ,
a' d i s c u s s i o n
of the
im portant
param eters fo llo w s .
The 2 4 - h o u r p r e c i p i t a t i o n t o t a l
a t c lim a te s t a t i o n s parameters
g e n e r a l l y a c c o u n t e d f o r more p r e d i c t i v e a b i l i t y o f t h e r e g r e s s i o n ■
equations
than m e te o r o lo g ic a l p aram eters.
F o r s i x snow c o u r s e s ,
c l i m a t e s t a t i o n p a r a m e t e r s a c c o u n te d f o r 100 p e r c e n t o f t h e e s t i m a t e .
At f o u r snow c o u r s e s ,
least
76 p e r c e n t o f t h e e s t i m a t e
courses,
It
c lim a te s t a t i o n param eters accounted for at
clim ate s ta tio n
is not
indicators
su rp risin g
an d f o r
the rem aining
two snow
p a r a m e t e r s a c c o u n t e d f o r o n l y 27 p e r c e n t .
that
clim ate
statio n
param eters
are b e t te r
than m e te o r o lo g i c a l param eters c onsidering th e s i m p l i c i t y
o f t h e m e t e o r o l o g i c a l p a r a m e t e r s and t h e c o m p l e x i t y o f t h e w e a th e r and
t e r r a i n i n s o u th w e s t Montana.
On t h e o t h e r hand, a s t h e snow c o u r s e s .
C a r r o t B a s i n a n d T w e n ty - O n e M il e , show, c l i m a t e s t a t i o n d a t a i s n o t
always
a go od p r e d i c t o r .
For th e s e
snow c o u r s e s ,
d y n a m i c 4 a c c o u n t s f o r 68 p e r c e n t o f t h e e s t i m a t e .
the
param eter
And f o r h a l f o f
t h e snow c o u r s e s u s e d i n t h e s t u d y , a c o m b i n a t i o n o f m e t e o r o l o g i c a l
and c l i m a t e p a r a m e t e r s e s t i m a t e m o n t h l y snow a c c u m u l a t i o n b e t t e r t h a n
e ith e r m eteorological
or c lim a te param eters alo n e.
This
shows t h a t
47
n e i t h e r c lim a te s t a t i o n d a ta nor m e te o r o lo g i c a l param eters alo n e,
a d e q u a t e l y a c c o u n t f o r snowpack amount i n a l l
can
locations.
Because of th e im portance of o ro g ra p h ic p r e c i p i t a t i o n in the
mountains,
two c l i m a t e s t a t i o n s , - Bozeman 12 NE and West Y e l l o w s t o n e
r e p r e s e n t m o u n t a in w e a t h e r w e l l b e c a u s e t h e y . b o t h a r e l o c a t e d a t h i g h
e l e v a t i o n s and h a v e a. l a r g e , t o p o g r a p h i c r i s e n e a r b y i n a n u pw ind
d irectio n .
H o w e v e r , n o t i c e t h a t t h e G a l l a t i n G a t e w a y 26 c l i m a t e
;
s t a t i o n i s l o c a t e d a t . a h i g h e l e v a t i o n a n d i n an a r e a o f h i g h l o c a l
r e l i e f b u t i t p o o r l y r e p r e s e n t s m o u n t a i n sn o w p a ck am ou nt ( F i g u r e I ,
T a b l e 4).
This s t a t i o n is
l o c a t e d i n G a l l a t i n Canyon an d v a l l e y
bo tt om l o c a t i o n s r e c e i v e p r e c i p i t a t i o n p r i m a r i l y from dynamic systems.
Any o r o g r a p h i c p r e c i p i t a t i o n . r e a c h i n g t h i s
tran sp o rt
distant.
s t a t i o n must come v i a wind
f r o m an u p w in d t o p o g r a p h i c , b a r r i e r . o v e r
25 k i l o m e t e r s
Armstrong and W i l l i a m s (1981). a l s o found t h a t v a l l e y bottom
clim ate s ta t io n s poorly represent orographic p re cip ita tio n *
The r e s u l t s
show t h e
im portance, of
testin g
v alley
clim ate
s t a t i o n s as p r e d i c t o r s o f s n o w f a l l as w e l l a s c l i m a t e s t a t i o n s l o c a t e d
i n o r n e a r t h e m ou n t ai n s .
For.example,
n o t i c e two t h i n g s : ( T a b l e 4; F i g u r e 1 ) :
a t t h e Li ck Creek snow c o u r s e ,
F i r s t , two l o w e r e l e v a t i o n
c l i m a t e s t a t i o n s , Enni s and N o r r i s Madison PH ac c o u n t f o r t h e m a j o r i t y
of the p r e d i c t i v e a b i l i t y of the r e g r e s s io n equation.
c lim a te s ta t io n s w ith l i t t l e
local
relief
V a l l e y bott om
such as En ni s and N o r r i s ,
r e c e i v e p r e c i p i t a t i o n from p r i m a r i l y d y n a m i c s o u r c e s b e c a u s e o f t h e
absence of orographic p r e c i p i t a t i o n - i n d u c i n g t e r r a i n .
Second,
th at
dynam ic 4 and
the
two w e a t h e r
param eters
in
the
d i v e r g e n c e , b o t h r e f l e c t dynamic p r o c e s s e s .
equation,
notice
Thus, t h e L i c k Creek snow
48
course is
apparently
a low er e l e v a t i o n
do minate.
snow c o u r s e w h e r e d y n a m i c p r o c e s s e s
A l t h o u g h dynamic p r o c e s s e s a r e g e n e r a l l y l e s s
im portant than orographic processes
i n t h e m o u n t ai n s ,
t h e L i ck Creek
snow c o u r s e shows t h e im p o r ta n ce o f a c c o u n t i n g f o r. b o t h p r o c e s s e s .
Cost A ssessment
In t h i s paper,
of t h i s study?
locations
t h e word expens e a p p e a r s o f t e n .
What e x p e n s e c o u l d u s e r s o f t h i s t e c h n i q u e i n o t h e r
encounter?
t h i s study t o t a l l i n g
salaries
What was t h e c o s t
T a b l e 5 p r e s e n t s a g e n e r a l expen se ac c o u n t o f
$13,150.
an d c o m p u t e r u s e .
N o t i c e most o f t h e expense went toward
A lso,
n o t e t h a t t h e r e was a o n e - t i m e
ex pe ns e f o r d e v e l o p m e n t and t e s t i n g o f t h e mod el,
once a c c o m p l i s h e d ,
t h e r e w ou ld o n l y be a s m a l l a n n u a l ex p en se f o r d a t a e n t r y and computer
1 ■
i
use.
However, u s i n g o t h e r t e c h n i q u e s , f u t u r e r e s e a r c h e r s c o u l d d e v e l o p
a s i m i l a r model w ith even l e s s expense.
R e c a l l t h a t t h i s s t u d y was
d i v i d e d i n t o two p a r t s — d e v e l o p m e n t o f t h e e q u a t i o n s and t e s t i n g f o r
success.
D e v e l o p i n g t h e d a i l y e q u a t i o n s r e q u i r e d o n l y 200 d a y s o f
d a t a w h er ea s b e c a u s e t h i s s tu d y chos e t o e s t i m a t e m o n t h l y snow c o u r s e
accumulation,
t e s t i n g r e q u i r e d 17 y e a r s o f d a t a .
expense in v o lv e d
testin g
By f a r t h e
of th e model o v e r a la r g e
largest
tim e p e rio d .
F u t u r e r e s e a r c h e r s mi gh t e s t i m a t e d a i l y s n o w f a l l a t s i t e s which o n l y
p r o v i d e d a i l y t o t a l s o f s n o w f a l l , f o r exam ple, a SNOTEL s i t e .
case,
th e model
c o u l d be b o th d e v e l o p e d
and t e s t e d
s m a l l e r , y e t s t a t i s t i c a l l y s i g n i f i c a n t amount o f d a t a .
using
In th i s
a far
49
Ta b le 5.
G e n e r a l i z e d expense ac c o u n t o f t h e s t u d y .
Amount
S a l a r i e s o f r e s e a r c h a s s i s t a n t , key p u n c h e r s , and
pr ogr am m ers ....................................................................... ..
$
Computer..................................................................
D a t a * . ............................................................................................ .............................
M i s c e l l a n e o u s . . . . ...........................
7,36 0
3,000
1 ,680
1, 1 1 0
TOTAL..............................................................................
* D i g i t a l t a p e c h a r g e s f o r 17 y e a r s o f d a i l y w e a th e r and c l i m a t e d a t a
from W.O.A.A. N a t i o n a l C l i m a t i c C e n t e r i n A s h e v e l l e , N o r th C a r o l i n a .
W i th a s m a l l e r amount o f d a t a , i t i s e v e n f e a s i b l e t o c a l c u l a t e t h e
v a r i o u s m e t e o r o l o g i c a l a n d . c l i m a t e s t a t i o n p a r a m e t e r s on a good hand
calcu lato r.
E x t r a p o l a t i n g f u r t h e r u s i n g t h i s m ethod, a u s e r m ight
e r e c t an a r r a y of p o r t a b l e snow a c c u m u l a t i o n m o n i t o r i n g i n s t r u m e n t s i n
a mou nt ain ou s a r e a o f i n t e r e s t ; a f t e r p e r h a p s o n l y two s e a s o n s o f d a t a
collection,
and c a l i b r a t i o n of t h e model t h e s e i n s t r u m e n t s c o u l d be
relo cated
to
another
area.
In
th is
way, m o n ito rin g
of
snow
a c c u m u l a t i o n i n t h e m o u n ta in s would be v e r y f l e x i b l e and i n e x p e n s i v e .
Th is ap p ro ac h c o u l d a l s o complement c u r r e n t S o i l C o n s e r v a t i o n S e r v i c e
snow s u r v e y e f f o r t s .
50
SUMMARY AND CONCLUSIONS
This
study
tests
the
snowpack w a t e r e q u i v a l e n t a t
feasib ility
snow c o u r s e
of
adequately
sites
estim ating.
i n s o u th w e s t M o n ta n a .
u s i n g m e t e o r o l o g i c a l p a r a m e t e r s and p r e c i p i t a t i o n and t e m p e r a t u r e d a t a
. from l o c a l c l i m a t e s t a t i o n s i n an i n e x p e n s i v e s t a t i s t i c a l model.
The
.model was d e v e l o p e d u s i n g a sample o f 200 days where m e t e o r o l o g i c a l
and c l i m a t e p a r a m e t e r s w e r e e n t e r e d a s i n d e p e n d e n t v a r i a b l e s i n a
s t a t i s t i c a l stepwise m u l t i p l e re g re s s io n equation w ith d a i l y snow fall
• " .
.. . a t snow c o u r s e s i t e s as t h e dep endent v a r i a b l e .
In order to t e s t the
m o d e l , t h e e q u a t i o n s g e n e r a t e d w e r e i n t e g r a t e d o v e r a p e r i o d o f 17
y e a r s t o e s t i m a t e m o n t h l y snow a c c u m u l a t i o n a t snow c o u r s e s i t e s and
t h e n compared to a c t u a l m o n th ly t o t a l s to d e te r m in e s u c c e s s of th e
m odel.
R esults
show t h a t e s t i m a t e s o f m o n t h l y snow a c c u m u l a t i o n
c o r r e l a t e w i t h a c t u a l v a l u e s w i t h c o r r e l a t i o n c o e f f i c i e n t s o f 0.90 and
a b o v e f o r s i x o f t h e t w e l v e snow c o u r s e s i t e s t e s t e d ( h i g h e s t , 0. 98 )
an d 0 . 8 4 a nd a b o v e f o r 11 o f t h e 12 s i t e s .
T h i s m e th o d o lo g y c o u l d augment snow c o u r s e m e a s u r e m e n t s o r ,
some c a s e s , r e p l a c e snow c o u r s e s .
L ittle
Park m onthly
snow c o u r s e
in
F o r e x a m p l e , t h e B e a r B a s i n and
to tals
c a n be e s t i m a t e d w i t h
c o r r e l a t i o n c o e f f i c i e n t o f 0.98 u s i n g t h i s t e c h n i q u e .
a
A lso, th is
t e c h n i q u e can e a s i l y be u se d i n o t h e r l o c a t i o n s t o augment o r r e p l a c e
m o u n ta in snowpack m easu re m en ts as lo n g a s th e a r e a i n q u e s t i o n has
f a i r l y r e p r e s e n t a tiv e clim ate s ta t io n data.
51
F u t u r e r e s e a r c h e r s may e l e c t t o e s t i m a t e d a i l y s n o w f a l l t o t a l s a t
snow c o u r s e s i t e s p r o v i d i n g d a i l y d a t a r a t h e r t h a n m o n t h l y d a t a a s
t h i s s t u d y has done.
In t h i s case,
t h e model c o u l d be d e v e l o p e d and
t e s t e d u s i n g , a f a r s m a l l e r amount o f d a t a and be a b l e . t o p e r f o r m
c a l c u l a t i o n s on a hand c a l c u l a t o r .
w ith
in stallin g
instrum ents
in
arrays
of
T h i s t e c h n i q u e c o u l d be combined
p o rtab le
the m ountains
of
snow a c c u m u l a t i o n . m e a s u r i n g
in terest.an d
after
an a d e q u a te
c a l i b r a t i o n tim e, th e s e in s tru m e n ts c o u ld .b e r e l o c a t e d to an o th er
a r e a . I n t h i s way, m o n i t o r i n g o f snow a c c u m u l a t i o n i n t h e m o u n t a i n s
wou ld be v e r y f l e x i b l e , i n e x p e n s i v e , and c o u l d complement c u r r e n t S o i l
C o n s e r v a t i o n S e r v i c e snow s u r v e y e f f o r t s .
■52
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:
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-
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<
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-
V
55
U. S . D e p a r t m e n t o f A g r i c u l t u r e S o i l C o n s e r v a t i o n S e r v i c e , 19 8 3 ,
M o n t h l y Snow S u r v e y and W a t e r S u p p l y F o r e c a s t : O f f i c e o f t h e
S o i l C o n s e r v a t i o n S e r v i c e Snow S u r v e y Bozeman Montana, 6 p.
Young, K„ C., 1 9 7 4 , A N u m e r i c a l S i m u l a t i o n o f W i n t e r t i m e O r o g r a p h i c
P r e c i p i t a t i o n : J o u r n a l o f A tm os p h er ic S c i e n c e , v . 31, . No. 7, pp.
1735-1748.
APPENDIX
57
APPENDIX
PROGRAM LISTING
o o o o o o n o o n o n o o o o o o o o o o o o o o n o o o n o o o o o o o o o o o o o n o n o o n n o o o o o o n o n o
58
C
i » c * * * * y < * * * * y t * * * i k * * * * * A * * * * 7 t * i i e * * * * * * y t * * * * * k * * * A A * * * * > t * w * * * * * *
* MAINLINE PROGRAM-- WEATHER *
******************************
This program c a l c u l a t e s a v a r i e t y of m e t e o r o l o g i c a l
p a r a m e t e r s from t h r e e upper a Ir rawinsonde s t a t l o n s - G r e a t F a l l s , M t . , L a n d e r , Wyomi ng, a n d B o i s e , I d a h o .
The p r o g r a m c a l c u l a t e s t h e f o l l o w i n g p a r a m e t e r s :
I) I t f i r s t u t i l i z e s a weighted a v e r a g e of t h e t h r e e
s t a t i o n s c r e a t i n g a v a l u e f o r t h e Bozeman a r e a u s i n g t h e
d i s t a n c e s t o t h e s t a t i o n s a s f o l l o w s : G r e a t F a l l s , 2 3 0 km.
L a n d e r , 3 5 0 km. B o i s e , 445 km.
( 2 ) C a l c u l a t e t h e v e c t o r a v e r a g e wi n d d i r e c t i o n f o r t h e
Bozeman a r e a .
<3> T e m p e r a t u r e a n d p r e s s u r e g r a d i e n t f o r t h e l e v e l s :
8 5 0 , 7 0 0 , 5 0 0 mbs .
( 4 ) Fr om a n d u p wi n d s t a t i o n . I t c a l c u l a t e s K - I n d e x ,
t h e r m a l a d v e c t l o n a nd p r e c l p l t a b l e w a t e r .
( 5 ) Using a l l t h r e e s t a t i o n s . I t c a l c u l a t e s v o r t l c l t y ,
v o r t l c l t y a d v e c t l o n a n d d i v e r g e n c e u s i n g 500 mb. wi n d
d i r e c t i o n s and v e l o c i t i e s .
(6) A v a r i e t y of o r o g r a p h i c l i f t i n g p a r a m e te rs .
( 7 ) A v a r i e t y o f d y n a mi c l i f t i n g p a r a m e t e r s .
( 8 ) P a r a m e t e r s b a s e d on l o c a l c l i m a t e s t a t i o n d a t a o f
p r e c i p i t a t i o n and t e m p e r a t u r e .
**************************************************************
* USER INFORMATION *
********************
I n p u t d a t a Is o r g a n i z e d a s f o l l o w s :
Thr ee r e c o r d s of morning ma nda tor y d a t a , l . e . d a t a from
8 5 0 , 7 0 0 a n d 500 m i l l i b a r l e v e l s .
Data c o n s i s t s o f
p r e s s u r e h e i g h t , t e m p e r a t u r e , r e l a t i v e h u m i d i t y , wi n d
d i r e c t i o n , wi n d v e l o c i t y . The f i r s t r e c o r d I s f r o m t h e
G r e a t F a l l s s t a t i o n , t h e second from t h e Lander s t a t i o n
and t h e t h i r d f r om t h e B o i s e s t a t i o n .
Next, t h e r e a r e t h r e e r e c o r d s o f morning s i g n i f i c a n t d a t a
a r r a n g e d l i k e above e x c e p t t h a t p r e s s u r e Is t h e f i r s t
p a r a m e t e r a n d t h e f o l l o w i n g a r e a s a b o v e ma k i n g s i x
parameters t o t a l per l e v e l .
T h e r e I s a maximum o f t e n
levels .
N e x t , t h e r e a r e t h r e e r e c o r d s o f a f t e r n o o n m a n d a t o r y d a t a a nd
t h r e e records of afte rn o o n s i g n i f i c a n t data j u s t as above.
Next, t h e r e Is one r e c o r d of c l i m a t i c d a t a .
It consists
of t h i r t e e n s t a t i o n s with each s t a t i o n y i e l d i n g d a t a of
mi ni mum a n d maximum t e m p e r a t u r e , p r e c i p i t a t i o n , a n d 2 4 snow a c c u m u l a t i o n .
T h e r e a r e 14 r e c o r d s p e r d a y .
Co Iumn F o r m a t P a r a m e t e r
Record
1- 2
12
Ye a r
I
3-4
I
12
Mont h
5-6
I
12
Day
2
4-7
F4 .0
850 mb p r e s s u r e h e i g h t
2
850 mb t e m p e r a t u r e
9-13
F5 . I
85 0 mb r e l a t i v e h u m i d i t y
2
16-18
F3.0
85 0 mb w i n d v e l o c i t y
2
21-23
F3.0
85 0 mb w i n d d i r e c t i o n
3
F3 . 0
26-28
The 7 0 0 mb a n d 5 0 0 mb d a t a f o l l o w s t h e same f o r m a t .
The
7 0 0 mb d a t a b e g i n s on c o l u mn 30 a n d 500 mb d a t a on c o l u mn
6 0 . The s e c o n d r e c o r d I s G r e a t F a l l s , R e c o r d t h r e e I s B o i s e
and r e c o r d f o u r Is L a n d e r .
Record f i v e Is t h e b e g i n n i n g of
n o o o o n n n n n n n n o n n n n n n n o n n n o n o n n n o o o o o o n n n o n n n n n o n o n o n o o n o o o n o o o n
59
t h e s i g n i f i c a n t d a t a a nd a p p e a r s a s f o l l o w s :
Record
Co!umn F o r m a t P a r a m e t e r
5
3-6
F4 . # P r e s s u r e
5
1#-13
F 4.0
pressure height
5
15-19
F5. I temperature
5
22-24
F3.0
r e l a t i v e humidity
6
27-29
F 3 . 0 wi n d v e l o c i t y
6
32-34
F 3 . 0 wi n d d i r e c t i o n
The n e x t s i g n i f i c a n t l a y e r b e g i n s a t c o l u mn 3 6 , t h e n e x t a t
c o l u mn 72 a n d s o on w i t h 12 s i g n i f i c a n t l a y e r s t o t a l p o s s i b l e
Record f i v e Is G r e a t F a l l s .
Record s i x Is Lander and r e c o r d
seven is B o i s e . Be gi nni ng w i t h r e c o r d e i g h t Is t h e a f t e r n o o n
d a t a In t h e s a me ma n n e r e n d i n g on r e c o r d t w e l v e .
Record
t h i r t e e n Is t h e c l i m a t e s t a t i o n d a t a o r g a n i z e d as f o l l o w s :
R e c o r d Col umn
13
3-5
13
8-10
13
12-18
13
20-25
Format P a r a m e t e r
F3.0
max Imum
F3 . 0
mi n i mum
F7.3
24-hour
F6 . 2
24-hour
temperature
temperature
p r e c I p I t a t I on
snowfa I I t o t a I
The n e x t c l i m a t e s t a t i o n d a t a b e g i n s on c o l u mn 2 7 , t h e n e x t
on c o l u mn 54 a n d s o on w i t h 13 c l i m a t e s t a t i o n s p o s s i b l e
The c l i m a t e s t a t i o n o r d e r I s t h e s a me a s t h e i r p o s i t i o n s
e n t e r e d In t h e a r r a y s a s d e s c r i b e d b e l o w .
The d a t a I s r e a d I n t o a r r a y s a s f o l l o w s :
A r r a y MAN( I , J , K> c o n t a i n s m a n d a t o r y d a t a .
1= s t a t i o n : I =I I s G r e a t F a l l s ; 1=2 1s L a n d e r ; 1=3 I s
Boise.
J I s t h e l e v e l : J = I I s 8 5 # m b . ; J =2 I s t h e 7 0 8 mb. a n d
J = 3 I s t h e 5 # # mb. l e v e l .
K I s t h e p a r a m e t e r : K=I I s p r e s s u r e h e i g h t , K=2 I s t h e
t e m p e r a t u r e , K=3 I s t h e r e l a t i v e h u m i d i t y , K=4 I s t h e
w i n d d i r e c t i o n a n d K=5 I s t h e w i n d v e l o c i t y .
A r r a y S I G ( I 1J 1K) c o n t a i n s s i g n i f i c a n t d a t a w h e r e I I s t h e
t h e s t a t i o n a s a b o v e a nd J 1s t h e l e v e l ( a maximum o f 1#
l e v e l s ) a nd K I s t h e p a r a m e t e r a s a b o v e b u t t h e p r e s s u r e
o f t h a t p a r t i c u l a r l e v e l I s In t h e f i r s t p o s i t i o n a n d t h e
o t h e r p a r a m e t e r s a r e bumped up o n e p o s i t i o n s o t h e r e a r e
six parameters t o t a l .
A r r a y C L I M ( I 1J ) c o n t a i n s c l i m a t i c d a t a w h e r e I I s t h e
s t a t i o n a nd J I s t h e p a r a m e t e r a s f o l l o w s :
I IS Belgrade Airport
2 I S Mo n t a n a S t a t e U n i v e r s i t y
3 I S The F o r s y t h r a n c h n e a r B r l d g e r ( Boz e ma n 12 NE)
4 is Ennis.
5 I S G a l l a t i n Ga t e wa y 9 S .
6 I S G a l l a t i n Ga t e wa y 27 S. ( 1 9 5 2 - 1 9 6 2 >
7 I s G a l l a t i n Ga t e wa y 26 S . ( 1 9 6 7 - p r e s e n t >
8 I s Hebga n Dam.
9 I s L l v l n g s t o n 12 S .
I = 1# I s L i v i n g s t o n A i r p o r t .
I = 11 I s N o r r I s .
I = 12 I s V i r g i n i a C i t y .
I = 13 I s V e s t Y e l l o w s t o n e .
J
J
J
J
= I I
= 2
= 3
= 4
s
Is
Is
Is
maximum t e m p e r a t u r e .
mi ni mum t e m p e r a t u r e .
p r e c i p i t a t i o n In I n c h e s .
2 4 - h o u r s n o w f a l l In I n c h e s .
60
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
Output of t h i s
Record
I
I
I
2
2
2
2
The 700
be g I ns
54.
2
2
3
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
program
Is o r g a n i z e d a s f o l l o w s :
Co Iumn F o r m a t P a r a m e t e r
2-3
12
year
5-6
12
mont h
8-9
12
da y
2-6
F5.0
8 5 0 mb p r e s s u r e h e i g h t
7- 1 1
F5 . 0
850 mb t e m p e r a t u r e
12-16
F5 . 0
85 0 mb r e l a t i v e h u m i d i t y
1 7- 21
F5 . 0
85 0 mb w i n d v e l o c i t y
mb a n d 5 0 0 mb d a t a a r e a s a b o v e , t h e 70 0 mb d a t a
In c o l u mn 27 a nd t h e 5 0 0 mb d a t a b e g i n s In c o l u mn
62-66
67-71
2-5
6-10
11-15
16-20
21-25
26-30
31-35
36-40
41-48
49-55
56-62
63-69
70-76
2-7
8-14
15- 21
22-28
29-35
36-41
42-47
48-53
54-59
60-65
66-71
2-7
8-14
15- 21
22-28
29-33
34-38
F4 . 0
F4 . 0
F4.0
F4.0
F4.0
F4.0
F4.0
F4.0
F4.0
F4 . 0
F7 . 3
F6.2
F6 . 2
F6 . 2
F6 . 2
F6 . 2
F6 . 2
F6.2
F6.2
F5. I
F5. I
F5 . I
F5.0
FS . 0
F5.0
F5 . 0
F6 . I
F6 . I
F6. I
F6. I
F4 . 0
F4.0
700 mb w i n d d i r e c t i o n
500 mb w i n d d i r e c t i o n
85 0 mb p r e s s u r e h e i g h t g r a d i e n t
70 0 mb p r e s s u r e h e i g h t g r a d i e n t
50 0 mb p r e s s u r e h e i g h t g r a d i e n t
850 mb t e m p e r a t u r e g r a d i e n t
700 mb t e m p e r a t u r e g r a d i e n t
500 mb t e m p e r a t u r e g r a d i e n t
K I nde x
850 mb dew p o i n t s p r e a d
p r e c I p l t a b l e water
t h e r m a l a d v e c t I on
c o l d t h e r m a l a d v e c t I on
warm t h e r m a l a d v e c t I on
thermal advectIon squared
warm t h e r m a l a d v e c t I o n s q u a r e d
c o l d t h e r m a l a d v e c t I on s q u a r e d
d I vergence
divergence squared
vortlc1ty
v o r t Iclty advection
v o r t l c I t y a d v e c t I on s q u a r e d
orographic parameter I
orographic parameter 2
orographic parameter 3
orographic parameter 4
d y n a mi c p a r a m e t e r I
dynamic p a r a m e t e r 2
d y n a mi c p a r a m e t e r 3
d y n a mi c p a r a m e t e r 4
Bozeman 12 NE 2 4 - h o u r m i n . t e m p , c h a n g e
M. S . U. 2 4 - h o u r mi n . t e m p , c h a n g e
The f o l l o w i n g p a r a m e t e r s a r e c l i m a t e s t a t i o n p a r a m e t e r s .
F 4 . 0 maximum t e m p e r a t u r e
6
2-5
6-10
F4 . 0
6
mi ni mum t e m p e r a t u r e
11-18
6
F7 . 3
24-hour p r e c i p i t a t i o n
19-25
6
F6.2
24-hour snowfall
There a r e t h r e e c l i m a t e s t a t i o n s per re co rd with t h e second
o n e b e g i n n i n g In c o l u mn 29 a n d t h e t h i r d i n c o l u m n 5 8 .
Aga I n , t h e o r d e r o f t h e c l i m a t e s t a t i o n s I s t h e s a me
as I Isted above.
**************************************************************
* DI VISION OF MAINLINE PROGRAM *
****************************
* Read
In d a t a
61
a v e r a g e f o r Bozeman a r e a
* A v e r a g e wi nd d i r e c t i o n
* T e m p e r a t u r e and p r e s s u r e g r a d i e n t s
* T h e r m a l a d v e c t l o n , K - I n d e x 1 p r e c l p l t a b l e w a t e r a n d 850
m i l l i b a r dew p o i n t s p r e a d .
* Divergence
* Vortlclty
* Orographic parameters
* Dyna mi c l i f t i n g p a r a m e t e r s
* Climate s t a t i o n parameters
o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
* Weighted
***************************************************************
* SUBROUTINES REQUIRED *
************************
*
*
*
*
ADVECTI O N - - c a I c u I a t e s t h e r m a l a d v e c t l o n
WATER--calculates p r e c l p l t a b l e water
STABLE- -Ca lc ula te s K-Index
VORT--calculates v o r t l c l t y
***************************************************************
**************************************************************
* MODULE TO DIMENTION VARI ABLES *
*********************************
INTEGER DAY,YEAR,MONTH
REAL GRADSAVE( 2 , 3 , 2 ) , GRADAVE( 3 , 2 > , LASTFOR, LANSRREAD,
*LASTBZN,BZNAVE(3 , 5 ) , BZN( 3 , 5 ) ,GRAD( 3 , 2 ),BZNSAVE( 2 , 3 , 5 ) ,
*D< 3 >,MAN(3 , 3 , 5 >,SIG< 3 , 1 2 , 6 ) ,DIR< 3 ) , L 1PWATER,
*LANWATER, LANADV, LANWADV, LANCADV, LAN I NDE X, LASTVORT,
*GFMAN( 3 , 5 ) , LANMAN( 3 , 5 ) , BOI MAN( 3 , 5 > , GF S I G ( I 2 , 6 ) , STORE ( 9 > ,
"LANS I G<1 2 , 6 ) , BOI SIG< I 2 , 6 ) , KI NDEX, LAN S I N, LANCOS, LAND I R ,
•PAVE( 2 5 ) , PARAMI2 , 2 5 ) , CL I Mt 1 3 , 4 )
o n o o o
LOGICAL F I RS T
DATA F I R S T / . TRUE. / , READCOUNT/ I /
OPENt UNI T = 1 0 5 , RECL = 4 4 0 , S T AT US = ' OL D' )
Read In d a t a .
I F t READCOUNT.EQ.I )THEN
READt 1 0 5 , 5 , END=270)YEAR,MONTH,DAY
END IF
READt 1 0 5 , 1 0 , END = 2 7 0 X t ( MANtI , J , K ) , K = 1 , 5 ) , J = 1 , 3 ) , I = 1 , 3 )
READt 1 0 5 , 12,END = 2 7 0 > ( t ( SI Gt I , J , K) , K= I , 6 ) , J = I , I 2 > , I = I , 3 )
I F t READCOUNT.EQ.2 )THEN
READt1 0 5 , 14,END = 2 7 0 > ( ( C L I M t I , J >, J = 1 , 4 > , I = I , 1 3 )
END IF
o
4
5 FORMATl3 ( 1 2 ) )
FORMATt2 ( 3 ( 3X, F4 . 0 , X, F5 . I , 3 ( 2X, F3 . 0 > , 2 X ) / ) , 3 ( 3X, F 4 . 0 , X, F S . I ,
*3(2X,F3.0),2X>>
12 FORMATt2 ( 1 2 ( 2 X , F 4 . 0 , 3 X , F 4 . 0 , X , F 5 . 1 , 3 ( 2 X , F 3 . 0 > , 2 X ) / ) , 1 2 ( 2 X , F 4 . 0 ,
»3X,F4.0,X,F5.I ,3(2X,F3.0),2X))
14 FORMATt1 3 ( 2 ( 2 X , F 3 . 0 ) , X , F 7 . 3 , X , F 6 . 2 , 2 X ) >
n o n
10
*************************************************************
* MODIFY ARRAYS AND EXTRAPOLATE MISSING VALUES *
************************************************
O O O O O
62
In t h i s d a t a , s i g n i f i c a n t l e v e l p r e s s u r e s n u m e r i c a l l y
t e n t i m e s t h e i r a c t u a l v a l u e s , s o I d i v i d e by 10.
16
O O O O O O O O O O O O O
17
18
DO 18 1 - 1 , 3
DO 1 7 , 0 = 1 , 12
I F ( S I G ( 1 , 0 , 1 ) . E O . - 9 9 . 0 ) G O TO 17
SI Gt 1 , 0 , 1 ) = S I G( 1 , 0 , 1 > / 10
CONTINUE
CONTINUE
The s t a t i o n a t L a n d e r , Wy. i s a b o v e t h e 850 mb. l e v e l a n d
c o n s e q u e n t l y , t h e 85 0 mb. m a n d a t o r y d a t a I s u s u a l l y
missing.
So h e r e , I u s e d a t a t a k e n f r o m t h e f i r s t
s i g n i f i c a n t l a y e r a b o v e Lander and e x t r a p o l a t e t h e s e
v a l u e s t o t h e 85 0 mb. l e v e l .
At t h i s l e v e l , p r e s s u r e
I n m i l l i b a r s a n d h e i g h t In m e t e r s I s n e a r l y n u m e r i c a l l y
e q u l v l l e n t , so I us e them I n t e r c h a n g e a b l y .
T e m p e r a t u r e l a p s e r a t e = .065 d e g r e e s C / m e t e r .
R e l a t i v e h u m i d i t y l a p s e r a t e = -10% / 50 m e t e r s .
H e i g h t In m e t e r s = p r e s s u r e In m i l l i b a r s .
Wi nd v e l o c i t y a n d d i r e c t i o n e x t r a p o l a t e d i r e c t l y .
O O O
19
DO 22 1 = 1 , 3
DO 20 K = I , 5
IFtMANt I , I , K > . N E . - 9 9 . 0 ) G O TO 20
I F t SI Gt I , I , I > . LT. 7 5 0 )THEN
GO TO 22
ELSE
O
O O
S e t DP = p r e s s u r e d i f f e r e n c e b e t w e e n 850 mb. a n d t h e
p r e s s u r e of t h e f i r s t s i g n i f i c a n t l a y e r .
DP = 8 5 0 - S I Gt 1 , 1 , 1 )
T e s t f o r m i s s i n g d a t a In MAN a n d I f s o a s s i g n e x p t a p o l a t e d
v a l u e f r o m SIG
IFtMANt I , I , I ) . E Q . - 9 9 . 0 . AND. S I G t I 1I , 2 ) . N E . - 9 9 . 0 )
* MANt I , I , I I = SI Gt I , I , 2 1-DP
IFtMANt I , I , 2 > . E Q . - 9 9 . 0 . AND. SIGt I , 1 , 3 ) . N E . - 9 9 . 0 )
* MANt I , I , 2 >= S I G ( I , I , 3 >+ < DP*. 065 >
I Ft MANt I , I , 3 > . E Q . - 9 9 . 0 . AND. SIGt I , I , 4 > . NE. - 9 9 . 0 )
* MANt I , I , 3 >= S I G ( I , I , 4>- < . 2 * D P >
I F ( MAN < I , I , 4 ) . E Q . - 9 9 . 0 . AND. SIGt I , I , 5 ) . NE. - 9 9 . 0 )
" MANt I , I , 4 I = SI Gt I , I , 5>
IFtMANt I , I , 5 ) . E Q . - 9 9 . 0 . AND. SI Gt I , I , 6 ) . N E . - 9 9 . 0 )
* MANt I , I , 5 ) = S I G < 1 , 1 , 6 )
END IF
O O O O O O O O O O O O O
20
22
CONTINUE
CONTINUE
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** *
* WEIGHTED AVERAGE *
********************
Here, I c a l c u l a t e t h e w e i g h t e d a v e r a g e .
Dt?)= I n v e r s e
of t h e d i s t a n c e from t h e G a l l a t i n d r a i n a g e t o each of t h e
raw lnsonde s t a t i o n s .
D t l ) = G r e a t F a l l s , Dt 2 )= L a n d e r ,
Dt 3 ) = B o i s e .
I t c a l c l a t e s a weighted average fo r a ll
5 p a r a m e t e r s a l t h o u g h t h e a v e r a g e f o r wi n d d i r e c t i o n
( k = 4 ) h a s no m e a n i n g In t h i s c a s e a n d I n e v e r u s e I t .
O O O
63
The a v e r a g e w i n d d i r e c t i o n
following section.
Is c a l c u l a t e d
In t h e
O O O
O O O
O O O O O O O O O O O O O O O O O O O O O O O O O O O
DO 4 0 0 = 1 , 3
DO 30 K = I , 5
D(I )=.004348
D( 2 ! = . 0 0 2 8 5 7
D( 3 ! = . 0 0 2 2 4 7
DO 25 1 = 1 , 3
25
I F ( MANt I , 0 , K I . H O . - 9 9 . 0 ID ( I 1=0
I F ( ( D ( I ) . E O . 0 . A N D . D ( 2 1 . E O . 0 ) . O R . ( D ( I I . EQ. 0. AND. D ( 3 1 . E Q . 0 1
* . 0 R . ( D( 2 I . E Q . 0 . A N D . D ( 3 J . E Q . 0 1 . O R . ( D ( I 1. EQ. 0. AND.
*D(2!.EQ.0.AND.D(31.EQ.01!THEN
BZNt J , K ! = - 9 9 . 0
GO TO 30
END IF
DIST=DI I 1+ D( 2 1+ D( 3 I
BZN ( O , K! = ( MAN ( I , J , K 1 * D ( I I *MAN( 2 , J , K1*D( 2 1+MAN(3 , J , K I * D( 3 11
*
/ DI ST
30
CONTINUE
40 CONTINUE
* AVERAGE WIND DIRECTION *
**************************
A v e r a g e w i n d s by s e p a r a t i n g t h e m I n t o X a n d Y c o m p o n e n t s
a n d f i n d i n g an a v e r a g e f o r t h e m f o r 700 a n d 5 0 0 m b s .
F i r s t , I c a l c u l a t e t h e r a d i a n d i r e c t i o n o f t h e wi nd v e c t o r ,
s e p a r a t e d i r e c t i o n s I n t o c o m p o n e n t s a n d f i n d sum o f
s i n e and c o s i n e .
Add . 0 0 0 1 t o SUMCOS s o I d o n ' t d i v i d e
by z e r o .
0=2 I s 7 0 0 m b . ; 0=3 I s 50 0 mb.
VARIABLE DIRECTORY:
DI RCOUNT
- C o u n t s t h e numbe r o f s t a t i o n s w i t h m i s s i n g d a t a .
GFDIR
-radian directio n converted to t r i g , coordinates.
LAND I R
-radian d ir e c tio n converted to t r i g . coord In a t e s .
BOIDIR
-radian d ir e c tio n converted to t r i g . coord In a t e s .
GFSIN
- S i n e of t h e G reat F a l l s S t a t i o n .
LANS I N
- S i n e of t h e Lander S t a t i o n .
BOISIN
-Sin e of t h e Boise S t a t i o n .
GFCOS
-Cosine of the Great F a lls s ta tio n .
LANCOS
- C o s i n e o f t h e Lander s t a t i o n .
BOICOS
-Cosine of th e Boise s t a t i o n .
SUMS I N
-Sum o f t h e s i n e s o f t h e s t a t i o n s .
SUMCOS
-Sum o f t h e c o s i n e s o f t h e s t a t i o n s .
ANGLE
-Average d i r e c t i o n
In r a d i a n s In t r i g , c o o r d i n a t e s .
DI R( U)
-Average d i r e c t i o n
In c o m p a s s c o o r d I n a t e s - - DI R ( 2 !
I s f o r 7 0 0 mb. a n d DI R ( 3 ) I s f o r 50 0 mb.
Loop t h r o u g h t w i c e t o f i g u r e 70 0 a n d 5 0 0 mb. d i r e c t i o n s .
DO 45 J = 2 , 3
DI RCOUNT=0
C h a n g e c o m p a s s d i r e c t i o n s In a r r a y MAN t o r a d i a n t r i g ,
coord In a t e s .
GFDI R=C -<MAN(I , U , 4 ) + 9 0 ) ) * . 0 1 7 4 5 3 3
LANDIR=C-< MAN(2 , J , 4 ) + 9 0 ) ) * . 0 1 7 4 5 3 3
BOI DI R = C- CMANC 3 , J , 4 ) + 9 0 ) ! * . 0 1 7 4 5 3 3
Fi nd s i n e and c o s i n e of d i r e c t i o n s .
GFSIN = SI N( GFDI R)
LANSIN = SIN( LANDI R)
BOISIN = SI N( BOI DI R)
GFCOS = COS(GFDIR)
64
O O O O O
LANCOS = COS(LANDIR)
BOICOS = COS ( BOI DI R)
Test for missing d a t a .
I f s o . I n c r e m e n t c o u n t e r (DIRCOUNT) a nd
s e t s i n e and c o s i n e f o r s t a t i o n t o U s o t h e y w o n ’t c o n t r i b u t e
t o t h e sum.
I F ( MAN( I , J, 4>. EQ. - 99. j 0T) THEN
GFSIN=JEr
GFCOS=JBr
O
O
O
Di r c o u n t =DI Re o u n t + i
END IF
I F ( MAN ( 2 , J , 4 ) . E Q . - 9 9 . j e f ) T H E N
LANSIN=JB
LANCOS=JBr
0 I RCOUNT=D I RCOUNT+I
END IF
1 F ( MAN ( 3 , 0 , 4 > . E Q . - 9 9 . j e r ) T H E N
BOISIN=JBr
Boi cos=j er
Di r c o u n t =Di Re o u n t + i
END IF
If a I I th re e d ir e c tio n s
I F( DI RC0UNT. E0. 3) THEN
D I R t J >= -99. j er
are missing,
s e t D I R ( J ) TO = 9 9 . # .
GO TO 45
O O O
O O
O O
O O O O
END IF
Sum s i n e s a n d c o s i n e s .
SUMSIN = GFSIN + LANSIN + BOISIN
SUMCOS = GFCOS + LANCOS + BOICOS
Find a v e r a g e d i r e c t i o n .
I F( SUMCOS.EQ.0)SUMCOS = .BZBBSl
ANGLE=ATAN<SUMS I N/SUMCOS)
Convert d i r e c t i o n
AVED I R=ANGLE* 5 7 . 2 9 5 7 7
back t o d e g r e e s a g a i n .
T e s t s i g n s o f sums In a n d s u mc o s t o s e e w h a t q u a d r a n t
s h o u l d be I n .
IF ( SUMS I N. GT. jBt. AND. SUMCOS. LT.J0T)AVE DI R=AVED IR+18J0f
It
O O O O O O O O O
O O O
IF ( SUMS I N. LT. 0 . AND. SUMCOS. LT. JBnAVEDIR=AVE DI R + 18#
Now s u b t r a c t 90 d e g r e e s a n d c h a n g e s i g n s t o g e t ANGLE
back I n t o compass d i r e c t i o n s a g a i n .
DI R ( J >= - ( AVEDI R- 9 0 )
I F ( D I R t J ) . G T . 3 6 0 ) D I R ( J ) = D I R ( J ) - 3 60
I F ( D I R ( J ) . L E . 0 ) D I R ( J ) = D I R ( J ) + 360
45 CONTINUE
***************************************************************
* PRESSURE AND TEMPERATURE GRADIENTS *
**************************************
Here I c a l c u l a t e t e m p e r a t u r e and p r e s s u r e g r a d i e n t s s i mp l y
u s i n g t h e maximum d i f f e r e n c e b e t w e e n t h e r e a d i n g s f o r t h e
three stations.
GRAD ( I , J ) = g r a d 1 e n t o f p r e s s u r e ( when J = I )
65
o n o o o o o n n o o o o o o o n o o
n o
o r g r a d i e n t o f t e m p e r a t u r e ( whe n 0 = 2 ) f o r t h e
( 1 = 1 ) , 7 # j 0 mb ( I = 2 ) , 5 0 0 m b ( 1=3)
50 DO 80 0 = 1 , 3
DO 70 K = I , 2
DO 60 1 = 1 , 3
I F ( MAN( I , O , K ) . E O . - 9 9 . 0 ) T H E N
GRAD( 0 , K ) = - 9 9
GO TO 70
END IF
60
CONTINUE
H=MAX(MAN(I , 0 , K > , M A N ( 2 , 0 , K ) , M A N ( 3 , 0 , K ) )
L= MIN(MAN( I , 0 , K ) , MAN ( 2 , 0 , K ) , MAN ( 3 , 0 , 0 )
GRADt O, O = H-L
70
CONTINUE
80 CONTINUE
85Zmb
* PRECI P !TABLE WATER, THERMAL ADVECTION AND K-INDEX *
*****************************************************
F i r s t , I read t h e d a t a Into s e p a r a t e a r r a y s - - o n e f o r each
statI on:
GFMAN = m a n d a t o r y d a t a f o r G r e a t F a l l s .
LANMAN = m a n d a t o r y d a t a f o r L a n d e r .
BOI MAN = m a n d a t o r y d a t a f o r B o i s e .
GFSIG = s i g n i f i c a n t l e v e l d a t a f o r G r e a t F a l l s .
LANS I G = s i g n i f i c a n t l e v e l d a t a f o r L a n d e r .
BOISIG = s i g n i f i c a n t l e v e l d a t a f o r B o i s e .
F i r s t , I t e s t w h i c h way t h e a v e r a g e 7 0 0 m i l l i b a r w i n d s
b l o w a n d u s e d a t a f r o m an u p wi n d s t a t i o n o r a n a v e r a g e o f t wo
u p wi n d s t a t i o n s t o c a l c u l a t e t h e r m a l a d v e c t l o n ( s u b r o u t i n e
ADVECTION) , K - I n d e x a nd 850 mb. dew p o i n t s p r e a d ( s u b r o u t i n e
STABLE) a n d
p r e c I p l t a b l e w a t e r ( s u b r o u t i n e WATER).
I do t h i s by u s i n g t h e a p p r o p r i a t e a r r a y s a s a r g u m e n t s
I n t h e s u b r o u t i n e s b a s e d on t h e w i n d d i r e c t i o n .
o o n o o o o r> o o o o
C
VARIABLE LI ST:
PWATER = P r e c I p l t a b l e w a t e r .
ADV
= Absolute advectlon.
CADV
= Cold a d v e c t l o n
WADV
= Warm a d v e c t l o n
KINDEX = K - I n d e x .
SPREAD= 85 0 m i l l i b a r dew p o i n t s p r e a d .
90
93
DO 93 0 = 1 , 3
DO 90 K=I , 5
GFMAN(0 , K )=MAN(I , 0 , K )
LANMAN(J, K>=MAN(2, J, K>
B0 I MAN( J , K) = MAN( 3 , J , K)
CONTINUE
CONTINUE
95
97
DO 97 0 = 1 , 1 2
DO 95 K = I , 6
G F S I G ( 0 , K ) = S I G ( 1 , 0 , K)
LANSIG(0,K)=SIG(2,0,K)
BOISIG(0,K)=SIG(3,0,K)
CONTINUE
CONTINUE
C
C
levels
o o o o
66
c = = a = = =: = = = = = = = a = = = = = = a = g: s
I f 7 Z 0 mb. w i n d s b l o w f r o m G r e a t F a l l s .
= = = = = = = = = = = = = = = = = a = = = = = = a 3 = = = . = = = 5 = a a m = 5 = a = a = = s = : = a = s —=
I f 7tftf mb. w i n d s b l o w f r o m a d i r e c t i o n
and L a n d e r .
IF(DIR(2>.GT.210.AND.DIR(2).LE.27tf!THEN
between G r e a t F a l l s
o
o o o o o
I F ( D I R < 2 > . L E . 2 1 0 . A N D . D I R ( 2 > . G T . I StflTHEN
CALL WATER( G F S I G 1GFMAN, PWATER> x
CALL ADVECTI ON(GFMAN1ADV1WADV,CALVI
CALL STABLE( GFMAN, K I NDEX, SPREAD I
END IF
o
CALL WATER!GFSI Gt GFMAN1GFWATER I
CALL WATERt LANS I G, LANMAN, LANWATERI
PWATER=( GFWATER+LANWATER) / 2
o
I F ( GFWATER. E Q . - 9 9 . 0 . AND.LANWATER. N E . - 9 9 . 0 I PWATER = LANWATER
I F < GFWATER . N E . - 9 9 . 0 . A N D . LANWATER . E Q . - 9 9 . 0 ) PWATER=GFWATEr
I F( GFWATER. EQ. - 9 9 . 0 . AND.LANWATER.EQ.- 9 9 . 0) PWATER=- 99. 0
SPREAD = ( GFSPREAD+ LANSPREAD I / 2
I Ft GFSP READ. EQ. - 99. 0. AND. LAN SP READ. NE. - 9 9 . 0 ) SPREAD = LANSPREAD
I Ft GFSP READ.N E . - 9 9 . 0 . AND. LANSP READ. E Q . - 9 9 . 0 ISP READ=GF SPREAD
I Ft GFSP READ. EQ. - 9 9 . 0 . A N D . LAN SP READ. EQ. - 9 9 . 0 ) SP READ = - 9 9 . 0
o
o
CALL STABLE(CF MAN,GF I NDEX1GFSP READ I
CALL STABLE( LANMAN,LAN I NDEX1LAN SP READ I
KINDEX=(GFINDEX+LANINDEX)/2
I F( GFI NDEX. NE. - 99. 0. AND. LANI NDEX. EQ. - 99. 0) KI NDEX=GFI NDEX
I F ( G F I N D E X . E Q . - 9 9 . 0 . A N D . L A N I N D E X . N E . - 9 9 . 0 ) K I NDEX = LAN INDEX
I F t G F I NDEX.E Q . - 9 9 . 0 . AND.LAN I NDEX. EQ. - 9 9 . 0)KINDEX = - 9 9 . 0
o o n o o o o o
CALL ADVECTI ON(GFMAN,GFADV,GFWADV1GFCADV)
CALL ADVECTIONtLANMAN,LANADV1LANWADV1LANCADV)
ADV= t GFADV+LANADV>/2
WADV=( GFWADV+LANWADV) / 2
CADV=( GFCADV+LANCADV1/ 2
I F( GFADV. EQ. - 99. 0. AND. LANADV. NE. - 99. 0) ADV=LANADV
I F( GFADV. NE. - 99. 0. AND. LANADV. EQ. - 99. 0) ADV=GFADV
I F ( GF AD V . E Q . - 9 9 . 0 . A N D . L A N A D V . E Q . - 9 9 . 0 ) A D V = - 9 9 . 0
IFtGFCADV . E Q . - 9 9 . 0. AND. LANCADV. N E . - 9 9 . 0)CADV=LANCADV
I F t GFCADV. NE. - 9 9 . 0 . AND.LANCADV.EQ.- 9 9 . 0)CADV=GFCADV
I F t GFCADV. EQ. - 9 9 . 0 . AND.LANCADV.EQ.- 9 9 . 0 ) CADV= - 9 9 . 0
I F ( GFWADV. E Q . - 9 9 . 0 . AND.LANWADV. NE. - 9 9 . 0 ) WADV= LANWADV
IFtGFWADV . NE . - 9 9 . 0.AND.LANWADV.EQ.- 9 9 . 0IWADV=GFWADV
I F t G F WADV.EQ.- 9 9 . 0 . AND.LANWADV.EQ. - 9 9 . 0 )WADV=-99. 0
END IF
I f 70 0 mb. w i n d s b l o w f r o m L a n d e r .
IF<DIR(2).GT.270.AND.DIR(2).LE.330)THEN
CALL WATERt LANSIG1LANMAN, PWATER I
CALL ADVECTIONt LANMAN,ADV,WADV.CADV)
CALL STABLEtLANMAN1KINDEX1SPREAD>
67
====================3================a=====a===s=======m
I f 7 0 0 mb. w i n d s b l o w f r o m b e t w e e n L a n d e r a n d B o i s e .
I F ( D I R ( 2 ) . G T . 3 3 0 . A N D . D I R ( 2 > . LE. 3 0 >THEN
CALL WATER(BOIS I G1BOI MAN,BOI WATER)
CALL WATER!LANSIG, LANMAN, LANWATER)
PWATER=!B0IWATER+LANWATER)/2
I F ( BOIWATER. E Q. - 9 9 . 0 . AND. LANWATER. NE. - 9 9 . 0 >PWATER=LANWATER
I F ! BOI WATER. NE. - 9 9 . 0 . AND.LANWATER . E Q . - 9 9 . 0 ) PWATER=Bo I WATER
I F ! BOI WATER. E Q . - 9 9 . 0 . AND.LANWATER. EQ. - 9 9 . 0 ) PWATER=-9 9 . 0
O
O
O
O O O O O O
END IF
O
CALL STABLE!BOIMAN.BOII NDEX1BOI SPREAD)
CALL STABLE!LANMAN,LAN I NDEX,LANSP READ)
KI NDEX=! BOI INDEX+LANINDEX)/2
I F ! BOI I NDEX. EQ. - 9 9 . 0 . AND. LANINDEX. NE. - 9 9 . 0)KINDEX = BOIINDEX
I F ! BOI INDEX. N E . - 9 9 . 0 . AND. LAN I NDEX. EQ. - 9 9 . 0 ) K I NDEX = LAN I NDEX
I F ! BOI I NDEX. EQ. - 9 9 . 0 . AND.LANINDEX. EQ. - 9 9 . 0)KINDEX = - 9 9 . 0
O O
SPREAD=!LANSPREAD+BOISPREAD) / 2
I F ! BOISP READ. E Q . - 9 9 . 0 . A N D . LANSPREAD.NE. - 9 9 . 0 ) SPREAD= LANSP READ
I F ! BOISP READ. N E . - 9 9 . 0. AND. LANSPREAD. EQ. - 9 9 . 0 ) SPREAD = BOISP READ
I F ! BOI S P READ. EQ. - 9 9 . 0 . AND. LANS P READ. EQ. - 9 9 . 0 ) S P READ= - 9 9 . 0
O O O O O O
CALL ADVECTIONfBOIMAN.BOIADV.BOIWADV.BOICADV)
CALL ADVECTI ON! LANMAN,LANADV,LANWADV,LANCADV)
ADV=!B0IADV+LANADV)/2
WADV=!BOI WADV+ LANWADV >/2
CADV=!BOICADV+LANCADV) / 2
I F! BOI ADV. EQ. - 9 9 . 0 . AND. LANADV. NE. - 9 9 . 0 )ADV=LANADV
I F ! B O I A D V . N E . - 9 9 . 0 . A N D . LANADV. E Q . - 9 9 . 0 >ADV=B0IADV
I F! BOI ADV. EQ. - 9 9 . 0 . AN D. LANADV. EQ. - 9 9 . 0 )ADV = - 9 9 . 0
I F ! B 0 I CADV. EQ. - 9 9 . 0 . AND.LANCADV.N E . - 9 9 . 0 )CADV=LANCADV
I F ! BOICADV. NE. - 99. 0. AND. LANCADV. EQ. - 9 9 . 0)CADV=BOICADV
I F ( B O I CADV.E Q . - 9 9 . 0 . AND.LANCADV.EQ.- 9 9 . 0 >CADV=-99. 0
I F ! BOIWADV.EQ.- 9 9 . 0 . AND.LANWADV. NE. - 9 9 . 0 ) WADV=LANWADV
I F ( BOIWADV. NE. - 9 9 . 0 . AND.LANWADV. EQ. - 9 9 . 0 )WADV= BO I WADV
I F( BOI WADV. EQ. - 9 9 . 0 . AND.LANWADV.EQ.- 9 9 . 0) WADV=- 99. 0
END IF
I f 7 0 0 mb. w i n d b l o w f r o m B o i s e .
I F ! D I R ! 2 ) . G T . 3 0 . A N D . D I R ! 2 >. LE. 90) THEN
CALL WATER!BOI S I G , BOI MAN, PWATER)
CALL ADVECTI ON! BOI MAN, ADV,WADV, CAOV)
CALL STABLE! BOI MAN, K I NDEX, SP READ)
O O Cl O O
END IF
C
= = = = = = = = 3 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = a s s s = z m = = s m
I f 7 0 0 mb. w i n d s b l o w f r o m b e t w e e n G r e a t F a l l s a n d B o i s e .
IF(DIR(2).GT.90.AND.DIR(2).LE.150)THEN
68
CALL WATER( GFSI G1GFMAN, GFWATER)
CALL WATER( BOI SI G. BOI MAN, BOIWATER >
PWATER = <GFWATER + BOIWATER)/2
C
I F ( GFWATER. E Q. - 9 9 . 0 . AND. BOIWATER. NE. - 9 9 . 0 ) PWATER = BOIWATER
I F ( GFWATER.NE. - 9 9 . 0 . AND.BOIWATER . E Q . - 9 9 . 0)PWATER=GFWATEr
I F ( GFWATER . E Q . - 9 9 . 0 . A N D . BOIWATER . E O . - 9 9 . 0>PWATER=- 99. 0
C
CALL STABLE!GFMAN.GFINDEX,GFSPREAD>
CALL STABLE!BOI MAN,BOI I NDEX. BOISP READ)
KINDEX=!GFINDEX+BOIINDEX)/2
I F ! GF I NDEX. EQ. - 9 9 . 0 . AND. BOI INDEX. N E . - 9 9 . 0)KINDEX =GFINDEX
I F ! GF INDEX. NE . - 9 9 . 0 . AND. BOI I NDEX. EQ. - 9 9 . 0>KINDEX= BO I INDEX
I F ! GF INDEX. E O . - 9 9 . 0 . AND. BOI I NDEX. EQ. - 9 9 . 0)KINDEX = - 9 9 . 0
C
SPREAD = ! BOI SPREAD+GFSPREAD I / 2
I F( GFSPREAD. EQ. - 99. 0. AND. BOI SPREAD. NE. - 99. 0>SPREAD=BOI SPREAD
I F ! GFSP READ. NE . - 9 9 . 0 . A N D . BOI SPREAD. EO. - 9 9 . 0 ) SPREAD =GF SPREAD
I F ! GFSP READ. EQ. - 9 9 . 0 . A N D . BOISP READ. E Q . - 9 9 . 0 ) SPREAD = - 9 9 . 0
C
n o
CALL ADVECTI ON!GFMAN1GFADV , GFWADV , GFCADV)
CALL ADVECTI ON! BOI MAN,BOI ADV1BOI WADV1BOI CADV)
ADV=!GFADV+B0IADV)/2
WADV=!GFWADV +BOI WADV >/2
CADV=!GFCADV+B0ICADV)/2
I F! GFADV. EQ. - 99. 0. AND. BOI ADV. NE. - 99. 0) ADV=BOI ADV
I F ! G F A D V . N E . - 9 9 . 0 . A N D . BOIADV. EQ. - 99. 0) ADV=GFADV
IFIGFADV. EQ. -99. 0. AND. BOIADV. EQ. -99. 0)ADV=-99. 0
I F( GFCADV. EQ. - 99. 0. AND. BOI CADV. NE. - 99. 0) CADV=BOI CADV
I F ! G F CADV. NE. - 9 9 . 0 . AND. BOICADV. EQ. - 9 9 . 0 JCADV=GFCADV
I F! GF CADV. EQ. - 9 9 . 0 . AND. BOI CADV. EQ. - 9 9 . 0 ) CADV= - 9 9 . 0
I F ( GFWADV. E Q . - 9 9 . 0 . AND. BOI WADV. NE. - 9 9 . 0 ) WADV= BOI WADV
I F ( GF WADV.NE.- 9 9 . 0 . AND. BOIWADV.EQ.- 9 9 . 0 JWADV=GFWADV
I F ! GFWADV. E Q . - 9 9 . 0 . AND. BOIWADV. EQ. - 9 9 . 0 )WADV= - 9 9 . 0
o o o o o o o o o o r>
o o o o o
98
END IF
I F ! ( SPREAD. G T . 6 0 . OR. SPREAD. L T . - 0 . 5 ) . AND. I SPREAD. N E . - 9 9 . 0) ) THEN
WRI TE! 6 , 9 8 )SPREAD
END IF
FORMAT!X,' TROUBLE SPREAD= ' , E 6 . 2 )
C a l c u l a t e t h e s q u a r e o f war m, c o l d a n d a b s o l u t e a d v e c t l o n .
I add one t o t h e t e r m s b e f o r e m u l t i p l i c a t i o n s o t h e p r o d u c t
Is g r e a t e r th a n o n e .
SQADV = !ADV+I ) * ( ADV+1 )
SQWARM=!WADV+I >*<WADV+1)
SQC0LD = (CADV+1 ) * ( CADV+1>
IF(ADV.EQ.-99.0)SQADV=-99.0
I F! WADV. EQ. - 9 9 . 0) SQWARM=-99. 0
I F! CADV. EQ. - 9 9 . 0 ) SQCOLD= - 9 9 . 0
*************************************************************
* DIVERGENCE *
**************
Th I s s e c t i o n c a l c u l a t e s d i v e r g e n c e by c o n v e r t i n g e a c h o f
t h e wi n d d i r e c t i o n s f o r e a c h o f t h e t h r e e s t a t i o n s t o
v e c t o r s and t h e n c a l c u l a t i n g t h e a r e a o f t h e r e s u l t i n g
t r i a n g l e ! see paper f o r f u t h e r d a t l l s ) .
D i v e r g e n c e Is
th en t h e p e r c e n t change of a r e a f o r a given ti m e I n t e r v a l .
In t h i s c a s e , I use on l y t h e a r e a o f t h e t r i a n g l e
(AREA) b e c a u s e I t I s p r o p o r t i o n a l t o d i v e r g e n c e
o o o o o n o o o o n o o o o o o
69
a nd
Is t h u s
statistically
equivalent.
VARIABLE LI ST:
RADDI R#= The d i r e c t i o n 1n r a d i a n s o f t h e wi n d v e c t o r .
RADDIR1= G r e a t F a l l s , RADDI R2= L a n d e r , RADDI R3= B o i s e .
Xl= The X c o m p o n e t o f t h e G r e a t F a l l s s t a t i o n .
Yl= The Y c o m p o n e t o f t h e G r e a t F a l l s s t a t i o n .
X2= The X c o m p o n e t o f t h e L a n d e r s t a t i o n .
Yl= The Y c o m p o n e t o f t h e L a n d e r s t a t i o n .
X3= The X c o m p o n e t o f t h e B o i s e s t a t i o n .
Yl= The Y c o m p o n e t o f t h e B o i s e s t a t i o n .
AREA= The r e s u l t i n g a r e a o f t h e t r i a n g l e a f t e r d i s p l a c e m e n t
by t h e w i n d v e c t o r s .
SQAREA = s q u a r e o f t h e a r e a .
T e s t f o r mi ssi ng d a t a ; If so d o n ' t c a l c u l a t e d i v e r g e n c e .
DO I I jET 1 = 1 , 3
DO 100 K= 4 , 5
IFIMANt I , 3 , K> . E Q . - 9 9 . 0 !THEN
SQAREA=-99. 0
AREA=- 99. 0
GO TO 115
END IF
100
CONTINUE
I 10 CONTINUE
n
99
o o o o o o n o o o o n o o o o o o n o n o o o o n o o
Xl = ( ( COS( GFDI R) >*MAN( I , 3 , 5 ) > + 100
Y l = ( ( S I N t G F D I R ) >*MAN(1 , 3 , 5 ) ) +200
X2=<( COSt LANDIR) )*MAN< 2 , 3 , 5 ) ) + 200
V 2 = ( ( S I N t L A N D I R ) >*MAN(2 , 3 , 5 ) )
X 3 = ( ( C O S t B O I D I R ) )*MAN(3 , 3 , 5 ) )
Y3 = ( ( SINt BOI DI R) )*MAN(3 , 3 , 5 ) )
AREA=< . 5*ABS( X1*Y2- X2*Y1+X2*Y3- X3*Y2 + X3*Y1- X1*Y3> >*. 01
SQAREA=AREA*AREA*.01
************************************************************
* VORTICITY *
************
Th I s p a r t o f t h e p r o g r a m c a l c u l a t e s v o r t l c 1 t y f r o m t h e
500mb wi n d d i r e c t i o n a nd v e l o c i t y .
The v e l o c i t y I s I n p u t
k n o t s and I c o n v e r t them t o m e t e r s p e r s e c o n d .
The
d i r e c t i o n I s I n p u t a s d e g r e e s on a c o mp a s s a n d I m u s t go
through a Io t of pains to c o n v e rt It to to stan d ard t r i g ,
f or m a t t h a t t h e computer u s e s .
I a l s o c o n v e r t t h e wi n d
f r o m t h e d i r e c t i o n t h e wi n d b l o w s f r o m t o a v e c t o r
d i r e c t i o n I . e . t h e d i r e c t i o n t h e wi n d b l o w s t o .
In t h i s
p r o g r a m , I p r e t e n d t h e wi n d I s b l o w i n g o u t o f t h e w e s t
by r o t a t i n g t h e wi n d b a c k t o t h a t o r e n t a t I on e a c h t i m e .
I r e f e r t o t h e s t a t i o n s by name b u t t h i s o n l y s i g n i f i e s
t h e p o s i t i o n In t h e t r i a n g l e a f t e r r o t a t i o n a n d may o r
may n o t be t h e i r r e a l p o s i t i o n s o r n a m e s .
VARIABLE DIRECTORY:
VORTICI TY= Ab s o l u t e v o r t l c I t y f i g u r e d In u n i t s o f 1 0 * * 5 / s e c .
RADDI R#= Wind d i r e c t i o n s o f t h e t h r e e s t a t i o n s c o n v e r t e d t o
standard trigonometric coordinates for v e c to rs.
SUMS I N= Sum o f t h e s i n e s o f t h e d i r e c t i o n s .
In
SUMCOS= Sum o f t h e c o s i n e s o f t h e d i r e c t i o n s .
AVERAD= D i r e c t i o n o f a v e r a g e wi n d v e c t o r I n r a d i a n s .
AVEDIR= D i r e c t i o n o f a v e r a g e w i n d v e c t o r In d e g r e e s .
VORTADV = v o r t I c l t y a d v e c t I o n .
SQVORTADV = t h e s q u a r e o f v o r t I c I t y a d v e c t l o n .
N= D i s t a n c e f r o m t h e a p e x t o t h e bI s e c t o r o f t h e o p p o s i t e s i d e
and Is us e d f o r c a l c u l a t i n g t h e v e l o c i t y c h a n g e o v e r N
dI s t a n c e .
S= The d i s t a n c e b e t w e e n s t a t i o n s .
Che c k f o r m i s s i n g v a l u e s ; I f s o d o n ' t c a l c u l a t e v o r t I c I t y .
115 DO 130 1 = 1 , 3
DO 120 K=4, 5
IFIMANI I , 3 , K > . E O . - 9 9 . 0 . O R . D I R ( 3 ) . E O . - 9 9 . 0 ) T H E N
VORTADV=-99. 0
SQVORTADV=-99.0
LASTVORT=-99. 0
VORTI CI TY=- 9 9 . 0
GO TO 134
END IF
120
CONTINUE
130
CONTINUE
Now s e t f u n c t i o n p a r a m e t e r s f o r v o r t l c I t y .
Th e f u n c t i o n
c a l c u l a t e s v o r t I c l t y as If wind wer e from t h e w e s t .
He r e
I t e s t w h i c h way t h e wi n d I s b l o w i n g a n d s e t t h e
function parameters accordingly.
I t Is s i m i l a r t o
r o t a t i n g t h e wi n d b a c k t o t h e w e s t e a c h t i m e .
I F d D I R I 3 ) . G E . 2 4 0 . AND. D I R I 3 > . LE. 3 0 0 > . OR. < DI R ( 3 ) . G E . 6 0 . AND. D I R I 3)
* . LE. I 2 0 ) !THEN
N=473000
5=621000
CALL VORTSUBIVORT, MANI I , 3 , 4 ) , MAN( I , 3 , 5 ) , MANI2 , 3 , 4 ) , MANI2 , 3 , 5 ) ,
*MAN(3 , 3 , 4 > , MAN( 3 , 3 , 5 ) , N , S , D I R ( 3 > >
VORTICITY=VORT
END IF
O
o o o o o o
o o o o o o o o o o o
70
O
IF I D I R I 3 ) . L E . 6 0 . O R . <D I R I 3 > . G E . 1 8 0 . AND. D I R I 3 > . L E . 2 4 0 MTHEN
N=421000
5=575000
CALL VORTSUBIVORT,MANI2 , 3 , 4 ) , M A N ( 2 , 3 , 5 ) , M A N ( 3 , 3 , 4 ) , MAN(3 , 3 , 5 ) ,
wMANI I , 3 , 4 ) , MAN( I , 3 , 5 > , N , S , D I R ( 3 ) )
VORTICITY=VORT
END IF
OOO
I F <DI Rf 3 ) . G E . 3 0 0 . O R d D I R I 3 ) . GE . I 2 0 . AND . DI R( 3 >. LE . 1 80 > )THEN
N=526000
S=600000
CALL V0RTSUB1VORT,MAN( 3 , 3 , 4 ) ,MAN(3 , 3 , 5 ) ,MANI I , 3 , 4 ) , MANI1 , 3 , 5 ) ,
wMANt 2 , 3 , 4 ) , MANI2 , 3 , 5 ) , N , S , D I R ( 3 ) >
VORTICITY=VORT
END IF
C alculate v o r t l c Ity advectlon.
I F( FI RST) THEN
VORTADV=-99. 0
SQVORTADV=-99. 0
LASTVORT=VORTICITY
GO TO 134
END IF
VORTADV=VORTICI TY-LASTVORT
SQVORTADV=(VORTADV) * ( VORTADV)
71
ifcvortadv.
sqvortad v= - sqvortadv
Here I c a l c u l a t e p a r a m e t e r s d e s i g n e d t o p r e d i c t
orographic precip itatio n ( l i f t # ) .
134 L I FTl =BZN( 2 , 5 ) * ( 10/ <SPREAD+I ) )
I F ( BZN( 2 , 5 ) . E Q . - 9 9 . O R. PWATER . E Q . - 9 9 . 0 J L I F T l = - 9 9 . 0
LI FT2 = BZN( 2, 5 >*PWATE R
I F ( B Z N ( 2 , 5 J . E Q . - 9 9 . 0 R . PWATER. E Q . - 9 9 . 0 ) L I F T 2 = - 9 9 . 0
L I FT3 = ( BZN ( 2 , 5 J ii Pwa t e r wKINDEX J/ 1 0
I F ( B Z N ( 2 , 5 ) . E Q . - 9 9 . 0 R . PWATER. E Q . - 9 9 . 0 . O R . K I N D E X . E Q . - 9 9 . 0 J L I F T 3 = - 9 9
L I FT4 = ( BZN( 2 , 5 JwPWATERwKlNDEX * ( 10/< SP READ+I J J J / 1 0
I F ( B Z N ( 2 , 5 J . E Q . - 9 9 . 0 R . PWATER. E Q . - 9 9 . 0 . O R . K I N D E X . E Q . - 9 9 . 0 J L I F T 4 = - 9 9
o o o n n n n o n
o o o r> o
I F ( VORTICI T V . E Q . - 9 9 . 0. OR. LASTVORT. EQ. - 9 9 . 0 )THEN
VORTADV= - 9 9 . 0
SQVORTADV=-99.0
END IF
LASTVORT=VORTI CITY
C******************************************************************
OROGRAPHIC PRECIPITATION PARAMETERS
***********************************
n o o n
135
S S S S S S S S S S S S S S S S S S S S S S S S B B S S SB B B S S B S S S S S S
140
o o o o o o r> o o o o o o o r> o o o
DYNAMIC LIFTING PARAMETERS
**************************
C a l c u l a t e p a r a m e t e r DYN# w h i c h a t t e m p s t o p r e d i c t
dynami c I I f 1 1 n g .
DYNl =I ADV+1JwPWATER
DYN2 = <(KIND EX + 4 0 JwPWATERJ/10
DYN3=(AREA*PWATER J / 10
DYN4 = ( ABS( 10 +VORTADVJ WPWATERW( KI NDEX + 4 0 J J / 10
I F ( A D V . E Q . - 9 9 . 0 . O R . PWATER. E Q . - 9 9 . 0 ) D Y N l = - 9 9 . 0
I F ( K I N D E X . E Q . - 9 9 . 0 . O R . P WA T E R . E Q . - 9 9 . 0 J DYN2=- 99. 0
I F ( A R E A . E Q . - 9 9 . 0 . O R . PWATER. E Q . - 9 9 . 0 J D Y N 3 = - 9 9 . 0
I F ( VORTADV . E Q . - 9 9 . 0 . O R. PWATER . E Q . - 9 9 . 0 . OR. KI NDEX. EQ. - 9 9 . 0 J DYN4 =- 9 9
Change d i r e c t i o n s back t o compass d i r e c t i o n s a g a i n .
DO 140 1 = 2 , 3
D I R d J = DI R( I J + I 80
I F ( D I R ( I ) . G T . 3 6 0 ) D I R ( I J= D I R ( I J - 3 6 0
CONTINUE
************************************************************
"AVERAGE MORNING AND AFTERNOON PARAMETERS w
**************************************
T h i s s e c t i o n of t h e program s t o r e s morni ng and a f t e r n o o n p a r a m e t e r s
I n t o a r r a y s s o t h e y c a n be a v e r a g e d f o r t h e d a y .
Some p a r a m e t e r s
a r e c a l c u l a t e d f r o m u p wi n d s t a t i o n s s o t h e y a r e d e l a y e d f o r
12 h o u r s by a v e r a g i n g t h e m o r n i n g v a l u e w i t h t h e a f t e r n o o n
v a l u e s t h e day b e f o r e .
VARIABLE DIRECTORY:
BZNSAVE ( READCOUNT, ! , JJ = A r r a y t h a t s t o r e s t h e v a l u e s f o r t h e
w e i g h t e d a v e r a g e f o r t h e Bozeman a r e a , w h e r e :
READCOUNT = 1
Is f o r t h e morning d a ta
READCOUNT = 2
Is f o r t h e a f t e r n o o n d a t a .
I = Th e l e v e l ( a s d e f i n e d b e f o r e J .
72
O O O O O O O O O O O O O O O O O O O O O O O O O O O
J = Th e p a r a m e t e r ( a s d e f i n e d b e f o r e ) .
GRADSAVEIREADCOUNT, I , J ) = A r r a y t o s t o r e t h e t e m p e r a t u r e a n d
pressure gradients.
PARAMIREADCOUNT, # ) = An a r r a y w h i c h s t o r e s t h e v a r i o u s p a r a m e t e r s
e a c h a s s i g n e d t o a l o c a t i o n d e s i g n a t e d by # .
BZNAVEt I , J ) ■ an a r r a y c o n t a i n i n g t h e a v e r a g e o f m o r n i n g a n d
a f t e r n o o n r e a d i n g s f o r t h e a r r a y BZNSAVE.
GRADAVEt l . J ) = The a v e r a g e o f t h e m o r n i n g a n d a f t e r n o o n p a r a m e t e r s
f r o m t h e a r r a y GRADSAVE.
PARAMAVE(I1J ) = The a v e r a g e o f t h e t wo r e a d i n g s f r o m t h e a r r a y
PARAM.
STORE( I ) =
Contains the stored values for the parameters
w h i c h a r e m e a s u r e d f r o m u p wi n d s t a t i o n s .
LASTFOR =
The mi ni mum t e m p e r a t u r e f r o m t h e F o r s y t h Ra nc h
c l i m a t e s t a t i o n f r o m t h e da y b e f o r e .
LASTBZN The mi ni mum t e m p e r a t u r e f r o m t h e B e l g r a d e a i r p o r t
c l i m a t e s t a t i o n f r o m t h e da y b e f o r e .
FORCHANGE
The 2 4 - h o u r c h a n g e In mi ni mum t e m p e r a t u r e a t
F o r s y t h Ra nc h c l i m a t e s t a t i o n ( Boz e ma n 12 NE)
BZNCHANGE
The 2 4 - h o u r c h a n g e In mi ni mum t e m p e r a t u r e a t
Belgrade A irport clim ate s t a t i o n .
170
DO 170 1 = 1 , 3
BZNSAVEtREADCOUNT,I, 5 ) = B Z N ( 1 , 5 )
180
190
DO 190 1 = 1 , 3
DO 180 J = I , 2
GRADSAVE(READCOUNT,I , J >=GRAD(I , J )
CONTINUE
O O O O O
O O
O O
150
160
S t o r e mo r ni ng and a f t e r n o o n p a r a m e t e r s
d e s c rib e d above.
DO 160 1 = 1 , 3
DO 150 J = I , 3
BZNSAVE( READCOUNT,I. J l = B Z N ( I 1J )
CONTINUE
PARAM(READCOUNT,I I = KINDEX
PARAM(READCOUNT,2 I=SPREAD
PARAMt READCOUNT,3 I = PWATER
PARAMt READCOUNT,4 ) =ADV
PARAMt READCOUNT,5 >=WADV
PARAM(READCOUNT,6 )=CADV
PARAMt READCOUNT,7 I = SQADV
PARAM<READCOUNT,8 ) =SQWARM
PARAM(READCOUNT,9 I=SQCOLD
PARAM(READCOUNT,10)=AREA
PARAM(READCOUNT,I I >= SQAREA
PARAM(READCOUNT,I 2 ) =VORTI C I TY
PARAM(READCOUNT,1 3 )=VORTADV
PARAM(READCOUNT,1 4 )=SQVORTADV
PARAM(READCOUNT,15 >= L I F T l
PARAM(READCOUNT,16 >= L I FT2
PARAM(READCOUNT,1 7 ) = L I FT3
Into various arrays
73
O O O O O O
PARAM( READCOUNT,18>=LI FT4
PARAM( READCOUNT,19 J = DYNl
PARAMlREADCOUNT,20)=DYN2
PARAMlREADCOUNT,2 I J = DYN3
PARAMlREADCOUNT,22 >= DYN4
PARAMlREADCOUNT,2 3 J = MANl I , I , 4 J
PARAMlREADCOUNT,2 4 J = D I R l 2 J
PARAMlREADCOUNT,2 5 J = D I R l 3 J
C h a n g e READCOUNT t o t h e a f t e r n o o n v a l u e ( 2 J a n d r e t u r n t o t h e
beginning t o read the afte rn o o n re a d in g s .
If afternoon reading
h a v e a l r e a d y b e e n c a l c u l a t e d a n d s t o r e d , go t o t h e t o a v e r a g i n g
s e c t i o n of t h e program below.
I
A v e r a g e t h e mor ni ng and a f t e r n o o n d a t a and s t o r e
a r r a y s as d e f in e d a b o v e .
DO 2 1 0 1 = 1 , 3
DO 2 0 0 J = I , 3
BZMAVE I I , 0 J = IBZNSAVEI I , I , 0 J + BZNSAVE12 , I , 0 11/ 2
I F l BZNSAVEI I , I , J J . E Q . - 9 9 . A N D . BZNSAVEl2 , I , 0 I . N E . - 9 9 J
x * BZNAVEl I . J J = BZNSAVEl2 , I , J J
I F l BZNSAVE! I , I , 0 1 . N E . - 9 9 . AND.BZNSAVE!2 , I , 0 J . E Q . - 9 9 J
* BZNAVE I 1 , 0 ) = BZNSAVE!1 , 1 , 0 )
I F l BZNSAVE! I , I , J J . EQ. - 9 9 . AND. BZNSAVEI 2 , 1 , J J . EQ. - 9 9 J
* BZNAVEl I , 0 > = - 9 9
200
CONTINUE
2 1 0 CONTINUE
O O O
O O O O O O
I F l READCOUNT.EQ.I JTHEN
READC0UNT=2
GO TO 4
END IF
O
DO 2 2 0 1 = 1 , 3
BZNAVEl I , 5 >= < BZNSAVE! I , I , 5 J+ BZNSAVE( 2 , 1 , 5 ) J / 2
I F l BZNSAVE! I , I , 5 J . EQ. - 9 9 .AND. BZNSAVEI 2 , I , 5 J . NE. - 9 9 J
BZNAVElI . 5 J=BZNSAVEl2 , I , 5 J
I F l BZNSAVE! I , I , 5 J . NE. - 9 9 . AND. BZNSAVEI 2 , 1 , 5 J . EQ. - 9 9 J
* BZNAVElI , 5 J = BZNSAVEl I , I , 5 J
I F ! BZNSAVE! I , I , 5 J . EQ. - 9 9 .AND. BZNSAVEI 2 , I , 5 J . EQ. - 9 9 J
"
BZNAVEl1, 0 >= - 9 9
2 2 0 CONTINUE
O O
"
DO 2 4 0 I = I , 3
DO 2 3 0 0 = 1 , 2
C
GRADAVEI I , 0 > • ( GRADSAVE! I , I , O J+GRADSAVE I 2 , 1 , 0 J J / 2
C
IFl GRADSAVEl I , I , J J . E Q . - 9 9 . AND. GRADSAVEl 2 , 1 , 0 ) . N E . - 9 9 J
GRADAVEl 1 , 0 J=GRADSAVEl 2 , 1 , 0 J
IF I GRADSAVE I I , 1 , 0 ) . N E . - 9 9 . AND. GRADSAVEl 2 , 1 , J J . E Q . - 9 9 >
*
GRADAVEl 1 , 0 J=GRADSAVEl I , I . OJ
IFl GRADSAVEl I , I , 0 J . E Q . - 9 9 . AND. GRADSAVEl 2 , I , O J . E Q . - 9 9 J
"
GRADAVE! I , 0 >= - 9 9
230
CONTINUE
240
CONTINUE
"
In t h e v a r i o u s
n n
74
245
n
247
DO 245 1 = 1 , 9
PAVE < I ) = ( STORE( I ) + PARAM(I , I ) }/ 2
I F <STOREt I >. EQ. - 9 9 . J0r. AND. PARAMt 1 , 1 ) . NE . - 9 9 . 0 ) PAVE ( I >= PARAMt 1 , 1 )
I Ft STOREt I > . N E . - 9 9 . 0 . AND. PARAMt1 , 1 ) . EQ. - 9 9 . 0 ) PAVEt I ) = STOREt I )
I F t STOREt I ) . E Q . - 9 9 . 0 . AND. PARAMt1 , 1 ) . EQ. - 9 9 . 0 ) PAVEt I ) = - 9 9 . 0
CONTINUE
I F( FI RST) THEN
DO 247 1 = 1 , 9
PAVEt I ) = - 9 9 . 0
END IF
o
DO 2 5 0 1 = 1 0 , 2 5
n
PAVEt I ) = ( PARAMt I , I HPARAMt 2 , I ) >/2
n o o o n o o o
n o n
250
I F t PARAMt I , I ) . E Q . - 9 9 . 0 . AND. PARAMt2 . 1 ) . NE. - 9 9 . 0 ) PAVE( I HPARAMt 2 , 1 )
I F t PARAMt 1 , 1 ) . N E . - 9 9 . 0 . AND. PARAMt2 , I > . E Q . - 9 9 . 0 IPAVEt I HPARAMt 1 , 1 )
I Ft PARAMt 1, 1 > . E Q . - 9 9 . 0 . AND. PARAMt 2 , I ) . EQ. - 9 9 . 0 ) PAVE( I ) = - 9 9 . 0
CONTINUE
Now s t o r e t h e v a l u e s c a l c u l a t e d f r o m t h e u p wi n d s t a t i o n s s o
can
be a v e r a g e d on t h e n e x t l o o p o f t h e p r o g r a m ( t o m o r o w ) .
STOREt I HKINDEX
STOREt 2 HSPREAD
STOREt 3 HPWATER
STOREt 4 >=ADV
STOREt 5 I=WADV
STOREt 6 I=CADV
STOREt 7) = SQADV
STOREtSI=SQWARM
STOREO ) = SQCOLD
He r e , I c a l c u l a t e a t e m p e r a t u r e c h a n g e p a r a m e t e r . I do t h i s
by t a k i n g t h e d i f f e r e n c e b e t w e e n t o d a y ' s mi ni mum
a n d y e s t e r d a y ' s mi ni mum t e m p e r a t u r e .
The d i f f e r e n c e
m u s t be mo r e t h a n 15 d e g r e e s In o r d e r t o r e g i s t e r o t h e r
than a zero.
This p a r a m e t e r Is d e s i g n e d t o I n d i c a t e
t h e pasage of a co ld f r o n t .
n o o o o o o
n o o n
FORCHANGE = LASTFOR-CLIMt 3 , 2 ) - 1 0
BZNCHANGE = LASTBZN-CLIMt 2 , 2 ) - 1 0
I Ft FORCHANGE. LT.0)FORCHANGE=0
I F ( BZNCHANGE. L T . 0) BZNCHANGE=0
I F( FI RST) THEN
FORCHANGE=-99
BZNCHANGE=-99
END IF
I F ( L A S T F O R . E Q . - 9 9 . O R . C L I M ( 3 , 2 ) . E Q . - 9 9 . 0 ) FORCHANGE= - 9 9
I Ft LASTBZN. E Q . - 9 9 . O R . CLIMt 2 , 2 ) . E Q . - 9 9 . 0 ) C L I M ( 2 , 2 H - 9 9
Now, c h a n g e v a r i a b l e FI RST t o . FALSE. s o I know I h a v e b e e n
th ro ug h t h e program a t l e a s t once.
FI RST=. FALSE.
*************************************************************
" WRITE THE PARAMETERS *
************************
75
I
WRI TE( 1 0 6 , 266>YEAR,MONTH,DAY
WRI TE! 1 0 6 . 2 6 7 X BZNAVE< I , 0 ) , 0 = I , 3 > , BZNAVE( 1 , 5 ) ,
* < B Z N A V E ( 2 , J ) , J = 1 , 3 ) , BZNAVE< 2 , 5 ) , ( BZNAVE( 3 , J ) , 0 = 1 , 3 >,BZNAVE ( 3 , 5 ) ,
• PAVE( 2 3 ) , PAVE! 2 4 ) , PAVE( 2 5 ) ,
C
• ( GRADAVE( I , I > , I = I , 3 > , ! GRADAVE( I , 2 ) , 1 = 1 , 3 ) , ( PAVE! I >,1 = 1 , 2 2 ) ,
e FORCHANGE1BZNCHANGE
WRI TE! 1 0 6 , 2 6 0 X ( CL I M ( 1 , 0 ) , 0 = 1 , 4 ) , 1 = 1 , 1 3 )
260
F ORMAT( 4 ! 3 ( 2 ( X , F 4 . 0 > , X , F 7 . 3 , X , F 6 . 2 , 2 X > / ) 2 ( X , F 4 . 0 ) , X , F 7 . 3 , X , F 6 . 2 / )
Now, s t o r e t o d a y ' s mi ni mum t e m p e r a t u r e s
mi ni mum t e m p e r a t u r e s .
LASTFOR=CLIM!3 , 2 )
LASTBZN=CLIM!2 , 2 )
Into y e s te r d a y 's
n o n
non
266
FORMAT!3 ! X, 1 2 ) >
267 F O R M A T ( X , 3 ( 4 ( F 5 . 0 ) ) 3 ( X , F 4 . 0 ) / ,
e8(X,F4.0),X,F7.3,4(X,F6.2)/,
e4(X,F6.2),X,3(X,F5.1),4(X,F5.0)/,
* 4 ( X, F 6 . I > , 2 ( X , F 4 . 0 > >
n
IF(READCOl)NT.E G. 2 !THEN
READCOUNT=I
GO TO 4
END IF
o o o o o o o o o o n o o o o o o o o o
o o o o o o o o o n o o o o
270 END
*******************************************************************
*******************************************************************
* SUBROUTINES *
***************
* SUBROUTINE WATER *
********************
SUBROUTINE WATER!S I G, MAN, H 2 0 >
In t h i s s u b r o u t i n e , b ot h m a nd a to r y and s i g n i f i c a n t d a t a a r e used
t o t o t a l up t h e p r e c I p l t a b l e w a t e r In a c o l u m n o f a i r .
First
m a n d a t o r y l e v e l s m u s t be I n s e r t e d I n t o t h e p r o p e r o r d e r w i t h i n t h e
s i g n i f i c a n t lev els according to pressure.
I d o t h i s by p u t t i n g
In a n a r r a y c a l l e d LI ST.
The 8 5 0 a n d 500 mb. d a t a g o on t h e t h e t o p
a n d b o t t o m a n d t h e 700 mb. d a t a g o e s In t h e m i d d l e w h e r e v e r I t
belongs according to pressure.
The n t h e w a t e r In e a c h l a y e r o f
a i r ( now c o n t a i n e d In t h e a r r a y L I S T ) I s summed up t o p r o d u c e
t o t a l p r e c I p l t a b l e w a t e r In t h e c o l Iumn o f a i r .
MAN!0 , K >
S I G( 0 , K )
L I ST! 0 , K )
W(I) =
H20 =
COUNT =
VARIABLE DIRECTORY:
Mandatory d a t a .
Significant data.
A l i s t o f m a n d a t o r y a n d s i g n i f i c a n t d a t a In
o r d e r of p r e s s u r e .
K = the parameter (as defined b e f o r e )
0 = pressure level (as defined b e f o r e )
c o n t a i n s p r e c I p l t a b l e water f o r each l e v e l ,
to ta l p re c Ip ltab le water.
t h e c o u n t o f t h e n u mb e r o f l a y e r s w i t h m i s s i n g d a t a .
76
o o o o o o o o o o
MARK700 =
FI RST =
ES =
E =
LASTMIX =
LASTHEIGHT =
L o g i c a l v a r i a b l e s i g n a l i n g when t h e 7 0 0 mb. l e v e l was
i n s e r t e d I n t o a r r a y LI ST.
Logical v a r i a b l e s i g n a l i n g t h e f i r s t time through
l o o p w h i c h sums p r e c I p l t a b l e w a t e r .
S a t u r a t e d vapor p r e s s u r e .
Vapor p r e s s u r e .
Mi x i n g r a t i o f r o m t h e n e x t l a y e r b e l o w .
P r e s s u r e h e i g h t f o r t h e n e x t l a y e r below.
o o o
REAL SIGl 1 2 , 6 ) , H20,W< I 5 ) , MAINI 3 , 5 ) , LI ST! 1 5 , 4 ) , LASTMIX
LOGICAL FIRST, MARK700
COUNT=0
H2O=0
FI RST=. TRUE.
MARK700=.FALSE.
o o o o o o o
10
P u t 8 5 0 a n d 5 0 0 mb. d a t a on t h e b o t t o m a n d t o p r e s p e c t I v I y .
LI STI I , I >= 8 5 0
L I S T ( 1 5 , I ) =500
DO 10 K = I , 3
L I S T C l , K + l ) =MANC I , K)
L I S TC1 5 , K+l ) =MAN( 3, K)
o
H e r e , I l o o p t h r o u g h t h e 12 p o s s i b l e s i g n i f i c a n t l e v e l s a nd In
t h e d a t a b e l o w 7 0 0 mb. I n t o a r r a y LI S T .
T h e n , when t h e f i r s t
a b o v e 70 0 mb. I s e n c o u n t e r e d , I I n s e r t t h e 70 0 mb. d a t a .
OOOO
15
T e s t f o r f i r s t s i g n i f i c a n t l e v e l e n c o u n t e r e d a b o v e 7 0 0 mb.
If so.
I n s e r t 7 0 0 mb. d a t a I n t o LI ST a n d s e t m a r k e r CMARK700 = . TRUE) .
IFC SIGC J - I , I ) . L T . 7 0 0 . AND. S I G C J - I , I ) . N E . - 9 9 . 0 . AND. . NOT. MARK700)THEN
LI STCJ , I >=700
DO 20 K=2, 4
L I S T C J 1K) =MANC2,K - I >
MARK7 0 0 = .TRUE.
O
20
DO 40 J = 2, 13
I n s e r t d a t a b e l o w 70 0 mb.
IFC S I G C J - I , I ) . G T . 7 0 0 )THEN
DO 15 K = I , 4
LI STCJ , K J = S I G C J - I , K)
END IF
OOOOO
END IF
I f t h e 7 0 0 mb. d a t a h a s n ' t b e e n I n s e r t e d y e t by t h e t i m e t h e
1 3 t h p o s i t i o n h a s come u p . I n s e r t t h e h i g h e s t s i g n i f i c a n t d a t a
I n t o t h e 13 t h s l o t a nd I n s e r t t h e 7 0 0 m b . d a t a I n t o t h e 14 t h s l o t .
23
27
I F C J . E Q . 1 3 . AND. . NOT. MARK700>THEN
DO 23 K = I ,4
LISTCJ,K)=SIGCJ-1,K>
LI STC1 4 , I ) = 70 0
DO 27 K=2, 4
L I S TC1 4 , K) =MAN( 2, K - I )
C
MARK7 0 0 = . TRUE.
END IF
O O O
77
O
30
I n s e r t d a t a a b o v e 1Z9S mb. I n t o L I S T .
IF(MARK7 j0T0>THEN
DO 3 0 K = I , 4
L I S T ( J t l t K ) = S I G ( J - I 1K)
END IF
CONTINUE
T e s t l i s t t o make s u r e I t I s In o r d e r o f d e c l i n i n g p r e s s u r e .
s o me t hi n g Is w r o n g .
Make H20 = - 9 9 . 0 a n d r e t u r n .
DO 45 J = I . 1 4
I F ( L I S T ( J , I ) . N E . - 9 9 . 0 . AND. L I S T t J + 1 , 1 ) . NE. - 9 9 . 0 . AND. ( L I S T ( J . I )
*
-LIST(J+1,1>).LE.0)THEN
WRI TE( 6 , 4 3 )
43
FORMATt X, ' TROUBLE I ARRAY LI ST I S TURNED AROUND.' )
RETURN
END IF
45
CONTINUE
---= = —= = = = = = = = = = = = = = = = = = = = = = = = = = = = = a = = = = 3 = = = = = = = = =a = = = a = ——= —s s *
C a l c u l a t e w a t e r ( m i x i n g r a t i o ) f o r e a c h l a y e r a n d s t o r e In W( I )
DO 50 1 = 1 , 1 5
I F ( L I S T ( I 1 1 > . E Q . - 9 9 . 0 . O R . L I S T ( I , 3 ) . E Q . - 9 9 . 0 . O R . L I S T ( I 14 ) . E Q .
* - 9 9 . 0 )THEN
W( I > = - 9 9 . 0
GO TO 50
END IF
ES = 10**( 9 . 2 8 6 - ( 2 3 2 2 . 3 7 8 9 / « L I S T ( I , 3 >+ 2 7 3 ) ) >
E= ( ( LI STt I . 4 > + . 0 0 0 0 1 ) / 1 0 0 >*ES
W( I ) = ( . 6 2 2 * E ) / ( L I S T ( I 1I ) - E )
50 CONTINUE
O O
O O O
O O O
40
O O
O O
T e s t f o r m i s s i n g d a t a ; I f s o . I n c r e m e n t COUNT a n d
I f n o t , a dd up p r e c I p l t a b l e w a t e r .
I F ( W ( I > . E 0 . - 9 9 . 0 . O R. LI STt I , 2 > . EQ. - 9 9 . 0 )THEN
COUNT=COUNT+!
GO TO 60
END IF
O O O O
S t o r e t h e l o w e s t n o n - m i s s i n g m i x i n g r a t i o and h e i g h t .
I F( FI RST) THEN
LASTMIX=Wt I >
LASTHEI GHT=LI ST( 1 , 2 )
FI RST=. FALSE.
GO TO 60
M u l t i p l y a v e r a g e w a t e r In e a c h l a y e r by t h e t h i c k n e s s o f e a c h
l a y e r a n d sum t h e l a y e r s t o d e t e r m i n e t o t a l p r e c I p l t a b l e
water.
60
O O O
loop a g a in .
ELSE
H20 = H20+<( ( W( I ) + LASTMIX) / 2 > * ( ( L I S T ( I , 2 >-LASTHEI GHT) / . 9 8 > )
LASTMIX=Wt I >
LASTHEI GHT=LI STt 1 , 2 )
END IF
CONTINUE
78
O O
O O
I f mor e t h a n 7 l a y e r s a r e m i s s i n g , a s s i g n - 9 9 . 0 ( m i s s i n g ) t o
p r e c I p l t a b l e w a t e r ( H20 >.
I F ( < W < 1 5 > . E O . - 9 9 . 0 . O R . L I S T ( 1 5 , 2 > . E Q . - 9 9 . 0 ) . AND.COUNT.G E . 7)
* H2 0 = - 9 9
I F U W< I >. E Q . - 9 9 . 0 R . L I S T C I , 2 > . EO. - 9 9 ) . AND. COUNT. GE. 7 > H2 0 = - 9 9 .
I F ( C 0 U N T . G E . 9 ) H2 0 = - 9 9
O
70
Test for unreasonable d a ta .
I F < ( H 2 0 . N E . - 9 9 . 0 > . A N D . ( H2 0 . GT. 4 0 . OR. H 2 0 . LE. 0 . I ) )THEN
WRI TE( 6 , 7 0 ) H20
FORMAT!X , ' TROUBLE I PRECI P !TABLE WATER = ■ F 1 0 . 2 )
END IF
O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
RETURN
END
*******************************************************************
* SUBROUTINE ADVECTION *
************************
Th i s Is a s u b r o u t i n e t o c a l c u l a t e t h e r m a l a d v e c t l o n from
a r a o b s o u n d i n g b a s e d on t h e c h a n g e o f wi n d d i r e c t i o n a nd
magnitude with h e i g h t .
I t f i g u r e s t h e r m a l a d v e c t l o n In t wo l a y e r s
I t f i r s t f i g u r e s t h e r m a l a d v e c t l o n f o r t h e 8 5 0 t o 70 0 mb. l e v e l s ,
t h e n f o r t h e 7 0 0 t o 50 0 mb. l e v e l .
Then I t a v e r a g e s t h e v a l u e s
t h e t wo l a y e r s .
I t c a l c u l a t e s b o t h warm a n d c o l d a d v e c t l o n
e a c h l a y e r a n d a l s o an a b s o l u t e v a l u e f o r e a c h l a y e r .
VARIABLE DIRECTORY:
Mandat or y d a t a , w h e r e :
I = L e v e l ( a s d e f i n e d In t h e ma i n p r o g r a m )
U = P a r a m e t e r ( a s d e f i n e d In t h e ma i n p r o g r a m )
ADV =
The a b s o l u t e t h e r m a l a d v e c t l o n v a l u e .
COLD Cold a d v e c t l o n v a l u e .
WARM =
Warm a d v e c t l o n v a l u e .
LOW(U) Lower l e v e l p a r a m e t e r s o f e a c h l a y e r c o n s i d e r e d
HIGH(U) =
Up p e r l e v e l p a r a m e t e r s o f e a c h l a y e r c o n s i d e r e d
HALFWARM1I ) = Warm a d v e c t l o n f o r e a c h l a y e r .
HALFCOLD!I > = C o l d a d v e c t l o n f o r e a c h l a y e r .
HALDADV!I>
The a b s o l u t e v a l u e f o r a d v e c t l o n f o r e a c h l a y e r
H =
The t h i c k n e s s o f e a c h l a y e r .
TEMP =
Average t e m p e r a t u r e of t h e l a y e r .
ANGLE =
The r a d i a n m e a s u r e o f t h e a n g l e c r e a t e d by t h e
d i f f e r e n c e In w i n d d i r e c t i o n s b e t w e e n t h e b o t t o m
and t h e t o p o f e a c h l a y e r .
SHEAR =
The s h e a r v e c t o r b e t w e e n t h e t w o w i n d s .
TG =
Temperature g r a d i e n t .
XISO =
The c r o s s - i s o t h e r m c o m p o n e n t o f t h e w i n d .
SIGN =
Th e s i g n ( + o r - ) o f v a r i a b l e ANGLE.
MAN( I , J ) =
O O
SUBROUTINE ADVECTI ON<MAN,ADV,COLD,WARM)
INTEGER LOW( 5) , HI GH<5)
REAL H, HAL FADV( 2) , HALFCOLD( 2>, HAL FWARM!2 ) , MAN(3 , 5 )
LOGICAL SWITCH
Re a d l o w e r a n d u p p e r m a n d a t o r y v a l u e s
DO 5 1 = 1 , 2
SWITCH=.FALSE.
DO 4 U = I , 5
Into array s
LOW(U) AND
79
I LOW(J >= MAN<I , J )
4
n o n
n o n
n o n
n n n n
n n
n n n n n
n n
n n
C
HI GH(0 ) = MAN(1 + 1 , 0 )
Che c k f o r m i s s i n g d a t a a n d a s s i g n - 9 9 t o a d v e c t l o n s .
I F ( L 0 W ( I ) . E Q . - 9 9 . 0 . O R . L O V ( 2 ) . E Q . - 9 9 . £ T . O R . L0W(4 > . E Q . - 9 9 . 0 . O R .
*L 0 W( 5 > . E Q . - 9 9 . j e r . O R . H I G H ( l ) . E Q . - 9 9 . J 3 r . O R . H I G H ( 2 ) . E Q . - 9 9.J0r.OR.
,' H I G H ( 4 > . E O . - 9 9 . 0 . O R . H I G H ( 5 ) . E Q . - 9 9 . j 0 r>THEN
HALFADVI I >= - 9 9 . 0
HALFCOLDI I ) = -99.J0f
HALFWARMI I >= - 9 9 . 0
GO TO 5
END IF
Calculate thickness
H= HIGHC I J-LOWC I )
of
layer.
C a l c u l a t e a v erag e t e m p e r a t u r e of t h e
TEMP = CC LOWC 2 ) + HI GH( 2 > ) / 2 >+ 273
layer.
F i n d a n g l e c h a n g e o f wi n d a s yo u go u p .
I f t wo p o i n t s
s t a d d l e 3 6 0 d e g r e e s , I am In t r o u b l e , s o In t h a t c a s e , I
w i l l add 360 d e g r e e s t o t h o s e b e t we e n 0 and 90, t h e n
subtract to find the difference.
IFCCLOWC4 ) . G T . 2 7 0 . O R . HIGHC4 ) . G T . 2 7 0 ) . AND. CLOWC4 ) . L T . 9 0 . OR.
wHIGHC4 >. L T . 9 0 ) JTHEN
IFC LOWC 4 J . L T . 9 0 ) L O W( 4 J = LOWC 4 J+ 360
IFCHIGHC4 ) . L T . 9 0 JHIGHC4 J=HIGHC4 J +360
END IF
IANGLE=ABSC HIGHC 4 ) - L0 W( 4 J J
I F C !ANGLE. G T . 180JTHEN
I AMGLE= 3 6 0 - I ANGLE
SWITCH=.TRUE.
END IF
ANGLE=!ANGLE*. 0 1 7 4 5 3 3
C a l c u l a t e t h e s h e a r v e c t o r u s i n g t h e law o f c o s i n e s .
SHEAR = SQRTCLOWC 5 >WW2 + HI GH( 5 >ww2-< 2*L0WC 5 JwHIGHC5 J wCOSC ANGLE J J )
C a l c u l a t e t h e r m a l g r a d i e n t w h i c h I s Cs h e a r / t h I c k n e s s J w
C c o r l o l I s pa r a m e t e r wa v e r a g e t e m p e r a t u r e J / a c c e l e r a t I on
of g r a v i t y .
TG = CSHEAR*. 0 0 0 1 0 3 wTEMP J/C Hw9 . 8 J
C a l c u l a t e t h e c r o s s I s o th e rm component o f winds which
d e r i v e d f r o m t h e law o f s i n e s .
IFC SHEAR. EO. 0)SHEAR = SHEAR+.000001
XISO=C LOWC 5 JwHIGHC 5 JwCSI N( ANGLE) J J/SHEAR
C a l c u l a t e t h e t h e r m a l a d v e c t I on
C3 6 0 0 s e c o n d s In o n e h o u r J .
HALFADVC I J = TGwXI SOW3 6 0 0
Determine whether
with h eight, th e re
SIGN = HIGHC4 J-LOWC4 J
IFC SWITCH JSIGN = -SIGN
IFC SI GN. GT. 0JTHEN
HALFWARMC I J = HALFADVC
HALFCOLDC I >=0
END IF
IFC S I G N . LE. 0 JTHEN
HALFWARMC I >=0
HALFCOLDC I J = HALFADVC
END IF
Is
In d e g r e e s p e r h o u r .
a d v e c t I on I s war m o r c o l d .
I f wi nds back
I s c o l d a d v e c t I o n ; wa r m, v e e r .
IJ
IJ
80
O O
5
CONTINUE
A v e r a g e l ow a d v e c t I on a n d h i g h a d v e c t l o n .
ADV=< HALFADVt I >+ HALFADV(2 ) >/2
COLO = <HALFCOLD< I ) + HALFCOLD< 2 ) >/2
WARM=(HALFWARMt I ) + HALFWARM(2 ) ) / 2
I Ft HALFADVt I ) . EO. - 9 9 . J0T. OR . HAL FADVt 2 ) . E O. - 9 9 . 0 ) A D V = - 9 9 . 0
O O O O O O O O O O O
O O O
I Ft HALFCOLDt I ) . EQ. - 9 9 . 0 . OR. HALFCOLDt 2 ) . EQ. - 9 9 . 0 )COLD = - 9 9 . 0
IFtHALFWARMt I ) . EQ . - 9 9 . 0 . OR . HALFWARMt 2 ) . EQ. - 9 9 . 0 ) WARM=- 99 . 0
Test for unreasonable values.
I F t ( ADV. LT. 0. OR. ADV. GT. 10). AND. (ADV. NE. -99. 0))THEN
WRI TE( 6 , 7 )ADV
7 FORMATt X, 1TROUBLE I ADVECTION = ' , F 1 0 . 3 )
END IF
10 RETURN
END
* SUBROUTINE TO CALCULATE K-INDEX *
***********************************
O O O O O O O O O O O O O O O O O
SUBROUTINE STABLE( MAN, KI NDEX, SR READ >
Th I s s u b r o u t i n e c a l c u l a t e s K - I n d e x w h i c h I s :
85 0 mb. t e m p e r a t u r e - 500 mb. t e m p e r a t u r e + 85 0 mb. dew
p o i n t - 7 0 0 mb. dew p o i n t s p r e a d .
VARIABLE LI ST:
TEMP8 = 85 0 mb. t e m p e r a t u r e .
TEMP7 = 70 0 mb. t e m p e r a t u r e .
TEMPS = 5 0 0 mb. t e m p e r a t u r e .
RH8 = 85 0 mb. r e l a t i v e h u m i d i t y .
RH7 = 70 0 mb. r e l a t i v e h u m i d i t y .
KINDEX = K - I n d e x .
SPREAD = 850 mb. dew p o i n t s p r e a d .
ES8 = S a t u r a t i o n v a p o r p r e s s u r e a t 8 5 0 mb.
ES? = S a t u r a t i o n v a p o r p r e s s u r e a t 7 0 0 mb.
O
REAL MANt 3 , 5 I 1KINDEX
O O O
I F ( MANt 3 , 2 ) . E Q . - 9 9 . 0 . OR. MANt 2 , 3 > . E Q . - 9 9 . 0 . O R . M A N t 2 , 2 ) . E Q . - 9 9 . 0
* . OR. MANt I , 3 ) . E Q . - 9 9 . 0 . OR. MANt I , 2 I . EQ. - 9 9 . 0 ITHEN
KI NDEX=- 99. 0
SPREAD=-99
GO TO 30
END IF
Put a r r a y v a r i a b l e s
TEMP7 =MAN(2 , 2 I
TEMPS=MANt 3 , 2 1
RH? =MAN( 2 , 3 )
TEMPS=MANt1 , 2 )
RHS=MANt1 , 3 )
Into v a ria b le s .
O O O
81
O O
C a l c u l a t e s a t u r a t i o n v a p o r p r e s s u r e a t 8 5 0 a n d 70 0 mb.
E5 8 = 1 0 * * ( ( 9 . 2 8 6 - < 2 3 2 2 . 3 7 8 9 / « TEMP8 + 273 )> >)
E5 7 = 1 0 * * ( ( 9 . 2 8 6 - ( 2 3 2 2 . 3 7 8 9 / ( TEMP7 + 273 >) ) )
C a l c u l a t e dew p o i n t s .
O O
DP8 = < 2 3 2 2 . 3 7 8 9 / « 9 . 2 8 6 - A L O G 1 0 ( ( R H 8 / 1 0 0 ) * E S 8 > ) ) - 2 7 3
DP7 = ( 2 3 2 2 . 3 7 8 9 / ( 9 . 2 8 6 - ALOG1 0 ( ( R H 7 / 1 0 0 ) * E S 7 > ) > - 2 7 3
C a l c u l a t e K- I n d e x .
O O
KINDEX = TEMP8 - TEMP5 + DP8 - ( TE MP 7 - DP 7 >
O O O
SPREAD=TEMPS-DPS
O
10
Test for unreasonable values.
I F ( ( KI NDEX. GT. 1 0 0 . OR. KI NDEX. LT. - 1 0 0 >. AND. ( K I N D E X . N E . - 9 9 . 0 ) JTHEN
WRITE< 6 , 10)KINDEX
FORMAT(X , ' TROUBLE I KINDEX = ' , F 1 0 . 2 )
END IF
O
20
I F ( ( SPREAD. G T . 6 0 . OR. SPREAD. LT. - 0 . 5 ) . AND. ( SPREAD. NE . - 9 9 . 0>>THEN
WRI TE( 6 , 2 0 !SPREAD,TEMPS.RH8
FORMATf X,' TROUBLE I SPREAD = ' , F 1 0 . 2 / 9 X , ‘TEMP 8 = ' . F 1 0 . 2 /
*
SX1 1RHS = 1 , F 1 0 . 2 )
END IF
O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O o
30
RETURN
END
*************************************************************
* SUBROUTINE VORTICITY *
*********************************
Th I s s u b r o u t i n e c a l c u l a t e s r e l a t i v e v o r t I c I t y v a l u e s b a s e d
on t h e d i r e c t i o n a nd m a g n i t u d e o f t h e 500 mb w i n d v e c t o r s
f o r t h e t h r e e r a w l n s o n d e s t a t i o n s a s d e s c r i b e d I n t h e ma i n
program.
R e c a l l t h a t t h e ma i n p r o g r a m " r o t a t e s " t h e w i n d s
to the west to simplify c a l c u l a t i o n s .
Therefore, I refer
t o t h e s t a t i o n s by name a s I f t h e w i n d I s comm I ng f r o m t h e
west.
**********************
* VARIABLE DIRECTORY "
**********************
DIR= t h e a v e r a g e v e c t o r d i r e c t i o n t h e w i n d b l o w s .
D I R ( J ) = The d i r e c t i o n t h e wi n d b l o w s f r o m In c o m p a s s d i r e c t i o n s .
CHANGE= D i r e c t i o n c h a n g e b e t w e e n L a n d e r a n d B o i s e .
Positive
me a n s c o u n t e r c l o c k w i s e .
V#= V e l o c i t i e s a t s t a t i o n s In m e t e r s p e r s e c o n d .
AVEV= A v e r a g e w i n d v e l o c i t y o f L a n d e r a n d B o i s e .
ADI R= A v e r a g e w i n d d i r e c t i o n o f L a n d e r a n d B o i s e In c o m p a s s d i r e c t i o n
DCHANGE= A b s o l u t e v a l u e o f wi n d d i r e c t i o n c h a n g e b e t w e e n t h e
L a n d e r / B o i s e a v e r a g e a nd G r e a t F a l l s .
DV= The w i n d v e l o c i t y c h a n g e b e t w e e n t h e L a n d e r / B o i s e a v e r a g e
and G r e a t F a l l s .
THEDA= c o n v e r s i o n o f CHANGE t o r a d i a n s .
R= The r a d i u s o f c u r v a t u r e o f t h e w i n d s t r e a m l i n e .
Positive
me a n s c o u n t e r c l o c k w i s e .
82
O O
VORT= A b s o l u t e v o r t I c 1t y m u l t i p l i e d
by 1 0 * * 5 .
O O O O
SUBROUTINE VORTSUB( VORT, DI RI , VEL I , DI R 2 . VEL2 , DI R3 , VEL3, N, S , DI R >
INTEGER N, S
REAL V O R T , D I R l , V E L l , D I R 2 , V E L 2 , D I R 3 , V E L 3 , D I R
O O
T e s t I n d i v i d u a l wi n d s t o s e e I f t h e y s t r a d d l e 360 d e g r e e s
I f s o , a d d 3 6 0 d e g r e e s t o t h e o n e s b e t w e e n 0 a n d 90 d e g r e e s
a n d s u b t r a c t t o g e t c h a n g e In d I r e t c t I o n .
I F K D I R l .GT.270.OR.DIR2.GT.270.OR.OIR3.GT.270).AND.
*( D I R l . L T . 9 0 . OR. DI R 2 . L T . 9 0 . OR. DI R 3 . L T . 9 0 ) >THEN
I F ( D I R l.LT.90)DIRl=DIRl+360
I F ( D I R 2 . L T . 9 0 ) DI R2=DI R2+360
I F ( D I R 3 . L T . 9 0 ) DIR3 = DIR3 + 3 6 0
END IF
CHANGE=DIR3-DIR2
O O
Change k n o t s t o m e t e r s
V l = V E L l * . 514
V2 = VE L 2 * . 5 I 4
V3=VEL3*. 5 1 4
O O O O
Average v e l o c i t i e s
AVEV=CV3+V2 ) / 2
per second.
a t Lander and B o i s e .
O O O O O O O O
H e r e , I c a l c u l a t e t h e c h a n g e In v e l o c i t y b e t w e e n G r e a t
F a l l s and t h e a v e r a g e v e l o c i t y c a l c u l a t e d a b o v e , b u t I us e
onl y t h e component p a r a l l e l t o t h e s t r e a m l i n e f l o w .
ADIR=C DIR2 + D I R 3 ) / 2
DCHANGE=ABSCADIR-DIRl> * . 0 1 7 4 5 3 3
DV=AVEV-C CCOSCDCHANGE) >*V1>
I n t h i s m e t h o d , I f t h e wi n d b l o w s f r o m t h e w e s t ,
c o u n t e r c l o c k w i s e f l o w Is p o s i t i v e , b u t I f t h e wi nd bl ows
f r o m t h e e a s t In c o u n t e r c l o c k w i s e f l o w I m u s t c h a n g e t h e
s i g n s on CHANGE a n d DV t o g e t t h e m t o come o u t p o s i t i v e .
So, I t e s t f o r e a s t f l o w a n d a l s o f o r f l o w f r o m t h e o t h e r
t wo q u a d r a n t s w h i c h c o r r e s p o n d t o e a s t f l o w a f t e r r o t a t i o n .
O O
IFC CD I R . G T . 0 . A N D . D I R . L T . 6 0 ) . O R . CD I R . G T . 1 2 0 . A N D . D I R . L T . 180)
* . O R . CD I R . G T . 2 4 0 . AND. DI R. L T . 3 0 0 ) )THEN
CHANGE=-CHANGE
DV=-DV
END IF
O O
Change d e g r e e s t o r a d i a n s .
THEDA=.0174533*CHANGE
O O O O O
C alculate the radius of curvature of the stream line.
IFC THEDA.EO.0)THEDA=THEDA+.00001
R=SZTHEDA
C
10
And ( f i n a l l y ) c a l c u l a t e v o r t l c I t y . H e r e , I m u l t i p l y by
10**5 t o g e t a w o r k a b l e n u mb e r a n d I a d d 1 0 . 3 w h i c h I s t h e
v o r t l c I t y c a u s e d by t h e r o t a t i o n o f t h e e a r t h a t 45
degrees la titu d e .
VORT=C CCDVZN ) + ( AVEVZR) ) * 1 0 0 0 0 0 ) + 1 0 . 3
Test for unreasonable values.
IFC CVORT. GT. 2 0 . OR. VORT. LE . 2 ) . AND. CVORT. NE. - 9 9 . 0 ) !THEN
WRITEC 6 , 10) VORT, DI R
FORMAT CX, 1TROUBLE I VORTICITY =' , F 1 0 . 2 Z 9 X , ' D I R E C T I O N = ' , F I 0 . 2 )
END IF
RETURN
END
MONTANA STATE UNIVERSITY LIBRARIES
CM
CO
h-
Ill III I 100
linn 36274
111 III I I5I
3
//3 7 8
T V *
(Lop- 3.