S p ati al A n al y si s of Pr e ci pit ati o n a n d S n o w 

W at er E q ui v al e nt E xtr e m e s f or t h e C ol u m bi a 

Ri v er B a si n 

Bri a n E. S k a hill A n g el a M. D ur e n , L u ci a n a C u n h a a n d C hri s B a h n er J u n e 2 0 2 0

A p pr ov e d f or p u bli c r el e a s e; di stri b uti o n i s u nli mit e d. 
T h e U S A r m y E n gi n e e r R e s e a r c h a n d D e v el o p m e nt C e nt e r ( E R D C) s ol v es t h e 

n ati o n’s t o u g h est e n gi n e eri n g a n d e n vir o n m e nt al c h all e n g es. E R D C d e v el o ps i n n o v ati v e 

s ol uti o ns i n ci vil a n d milit ar y e n gi n e eri n g, g e os p ati al s ci e n c es, w at er r es o ur c es, a n d 

e n vir o n m e nt al s ci e n c es f or t h e Ar m y, t h e D e p art m e nt of D ef e ns e, ci vili a n a g e n ci es, a n d 

o ur ati o n’s p u blic g o o d. Fi n d o ut m or e at w w w. er d c. us a c e. ar m y. mil . 

T o s e ar c h f or ot h er t e c h ni c al r e p orts p u blis h e d b y E R D C, visit t h e E R D C 

o nli n e li br ar y at htt ps: / /er dcli br ary. o n. w orl dc at. or g / disc overy . 
E R D C C H L T R 2 0 1 0

J u n e 2 0 2 0

S p ati al A n al y si s of Pr e ci pit ati o n a n d S n o w 

W at er E q ui v al e nt E xtr e m e s f or t h e C ol u m bi a 

Ri v er B a si n 

Bri a n E. S k a hill 

C o a st al a n d Hy dr a uli c s L a b or at or y

U S Ar my E n gi n e er R e s e ar c h a n d D ev el o p m e nt C e nt er

3 9 0 9 H all s F err y R o a d

Vi c k s b ur g, M S 3 9 1 8 0 6 1 9 9

A n g el a M. D ur e n 

U S Ar my C or p s of E n gi n e er s, N ort h w e st er n Divi si o n 

P O B ox 2 8 7 0

P ortl a n d, Or e g o n 9 7 2 0 8 2 8 7 0

L u ci a n a C u n h a 

W E S T C o n s ult a nt s

1 0 1 P ar k s h or e Driv e

F ol s o m, C alif or ni a 9 5 6 3 0

C hri s B a h n er 

W E S T C o n s ult a nt s 

2 6 0 1 2 5t h St. S E

S uit e 4 5 0

S al e m, Or e g o n 9 7 3 0 2

Fi n al r e p ort 

A p pr ov e d f or p u bli c r el e a s e; di stri b uti o n i s u nli mit e d. 

Pr e p ar e d f or U S Ar my C or p s of E n gi n e er s, N ort h w e st er n Di vi si o n 

P ortl a n d, O R 9 7 2 0 8 2 8 7 0

U n d er F u n di n g A c ct C o d e U 4 3 6 3 3 1 2; A M S C O C o d e 0 3 1 3 9 8
E R D C / C H L T R 2 0 1 0 ii 

A b str a ct 

R e c e nt a d v a n c es i n t h e s p ati al st atisti cs of e xtr e m es a n d m o d el c ali br ati o n 

w er e a p pli e d t o d e v el o p a n d d eli v er ar e al e xc e e d a n c e esti m at es f or 

pr e ci pit ati o n ( P R E C), b y s e as o n a n d d ur ati o n, a n d s n o w w at er e q ui v al e nt 

( S W E), b y c o ol s e as o n m o nt h a n d f or t h e w at er y e ar, f or 7 5 8 d eli n e at e d 

s u b b asi ns of t h e C ol u m bi a Ri v er B asi n ( C R B) , w hi c h c orr es p o n d t o a n e w 

R B h y dr ol o g y m o d el w at ers h e d d eli n e ati o n. U n d erst a n di n g t h at f ut ur e 

U S Ar m y C or ps of E n gi n e ers, N ort h w est er n Di visi o n, missi o n 

r e q uir e m e nts m a y c h a n g e, pr oj e ct e x e c uti o n als o i n cl u d e d t h e 

d e v el o p m e nt a n d d eli v er y of a n a p pli c ati o n g ui d a n c e d o c u m e nt t o cr e di bl y 

c o m p ut e ar e al e xc e e d a n c e esti m at es, i n cl u di n g u n c ert ai nt y, f or P R E C or 

S W E f or a n y ar bitr ar y ar e a wit hi n t h e C R B. R, a fr e e s oft w ar e e n vir o n m e nt 

f or st atisti c al c o m p uti n g a n d gr a p hi cs (htt ps: / / w w w.r pr oject. or g / ), a n d Q GI S, a 

fr e e a n d o p e n s o ur c e g e o gr a p hi c i nf or m ati o n s yst e m 

htt ps: / / qgis. or g /e n /site /i n dex. ht ml ), w er e t h e pri m ar y t o ols us e d f or pr o d u ct 

d e v el o p m e nt a n d d eli v er y. T h e f oll o wi n g R s oft w ar e p ac k a g es w er e 

pri m aril y us e d d uri n g pr oj e ct e x e c uti o n: e v d, Gl m n et, m a ps, r ast er, r g d al, 

S D M T o ols, s p, a n d S p ati al E xtr e m es.

DI S C L AI M E R: T h e c o nt e nts of t his r e p ort ar e n ot t o b e us e d f or a d v ertisi n g, p u bli c ati o n, or pr o m oti o n al p ur p os es. 

Cit ati o n of tr a d e n a m es d o es n ot c o nstit ut e a n offi ci al e n d ors e m e nt or a p pr o v al of t h e us e of s u c h c o m m er ci al pr o d u cts. 

All pr o d u ct n a m es a n d tr a d e m ar ks cit e d ar e t h e pr o p ert y of t h eir r es p ecti v e o w n ers. T h e fi n di n gs of t his r e p ort ar e n ot t o 

b e c o nstr u e d as a n offi ci al D e p art m e nt of t h e Ar m y p ositi o n u nl ess s o d esi g n at e d b y ot h er a ut h oriz e d d oc u m e nts.

D E S T R O Y T HI S R E P O R T W H E N N O L O N G E R N E E D E D. D O N O T R E T U R N I T T O T H E O R I GI N A T O R.
E R D C / C H L T R 2 0 1 0 iii 

C o nt e nt s 

A b str a ct .................................................................................................................................... ii

Fi g ur es a n d T a bl es ...................................................................................................................

Pr ef a c e ....................................................................................................................................vii

I ntr o d u cti o n ......................................................................................................................

1. 1 B a c k gr o u n d ........................................................................................................ 

1. 2 O bj e ctiv e ............................................................................................................. 

1. 3 A p pr o a c h ............................................................................................................ 

D at a ...................................................................................................................................

2. 1 Pr e ci pit ati o n ( P R E C) d at a .................................................................................. 

2. 2 S n o w w at er e q uiv al e nt ( S W E) d at a ................................................................... 

2. 3 S p ati al c ov ari at e d at a ....................................................................................... 

2. 4 T e m p or al c ov ari at e d at a .................................................................................... 

M o d eli n g A n aly sis M et h o d ol o gy ....................................................................................

M o d el D ev el o p m e nt .......................................................................................................1 4

4. 1 P R E C ................................................................................................................. 1 4

4. 2 S W E .................................................................................................................. 1 7

R es ults .............................................................................................................................2 0

R ef er e n c es .............................................................................................................................2 1

A p p e n di x A: I n str u cti o n s o n H o w t o O bt ai n E x c e e d a n c e Pr o b a bility Esti m at es 

f or a S p e cifi c Ar e a ( e. g., s u b w at er s h e d) ....................................................................2 4

A p p e n di x B: Pr e ci pit ati o n D at a C oll e cti o n, Q u ality C o ntr ol, a n d Pr o c es si n g ...............3 0

A p p e n di x C: Sit e L o c ati o n s f or C ali br ati o n a n d V ali d ati o n of P R E C M o d els by 

S e a s o n a n d D ur ati o n .....................................................................................................4 4

A p p e n di x D: Sit e L o c ati o n s f or C ali br ati o n a n d V ali d ati o n of S W E M o d els by 

M o nt h a n d f or t h e W Y ....................................................................................................4 8

A p p e n di x E: C o ol S e a s o n P R E C P oi nt wis e 1 0 0 Y e ar R et ur n L ev els f or t h e C R B ........5 0

A p p e n di x F: W ar m S e a s o n P R E C P oi nt wis e 1 0 0 Y e ar R et ur n L ev els f or t h e 

C R B ..................................................................................................................................5 2

p p e n di x G: M o nt hly ( D e c e m e b er J u n e) a n d W Y S W E P oi nt wis e 1 0 0 Y e ar 

R et ur n L ev els f or t h e C R B .............................................................................................5 4

A p p e n di x H: C o ol S e a s o n P R E C M e a n Ar e al E x c e e d a n c e Pr o b a biliti es f or 1 0 0

Y e ar R et ur n P eri o d f or 7 5 8 D eli n e at e d S u b B a si n s of t h e C R B ...............................5 6
E R D C / C H L T R 2 0 1 0 i v 

A p p e n di x I: W ar m S e a s o n P R E C M e a n Ar e al E x c e e d a n c e Pr o b a biliti es f or 

1 0 0 Y e ar R et ur n P eri o d f or 7 5 8 D eli n e at e d S u b B a si n s of t h e C R B .......................5 8

A p p e n di x J: M o nt hly ( N ov e m b er J u n e) a n d W Y S W E M e a n Ar e al E x c e e d a n c e 

Pr o b a biliti es f or 1 0 0 Y e ar R et ur n P er i o d f or 7 5 8 D eli n e at e d S u b B a si n s of 

t h e C R B ...........................................................................................................................6 0

A cr o ny m s a n d A b br evi ati o n s ...............................................................................................6 2

R e p ort D o c u m e nt ati o n P a g e
E R D C / C H L T R 2 0 1 0 v 

Fi g ur e s a n d T a bl e s

Fi g ur e s

Fi g ur e . C R B P R E C d at a c oll ecti o n b o u n d ari es.......................................................................

Fi g ur e 2. Fiv e i n d e p e n d e nt r e aliz ati o ns of t h e S mit h, S c hl at h er, Br o w n R es nic k, 

a n d Extr e m al t pr oc ess es o n X = 0, 1 0 ( Ri b at et 2 0 1 5 )............................................................

Fi g ur e 3. O n e r e aliz ati o n of t h e S mit h pr oc ess wit h giv e n by t h e i d e ntity m atrix, 

Sc hl at h er pr oc ess wit h h = e x p h 2 1 . 5, a n d t h e extr e m al t pr oc ess, wit h = 5

a n d h = e x p h 2 1 . 5, o n a 2 5 0 x 2 5 0 gri d ( Ri b at et et al. 2 0 1 5 ). ..........................................

Fi g ur e . Fitt e d si m pl e m ax st a bl es f or P R E C by s e as o n a n d d ur ati o n ( h is 

n or m aliz e d dist a nc e). ..................................................................................................................1 5

Fi g ur e 5. C o m p aris o ns of t h e fitt e d tr e n d s urf ac e m o d el wit h c orr es p o n di n g at

sit e esti m at es f or ( a) 1 2 0 d ay d ur ati o n c o ol s e as o n a n d ( b) 1 0 d ay d ur ati o n w ar m 

s e as o n ( = G E V l oc ati o n; = G E V sc al e; = G E V s h a p e; M o d el = s p ati al m o d el; 

M L E = at sit e m axi m u m li k eli h o o d esti m at e). .........................................................................1 7

Fi g ur e . Fitt e d si m pl e m ax st a bl es f or S W E ( h is n or m aliz e d dist a nc e; M ay a n d 

W Y pl ots w er e i d e ntic al). ............................................................................................................1 8

Fi g ur e 7. C o m p aris o ns of t h e fitt e d tr e n d s urf ac e m o d el wit h c orr es p o n di n g at

sit e esti m at es f or M arc h S W E ( = G E V l oc ati o n; = G E V sc al e; = G E V s h a p e; 

M o d el = s p ati al m o d el; M L E = at sit e m axi m u m li k eli h o o d esti m at e). ................................1 9

Fi g ur e . S h a p efil e attri b ut e t a bl e f or ex a m pl e fil e.................................................................2 4

Fi g ur e . U nc ert ai nty as a f u ncti o n of t h e N SI M S...................................................................2 8

Fi g ur e 1 0. C o m p ut ati o n al ti m e (s ec o n ds) as a f u n cti o n of t h e b asi n ar e a (s q u ar e

mil e). ..............................................................................................................................................2 9

Fi g ur e 1 1 . C R B d at a c oll ecti o n b o u n d ari es. ............................................................................3 2

Fi g ur e 1 2 . C R B d at a c oll ecti o n b o u n d ari es a n d s e as o n ality of A M P....................................3 4

Fi g ur e 1 3 . P R E C ti m e s eri e s d o w nl o a d a n d r e f or m atti n g fl o wc h art....................................3 7

Fi g ur e 1 4 . St ati o n scr e e ni n g fl o wc h art.....................................................................................3 7

Fi g ur e 1 5. A M P pr oc essi n g a n d q u ality c o ntr ol fl o wc h art. .....................................................3 8

Fi g ur e 1 6 . Tr e n ds i n d aily A M P f or t h e c o ol a n d w ar m s e as o n b as e d o n li n e ar 

r e gr essi o n a n d M a n n K e n d all. ...................................................................................................4 3

Fi g ur e 1 7. D E M, st at e li n e, a n d P R E C o bs er v ati o n sit e l oc ati o n d at a by s e as o n 

a n d d ur ati o n (▪ =C ali br ati o n, = V ali d ati o n). ..............................................................................4 4

Fi g ur e 1 8. D E M, st at e li n e, a n d S W E o bs er v ati o n sit e l oc ati o n d at a by m o nt h a n d 

f or t h e W Y (▪ =C ali br ati o n, = V ali d ati o n). ...................................................................................4 8

Fi g ur e 1 9. C o ol s e as o n P R E C p oi nt wis e 1 0 0 y e ar r et ur n l ev els f or t h e C R B (f or 1- , 

2- , 3- , 5- , 1 0 , 3 0 , 6 0 , 9 0 , a n d 1 2 0 d ay d ur ati o ns) (v al u es i n milli m et ers). .....................5 0

i g ur e 2 0. W ar m s e as o n P R E C p oi nt wis e 1 0 0 y e ar r et ur n l ev els f or t h e C R B (f or 

1- , 2- , 3- , 5- , 1 0 , 3 0 , 6 0 , a n d 9 0 d ay d ur ati o ns) (v al u e s i n milli m et ers). ..........................5 2

Fi g ur e 2 1. M o nt hly ( D ec e m b er – J u n e) a n d W Y S W E p oi nt wis e 1 0 0 y e ar r et ur n 

l ev els f or t h e C R B (v al u es i n milli m et ers).................................................................................5 4
E R D C / C H L T R 2 0 1 0 vi

Fi g ur e 2 2. C o ol s e as o n P R E C m e a n ar e al exc e e d a nc e pr o b a biliti es f or 1 0 0 y e ar 

r et ur n p eri o d f or 7 5 8 d eli n e at e d s u b b asi ns of t h e C R B (f or 1- , 2- , 3- , 5- , 1 0 , 3 0 , 

6 0 , 9 0 , a n d 1 2 0 d ay d ur ati o ns) (v al u es i n milli m et ers). ......................................................5 6

Fi g ur e 2 . W ar m s e as o n P R E C m e a n ar e al exc e e d a nc e pr o b a biliti es f or 1 0 0 y e ar 

r et ur n p eri o d f or 7 5 8 d eli n e at e d s u b b asi ns of t h e C R B (f or 1- , 2- , 3- , 5- , 1 0 , 3 0 , 

6 0 , a n d 9 0 d ay d ur ati o ns) (v al u es i n milli m et ers). ................................................................5 8

Fi g ur e 2 4 . M o nt hly ( N ov e m b er – J u n e) a n d W Y S W E m e a n ar e al exc e e d a nc e 

pr o b a biliti es f or 1 0 0 y e ar r et ur n p eri o d f or 7 5 8 d eli n e at e d s u b b asi ns of t h e C R B 

(v al u es i n milli m et ers).................................................................................................................6 0

T a bl e s

Ta bl e . S u m m ary listi n g of t h e c oll ect e d a n d pr oc ess e d c ov ari at e d at as ets......................

Ta bl e . N u m b er of sit es us e d f or c ali br ati o n a n d v ali d ati o n of P R E C m o d els...................1 5

Ta bl e 3. C orr el ati o n of t h e fitt e d c o ol s e as o n tr e n d s urf ac e m o d els, by d ur ati o n, 

wit h t h eir at sit e esti m at es f or t h e c ali br ati o n a n d v ali d ati o n sit es. .....................................1 6

Ta bl e 4. C orr el ati o n of t h e fitt e d w ar m s e as o n tr e n d s urf ac e m o d els, by d ur ati o n , 

wit h t h eir at sit e esti m at es f or t h e c ali br ati o n a n d v ali d ati o n sit es. .....................................1 6

Ta bl e . N u m b er of sit es us e d f or c ali br ati o n a n d v ali d ati o n of S W E m o d els. ...................1 8

Ta bl e . C orr el ati o n of t h e fitt e d S W E tr e n d s urf ac e m o d els wit h t h eir at sit e 

esti m at es f or t h e c ali br ati o n a n d v ali d ati o n sit es. ..................................................................1 9
E R D C / C H L T R 2 0 1 0 vii

Pr ef a c e

T his st u d y w as c o n d u ct e d f or t h e U S Ar m y C or ps of E n gi n e ers, 

N ort h w est er n Di visi o n, u n d er F u n di n g A c c o u nt C o d e U 4 3 6 3 31 2, A M S C O 

C o d e 0 31 3 9 8. 

T h e w or k w as p erf or m e d b y t h e H y dr ol o gi c S yst e ms Br a n c h of t h e Fl o o d 

a n d St or m Pr ot e cti o n Di visi o n , U S Ar m y E n gi n e er R es e ar c h a n d 

D e v el o p m e nt C e nt er , C o ast al a n d H y dr a uli cs L a b or at or y ( E R D C- CH L ). 

At t h e ti m e of p u bli c ati o n of t his r e p ort , Dr. H w ai Pi n g C h e n g w as 

Br a n c h C hi ef; Dr. C ar y A. T al b ot w as Di vis i o n C hi ef; a n d Dr. J uli e R os ati

w as t h e T e c h ni c al Dir e ct or f or Fl o o d Ris k M a n a g e m e nt . T h e D e p ut y 

Dir e ct or of E R D C - C H L w as Mr. J effr e y R. E c kst ei n , a n d t h e Dir e ct or w as

Dr. T y V. W a msl e y . 

T h e C o m m a n d er of E R D C w as C O L T er es a A. S c hl oss er , a n d t h e Dir e ct or 

w as Dr. D a vi d W. Pitt m a n . 
E R D C / C H L T R 2 0 1 0 1 

I ntr o d u cti o n

1. 1 B a c k gr o u n d

T h e N ort h w est er n Di visi o n ( N W D) of t h e U S Ar m y C or ps of E n gi n e ers 

( U S A C E) is d e v el o pi n g a n e w h y dr ol o gi c m o d eli n g s yst e m f or t h e 

C ol u m bi a Ri v er B asi n ( C R B). T h e n e w C R B h y dr ol o gi c m o d eli n g s yst e m 

c o nsists of i nt e gr at e d m o d els, st u di es, a n d i nfr astr u ct ur e t o s u p p ort t h e 

w at er m a n a g e m e nt, d a m a n d l e v e e s af et y, a n d pl a n ni n g missi o ns of t h e 

U S A C E. T h e o bj e cti v e of t h e C R B h y dr ol o g y st u d i es is t o pr o vi d e a 

c o h esi v e h y dr ol o gi c d at as et a n d s yst e m t h at s u p p ort all t hr e e pr o gr a ms 

( w at er m a n a g e m e nt, d a m a n d l e v e e s af et y, a n d pl a n ni n g) a n d, t o t h e 

e xt e nt pr acti c a bl e, mi ni miz es d u pli c ati v e a n d / or di v er gi n g m et h o d ol o gi es, 

m o d els, d at as ets, a n d r es ults. T h e t e c h ni c al a p pr o ac h of t h e C R B 

h y dr ol o g y st u di es i n cl u d es s e v e n k e y t as ks, a n d o n e i n v ol v es t h e 

d e v el o p m e nt of r e gi o n al fr e q u e n c y a n al ysis ( R F A) esti m at es f or 

pr e ci pit ati o n ( P R E C) a n d s n o w w at er e q ui v al e nt ( S W E) d at a f or t h e C R B. 

T h e N ati o n al W e at h er S er vi c e pr o vi d es p oi nt pr e ci pit ati o n fr e q u e n c y 

esti m at es f or t h e U nit e d t at es; h o w e v er, c urr e nt u p d at e d esti m at es ar e 

u n a v ail a bl e f or t h e st at es of W as hi n gt o n, Or e g o n, I d a h o, M o nt a n a, a n d 

W y o mi n g ( htt ps: / / h dsc. n ws. n o a a.g ov / h dsc / pf ds /i n dex. ht ml ). I n a d diti o n, 

a p pr o xi m at el y 3 9, 7 0 0 mi of t h e C R B 2 5 8, 0 0 0 mi 2 t ot al dr ai n a g e ar e a als o 

i nt ers e cts t h e C a n a di a n pr o vi n c e of Britis h C ol u m bi a. M or e o v er, t h e 

d e pl o y m e nt of a n L-m o m e nts b as e d R F A r e q uir es t h e st u d y ar e a t o b e 

d e c o m p os e d i nt o h o m o g e n e o us s u b r e gi o ns, a n d t his is pr o bl e m ati c al f or 

t h e C R B h y dr ol o g y st u di es d u e t o t h e C R B b asi n si z e a n d t h e 

p h ysi o gr a p hi c a n d cli m at ol o gi c al v ari a bilit y t h at e xists wit hi n t h e C R B . 

 

U S A C E ( U S Ar my C or p s of E n gi n e er s). U n p u bli s h e d dr aft . C ol u m bi a Riv er B a si n Hy dr ol o gy St u di e s . 

A n g el a D ur e n, P. E., P. H., U S A C E N W P E C - H-H Y, Te c h ni c al L e a d, a n d P et e Di c k er s o n, P. E., P. H., D. W R E, 

U S A C E N W D, S e ni or A dvi s or. Pr e p ar e d f or U S Ar my C or p s of E n gi n e er s, N o rt h w e st Divi si o n, J uly.

F or a f ull li st of t h e s p ell e d o ut f or m s of t h e u nit s of m e a s ur e u s e d i n t hi s d o c u m e nt, pl e a s e r ef er t o U S 

G ov er n m e nt P u bli s hi n g Offi c e Styl e M a n u al , 3 1 st e d. ( W a s hi n gt o n, D C: U S G ov er n m e nt P u bli s hi n g 

Offi c e, 2 0 1 6), 2 4 8 - 5 2, htt ps: / / w w w.g ovi nf o.g ov /c o nte nt / pkg / G P O STYL E M A N U AL 2 0 1 6 / p df / G P O

STYL E M A N U AL 2 0 1 6. p df . 

F or a f ull li st of t h e u nit c o nv er si o n s u s e d i n t hi s d o c u m e nt, pl e a s e r ef er t o U S G ov er n m e nt P u bli s hi n g 

Offi c e Styl e M a n u al , 3 1 st e d. ( W a s hi n gt o n, D C: U S G ov er n m e nt P u bli s hi n g Offi c e, 2 0 1 6), 3 4 5- 7, 

htt ps: / / w w w.g ovi nf o.gov /c o nte nt / pkg / G P O STYL E M A N U AL 2 0 1 6 / p df / G P O STYL E M A N U AL 2 0 1 6. p df . 

E R D C / C H L T R 2 0 1 0 3 

1. 3 A p pr o a c h

E ac h m a x st a bl e pr o c ess m o d eli n g a n al ysis i n v ol v e d t h e esti m ati o n of 

ar e al b as e d e x c e e d a n c e pr o b a biliti es f or 7 5 8 d eli n e at e d s u b b asi ns of t h e 

C R B, w hi c h c orr es p o n ds t o t h e n e w C R B h y dr ol o g y m o d el w at ers h e d 

d eli n e ati o n. F ut ur e U S A C E N W D missi o n m a y r e q uir e t h e e v al u ati o n of 

E q u ati o n 1 f or s u b ar e as diff er e nt fr o m t h e n ot e d C R B h y dr ol o g y m o d el 

at ers h e d d eli n e ati o n. A n a p pli c ati o n g ui d a n c e d o c u m e nt w as d e v el o p e d 

t o s u p p ort t h e c o m p ut ati o n of E q u ati o n 1 f or a n y ar bitr ar y ar e a wit hi n t h e 

C R B (s e e A p p e n di x A: I nstr u cti o ns o n H o w t o O bt ai n E xc e e d a n c e 

Pr o b a bilit y Esti m at es f or a S p e cifi c Ar e a e. g., s u b w at ers h e d ]). 

T h e r e m ai n d er of t his r e p ort s u m m ariz es t h e d at a us e d, t h e m et h o d ol o g y 

e m pl o y e d f or t h e s p ati al a n al ysis of e xtr e m e P R E C a n d S W E f or t h e C R B, 

d et ails of t h e m o d eli n g a n al ys es f or P R E C a n d S W E, a n d t h e s p e cifi c 

pr o d u cts d e v el o p e d a n d d eli v er e d t o t h e U S A C E N W D t o s u cc essf ull y 

s atisf y t h e R F A t as k r e q uir e m e nts of t h e C R B h y dr ol o g y st u di es.
E R D C / C H L T R 2 0 1 0 4 

D at a

St u d y d at a r e q uir e m e nts i n cl u d e d o bs er v e d P R E C a n d S W E ti m e s eri es 

d at a ass o ci at e d wit h g a g e sit es l o c at e d wit hi n a n d / or s urr o u n di n g t h e C R B 

a n d gri d d e d c o v ari at es t h at c h ar a ct eriz e t h e cli m at ol o g y a n d p h ysi o gr a p h y 

of t h e C R B. T h e S W E m o d eli n g a n al ys es als o c o nsi d er e d t e m p or al 

c o v ari at es — i n p arti c ul ar, cli m at e i n di c es t h at h a v e pr e vi o usl y b e e n 

s h o w n t o i nfl u e n c e t e m p er at ur e a n d pr e ci pit ati o n acr oss t h e C R B ( s e e 

B e c k ers et al. 2 01 6 ]; P ytl a k et al. 2 01 6 ]; a n d r ef er e n c es cit e d wit hi n ).

2. 1 Pr e ci pit ati o n ( P R E C) dat a 

R E C ti m e s eri es d at a w er e c oll e ct e d f or g a g e st ati o ns l o c at e d wit hi n t h e 

C R B a n d als o f or a b o x r e gi o n s urr o u n di n g t h e C R B as is s h o w n in Fi g ur e 

1. Ti m e s eri es of a n n u al m a xi m u m pr e ci pit ati o n ( A M P) w er e pr o c ess e d f or 

d efi n e d w ar m ” ( M a y t o S e pt e m b er) a n d c o ol ” ( Oct o b er t o A pril) s e as o ns 

f or t h e f oll o wi n g d ur ati o ns (1 , 2 , 3 , 5 , 1 0 , 3 0 , 6 0 , 9 0- a n d 1 2 0 d a y). A 

d et ail e d d es cri pti o n of t h e pr e ci pit ati o n d at a c oll e cti o n a n d pr o c essi n g 

pr o c e d ur e is pr o vi d e d i n A p p e n di x B: Pr e ci pit ati o n D at a C oll e cti o n, 

Q u alit y C o ntr ol a n d Pr o c essi n g . 

Fi g ur e C R B P R E C d at a c oll e cti o n b o u n d ari e s
E R D C / C H L T R 2 0 1 0 5 

2. 2 n o w at er q ui v al e nt ( S W E) dat a

W E ti m e s eri es d at a w er e c oll e ct e d fr o m t h e S n o w T el e m etr y ( S N O T E L)

n et w or k m ai nt ai n e d b y t h e U S D e p art m e nt of A gri c ult ur e N at ur al 

R es o ur c es C o ns er v ati o n S er vi c e , N ati o n al W at er a n d Cli m at e C e nt er 

htt ps: / / w w w. wcc. nrcs. us d a.g ov /s n o w / a n d a ut o m at e d s n o w w e at h er st ati o ns ’ d at a 

fr o m C a n a d a ( tt ps: / / w w w 2.g ov. bc.c a /g ov /c o nte nt /e nvir o n me nt / air l a n d w ater / w ater / w ater

scie nce d at a / w ater d at a t o ols /s n o w s urvey d at a / a ut o m ate d s n o w we at her st ati o n d at a ). W hil e 

ot h er s o ur c es of S W E d at a d o e xist i n t h e U nit e d t at es a n d C a n a d a e. g., 

s n o w c o urs e sit es , t h eir o bs er v ati o n r e p orti n g fr e q u e n c y w as i d e ntifi e d t o 

b e i n a d e q u at e t o s u p p ort e xtr e m al a n al ys es.

2. 3 S p ati al c ov ari at e d at a

Gri d d e d d at as ets of p h ysi o gr a p hi c a n d cli m at ol o gi c al c o v ari at es w er e 

c oll e ct e d a n d pr o c ess e d t o s u p p ort tr e n d s urf ac e m o d eli n g of e xtr e m e 

P R E C, b y d ur ati o n a n d s e as o n, a n d S W E, b y c o ol s e as o n m o nt h or f or t h e 

W Y . T a bl e 1 is a s u m m ar y listi n g of t h e c oll e cte d a n d pr o c ess e d gri d d e d 

c o v ari at e d at as ets a n d t h eir s o ur c es. M o nt hl y, a n n u al, a n d s e as o n al 

pr o d u cts w er e c oll e ct e d a n d pr o c ess e d f or t h e cli m at ol o g y d at as ets list e d 

i n T a bl e 1 ( P R E CI P, T M E A N, T M A X, T MI N, D L W R F, D S W R F, E WI N D, 

N WI N D ). E ac h c o v ari at e d at as et w as a g gr e g at e d or r es a m pl e d t o a 3 0 ar c 

s e c o n d gri d c ell r es ol uti o n t o s u p p ort t h e s p ati al m o d eli n g a n al ysis. E ac h 

s p ati al a n al ysis f or P R E C, b y s e as o n a n d d ur ati o n, a n d S W E, b y c o ol 

s e as o n m o nt h a n d f or t h e W Y , us e d n or m aliz e d s p ati al c o v ari at es.

T a bl e S u m m ary li sti n g of t h e c oll e ct e d a n d pr o c e s s e d c ov ari at e d at a et s . 

C ov ari at e s D e s cri pti o n R e s ol uti o n

S o ur c e: Cli m at e d at a f or W e st er n N ort h A m eri c a ( htt ps: / /sites. u al bert a.c a / ~ a h a m a n n / d at a. ht ml ) 

P R E CI P ot al pr e ci pit ati o n

1 k m ( L a m b ert 

C o nf or m al 

C o ni c 

pr oj e cti o n)

T M A X M axi m u m t e m p er at ur e

T MI N Mi ni m u m t e m p er at ur e

T M E A N 0. 5 *( T M A X + T MI N)

P A S Pr e ci pit ati o n a s s n o w

S o ur c e: N ati o n al el ev ati o n d at a s et ( M o s ai c of d e gr e e til e s U S G e ol o gi c al S ur v ey

X, Y, Z (fr o m di git al 

el ev ati o n m o d el 

D E M ) 

C o or di n at e s a n d el ev ati o n f or e a c h r a st er gri d c ell 1 ar c s e c o n d
E R D C / C H L T R 2 0 1 0 6 

C ov ari at e s D e s cri pti o n R e s ol uti o n

S o ur c e: U s e of t h e G e o gr a p hi c R e s o ur c e s A n aly si s S u p p ort Sy st e m G e o gr a p hi c I nf or m ati o n 

Sy st e m , f u n cti o n r. sl o p e. a s p e ct. (htt ps: / /gr ass. osge o. org /gr ass 7 0 / m a n u als /r.sl o pe. as pect. ht ml ) 

S L O P E Sl o p e

3 0 arc s e c o n d s

A S P E C T A s p e ct

P R O FI L E 

C U R V AT U R E Pr ofil e c ur v at ur e

T A N G E N TI A L 

C U R V AT U R E T a n g e nti al c ur v at ur e

S o ur c e: Tr e e c a n o py c ov er cir c a 2 0 1 0 ( htt ps: / /l a n dc over. usgs.g ov /glc /Tree C over Descri pti o n A n d D o w nl o a ds. p h p

T R E E C O V E R er c e nt m axi m u m ( p e a k of gr o wi n g s e a s o n) tr e e c a n o py c ov er 1 ar c s e c o n d

S o ur c e: N ort h A m eri c a n L a n d D at a As si mil ati o n Sy st e m

htt ps: / / hy dr o 1.ges disc.e os dis. n as a.g ov / d at a / NL D A S / R E A D M E. NL D A S 2. p df ) 

D L W R F D o w n w ar d l o n g w av e r a di ati o n fl ux . 1 2 5 d e gr e e D S W R F D o w n w ar d s h ort w av e r a di ati o n fl ux

S o ur c e: N ati o n al C e nt er s f or E nvir o n m e nt al Pr e di cti o n Cli m at e F or e c a st Sy st e m R e a n aly si s d at a s et

htt ps: / / a p p.cli m atee ngi ne. or g /)

E WI N D E a st w ar d wi n d c o m p o n e nt . 2 d e gr e e N WI N D N ort h w ar d wi n d c o m p o n e nt

2. 4 T e m p or al c ov ari at e d at a

T e m p or al c o v ari at e d at a w er e c oll e ct e d a n d pr o c ess e d t o s u p p ort tr e n d 

s urf ac e m o d eli n g of e xtr e m e S W E b y m o nt h a n d f or t h e W Y . Ei g ht cli m at e 

i n di c es w er e c o nsi d er e d, viz., t h e Ar cti c Os cill ati o n 

htt ps: / / w w w. nc dc. n o a a.g ov /telec o n necti o ns / a o / ), Oc e a ni c Ni n o I n d e x 

htt p: / / origi n.c pc. nce p. n o a a.g ov / pr o d ucts / a n alysis _ m o nit ori ng /e ns ost u ff / O NI _v 5. p h p), 

ulti v ari at e El Ni n o S o ut h er n Os cill ati o n i n d e x

htt ps: / / w w w.esrl. n o a a.g ov / ps d /e ns o / mei / ), P acifi c N ort h A m eri c a p att er n 

htt ps: / / w w w. nc dc. n o a a.g ov /telec o n necti o ns / p n a / ), P acifi c D e c a d al Os cill ati o n 

htt ps: / / w w w. nc dc. n o a a.g ov /telec o n necti o ns / p d o / ), S o ut h er n Os cill ati o n I n d e x 

htt ps: / / w w w. nc dc. n o a a.g ov /telec o n necti o ns /e ns o /i n dic at ors /s oi / ), Q u asi Bi e n ni al 

Os cill ati o n ( htt ps: / / w w w.esrl. n o a a.g ov / ps d / d at a /c orrel ati o n / q b o. d at a ), a n d t h e E ast

N ort h P acifi c I n d e x ( ft p: / /ft p.c pc. nce p. n o a a.g ov / w d 5 2 dg / d at a /i n dices /e p n p _i n dex.ti m) (s e e 

B e c k ers et al. 2 01 6 ]; P ytl a k et al. 2 01 6 ]; a n d r ef er e n c es cit e d wit hi n ).






E R D C / C H L T R 2 0 1 0 1 3

T h e m a x st a bl e pr o c ess d e pl o y m e nt h er ei n w as a t w o st e p pr o c e d ur e 

i n v ol vi n g tr e n d s urf ac e a n d si m pl e m a x st a bl e pr oc ess m o d el s el e cti o n, wit h 

e ac h st e p ass u mi n g i n d e p e n d e n c e a m o n g t h e e xtr e m es a n d fi x e d m ar gi ns, 

r es p ecti v el y. T h e r es ults fr o m t h es e t w o s e p ar at e st e ps w er e s u bs e q u e ntl y 

c o m bi n e d t o b uil d a g e n er al m a x st a bl e pr o c ess w h er ei n t h e tr e n d s urf ac e 

a n d d e p e n d e n c e p ar a m et ers w er e si m ult a n e o usl y fitt e d. T h er e aft er, 

p oi nt wis e a n d ar e al b as e d r et ur n l e v els c a n b e c o m p ut e d f or a n y ar bitr ar y 

ar e a wit hi n t h e m o d el d o m ai n. Ar e al b as e d e xc e e d a n c es ar e o bt ai n e d b y 

si m ul ati n g m ulti pl e i n d e p e n d e nt c o pi es of t h e fitt e d m a x st abl e pr oc ess 

( Ri b at et 2 0 0 9, 2 01 3 , 2 01 5 , 2 01 7). Sc hl at h er ( 2 0 0 2) i ntr o d u c e d t h e b asis f or 

si m ul ati n g a n i n d e p e n d e nt r e aliz ati o n of a si m pl e m a x st a bl e pr o c ess wit h 

o n o nl y a fi nit e n u m b er of r e plic at es.
E R D C / C H L T R 2 0 1 0 1 4

M o d el D e v el o p m e nt

T h e d e v el o p m e nt of a m a x st a bl e pr o c ess m o d el f or P R E C or S W E 

i n v ol v es t w o k e y st e ps: 

1. acc o u nti n g f or t h e i nt er sit e d e p e n d e n c e a m o n g t h e e xtr e m e d at a (i. e., 

si m pl e m a x st a bl e m o d el s el e cti o n)

2. c h ar a ct erizi n g t h e s p ati al /s p ati ot e m p or al v ari ati o n of t h e e xtr e m e d at a 

(i. e., tr e n d s urf ac e m o d el sel e cti o n). 

T his s e cti o n hi g hli g hts s ali e nt f e at ur es ass o ci at e d wit h t h es e t w o st e ps 

n e c ess ar y f or t h e d e pl o ym e nt of e ac h m a x st a bl e pr o c ess m o d el f or P R E C 

b y s e as o n a n d d ur ati o n a n d f or S W E b y c o ol s e as o n m o nt h or f or t h e W Y . 

4. 1 P R E C

T a bl e 2 lists t h e n u m b er of o bs er v ati o n sit es t h at w er e us e d f or t h e 

c ali br ati o n a n d v ali d ati o n of e ac h P R E C m o d el b y s e as o n a n d d ur ati o n. 

Fi g ur e 1 7 d e pi cts t h e l o c ati o ns of t h e c ali br ati o n a n d v ali d ati o n sit es t h at 

w er e us e d f or e a c h P R E C m o d el b y s e as o n a n d d ur ati o n (s e e A p p e n d i x C: 

Sit e o c ati o ns f or ali br ati o n a n d ali d ati o n of P R E C o d els b y e as o n 

a n d ur ati o n ). 

o c ati o n (X a n d Y , X Y, el e v ati o n, m o nt hl y, a n n u al, a n d s e as o n al 

s u m m ari es of t h e ei g ht gri d d e d cli m at ol o gi c al d at a s ets s u m m ariz e d i n 

T a bl e 1 ( e xcl u di n g pr e ci pit ati o n as s n o w), a n d all of t h eir s q u ar es, 

c o nstit ut e t h e e ntir e s et of 2 3 2 c o v ari a bl es c o nsi d er e d d uri n g t h e tr e n d 

s urf ac e m o d eli n g a n al ysis f or e a c h P R E C m o d el d e pl o y m e nt. 

Fi g ur e 4 d e pi cts pl ots of t h e e xtr e m al c o effi ci e nt f u n cti o n ( c hl at h er a n d 

T a w n 2 0 0 3 ), a s u c ci n ct m e as ur e of s p ati al d e p e n d e n c e as a f u n cti o n of 

dist a n c e, f or e ac h of t h e fitt e d si m pl e m a x st a bl e m o d els f or P R E C b y 

d ur ati o n a n d s e as o n. 

T a bl e 3 a n d T a bl e 4 list b y d ur ati o n c o m p ut e d c orr el ati o ns f or e ac h of t h e 

fitt e d P R E C tr e n d s urf ac e m o d els wit h t h eir at sit e esti m at es f or c o ol a n d 

w ar m s e as o n, r es p e cti v el y. F or p ers p e cti v e, Fi g ur e 5 i n cl u d es s c att er pl ots , 

o nl y f or t h e c ali br ati o n sit es, w hi c h c o m p ar e t w o of t h e fitt e d tr e n d s urf ac e 

m o d els wit h t h eir at sit e esti m at es. 
E R D C / C H L T R 2 0 1 0 1 5

T a bl e N u m b er of sit e s u s e d f or c ali br ati o n a n d v ali d ati o n of P R E C m o d el s.

C o ol S e a s o n P R E C W ar m S e a s o n P R E C

 C ali br ati o n V ali d ati o n C ali br ati o n V ali d ati o n

 C o u nt C o u nt

d ay 1 1 3 9 1 2 6 d ay 1 1 5 9 1 2 8

d ay 1 1 3 1 1 2 5 d ay 1 1 6 2 1 2 9

d ay 1 1 3 4 1 2 6 d ay 1 1 6 3 1 2 9

d ay 1 1 2 6 1 2 5 d ay 1 1 5 7 1 2 8

1 0 d ay 1 1 2 8 1 2 5 1 0 d ay 1 1 5 6 1 2 8

3 0 d ay 1 1 2 3 1 2 4 3 0 d ay 1 1 2 1 1 2 4

6 0 d ay 1 1 0 6 1 2 2 6 0 d ay 8 3 1 9 2

9 0 d ay 1 0 7 2 1 1 9 9 0 d ay 3 2 8 3 6

1 2 0 d ay 9 6 6 1 0 7 1 2 0 d ay N A N A

Fi g ur e Fitt e d si m pl e m ax st a bl e s f or P R E C by s e a s o n a n d d ur ati o n ( h i s n or m aliz e d di st a n c e)
E R D C / C H L T R 2 0 1 0 1 6

T a bl e C orr el ati o n of t h e fitt e d c o ol s e a s o n t r e n d s urf a c e m o d els, by 

d ur ati o n, wit h t h eir at sit e e sti m at e s f or t h e c ali br ati o n a n d 

v ali d ati o n sit e s.

C o ol S e a s o n P R E C

C ali br ati o n V ali d ati o n

 L o c ati o n S c al e S h a p e L o c ati o n S c al e S h a p e

d ay 0. 9 7 2 0. 9 3 1 0. 2 3 1 0. 9 5 7 0. 8 5 1 0. 2 6 1

d ay 0. 9 7 5 0. 9 3 0 0. 2 8 1 0. 9 7 9 0. 9 4 5 0. 1 1 6

d ay 0. 9 7 6 0. 9 3 3 0. 1 9 6 0. 9 7 5 0. 9 4 0 0. 1 0 8

d ay 0. 9 7 8 0. 9 3 1 0. 2 0 6 0. 9 8 3 0. 9 5 2 0. 0 5 1

1 0 d ay 0. 9 8 1 0. 9 4 0 0. 2 6 7 0. 9 8 6 0. 9 3 7 0. 4 0 3

3 0 d ay 0. 9 8 1 0. 9 5 4 0. 2 8 1 0. 9 8 2 0. 9 4 0 0. 3 5 6

6 0 d ay 0. 9 8 1 0. 9 5 5 0. 2 7 5 0. 9 8 5 0. 9 6 1 0. 4 2 6

9 0 d ay 0. 9 8 1 0. 9 5 3 0. 1 9 7 0. 9 8 6 0. 9 5 0 0. 1 5 0

1 2 0 d ay 0. 9 8 1 0. 9 5 1 0. 0 0 8 0. 9 7 8 0. 9 6 1 0. 0 5 6

T a bl e C orr el ati o n of t h e fitt e d w ar m s e a s o n t r e n d s urf a c e m o d els, 

by d ur ati o n, wit h t h eir at sit e e sti m at e s f or t h e c ali br ati o n a n d 

v ali d ati o n sit e s.

W ar m S e a s o n P R E C

C ali br ati o n V ali d ati o n

 L o c ati o n S c al e S h a p e L o c ati o n S c al e S h a p e

1- d ay 0. 9 3 8 0. 8 3 6 0. 2 2 7 0. 9 3 8 0. 8 4 1 0. 2 1 2

2- d ay 0. 9 4 3 0. 8 5 8 0. 2 2 8 0. 9 3 3 0. 8 5 4 0. 1 9 0

3- d ay 0. 9 5 3 0. 8 8 9 0. 2 8 1 0. 9 5 2 0. 8 5 4 0. 4 0 9

5- d ay 0. 9 5 0 0. 8 9 7 0. 2 5 7 0. 9 3 7 0. 8 7 9 0. 1 2 4

1 0 d ay 0. 9 5 5 0. 9 0 4 0. 2 5 5 0. 9 5 5 0. 9 0 8 0. 1 7 1

3 0 d ay 0. 9 6 4 0. 9 2 2 0. 2 8 4 0. 9 6 1 0. 9 0 7 0. 4 1 0

6 0 d ay 0. 9 6 6 0. 8 9 2 0. 1 4 5 0. 9 4 4 0. 8 6 0 0. 2 4 3

9 0 d ay 0. 9 6 9 0. 8 7 6 0. 2 6 2 0. 9 7 0 0. 8 3 2 0. 1 1 6

1 2 0 d ay N A N A N A N A N A N A
E R D C / C H L T R 2 0 1 0 1 7

Fi g ur e C o m p ari s o n s of t h e fitt e d tr e n d s urf a c e m o d el wit h c orr e s p o n di n g at sit e 

e sti m at e s f or ( a) 1 2 0 d ay d ur ati o n c o ol s e a s o n a n d ( b) 1 0 d ay d ur ati o n w ar m s e a s o n 

= G E V l o c ati o n; = G E V s c al e; = G E V s h a p e; M o d el = s p ati al m o d el; M L E = at sit e 

m axi m u m li k eli h o o d e sti m at e

( a) ( b) 

4. 2 W E

T a bl e 5 lists t h e n u m b er of o bs er v ati o n sit es t h at w er e us e d f or t h e 

c ali br ati o n a n d v ali d ati o n of e ac h S W E m o d el b y m o nt h a n d f or t h e W Y . 

Fi g ur e 1 8 d e pi cts t h e l o c ati o ns of t h e c ali br ati o n a n d v ali d ati o n sit es t h at 

w er e us e d f or e a c h S W E m o d el (s e e A p p e n di x : Sit e o c ati o ns f or 

ali br ati o n a n d ali d ati o n of S W E o d els b y o nt h a n d f or t h e W Y ). 

T h e ei g ht p h ysi o gr a p hi c c o v ari at es, pr e ci pit ati o n as s n o w, a n d m o nt hl y, 

a n n u al, a n d s e as o n al s u m m ari es of t h e ei g ht gri d d e d cli m at ol o gi c al 

d at a s ets s u m m ariz e d i n T a bl e , a n d all of t h eir s q u ar es, c o nstit ut e t h e 

e ntir e s et of 2 4 2 c o v ari a bl es c o nsi d er e d d ur i n g t h e tr e n d s urf ac e m o d eli n g 

a n al ysis f or e ac h S W E m o d el d e pl o y m e nt.

Fi g ur e 6 d e pi cts pl ots of t h e e xtr e m al c o effi ci e nt f u n cti o n ( S c hl at h er a n d 

T a w n 2 0 0 3), a s u c ci n ct m e as ur e of s p ati al d e p e n d e n c e as a f u n cti o n of 

n or m ali z e d dist a n c e, f or e a c h of t h e fit t e d si m pl e m a x st a bl e m o d els f or 

S W E. 

T a bl e 6 lists c o m p ut e d c orr el ati o ns f or e ac h of t h e fitt e d S W E tr e n d 

s urf ac e m o d els wit h t h eir at sit e esti m at es. F or p ers p e cti v e, Fi g ur e 7 
E R D C / C H L T R 2 0 1 0 1 8

i n cl u d es s c att er pl ots , o nl y f or t h e c ali br ati o n sit es, t h at c o m p ar e t h e fitt e d 

tr e n d s urf ac e m o d el f or M ar c h S W E wit h t h eir at sit e esti m at es. 

T a bl e 5. N u m b er of sit e s u s e d f or 

c ali br ati o n a n d v ali d ati o n of 

S W E m o d el s.

S W E

C ali br ati o n V ali d ati o n

C o u nt

N ov 2 9 0 3 2

D e c 3 1 6 3 5

J a n 3 1 9 3 5

F e b 3 1 5 3 5

M ar 3 1 1 3 4

A pr 2 8 0 3 1

M ay 1 6 2 1 7

J u n 6 1 6 

W Y 3 6 6 4 0

Fi g ur e 6. Fitt e d si m pl e m ax st a bl e s f or S W E ( h i s 

n or m aliz e d di st a n c e ; M ay a n d W Y pl ot s w er e i d e nti c al . 
E R D C / C H L T R 2 0 1 0 1 9

T a bl e C orr el ati o n of t h e fitt e d S W E t r e n d s urf a c e m o d els wit h 

t h eir at sit e e sti m at e s f or t h e c ali br ati o n a n d v ali d ati o n sit e s.

S W E

C ali br ati o n V ali d ati o n

L o c ati o n S c al e S h a p e L o c ati o n S c al e S h a p e

N ov 0. 8 9 9 0. 8 7 9 0. 5 7 1 0. 8 7 1 0. 8 5 3 0. 6 4 3

D e c 0. 9 2 7 0. 9 1 8 0. 3 4 9 0. 8 6 0 0. 8 9 4 0. 3 6 2

J a n 0. 9 2 5 0. 9 1 2 0. 4 7 2 0. 8 7 8 0. 9 2 5 0 . 3 7 4

F e b 0. 9 3 0 0. 9 3 2 0. 5 7 2 0. 9 2 7 0. 9 5 1 0. 5 5 3

M ar 0. 9 2 1 0. 9 2 3 0. 5 4 5 0. 9 4 2 0. 9 3 2 0. 5 1 5

A pr 0. 9 3 3 0. 9 2 5 0. 4 3 5 0. 8 1 1 0. 9 1 1 0. 3 2 9

M ay 0. 9 3 6 0. 8 8 2 N A 0. 8 9 4 0. 7 8 6 N A

J u n 0. 9 1 3 0. 9 3 3 0. 4 7 6 0. 5 3 3 0. 7 0 6 0. 3 1 4

W Y 0. 9 2 2 0. 8 6 1 0. 3 8 5 N A N A N A

Fi g ur e C o m p ari s o n s of t h e fitt e d tr e n d s urf a c e m o d el wit h 

c orr e s p o n di n g at sit e e sti m at e s f or M ar c h S W E = G E V l o c ati o n; = 

G E V s c al e; = G E V s h a p e; M o d el = s p ati al m o d el; M L E = at sit e 

m axi m u m li k eli h o o d e sti m at e
E R D C / C H L T R 2 0 1 0 2 0

R e s ult s 

T h e m o d els d e v el o p e d w er e a p pli e d t o esti m at e ar e al e xc e e d a n c es f or 

P R E C a n d S W E f or t h e 7 5 8 d eli n e at e d s u b b asi ns of t h e C R B t h at 

c orr es p o n d t o t h e n e w C R B h y dr ol o g y m o d el w at ers h e d d eli n e ati o n. T h es e 

esti m at es w er e d eli v er e d t o t h e U S A C E N W D i n i n di vi d u al E n vir o n m e nt al 

S yst e ms R es e ar c h I nstit ut e (E S RI ) s h a p efil es, f or P R E C b y s e as o n a n d 

d ur ati o n a n d f or S W E b y c o ol s e as o n m o nt h a n d f or t h e W Y . C o nfi d e n c e is 

assi g n e d t o t h e ar e al e xc e e d a n c e esti m at es i n e ac h of t h e i n di vi d u al E S RI 

s h a p efil e pr o d u cts o nl y f or ass o ci at e d r et ur n p eri o ds l ess t h a n or e q u al t o 

2 0 0 y e ars. H o w e v er, t h e a p pli c ati o n g ui d a n c e d o c u m e nt t h at w as 

m e nti o n e d i n t h e I ntr o d u cti o n, t o s u p p ort t h e c o m p ut ati o n of E q u ati o n 1 

f or a n y ar bitr ar y ar e a wit hi n t h e C R B , c a n als o b e us e d t o r efi n e, as 

n e e d e d, t h e ar e al e xc e e d a n c e esti m at es f or a n y of t h e 7 5 8 d eli n e at e d s u b

b asi ns of t h e C R B t h at c orr es p o n d t o t h e n e w C R B h y dr ol o g y m o d el 

w at ers h e d d eli n e ati o n. T h e g ui d a n c e d o c u m e nt c a n b e f urt h er us e d t o 

q u a ntif y t h e u n c ert ai nt y of esti m at es f or a n y ar bitr ar y ar e a wit hi n t h e C R B 

(s e e A p p e n di x A: I nstr u cti o ns o n o w t o O bt ai n E xc e e d a n c e Pr o b a bilit y 

Est i m at es f or a s p e cifi c ar e a e. g., s u b w at ers h e d ). Of c o urs e, wit h a n y of 

t h e d e v el o p e d m o d els, tr a diti o n al p oi nt wis e r et ur n l e v el m a ps c a n als o b e 

pr o d u c e d. R e pr es e nt ati v e w or k pr o d u cts ar e s h o w n i n t h e f o ll o wi n g 

a p p e n di c es: 

1. 1 0 0 y e ar p oi nt wis e r et ur n l e v el m a ps f or c o ol s e as o n P R E C b y d ur ati o n 

( S e e A p p e n di x E).

2. 1 0 0 y e ar p oi nt wis e r et ur n l e v el m a ps f or w ar m s e as o n P R E C b y 

d ur ati o n ( S e e A p p e n di x F).

3. 1 0 0 y e ar p oi nt wis e r et ur n l e v el m a ps f or S W E b y m o nt h a n d f or t h e 

W Y ( S e e A p p e n di x G).

4. M e a n ar e al e x c e e d a n c es f or c o ol s e as o n P R E C f or 1 0 0 y e ar r et ur n 

p eri o d f or 7 5 8 d eli n e at e d s u b b asi ns of t h e C R B ( S e e A p p e n di x H).

5. M e a n ar e al e x c e e d a n c es f or w ar m s e as o n P R E C f or 1 0 0 y e ar r et ur n 

p eri o d f or 7 5 8 d eli n e at e d s u b b asi ns of t h e C R B ( S e e A p p e n di x I). 

6. M e a n ar e al e x c e e d a n c es f or S W E f or 1 0 0 y e ar r et ur n p eri o d f or 7 5 8 

d eli n e at e d s u b b asi ns of t h e C R B ( S e e A p p e n di x J).
E R D C / C H L T R 2 0 1 0 2 1

R ef er e n c e s 

B e c k ers, J. V. L., A. H. W e erts, E. Tij d e m a n, a n d E. W ells. 2 01 6. “E N S O C o n diti o n e d 

W e at h er R es a m pli n g M et h o d f or S e as o n al E ns e m bl e Str e a mfl o w Pr e dicti o n. ” 

H y d r ol. E a rt h S yst. S ci . 2 0: 1 –11. htt ps: / / d oi. or g / 1 0. 5 1 9 4 / hess 2 0 3 2 7 7 2 0 1 6

Bl a n c h et, J. 2 0 0 9. M a x St a bl e Pr o c ess es a n d A n n u al M a xi m u m S n o w D e pt h .” 6t h 

I nt e r n ati o n al C o nf e r e n c e o n E xt r e m e V al u e A n al ysis , J u n e 2 3 2 6, 2 0 0 9 , F ort 

C olli ns, C O, U nit e d St at es.

Bl a n c h et, J uli ett e , a n d A nt h o n y C. D a vis o n . 2 011. “ p ati al M o d eli n g of E xtr e m e S n o w 

D e pt h. ” A n n. A p pl. St at. 5( 3): 1 6 9 9 –1 7 2 5. d oi:1 0.1 21 4 /11 A O A S 4 6 4. 

htt ps: / / pr ojecte ucli d. or g /e ucli d. a o as / 1 3 1 8 51 4 2 8 2

Br o w n, B. M. , a n d S. I. R es nic k . 1 9 7 7. “ Extr e m e V a l u es of I n d e p e n d e nt St o c h astic 

Pr o c ess es. ” J o u r n al of A p pli e d P r o b a bilit y 1 4: 7 3 2 7 3 9. 

C ol es, St u art . 2 0 01. A n I nt r o d u cti o n t o St atisti c al M o d eli n g of E xt r e m e V al u es . L o n d o n, 

U K: S pri n g er V erl a g.

C o ol e y D., J. Cis e ws ki , R. Er h ar dt, S. J e o n , E. M a n ns h ar dt, B. O m ol o , a n d Y. S u n . 2 01 2. 

A S ur v e y of S p ati al E xtr e m es: M e as uri n g S p ati al D e p e n d e n c e a n d M o d eli n g 

S p ati al Eff e cts. ” R e v St at 1 0: 1 3 5–1 6 5. 

C o ol e y, D. , P. N a v e a u , a n d P. P o n c et . 2 0 0 6. “ V ari o gr a ms f or S p ati al M a x St a bl e R a n d o m 

Fi l ds. L e ct. N ot es St atist. 1 8 7 3 7 3– 3 9 0. N e w Y or k : S pri n g er . 

D a vis o n , A. C., a n d M. M. G h ol a mr ez a e e . 2 011. P r o c. R. S o c. A 2 011 d oi : 

1 0.1 0 9 8 /rs p a. 2 011. 0 41 2 

D a vis o n, A., S. P a d o a n , a n d M. Ri b at et . 2 01 2 . “ St atistic al M o d elli n g of S p ati al E xtr e m es. ” 

St atisti c al S ci e n c e 2 7( 2): 1 61 1 8 6.

d e H a a n, L. 1 9 8 4. A S p e ctr al R e pr e s e nt ati o n f or M a x St a bl e Pr o c ess es. ” T h e A n n als of 

P r o b a bilit y 1 2( 4): 11 9 4 1 2 0 4.

Fri e d m a n , J er o m e, Tr e v or H asti e , a n d R o b Ti bs hir a ni. 2 01 0. R e g ul ariz ati o n P at hs f or 

G e n er aliz e d Li n e ar M o d els vi a C o or di n at e D es c e nt .” J o u r n al of St atisti c al 

S oft w a r e 3 3(1) : 1 –2 2 . 

G ar et h J a m es, D a ni el a Witt e n, Tr e v or H asti e, a n d R o b ert Ti bs hir a ni. 2 01 3. A n 

I nt r o d u cti o n t o St atisti c al L e a r ni n g: wit h A p pli c ati o ns i n R. N e w Y or k: 

S pri n g er.

H o erl, A. E., a n d R. W. K e n n ar d. 1 9 7 0. “ Ri d g e R e gr essi o n: Bi as e d Est i m ati o n f or 

N o n ort h o g o n al Pr o bl e ms. ” T e c h n o m et ri cs 1 2(1): 5 5 6 7.

K a bl u c h k o, Z., M. S c hl at h er, a n d L. d e H a a n . 2 0 0 9. “ St ati o n ar y M a x St a bl e Fi el ds 

As s o ci at e d t o N e g ati v e D e finit e F u n cti o ns.” A n n als of P r o b a bilit y 3 7( 5): 2 0 4 2

2 0 6 5. 
E R D C / C H L T R 2 0 1 0 2 2

M e n n e, M. J., I. D urr e, R. S. V os e, B. E. Gl e as o n, a n d T. G. H o ust o n . 2 01 2 . “ A n Ov er vi e w 

of t h e Gl o b al Hist oric al Cli m at ol o g y N et w or k D ail y D at a b as e. ” J o u r n al of 

At m os p h e ri c a n d O c e a ni c T e c h n ol o g y 2 9 : 8 9 7 – 91 0. d oi:1 0.11 7 5 / J T E C H - D-11

0 01 0 3.1

N C D C ( N ati o n al Cli m atic D at a C e nt er). 2 0 0 3. D at a d o c u m e nt ati o n f or d at a s et 3 2 4 0 

( D SI 3 2 4 0) . N ati o n al Cli m atic D at a C e nt er, 1 51 P att o n A v e, As h e vill e, N C 2 8 8 01

5 0 01, U S A. ft p: / /ft p. nc dc. n o a a.g ov / p u b / d at a / h o urly _ preci p 3 2 4 0 / dsi 3 2 4 0. p df 

Nic ol et , Gill es , Nic ol as E c k ert, S a m u el M ori n, a n d J uli ett e Bl a n c h et . 2 01 5. “I nf erri n g 

S p ati o - T e m p or al P att er ns i n E xtr e m e S n o wf all i n t h e Fr e n c h Al ps Usi n g M a xst a bl e Pr o c ess es .” P r o c e di a E n vi r o n m e nt al S ci e n c es 2 6 . 

htt ps: / / d oi. or g / 1 0. 1 0 1 6 /j. pr oe nv. 2 0 1 5. 0 5. 0 1 8 . 

Oli n d a, R. A., J. Bl a n c h et , C. A. C. d os S a nt os , V. A. Oz a ki , a n d P. J. Ri b eir o Jr. “S p ati al 

E xtr e m es M o d eli n g A p pl i e d t o E xtr e m e Pr e ci pit ati o n D at a i n t h e t at e of 

P ar a n á.” H y d r ol. E a rt h S yst. S ci. Dis c uss. 11: 1 2 7 31 1 2 7 6 4. 

htt ps: / / d oi. or g / 1 0. 5 1 9 4 / hess d 1 1 1 2 7 3 1 2 0 1 4

O pitz, T. 2 01 3. “ Extr e m al T Pr o c ess: Elli ptic al D o m a i n of ttr a cti o n a n d a S p e ctr al 

R e pr es e n t ati o n.” J o u r n al of M ulti v a ri at e A n al ysis 1 2 2: 4 0 9 41 3.

P ytl a k, E. , A. M c M a n a m o n , S. P. H u g h es , R. A. V a n D er Z w e e p, P. B ut c h er , C. K ar af oti as . 

J. B e c k ers , a n d E. W ell es . 2 01 6 . “O bj e cti v e Us e of Cli m at e I n dic es t o I nf or m 

E ns e m bl e Str e a mfl o w F or e c asts i n t h e C ol u m bi a Ri v er B asi n - A n I niti al R e vi e w.” 

A G U F all M e eti n g A bst r a cts . S essi o n H 4 3 C 1 4 3 0. 

htt p: / / a ds a bs. h ar v ar d. e d u / a bs / 2 01 6 A G U F M. H 4 3 C1 4 3 0 P

R eic h, Bri a n J. , a n d B e nj a mi n A. S h a b y . 2 01 2. “ A Hi er ar c hic al M a x St a bl e S p a ti al M o del 

f or E xtr e m e Pr e ci pi t ati o n.” A n n. A p pl. St at . 6( 4): 1 4 3 0 1 4 51. d oi:1 0.1 21 4 /1 2

A O A S 5 91. htt ps: / / pr ojecte ucli d. or g /e ucli d. a o as / 1 3 5 6 6 2 9 0 4 6

Ri b at et, M. 2 01 3 . “S p ati al E xtr e m es: M a x St a bl e Pr o c ess es at W or k. ” J o u r n al of S o ci ét é 

F r a n ç ais e d e St atisti q u e (s p e ci al e diti o n o n e xtr e m e v al u e t h e or y) 1 5 4( 2): 1 5 6

1 7 7.

Ri b at et, M. 2 01 5. M o d elli n g S p ati al E xtr e m es wit h t h e S p ati al E xtr e m es P a c k a g e .” 9t h 

I nt e r n ati o n al C o nf e r e n c e o n E xt r e m e V al u e A n al ysis: E V A 2 01 5 . 1 5 J u n e - 1 9 

J u n e, A n n Ar b or, Mic hi g a n . 

Ri b at et, M. 2 01 7 . “ Mo d elli n g S p ati al E xtr e m es Usi n g M a x St a bl e Pr o c ess es. ” N o nli n e a r 

a n d St o c h asti c Cli m at e D y n a mi cs . E dite d b y C. Fr a nz k e a n d T. O' K a n e . 

C a m bri d g e: C a m bri d g e U ni v ersit y Pr es s. htt ps: / / d oi. or g / 1 0. 1 0 17 / 9 7 8 1 3 1 6 3 3 9 2 51

Ri b at et, M., C. D o m br y , a n d M. O esti n g . 2 01 5 . “ Sp ati al E x tr e m es a n d M a x St a bl e 

Pr o c ess e .” xt r e m e V al u e M o d eli n g a n d Ris k A n al ysis: M et h o ds a n d 

p pli c ati o ns . E dite d b y D. K. D e y a n d J. Y a n . B o c a R at o n: T a yl or & Fr a n cis. 

S c hl at h er, M. 2 0 0 2. M o d els f or St ati o n ar y M a x St a bl e R a n d o m Fi el ds. ” E xt r e m es , 5(1):

3 3 4 4.

S c hl at h er, M. , a n d J. T a w n . 2 0 0 3. “ A D e p e n d e n c e M e as ur e f or M ulti v ari at e a n d S p ati al 

E xtr e m es: Pr o p er ti es a n d I nf er e n c e.” Bi o m et ri k a 9 0(1):1 3 9 –1 5 6. 

htt ps: / / w w w.jst or. or g /st a ble / 3 0 0 4 2 0 2 5
E R D C / C H L T R 2 0 1 0 2 3

Si m o n, N o a h, J er o m e Fri e d m a n, Tr e v or H asti e , a n d R o b Ti bs hir a ni. 2 011. 

R e g ul ariz ati o n P at hs f or C o x s Pr o p orti o n al H az ar ds M o d el vi a C o or di n at e 

D es c e nt .” J o u r n al of St atisti c al S oft w a r e 3 9( 5) : 1 –1 3. 

htt ps: / / w w w.jst ats oft. or g / article /vie w /v 0 3 9i 0 5

St e p h e ns o n, A. G. , E. A. L e h m a n n, a n d A. P h at a k. 2 01 6. A M a x St a bl e Pr o c ess M o d el f or 

R ai nf all E x tr e m es at Diff er e nt A c c u m ul ati o n D ur ati o ns. ” W e at h e r a n d Cli m at e 

E xt r e m es 1 3: 4 4 5 3 . htt ps: / / d oi . or g / 1 0. 1 0 1 6 /j. w ace. 2 0 1 6. 0 7. 0 0 2

T a k e u c hi, K. 1 9 7 6 . “ Distri b uti o n of I nf or m ati o n al St atistics a n d a rit eri o n of Fi tti n g” [i n 

J a p a n es e]. S u ri K a g a k u 1 5 3: 1 2 1 8.

Ti bs hir a ni, R. 1 9 9 6. R e gr essi o n S hri n k a g e a n d S el e cti o n vi a t h e L ass o. ” J. R o y al. St atist. 

S o c . 5 8(1): 2 6 7 2 8 8.

Ti bs hir a ni, R o b ert, J a c o b Bi e n, J er o m e Fri e d m a n, Tr e v or H asti e, N o a h Si m o n, J o n at h a n 

T a yl or, a n d R y a n J. Ti bs hir a ni. 2 01 0. “ Str o n g R ul es f or Dis c ar di n g Pr e dict ors i n 

L ass o t y p e Pr o bl e ms.” J o u r n al of t h e R o y al St atisti c al S o ci et y: S e ri es 

( St atistic al M et h o d ol o g y) 7 4( 2): 2 4 5 2 6 6. htt ps: / / arxiv.or g / a bs / 1 0 1 1. 2 2 3 4

Ti k h o n o v, A. N. 1 9 4 3. “O n t h e t a bilit y of I n v ers e Pr o bl e ms. D o kl a d y A k a d e mii N a u k 

S S S R 3 9 ( 5): 1 9 5 –1 9 8. 

Z o u , H., a n d T . H asti e . 2 0 0 5. “ R e g ul ariz ati o n a n d V ari a bl e S el e cti o n vi a t h e El asti c N et. ” 

J o u r n al of t h e R o y al St atisti c al S oci et y B 6 7( 2) : 3 01 3 2 0.
E R D C / C H L T R 2 0 1 0 2 4

A p p e n di x A: I n str u cti o n s o n o w t o bt ai n 

E x c e e d a n c e Pr o b a bilit y 

E st i m at e s f or a S p e cifi c A r e a 

( e. g., s u b- w at er s h e d) 

P ur p o s e

Pr o vi d e i nstr u cti o ns o n h o w t o g e n er at e a fr e q u e n c y c ur v e f or P R E C (f or a 

s p e cifi c s e as o n a n d d ur ati o n) or S W E (f or a m o nt h ( N o v e m b er – J u n e) or 

t h e W Y ) f or a n ar bitr ar y s u b ar e a wit hi n t h e C R B. 

S oft w ar e r e q uir e m e nt s 

R- St u di o ( d o w nl o a d at htt ps: / / w w w.rst u di o.c o m / pr o d ucts /rst u di o / d o w nl o a d / ) or R 

htt ps: / /cr a n.r pr oject. or g / ) 

R- St u di o i br ari e s r e q uir e m e nt s 

T h e r e q uir e d li br ari es will b e i nst all e d t h e first ti m e t h e pr o c e d ur e is 

e x e c ut e d i n R. T h e f oll o wi n g li br ari es ar e r e q uir e d: (1) S p ati al E xtr e m es , 

( 2) m a ps, ( 3) r ast er, ( 4) S D M T o ols , ( 5) r g d al, ( 6) s p, ( 7) fit distr pl us, ( 8) 

V G A M , ( 9) l m o m c o, (1 0) act u ar , (11) F A dist , (1 2) e xtr e m e St a , (1 3) g a mlss , 

a n d (1 4) pl otri x .. 

I n p ut r e q uir e m e nt s

A p ol y g o n E S RI s h a p efil e, i n g e o gr a p hi c c o or di n at es ( G e o gr a p hi c 

C o or di n at e S yst e m G C S _ N ort h _ A m eri c a n _1 9 8 3, a n d d at u m 

D _ N ort h _ A m eri c a n _1 9 8 3), f or a si n gl e ar e a of i nt er est i n t h e C R B 

( e x a m pl e pr o vi d e d: U p p er T o u c h et Ri v er.s h p ”). T h e s h a p efil e attri b ut e 

t a bl e m ust c o nt ai n o n e c ol u m n wit h v al u e e q u al t o 1 f or t h e ar e a of 

i nt er est. A n e x a m pl e is s h o w n i n Fi g ur e . Fi g ur e 8 s h o ws t h e attri b ut e 

t a bl e as s e e n i n Ar c GI S. I n t h at c as e, c ol u m n O B J E C TI D ” i n di c at es a 

v al u e e q u al t o 1 f or t h e p ol y g o n of i nt er est. 

Fi g ur e S h a p efil e attri b ut e t a bl e f or ex a m pl e fil e
E R D C / C H L T R 2 0 1 0 2 5

Dir e ct or y / Fil e str u ct ur e

T h e f oll o wi n g fil e str u ct ur e is pr o vi d e d i n t h e H o w T o Fi n al.zi p ” fil e:

H o w T o Fi n al /

/ I nstr u cti o ns. d o c x: C o nt ai ns i nstr u cti o n s o n h o w t o g e n er at e a 

fr e q u e n c y c ur v e f or P R E C or S W E f or a s p e cifi c s u b ar e a s p e cifi e d b y t h e 

us er . 

/ C o d e / C R B _ Q u a ntil es U n c e .r.r: C o d e t o b e m o difi e d b y t h e us er. 

/ E x a m pl e /: A n e x a m pl e of r u n f or t h e us er d efi n e d s u b w at ers h e d, 

U p p er T o u c h et Ri v er ”. 

/ D at a /: Dir e ct or y c o nt ai ni n g t h e d at as ets r e q uir e d f or t h e si m ul ati o ns 

f or e ac h s e as o n a n d d ur ati o n. D o n ot m o dif y t h es e fil es. 

R u n t h e c o d e t o g e n er at e s u b b a si n q u a ntil e s

1. O p e n R St u di o or R . 

2. O p e n R c o d e at / C o d e / C R B _ Q u a ntil es U n c e .r. 

3. S a v e c o d e wit h a diff er e nt n a m e . 

4. M o dif y li n es 3 5 t o 4 6 i n t h e c o d e . 

a. Li n e 3 5 – Dir S u b b asi n : Dir e ct or y c o nt ai ni n g s h a p efil e f or i n p ut

b. Li n e 3 6 – s h p n a m e: S h a p efil e n a m e. E x a m pl e: 

U p p er T o u c h et Ri v er.s h p “ 

c. Li n e 3 7 – C ol u m n: C ol u m n i n s h a p efil e attri b ut e t a bl e t h at c o nt ai ns 

v al u e e q u al t o 1 f or t h e p ol y g o n of i nt er est. E x a m pl e: O B J E C TI D ” 

d. Li n e 3 8 – P R E C e q u al t o o n e if r u n ni n g pr e ci pit ati o n a n al ysis, z er o 

ot h er wis e 

e. Li n e 3 9 – S e as o n: if r u n ni n g pr e ci pit ati o n, d efi n e t h e s e as o n f or t h e 

a n al ysis ( c o ol or w ar m)

f. Li n e 4 2 – D ur ati o n: , 2, 3, 5,1 0, 3 0, 6 0, 9 0,1 2 0 d a y f or c o ol a n d 

1, 2, 3, 5,1 0, 3 0, 6 0, 9 0 d a y f or w ar m s e as o n

g. Li n e 4 0 – S W E e q u al t o o n e if r u n ni n g s n o w a n al ysis, z er o 

ot h er wis e 

h. Li n e 41 – M o nt h: if r u n ni n g s n o w, d efi n e t h e m o nt h f or t h e a n al ysis 

or wi nt er f or all wi nt er m o nt hs . 

N O V, D E C, J A N, F E B, M A R, A P R, M A Y, J U N, W Y ) 
E R D C / C H L T R 2 0 1 0 2 6

i. Li n e 4 3 – N SI M S: N u m b er of si m ul ati o ns ( r e aliz ati o ns fr o m a m a x

st a bl e r a n d o m fi el d) . As a r ul e of t h u m b, N SI M S = R P ( y e ars) / 2 

w h er e R P is t h e m a xi m u m r et ur n p eri o d f or w hi c h hi g h a cc ur a c y is 

r e q uir e d. 

j. Li n e 4 4 – Pr o b: Pr o b a biliti es f or t h e q u a ntil es c al c ul ati o n. N ot e t h e 

f oll o wi n g: 

h er e R P is t h e et ur n p eri o d i n y e ars a n d Pr o b is t h e pr o b a bilit y f or t h e 

c al c ul ati o n of t h e r et ur n p eri o d. St a n d ar d v al u es ar e 0. 9 9 9 9, 0. 9 9 9, 

0. 9 9 8, 0. 9 9 5, 0. 9 9, 0. 9 8, 0. 9 5, 0. 9, 0. 8, 0. 5, 0. 2, 0.1 , w hi c h c orr es p o n d 

t o r et ur n p eri o ds of 1 0 0 0 0 , 1 0 0 0 , 5 0 0 , 2 0 0 , 1 0 0 , 5 0 , 2 0 , 1 0 , 5 , 2 , 

1. 2 5 , 1 y e ar.

5. V erif y li n e 4 6: V erif y if t h e p at h t o t h e / D at a / dir e ct or y i n y o ur 

c o m p ut er is c orr e ctl y s p e cifi e d. Us e d o u bl e sl a s h (\ \ ) t o s p e cif y p at h t o 

dir e ct ori es . 

6. S el e ct all t h e li n es i n t h e c o d e . 

7. R u n t h e s cri pt. T h e r u n is o v er w h e n t h e s y m b ol “ >” is s h o w n i n t h e R 

or R St u di o C o ns ol e . 

8. V erif y if t h e o ut p ut w as g e n er at e d. S e e t h e list of o ut p ut i n t h e O ut p ut ” 

s essi o n.

O ut p ut

ulti pl e distri b uti o ns ar e fit t o t h e si m ul ati o n r es ults. T h e b est fit 

distri b uti o n is t h e n s el e ct e d a n d us e d t o esti m at e q u a ntil es. T h e o ut p uts of 

t h e si m ul ati o ns a n d q u a ntil es esti m ati o n ar e s a v e d at t h e Dir S u b b asi n 

dir e ct or y. Pr e ci pit ati o n a n d S W E q u a nti l es ar e i n milli m et ers . T h e 

f oll o wi n g fil es ar e g e n er at e d as t h e r es ult of t h e si m ul ati o n:

1. Q u a ntil e _ CI.t xt: T his fil e c o nt ai ns t h e f oll o wi n g: 

a. T h e distri b uti o n t h at b est fits t h e d at a. T h e b est fitti n g distri b uti o n 

is s el e ct e d a m o n g t h e f oll o wi n g distri b utio ns: 

(1) l n or m

( 2) p ois

( 3) e x p

( 4) g a m m a

( 5) bi n o m
E R D C / C H L T R 2 0 1 0 2 7

( 6) n bi n o m

( 7) b et a

( 8) c a u c h y

( 9) u nif

(1 0) l o gis

(11) w ei b ull

(1 2) g e v

(1 3) b urr 

(1 4) p ar et o

(1 5) k a p p a 4

b. T h e p ar a m et ers of t h e s el e ct e d distri b uti o n a n d t h e 9 5 % p er c e ntil e 

c o nfi d e n c e i nt er v al f or t h e p ar a m et ers . 

c. Q u a ntil es

(1) C al c ul at e b as e d o n t h e ori gi n al distri b uti o n p ar a m et ers . 

( 2) C al c ul at e d b as e d o n t h e m e di a n b o otstr a p esti m at es . 

( 3) C al c ul at e d b as e d o n t h e 9 5 % p er c e ntil e c o nfi d e n c e i nt er v als 

( 2. 5 % a n d 9 7. 5 %).

2. C D F _ A L L. p n g : a pl ot c o nt ai ni n g t h e e m piri c al a n d t h e or eti c al 

c u m ul ati v e distri b uti o n f u n cti o n ( C D F) f or all distri b uti o ns t est e d;

3. R es ult _ CI . p n g: a pl ot c o nt ai ni n g pr e ci pit ati o n esti m at es f or m ulti pl e 

r et ur n p eri o ds wit h c o nfi d e n c e i nt er v al. 

4. R d at a wit h t h e p ar a m et ers f or t h e c al c ul ati o n a n d fi n al r es ults ( e. g., if 

s h p n a m e <- " U p p er T o u c h et Ri v er.s h p"; c ol u m n <- " O B J E C TI D"; 

P R E C < 1; S e as o n < " c o ol"; D ur ati o n < "1 0", t h e n t h e fil e n a m e w o ul d 

b e U p p er T o u c h et Ri v er _ c o ol _1 0. R D at a ).

N u m b er of si m ul ati o n s a n d u n c ert ai nty

G e n er all y , N SI M S = R P ( y e ars) / 2 w h er e R P is t h e m a xi m u m r et ur n p eri o d 

f or w hi c h hi g h ac c ur ac y is r e q uir e d. T o g ui d e t h e us er o n t h e a p pli c ati o n of 

t h e r es ults of t his a n al ysis, a b o otstr a p m et h o d is a p pli e d t o g e n er at e 

c o nfi d e n c e i nt er v als f or si m ul ati o n. Fi g ur e 9 s h o ws h ow t h e pr e ci pit ati o n 

esti m at es a n d c o nfi d e n c e i nt er v als c h a n g e wit h c h a n g es i n t h e N SI M S.
E R D C / C H L T R 2 0 1 0 2 8

Fi g ur e U n c ert ai nty a s a f u n cti o n of t h e N SI M S

C o m p ut ati o n ti m e f or si m ul ati o n s

T h e c o m p ut ati o n ti m e r e q uir e d t o g e n er at e m ulti pl e i n d e p e n d e nt s a m pl es 

fr o m a n y o ne of t h e m a x st a bl e m o d els d e v el o p e d f or P R E C a n d S W E 

d e p e n ds o n t h e siz e of t h e b asi n. Fi g ur e 1 0 s h o ws h o w c o m p ut ati o n al ti m e 

i n cr e as es as t h e b asi n siz e i n cr e as es f or t h e g e n er ati o n of 5 0, 1 0 0, 2 5 0, 

5 0 0, a n d 1, 0 0 0 s a m pl es. L o g arit h mi c c ur v es ar e fitt e d t o t h e d at a, a n d 

e q u ati o ns t o esti m at e t h e r u n ti m e ( n u m b er of s e c o n ds) as a f u n cti o n of 

t h e b asi n siz e i n s q u ar e mil es ar e pr o vi d e d. T h es e pl ots pr o vi d e a n 

a p pr o xi m at e esti m at e f or c o m p ut ati o n ti m e. T h e e x act ti m e t o r u n a n y 

gi v e n si m ul ati o n m a y v ar y d e p e n di n g o n t h e c o m p ut er c o nfi g ur ati o n. T h e 
E R D C / C H L T R 2 0 1 0 2 9

i nf or m ati o n pr es e nt e d i n Fi g ur e 1 0 w as g e n er at e d usi n g a Wi n d o ws 

c o m p ut er wit h t h e f oll o wi n g s p e cifi c ati o ns:

Pr o c ess or: I nt el( R) X e o n( R) W 21 5 5 C P U @ 3. 3 0 G Hz, 3 31 2 M hz, 1 0 

C or e(s), 2 0 L o gi c al Pr o c ess or(s)

I nst all e d Ph ysi c al M e m or y ( R A M): 3 2. 0 G B

T ot al P h ysi c al M e m or y: 31. 7 G B

A v ail a bl e P h ysi c al M e m or y: 2 2. 5 G B

T ot al Virt u al M e m or y 3 6. 4 G B

A v ail a bl e Virt u al M e m or y: 2 4. 6 G B . 

Fi g ur e 1 0 C o m p ut ati o n al ti m e ( s e c o n d s) a s a f u n cti o n of t h e b a si n ar e a ( s q u ar e mil e
E R D C / C H L T R 2 0 1 0 3 0

A p p e n di x B: Pr e ci pit ati o n D at a C oll e cti o n, 

Q u alit y C o ntr ol , a n d Pr o c e s si n g 

T his p p e n di x d es cri b es t h e pr o c e d ur es i n t h e d e v el o p m e nt of t h e 

pr e ci pit ati o n d at a s et f or t h e C R B Pr e ci pit ati o n Ti m e S eri es T as k Or d er. 

T his t as k or d er c o nsists of o bt ai ni n g a n d pr o c essi n g e xisti n g pr e ci pit ati o n 

ti m e s eri es d at a c oll e ct e d at pr e ci pit ati o n g a gi n g st ati o ns l o c at e d wit hi n 

t h e e ntir e C R B a n d a b uff er r e gi o n s urr o u n di n g t h e C R B. 

Ti m e s eri es of A M P w as g e n er at e d f or t h e w ar m ( M a y t o S e pt e m b er) a n d 

c o ol ( Oct o b er t o A pri l) s e as o ns f or v ari o us d ur ati o ns (1 , 3 , 6 , 1 2 , 2 4 , 

4 8 , 7 2 h o ur, 5 , 1 0 , 3 0 , 6 0 , 9 0- a n d 1 2 0 d a y). 

T hr o u g h o ut t his d o c u m e nt, st ati o n r ef ers t o a u ni q u e s e ns or t h at b el o n gs 

t o a s p e cifi c n et w or k a n d is i d e ntifi e d b y a u ni q u e st ati o n i d e ntifi c ati o n 

(I D). O v er ti m e, w e at h er st ati o ns m a y b e i nst all e d, r e m o v e d or m o v e d , or 

t h e I Ds us e d t o d es cri b e t h e st ati o n mi g ht c h a n g e. D at a fr o m t h e s a m e 

w e at h er st ati o ns mi g ht als o b e r e p ort e d b y m ulti pl e n et w or ks. As a 

c o ns e q u e n c e, t h e d at a m e as ur e d at a s p e cifi c l o c ati o n mi g ht b e r e c or d e d 

b y g a u g es i d e ntifi e d b y diff er e nt st ati o n n a m es a n d I Ds. T o o v er c o m e t his 

iss u e, c o l o c at e d st ati o ns w er e c o m bi n e d i n a cl ust er of st ati o ns a n d t h eir 

r e c or ds w er e c o m bi n e d i nt o a si n gl e ti m e s eri es. T his pr o c e d ur e a v oi ds 

r e d u n d a n cy a n d all o ws t h e cr e ati o n of l o n g er r e c or ds t h at c orr es p o n d t o 

g a u g es f or a s p e cifi e d l o c ati o n. I n t his A p p e n di x, sit e r ef ers t o a si n gl e 

l o c ati o n w hi c h ti m e s eri es mi g ht b e m a d e of o n e or m or e c o l o c at e d 

st ati o ns. W h e n a cl ust er of c o l o c at e d st ati o ns is r e d u c e d t o a si n gl e 

r e pr es e nt ati v e p oi nt, it b e c o m es a sit e.

T h e f oll o wi n g d eli v er a bl es ar e i n cl u d e d as p art of t his p p e n di x:

I n v e nt or y of st ati o ns

List of d u pli c at e st ati o ns

List of c o l o c at e d st ati o ns

I n v e nt or y of sit es, w hi c h c orr es p o n d t o t h e list of st ati o ns wit h o ut 

d u pli c at e d st ati o ns a n d i n cl u di n g o nl y o n e of t h e c o l o c at e d st ati o ns

List of cl os est 4 0 sit es t o e ac h sit e , w hi c h will b e us e d t o c h e c k o utli ers

Ti m e s eri es of r a w pr e ci pit ati o n d at a at t h e hi g h est t e m p or al 

r es ol uti o n a v ail a bl e ( T X T a n d DS S f or m at)
E R D C / C H L T R 2 0 1 0 3 1

Ti m e s eri es of A M P f or t h e w ar m a n d c o ol s e as o n f or all st ati o n 

( d ur ati o ns r a n gi n g fr o m 1 h o ur t o 1 2 0 d a ys) 

Q u alit y c o ntr ol ti m e s eri es of A M P f or t h e w ar m a n d c o ol s e as o n f or all 

sit es a n d d ur ati o ns

C o nstr ai n e d o bs er v ati o ns c orr e cti o n f a ct ors

A M P r e m o v e d f or e ac h st ati o n ( d u e t o l ar g e p er c e nt a g e of missi n g d at a 

or d u e t o o utli er d et e cti o n)

St ati o n arit y e v al u ati o ns . 

Pr oj e ct a n d d at a c oll e cti o n a r e a

D at a w er e c oll e ct e d f or a n ar e a l ar g er t h a n t h e C R B b o u n d ari es t o 

g u ar a nt e e t h at st ati o ns wit h si m il ar h y dr o m et e or ol o gi c al p att er ns t o t h e 

st ati o ns i n t h e C R B b o u n d ar y w er e i n cl u d e d. T h e ar e a f or w hi c h d at a w er e

c oll e ct e d is s h o w n i n Fi g ur e 11. 

D at a s et s

Ti m e s eri es of pr e ci pit ati o n w er e o bt ai n e d fr o m t h e f oll o wi n g s o ur c es . 

0 1 – Gl o b al Hi st ori c al Cli m at ol o gy N et w or k ( G H C N) D aily D at a ( N ati o n al 

Cli m ati c D at a C e nt er D aily [ N C D C D aily ) 

G H C N is a c o m pr e h e nsi v e d at a b as e of gl o b al cli m at ol o gi c al d ail y d at a 

w hi c h c o nt ai ns r e c or ds fr o m o v er 8 0, 0 0 0 st ati o ns i n 1 8 0 c o u ntri es a n d 

t errit ori es. A d es cri pti o n of t h e d at a b as e is pr o vi d e d b y M e n n e et al. 

( 2 01 2). O n e of t h e m ai n a d v a nt a g es of usi n g t his d at as et is t h at d ail y d at a 

h as b e e n pr e vi o usl y q u alit y c o ntr oll e d b as e d o n a st a n d ar d pr o c e d ur e. 

T his d at as et c o m pil es d at a fr o m m ulti pl e s o ur c es, i n cl u di n g t h e f oll o wi n g: 

U nit e d St at es Hist ori c al Cli m at ol o g y N et w or k 

U S C o o p er ati v e S u m m ar y of t h e D a y ( N C D C D SI 3 2 0 0)

C D M P C o o p er ati v e S u m m ar y of t h e D a y ( N C D C D SI 3 2 0 6)

U S C o o p er ati v e S u m m ar y of t h e D a y – Tr a ns mitt e d vi a W x C o d er 3 

( N C D C D SI 3 2 0 7)

U S A ut o m at e d S urf ac e O b s er vi n g S yst e m ( A S O S) r e al ti m e d at a (si n c e 

J a n u ar y 1, 2 0 0 6)

U S A S O S d at a f or Oct o b er 2 0 0 0 D e c e m b er 2 0 0 5 ( N C D C D SI - 3 211) 
E R D C / C H L T R 2 0 1 0 3 2

0 2 N C D C H o urly D at a ( N C D C H o urly) 

H o url y pr e ci pit ati o n d at a fr o m t h e D SI 3 2 4 0 d at as et ( h o url y pr e ci pit ati o n 

f or pri m aril y U S l o c ati o ns) w as als o i n cl u d e d i n t his st u d y. T h e h o url y d at a 

ar e a v ail a bl e at ft p: / /ft p. nc dc. n o a a.g ov / p u b / d at a / h p d / a ut o /v 2 / bet a /. T h e pr e ci pit ati o n 

v al u es pr o vi d e d i n t his d at as et ar e c h e c k e d a n d e dite d b y a ut o m at e d a n d 

m a n u al q u alit y c o ntr ol pr o c e d ur es. M or e i nf or m ati o n a b o ut t his d at as et is 

pr o vi d e d b y N C D C ( 2 0 0 3).

Fi g ur e 1 1 R B d at a c oll e cti o n b o u n d ari e s.

0 3 – N C D C 1 5 – M i n ut e s at a ( N C D C 1 5 mi n): 

T h e 1 5-mi n ut e o bs er v ati o ns t h at ar e us e d t o c o m p ut e h o url y pr e ci pit ati o n 

t ot als i n t h e N ati o n al C e nt ers f or E n vir o n m e nt al I nf or m ati o n C o o p er ati v e 

O bs er v ers Pr o gr a m ( C O O P) H o url y Pr e ci pit ati o n D at as et. T h es e d at a ar e 

pr o vi d e d f or t h e y e ars 2 01 4 t hr o u g h t h e pr es e nt. T h er ef or e, t h es e d at a 

w er e o nl y us e d t o c al c ul at e t h e c orr e cti o n f or c o nstr ai n e d o bs er v ati o ns, 

s u c h as d ail y o bs er v ati o ns.
E R D C / C H L T R 2 0 1 0 3 3

0 4 – S N O T E L

T h e S N O T E L d ail y pr e ci pit ati o n d at a ar e a v ail a bl e at 

htt p: / / w w w. wcc. nrcs. us d a.g ov /s n o w / . Pr e ci pit ati o n v al u es i n t his d at as et ar e 

r e p ort e d as ac c u m ul ati o ns i n i n c h es f or t h e cli m at ol o gi c al y e ar st arti n g 

Oct o b er 1. T h e S N O T E L n et w or k is i nst all e d, o p er at e d, a n d m ai nt ai n e d b y 

t h e N at ur al R es o ur c es C o ns er v ati o n S er vi c e. M or e i nf or m ati o n a b o ut 

S N O T E L c a n b e f o u n d at htt p: / / w w w. wcc. nrcs. us d a.g ov /f act p u b /s ntlfct 1. ht ml a n d N C D C 

( 2 0 0 2). 

0 5 – U S A C E 

T h es e d at a ar e st or e d i n t h e N ort h w est er n Di visi o n C or ps W at e r 

M a n a g e m e nt S yst e m d at a b as e at htt p: / / w w w. n w d

wc. us ace. ar my. mil / d d /c o m m o n / d at a q uery / w w w / . F or t his n et w or k , d at a ar e pr o vi d e d i n 

t e m p or al r es ol uti o n of 1 5 mi n ut e , 1 h o ur, 6 h o ur , a n d 1 d a y. T h e I D f or 

t h e g a u g es a n d l o c ati o n s o m eti m es ar e t h e s a m e, b ut t h e p eri o d of r e c or d 

v ari es. F or e x a m pl e, d at a f or t h e A R K st ati o n w er e pr o vi d e d at t h e 1 h o ur 

r es ol uti o n f or t h e p eri o d of A u g 1 9 9 2 t o D e c 2 01 7; at 6 h o ur fr o m A u g ust

1 9 9 2 t o A u gust 2 01 8 ; a n d at 1 d a y fr o m N o v e m b er 1 9 7 4 t o D e ce m b er

2 01 7. T o a v oi d l osi n g a n y d at a, a n et w or k I D n u m b er w as attri b ut e d t o 

e ac h t e m p or al r es ol uti o n: (1) 51 w as assi g n e d f or 1 5 mi n ut e; ( 2) 5 2 w as 

assi g n e d f or 1 h o ur; ( 3) 5 3 w as assi g n e d f or 6 h o ur; a n d ( 4) 5 4 w as 

assi g n e d f or 1 d a y. I niti all y, e ac h ti m e s eri es will b e pr o c ess e d 

i n d e p e n d e ntl y. H o w e v er, sit es t h at h a v e t h e s a m e it e I D a n d l o c ati o n 

w er e cl assifi e d as c o l o c at e d d uri n g t h e s cr e e ni n g pr o c ess, a n d t h e d at a 

fr o m m ulti pl e t e m p or al r es ol uti o ns w er e c o m bi n e d i n a u ni q u e ti m e s eri es 

f or t h e g a u g e sit e. 

0 6 – S o ut h w e st Cli m at e a n d E nvir o n m e nt al I nf or m ati o n C oll a b or ati v e

( S C E NI C) 

D at a c oll e ct e d t hr o u g h t h e S C E NI C d at a b as e. T his d at a b as e i n cl u d es d at a 

fr o m t h e f oll o wi n g n et w or ks:

E at h er B ur e a u Ar m y N a v y

C O O P

F e d er al A vi ati o n A d mi nistr ati o n

W orl d M et e or ol o gi c al Or g a niz ati o n

I nt er n ati o n al Ci vil A vi ati o n Or g a ni z ati o n

G H C N

N ati o n al W e at h er S er vi c e L o c ati o n I d e ntifi er 

T hr e a d E x . 
E R D C / C H L T R 2 0 1 0 3 4

0 7 – E nvir o n m e nt al C a n a d a D aily D at a ( C A D aily) 

D ail y d at a pr o vi d e d b y t h e E n vir o n m e nt a n d Cli m at e C h a n g e C a n a d a

( E C C C), G o v er n m e nt of C a n a d a . 

0 8 – E nvir o n m e nt al C a n a d a H o urly Dat a ( C A H o urly) 

H o url y d at a pr o vi d e d b y M et e or ol o gi c al S er vi c es of C a n a d a E C C C,

G o v er n m e nt of C a n a d a. 

E ac h st ati o n is i d e ntifi e d b y t h e n u m b er of t h e n et w or k a n d t h e t ati o n I D. 

F or e x a m pl e: 01 C A1 B C 0 0 0 011 r ef ers t o a g a u g e fr o m t h e N C D C D ail y 

n et w or k, wit h St ati o n I D C A1 B C 0 0 0 011 . 

S e a s o n ality

h e f oll o wi n g s e as o ns w er e d efi n e d as e d o n t h e a n al ysis of m o nt h l y 

n or m al pr e ci pit ati o n , s e as o n alit y of a n n u al m a xi m u m pr e ci pit ati o n (s e e 

Fi g ur e 1 2), a n d t h e s e as o n alit y of t e m p er at ur e:

1. W ar m e as o n (M a y t o S e pt e m b er ). A n n u al m a xi m u m e v e nts d uri n g 

t h es e m o nt hs o c c ur m ai nl y o n t h e e ast er n p art of t h e b asi n.

2. C o ol S e as o n ( Oct o b er t o A pril). A n n u al m a xi m u m e v e nts d uri n g t h es e 

m o nt hs ar e m ai nl y ass o ci at e d wit h at m os p h eri c ri v ers a n d ar e m ost 

c o m m o n i n t h e w est er n p art of t h e b asi n. 

Fi g ur e 1 2 R B d at a c oll e cti o n b o u n d ari e s a n d s e a s o n ality of A M P
E R D C / C H L T R 2 0 1 0 3 5

D at a c oll e cti o n a n d p r o c e s si n g

T h e f oll o wi n g t as ks w er e p erf or m e d t o c oll e ct a n d pr o c ess t h e A M P d at a . 

D at a o w nl o a d a n d or m a tti n g 

F or e ac h n et w or k, a yt h o n c o d e w as d e v el o p e d t o pr o c ess t h e ori gi n al 

d at a a n d t o s a v e t h e d at a i nt o a st a n d ar d T X T f or m at wit h st a n d ar d u nits 

milli m et ers ) a n d t h e i n cl usi o n of d at a fl a gs. T h e P R E C ti m e s eri es w er e 

als o s a v e d i n D S S f or m at. H o w e v er, n ot e t h at D S S d o es all o w t h e i n cl usi o n 

of d at a fl a gs. T h e c o d e als o g e n er at es a n i n v e nt or y of st ati o ns f or e ac h 

n et w or k (s e e fl o w c h art i n Fi g ur e 1 3). 

1. St ati o n a n d Sit e I n v e nt o r y: All st ati o ns ( all n et w or ks) w er e 

e v al u at e d t o i d e ntif y d u pli c at e d a n d c o l o c at e d st ati o ns. D u pli c at es 

o cc ur w h e n t w o st ati o ns ar e l o c at e d at t h e s a m e g e os p ati al l o c ati o n 

(l atit u d e a n d l o n git u d e), h a v e t h e s a m e p eri o d of r e c or d, a n d at l e ast 

8 0 % of t h e A M P d at a fr o m o n e st ati o n ar e t h e s a m e as t h e d at a fr o m 

t h e ot h er st ati o n (s e e fl o w c h art i n Fi g ur e 1 4). Si n c e diff er e nt n et w or ks 

st or e l atit u d e a n d l o n git u d e wit h diff er e nt pr e cisi o n, sit es l o c at e d cl os e 

t o e ac h ot h er w er e als o c h e c k e d t o g u ar a nt e e t h e y d o n ot h a v e t h e s a m e 

d at a a n d p eri o d of r e c or d. If t h e dist a n c e b et w e e n t h e st ati o ns is l ess 

t h a n 1. 5 k m a p art, t h e n t h e st ati o n is c o nsi d er e d c o l o c at e d if b ot h 

g a u g es pr es e nt diff er e nt d at a a n d is c o nsi d er e d d u pli c at e d if t h e p eri o d 

of r e c or d is t h e s a m e, a n d at l e ast 8 0 % of t h e A M P d at a fr o m o n e 

st ati o n is t h e s a m e as t h e d at a fr o m t h e ot h er st ati o n d at a. D u pli c at e d 

a n d c o l o c at e d st ati o ns w er e r e pr es e nte d b y o n e st ati o n i n t h e fi n al 

i n v e nt or y of sit es. Fil es w er e cr e at e d c o nt ai ni n g t h e t ati o n I D of 

d u pli c at e d a n d c o l o c at e d sit es. If t h e ori gi n al n et w or k d o es n ot 

c o nt ai n el e v ati o n d at a f or t h e st ati o n, el e v ati o n d at a w er e c al c ul at e d 

b as e d o n t h e H y dr o S H E D 1 5 s e c) d at as et a v ail a bl e at 

htt ps: / / w w w. hy dr os he ds. or g / . T his d at as et w as s el e ct e d si n c e it c o v ers C a n a d a 

a n d t h e U nit e d St at es , a n d t h e d at a f or b ot h c o u ntri es w er e pr o d u c e d 

i n a c o nsist e nt w a y. H y dr o S H E D S is b as e d o n hi g h r es ol uti o n 

el e v ati o n d at a o bt ai n e d d uri n g a S p ac e S h u ttl e fli g ht f or t h e N A S A 

S h uttl e R a d ar T o p o gr a p h y Missi o n. A fil e c o nt ai ni n g t h e t ati o n I D f or 

t h e cl os est 4 0t h st ati o ns t o e ac h st ati o n w as als o g e n er at e d. T his fil e 

w as us e d t o e v al u at e o utli ers i n A M P ti m e s eri es (s e e fl o w c h art i n

Fi g ur e 1 4). 

2. C al c ul at e Co n st r ai n e d b s e r v ati o n s C o r r e cti o n F a ct o r s: 1 5- 

a n d 6 0 mi n ut es g a u g es w er e us e d t o c al c ul at e t h e c o nstr ai n e d 
E R D C / C H L T R 2 0 1 0 3 6

o bs er v ati o n c orr e cti o n f act ors. T h e n e e d f or c o nstr ai n e d o bs er v ati o n 

c orr e cti o n aris es fr o m usi n g r ai nf all o bs er v ati o ns t h at ar e us u all y b as e d 

o n a fi x e d a cc u m ul ati o n ti m e p eri o d ( e. g. , 0 0: 0 0 t o 2 3: 5 9) t o c al c ul at e 

A M P. F or t h es e ti m e s eri es , it is p ossi bl e t h at a l ar g er v al u e of A M P 

c o ul d h a v e b e e n o bs er v e d if a fi x e d b e gi n ni n g a n d e n di n g p eri o d w er e

n ot c o nsi d er e d. T o a cc o u nt f or t his li k el y u n d e r esti m ati o n of A M P, a 

c orr e cti o n f act or is a p pli e d f or A M P v al u es o bt ai n e d fr o m d at a wit h 

t e m p or al r es ol uti o n l ar g er t h a n 1 5 mi n ut es. T o c al c ul at e t h e c orr e cti o n 

f act ors, t h e 1 5 mi n ut es a n d 6 0 mi n ut es r es ol uti o n d at a w er e us e d t o 

c al c ul at e A M P b as e d o n t w o m et h o ds: 1) U nc o nstr ai n e d, w hi c h is 

b as e d o n t h e m o vi n g a v er a g e s u ms a n d g u ar a nt e es t h at t h e hi g h est 

v al u e is s el e ct e d, a n d ( 2) C o nstr ai n e d , w hi c h is b as e d o n acc u m ul ati o ns 

b as e d o n a pr e d efi n e d b e gi n ni n g a n d e n d ti m e t h at u n d er esti m at es 

t h e A M P. T h e r a ti o b et w e e n u n c o nstr ai n e d a n d c o nstr ai n e d A M P w er e 

c al c ul at e d, a n d t h e m e a n, m e di a n, 7 5 t h a n d 9 0 t h p er c e ntil e of t h e r ati o 

w er e r e c or d e d f or g a u g es t h at h a v e at l e ast 5 y e ars of d at a. Diff er e nt 

c orr e cti o n f act ors w er e c al c ul at e d f or e a c h s e as o n . 

3. D at a P r o c e s si n g 1: I n t his t as k, A M P ti m e s eri es w er e g e n er at e d f or 

all st ati o ns. A u xili ar y d at a t h at s u p p orts t h e q u a lit y ass ur a n c e / q u alit y 

c o ntr ol w as als o c o m p ut e d, i n cl u di n g (1) er c e nt of missi n g d at a i n 

s e as o n ( M D S), ( 2) u m b er of d a ys wit h r ai n > 0 ( N D R), ( 3) tot al 

s e as o n al r ai nf all ( T S R), ( 4) er c e nt of missi n g v al u es f or t h e ti m e of 

o c c urr e n c e of t h e A M P Missi n g D at a Ti m e ( M D T), ( 5) fl a gs, a n d ( 6) 

er c e nt of v al u es fl a g g e d f or t h e ti m e of o c c urr e n c e of t h e A M P (s e e 

fl o w c h art i n Fi g ur e 1 5).
E R D C / C H L T R 2 0 1 0 3 7

Fi g ur e 1 3 R E C ti m e s eri e s d o w nl o a d a n d 

r e f or m atti n g fl o w c h art.

Fi g ur e 1 4 St ati o n s cr e e ni n g fl o w c h art.
E R D C / C H L T R 2 0 1 0 3 8

Fi g ur e 1 5 M P pr o c e s si n g a n d q u ality c o ntr ol fl o w c h art.
E R D C / C H L T R 2 0 1 0 3 9

4. D at a r o c e s si n g 2: I n t his t as k, q u alit y c o ntr oll e d A M P ti m e s eri es 

w er e g e n er at e d f or all sit es (s e e fl o w c h art i n Fi g ur e 1 5). C o l o c at e d 

st ati o ns w er e first i d e ntifi e d. T h e A M P f or e a c h st ati o n w as c orr e ct e d 

f or c o nstr ai n e d o bs er v ati o ns a n d q u alit y c o ntr ol t o i d e ntifi e d a n d 

r e m o v e o utli ers. T h e c orr e cti o n f or c o nstr ai n e d o bs er v ati o n a p pli e d t h e 

m e di a n c orr e cti o n f act or f or t h e cl os est st ati o n f or t h e s p e cifi c s e as o n. 

nl y o n e f act or is a p pli e d or h o url y d at a t h at c orr es p o n d t o t h e 

c orr e cti o n fr o m 1 5 mi n ut es t o 6 0 mi n ut es . w o f act ors w er e a p pli e d f or 

d at a r es ol uti o n gr e at er t h a n 6 0 mi n ut es : (1) F act or 1: orr e cts fr o m 1 5

mi n ut es t o 6 0 mi n ut es ; a n d ( 2) F act or 2: orr e cts fr o m 6 0 mi n ut es t o 

t h e r es ol uti o n of t h e d at a. T h e q u alit y c o ntr ol st arts wit h r e m o vi n g all 

v al u es f or w hi c h M D S or M D T ar e m or e t h a n 2 0 %. Wit hi n t h e 

r e m ai ni n g v al u es, o utli ers ar e d ete ct e d b as e d o n t h e Gr u b bs B e c k 

st atisti c al t est a n d t h e m e di a n ( + / ) t w o st a n d ar d d e vi ati o ns 

t hr es h ol ds. T h e i d e ntifi e d o utli ers w er e t h e n c h e c k e d b y c o nsist e n c y 

wit h s urr o u n di n g g a u g es a n d wit h t h e s e as o n al i nf or m ati o n ( n u m b er of 

r ai n y d a ys a n d s e as o n t otal r ai nf all). O utli ers w er e r e m o v e d i n c as e t h e 

v al u e als o f ail e d eit h er t h e L o w er a n d Hi g h O utli er C h e c ks : 

a. L o w O utli ers

(1) N D R f or t h e s e as o n t h at t h e o utli er o cc urs is l ess t h a n t h e 

m e di a n N D R f or t h e g a u g e mi n us t w o st a n d ar d d e vi ati o ns.

( 2) T S R f or t h e s e as o n t h at t h e o utli er o cc urs is l ess t h a n t h e 

m e di a n T S R f or t h e g a u g e mi n us t w o st a n d ar d d e vi ati o ns. 

b. Hi g h O utli ers

(1) N D R f or t h e s e as o n t h at t h e o utli er o cc urs is gr e at er t h a n t h e 

m e di a n N D R f or t h e g a u g e pl us t w o st a n d ar d d e vi ati o ns.

( 2) T S R f or t h e s e as o n t h at t h e o utli er o cc urs is gr e at er t h a n t h e 

m e di a n T S R f or t h e g a u g e pl us t w o st a n d ar d d e vi ati o ns. 

( 3) C oll e ct e d A M P f or t h e 4 0 cl os est st ati o ns f or t h e s a m e y e ar 

( w h e n a v ail a bl e). T h e p oi nt is r e m o v e d if t h e A M P f or t h e 

st ati o n is l ar g er th a n t h e m e di a n A M P pl us t w o st a n d ar d 

d e vi ati o ns f or all 4 0 st ati o ns. If f e w er t h a n fi v e n e ar b y g a u g es 

ar e a v ail a bl e, t h e o utli er is n ot r e m o v e d b as e d o n t his crit eri a. 

( 4) A M P is l ar g er t h a n t h e m e di a n A M P pl us t hr e e st a n d ar d 

d e vi ati o ns . 
E R D C / C H L T R 2 0 1 0 4 0

Fil e s o r g a niz ati o n

T h e f oll o wi n g f ol d er a n d fil es ar e i n cl u d e d as d eli v er a bl es f or t his 

s u b mitt al: 

A p p e n di x : o nt ai n s a di git al c o p y ( W or d f or m at) of t his a p p e n di x . 

2- Pr e c D at a 

o nt ai n s t h e c oll e ct e d ti m e s eri es of pr e ci pit ati o n. E ac h n et w or k pr o vi d es 

d at a i n diff er e nt f or m ats. T h e pr e ci pit ati o n d at a o bt ai n e d fr o m e ac h 

n et w or k w er e c o n v ert e d i nt o a u ni q u e f or m at f or all n et w or ks. T h e d at a 

w er e s a v ed i n T X T, w hi c h als o c o nt ai ns fl a gs, a n d D S S fil e f or m at, w hi c h 

o nl y c o nt ai n s pr e ci pit ati o n v al u es. All pr e ci pit ati o n d at a ar e i n

milli m et ers . 

3- A M P 

o nt ai n s t h e o ut p ut of t h e D at a Pr o c essi n g 1” r o uti n e, w hi c h c orr es p o n ds 

t o t h e ti m e s eri es of AM P f or all sit es a n d n et w or ks f or t h e o ol ( dir e ct or y 

C o ol S) a n d ar m ( dir e ct or y W ar m S) s e as o ns. N o q u alit y c o ntr ol of t h e 

d at a w as p erf o r m e d i n t his st e p. T h e fil e n a m e c orr es p o n ds t o t h e d ur ati o n 

( e. g., 1 h o ur, 1 d a y) a n d t h e t ati o n I D ( e. g., 01 C A1 A B 0 0 0 0 01 , 0 6

U S1 O R L A 0 0 6 5 ). T h e fil es c o nt ai n t h e f oll o wi n g i nf or m ati o n:

Y e ar: Y e ar of t h e A M P.

A M P( milli m et ers ): A M P i n milli m et ers

E n d D at e : T his c orr es p o n ds t o t h e e n d d at e of t h e ac c u m ul ati o n p eri o d 

f or t h e A M P. T his is es p e ci all y i m p ort a nt f or l ar g er a cc u m ul ati o n ( e. g., 

5 d a ys or m or e). 

P or Missi n g S e as o n : P er c e nt a g e of missi n g v al u es i n t h e s e as o n.

P or Missi n g A c c u m : P er c e nt a g e of missi n g v al u es i n t h e a cc u m ul ati o n 

p eri o d. T his v al u e is m or e r el e v a nt f or l ar g er acc u m ul ati o n p eri o ds 

( e. g., 5 d a ys or m or e).

R ai n y D a ys: N u m b er of r ai n y d a ys i n t h e s e as o n.

T ot al R ai n: T ot al acc u m ul at e d r ai n i n t h e s e as o n.

Fl a gs: F or t h e ori gi n al d ur ati o n , t h e fil e s h o ws t h e ori gi n al fl a g. F or 

ot h er acc u m ul ati o ns , t h e p er c e nt a g e of t h e v al u es t h at ar e fl a g g e d i n 

t h e acc u m ul ati o n p eri o d is pr o vi d e d. 
E R D C / C H L T R 2 0 1 0 4 1

Si n c e t h es e fil es c o nt ai n m or e i nf or m ati o n t h a n o nl y t h e ti m e s eri es of 

A M P, t h es e fil es w er e s a v e d i n c o m m a s e p ar at e d v al u es ( C S V ) f or m at ( a n d 

n ot i n D S S f or m at). T h e fil e n a m e str u ct ur e is t h e f oll o wi n g: 

S e as o n: C o ol S or W ar mS ] +”/” + [ d ur ati o n ] +” _” +[St ati o n I D ] +”.csv” 

T his f ol d er als o c o nt ai ns t h e C o nstr ai ns C orr e cti o n. cs v fil e, w hi c h lists t h e 

c o nstr ai n e d o bs er v ati o n c orr e cti o n f a ct or f or all 1 5 mi n ut es a n d 6 0

mi n ut es g a u g es f or m ulti pl e d ur ati o n a n d f or t h e c o ol a n d w ar m s e as o n. 

5- St ati o n S cr e e ni n g 

C o nt ai ns t h e r es ults of t h e st ati o n s cr e e ni n g pr o c ess es. T h e f oll o wi n g fil es 

ar e i n cl u d e d:

C ol o c at e d. cs v ”: List of c oll o c at e d g a u g es . 

D u pli c at e d. cs v ”: List of d u pli c at e d g a u g es . 

Eli mi n at e d . cs v”: List of eli mi n at e d g a u g es b e c a us e of l ac k of v ali d d at a 

( n u m b er of A M P < 4). 

I n v N o Du pli c at es. cs v ”: I n v e nt or y of sit es ( St ati o ns t h at ar e n ot 

d u pli c at e d a n d o nl y o n e st ati o n r e pr es e nti n g cl ust er of c o l o c at e d 

st ati o ns). 

N e ar b y G a u g e. cs v ”: List of 4 0 t h cl os est st ati o ns t o e ac h sit e . 

S u m m ar y . cs v”: S u m m ar y of t h e s cr e e ni n g pr o c ess. A t ot al of 1 0, 9 5 4 

st ati o ns ar e a v ail a bl e i n t h e ar e a. S e v e nt y ei g ht st ati o ns w er e 

d u pli c at e d, 2, 7 9 9 st ati o ns w er e c o l o c at e d. A t ot al of 6, 5 4 3 sit es w er e 

i d e ntifi e d. 

5- Q C A M P 

C o nt ai ns t h e q u alit y c o ntr oll e d A M P f or all sit es a n d s e as o ns. T h e 

f oll o wi n g fil es ar e in cl u d e d:

[ S e as o n: C o ol S o r W a r m S] + [ d ur ati o n] + A M P M atri x. cs v ”: all v ali d 

A M P d at a st or e d i n a m atri x of sit e v ers us y e ar of d at a. T h e fil e 

i n cl u d es i nf or m ati o n f or t h e sit e: St ati o n I D, L at, L o n g, El e v ati o n a n d 

n u m b er of v ali d A M P ( N V al Y e ars)

S e as o n: C o ol S o r W a r m S + [ d ur ati o n] + All A M P. cs v ”: all v ali d A M P 

d at a st or e d i n s e q u e n c e c o nt ai ni n g all t h e a u xili ar y i nf or m ati o n list e d 

i n 3 A M P: Y e ar , A M P(milli m et er ), E n d D at e, P or Missi n g S e as o n, 

P or Missi n g A c c u m, R ai n y D a ys, T ot al R ai n, a n d Fl a gs. T his fil e c a n b e
E R D C / C H L T R 2 0 1 0 4 2

us e d t o e v al u at e t h e d at a ; f or e x a m pl e: e v al u at e s p e cifi c e v e nts (s ort 

d at a b y d at e) or v erif y hi g h a n d l o w v al u es of A M P (s ort b y A M P 

v al u es)

[ S e as o n: C o ol S o r W a r m S] + [ d u r ati o n] + A M P C o nst O bs C o r r. cs v ”: 

c o nt ai n t h e c orr e cti o n f act or f or c o nstr ai n e d o bs er v ati o ns. I niti all y , 

t w o c o nstr ai n e d c orr e cti o n f act ors w er e c al c ul at e d: (1) C o ef1 5: 

C orr e cti o n fr o m 1 5 mi n ut es t o 1 h o ur, c al c ul at e d b as e d o n 1 5 mi n ut es 

pr e ci pit ati o n d at a. O nl y 11 st ati o ns h a d e n o u g h d at a t o c al c ul at e t his 

c o effi ci e nt; ( 2) C o ef: C orr e cti o n fr o m 1 h o ur t o t h e d ur ati o n b ei n g 

e v al u at e d c al c ul at e d b as e d o n h o url y d at a. F or e ac h st ati o n, t h e 

m e di a n v al u e of t h e r ati o b et w e e n n o n c o nstr ai n e d a n d c o nstr ai n e d 

A M P w as c al c ul at e d a n d us e d i n t h e a n al ysis. T h e c o effi ci e nt f or t h e 

cl os est st ati o n t o t h e sit e b ei n g e v al u at e d w as us e d. T h e C o ef v al u e w as 

us e d t o c orr e ct d ail y A M P. T h e m a xi m u m c orr e cti o n f act or a p pli e d t o 

t h e d at a is 1. 2 2 f or t h e C o ol s e as o n a n d 1. 2 5 f or t h e ar m s e as o n. 

S e as o n: C o ol S o r W a r m S + [ d ur ati o n] + St ati o n arit y. cs v ”: 

st ati o n arit y t ests f or t h e m e a n w er e p erf or m e d f or sit es wit h m or e t h a n 

3 0 y e ars of v ali d d at a. St ati o n arit y t est f or t h e v ari a n c e w as p erf or m e d 

f or sit es wit h m or e t h a n 6 0 y e ars of d at a. R es ults i n cl u d e t h e f oll o wi n g

L R Sl o p e : Sl o p e of t h e li n e ar r e gr essi o n m o d el . 

L Rr v al u e: I nt er c e pt of t h e li n e ar r e gr essi o n m o d el . 

L R p v al u e: p v al u e of t h e li n e ar r e gr essi o n m o d el. Tr e n d is o bs er v e d 

if p v al u e < 0. 0 5 . 

L Rtr e n d: n o tr e n d, i n cr e asi n g or d e cr e asi n g tr e n d

M Ktr e n d: M a n n K e n d all t est r es ult. F als e i n di c at es n o Tr e n d . 

M K h: n o tr e n d, i n cr e asi n g or d e cr e asi n g tr e n d f or M a n n K e n d all . 

M K p m k: p v al u e of t h e si g nifi c a n c e t est f or M a n n K e n d all . 

M Kz: n or m ali z e d t est st atisti cs . 

L e W v: r es ults of t h e L e v e n e t est. T h e L e v e n e t est t ests t h e n ull . 

h y p ot h esis t h at all i n p ut s a m pl es ar e fr o m p o p ul ati o ns wit h e q u al 

v ari a n c es . 

L e p v: p v al u e of t h e si g nifi c a n c e t est f or h e L e v e n e t est. P- v al u e 

l o w er t h a n 5 % i n di c at es tr e n d i n t h e v ari a n c e. 

Fi g ur e 1 6 s h o ws t h e r es ults of t h e st ati o n arit y t est. T h e l ar g e m aj orit y of 

t h e sit es d o n ot pr es e nt a n y tr e n d. N o cl e ar s p ati al p att er n is o bs er v e d f or 

t h e sit es t h at tr e n ds w er e i d e ntifi e d. Tr e n ds w er e n ot r e m o v e d f or t h e

c al c ul ati o n of A M P. 
E R D C / C H L T R 2 0 1 0 4 3

S e as o n: C o ol S o r W a r m S + [ d ur ati o n] + V ali dI n v. cs v ”: I n v e nt or y of 

sit es wit h v ali d d at a

S e as o n: C o ol S o r W a r m S + [ d ur ati o n] + E ntir eI n v . cs v”: c o m pl et e 

i n v e nt or y of st ati o ns, i n cl u di n g d u pli c at e d a n d c o l o c at e d st ati o ns

S e as o n: C o ol S o r W a r m S + [ d ur ati o n] + R e m o v e d A M P . cs v”: A M P 

v al u es t h at w er e e xcl u d e d of t h e ti m e s eri es d u e t o a n y of t h e q u alit y 

c o ntr ol pr o c e d ur es, i n cl u di n g e xc e e di n g 2 0 % missi n g d at a i n t h e 

s e as o n or 2 0 % missi n g d at a i n t h e a cc u m ul ati o n p eri o d, or v al u es t h at 

w er e i d e ntifi e d as o utli ers a n d f ail e d t h e v ali d ati o n t est.

Fi g ur e 1 6 Tr e n d s i n d aily A M P f or t h e c o ol a n d w ar m s e a s o n b a s e d o n li n e ar 

r e gr e s si o n a n d M a n n K e n d all.
E R D C / C H L T R 2 0 1 0 4 4

A p p e n di x C: Sit e L o c ati o n s f or ali br ati o n 

a n d ali d ati o n of P R E C o d el s 

b y e a s o n a n d ur ati o n

Fi g ur e 1 7 E M , st at e li n e, a n d P R E C o b s er v ati o n sit e l o c ati o n d at a by s e a s o n a n d 

d ur ati o n (▪ =C ali br ati o n, = V ali d ati o n).

= C ali br ati o n, = V ali d ati o n
E R D C / C H L T R 2 0 1 0 4 5

= C ali br ati o n, = V ali d ati o n
E R D C / C H L T R 2 0 1 0 4 6

= C ali br ati o n, = V ali d ati o n
E R D C / C H L T R 2 0 1 0 4 7

= C ali br ati o n, = V ali d ati o n
E R D C / C H L T R 2 0 1 0 4 8

A p p e n di x D : Sit e L o c ati o n s f or ali br ati o n 

a n d ali d ati o n of S W E o d el s b y 

o nt h a n d f or t h e W Y

Fi g ur e 1 8 E M , st at e li n e, a n d S W E o b s er v ati o n sit e l o c ati o n d at a by m o nt h a n d f or 

t h e W Y (▪ =C ali br ati o n, = V ali d ati o n).

= C ali br ati o n, = V ali d ati o n
E R D C / C H L T R 2 0 1 0 4 9

= C ali br ati o n, = V ali d ati o n
E R D C / C H L T R 2 0 1 0 5 0

A p p e n di x E: C o ol S e a s o n P R E C P oi nt wi s e 

1 0 0 Y e ar R et ur n L e v el s f or t h e 

C R B

Fi g ur e 1 9 C o ol s e a s o n P R E C p oi nt wi s e 1 0 0 y e ar r et ur n l ev el s f or t h e C R B (f or 1

1 0 3 0 6 0 9 0 , a n d 1 2 0 d ay d ur ati o n s) (v al u e s i n milli m et er s ).
E R D C / C H L T R 2 0 1 0 5 1
E R D C / C H L T R 2 0 1 0 5 2

A p p e n di x F: W ar m S e a s o n P R E C P oi nt wi s e 

1 0 0 Y e ar R et ur n L e v el s f or t h e 

C R B

Fi g ur e 2 0 W ar m s e a s o n P R E C p oi nt wi s e 1 0 0 y e ar r et ur n l ev el s f or t h e C R B (f or 1

1 0 3 0 6 0 , a n d 9 0 d ay d ur ati o n s) (v al u e s i n milli m et er s
E R D C / C H L T R 2 0 1 0 5 3
E R D C / C H L T R 2 0 1 0 5 4

A p p e n di x G: M o nt hl y ( D e c e m e b er J u n e) a n d 

W Y S W E P oi nt wi s e 1 0 0 - Y e ar 

R et ur n L e v el s f or t h e C R B

Fi g ur e 2 1 M o nt hly ( D e c e m b er J u n e) a n d W Y S W E p oi nt wi s e 1 0 0 y e ar r et ur n l ev el s 

f or t h e C R B (v al u e s i n milli m et er s
E R D C / C H L T R 2 0 1 0 5 5
E R D C / C H L T R 2 0 1 0 5 6

A p p e n di x H: C o ol S e a s o n P R E C M e a n Ar e al 

E x c e e d a n c e Pr o b a biliti e s f or 

1 0 0 Y e ar R et ur n P eri o d f or 7 5 8 

D eli n e at e d S u b B a si n s of t h e 

C R B

Fi g ur e 2 2 C o ol s e a s o n P R E C m e a n ar e al ex c e e d a n c e pr o b a biliti e s f or 1 0 0 y e ar 

r et ur n p eri o d f or 7 5 8 d eli n e at e d s u b b a si n s of t h e C R B (f or 1 1 0 3 0 6 0

9 0 , a n d 1 2 0 d ay d ur ati o n s) (v al u e s i n milli m et er s

 
E R D C / C H L T R 2 0 1 0 5 7
E R D C / C H L T R 2 0 1 0 5 8

A p p e n di x I: W ar m S e a s o n P R E C M e a n Ar e al 

E x c e e d a n c e Pr o b a biliti e s f or 

1 0 0 Y e ar R et ur n P eri o d f or 7 5 8 

D eli n e at e d S u b B a si n s of t h e C R B

Fi g ur e 2 3 W ar m s e a s o n P R E C m e a n ar e al ex c e e d a n c e pr o b a biliti e s f or 1 0 0 y e ar 

r et ur n p eri o d f or 7 5 8 d eli n e at e d s u b b a si n s of t h e C R B (f or 1 1 0 3 0 6 0 , 

a n d 9 0 d ay d ur ati o n s) (v al u e s i n milli m et er s . 
E R D C / C H L T R 2 0 1 0 5 9
E R D C / C H L T R 2 0 1 0 6 0

A p p e n di x J: M o nt hl y ( N o v e m b er J u n e) a n d W Y

S W E M e a n Ar e al E x c e e d a n c e 

Pr o b a biliti e s f or 1 0 0 Y e ar R et ur n 

P eri o d f or 7 5 8 D eli n e at e d S u b

B a si n s of t h e C R B

Fi g ur e 2 4 M o nt hly ( N ov e m b er J u n e) a n d W Y S W E m e a n ar e al exc e e d a n c e 

pr o b a biliti e s f or 1 0 0 y e ar r et ur n p eri o d f or 7 5 8 d eli n e at e d s u b b a si n s of t h e C R B 

(v al u e s i n milli m et er s
E R D C / C H L T R 2 0 1 0 6 1
E R D C / C H L T R 2 0 1 0 6 2

A cr o n y m s a n d A b br e vi ati o n s

A M P a n n u al m a xi m u m pr e ci pit ati o n 

A S O S A ut o m at e d S urf ac e O bs er vi n g S yst e m 

C O O P C o o p er ati v e O bs er v ers Pr o gr a m 

C R B C ol u m bi a Ri v er B asi n 

C S V c o m m a s e p ar at e d v al u es 

D E M di git al el e v ati o n m o d el 

E C C C E n vir o n m e nt a n d Cli m at e C h a n g e C a n a d a

E S RI E n vir o n m e nt al S yst e ms R es e ar c h I nstit ut e

E V T e xtr e m e v al u e t h e or y 

G E V g e n er aliz e d e xtr e m e v al u e

G H C N Gl o b al Hist ori c al Cli m at ol o g y N et w or k 

I D i d e ntifi c at o n

M D S missi n g d at a i n s e as o n

M D T Missi n g D at a Ti m e

M L E m a xi m u m li k eli h o o d esti m at e

N D R n u m b er of d a ys wit h r ai n 

N L D A S N ort h A m eri c a n L a n d D at a Assi mil ati o n S yst e m 

N SI M S u m b er of si m ul ati o ns 

N W D N ort h w est er n Di visi o n 

P R E C pr e ci pit ati o n

Pr o b pr o b a blilit es

R F A r e gi o n al fr e q u e n c y a n al ysis 

R P r et ur n p eri o d

S C E NI C S o ut h w est Cli m at e a n d E n vir o n m e nt al I nf or m ati o n C oll a b or ati v e 

S N O T E L S n o w T el e m etr y 

S W E s n o w w at er e q ui v al e nt 

T S R ot al s e as o n al r ai nf all 

U S A C E U S Ar m y C or ps of E n gi n e ers

W Y w at er y e ar
R E P O R T D O C U M E N T A TI O N P A G E F or m A p pr o v e d

O M B N o. 0 7 0 4 0 1 8 8

T h e p u bli c r e p orti n g b ur d e n f or t hi s c oll e cti o n of i nf or m ati o n i s e sti m at e d t o a v er a g e 1 h o ur p er r e s p o n s e, i n cl u di n g t h e ti m e f or r e vi e wi n g i n str u cti o n s, s e ar c hi n g e xi sti n g d at a 

s o ur c e s, g at h eri n g a n d m ai nt ai ni n g t h e d at a n e e d e d, a n d c o m pl eti n g a n d r e vi e wi n g t h e c oll e cti o n of i nf or m ati o n. S e n d c o m m e nt s r e g ar di n g t hi s b ur d e n e sti m at e or a n y ot h er a s p e ct

of t hi s c oll e cti o n of i nf or m ati o n, i n cl u di n gs u g g e sti o n s f or r e d u ci n g t h e b ur d e n, t o D e p art m e nt of D ef e n s e, W a s hi n gt o n H e a d q u art er s S er vi c e s, Dir e ct or at e f or I nf or m ati o n O p er ati o n s

a n d R e p ort s ( 0 7 0 4 0 1 8 8), 1 2 1 5 J eff er s o n D a vi s Hi g h w a y, S uit e 1 2 0 4, Arli n gt o n, V A 2 2 2 0 2 4 3 0 2. R e s p o n d e nt s s h o ul d b e a w ar e t h at n ot wit h st a n di n g a n y ot h er pr o vi si o n of

l a w, n o p er s o n s h all b e s u bj e ct t o a n y p e n alt y f or f aili n g t o c o m pl y wit h a c oll e cti o n of i nf or m ati o n if it d o e s n ot di s pl a y a c urr e ntl y v ali d O M B c o ntr ol n u m b er.

P L E A S E D O N O T R E T U R N Y O U R F O R M T O T H E A B O V E A D D R E S S.

1. R E P O R T D A T E 

J u ne 2 0 2 0

2. R E P O R T T Y P E

Fi nal Re p ort

3. D A T E S C O V E R E D ( Fr o m T o)

4. TI T L E A N D S U B TI T L E

S patial A nal ysis of Preci pitati o n a n d S n o w W ater E q ui vale nt E xtre mes f or t he C ol u m bia 

Ri ver B asi n

5 a. C O N T R A C T N U M B E R

5 b. G R A N T N U M B E R

5 c. P R O G R A M E L E M E N T N U M B E R

6. A U T H O R( S)

Bria n E. S ka hill, A n gela M. D ure n, L ucia na C u n ha, a n d C hris B a h ner

5 d. P R O J E C T N U M B E R

5 e. T A S K N U M B E R

5f. W O R K U NI T N U M B E R

7. P E R F O R MI N G O R G A NI Z A TI O N N A M E( S) A N D A D D R E S S( E S) ( s e e r e v er s e) 8. P E R F O R MI N G

O R G A NI Z A TI O N R E P O R T

N U M B E R

E R D C/ C H L T R 2 0 1 0

9. S P O N S O RI N G/ M O NI T O RI N G A G E N C Y N A M E( S) A N D A D D R E S S( E S)

U S Ar m y C or ps of E n gi neers, N ort h wester n Di visi o n

P ortla n d, O R 9 7 2 0 8 2 8 7 0

1 0. S P O N S O R/ M O NI T O R' S A C R O N Y M( S)

U S A C E N W D

1 1. S P O N S O R/ M O NI T O R' S

R E P O R T N U M B E R( S)

1 2. DI S T RI B U TI O N/ A V AI L A BI LI T Y S T A T E M E N T

A p pr o ve d f or p u blic release; distri b uti o n is u nli mite d.

1 3. S U P P L E M E N T A R Y N O T E S

F u n di n g Acct C o de U 4 3 6 3 3 1 2; A M S C O C o de 0 3 1 3 9 8

1 4. A B S T R A C T

Rece nt a d va nces i n t he s patial statistics of e xtre mes a n d m o del cali brati o n were a p plie d t o de vel o p a n d deli ver areal e xc ee da nce 

esti mates f or preci pitati o n ( P R E C), b y seas o n a n d d urati o n, a n d s n o w water e q ui vale nt ( S W E), b y c o ol seas o n m o nt h a n d f or t he water 

year, f or 7 5 8 deli neate d s u b basi ns of t he C ol u m bia Ri ver B asi n ( C R B), w hic h c orres p o n d t o a ne w C R B h y dr ol o g y m o del waters he d 

deli neati o n. U n dersta n di n g t hat f ut ure U S Ar m y C or ps of E n gi neers, N ort h wester n Di visi o n, missi o n re q uire me nts ma y c ha n ge, pr oj ect 

e xec uti o n als o i ncl u de d t he de vel o p me nt a n d deli ver y of a n a p plicati o n g ui da nce d oc u me nt t o cre di bl y c o m p ute areal e xcee da nce 

esti mates, i ncl u di n g u ncertai nt y, f or P R E C or S W E f or a n y ar bitrar y area wit hi n t he C R B. R, a free s oft ware e n vir o n me nt f or s tatistical 

c o m p uti n g a n d gra p hics ( htt ps:// w w w.r pr oj ect. or g/), a n d Q GI S, a free a n d o pe n s o urce ge o gra p hic i nf or mati o n s yste m 

( htt ps:// q gis. or g/e n/site/i n de x. ht ml), were t he pri mar y t o ols use d f or pr o d uct de vel o p me nt a n d deli ver y. T he f oll o wi n g R s oftware 

pac ka ges were pri maril y use d d uri n g pr oj ect e xec uti o n: e v d, Gl m net, ma ps, raster, r g dal, S D M T o ols, s p, a n d S patial E xtre mes.

1 5. S U B J E C T T E R M S 

C ol u m bia Ri ver W aters he d, H y dr ol o gic m o dels, H y dr ol o g y, Preci pitati o n ( Mete or ol o g y), R u n off, S n o w

1 6. S E C U RI T Y C L A S SI FI C A TI O N O F: 1 7. LI MI T A TI O N O F 

A B S T R A C T

S A R

1 8. N U M B E R 

O F 

P A G E S

7 3

1 9 a. N A M E O F R E S P O N SI B L E P E R S O N

Bria n E. S ka hill a. R E P O R T

U nclassifie d

b. A B S T R A C T

U nclassifie d

c. T HI S P A G E

U nclassifie d 1 9 b. T E L E P H O N E N U M B E R (I n cl u d e ar e a c o d e)

9 7 1 8 0 4 0 3 7 3

St a n d ar d F or m 2 9 8 ( R e v. 8/ 9 8)

Pr e s cri b e d b y A N SI St d. Z 3 9. 1 8
7. P E R F O R MI N G O R G A NI Z A TI O N N A M E( S) A N D A D D R E S S( E S) ( c o nti n u e d)

 

C oastal a n d H y dra ulics La b orat or y

U S Ar m y E n gi neer Researc h a n d De vel o p me nt Ce nter

3 9 0 9 Halls Ferr y R oa d

Vic ks b ur g, M S 3 9 1 8 0 6 1 9 9

U S Ar m y C or ps of E n gi neers, N ort h wester n Di visi o n 

P O B o x 2 8 7 0

P ortla n d, Ore g o n 9 7 2 0 8 2 8 7 0

W E S T C o ns ulta nts

1 0 1 P ar ks h ore Dri ve

F ols o m, Calif or nia 9 5 6 3 0

W E S T C o ns ulta nts 

2 6 0 1 2 5t h St. S E

S uite 4 5 0

Sale m, Ore g o n 9 7 3 0 2