Secood Confmrancr on Hydro&printad fro. Praprint Vol-:
utaorolom. October 25-27. 1977. I o r o m t o . h t . . C d .
Pub1imh.d by h c i c a m neteoro10gic.l S o e i a y . Borntoo. ..aM
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SPATIAL CHARACTERISTICS OF PRAIRIE RAINFALL
G. E. Dyck and D. M. Gray
D i v i s i o n of Hydrology
U n i v e r s i t y cbf Saskatchewan
Saskatoon, Saskatchewan
1.
INTRODUCTION
R e l i a b l e i n f o r m a t i o n on r a i n f a l l chara c t e r i s t i c s is required f o r hydrologic design.
E s t i m a t e s of i n t e n s i t i e s and d e p t h s ; t h e i r f r e quency-of-occurrence and a r e a l and temporal d i s t r i b u t i o n a r e used t o d e t e r m i n e w a t e r y i e l d ,
s u r f a c e r u n o f f r a t e s and s e d i m e n t p r o d u c t i o n .
F u r t h e r t h e s e d a t a a r e used by m e t e o r o l o g i s t s
f o r many p u r p o s e s which i n c l u d e , t h e p h y s i c a l
d e s i g n and s e l e c t i o n o f p r e c i p i t a t i o n gauges and
t h e d e s i g n of n e t w o r k s .
The d e t e r m i n a t i o n of a c c u r a t e , funct i o n a l d e s c r i p t i o n s of t h e c h a r a c t e r of P r a i r i e
r a i n f a l l , b e c a u s e of i t s wide v a r i a b i l i t y , depends on t h e a c c u r a c y w i t h which t h e amount of
r a i n f a l l c a n b e measured a t a p o i n t i n s p a c e and
t i m e . I t i s g e n e r a l l y assumed t h a t t h e r a i n f a l l
measurements o b s e r v e d a t e a c h gauge ( p o i n t ) i n a
n e t w o r k r e p r e s e n t t h e t e m p o r a l v a r i a t i o n and
a v e r a g e d e p t h of r a i n f a l l o v e r a n a d j a c e n t a r e a .
I f gauges of a c c e p t a b l e a c c u r a c y a r e used and
placed i n r e p r e s e n t a t i v e l o c a t i o n s t h e accuracy
of e x t r a p o l a t i n g t h e p o i n t measurements i n s p a c e
i s a f u n c t i o n o f t h e n a t u r a l v a r i a b i l i t y of t h e
e v e n t . The a c c u r a c y of t h e e s t i m a t e s of r a i n f a l l volume and r a i n f a l l v a r i a b i l i t y o v e r a n e t work depends i n p a r t o n t h e number of gauges
used t o sample t h e e v e n t . To o b t a i n t h e same
d e g r e e of a c c u r a c y i n a r e a l e s t i m a t e s of t h e s e
v a l u e s f o r u n i f o r m l y and non-uniformly d i s t r i b u t e d e v e n t s fewer gauges would b e r e q u i r e d t o
s a m p l e a u n i f o r m l y - d i s t r i b u t e d e v e n t a s t h e measurement from e a c h gauge may b e assumed t o r e present a larger area.
Long-duration and l a r g e - a r e a p r e c i p i t a t i o n i s much less v a r i a b l e t h a n s h o r t - d u r a t i o n
and s m a l l - a r e a p r e c i p i t a t i o n (McKay, 1 9 7 0 ) . I t
h a s a l s o b e e n s u g g e s t e d by some i n v e s t i g a t o r s
(McKay, 1970) t h a t t h e network d e n s i t y r e q u i r e ments f o r long-term a v e r a g e s may b e less s t r i n gent than f o r i n d i v i d u a l storm a n a l y s i s because
w i t h i n c r e a s i n g t i m e t h e e f f e c t s of h i g h l y v a r i a b l e s t o r m s a r e masked by o t h e r r a i n s t o r m s r e s u l t i n g i n a more u n i f o r m s p a t i a l d i s t r i b u t i o n .
I n t h e p a p e r r a i n f a l l d a t a a r e p r e s e n t e d showing
t h e intensity-duration-frequency c h a r a c t e r i s t i c s
a s s o c i a t e d w i t h P r a i r i e r a i n f a l l and t h e s p a t i a l
v a r i a b i l i t y of s e a s o n a l , monthly and i n d i v i d u a l
s t o r m amounts. S t a n d a r d s t a t i s t i c a l t e s t s w e r e
a p p l i e d t o i n d i v i d u a l s t o r m e v e n t s and long-term
r a i n f a l l t o t a l s t o d e t e r m i n e i f "reduced" n e t works p r o v i d e r e a s o n a b l e e s t i m a t e s of t h e " t r u e "
r a i n f a l l c h a r a c t e r i s t i c s o v e r small w a t e r s h e d
areas.
2.
BASIC DATA
The d a t a used i n t h e s t u d y w e r e obt a i n e d d u r i n g t h e 8-year per.iod; 1968 t h r o u g h
1975, from a "dense p r e c i p i t a t i o n network" on t h e
IHD R e p r e s e n t a t i v e B a s i n - The Bad Lake Watershed
- which i s l o c a t e d a p p r o x i m a t e l y 25 m i l e s s o u t h west of Rosetown i n west c e n t r a l Saskatchewan;
L a t i t u d e 51°18'N, L o n g i t u d e 108OW. The network
c o n s i s t s of 4 1 MSC s t a n d a r d gauges p l a c e d a p p r o x i m a t e l y on a one s q u a r e m i l e g r i d and 32 MSC t i p p i n g b u c k e t r a i n g a u g e s and 9 F i s c h e r P o r t e r p r e c i p i t a t i o n gauges (Note: t h e t i p p i n g b u c k e t gauges
and F i s c h e r P o r t e r gauges w e r e l o c a t e d a t t h e same
sites a s t h e s t a n d a r d g a u g e s ) . For t h o s e s t a t i o n s
h a v i n g b o t h a t i p p i n g b u c k e t gauge and a s t a n d a r d
gauge, t h e r e a d i n g from t h e s t a n d a r d gauge was
used t o v e r i f y t h e measurement from t h e r e c o r d i n g
gauge and t o a d j u s t i t s s t o r m t o t a l t o t h e s t a n d a r d c a t c h ( s e e Dyck, 1 9 7 7 ) .
The adequacy of t h e network f o r d e t e r mining t h e s p a t i a l c h a r a c t e r of r a i n f a l l e v e n t s
on t h e a r e a h a s been e v a l u a t e d by Dyck (1977)
u s i n g i n t e r - g a u g e c o r r e l a t i o n s . He found, a s s u ming a n a c c e p t a b l e l i m i t of a s s o c i a t i o n between
gauges, based on t h e t o t a l d e p t h s of i n d i v i d u a l
s t o r m s , b e i n g a n i n t e r - g a u g e c o r r e l a t i o n between gauges, r , e q u a l t o o r g r e a t e r t h a n 0 . 9 0 ,
t h a t t h e network was a d e q u a t e f o r d e t e r m i n i n g
t h e storm c h a r a c t e r i s t i c s over t h e a r e a a s a l l
gauges i n t h e network were encompassed by a t
l e a s t one i s o - c o r r e l a t i o n l i n e h a v i n g a v a l u e ;
r = 0.90.
H e r s h f i e l d (1965) and Huff and Shipp
(1969) i n t h e i r s t u d i e s i n t h e USA concerned
w i t h t h e s p a c i n g of r a i n g a u g e s have used t h e
same v a l u e of c o r r e l a t i o n c o e f i c i e n t a s a l i m i t
of a c c e p t a b i l i t y of a network.
3.
MONTHLY RAINFALL: I n t e n s i t y - D u r a t i o n Frequency C h a r a c t e r i s t i c s
The i n t e n s i t y - d u r a t i o n - f r e q u e n c y c h a r a c t e r i s t i c s of r a i n f a l l e v e n t s h a v e found common
u s a g e i n t h e d e s i g n of small h y d r a u l i c s t r u c t u r e s o r conveyance s y s t e m s s u c h a s c u l v e r t s ,
b r i d g e o p e n i n g s , s t o r m s e w e r s and d r a i n a g e
d i t c h e s . To g a i n i n f o r m a t i o n on t h e s e r a i n f a l l
c h a r a c t e r i s t i c s f o r t h e g e o g r a p h i c a r e a i n which
t h e network i s l o c a t e d a s t u d y was u n d e r t a k e n
u s i n g t h e maximum p r e c i p i t a t i o n amounts r e c o r d e d
by e a c h t i p p i n g b u c k e t gauge i n t h e network o v e r
t i m e p e r i o d s o f : 5 min, 1 0 min, 1 5 min, 30 min,
1 h r , 2 h r , 6 h r , 1 2 h r and 24 h r f o r a l l d a y s
d u r i n g t h e p e r i o d (1968-1975) i n which t h e d a i l y
t o t a l (24-hr) was e q u a l t o o r g r e a t e r t h a n 0 . 2 5
i n c h e s . The s e l e c t i o n of a d a i l y t o t a l 7 0.25
i n c h e s a s a l i m i t i n g v a l u e f o r storms t o be included i n t h e a n a l y s i s was somewhat a r b i t r a r y
g i v i n g c o n s i d e r a t i o n t o t h e f a c t t h a t i t would
b e h i g h l y u n l i k e l y t h a t any storm of l e s s e r
amount over t h e a r e a would produce measurable
r u n o f f . For each gauge t h e maximum monthly
amounts i n g i v e n d u r a t i o n , PM, were expressed a s
a r a t i o t o t h e maximum 24-hour t o t a l recorded
f o r t h e month, P24. Using t h e s e d a t a t h e cumul a t i v e r e l a t i v e frequency c u r v e s of t h e r a t i o
P /P24 were g e n e r a t e d f o r storm d u r a t i o n s f o r
M
each month. F i g u r e 1 shows t h e median v a l u e s of
t h e r a t i o , P /P24, which w i l l be e q u a l l e d o r
M
exceeded 50% of t h e time p l o t t e d w i t h storm dur a t i o n f o r t h e d i f f e r e n t months. The d a t a presented i n Figure 1 i l l u s t r a t e several features
of P r a i r i e r a i n f a l l :
(1) The r e l a t i o n s h i p between P / P Z 4 and storm
M
duration follows an exponential function.
(2) The shapes of t h e c u r v e s e x h i b i t ;
( a ) Larger p e r c e n t a g e s of t h e maximum
monthly 24-hour t o t a l , P24. a r e produced by s h o r t d u r a t i o n storms ( l e s s
than two hours d u r a t i o n ) i n J u l y and
August t h a n i n May and June. T h i s i s
assumed t o b e a s s o c i a t e d w i t h t h e f a c t
t h a t t h e major l i f t i n g mechanism producing r a i n i n J u l y and August i s convective activity.
( b ) No a p p r e c i a b l e d i f f e r e n c e s between;
July-August and May-June. These observations suggest the data f o r the four
months may b e combined t o two s e p a r a t e
groups: May-June and July-August.
When t h e d a t a a r e combined i n t h i s
manner t h e l a r g e s t d e p a r t u r e s from t h e
"average" c u r v e s of P / P Z 4 f o r J u l y
and August occur a t t f e s h o r t d u r a t i o n s ,
whereas t h e l a r g e r d i f f e r e n c e s from a n
a v e r a g e c u r v e f o r May and June occur
w i t h t h e l o n g e r d u r a t i o n storms.
(3) September r a i n f a l l e x h i b i t s p a t t e r n s i n t e r mediate between t h o s e given by t h e May-June
and July-August groupings.
MAY
A
A
JUNE
0
JULY
AUGUST
SEPTEMBER
D
0
1
2
3
4
5
6
7
DURATION
8
9
1
0
I
I
1
(HOURS)
F i g u r e 1. Maximum monthly p r e c i p i t a t i o n amounts
f o r storms of d i f f e r e n t d u r a t i o n s compared
w i t h 24-hr maximum f o r d i f f e r e n t months, r e l a t i v e frequency of o c c u r r e n c e 50%, Bad Lake
Watershed; May through September i n c l u s i v e ,
1968-1975.
2
Also p l o t t e d i n F i g u r e 1 i s t h e average curve of
P /P24 v e r s u s storm d u r a t i o n derived from d a t a
gyven by McKay (1970) f o r t h e r e g i o n i n which
t h e network i s l o c a t e d . I t can be observed t h a t
f o r storms of d u r a t i o n s l e s s than t h r e e h o u r s ,
McKay's r e s u l t s correspond approximately t o t h e
a v e r a g e of t h e v a l u e s o b t a i n e d from t h e network.
For l o n g e r d u r a t i o n storms (> 3 h r ) t h e r a t i o s
of PM/P24 suggested by McKay a r e s l i g h t l y l e s s
than t h e average v a l u e s recorded.
The d a t a g i v e n i n F i g u r e 1 a r e u s e f u l
i n d e s i g n f o r e s t i m a t i n g t h e r a i n f a l l amounts
f o r s h o r t - d u r a t i o n storms from t h e 24-hr t o t a l s .
Such i n f o r m a t i o n i s f r e q u e n t l y r e q u i r e d i n t h e
d e s i g n of h y d r a u l i c s t r u c t u r e s (eg. b r i d g e s ,
c u l v e r t s , e t c . ) f o r s m a l l d r a i n a g e a r e a s when
only t h e 24-hr t o t a l s a r e a v a i l a b l e . For example,
i f t h e d e s i g n storm was of six-hour d u r a t i o n and
occurred i n June, from F i g u r e 1 t h e median r a t i o
of P6/P24 would be t a k e n a s 0.8.
This value rep r e s e n t s t h e r a t i o which would be e q u a l l e d o r
exceeded 50 p e r c e n t of t h e time. Values of P24
f o r various r e t u r n periods a r e r e a d i l y a v a i l a b l e
from p u b l i c a t i o n s such a s ; "Atlas of R a i n f a l l Intensity-Duration-Frequency Data f o r Canada"
(Bruce, 1968). For t h i s example, t h e 25-year,
24-hour r a i n f a l l f o r t h e network a r e a i s 3.0
inches. T h e r e f o r e , t h e e s t i m a t e d six-hour r a i n f a l l would b e taken a s 2.4 i n c h e s . Note, by
t h i s procedure one h a s e s s e n t i a l l y d e r i v e d a
six-hour storm having a d i f f e r e n t r e t u r n p e r i o d
than a 25-year storm.
4.
SPATIAL CHARACTER OF RAINFALL
4.1
Storm A n a l y s i s
Whenever r a i n f a l l amounts a r e measured
over f i x e d p e r i o d s of time, such a s a day, i t i s
possible t h a t t h e depth reported f o r the period
r e p r e s e n t s r a i n f a l l produced by more t h a n one
weather system. Also, r a i n a s s o c i a t e d w i t h a
p a r t i c u l a r system does n o t n e c e s s a r i l y s t a r t and
end on t h e same c a l e n d a r day. I n o r d e r t o del i n e a t e "unique" r a i n e v e n t s a r a i n storm was
defined a s ; a r a i n p e r i o d which was s e p a r a t e d
from preceeding and succeeding r a i n e v e n t s o r
measurable p r e c i p i t a t i o n amounts by a p e r i o d of
s i x o r more h o u r s . Any storm producing a meas u r a b l e depth of r a i n a t any network raingauge
was included i n t h e s t u d y . A s i m i l a r d e f i n i t i o n
of a storm was used by Huff (1966) and Huff and
Shipp (1969) i n s t u d i e s of r a i n f a l l c h a r a c t e r i s t i c s i n Illinois. Partitioning the rainfall
d a t a c o l l e c t e d by t h e 32 t i p p i n g bucket r a i n
gauges i n t o storms a c c o r d i n g t o t h i s d e f i n i t i o n
r e s u l t e d i n t h e d e l i n e a t i o n of 516 storms over
t h e network d u r i n g t h e 8-year period.
These
storms were s t r a t i f i e d i n t o e i g h t r a i n f a l l depth
c l a s s e s based on t h e maximum r a i n f a l l depth r e corded by any gauge i n t h e network i n a given
storm. The d e p t h s and depth-increments used t o
d e f i n e t h e c l a s s e s were: 0.01, 0.02-0.10, 0.110.25, 0.26-0.50, 0.51-1.00,
1.01-1.50, 1.51-2.00
and g r e a t e r t h a n 2.00 i n c h e s . From t h e s e d a t a
( s e e Table 1 ) i t can be observed t h a t :
1. The maximum d e p t h of r a i n f a l l recorded by
approximately 64 p e r c e n t of t h e s t o r m s was l e s s
t h a n 0.11 inches.
2. Twenty-two storms, o r 4.3% of t h e t o t a l numb e r , produced a maximum p o i n t r a i n f a l l g r e a t e r
than 1 . 0 i n c h .
3. Only t h r e e storms o r 0.6% of t h e t o t a l number
produced a maximum p o i n t r a i n f a l l amount g r e a t e r
t h a n 2.0 i n c h e s .
The d a t a g i v e n i n Table 1 a l s o shows
t h e p r o p o r t i o n a t e amount of s e a s o n a l r a i n f a l l
(May through September) which i s produced by
storms f a l l i n g within t h e d i f f e r e n t depth c l a s s e s
a s measured by a c e n t r a l l y - l o c a t e d gauge i n t h e
network. It can b e observed t h a t :
1. I n t h e p e r i o d of r e c o r d t h e h i g h e s t percent a g e of t h e s e a s o n a l r a i n f a l l (May-September),
a n a v e r a g e 31.3%, was produced by s t o r m s i n
which t h e maximum d e p t h of p r e c i p i t a t i o n was between 0.51 and 1 . 0 0 i n c h e s .
2. Only a s m a l l p e r c e n t a g e of t h e t o t a l s e a s o n a l
p r e c i p i t a t i o n , on t h e a v e r a g e 14%, was produced
by s t o r m s w i t h d e p t h s l e s s t h a n 0.25 i n c h e s . A
r e l a t i v e l y s m a l l number of storms c o n t r i b u t e t h e
major p a r t of t h e t o t a l s e a s o n a l r a i n f a l l a t a
g i v e n l o c a t i o n . For example, 68 s t o r m s having a
d e p t h g r e a t e r t h a n 0.50 i n c h e s , which r e p r e s e n t s
13.2% of t h e t o t a l number of s t o r m s , produced
70.8% of t h e t o t a l r a i n recorded i n t h e p e r i o d .
between 0.25 and 1.50 i n c h e s r e s u l t e d i n r a i n
over t h e e n t i r e network, whereas o n l y 33% of
t h o s e storms w i t h a maximum p o i n t r a i n f a l l between 0.02 and 0.25 i n c h e s r e s u l t e d i n r a i n over
t h e e n t i r e network.
These r e s u l t s s u g g e s t t h a t f o r t h e
t y p e s of s t o r m r e c o r d e d t h e a r e a l e x t e n t of
r a i n f a l l o v e r a watershed c a n b e a s s o c i a t e d w i t h
t h e depth of r a i n f a l l ; t h e g r e a t e r t h e d e p t h of
point r a i n f a l l recorded, the l a r g e r the a r e a receiving precipitation.
Table 2. Number of storms producing measurable
r a i n over e n t i r e network; May-September,
1968-1975.
Depth C l a s s
(inches)
.01
.02-. 1 0
.11-. 25
.26-. 50
.51-1.00
1.01-1.50
1.51-2.00
>2.00
Total
T a b l e 1. Number of s t o r m s f a l l i n g w i t h i n
d i f f e r e n t maximum d e p t h i n c r e m e n t s ( c l a s s e s ) ;
May-September, 1968-1969.
Maximum P o i n t
P e r c e n t of T o t a l
R a i n f a l l ( i n c h e s ) No. of Storms R a i n f a l l (cenClass
trally-located
gauge)
.01
.02-. 1 0
.11-. 25
.26-.50
.51-1.00
1.01-1.50
1.51-2.00
>2.00
Total
154
174
75
45
46
12
7
3
516
The d a t a p r e s e n t e d i n T a b l e 1 i n d i c a t e t h a t
w i t h i n t h e p e r i o d of r e c o r d no i n t e n s e heavy
r a i n f a l l a c t i v i t y o c c u r r e d o v e r t h e network.
Hence, t h e r e s u l t s p r e s e n t e d i n t h i s paper a r e
l i m i t e d i n t h e i r a p p l i c a t i o n t o low i n t e n s i t y ,
s m a l l r a i n f a l l e v e n t s . However, i t should be
r e c o g n i z e d t h a t r a i n s of t h i s c h a r a c t e r a r e t h o s e
most f r e q u e n t l y e x p e r i e n c e d throughout t h e
P r a i r i e s i n which t h e network i s l o c a t e d . Dyck
(1977) r e p o r t e d t h a t t h e mean r a i n f a l l s t a t i s t i c s
r e c o r d e d i n t h e s t u d y p e r i o d were i n c l o s e agreement w i t h t h e long-term s t a t i s t i c s f o r t h e r e g i o n
r e p o r t e d by Longley (1972) and McKay (1970).
Of t h e 516 s t o r m s r e p o r t e d on t h e n e t work o n l y 183 produced 'measurable' r a i n f a l l a t
a l l gauges ( s e e T a b l e 2 ) . These d a t a i n d i c a t e
t h a t no s t o r m i n which t h e maximum recorded
amount by a p a r t i c u l a r gauge was 0.01 i n c h e s
produced 'measurable' r a i n f a l l amounts over t h e
e n t i r e network. By comparing t h e d a t a g i v e n i n
T a b l e s 1 and 2 i t i s e v i d e n t t h a t a l l storms
having a maximum p o i n t p r e c i p i t a t i o n amount
g r e a t e r t h a n 1.50 i n c h e s r e s u l t e d i n measurable
r a i n f a l l amounts a t a l l gauges. I n most c a s e s
t h e s e storms could be associated with r e l a t i v e l y widespread f r o n t a l a c t i v i t y . Approximately 88%
of t h o s e s t o r m s having a maximum p o i n t r a i n f a l l
No. of
Storms
4.2
0
36
47
39
40
11
7
3
183
S p a t i a l D i s t r i b u t i o n of Storm Events
A s t u d y of t h e s p a t i a l d i s t r i b u t i o n of
storm e v e n t s was conducted u s i n g t h e s t a t i s t i c .
t h e c o e f f i c i e n t of v a r i a t i o n , CV, - t h e r a t i o of
t h e s t a n d a r d d e v i a t i o n of t h e d e p t h s of r a i n f a l l
recorded a t t h e d i f f e r e n t gauges t o t h e mean
d e p t h of r a i n f a l l over t h e network, e x p r e s s e d a s
a p e r c e n t a g e , a s a measure of t h e s p a t i a l v a r i a b i l i t y . Longley (1952) and Kendall e t a 1 (1956)
have a l s o used t h e c o e f f i c i e n t of v a r i a t i o n a s a
measure of p r e c i p i t a t i o n v a r i a b i l i t y i n t h e i r
studies.
I n t h e a n a l y s i s 120 s t o r m s t h a t produced measurable r a i n f a l l amounts a t a l l gauges
i n t h e network d u r i n g t h e 5-year p e r i o d ; 19711975, were used. The magnitudes of CV of t h e s e
storms grouped a c c o r d i n g t o a g i v e n r a i n f a l l
depth c l a s s a r e g i v e n i n Table 3. It i s e v i d e n t
from t h e s e d a t a t h a t w i t h i n any g i v e n d e p t h
c l a s s t h e magnitude of CV may v a r y o v e r a wide
r a n g e of v a l u e s . I n o t h e r words, t h e s p a t i a l
c h a r a c t e r of t h e s e low i n t e n s i t y , s m a l l r a i n f a l l
amounts a r e h i g h l y v a r i a b l e . However, t h e d a t a
indicate a trend f o r the s p a t i a l v a r i a b i l i t y t o
d e c r e a s e a s t h e maximum p o i n t r a i n f a l l amount
i n c r e a s e s ; a l l s t o r m s i n which t h e p o i n t r a i n f a l l
d e p t h was g r e a t e r t h a n 2.00 i n c h e s had v a l u e s
of CV < 30%.
T a b l e 3 . S p a t i a l v a r i a b i l i t y of r a i n f a l l ,
Bad Lake Watershed; 1971-1975.
Maximum btorrn
R a m f a l l (In)
Number of R a n ~ v c n t sHaving Speclfled Variability
Coefflclent of Variatlnn 1 % )
11-i!)
21-30
31-40
41-50
51-60 61-90
>Q0
--
0-10
-
.02-.10
0
I
7
I,
5
3
1
.11-.25
0
10
B
9
3
2
2
0
.26-.'10
0
9
5
1
3
2
3
0
3
9
B
2
1
3
1
6
0
4
0
3
0
1
3
0
.51-1.00
1.01-1.50
1.51-2.00
>2.00
Total
J
1
0
0
-
1
-
~-
2
'
I
1
1
34
33
21
13
0
)
0
"
11
1
0
?
9
1
S p a t i a l V a r i a b i l i t y of Monthly and
Seasonal R a i n f a l l
4.3
To a s s e s s t h e s p a t i a l v a r i a b i l i t y
a s s o c i a t e d w i t h long-term r a i n f a l l t o t a l s over a
P r a i r i e r e g i o n , t h e s p a t i a l c h a r a c t e r of monthly
r a i n f a l l t o t a l s were examined. The d a t a used i n
t h i s a n a l y s i s were t h e monthly r a i n f a l l t o t a l s
measured a t each of t h e 41 gauge l o c a t i o n s f o r
t h e months May through September; 1971-1975 inc l u s i v e . T a b l e 4 summarizes t h e network s t a t i s t i c s ; t h e mean, t h e s t a n d a r d d e v i a t i o n and t h e
c o e f f i c i e n t of v a r i a t i o n of t h e monthly r a i n f a l l
amounts f o r t h e s t u d y period. There i s no appa r e n t t r e n d i n t h e d a t a f o r t h e r a i n f a l l amounts
i n any p a r t i c u l a r month t o e x h i b i t c o n s i s t e n t l y
e i t h e r a lower o r higher s p a t i a l v a r i a b i l i t y
t h a n amounts recorded i n any o t h e r month. The
v a l u e s of CV ranged between 9.7% t o 41.3%. Howe v e r , t h e g r e a t e s t v a r i a b i l i t y i n t h e mean r a i n f a l l d e p t h s among gauges f o r each p a r t i c u l a r
month were a s s o c i a t e d with t h o s e months r e c e i v i n g
t h e lowest mean network p r e c i p i t a t i o n . For example, t h e f i v e months; August 1972, May 1973,
June 1973, J u l y 1973 and September 1973, which
recorded t h e s m a l l e s t mean monthly d e p t h s d u r i n g
t h e 5-year p e r i o d e x h i b i t e d t h e widest s p a t i a l
variability.
Table 4. Monthly and s e a s o n a l (May-September)
R a i n f a l l summary f o r Bad Lake Watershed
" ~ e n s eP r e c i p i t a t i o n Network", 1971-1975.
1972
1974
1971-1975
0.88
Hean I I ~ I
I
s t . ~ e v . !1n1
C o e f . of var.
($1
m a n llnl
I t . Dev. linl
CorE. of V a r .
1%)
Total (lnl
S t . Dev. linl
Caef. of :Jar. ($1
(
0.11
ll.'!
2.54
0.25
9.7
1.40
0.15
l'J.8
3 50
3.21
41.3
3.18
0.11
10.3
2.16
0.29
13.:
2.61
4 3
16.2
10.3
6.17
11.11
0.51
4.6
8.87
0.54
6.1
0.44
7.1
4.51
0.40
0.41
ill
24.7
1
12.11
i.64
5.1
7.82
0.56
1.11
7.2
When t h e r a i n f a l l amounts a r e i n t e g r a t e d over time p e r i o d s g r e a t e r than one month
t h e r e i s a marked d e c r e a s e i n t h e s p a t i a l v a r i a b i l i t y . For example, t h e c o e f f i c i e n t of v a r i a t i o n f o r s e a s o n a l amounts (May through September)
recorded by t h e gauges f o r 1971 was 7.5%, a
v a l u e s u b s t a n t i a l l y lower than t h e c o e f f i c i e n t s
f o r monthly v a l u e s . Likewise, t h e v a l u e of CV
f o r t h e f i;e-year
s e a s o n a l t o t a l s was 3.1% ( s e e
Table 4).
5.
REPRESENTATIVENESS OF REDUCED NETWORKS
One of t h e primary purposes of t h e
"Dense p r e c i p i t a t i o n network" was t o o b t a i n inf o r m a t i o n on t h e s p a t i a l c h a r a c t e r of r a i n e v e n t s
over t h e a r e a w i t h t h e view of applying t h e s e
d a t a t o network design. The o p e r a t i o n of
densely-gauged r a i n f a l l networks i s c o s t l y and
I n designing a p r e c i p i t a t i o n
time consuming.
network, f i r s t p r i o r i t y must be given t o obtaini n g measurements of r a i n f a l l c h a r a c t e r i s t i c s of
s u f f i c i e n t accuracy t o s a t i s f y t h e study object i v e s . I f i t can be e s t a b l i s h e d t h a t measurements from a "reduced" network r a t h e r than t h e
"dense" network w i l l f u l f i l l t h e s e requirements
a s u b s t a n t i a l saving i n c o s t s may be r e a l i z e d .
Credence f o r a r e d u c t i o n i n gauge dens i t y of t h e network would be e s t a b l i s h e d i f i t
could be shown t h a t e s t i m a t e s of t h e "true"
s p a t i a l c h a r a c t e r of r a i n f a l l measured by a reduced network d i d n o t d i f f e r s i g n i f i c a n t l y from
t h o s e measured by t h e dense network. I n t h i s
paper, t h e adequacy of d i f f e r e n t reduced networks was t e s t e d by comparing t h e network mean,
P , and t h e s t a n d a r d d e v i a t i o n , s, f o r i n d i v i d u a l
storm e v e n t s obtained w i t h a reduced network
with t h e v a l u e s obtained w i t h t h e dense network.
Acceptance o r r e j e c t i o n of t h e reduced network
was based on t h e well-known s t a t i s t i c a l "t" and
"F" t e s t s ( N e v i l l e , e t a l , 1966).
P r i o r t o undertaking t h i s a n a l y s i s t h e
i n d i v i d u a l storms were c l a s s i f i e d according t o
t h e i r s p a t i a l uniformity.
It was i n d i c a t e d prev i o u s l y t h a t i f gauges of a c c e p t a b l e accuracy
a r e used and placed i n r e p r e s e n t a t i v e l o c a t i o n s
t h e accuracy of e x t r a p o l a t i n g p o i n t measurements
i n space depends on t h e n a t u r a l s p a t i a l v a r i a b i l i t y of t h e r a i n f a l l . N a t u r a l l y , t h e r e f o r e ,
t h e u n i f o r m i t y of t h e e v e n t ( s ) g r e a t l y a f f e c t
network design; t h e more uniform t h e storm t h e
lower t h e network o r sampling d e n s i t y r e q u i r e d .
I n i t i a l l y , i n t h i s s t u d y , it was a n t i c i p a t e d
t h a t t h e c o e f f i c i e n t may b e used t o d i f f e r e n t i a t e
between r a i n storms o r i g i n a t i n g from convective
and f r o n t a l a c t i v i t y . However, t h e s e a t t e m p t s
proved u n s u c c e s s f u l ; i n p a r t because of a l a c k
of information. After e x t e n s i v e review of t h e
d a t a i t appeared t h a t most storms which produced
uniform r a i n f a l l over t h e network had v a l u e s of
CV < 30%. Subsequently each of t h e storms l i s t e d
i n Table 3 were c l a s s i f i e d a s being of uniform
o r non-uniform v a r i a b i l i t y - b a s e d on t h e v a l u e of
CV; t h a t i s uniform i f CV < 30% o r non-uniform
i f CV
30%. On t h e b a s i s of t h i s c r i t e r i o n ,
65 uniform storms and 55 non-uniform storms were
d e l i n e a t e d . Using t h e i n d i v i d u a l storms included
i n each of t h e groups t h e v a l u e s "t" and "F" were
c a l c u l a t e d f o r t h i r t e e n d i f f e r e n t reduced networks and compared a n a i n s t t h e t h e o r e t i c a l
v a l u e s of "t"-and "F' a t t h e 95% p r o b a b i l i t y
l e v e l . These reduced networks included 28,
24, 20, 1 8 , 16, 15, 14, 12, 10, 8 , 4 and 2 gauges
r e s p e c t i v e l y a s compared t o 32 gauges i n t h e
dense network. The gauges included i n each of
t h e 1 3 reduced networks were s e l e c t e d s o t h a t on
t h e reduced networks t h e gauges were spaced i n
an approximate uniform g r i d .
The number of uniform and non-uniform
storms i n each reduced network f o r t h e storm
groups, uniform and non-uniform storms, i n which
t h e mean P and v a r i a n c e s 2 were s i g n i f i c a n t l y
d i f f e r e n t 195% l e v e l ) fromrthose c a l c u l a t e d f o r
t h e dense network a r e given i n Table 5. These
d a t a suggest t h a t t h e minimum number of gauges
required t o p r e s e r v e t h e dense network s t a t istics,
and s 2 , f o r uniform and non-uniform,
d
storms a r e 16 an2 18 gauges which r e p r e s e n t
gauge d e n s i t i e s (gauges/mile2) of 0.38 and 0.43
respectively.
Table 5. Number of storms in a particular reduced
network that had significant differences in
either their network mean or network variance
as compared to the "Dense" network mean and
variance.
Number of Gauges
in Wduced Network
D
~
~
~
Uniform Storms
?
~
Network
(w)
Variance
y
Netrrork
Hean
Non-L'niform Storms
Network
Network
Variance
Hean
28
0.67
0
0
0
0
24
0.57
0
0
0
0
20
3.48
0
0
2
0
18
0.43
0
0
0
0
16
0.38
0
0
1
0
15
0.36
4
0
5
0
14
0.33
3
I)
7
0
It is also evident from the data presented in Table 5 that the use of a reduced network for describing the "true" spatial character
of rain events is limited by the variance; its
magnitude and difference from the variance of
the dense network. It should be recognized that
in order for the "t" test applied to the means
to be valid, the variances, :
s and s2 must not
r'
be significantly different (Neville et al, 1966).
For both uniform and non-uniform rain events it
was found the means of the reduced and dense
network differed significantly only when the
network was reduced to two gauges (0.05 gauges/
mile2).
network included 41 gauges; 32 tipping-bucket
and 9 Fischer-Porter gauges. The fourteen reduced networks consisted of 32, 28, 24, 20, 18,
16, 15, 14, 12, 10, 8, 6, 4 and 2 gauges. The
reduced network containing 32 gauges included all
the tipping bucket gauges that were considered
to be the dense network in the analysis of individual storm events. The gauges included in
the other thirteen reduced networks are the
same as those used in the storm analysis.
The results of this analysis, shown in
Table 6, indicate that the minimum number of
gauges required to preserve the "dense" network
statistics Fd and s2 on the 42 square mile watershed area for monthfy, seasonal and 5-year rainfall amounts, are 16, 4 and 2 gauges respectively.
The gauge densities (gauges/mile2) of these
reduced networks are 0.38, 0.10 and 0.05 respectively. These results clearly indicate that
network gauge density requirements decrease as
the period over which precipitation is totalled
increases. However, if one compares the data in
Table 5 with that given in Table 6, it can be
observed that under certain conditions the network requirements for monthly and storm rainfall
may be the same as the minimum gauge density required-to preserve the dense network statistics; Pd and sj, for each was 0.38 gauges/mile2.
Table 6. Number of rain periods in a particular
reduced network that had significant differences in either their network mean or network
variance as compared to the "Dense" network
mean and variance.
The data presented in Table 5 also
indicate that different reduced networks reject
a different number of storms in each storm group
and that a reduction in gauge density does not
necessarily mean that more storms are rejected.
For example, for non-uniform storms and a reduced network containing 20 gauges, two storms
were rejected by the "F" test. However, in the
reduced network containing 18 gauges no storms
were rejected. This result suggests that the
positioning of gauges in a network is an important factor.
To determine the extent the gauge density of the dense network could be reduced before the network statistics, F and s2, become
significantly different from those for the dense
network for long term rainfall totals, the "t"
test and "F" test were applied to: (a) monthly
totals, (b) seasonal totals, and (c) 5-year
seasonal totals for various combinations of reduced gauge networks. The basic data used in the
analysis were the monthly precipitation totals
for the months May-September; 1971-1975. For
each of the long-term rainfall groupings the
values "t" and "F" were calculated for fourteen
different reduced networks and compared with
the corresponding theoretical values at the 95%
probability level.
In analysis of these data, the dense
It has been stated that a primary purpose of the "dense precipitation network" was to
obtain information on the spatial character of
rain events occurring over the study area. It
has also been shown that a network of lesser
density will provide statistically valid estimates of the areal mean and variance. The number and placement of gauges required in a reduced
letwork to preserve the dense network statistics;
P and si, depends on the spatial character of
tRe rain event and the length of time over which
rainfall amounts are integrated. The minimum
gauge densities (gauges/mile2) required to preserve the statistics;
and s2 on the 42 square
mile area for individuaf storm~'monthly, seasonal
and 5-year seasonal rainfall were found to be;
0.43, 0.38, 0.10 and 0.05 respectively. As Dyck
(1977) reported that the mean rainfall statistics
recorded in the study period were in close agreement with the long-term statistics for a large
geographical area surrounding the study area, it
is assumed that the gauge density requirements
established for the network may serve as general
guides for use in the design of precipitation networks on areas which experience similar climatic
conditions and of similar size to the dense
network.
It must be recognized that no single
rigorous, universally-applicable criteria can be
established for use in network design for a region.
The required density and placement of precipitation gauges within a specific area may in part
be influenced by unique climatic gradients such
as those which may be caused by consistant storm
tracks or major changes in elevation. In the
Canadian prairie region, rain storms may show
directional bias as westerly winds predominate in
the region. The accuracy of rainfall measurements
and/or the degree of association between gauges
for a given network can only be established after
adequate sampling has been conducted in the region
of interest.
5.1
Precision of Reduced Networks
The relative precision with which networks of different gauge density measure the
mean storm rainfall over the 42 square mile area
was based on the magnitude of the standard error
of the mean, s- , the standard deviation of the
rainfall depthgrrecorded by the different gauges
in a network divided by the square root of the
number of gauges. This statistic was calculated
for all storm events for fourteen networks of
different gauge density. These networks included:
32, 28, 24, 18, 16, 15, 14, 12, 10, 8, 6, 4 and
2 gauges which provided gauge densities (gauges/
mile2) of 0.76, 0.67, 0.57, 0.48, 0.43, 0.38,
0.36, 0.33, 0.29, 0.24, 0.19, 0.14, 0.10 and
0.05 respectively. Figures 2 and 3 show the
maximum value of s- plotted against gauge density for uniform af% non-uniform storms. Also
plotted on the figures is the mean value of the
standard error of the mean, s- corresponding to
a given gauge density. ~nvelg6ecurves have
been d r a s to encompass the maximum values of
s- and sPr
pr'
-
PE CURVE (MAX
ENVELOPE
0
Ol
0 2
03
04
05
06
GAUGE D E N S I T Y l q o u q ~ l m # l r 2 )
07
0 2
03
GAUGE DENSITY
04
05
0 6
(aouamlm~t.~l
07
C U R V E (%)
08
DENSE NETWORK
Figure 3. Range of values for the standard
error of the Mean, s- , for networks of
varying gauge densitgf Non-Uniform Storms.
It is evident from the data given in
the two figures that the shape of the "envelope"
curvqs encompassing the maximum values of sand s- for both uniform and non-uniform stghs
are sysilar in shape. It is readily apparent in
these data that the network density which provides the greatest precision in measuring mean
network rainfall over the study area is given
by the dense network. The maximum value for sfor a particular uniform storm-on the dense Pr
network was 0.07 inches while s- was 0.01 inches.
Similarly, the data shown in FiEEre 3 indicates
that the largest value of s- for a particular
non-uniform srorm on the de%e network was 0.06
inches while s- was 0.01 inches. For a particular gauge dengfty, the differences between the
maximum values of s- and s- for uniform and
non-uniform storms BHpresenFrdifferences resulting from the largest values of the standard dedeviation. The magnitude of the standard deviation for a given gauge density depends on such
factors as gauge configuration and the natural
spatial variability of the rain event over an
area. This result suggests that a network of
higher density would not necessarily increase
the precision of measuring mean network rainfall.
The data given in the figures have practical
application as they may be used in combination
with standard statistical techniques to assist
in the design of rainfall networks on the
Canadian Prairies.
6.
0
01
Spr)
SUMMARY
The paper presents the results of a
study concerned with the spatial character of
rainfall on the Canadian prairies, which was conducted during the period, 1968-1975 (inclusive)
on a dense precipitation network located on the
Bad Lake Watershed; Latitude 51°18'N. Longitude
108' W. Design curves are presented for use in
estimating the rainfall amounts for short duration storms (<24hr) from the 24-hour totals.
Results are also presented providing measures of
the spatial variability in the rainfall depths
of individual storm events, and monthly, seakDENSE
sonal and 5-year totals.
Figure 2. Range of values for the standard
error of the Mean; sfor networks of
varying gauge densit?; '~niformStorms.
On reappraisal of the dense network it
was found that the minimum gauge densities required to preserve the dense network statistics,
the mean and the variance, for individual storms
of uniform and non uniform character were 0.38
and 0.43 gauges/square mile respectively compared to the initial density of 0.78 gauges/
square mile. Other comparisons with reduced
networks are given based on monthly seasonal and
5-year totals. It is shown that the positioning
of the gauges in reduced networks is as important a factor as guage density in preserving the
statistics of the dense network.
Curves showing the variation in rainfall variance as a function of network density
are provided for use as an aid in the design of
rainfall networks for the region.
7.
ACKNOWLEDGEMENTS
The authors gratefully acknowledge
the loan of equipment and financial assistance
given to this study by:
Water Resources Support Program
Water Research Incentives Office
IWD/DOE
Ottawa, Ontario
and
Hydrometeorological Research Division
Atmospheric Environment Service
Environment Canada
Downsview, Ontario
8.
REFERENCES
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Services, Department of Environment, Environment Canada, Toronto.
Dyck, G.E., 1977. Areal precipitation estimates
from point measurements. Unpublished M.Sc.
Thesis. University of Saskatchewan. Saskatoon,
174p.
Herschfield, D.M., 1965. On the spacing of
raingages. IASH & WMO Symposium on Design of
Hydrometeorological Networks. Quebec City. 7p.
Huff, F.A., 1966. The effect of natural rainfall
variability in verification of rain modification experiments. Water Resources Research,
Vo1.2, No.4, pp.791-801.
Huff, F.A. and W.L. Shipp, 1969. Spatial correlation of storm, monthly and seasonal precipitation. Journal of Applied Meteorology, Vo1.8,
pp.542-550.
Kendall, R.G. and M.K. Thomas, 1956. Some characteristics of precipitation in the Canadian
Prairies. Separata De Miscelanea Geofisica.
Luanda.
Longley, R.W., 1952. Measures of the variability
of precipitation. Monthly Weather Review.
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