hmr52 probable maximum storm (eastern united states)

8/18/2019 HMR52 Probable Maximum Storm (Eastern United States)

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US Army Corps

of Engineers Hydrologic Engineering Center

HMR52Probable Maximum Storm(Eastern United States)

User's Manual

March 1984Revised: April 1987

Approved for Public Release. Distribution Unlimited. CPD-46

Generalized Computer Program


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Standard Form 298 (Rev. 8/98)Prescribed by ANSI Std. Z39-18

REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searchingexisting data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding thisburden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to the Department of Defense, ExecutiveServices and Communications Directorate (0704-0188). Respondents should be aware that notwithstanding any other provision of law, no person shall besubject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION.

1. REPORT DATE (DD-MM-YYYY) March 1984

revised April 1987

2. REPORT TYPE

Computer Program Documentation

3. DATES COVERED (From - To)

5a. CONTRACT NUMBER

5b. GRANT NUMBER

4. TITLE AND SUBTITLE HMR52

Probable Maximum Storm (Eastern United States)

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

5e. TASK NUMBER

6. AUTHOR(S) CEIWR-HEC

5F. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) US Army Corps of Engineers

Institute for Water ResourcesHydrologic Engineering Center (HEC)

609 Second Street

Davis, CA 95616-4687

8. PERFORMING ORGANIZATION REPORT NUMBER

CPD-46

10. SPONSOR/ MONITOR'S ACRONYM(S)9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

11. SPONSOR/ MONITOR'S REPORT NUMBER(S)

12. DISTRIBUTION / AVAILABILITY STATEMENT Approved for public release; distribution is unlimited.

13. SUPPLEMENTARY NOTES

14. ABSTRACT Computer program HMR52 computes basin-average precipitation for Probable Maximum Storms (PMS) for the eastern

United States in accordance with the criteria specified in Hydrometeorological Report (HMR) No. 52 (National Weather

Service, 1982). That HMR describes a procedure for developing a temporal and spatial storm pattern to be associated the

Probable Maximum Precipitation (PMP) estimates provide in Hydrometeorological Report No. 51.

15. SUBJECT TERMS HMR52, probable maximum storms, PMS, probable maximum precipitation, PMP, spatial storm patterns, temporal,

subbasins, river basin, watershed, time distribution

16. SECURITY CLASSIFICATION OF: 19a. NAME OF RESPONSIBLE PERSON

a. REPORT

Ub. ABSTRACT

Uc. THIS PAGE

U

17. LIMITATIONOF ABSTRACT

UU

18. NUMBEROFPAGES

100 19b. TELEPHONE NUMBER


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HMR52Probable Maximum Storm(Eastern United States)

User’s Manual

March 1984Revised: April 1987

US Army Corps of Engineers

Institute for Water ResourcesHydrologic Engineering Center609 Second StreetDavis, CA 95616

(530) 756-1104(530) 756-8250 FAXwww.hec.usace.army.mil CPD-46


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S e c t i o n

CONTENTS

Page

L i s t o f F i gu re s

. . . . . . . . . . . . . . . . . . . . . . . .

v

L i s t o f T a b l e s

. . . . . . . . . . . . . . . . . . . . . . . . .

v i i

1

.

I n t r o d u c t i o n

1.1 Program Purpose. . . . . . . . . . . . . . . . . . . . . . 1

1.2 Computer Requ irem ents . . . . . . . . . . . . . . . . . . . 2

1.3 Acknowledgements

. . . . . . . . . . . . . . . . . . . . .

2

2 Probab le Maximum Storm An aly s is Procedure

2.1 P r ob a bl e Maximum P r e c i p i t a t i o n D e f i n i t i o n . . . . . . . . . 3

2 .2 P robab le Maximum S torm D e f i n i t i o n . . . . . . . . . . . . . 3

3 . P ro b a b le Ma x imu m P re c ip i t a t i o n D e te rm in a t i o n

3.1 All- Sea son PMP Es ti m at es . . . . . . . . . . . . . . . . . 14

3.2 Example C a lc u la t i on of PMP

. . . . . . . . . . . . . . . .

15

4

Example Ca lc u l a t io n o f a PMS

4.1 De ter mi na t io n o f PMP Versus Du ra t io n

. . . . . . . . . . . 19

4.2 A d ju s tme n t f o r S torm O r i e n t a t i o n . . . . . . . . . . . . . 20

4.3 D e t e r m i n a t i o n o f B as in -A ve ra ge P r e c i p i t a t i o n . . . . . . . 20

4.4 Temporal Arrangement

. . . . . . . . . . . . . . . . . . . 20

4.5 PMF De te rm in at io n

. . . . . . . . . . . . . . . . . . . . .

29

5 Computer Program HMR52 Pr oc ed ures

5 .1 D i g i t a l D e f i n i t i o n o f B as i n Geom etry

. . . . . . . . . . .

30

5 .2 Ca lc u l a t io n o f PMP f o r a S to rm Area

. . . . . . . . . . . .

3 1

5 .3 Ca lc u l a t io n o f PMS f o r G iven S to rm Area and O r i en ta t i on 33

5 .4 Ca lc u l a t io n o f PMS f o r T ime I n t e r v a ls Less Than S ix Hours . 36

O p t i m i z a t i o n o f S torm-Area S i z e an d O r i e n t a t i o n

6 . 1 S t o r m c e n t e r

. . . . . . . . . . . . . . . . . . . . . . .

39

6.2 Storm-Area Si ze . . . . . . . . . . . . . . . . . . . . . . 39

6 .3 S to rm O r i e n t a t i o n . . . . . . . . . . . . . . . . . . . . . 39

6 .4 U se r C o n t ro l o f O p t i m i z a t i o n

. . . . . . . . . . . . . . .

39

. Input Data Requirements . . . . . . . . . . . . . . . . . . . . 40

8 Program Output

8 . 1 P r i n t o u t . . . . . . . . . . . . . . . . . . . . . . . . . 42

8.2

Error Messages . . . . . . . . . . . . . . . . . . . . . .

4

8.3 P r e c i p i t a t i o n F i l e f o r R a i n f a l l - R u n o f f M odel Usage . . . . 49


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S e c t i o n

CONTENTS (Continued)

Page

9

.

E x am p l e A pp l i c a t i on

9 . 1 I n t r o d u c t i o n

. . . . . . . . . . . . . . . . . . . . . . .

50

9.2 HMR52 I n p u t and Ou tpu t

. . . . . . . . . . . . . . . . . .

50

9.3 HEC-1 In p u t and Ou tput . . . . . . . . . . . . . . . . . . 54

9.4 PMF C a l c u l a t i o n . . . . . . . . . . . . . . . . . . . . . . 54

9.5 Co ncl us i on s and Recommendations . . . . . . . . . . . . . . 55

10

.

Computer Requirements

10.1 Source Language

. . . . . . . . . . . . . . . . . . . . . .

62

1 0 . 2 C o r e S t o r a g e

. . . . . . . . . . . . . . . . . . . . . . .

62

1 0.3 F i l e S t r u c t u r e . . . . . . . . . . . . . . . . . . . . . .

63

10.4 HEC-Suppl ied Magnet ic Tape . . . . . . . . . . . . . . . .

63

10.5 Mach ine-Spec i f i c Code . . . . . . . . . . . . . . . . . . .

63

11 References

. . . . . . . . . . . . . . . . . . . . . . . . . . .

65

Appendix

A

I n p u t D e s c r i p t i o n

. . . . . . . . . . . . . . . . . . . . .

67

Appendix B Error Messages . . . . . . . . . . . . . . . . . . . . . . . 85


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LIST

OF

FIGURES

T i t l e

Page

Regions Covered by Genera l ized PMP S t u d i e s . . . . . . . . . .

1

S ta n da rd I s o h y e t a l P a t t e r n

. . . . . . . . . . . . . . . . . .

3

P r e f e r r e d O r i e n t a t i o n f o r PMS

. . . . . . . . . . . . . . . .

PMP O r i e n ta t i o n Ad jus tment Fac to rs

. . . . . . . . . . . . . .

Com pariso n o f PMP De pth -Are a R e l a t i o n w i t h 1.00 0.mi2 PMS . . . 6

S p a t i a l Variation i n PMP I n t e n s i t i e s . . . . . . . . . . . . . 7

Schematic o f One Temporal Sequence Al lo wed f o r

. . . . . . . . . . . . . . . . . . .

-hr In cre me nt s o f PMP 8

R a t i o o f l - h r t o 6-hr P r e c i p i t a t i o n f o r

A

I s o h y e t o f a 20. 000 m i2 Sto rm . . . . . . . . . . . . . . .

8

A l l -Season

PMP

i n c h e s ) f o r 6 h o ur s. 1 0 m i . . . . . . . . . 14

. . . . . . . . . . . . . . . . . . .

eon Ri ve r Bas in. Texas 15

Depth -Area-Dura t ion Curves fo r Leon R ive r Bas in . . . . . . .

16

. . . . . . . . .

s o h y e t a l P a t t e r n P l a ce d on Le on R l v e r B a s i n

18

PMP D ep th -D u ra ti o n f o r 3.00 0.mi2 St orm on

. . . . . . . . . . . . . . . . . . . . . .

eon R iv er Bas in 19

. . . . . . . . . . . . .

omogram f o r 1 s t 6-hr PMP I n c r em en t

25

. . . . . . . . . . . . .

omogram f o r 2nd 6-hr PMP I n c r em en t

26

. . . . . . . . . . . . .

omogram f o r 3 r d 6-h r PMP In cre me nt

27

Nomogram f o r 4 th thr ou gh 1 2 th 6-hr PMP Inc remen ts . . . . . . 28

18-hr Bas in-Average recipitation f o r 3.66 0--mi2

. . . . . . . . . . . . . . . . . . . . . .

eon R iv er Bas in 29

L i n ea r A pp r ox i m a t i on o f D ep t h -A r ea -D u r a t ion R e l a t i on s 32

. . . . . . . . . . . . .

as in Area Encompassed by an E l l i p s e

34

R ep r e s en t a t i on o f P r e c i p i t a t i o n Volum e B etw een Two

. . . . . . . . . . . . . . .

s ohy e t s w i t h a T r unc a t ed C one

5

. . . . . . . . . . . . . . . . . .

MS Depth versus D ur a t i on 36


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L i s t o f F ig ur es ( C o n t d )

o

.

T i t l e

.

Page

. . . . . . . . . . . . . . .

3 . Inc rem en ta l PMS Depth His togr am 37

. . . . . . . . . . . . . . .

4

.

E xam ple 1 - hr D i s t r i b u t i o n o f P S 38

. . . . . . . . . . . . . . . . . .

5 Jones Re se rvo i r Watershed 50

. . . . . . . . . . . . .

6 . S t o rm P a t t e r n f o r T r i a l s 1. 2. a nd 6 55


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LIS T OF TABLES

T i t l e

S p a t i a l V a r i a t i o n i n PMP f o r L a r g e s t 6- h r I n cr e m e nt 9

S p a t ia l V a r i a t i o n i n P P f o r 2nd La r ges t 6 -hr Inc remen t

. . .

10

S p a t i a l V a r i a t i o n i n PMP f o r 3 r d L a r g e s t 6 -h r I n cr e m e nt 1 1

S p a t i a l V a r i a t i o n i n PMP f o r 4 t h t h r o u g h 1 2 t h 6 -h r

Inc rements

. . . . . . . . . . . . . . . . . . . . . . . .

12

R a t i o s o f 1 -h r t o 6- hr P P . . . . . . . . . . . . . . . . . 13

PMP Depths by Area and D ur a t io n) f o r Leon Riv er B as i n . . . 16

B a si n- Av er ag e P r e c i p i t a t i o n f o r L a r g e s t 6- hr I n cr e m e nt . . . 21

B a si n- Av er ag e P r e c i p i t a t i o n f o r 2nd L a r g e s t 6- hr

Inc rement 22

B as in -A ve ra ge P r e c i p i t a t i o n f o r 3 r d L a r g e s t 6 -h r

. . . . . . . . . . . . . . . . . . . . . . . . .

ncrement 23

Basin.. A ve ra ge P r e c i p i t a t i o n f o r 4 t h L a r g e s t 6 - hr

Inc remen t . . . . . . . . . . . . . . . . . . . . . . . . . 24

Sample I n p u t f o r HMR52

. . . . . . . . . . . . . . . . . . .

41

Sample O ut pu t f o r HMR52

. . . . . . . . .

. . . . . . . . 43

Punched Output from HMR52 . . . . . . . . . . . . . . . . . .

49

HMR52 In p u t f o r Jones Re se rv oir 51

S e l e c t i o n o f S to rm -A re a S i z e and O r i e n t a t i o n

. . . . . . . .

53

P M S f o r S u b b a s i n 1 . . . . . . . . . . . . . . . . . . . . . 56

P M S f o r S u b b a s i n 2

. . . . . . . . . . . . . . . . . . . . .

57

P M S f o r S u b b a s i n 3 . . . . . . . . . . . . . . . . . . . . . 58


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LISP OF TABLES (C on t d)

T i t l e

Page

19 PMS f o r Subbasin 4 59

20 HEC-1 Inp ut fo r Jones Re ser voi r Watershed 60

1 H E C - 1 S u m m a r y O u t p u t f o r T r i a l 1 61

22 Summary o f PMF C a lc u l a ti o n s 61

23 Memory and Time Req uirem ents

62

4 F i l e c h a r a c t e r i s t i c s

64


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S e c t i o n

1

INTRODUCTION

1.1 Program Purpose

Compute r p rog ram HMR52 computes bas in -ave rage p r e c i p i t a t i o n f o r P robab le

Maximum S to rm s (PMS) i n a cc or da nc e w i t h t h e c r i t e r i a s p e c i f i e d i n

Hyd rom eteo r o log i ca l Repor t No. 52 (N a t i on a l Weathe r Serv ice , 1982) . Tha t

H y d ro m e te o ro lo g i c a l R e p o r t (HMR) d e s c r i b e s a p ro c e d u re f o r d e v e lo p in g a

te mp o ra l an d s p a t i a l s t o rm p a t t e rn t o b e a s s o c ia te d w i t h t h e P ro b a b le Maximum

P re c ip i t a t i o n (PMP) e s t ima te s p ro v id e d i n H y d ro me te o ro lo g i c a l R ep o r t No. 51 ,

P ro b a b le Maximum P re c ip i t a t i o n E s t ima te s - U n i t e d S t a t e s E a st o f t h e 1 0 5 t h

M er id ian . The U.S. Na t i on a l Weather Se rv ic e (NWS) has dete rmin ed th e

a p p l i c a t i o n c r i t e r i a i n a c o op e r at iv e e f f o r t w i t h t h e U.S. Army Corps o f

Engineers and th e U.S. Bureau o f R ec lamat ion .

Ot he r r e p o r t s , HMR Nos. 36, 43, 49 and 55 (NWS, 1961, 1966, 1977, and

1 98 3, r e s p e c t i v e l y ) d e s c r i b e t h e PMP i n o th e r r e g io n s o f t h e U.S., F i g 1 .

T h i s p rog ra m, HMR52, i s a p p l i c a b le o n l y t o t h e e a s te rn U.S., a nd i s i n t e n d e d

f o r a re as o f 1 0 t o 2 0,000

m i 2 .

(HMR No. 52 a l s o co nt ai n s a l -miz,

l - h r PMP). t ime i n t e r v a l as s ma l l a s 5 m in u te s c a n be u se d f o r s t o rm

d e f i n i t i o n .

Be fo re us in g the HMR52 p rogram, one shou ld be tho rou gh l y f a m i l ia r

w i t h t h e p ro c e d u re s d e s c r i b e d i n H y d ro me te o ro lo g i c a l R e p o r t No. 5 2.

F ig u r e 1. Regions Covered by Ge ne ra li ze d PMP St ud ie s (NWS, 1980 )

1


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T h e g e n e ra l i z e d PMP maps o f HMR No. 51 a re s t i p p le d i n tw o re g io n s ,

i n d i c a t i n g e s t i m a t e s may be d e f i c i e n t b ec au se o f o r o g r a p h i c i n f l u e n c e s . M a j or

p r o j e c t s w i t h i n t h e s t i p p l e d a r e a s h o u ld be co n s i de r e d on a c as e-b y-c as e b a s i s

a n d e x p e r t h y d ro me te o ro lo g i c a l g u id a n c e s h o u ld b e s o u g h t .

D ata r e q u i r e d f o r a p p l i c a t i o n o f t h e HMR52 p rog ra m a re :

X Y

c o or d in a te s d e s c r i b i n g t h e r i v e r b a s i n

and subba s in watershed bou ndar ies ;

* PMP

f r o m

HMR

No. 51 (NUS, 1978); and

S to rm o r i e n t a t i o n , s i z e , c e n t e r i n g , an d t l m l n g .

The p rog ram computes th e s p a t i a l l y ave raged

PMP

f o r a n y o f t h e s u b b a s in s o r

com bin at io ns th er e of . The Pro bab le Maximum Flo od (PMF) can the n be computed

as t h e r u n o f f f r o m t h e

PMS

u s i n g an a p p r o p r i a t e p r e c i p i t a t i o n - r u n o f f p ro gr am

such as HEC-1 (H yd ro l og ic En g in ee r in g Center ,

HEC

1981) .

A

t y p i c a l

app l i ca t ion o f HMR52 does no t p roduce a PMS. The PMS i s d e f i n e d b y t h e C orp s

o f E n g in e e rs t o be t h a t s t o rm w h i c h p ro d uc e s t h e

PMF.

Thus, the

PMS

c a n o n l y

be d e te r m in e d b y c om p u ti ng ( an d m a x i m i z i n g ) r u n o f f . T h at i s , t h e r u n o f f

c h a r a c t e r i s t i c s o f a w a te rs h ed mu st be c o n s id e r e d i n

PMF

(and there fore PMS)

development.

HMR No. 52 r e q u i r e s t h a t a c r i t i c a l s to rm -a re a s i z e , o r i e n t a t i o n ,

c e n te r i n g and t i m in g be d e te rm in e d w h i c h prod u ce s t h e maximum p re c ip i t a t i o n .

The HMR52 computer program w i l l o p t i m i z e t h e s to rm -a re a s i z e and o r i e n t a t i o n

i n o rd e r t o p ro du ce

the maximum bas in -ave rage p r e c ip i t a t i o n . The use r must

p r o v id e t h e d e s i re d c e n t e r i n g a lt h o u gh t h e c e n t r o i d o f t h e b a s i n a re a i s

p r o v i d e d as a d e f a u l t o p t i o n .

The u se r m ust s p e c i f y t h e t i m e d i s t r i b u t i o n f o r t h a t st or m. U s in g t h a t

t i m e d i s t r i b u t i o n i n f o r m a t i o n , t h e HMR52 p ro g ra m

w i l l

prod uce a da ta f i l e

c o n t a i n i n g t h e i n cr e m e n t al b a si n- av e ra ge p r e c i p i t a t i o n v a lu e s f o r e v e r y

s ub ba si n r eq ue st ed . T ha t p r e c i p i t a t i o n d a ta f i l e

w i l l

s u b s e q u e n t l y b e i n p u t

t o a r a i n f a l l - r u n o f f m od el, su ch as HEC-1, f o r c o m p u t a ti o n o f t h e r e s u l t i n g

f l o o d . The u s e r th e n a n a l yz e s t h e v a r i o u s s to rm v a r i a b le s a nd rec omp u te s t h e

f l o o d s i n o r d e r t o d e t e rm i n e t h e s t o r m w hi c h p ro du ce s t h e m aximum r u n o f f .

T h at s t o rm and r u n o f f a r e d e f i n e d as t h e PMS

and

PMF

r e s p e c t i v e l y .

1.2 Computer Requ ireme nts

The HMR52 computer prog ram re q u ir e s a computer w i t h 45K (d ec im al ) words

o f c o r e s t o ra g e and 7 s c r a t c h t a p e/ d ls k f i l e s . P l o t s o f t h e b a s i n g eo me try

a nd s to r m p a t t e r n s c an be made on a l i n e p r i n t e r . S e c t i o n 10 o f t h i s m an ual

s p e c i f i e s d e ta i l e d c omp uter h a rd w are a nd s o f t w a re r e q u i r e me n ts .

1.3 Acknowledgements

The computer progra m HMR52 was w r i t t e n by Pa ul B . E l y o f t h e

HEC.

John C . P e t e r s p r o v i d e d much v a l u a b l e a s s i s t a n c e i n t h e d e s i g n o f t h e

p ro gr am s c a p a b i l i t i e s and a p p l i c a t i o n s m e th od ol og y.


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S e c t i o n 2

PROBABLE MAXIMUM STORM ANALYSIS PROCEDURE

2.1 P r ob a b le Maximum P r e c i p i t a t i o n D e f i n i t i o n

P r o b a bl e Maximum P r e c i p i t a t i o n PMP) i s t h e o r e t i c a l l y t h e g r e a t e s t d e p t h

o f p r e c i p i t a t i o n f o r a gi ve n d u ra t io n t h a t

i s

p h y s i c a l l y p o s s i b l e o ve r a g iv e n

s i z e s to rm a re a a t a p a r t i c u l a r g e o gr ap h ic a l l o c a t i o n a t a c e r t a i n t i m e o f t he

yea r . Hyd rom eteo rolog ical Repor t No. 51 HMR No. 51) co nt a i ns ge ne ra l iz ed

f o r a ny s t o r m a r e a ) a l l - s e a s o n e s t i m a t e s o f

PMP

f o r t h e U n i t e d S t a t e s , e a s t

o f t h e 1 0 5 th m e r i d i a n , F i g .

1.

2.2 Probab le Maximum Storm D e f in i t i o n

Probab le Maximum Storm PMS) i s a h yp ot he t i c a l s to rm wh ich produces the

Pr obab l e Maximum F l ood f r om a pa r t i c u l a r d r a i nage bas i n . Hyd r om e t eo r o l og ica l

Repo r t No. 52 HMR No. 52 ) p r ov i des c r i t e r i a and s t ep -by - s tep i n s t r u c t i o ns f o r

c o n f i g u r i n g a

PMS

u s i n g

PMP

es t i m a t es f r om HMR No. 51. Key co nc ep ts upon

w h ic h t h e p r oc e d ur e s i n

HMR

No. 52 ar e based ar e as f o l l o w s.

2.2.1 S p a t i a l D i s t r i b u t i o n

The s p a t i a l d i s t r i b u t i o n o f t h e PMP i s g o v e r n e d b y p r i n c i p a l s descri ed

under f ou r head ings : i so hy e t a l shape, o r i e n t a t i o n , s to rm - a rea s i ze , and

s p a t i a l v a r i a b i l i t y .

i ) I so hy e t a l shape . The

PMS i s

r ep re s en te d by e l l i p t i c a l i s o h ye t s ,

e ac h o f w h ic h has a r a t i o o f m a j or a x i s t o m in o r a x i s o f 2.5 t o 1 . S t an d a rd

e l l i p s e s h av e be en e s t a b l i s h e d c o n t a i n i n g a r ea s f r o m 1 0 t o 60,000 m i

F i g . 2 ) .

I

H 700

ISOHYET AREAS

1000

NOT SHOWN

0 10 20 30 40 5 0 J 1500

0

10000 n 2

I

K 2150 P 1 5 0 0 0

M I L E S

L

3000

0

25 00 0

M 4500

R 40000

N 500 S 60 00 0

Fi gu re 2 . S tandard I so hy et a l P a t te rn NWS, 1982)


14/100

i i ) O r i e n ta t i o n . There i s a p r e f e rr e d o r i e n t a t i o n f o r s torm s a t a

p a r t i c u l a r g eo gr ap hic l o c a t i o n . T ha t o r i e n t a t i o n i s r e l a t e d t o t h e g e ne ra l

movement o f s to rm systems and the d i r e c t io n o f mo is tu re -bea r ing w lnds .

C on to ur s o f p r e f e r r e d o r i e n t a t i o n a r e shown i n F i g .

3.

When developing a

PMS

t i s g e n e r a l l y d e s i r a b l e t o o r i e n t t h e s t or m t o p r od uc e maximum p r e c i p i t a t i o n

volume i n th e wa te rshed . PMP w i l l be reduced by an ad jus tme nt f a c to r shown

i n F ig .

4

when t he s t or m o r i e n t a t i o n d i f f e r s f ro m t he p r e f e r r e d o r i e n t a t i o n

by more tha n 40 deg rees .

i i i ) S torm -.A rea S i z e. The a ve ra ge p r e c i p i t a t i o n d e p th o ve r an a r ea i s

PMP f o r one and on ly one are a s iz e . Th is

i s

th e I is torm-area size .I i The

a ve ra ge p r e c i p i t a t i o n on a re as l a r g e r o r s m a l l e r t h an th e s to rm - ar ea s i z e i s

l e s s t h a n

PMP

f o r t he l a r g e r o r s m al le r a re as . F i g . i l l u s t r a t e s t h i s

concep t f o r a s to rm a rea o f 1000 mi2 . The sto rm-a rea s i ze

i s

chosen t o

y i e l d t h e m a x i m u m p r e c i p i t a t i o n v o l u m e f r o m a g i v e n d r a i n a g e b a s i n .

F i g u r e

3.

P r e f e rr e d O r i e n t a t i o n f o r

PMS

NWS, 1982)

4


15/100

t 24 25 k55 26 6 5

24 59

O R I E N T A T I O N D I F F E R E N C E d e g . 1

F i g u r e 4 .

PMP

o r i e n t a t i o n A dj us tm en t F a c t o r s

NWS,

1982


16/100

PM P DEPTH AREA RELAT ION

RELATION FOR ARE

TTERN STORM IS CONSIDERE

FOR AREAS W I TH I

PATTERN STORM

DEPTH id

F i g u r e 5 Compar ison of PMP Depth-Area Re la t i on

w i th 1 ,000

m i 2 PMS

NWS, 1982)

i v ) S p a t i a l V a r i a b i l i t y . S p a ti a l v a r i a t i o n o f p r e c i p i t a t i o n i s a

maximum du r i n g t he 6 -h r pe r i o d when t he maximum p r e c i p i t a t i o n occu rs . Sp a t i a l

v a r i a t i o n d i m i n is h e s f o r t h e se co nd an d t h i r d l a r g e s t 6 -h r a mo unts . F or t h e

r e m a in i n g 6 -h r p e r i o d s , t h e w i t h i n - s t o r m p r e c i p i t a t i o n i s u n i fo r m , b u t t h e re

i s s p a t i a l v a r i a t i o n i n th e r e s id u a l p r e c i p i t a t i o n o c c u r r in g o u ts i de t h e

e l l i p t i c a l bo un da ry t h a t c o rr e sp o n ds t o t h e s to rm -a re a s i z e . HMR No. 52

con t a i ns nomogram s wh i ch exp ress s p a t i a l v a r i a t i o n f o r each 6- hr pe r i o d as a

p e r c e n t o f

PMP.

P e rc e nt ag e s f o r s e l e c t e d a r e a s iz e s a r e t a b u l a t e d i n T a bl es 1

t h r ough 4. For each i sohy e t , t he pe r c en t o f PMP f o r t h e s to rm a re a i s

i n t e r p o l a t ed f r om Tab les 1 -4 . Those per cen tages a r e m u l t i p l i e d t im es t h e PMP

t o o b t a i n p r e c i p i t a t i o n f o r e ach i s o h y e t f o r each 6-h r i n t e r v a l .

A

g r a p h i c a l

i l l u s t r a t i o n o f a t y p i c a l s p a t i a l v a r i a t i o n

i s

shown i n F i g .

6.


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-

I 7

-

-

STORM AREA SIZE

=

3000 MI?

-

-

-

-

LARGEST 6HR INCREMENT

-

io

-

LND LARSEST

6 HR INCREMENT

6HR INCREMENT

I A

1

8 0 60 4 0 2 0

0 b

4 0

60 80

DISTANCE ALONG MAJOR AXIS

FROM STORM CENT ER

mile6

F i g u re 6. S p a t i a l V a r i a t i o n i n PMP I n t e n s i t i e s

2.2.2 Tempo ra l D i s t r i b u t i o n

The f a c t o r s g o v er n in g t he t em p or al d i s t r i b u t i o n o f t h e PMS are as

f o l l o w s :

* PMP f o r a 1 1 d u r a t i o n s u p t o 3 d a y s ) oc c u rs i n t h e same PMS

The PMP

p a t t e r n i s d ev e lo p ed so t h a t a ny d u r a t i o n o f s to rm s l e s s t h a n 72 ho u rs i s

c o n ta in e d i n t h e PMS

* The f o u r 6 -h r p e r i o d s w i t h t h e g r e a t e s t p r e c i p i t a t i o n may o c c u r a ny t i me

e x ce p t d u r i n g t h e f i r s t 2 4 h o ur s o f t h e s to rm .

* The 6 -h r i n cr e me nt s o f p r e c i p i t a t i o n a r e a r r a ng e d s uc h t h a t t h e

i n cr e m en t s d ec re as e p r o g r e s s i v e l y t o e i t h e r s i d e o f t h e g r e a t e s t 6 -h r

inc remen t .

An

e xam ple o f one s uc h d i s t r i b u t i o n i s shown i n F i g . 7.

* The 6 -h r i n cr e m en t s may be d i s t r i b u t e d i n t o s h o r t e r i n t e r v a l s . F i g . 8

shows r a t i o s o f 1 -h r t o 6 -h r p r e c i p i t a t i o n f o r t h e A i s o h y e t o f a

20,000 m i 2 s to rm . Th i s r a t i o i s d e te r m in e d f o r t h e s to r m- c e n te r

l o c a t i o n and us ed t o a d j u s t r a t i o s r e ad f ro m T ab le 5 f o r e a c h i s o h y e t

w i t h in the s to rm-a rea s i ze . Maximum

5-,

1 5 , and 30-m in i n t e r v a l s a r e

g iv en on ly f o r the maximum 1-hr inc rement w i t h i n t he maximum 6-hr

increment .


18/100

F i g u r e

7.

Schem atic o f One Temporal Sequence Al l ow ed

f o r 6- hr Inc rem ent s o f PMP NWS, 1982)

F i g u r e

8.

R a t i o o f l - h r t o 6-hr P r e c i p i t a t i o n f o r

A

I sohye t o f a 20 ,000 m i Storms NWS, 1982)


19/100

o 0 0 0 6 0 A n i n m i

i 6 d p . i

d A r i d i & $ O m &

0 4 6

@ 4 N M ~ Q ~m m

4 A b r j d d r i b

b m m e e O d d

- .-I-

o o

a

0 - d i d $ h i d i f f

4 6 n i i o

hduinjd 4 i G r i c i r i & & c i i

o i j

o o o o o O . M N

a r u m m e e e n s * t . m e o d ~ m e s b o

d d - ~ d d

ld-r l- d d d w r l

dd-r l- d d 6 N N N N N M N N O -

r o b n n o m o o n o

o o o o o

o o o o o o o o o o o o o o o

. - - r u m m t . o e b m o a m ~ o o o 0 0 ~ O O O O o o o o

W M M ~ J m m e m b m o n m r n soma n m o o o o o o

F C C

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20/100

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21/100

T

A

B

L

E

S

p

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M

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22/100

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

m

o o o d o o o o o o o o o o o

o d d d o o o o o o

o o d o o

o d d

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0

a o o o o d o o o o o o o o o o o o t i o o o o o o o

o o o o o - b N

4

a o d o o d o o o o o o o o o t i o o o o o o d o o o o-mm b r i i i

.+m

e n s

o o o o o o o o o o o o o o o

O O O O D

n o 0 0 0

O ~ O O O

0 0

a o o o o o o o o o o o o o o o o oo oo j U i G o j G - 6 4 4 6 - 6 0 0

. + d m

M m P U J b

CJzz

o o o o o o o o o o o o o n o o n o o n n n n n o n o 0 0 0 0 0 0

o o o o o o o o 6 6 o

N i G i e j

d G o i 4 o r i k r i i G u i ~ o oo o o

In

d - m m m mmmee n s b z z 2 5 2

C

W

o o o o o O O O O ~ o o o n o o n o n n n o o o o o o o o 0 0 0

z

d o o d d o A d b i i t - i u i - rim - i - h f i . j m o o d o 0 0 6

W

a

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mmmme e n n a b a ~ z z z z

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O O O ~ O n o o n

~ O O O O

o n n o o o o n o o o o o o o o o

r

o d o c i i i b o p jK c j r i i - 4 o o o o o

o

. . ~ c m ammmm * * * m a s s b m z o o o o o o o o

*d.+4.+ - I & . +

4 o n n o n o o o o n o o o m n o o o o o o o o o o o o o o o o o o

t s r i r . A u i i i m r i d i r i ~ o r i i NGciA d d o o d o o o d ~ i d o

m

M . H mmnmm e e n n n s sb m m o o o o o o o o o o

0 0 0

3

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4 * . +

n o 0 0 0 o n 0 0 0 o n o n i n o n n o o o o o o o o o o o o o o o

< >

J I r i b -

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G N ~ Q o

o o o o o o o d o 0 0 0

o

- - N N

m me*e n n s s b

r - m r n z z

z z z z z z z z z z 2 2 2

Z E

4 o o n o n o o n o o o rn o n o o o o o o o o o o o o o o o o 0 0 0

0 4 - 9 - b r j G - u i N u 5 - b u i N 6 Od d d c i t id b d o o d d

3

. + ~ m m m m e e n n s s f i b m t r o o o o o o o o o o o o o o o o o

I dddU 4 d d 4 . + d.+-d‘?, - I 4 4

o o o n n O O O ~ O o o o o o o o o o o o o o o o o o o o 0 0 0

w

s i A G A b

4 ~ 11 5 64 i G i .4 0 o o o o t i o o o o o d o o o o t i o o

o - m m m m

e e n n s b b m t r z z z z z z

z z z z z

z z z z z

2 2 2 .

LL

O O O O M

n o m o o o o o o o

o o o o o

o o o o o o o o o o 0 0 0

IL i r i o i r i A ai i r i~ S o o o o o

o o o d o o d d 0 6

d d o d d

o d d

IL

m m e e n s s b m m z z z z z z z z z z z z z z z z z z z z

2 2 2

t

O O ~ O O

n 0 0 0 o o o o o o o o o o o o o o o o o o o o 0 0 0

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o n n o o o o o o o

o o o o o 0 0 0 0 0

o o o o o o o o o o o o o

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i o j i i o o o o o o o o o o d t i d o d o o o o o ~ i o o o o o o O o

* Q b m z z z z z z cH zzz

zzC322 zcaazz

z z z z z 2 2 2

O ~ O O O

o o o o o o o o o o o o o o o o o o o o o o o o

0 0 0

-

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.

m

u ir i o oo o o o o o o o o a o

o o o o o o o o o o

o o o o o

t i o o

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z z z z z

z z z z s

z z z z z

c tz zz z z z z z z 2 5 2

a

d o 0 6 0 o d d d o o c io oo o o o o o o o o o o d o 0 0 6 o o o

2 2 2 2 2

2 2 2 2 2

2 2 2 2 2 2 2 2 2 2

2 2 2 2 2

2 2 2 2 2

z z z

o r- n n o n o o n 0 o o o o o o o o o o o o o o o o o o o o

0 0 0

a

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O W ~ 4 - t ~nmetnb m omam . +s o m m n n o o o o o o

a *-.+ drumme

m a m s m 2 2 2 %


23/100

o m m

m r - r l

m e w

000

- .

d o

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00

l l

m o m

b r l m

* d m

000

l l

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(Uem

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000

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m o w

mmm

000

000

m r - d

mmm

000

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o m m

r lm t -

mcyd

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o m m

crimm

Cdd l -

oqo

l l

mmm

wl-pt

r a r l r l

000

l l

mmm

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m r r o

00 0

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000

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000

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d r aw

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do0

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24/100

S e c t i o n 3

PROBABLE MAXIMUM PRECIPITATION DETERMINATION

3.1 A l l -Season

PMP

E s t lma te s

G e n e ra l l y , a t h re e - s te p p roc e s s

i s

f o l l o w e d i n d e t e rm i n in g

PMP

i n

n o n o ro g ra p h i c r e g i o n s : mo i s tu r e ma x im iz a t i o n , t r a n s p o s i t i o n a nd e n ve lo p me n t.

T ho se p roc e s se s a re b r i e f l y d e s c r i b e d b e lo w ;

HMR

No. 51 gi ve s a com plete

e x p l a n a t i o n o f t h e

PMP

procedure .

M o i s t u r e m a x i m i z a t i o n c on sis ,t s o f i n c r e a s i n g s t o r m p r e c i p i t a t i o n me asu re d

i n a m a jo r h i s t o r i c e ve n t by a f a c t o r t h a t r e f l e c t s t h e maximum am ount o f

m o i s tu r e t h a t c o u l d have e x i s t e d i n

t h e a tm o sp he re f o r t h e s t o r m l o c a t i o n and

t i m e o f t h e y ea r .

T r a n s p o s i t i o n r e f e r s

t o t h e p ro c e ss o f m o vi ng a s to r m i . e . ,

i s o h y e t a l

p a t t e r n ) f r o m th e l o c a t i o n where

t

o c cu r re d t o an ot he r l o c a t i o n o f i n t e r e s t ,

T r a n s p o s i t i o n

i s

c a r r i e d ou t o n l y w i t h i n a r e g i o n th a t i s homogeneous w i t h

r e s p e c t t o t e r r a i n a n d m e t e o r o l o g y .

E nv elop men t i n v o l v e s c o n s t r u c t i o n o f smoo th c u r ve s t h a t e n v e lo p e

p r e c i p i t a t i o n maxima f o r v a r i o u s d u r a t i o n s a nd a re a s i z e s

t o c o mp en sa te f o r

d a t a ga ps. A l s o g eo gr ap h ic s m oo th in g i s p e rf o rm e d t o i n s u r e r e g i o n a l

c o n s i s t e n c y .

U s i n g t h o s e p r i n c i p l e s ,

P MPts f o r v a r i o u s s i z e d a re a a nd s to rm d u ra t i o n s

were ca lc u l a te d by t he NWS.

The r e s u l t s a r e g e n e r a l i z e d and p l o t t e d

i n a

s e r i e s o f f i g u r e s 18-47) i n HMR No. 51. One o f those p lo ts , t he a l l - se as on

PMP f o r th e 6-hr 10-mi2

PMP i s

i l l u s t r a t e d h e re i n F ig .

9

F ig u re 9 . A l l -S e a s o n

PMP

i n c h e s ) f o r

6

hours , 10

m i 2

NWS, 1978)

14


25/100

3 .2 E xamp le C a l c u l a t i o n o f PMP

t i s d e s i r ed t o o b t a in

P P

es t i m a t es f o r t he Leon R i v e r b as i n above

Be l to n Res ervo i r , Texas, F ig . 10 . The d ra in age a rea

i s

3,660 miz; the

l o c a t i o n o f t he c e n t r o i d o f t he b a s l n i s 3 1°4 5 N 98 15 W

From the

PMP

maps i n HMR No. 51, th e

P P

v a l u e s f o r a r e a s i z e s l a r g e r

and

s m a l l e r t han t he d r a i nage a r ea a r e de t e rm l ned .

The al l - se as on PMP f o r

6

hou r s

and 10 m i 2 was shown i n F i g . 9 ( w h i c h i s F i g .

18 i n HMR No. 51 ) .

Values

t ak en f r om f i gu r e s 18 t h r ough 47 o f

HMR No.

51 a r e shown i n T ab l e

6.

M I L S

R S R V O I R

o

@

F ig u re 10. Leon Ri ve r Ba sin , Texas (NWS, 19 82)

15


26/100

Tab le 6

P P

Depths by Area and Du ra t i o n) f o r

Leon R iver Bas in

A rea Du r a t i on hou r s )

From t h e d e p t h - a r e a -d u r a t io n d a t a i n T a b le

6,

p l o t

P P

dep t h ve r sus t he

l o ga r i t h m o f d r a i nage a rea f o r each du r a t i on . Draw sm ooth cu r ves f o r each

d u r a t i o n . The c u rv es s h o u ld be p a r a l l e l or c on ve rg e s l i g h t l y w i t h i n c r e a s i n g

s i ze , as i l l u s t r a t e d i n F i g . 1 1.

PMP in.)

Fig ur e 11 . Depth-Area-Dura ti on Curves fo r

Leon R iver Bas in

NWS,

1982)


27/100

t

depth-ar

HMR 51 a

i s h i g h l y recommended t o p h y s i c a l l y p l o t t h e i n i t i a l

e a - d u ra t io n v a lu e s ta k en f r o m t h e v a r i o u s f i g u r e s f i g u r e s 1 8 -4 7) i n

s shown i n F i g . 11 o f t h i s us er s m anual. T h is i n i t i a l p l o t t i n g o f

the bas i c i np u t da ta se rves two fun c t i on s . One, i t e l i m i n a t e s r e a d e r e r r o r s

f ro m b a s ic m i s i n t e r p r e t a t i o n o f v alu es r ea d o f f t he f i g u r e s i n HMR 51.

Second, i n i t i a l i m p o r ta n t sm oo th ln g o f t h e b a s i c p r e c i p i t a t i o n d a ta i s

a p p l e d .

Us ing the dep th -a rea -du ra t i on g raph o f F ig . 11, de te rm ine PMP d e p t h s f o r

t h e s to rm- ar ea s i z e s o f i n t e r e s t . p l o t o f t h e a r e a - s p e c i f i c PMP v a l u e s

ve rsus du ra t l o n on l i n e a r g raph pape r can be used to ob t a i n PMP dep th fo r any

du ra t i on be tween 6 and 7 2 h o ur s. The above c u r v e f i t t i n g i s done

au to m at ic a l ly by the HMR52 program. The user need on ly p ro v i de the

d e p t h - a r e a - d u r a t io n d a ta , e .g . Ta b le 6, f o r t h e g e o gr a ph i c l o c a t i o n i n

q u e s t io n . U s i ng t h i s

PMP

d a t a , t h e PMS i s c a l c u l a t e d a s d e s c r ib e d i n t h e

n e x t s e c t i o n .


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S e c t i o n 4

EXAMPLE CALCULATION OF PMS

To i l l u s t r a t e t he p ro ce du re s gi v en i n HMR No. 52, suppose t h a t i t i s

d e s i r e d t o d e r i v e a s t o rm f o r a s t o rm - ar e a s i z e o f 3,000 m i f o r t h e L e o n

R ive r bas in . The s to rm i s t o be cen te red a t 31°45' N, 98 '15' w i t h an

o r i e n t a t i o n o f 3 14 , as shown i n F i g . 1 2.

5

1

M I L S

3 45'N 93 1 5 ' ~

_ _.

F ig u re '12, I s o h y e ta l P a t t e rn P la c e d on L eo n R i v e r B a s ln

(NWS, 1982)


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4.1

D e te rm i n a t i o n o f PMP In te n s i t y v er s u s D u ra t i o n

The

i n F i g . 1

a d d i t na

f o l l o w s :

PMP f o r an area o f 3,000

m i d e te rm i n e d f r o m F i g . 1 1 ) i s s hown

3.

The i n c r e m e n ta l p r e c i p i t a t i o n am ounts, c a l c u l a t e d i n c l u d i n g

.1 s mo o thi n g) f r o m th e c u mu l a t i v e amou nts g i v e n i n F i g . 1 3, a r e as

6-,hr

P P

Inc remen t Inches Inc remen t Inches

DURATION ours

F ig u re 13. PMP De pth -Du rat ion f o r 3,000

m i

Storm

on Leon R i ve r Bas in


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4 .2 A d ju s tm e n t f o r S to rm O r i e n t a t i o n

From F i g . 3, t h e p r e f e r r e d o r i e n t a t i o n f o r t h i s s to r m l o c a t i o n i s 2 08 ,

w h ic h d i f f e r s by 106 f r om t h e s e le c t e d o r i e n t a t i o n o f 3 14 . From F i g .

4

th e PMP must th e r e f o r e be m u l t i p l i e d by 0 .85 . The ad jus te d PMP i s as fo l l o ws :

6-hr

I n c re me n t

PMP

In c h e s

Inc rement Inches

4 .3 D e t e r m i n a t i o n o f B a si n- Av er ag e P r e c i p i t a t i o n

The nomograms i n F i g s . 1 4 t h ro u g h 17 a re r e q u i r e d f o r d e te rm i n i n g t h e

s p a t i a l d i s t r i b u t i o n o f p r e c i p i t a t i o n . T ab le s 7 t h ro u g h 10 show c o m pu ta ti on s

t o d e te r mi ne ba sin -a ve ra ge p r e c i p i t a t i o n f o r t h e f o u r l a r g e s t 6-hr

i nc re m e nt s. B as in -a ve ra ge p r e c i p i t a t i o n f o r t h e r e m a in i ng i nc r em e n ts ( 5 t h

t h r o u g h 1 2 t h ) c an be o b t a i n e d as a p r o p o r t i o n o f t h e 4 t h l a r g e s t i n cr e m e n t,

b ec au se t h e same s p a t i a l d i s t r i b u t i o n i s u se d. F or ex ample , t h e 3,0 00

m i 2 P P f o r t h e 5 t h l a r g e s t i n cr e m e n t i s 1. 39 i n c h e s . B a si n- av er ag e

precipit tion

f o r t h e i n c re me n t i s 1 .3 9 ( 1 .6 9 /1 .7 9 ) 1 .3 1 i n c h e s .

B as in -a ve ra ge p r e c i p i t a t i o n f o r t h e t w e lv e i nc re m e nt s i s as f o l l o w s :

6-hr PMP

In c re me n t

In c h e s I n c re me n t I n c h e s

4.4 Temporal Arrangem ent

An acce p tab le tempora l a rrangement (F ig . 7 ) o f the bas in ave rage

p r e c i p i t a t i o n i s as f o l l o w s :

6-hr Basin-Average

6-hr Basin-Average

P e r i o d P r e c i p i t a t i o n

ay

P e r i o d P r e c i p i t a t i o n

1 1 0.64 inch es 7 1.3 '1

2 0.64 8 2.17

3 0.73 3 9 8 .31

4 0.73 10 3.25

2 5 0.80 11 1.69

6 0.96 12 0.80


31/100

Table

Basin Average Precipitat ion for Largest 6 hr Increment

~ ~ ~ ~ ~ ii t h i n I s o h y e t an d I n c re m e n ta l o f 3000 I s o h y e t P r e c i p i t a t i o n

T

o lunle o f

I so hye t I so hy e t Bas in (A) Area AA sq .m i. PMP P re c i p i t a t i o n

on

AA P r e c i p i t a t i o

sq .m i. (9 .69 in . )

t

i n . i n . - s q . m in .

Basin-Avg. Ppt . = 30419.9 660 8.31 in .


32/100

Table

Basin-Average Precipitation for Second Largest 6-hr Increment

Basin-Avg. Ppt.

=

11879.2 3660 = 3 . 2 5 in.

Isohyet

C

D

E

F

G

ti

I

.

Area

Within

Isohyet

sq .mi.

1 0

25

50

100

1 7 5

300

450

700

1000

Area Within

Isohyet and

Basin A)

sq.nii .

1 0

25

50

100

175

300

450

.

700

971

1379.4

Incremental

Area AA

sq.nii

10

Isohyet

Precipitation

in.

4.21

o f

3000

sq.mi. PMP

3 . 5 2 in.)

1 1 9 . 5

K

M

1500

3.51

Average

Preei pi tati on

o n

in.

1 5

21 50

3000

4500

Volume of

Precipitation

in.-sq.mi.

4.15

25

50

62 . 2

1 6

1852 3 . 45 1683 .6

N

4.21

4.08

2434 3.38 3.40

3171 2.36 2.97

3660 489 1.58 2.17

7

500

42.1

1978 . 8

2188.9

1061.1

100 . 5

196 . 0

1 1 2 . 5

11 0

288.0

471 . 3

Ae

555.0

907 . 5

9 6 4 . 8

7 5

A

1 2 5

1 5 0

250

3 . 9 6

4 . 02

100 . 5 3 . 54 3 . 56

1 0 8

106

3 . 80

. 73

3.87

3.84

3 . 7 7

104

102

3.92

.

3 . 66

. .

3 . 59

.

3 , 7 0

3 . 6 3


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T ab le

9

B as in A ve ra ge P r e c i p i t a t i o n f o r T h l r d L a r g e s t 6 h r I n cr em e nt

rea P r e c i p i t a t i o

S q . mi . S q.m i. scl.m i. 2 . 3 0 i n . ) I i n . i n .

Basin Avg.

Ppt. = 7941.0 3660 = 2.17 i n .


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T ab le 10

Basin Average recipitation fo r F our th Largest 6 hr Increment

Bas in -Avg . Pp t . = f1.79 2434) 1193.9

+

625.91 : 660 = 1 .69 i n .

I s o h y e t

A

B

.

D

F

G

H

--

I

J

K

L

M

N

Area

W i t h i n

I s o h y e t

sq.mi.

10

25

50

100

175

300

.

A r e a W i t h i n

I s o h y e t a n d

Bas in A)

sq.mi.

1 0

25

50

100

175

I n c r e m e n t a l

Area AA

sq

. m i .

450 450 150

A

300 125

100

1.7900

o f

3000

sq.mi. PMP

1 . 7 9

i n . )

1.79

---

1 .79

100 1 .79 1 .79

700

I s o h y e t

P r e c i p i t a t i o n

i n .

1 0

1 5

-

1.79

-

1.79

1.79

1000

pa

1500

21 50

700

Average


on AA

i n .

2

5

50

75

100

100

250

Volume o f


i n . - s q m i .

1 . 7 9

1.79

971

1364

852

100

100

100

100 1 .79

76 1 .36 1 .62 1193.9

57 1 .02 1 .28 625.9

27

393

488

3000 2434

4500 3171

1.79

1 . 7 9

100 1 .79 1 .79

--

100 1 .79 1 .79

100 1 .79

582

737

6500 3660 48 9

1.79

1.79

1.79

1.79

-

.


35/100

~ Z I A ) 2 5

V M v

~ 8 1 s

Figure 14. Nomogram for st 6-hr PMP Increment

NWS,

1982


36/100


37/100

PERCENT

O

3rd 6 hr PMP INCREMENT

PERCENT O 3rd 6 hr

PMP INCREMENT

Figure

16

Nomogram for 3rd 6-hr

PMP

Increment

NUS,

1982


38/100

PERCENT OF 4 h THROUGH 1 2 ~ ~ 6 h r MP

Figure 17. Nomogram for 4th through 12th 6-hr PMP Increment

NWS,

1982)


39/100

4.5 PMF

D et e r m i na t i on

The example j u s t shown prov id es a s to rm f o r a sp e c i f i c s to rm-area s i z e

s t or m c e n t e r i n g and s t o rm o r i e n t a t i o n .

What would be re q u ir e d f o r a PMF

an al ys is however would be the storm th a t produces the maximum peak

d isch arge o r ru no f f vo lume depend ing on the p ro je c t purpose fo r t he 3 660

m l 2 d r a i nage bas i n .

t

i s t h e r e f o r e ne ce ss ary t o t r y v a r i o us

com b lna t ions o f st or m -a r ea s i ze cen t e r i ng o r i en t a t i o n and t em por a l

d i s t r i b u t i o n u n t i l m a x im i z at io n o f peak d is c h a rg e o r r u n o f f volum e I s

a ch ie ve d. F i g . 18 i l l u s t r a t e s how b a s i n a ve ra ge p r e c i p i t a t i o n v a r i e s w i t h

s to rm -a re a s i z e f o r t h e Le on R i v e r b a s i n . F or t h e p a r t i c u l a r c e n t e r i n g a nd

o r i e n t a t i o n u s e d

i n t he example a s to rm-area s i ze o f 2 150 m i 2 produces

t he m ax i m um bas i n ave r age p r ec i p i t a t i on . A s may be deduced from the example

p rob lem vo lum inous com pu t a ti ons a r e r equ i r e d t o de t e r m i ne t he PMS The

HMR52 computer p rogram has been deve loped t o f a c i l i t a t e t h a t t ask .

BASIN

AVERAGE PRECIPITATION

-

inches

F i gu r e 18. 18- hr Bas in -Ave rage P r e c i p i t a t i on f o r

3 660 mi2 Leon River Ba sin

29


40/100

S e c t i o n 5

COMPUTER PROGR M HMR52 PROCEDURES

5.1 D i g i t a l D e f i n i t i o n o f B a s in G eo me try

The HMR52 computer p rogram uses a d i g i t a l d e f i n i t i o n o f t he watershed

bounda ri es f o r com pu t ing bas in - aver age p r e c i p i t a t i o n f rom wa te r shed a rea and

supe rposed i so hy e t a l pa t t e r ns . The boundar y o f a d r a i nage ba s i n i s de f i ne d by

l i n e s egm ents j o i n i n g a s equ en ce o f c o o r d i n a t e p o i n t s .

The sequence o f

boundary po in t s sh ou ld be cou nter - c lockw ise around the bas in o r subbas in .

I f

t h e d i r e c t i o n i s c lo c k w is e , t h e pro gra m

w i l l

r e v e r s e t h e o r d e r t o b e

c o u n te r -c l o ck w i se f o r l a t e r c a l c u l a t i o n s .

5 .1 .1 Geometr ic Pr op er t i e s

The f o l l o w i n g g eo m e t ri c p r o p e r t i e s o f t h e w a te rs he d a r e c a l c u l a t e d u s i n g

t he n bounda r y po i n t s

h a v in g c o or di na te s x i , y i ) :

Area A) :

C e n t r o id c o o r d i n a te s x c , y c )

Moment o f I n e r t i a a b o ut x a nd y axe s I x , I y )


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P ro du ct o f I n e r t i a a bo ut t h e o r i g i n P ) :

xY

A n gl e t o r o t a t e c o o r d i n a t e a xe s

to p roduce mln imum moment o f i ner t i a about

t he x - ax i s . em )

em)

=

1 / 2 ) a r c t a n [-2P / I -I ]

XY x Y

f o r I

<

I . . 7 a )

Y

. . .

e m) 1 /2 ) a r c t a n {[-2P I 2 f o r I > 7 b )

X Y x Y Y

5.1.2 Co or din at e Systems

The bas in i s d e s c r ib e d i n an x,y c o o r d i n a t e s ys te m w i t h x -a x is d i r e c t e d

eas tward and y -ax i s d i re c te d nor thward . P lacement o f t he co ord ina te system

o r i g i n and t he c o o rd i na t e u n i t s a r e a r b i t r a r y .

The i sohye t a l

p a t t e r n o f t h e

PMS

i s d e s c r ib e d i n a u,v c o o r d i n a t e s y s te m

w h ic h has i t s o r i g i n a t t h e s t o rm c e n t e r and axe s p a r a l l e l t o t h e m aj or and

m in or axes o f t he e l l i p t i c a l p a t t e r n . The c o o r d in a t e u n i t s a r e i n m i l e s .

The t ra ns for ma t io n f ro m the x,y axes t o the u,v axes i s g i ven by :

u = x x s ) cos e + y y s ) s i n e

F s . . . . . . .

8 a )

v

=

y y s ) cos e x x s ) s l n

F s

. . . . . . . . .

8 b )

where x s , y s ) i s t h e p o s i t i o n o f t h e s to rm c e n te r , e i s t he an g l e o f

r o t a t i o n f r o m t h e x- a xi s t o t h e u - a x is , and F s i s a s c a le f a c t o r i n m i l e s

pe r x,y coo r d i na t e u n i t .

5 .2 C a l c u l a t i o n o f PMP f o r a S torm Area

T h is c a l c u l a t i o n i s made f o r a g i ve n s to rm area and depth-area -dura t i o n

da ta f ro m HMR No. 51. The pro ced ure used i s a s f o l l o w s :

5.2 .1 I n t e r p o l a t i o n o f PMP Depth-Area-Durat ion Curves

The user supp l i es PMP dep t hs f r om HMR No. 51 fo r s tandard areas and

d u ra t io n s t h a t br a ck e t t he st or m a re a o f i n t e r e s t . S t r a i g h t l i n e

i n t e r p o l a t i o n i s used i n t h e p ro gra m t o c a l c u l a t e PMP f o r t h e s to rm a re a f o r

d u r a t i o n s o f 6, 12, 24, 48, and 72 hours e.g. F ig . 19 ) .


42/100

Between 10 and 200

m i 2

t he e r r o r f r om u si n g s t r a i g h t l i n e

i n t e r p o l a t i o n v ers us c ur ve f i t t l n g i s s i g n i f i c a n t . To re du ce t h i s e r r o r an

a d d i t i o n a l p o i n t i s c a l c u l a t e d midway b etw ee n l o g l o 10 a nd l o g 1 0 200

m i 2 .

T h i s a r e a i s a p p r o x im a t e ly 4 4 7 m i 2 F i g . 19 . The d i f f e r e n c e i n

P P

f rom 10 to 200 m i 2 f o r t h i s curve was 8 .5 i nches . To es t ima te

P P

a t

4 4 7 m 2

f o r o t h e r l o c a t i o n s an a d j us t m e n t o f 1 /8 .5 t im e s t h e d i f f e r e n c e

i n

P P

f r om 10 t o 200

m i 2 i s

added to t he

P P

r e s u l t i n g f r o m s t r a i g h t l i n e

i n t e r p o l a t i o n .

F i gu r e 19 .

L i nea r App r ox i m a t i on o f D ep t h - A r ea - D u r a t i on

Relations


43/100

5.2.2 M P Depth-Duration Curve Fitting

A logarithmic curve is fit through the depth versus log duration data

using a least-squared-error fit.

The equation of the curve is

whe re P is PMP in inches; is dura tion in 6-hr periods; S is a shift

adjustment ranging from -1 to 2.5 6-hr period s; and a and b are derived

constant s. Th e shift adjustme nt is determin ed by trial and error to mini mize

the sum of squared errors to reproduce a cur ve such as was shown in Fig. 13.

5.2.3 Increment al PMP Calc ulat ion

PMP is computed from equation

9)

or durations from 6 to 7 2 hours.

Incremental 6-hr PMP is then computed as th e difference between the values of

PMP for success ive durations.

The PMP for the it h 6-hr period Pi is

5.3 Calculati on of PMS for Given Storm Area and Orientation

5.3.1 Ori ent ati on Adjustment

PMP is calc ulat ed for th e storm-ar ea s ize as describe d in Sect ion 3.

This PMP is multiplied by the orientati on factor

Fo which is computed from

for / O s Opl 40

OS Op 40

where C1=

for 40 5 10 Opl 65

25

1 for IOs Opl 6 5

0 for A s 300

A s

300

and C2

=

2700

for 300

5

A s

3000

1

for

A s

3000

where 0 is the storm orientation Op is the preferred orientation and A S

is the storm area.


44/100

The a d j u s t e d PMP, P i , f o r t h e i t h 6 -h r p e r i o d i s c a l c u l a t e d as

5 .3 .2 Is oh ye t va lues

The p e r c e n t o f PMP f o r e ac h i s o h y e t i s i n t e r p o l a t e d f r om t h e d a ta i n

T ab le s 1 t hr ou g h u s i n g s t r a i g h t l i n e i n t e r p o l a t i o n o f pe rc e nt v er su s n a t u r a l

l o g o f a r ea . M u l t i p l y i n g PMP b y t h e p e rc e nt ag e s g i v e s t h e p r e c i p i t a t i o n

amount f o r e a ch i s o h y e t f o r e ac h 6 -hr p e r i o d f o r a g i v e n sto rm-a re a s i z e .

Thus, th e PMP f o r th e j t h is oh ye t and ith- h r p e r l o d i s

where PCTj i s t he pe rcen tage o f the PMP i n the

jt

s o h y e t .

5.3.3 C a l c u la t i o n o f a re a e n c lo s e d b y an e l l i p s e and t h e b a s in b o u nd a ry

C o o rd ina te s o f t h e b o u nd a ry p o i n t s a r e t r a n s fo rme d t o t h e PMS c o o rd in a te

s ys te m u s i n g e q u at io n s ( 8 a ) and ( 8 b ) . The i n t e r s e c t i o n s o f t h e e l l i p s e w i t h

t h e b a s i n b ou nd ar y a r e l o c a t e d . Each a r c o f t h e e l l i p s e b etw ee n i n t e r s e c t i o n s

i s a p p ro x ima te d b y 20 p o in t s l o c a te d a t e q u ia n g u la r I n c re men ts. The a re a

o f

t h e b a s i n encom passed by t h e e l l i p s e ( se e F i g , 2 0) i s c a l c u l a t e d f r o m e q u a t l o n

( I ) *

-

llipse

sh bound ry

Fi gu re 20. Bas in Area Encompassed by E l l i p s e


45/100

5 3.4 B a s i n - a v e r a g e p r e c i p i t a t i o n

The p r e c i p i t a t i o n vo lum e, V be tween iso hy e ts i s com u ted as the volume

f a t r u n c a te d c on e s e e F ig .

2 1 ) .

The v olu me fo r t h e 6 -h r p e r i o d i s

where s u b s c r i p t i d e n t i f i e s t h e i s o h y e t and

A

i s t h e d r a in a g e b a s i n a re a

encompassed by t h e e l l i p s e c o r re s p o n d in g t o t h e i s o h y e t . B a s in a v e ra g e

p r e c i p i t a t i o n

i s

the sum o f volumes be tween isohy e ts d i v i de d by th e d ra ina ge

b a s i n a r e a .

rainage basin

barndory

sohyet i

F ig u re 21. R e p re s e n ta t i o n o f P re c i p i t a t i o n Volume B etw een

Two I so hy et s w i t h a Truncate d Cone


46/100

5.4 C a l c u l a t i o n o f PMS f o r T ime I n te rv a ls Less Than 6 Hours

A f te r t h e s torm-are a s i z e an d o r i e n ta t i o n h av e b ee n d e te rm in e d, t h e

p ro gr am c a l c u l a t e s t h e t em p or al d i s t r i b u t i o n . The r e q u i r e d d a t a f o r t h i s

c a l c u l a t i o n a r e: t h e d e s ir e d t im e i n t e r v a l , a t , i n m in ut es ; a nd t h e r a t i o

o f l - h r t o 6-h r p r e c i p i t a t i o n f o r t h e 20,000 m i 2 A 1 i s oh y e t, r e f e r r e d t o

as R16A20, fro m F i g 8.

The p roced ure used i n the HMR52 p rog ram i s as fo l l ow s .

The NWS has de ve lo p ed a s e t o f c u r v es d e s c r i b i n g t h e l - h r / 6 - h r r a t i o f o r

each is oh ye t and va r io us s torm-area s iz es f i g u r e 40, NUS, 1982) . Those

curves have been

ta b u la te d b y

HEC

i n t o a s e t o f d i s c r e t e v a lu e s as shown i n

Table 5.

Those T a bl e 5 v a lu e s a r e a u t o m a t i c a l l y s p e c i f i e d i n t h e

HMR52

program see Corn u t er Requirements s ec t i on and Tab le 24 ) .

T h e v a l u e o f t h a t

r a t i o f o r th e

jt

s o h y e t , R16TAB f o r a s p e c l f i c s to r m -a r ea s i z e , i s

i

n t e r p o l a t e d f ro m Ta bl e 5 d a t a us n g s t r a i g h t

l i n e i n t e r p o l a t i o n o f l og a ri th m s

o f t h e a r ea . Those g e n e r a l i z e d v a l ue s a r e a d j u s t e d b t h e r e q u i r e d i n p u t

v a l ue , R16A20, t o o b t a i n t h e r e q u t r e d r a t l o f o r t h e jih i s o h y e t , R l 6 j .

The l - h r r a i n f a l l f o r t h e j t h i s o h y e t i s com puted as

where PI,

i s

t h e maximum 6 -h r p r e c p i t a t i o n f o r i s o h y e t

j

c a lc u la te d i n

e q u a t i o n 1 1 3 ) .

A

l e a s t s q u a r e q u a d r a t i c e q u a t i o n

i s f i t

th rough the 0 - , I- -, 12-,

1 8- , a n d 2 4-hr p re c ip i t a t i o n amounts f o r e ac h i s o h y e t . F or r e s i d u a l

p r e c i p i t a t i o n o u t s i d e t h e s t or m a r e a ) t h e l - h r a mount i s o m i t t e d ,

P r e c i p i t a t i o n i s i n t e r p o l a t e d f o r 5-, l o - , 15-, 30-min, 2-, and 3-hr dur tions

f o r e ach i s o h y e t . The a ve ra g e p r e c i p i t a t i o n o ve r t h e b a s i n

i s

computed for

each o f these du r a t i ons , F ig . 22,

F igu re 22 . PMS Depth ve rsus Du ra t ion

36


47/100

I nc re m e nt al p r e c i p i t a t i o n i s c a l c u l a t e d f o r t he t o t a l number o f

~t

i n t e r v a l s fr o m t h e b a sin -a ve ra ge d d e p th v ers us d u r a t i o n d a ta . T h i s r e s u l t s i n

a sequence o f i n t e r v a l s w i t h d e cr ea s in g p r e c i p i t a t i o n i n t e n s i t y , F i g . 23.

I n c re m e n t al p r e c i p i t a t i o n i s assumed t o be u n i f o r m w i t h i n e ach 6 -h r p e r i o d

beyond 24 -h rs du r a t i o n . These i n t e r v a l s a r e r ea r r anged t o f o r m t he

PMS

as

f o l l o w s :

The p o s i t i on o f t he l a r g es t 6- hr i nc rem en t may occur any t i m e a f t e r

t he f i r s t 24 hou r s o f t he s t o r m as shown i n F i g . 24. The seven th

p o s i t i o n ( h o u r s 3 7-4 2) i s ch os en b y d e f a u l t .

T h e l a r g e s t

~t

i n cre me nt o f p r e c i p i t a t i o n i s p l ac ed i n t he m i dd le

o f t h e l a r g e s t 6 -h r p r e c i p i t a t i o n i n t e r v a l . The r e ma in in g ~t

i nc re m e n ts f o r t h a t 6 -h r p e r i o d a r e a r ra n g e d a l t e r n a t e l y b e f o r e a nd

a f t e r t h e l a r g e s t i n c r e m e n t .

The r e m a in i n g 6 -h r i n t e r v a l s , w i t h d e cr e as in g p r e c i p i t a t i o n

m a gn itu de , a r e a rr an g e d a l t e r n a t e l y b e f o r e and a f t e r t h e l a r g e s t

6 - h r - p r e c i p i t a t i o n i n t e r v a l , e x c e p t t h e second, t h i r d , and f o u r t h

l a r g es t 6-h r i nc rem en t s canno t be p l aced i n the i r s t 24 hours o f t he

s to rm . These inc r em ent s a r e p l aced a f t e r t he l a r ge s t inc r em en t, i f

t h e i r n orm al p o s i t i o n wou ld f a l l i n t he f i r s t 24 ho urs o f t he PMS

The

~t

i nc re m e n ts w i t h i n t h e se co nd, t h i r d and f o u r t h l a r g e s t 6 -h r

i nc r em en t a r e a r r anged t o i nc r ea se t ow a rds t he s t o r m s peak

p r e c i p i t a t i o n . T h is r e s u l t s i n a t r i a n g u l a r - l i k e h ye to gra ph o f PMS

p r e c i p i t a t i o n .

4

t

T ime hours)

F i g u r e 23. I nc r em en t a l

PMS

Depth H is togram


48/100

igure

24

xample 1 hr

Distribution o f

PMS


49/100

OPTIMIZATION

OF

STORM-AREA

S I Z

AND ORIENTATION

The am ount o f p r e c i p i t a t i o n on a b a s i n i s a f f e c t e d by t h e s t o r m

p la c eme n t, s t o rm-a rea s i z e an d s to rm o r i e n t a t i o n . HMR52 uses a pro ce du re t o

e s t i m a t e s t o rm - ar ea s i z e and o r l e n t a t i o n w h ic h w i l l produce maximum

p r e c i p i t a t i o n on t h e b a s i n . T h i s p r o ce d u re w i l l d e te rm in e t h e o p t ima l

s torm-a re a s i z e an d o r i e n t a t i o n f o r mos t b a s in s . Ho we ver, b ec au se o f t h e

i n t e r a c t i o n o f s t o rm p la ce m en t and o r i e n t a t i o n , s e v e r a l t r i a l s s h o u l d b e made

t o v e r i f y t h a t t h e o p t i m a l v a lu e s h av e been fo un d.

6.1 Storm Center

When th e s to rm pla ce me nt i s n o t g i v e n, t h e s to rm c e n te r i s p l a c e d a t t h e

b a s i n c e n t r o i d .

f t h e s to rm o r i e n t a t i o n i s n o t giv en , a t r i a l o r i e n t a t i o n a l on g th e a x i s

f o r w h i ch t h e b a s i n has a m inim um moment o f i n e r t i a i s use d. T h i s o r i e n t a t i o n

i s

s e le c te d as an a n a l y t i c a l l y d e te rm i na b le o r i e n t a t i o n w hi ch i s most l i k e l y

t o p r od uc e maximum p r e c i p i t a t i o n on t h e b a s i n w i t h o u t r e g a r d t o t h e

o r i e n t a t i o n a dj us tm e nt f a c t o r . U si ng t h e t r i a l o r i e n t a t i o n th e a vera ge

p r e c i p i t a t i o n on t h e b a s i n i s c a l c u l a t e d f o r s e v e r a l st or m-a re a s i z e s ( se e

example i s S e c t i o n

9 .

The s to rm-a rea s i ze wh ich p roduces maximum p re c ip i t a -

t i o n i s s e l e c t e d as th e c r i t i c a l sto rm -a re a s i z e . The c r i t i c a l st or m-a re a

s i z e may need t o be recomputed

i f o th e r o r i e n t a t i o n s o r p la c eme n ts a re u se d.

6.3 S to rm O r i e n t a t i o n

Be cause o f I n te ra c t i o n be tw ee n b a s in sh ape a nd t h e o r i e n t a t i o n a d ju s tme n t

f a c t o r , t h e t r i a l o r i e n t a t i o n used t o s e l e c t s to rm -a re a s i z e may n o t p ro du ce

maximum p r e c i p i t a t i o n on t h e b a s i n . U s i ng t h e c r i t i c a l s i z e s e l e c t e d abo ve ,

t h e s t or m p r e c i p i t a t i o n i s c a l c u l a t e d f o r o r i e n t a t i o n s a t 10-degree i nc re m en ts

b etwe en 135 d eg re es an d 315 d eg re es . S torm p re c ip i t a t i o n i s t h e n c a l c u la t e d

f o r o r i e n t a t i o n s a t p l u s o r m i nu s 5 d eg re es f r o m t h e p r e vi o u s b e s t

o r i e n t a t i o n . The o r i e n t a t i o n w hic h y i e l d s maximum p r e c i p i t a t i o n on t h e b a s i n

i s chosen as t h e c r i t i c a l o r i e n t a t i o n .

f

t he c r i t i c a l o r i e n ta t i o n i s n o t th e same as was used to s e le c t th e

c r i t i c a l s t o rm-a rea s i z e , t h e s to rm-a rea s i z e may h av e t o be r ec omp uted u s in g

t he c r i t i c a l o r i en t a t io n . T hi s i s t he u s e r s r e s p o n s i b i l i t y .

t

i s not done

a u t o m a t i c a l l y .

6.4

ser

C o n t r o l o f O p t i m i z a t i o n

P r e c i p i t a t i o n on t h e b a s i n f o r t h e pu rp os es o f s e l e c t i n g s to rm -, ar ea s i z e

a n d o r i e n t a t i o n i s t h e c u m ul at iv e p r e c i p i t a t i o n f o r t he

3

l a r g e s t 6 hr

pe ri od s. The number o f pe r i od s may be changed by th e use r.

S to rm p lacement , s to rm-a rea s ize , o r o r i e n ta t i o n may be f i x e d by the

u s e r .

n

a d d i t i o n t h e t r i a l o r i e n t a t i o n used t o s e l e c t c r i t i c a l s torm -a re a

s i z e may be s p e c i f i e d b y t h e u s e r .


50/100

S e c t i o n

7

INPUT D T REQUIREMENTS

I n p u t d a t a a r e d e s c r i b e d i n d e t a i l i n t h e A pp en di x. T a b le 11 shows t h e

s e c t i on s o f an i n p u t d a t a f i l e r e q u i r e d t o c a l c u l a t e a PMS.

D rain ag e -B a sin -G e ome t ry d a ta i n c l u d e s c o o rd in a te s o f p o in t s on th e b a s in

b o u n d a r y a n d a s c a l e f a c t o r .

R e q u i r e d H y d r o m e t e o r o l o g i c a l d a t a a r e t h e p r e f e r r e d s t o r m o r i e n t a t i o n

f r o m F i g .

3

and PMP es t im at es f r om f i g u r e s 18-47 i n HMR No. 51.

The S t o rm , -S pe ci f i c a t i o n d a t a d e f i n e t h e s o rm - ar ea s i z e , o r i e n t a t i o n , and

l o c a t i o n o f t h e s to r m c e n t e r . C a l c u l a t i o n o f a te mp or al s to rm d i s t r i b u t i o n

r e q u i re s t h e de s i r e d t i m e i n t e r v a l and r a t i o o f l - h r t o 6-hr p r e c i p i t a t i o n

f r o m F i g . 8.

T hr ee e xa mp le i n p u t d a t a s e t s a r e g i v e n i n t h i s docum en t:

Leon R ive r- - Tab le 11

Jones Re ser voi r-- Tab le 14

Oua chi ta R iver- -Appe ndix Example

The Leon R i v e r a p p l i c a t i o n i s f o r c o m p u ta t io n o f t h e PMS o ve r a s i n g l e

b a s i n f o r g i v e n s to rm - ar ea s i ze , o r i e n t a t i o n , c e n t e r in g , and ti m e p a t t e r n .

The Jones R e s er vo ir a p p l i c a t i o n i s f o r a m u l t i - su b b as i n r i v e r b a s i n i n

w h i ch t h e s t o rm - ar e a s i z e and o r i e n t a t i o n a r e o p t i m i z e d b y t h e pr og ra m f o r t h e

r i v e r b a s i n as a w ho le . The st o r m c e n t e r i n g was n o t s p e c i f i e d so th e d e f a u l t

c e n t e r i n g o f t h e b a s i n c e n t r o i d i s used. The t im e p a t t e r n i s g iv e n. A f te r

c o m p u ta t io n o f t h e PMS f o r t h e e n t i r e r i v e b a s i n , t h e PMS i s c a l c u l a t e d f o r

each subbas in .

The Ou ac hi t a R i v e r e xa mp le i s s i m i l a r t o t h e J ones R e s e r v o i r a p p l i c a t i o n

e x ce p t t h a t g i v e n s to rm - ar ea s i z e , o r i e n t a t i o n and c e n t e r i n g d a ta a r e p r o v i d ed

a f t e r t h e o p t i m i z a t i o n i s c om p le te d. T ha t g i v e n PMS i s t h e n c a l c u l a t e d an d

s u b b a s i n p r e c i p i t a t i o n

s

c ompu te d f o r t h e g i v e n PMS d a ta , n o t t h e o p t i m i z e d

v a lu e s


51/100

Table

Sample

Input

o r HMR5

Job De sc r ip t ion Ide n t i f i . c a t i on1

I D PROBABLE MAXIMUM STORM CALCU LATION F OR EXAMPLE

I N

HMR NO 52

I LEON

RIVER

AT BELTON RESER VOIR

Drainage Basin Geometry

BN LEON

Data

f r o m HMR N o

5 and

Storm Spec i f ica t i . sn


52/100

Se c t i o n 8

PROGR M OUTPUT

8 . 1 P r i n t o u t

HMR52 p r in ted ou tpu t beg ins w i th a

l i s t

o f t h e i n p u t da ta , Ta b l e 1 2 a ) .

f

a t a w ere e n te r e d u s i n g t h e f r e e - f o rm a t o p t i o n , t h i s l i s t shows t h e d a ta

v al ue s i n t h e i r p ro pe r f i e l d s .

Tab le 12 b) shows i n p u t

PMP

fr om HMR No. 51 and

PMP

i nc remen ts fo r each

6-hr i n t e r v a l and s tanda rd s to rm--area s iz e as i n te rp o la te d f rom the HHR No. 51

dep th -a rea -du ra t i on da ta .

Tab le 12 c ) shows coo rd in a tes o f subbas in boundary po in ts and subbas in

a r e a a n d c e n t r o i d l o c a t i o n c a l c u l a t e d f r o m t h e s e c o o r d i n a t e s .

Tab le 12 d ) shows th e ba s in a rea w i t h in each i so hy e t and the

p r e c i p i t a t i o n amount a s s ig n e d t o th e i s o h y e t s f o r each 6.-hr i n t e r v a l . T h i s

ta b l e a l s o shows the bas in -ave rage dep ths c a l cu la te d f rom these a reas and

i s o h y e t v a l u e s .

When a te m p or al d i s t r i b u t i o n i s r e qu e s te d f o r a n i n t e r v a l l e s s t h a n 6

hou rs , HMR52 compu tes a dep th ve rsus d u r a t i o n r e l a t i o n fo r each i so hy e t .

Thes e r e l a t i o n s a r e shown i n Ta b l e 1 2 e ) . They a r e us ed t o c a l c u l a t e an

a ve ra ge d e p th v er su s d u r a t i o n r e l a t i o n w h ic h I s u se d t o c a l c u l a t e i n c r e m e n t a l

p r e c i p i t a t i o n f o r t he t em po ra l d i s t r i b u t i o n i n Ta ble 1 2 f ) .

8.2 E rr o r Messages

The HMR52 program rec ogn ize s some in p u t and com puta t ion al e rr o rs and

p r i n t s e r r o r messages ac co rd i ng ly . These e r r o r messages have an

I d e n t i f i c a t i o n Number an d T i t l e ; App en dix

B

c o n t a i n s a n e x p l a n a t i o n o f e a c h

er ror message.

When an er r o r i s de te ct ed by HMR52, the program

w i l l

read th rough the

r e ma i n i n g d a t a and c he ck f o r i n p u t e r r o r s . No c a l c u l a t i o n s w i l l be made using

t h e r e ma i n i n g d a t a .

The computer o pe ra t in g sys tem may a ls o p r i n t e r ro r messages.

When an

e r r o r oc c u rs , t h e u s er s h o u l d f i r s t a s c e r t a i n i f

i t

i s genera ted by HMR52 or

by the system. f

i t

i s g e n er a te d b y HMR52 i . e . , i n t h e f o r ma t g i v e n i n

Ap pe nd ix B ) r e f e r t o t h a t a p p en d ix a nd t ak e t h e i n d i c a t e d a c t i o n s . f t h e

e r r o r i s sys tem genera ted , computer sys tems person ne l sho u ld be co ntac ted t o

a s c e r t a i n t h e m e a n i n g o f t h e e r r o r . f t hese sys tem e r ro rs canno t be res o lv ed

in-house or

i f

t h e r e

i s

an e r r o r i n the HMR52 program, the

H E C

shou ld be

c o n t a c t e d ,


53/100

LINE

1

2

T a b l e 2

Sample Output from HMR52

TABLE

12

a)

Sample

O u t p u t

from AMR52

HEC PROBABLE MAXIMUM

STORM

INPUT DATA

ID.......1.......2.......3.

.......5.... e.6.......7.......8.......9......10

I D

PROBABLE MAXIMUM

STORM

CALCULATION FOR EXAMPLE 1

I N RIXR

NO

52

I D LEON RIVER AT BELTON RESERVOIR

LEON

1.0062

46.4

18.7

-12.4

-51.6

-25.8

5.8

44.0

-45.9

-1.2

42.0

42.1

-1.6

-23.5

-46.9

20

10

200

1000

5000

10000

20000

3000

-2.2

1.20


54/100

*

PROBABLE MAXIMUM STORM HMR52)

*

NOVEMBER 1982

*

* REVISED 3 1 AUG 84 *

*

*

*

*

*

.........................................

AREA

SQ. MI.)

10.

200.

1000.

5000.

10000.

20000.

STORM AREA

10.

25.

50.

100.

175.

300.

450.

700.

1000.

1500.

2150.

3000.

4500.

6500.

10000.

15000.

20000.

PROBABLE MAXIMUM STORM CALCULATION FOR EXAMPLE 1 IN

MR

NO. 5 2

LEON RIVER AT BELTON RESERVOIR

PROGRAM IS GIVEN THE STORM AREA AND ORIENTATION

PMP DEPTHS FROM MR 51

DURATION

6-HR 12-HR 24-HR 48-HR 72-HR

29.80

36.20

41.80 46.70 49.80

22.30 27.40

33.00 37.50

41.40

16.20 21.20 26.80 31.00 34.50

9.30 13.10 18.10 22.60 25.90

7.20 10.40 14.90 18.8 0 21.00

5.20

8.20 11.70 15.40 18.40

PMP DEPTHS FOR 6-HOUR INCREMENTS

6.47 3.29 2.22 1.68 1.35 1.13 -9 7

6.17 3.25 2.22 1.69 1.36 1.14 .98

5.91 3.21 2.21 1.69 1.37 1.15

99

5.54 3.14 2.21 1.70 1.38 1.17 1.01

5.25 3.09 2.20 1.71 1.40 1.18 1.02

5.18 3.05 2.17 1.69 1.38 1.17 1.01

5.21 3.03 2.14 1.66 1.36 1.15 -9 9

5.21 3.00 2.12 1.64 1.33 1.13 -9 7

5.23 2.98 2.09 1.62 1.32 1.11 .96

4.91 2.90 2.07 1.61 1.31 1.11 .96

4.64 2.83 2.04 1.59 1.31 1.11 .97

4.39 2.75 2.01 1.59 1.31 1.11 .97

4.09 2.66 1.98 1.57 1.31 1.12 .98

3.88 2.50 1.85 1.47 1.22 1.04 .91

3.64 2.27 1.65 1.30 1.07 .91 .80

3.18 2.12 1.60 1.28 1.07 .92 .80

2.84 2.00 1.55 1.26 1.07 .92 .81

*

U.S. ARMY CORPS OF ENGINEERS

THE HYDROLOGIC ENGINEERING CENT

k

609 SECOND STREET

DAVIS, CALIFORNIA 956 16

916) 551-1748 OR FTS) 460-174

*

.......................................


55/100


56/100

TABLE 12

A )

Sample Outptlt

f

orn HMR52

continoed)

PROBABLE MAXIMUM STORM FOR LEON

STORM AREA 3000. SQ. MI., ORIENTATION 134., PREFERRED ORIENTATION 208.

STORM CENTER COORDINATES, -2.2, 2.4

AREA

ARW BASTN DEPTHS INCHES) FOR 6-HOUR INCREMENTS OF PMS

SQ.MI.\ ISQ.MI.) 2

3

4 5 6 7 8 9 10 11 12

DEPTH 8.24 3.41 2.19 1.60 1.26 1.04 0.89 0.77 0.68 0.61 0.56 0.51


57/100

TABLE 12 e)

Sample Output from

H M R 5

continued)

TIME INTERVAL 120. MINUTES

1-HR TO

6-FIR

RATIO FOR ISOHYGP

AT

20000 SQ.

MI

z0.306

EPTH VS DDRAT ION

ISCSYFP 5YIN lOMIN 15MIN 30MIN 1-HR 2-FIR 3-HR 6-AR 12-HR 18-HR 24-HR 30-HR 36-HR 42-HR 48-HR 54-HR 60-HR 66-HR 72

AVERAGE 0.21 0.42 0.63 1.21 2.18 3.69 5.07 8.24 11.64 13.84 15.43 16.69 17.73 18.62 19.39 20.07 20.68 21.24 21


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TABLE 12 f)

Sample Outnut from

HMR52

continued)

DAY 1

TIME PRECIPITATION

INCR TOTAL

6-HR TOTAL 0.51

DAY 2

TIME PRECIPITATION

INCR TOTAL

DAY 3

TIME PRECIPITATION

INCR TOTAL

6 HR

TOTAL 1.26

PROBABLE MAXIMUM STORM FOR LEON

TIME PRECIPITATION TIME PRECIPITATION TIME PRECIPITATION

INCR TOTAL INCR TOTAL INCR TOTAL



0800

0.95 5.48

1400 2.57

10.51 2000 0.83 17.00

1000

1.12

6.59 1600

3.69

14.19 2200

0.72 17.72

1200 1.34

7.94

1800 1.98

16.17

2400 0.64 18.36

3.41 8.24 2.19




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8 .3 P r e c i p i t a t i o n F i l e f o r R a i n f a l l - R u n o f f M od el Usage

H ye to gra ph s may be w r i t t e n t o a f i l e f o r use i n a r a i n f a l l - r u n o f f m odel

such as HEC-1.

8 .2 .1 P unch F i l e

The o p t i o n o f w r i t i n g hy et og ra p hs t o a pu nch o r c ard -im ag e f i l e i s

a v a i l a b l e . Each h y e t og r a p h i s p re c ed e d b y a l i n e g i v i n g t h e s u b b a s in name a nd

t i m e i n t e r v a l ( s ee T ab l e 13 . ) T he punch da t a must be m erged w i t h i n p u t da t a

f o r t he r a i n f a l l - r u n o f f model.

8 .2.2 DSS F i l e

For co mpu ter system s where t h e HEC Dat a St or ag e System (HECDSS)

i s

av a i l a b l e , hy e t og r aphs may be t r an s f e r r e d t o HEC-1 t h r ough a SS f i l e . S e e

Se c t io n 9 f o r an example .

Table 13

ilPUNCHfl O utp ut f i l e fr o m HMR52

LEON INTERVAL 1 2 0 MIN

P 1 0 1 6 9 0 1 6 9 0 1 6 9 0 2 0 4 0 2 0 4 0 2 0 4 0 2 5 7 0 2 5 7 0 2 5 7

P I 0 3 4 7 0 3 4 7 0 4 8 6 0 5 2 8 0 5 8 4 0 9 5 0

1 115

1 3 4 3 2 5 7 1

P 1 1 9 8 0 0 8 2 6 0 7 2 0 0 6 4 4 0 4 2 0

0 420

0 4 2 0 0 2 9 5 0 2 9 5

P 1 0 2 2 8 0 2 2 8 0 2 2 8 0 1 8 5 0 1 8 5 0 1 8 5


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S e c t i o n

EXAMPLE APPLICATION

9 . 1 I n t r o d u c t i o n

F i g . 25 shows t he watershed above Jones Re se rvo i r . HMR52 i s used t o

deve lop PMS hye tog raphs f o r th e fo u r subbas ins . HEC-1 i s used t o ca lc u l a te

and ro u t e the PMF th rough Jones Re ser vo i r . The hye tog raphs a r e t r an s f e r re d

fr om HMR52 t o HEC-1 u s in g th e HEC Data St or ag e System DSS). The HMR52 i n p u t

d a t a f o r t h i s e x am ple a r e shown i n T ab l e 1 4.

9 .2 mR52 In pu t

hmr52 probable maximum storm (eastern united states)

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