University of Nigeria and...University of Nigeria Research Publications Author OBIOHA, Ogbonna Gregory PG/M.ENG/89/7968 Title Rainfall and Evaporation Data Analysis for the Prediction

University of Nigeria

Research Publications

OBIOHA, Ogbonna Gregory

Aut

hor

PG/M.ENG/89/7968

Title

Rainfall and Evaporation Data Analysis for the Prediction of Hydrological Design Parameters Under Nsukka Tropical

Climate

/Fac

ulty

Engineering

Dep

artm

ent

Agricultural Engineering

Dat

e

October, 1991

Sign

atur

e

R . A I N F A L L A N D E V , A P , O R A T I O N

DATA A N A L Y S I S FOR THE PREDICTION OF HYDROLOGICAL

DESIGN PMAMETERS UNDBK NSUKKA TROPICAL CLIPV\TL

OBIOHA, OGBONNA GREGORY, a pos tg radua te s t u d e n t

i n t h e Department of A g r i c u l t u r a l Engineer ing and

wi th Reg. No. PG/M. ENG/09/7968 has s a t i s f a c t o r i l y - completed t h e requirements f o r the course and r e sea rc

work f o r t h e degree of Master of Engineer ing (M.Ena)

i n A g r i c u l t u r a l Engineer ing,

The work embodied i n this p r o j e c t r e p o r t is

o r i g i n a l and has n o t been submi t ted i n p a r t o r f u l l

f o r any o t h e r diploma o r degree of t h i s Un ive r s i t y or

a n v . o t h e r University.

v \

WCb - --.

Engr. D r . F.O.I. Ezeike Engr. D r . G.0, Chulcwun Head o f bepartment Supe rv i so r

- Dr. F.1. fd ikc

EXTERNAL EX/\.KINER u p e r v i s o r

!Phis work is for: Mum and the Girls: #

Gera ld ine , Uche.ma, Odiraa and

I wish t o acknowledge t he assist6ince received from

numerous individuals during t he production of t h i s project,

My highest thanks go t o my superir isws, Engr. (~r,

GOO, Chukwuma and Engr. (Dr.) F.1, Idike fo r t h e i r

spec ia l ausistance, understanding and wonderful supervision ,

during t he course of my academic career,

I am a l s o highly g ra te fu l t o the following important

yoreonrr i n my l i f e ; my pa~*onto Mr. J.1. Obioha, and MTR F.0,

Obioha fo r having suotained me s o far; ny uncle Dr. J.A

Obiora, My brother Barr iuter Yagazie Obioha and my brother-

in-law k g r . Chidi Njaka fo r t h e i r support.

I s h a l l , -forever remain grhtoful t o my rjpecial f r iends ,

Chuks Agwuncha, Okey Agwuncha, Okey meh, and Luke Azike for

t h e i r encouragements; especially during the d i f f i c u l t times,

Above a l l . , I wish t o express my (gratitude t o the members

,of the "Kpos-kposu Club; Bob Asogwa; my gal, and roomate,

Peroz, C, Obidiemu, Dozie Iyks (IW), LC. Igwe and the rest

of the crew, I s h a l l ulwaye remain grateful ,

Thank you al l ,

Table 1:

Table 2:

Table 4:

Table 5:

Table 6:

Table 7:

Table 8:

Table 9:

Table 10:

Table 11:

P A G E

20 year - Monthly Rainfal l Data ('197'1 - 1990) Ekom t h e University of Nigeria Nsukka Metewelogical S ta t ion - - - - - - - - - - - - 25

18 year - Montllly and Annual Evaporation Data

(1971 - 1988) lkom the University of Nigeria

Nsukka Meteorological S t a t i o n - - - - - - - - 2 6

Mean Monthly Rainfall. D is t r ibu t ion f o r Nsukka 2 8

Annual Rainfa l l Dis t r ibu t ion fo r N s u k h - - - 29

Return Period of the 2GYear Nsukka Rainfa l l

Using t h e A ~ u a l Series - - - - - - - - - - - 3 5

Return Period of t h e 20-Year Nsukka % i n f a l l

For 1 - 5 days Consecutive I b i n f a l l s - - - 37

Heturn Period of the 20-Year Nsukku Rainfa l l

For 6 and 7 day^ Consecutive Ra in fa l l s - - - - 38

Weelily Expected Rainfa l l (mm) a t Different

Percent Chancot; f o r Nsuklca - - - - - - - - - - it 1

Weekly Expected Evaporation (mm) at ~i f f e ren t

Percent Chances f o r Nsukka - - - - - - - - - - 43

Monthly and Annual Expected Rainfa l l (mm) at

.Different Percent Chances f o r Nsukka - -. - - - 45

~ o ~ . ~ t l ~ l y and Annual Ikpect ed Bvpora t ion (mm) a t

Different Percent Charlcos f o r 1"Jsukha - - - - - 14 6

L I s T o F T A B L E s (CONTD) v i - ..---

P A G E

Table 12: Mills Computational Procedure f o r Constants of

the Gornpertz and Log i s t i c Models - - - - - - - - - - 5 5

Table 13: Values of C o n ~ t a n t for t h e Gornpertz and

T ~ g i s t i c Models f o r Cummulative Surplus

Table 14: Values of Constants f o r t h e Gompertz and

Logis t ic Models f o r Cunmul.ative Def ic i t

Table 15: Values of S t a t i c t i c a l Purt~meterc of Cunlrnulutive

Ra in fa l l Surpluses and t h e i r Predic ted Valueu - 59

Table 16: - Values of Stat iut ic , ; l l Parameters of Cummulative , Rainfa l l D e f i c i t s and t h e i r Predicted Values- - 60

Table 17: P o t e n t i a l E h p o t r a n s p i r a t i o n and Crop Factors of

African Spinach (Arnamnthui; Mydritius) f o r the

7w Probab i l i ty Evaporati0.a Index (March - ~ a y ) 62

Table 18: P o t e n t i a l Evapotranspirat~ion and Crop Factors

of African Spinach (Amaranthus Ilybridus) f o r t h e

7% P r o b a b i l i t y Evapora t im lndex (Oct - . ~ e c ) 63

Tablc I y: P o t e n t i a l Evupotrunapi~ut ion arld Crop l h c t o r s (f)

of Cassuva (Mainihot Esculenta Crantz) f o r the

7091 Probab i l i ty Evaporation Index (Aug - J u l y ) 64

Table 20: Return Period and Magnitude of N~ukka Ra in fa l l

Using I - 7 days Consecutive Ra in fa l l s

(April - september) - - - - - - .. - - - - - - I 67

P A G E

, Table 22: Ani?ur;~l 1ta:i.nfull Defici ttj: e ~ t U i f f erent

Percent Chances at Nsukka - - - - - - - 73

viii

P A G E

Fippre 2: Annual Ra in fa l l Distr ibution.

For Nsukka (1971 - 1990) - - - - - - - - - 30

F i ~ u r e 4 : Ar~nual Evaporation at Nsukku (7971 - 1933) - 32

F i e r e : Mean Monthly'lhaporation a t Nsukka - - - - 33

F i f ~ u r e 6: Return Period (Using Annual Series) - - - - 3 6

Figure (2: Monthly Rainfa l l D i s t r ibu t ion a t 44% - 9% ,

Chances at Nsu&a - - - - - - - - - - - - - 49

Figure 11: Log-Probability of A n n ~ a l E V a p o r a t i o n a t

The Potent ial . ET,S Pred ic t ed by t he Three Models (March - May) - - - - - - - - - - The P o t e n t i a l ET,S Pred ic t ed by the Three Models (Oct. - Dee.) - - - - - - - - - -

C r ~ p Coeff icienLs of ' Amararrthus Hybr idw Determined with t h e Three llodels (March - May) - - - -. - - - - - - - - - Crop Coef f i c i en t of Amaranthus Hybridus Determined with t h e 'l'hrce Plodels ( ~ c t , - Dee,) - - - - - - - - - - - - - - -

Chart Showing Rainfall D e f i c i t dnd Surplus

Ax

P A G E

66

75

'? 6

77

78

79

80

82

7 2

20 yea r s (7971 - 1990) of r a i n f a l l &it& and 18 y e w s

(1971 - 1988) of evapora t ion d a t a were s t a t i s t i c a l 1 . y arialysed

f o r t h e purpose of determining t h e i r c h a r a c t e r i s t i c s , I t was

t h a t t he Nsukka rainfall h a s u nletin annual value of

1533mm with a monthly unimodal distributj .or: having a maximwn

value i n September and minimum value6 in January and December.

s i m i l a r l y t h e Nsukkn evaporat ion h a s a mean annual va lue of

160I,?Omm with peak i n January an'd minimum vtilue i n

~ e ~ t e m b e r ,

Two s t a t i s t i c a l models ( ~ o m ~ e r t z a d t h e Log i s t i c models)

were f i t t e d t o t h e r e s u l t s obtained fror.11 p r o b a b i l i t y m a l y s i s

of r a i n f a l l and evaporat ion d a t a on weekly and monthly b a s i s

r e s u l t a n t f i t , it was observed . that t h e Gornpertz model p red ic t ed

b e t t e r r a i n f a l l su rp luses o r r e s e r v o i r mcha rge while t h e

L o g i s t i c model p red ic t ed b e t t e r r a i n f a l l . d e f i c i t s o r r e s e r v o i r

evapora t ion l o s s , Using t h e same p r o b a b i l i t y analysis on

annual basis, I 0 y e a r s w a s ob ta ined as t h e minimum leng th of

d a t a t h a t may be adequate f o r hydro1ogic:al ana lyses i n the

~ ;va lua t . lon of evupox-ation d a t a a6 u means of e s t ima t ing

evapo t r ansp i r a t ion showed t h a t weekly arid monthly evapora t ions

at 7C$ probabi l i ty l e v e l ( ~ ~ 7 0 ) proved a good index f o r

predicting po ten t ia l evapotranspiration. However, i t

w t l ~ observed t o predict high evnpotran~spiration values

during hot and dry weathers whereas it predicted low

evapotranspirution during cold a,nd humid weathers. Using

' the EV7O index, crop fac tors were determined f o r African

Spinach (Amaranthus Hybri dus) f o r the growing seasons of

March - May and October - December, Similarly the crop

fac tor of Cassava (Manihot Esculenta Crantz) was determined

f o r period of August - July,

Finu l ly , constxtive duy ru in fu l l ( ~ p r i l - ~eptember)

was used t o determine t he drainage coef f ic ien ts of agric,ulturnl

land i n the Nsukka area. It was observed tha t consecutive day

r a i n f a i l is a good pr inciple fo r determining design drainage

coeff ic ient based on the physiological tolerance of crops t o

excess water.

x i i

T A B L E O F C O N T . E N ' I ' S ============-----==

P A G E

CHAPTER ONE: INTRODUCTION - - - - - - - - - - - - - - I

4.0 Data a v a i l a b i l i t y probletn i n ag r i cu l t u r a l

Engineering designs i n Nigeria - - - - - - - - I

1.1 Significance of the project - - - - - - - - - 6

1.2 Statement of objectives - - - - - - - - - - - 7

CHAPTER TWO: LITFfiTURE REVIEW - - -- - - - - - - - - 8

Analysis of 2a infu l i Data - - - - - - - - - - - 8 Frequency Analysis - - - - - - - - - - - - - - 9 Probabi l i ty Analysis - - - - - - - - - - - - - I1

Water Requirement of Crops - - - - - - - - - - 14 Estimation of Water Requirements of Crops - - - 7 5 Emperical Methods of Jikapotranspiration

Determination - - - - - - - - - - - - - - - - - 16 Estimation of Evapotranspiratian using the

Evaporation Index - - - - - - - - - - - - - - - 79 Estimation of Drainage Requirements - - - - - - 20

xiii

TAl3LE OF CONTENl'S (CONTD. )

P A G E

3.1 Data Col lec t ion - - - - - - - - - - - - - - - 3 . 1 Location and Description of the Study Area - - 1 2 Types of h t a - - - - - - - - - - - - - - - -

3.2.1 Monthly, Annual Rainfa l l and hhaporation - - - 3.2.2 Ra in fa l l Frequency Analysis - - - - - - - -.- 3,2.3 Rainfa l l and hkaporation Probab i l i ty Analysis

3.2.4 Do termination of Minirnum Aocep-t;uble Length o f .

R e c o r d s - - - - - - - - - - - - - - - - - - -

3.2.5 Predic t ion of Rainfa l l Def ic i to a n d Surpluses

3.2.6 Determination of Evapotranspiration and Crop

CHAPTEZ FOUR: RESULTS AND DISCUSSIOIYS

4.2.2 Frequency Analysis 7 - - - - - - - - - - - - 4.2.3 Probabi l i ty Analysis - - - - - - - - - - - - 4.2.4 Predic t ion of Rainfa l l D e f i c i t s and Surplusee

4.2.5 Determination of hkapotran~p. i ra t ion and Crop

TABLE OF CONTlQ4TS (CONTD. ) - xiv

P A Ci E

4,2.6 Determination of Drainage Coefficients - - - - CHAPTm FIVE: CONCLUSIONS AND RECOMMmDATIONS - - - -

REFERENCES

APPEXlDICES

CIIAPTEH ONE

INTRODUCTION

7.0 Da.ta Avai lab i l . i ty Problem i n A p ~ i c u l t u r a l . Bsgineerin6j

1%e inadequacy of r e l i a b l e data a n d :ini:oralation t h a t a r e

necessary f o r t h e design and c o n s t r u c t i o n of water management

p r o j e c t s is one of t h e major problems t h a t is adverse ly

a f f ect inp; water r e sou rces development i n Nigeria ,

S p e c i f i c a l l y a f f e c t e d i n t h i v a r e a is t h e design of '

i r r i g a t i o n and drainage, as w e l l as s o i l . and water conserva t ion

systems. It 1s obvious t h a t t h e estinlilt.ion of t h e i r r i g a t i o n

and dra inage needs of propoe;ed p r o j e c t s o r echemes r e q u i r e s a

,knowledge of t h e cl imutological . c h u r a c t e r i r t i c s of t h e a r e a

involved , i n a d d i t i o n t o such o the r f ac t . o r s involv ing f inance ,

l o g i s t i c s ana ergonomics, Cases are abcrund where t h e f a i l u r e &

of laany i r r i g a t i o n p r o j e c t s i n t h e cour1t.r~ have been t r a c e d t o

a n ove r s igh t i n t h e cons ide ra t ion of' t h e m va r i ab l e s ,

Water l o s s e s through evapqra t ion and or evapo t r ansp i r a t ion

have commanded a g r e a t e r r e sea rch a t t e n t i o n among t h e v a r i a b l e s

o u t l i n e d wiibove i n r ecen t times. l 'h is is because, t h e r a t e of water

loss from both l a n d and ponded water o r r e s e r v o i r s h a s a very important

r o l e t o p lay i n detorrnining t h e e f f e c t i v e q u a n t i t y of water a v a i l a b l e

i n any p ro j ec t , This phenomenon has lorig been i d e n t i f i e d as one of

2

the most problematic i n the t rop i ca l regions of the t h i r d world

and Africa i n particular, One mjor reason being highlighted

.as t he cause of t h i s problem is tha t the f a c i l i t i e s f o r d i r ec t

determination and quant i f icat ion of the process of evapotrans-

p i ra t ion and other proce6ses of water l o s se s are not generally

avai lable and i n some cases where they are avai lable , the

data col lect ion and analysis mechanisms are e r a t i c n n d * b ~ o s s l y

unreliable,thus i n some cases causing problems of overdesign

and i n other caees, underdesign i n alroady existing project;^ - ( ~ n e k e and Duru, 1385, Aniekwe, 1 9 8 9 ) ~ ,

Ip view of tho above, most of the evapotranspiration and

other water l o s s values have been estimated from emperical , .

formulaeut i l iz ing commonly avai lable cl imatic variables

Anyadike (1987). Sonre of these a ~ a i l ~ b l e f o r m u l a e t h a t have been

extensively used f o r such research i n the country include the *

Penman (1948); t he Blaney Criddle (1930), a.nd the Uaney

Morin Nigeria ( D u n 1982) formula,

Unfortumtely , the applications o.f these f orrnulao have

been plagued by numerous 1 imi t a t i ons . i n most of the areas where

they a r e used, This is because o f . t h e dependence of these

formulae on a wide range of cl imatic vwiab l e s such as temperature,

r e l a t i v e humidity, vapour pressure, wind, so l a r radia t ion and

s e r i e s of other environmental constant 1; which a r e unfortunately

not r e l i a b l y ava i l ab le i n , the country a s s p e c i f i c a l l y highlighted

by Aneke and Duru (19051, Sonuga (1990) etc. Cascs of adjustments

of those formulae have produced dup l ica t ion ,o f information and

data leading t o d i f f i c u l t i e s i n t h e choice of

appropriate mater ia ls t o use i n research or design.

Moreover, the imfluence of r a i n f a l l , on the a@cul tu ra l

environment i n p a r t i c u l a r has not been given a d e t a i l e d a t t e n t i o n

i n most r e ~ e a r c h works i n t h e country desp i t e the f a c t t h a t it

f o r m one of the major problem areas i n Nigerian a g r i c u l t u r e

espec ia l ly i n t h e South - where i t is genera l ly known t h a t r a i n f a l l

inf luences a @ i c u l t u r a l production and wster use i n two opposite

ways ; corresponding with seasons of adve.rse 8carc:it y and huge

~ u r p l U s ~ f i .

According t o Sharma e t a 1 (1979), r a i n f u l l i s the governing

f a c t o r i n the planning of a g r i c u l t u r a l p ro jec t s i n ra iny areas ,

he impl ica t ion of t h i s observation is t h a t tho various cori tr ibutions

of: r a i n f a l l i n a g r i c u l t u r e [nay t u r n out t o be harzadous i f t h e 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 terms of seasona l i ty , a rea d i s t r i b u t i o n , and

quant i ty over time i n a given a rea a r e overlooked during t h e

de s ign , in~p l icu t ion and manugernent of an;y wclter rosourcttr; based

project . For i n ~ t n n c e , the consumptiv13 use and thus t h e

i r r iga t ion arld drainage needs of crop& m y d i f f e r g r e a t l y i n

a r e a s where crops may be planted at d i f f e r e n t seasons o f . t h e year

( ~ w o t i t e , 1986); thus requ i r ing t h e est imation of t h e seasonal evn- .

t r a n s p i r a t i o n needs and the corresponding water requirements

f o r .each season. I n o ther words, t o avoid unnecessary

approximat ions of i r r i g a t i o n requirements and problems of

unexpected drainage between i r r i g a t i o n s , t h e crop growing

periog should be 6cheduled t o e f f e c t i v e l y harness the changing

evapotranspirat ion and corresponding changee i n r a i n f a l l values

during the period.

Many methods have been u t i l i z e d i n water management

research and projec t planning t o determine the quant i ty of

water a v a i l a b l e from r a i n f a l l , Moisture or water accounting

is one of t h e methods t h a t i r j being widely med. !This method

involves lls ' tarting with a known s o i l moisture l e v e l ; usual ly

t h e f i e l d capacity, and subtrilct;i.ng the amount of water

cumaumptivcly Wed by the crop ouch day and adding whatever

r a i n f a l l tha t .occurred u n t i l the balance shows t h a t s o i l

moisture has been depleted t o the p ~ i n t where i r r i g a t i o n is

appl ied which should r e t u r n t h e s o i l mo:isture t o f i e l d capacityff

Nwotite (1986). The other cormon method which is c lose ly

r e l a t e d t o moisture accounting is t h e method which u t i l i z e s t h e

concept of "ef fec t ive r a i n f a l l w , This tnothod involves a n

emperical establishment of r e l a t i o n s h i p s between the s o i l ,

vegetat ion, and other environmental cha:racteiSic t i c s i n an area

s o as t o est imate t h e amount of rainwater e f f e c t i v e l y ava i l ab le

f o r crop uce etc . Aneke (19851, SCS (11376).

Unfortunately,

problems among

hawever,

which is

5

these procedures are beset with

the problem of numerous emperical

formula whose general app l i c ab i l i t y a r c i n doubt due Lo

v a r i a b i l i t y of s i t e and environmental parameters.

S t a t i s t i c a l hydrology ha6 come t o be a very good procedure

i n recent times a s a means of est imating the periodic water

a v a i l a b i l i t y and the water demand of crops as well as f o r the

design of other water mmagement s y s t e m , Sonuga (1790). I n

crop production, t h i a methods involves t he de te rmhat ion of

da i ly , weekly, monthly, seasonal. and even annual water

( r a i n f a l l ) , - d e f i c i t s o r surpluses a t d i f fe ren t l e v e l s of

probabi l i ty using r a i n f a l l and evaporation recorda.

Successes have been achieved through t h i s method i n t he

predic t ion of hydrologic events such as r a i n f a l l d e f i c i t s

Malik and Agarwd. (1982), tho design o.f i r r i g a t i o n and drainage

and the planning of agAxul tu ra1 production programs Sharma e t al

(1979) S a s t r i e t a 1 (1982).

Many of these successful project6 a r e abound i n such t h i r d

world countr ies a s India which has sim:ilar environmental, socio-

p o l i t i c a l and economic fea tu res as Nigeria. It is believed

therefore t h a t the attainment of similar height i n Nigeria's .I. (

agricultural . water resources development can be possible through

t h e adapta t ion of such technologies i n research wi th in the

country. I b i s , when done t o a large extent would make a

s i g n i f i c a n t l y invaluable con t r ibu t ion t o t h e establishment of

q u a l i t a t i v e and simple rosearch and der;ign information and

data f o r water resources; and ag; r icul tura l developments i n

t h e country.,

1.1 S i ~ n i f i c a n c e of t h e Projec t :

The s ign i f i cance of t h i s work is unique by v i r t u e of its

simple approach t o the so lu t ion of t h e problems confronting

water supply and management across t h e v a r i o u r e g i o m of the

country. By address ing t h e v a r i o u problems associa ted w i t h

uneven and poor water supply i n Southern Nigeria despite t h e

abundance of r e i n f a l l , the p ro jec t w i l l constitute an input i n

the planning and development of Nigerian r u r a l water supply

schemes both for a g r i c u l t u r e and o ther a l l i e d uses.

Moreover, it has a f a r reaching si.gnificance i n t h e

Southereastern Nigeria, and t h e Nsukka a g r i c u l t u r a l zone i n

p a r t i c u l a r where t h e r e is a s e r i o u s problem of r u r a l water

supply. Above a l l , i t w i l l con t r ibu te immensely t o t he on-

going p ro jec t i n t h e urea, i n t h e determi.riation of t h e quan t i ty

of water acruable from r a i n f a l l f o r t h e purpose of e a r t h pond

desigH and t h e corresponding d e f i c i t r a t e s .

Fina l ly , t he methodology and r e s u l t s of t h i e work w i l l

provide a b a s i s f o r f u r t h e r ,studies i n o the r a g r i c u l t u r a l zones

i n the' country where r a i n f e d a g r i c u l t u r e is dominant and.also '

i n areas t h a t have prospects f o r dry season i r r i g a t e d

a g r i c u l t u r e us ing s t a r e d rainwater,

1.2 Statement of Objectives:

The objec t ives of t h i s work w e as follows:

1, ,TO conduct s t a t i s t i c a l a n a l y s i s of Nsukka r a i n f a l l

and ev6poration (18 - 20 years) da ta f o r 40 - 3W pr-obabil i ty on weeldy, monthly and annual bas is .

2, To evaluate two s t a t i s t i c a l m ~ d e l s f o r p red ic t ing

r e s e r v o i r evaporation l o s s using weakly r a i n f a l l

deficit13 and surpluses f u r t h e r e t o l4alik and Agarwal

(1982).

3. To i n v e s t i g a t e t h e use of long-term evaporation da ta

i n p red ic t ing evapotranspi ra t ion on weekly and

monthly bas is ,

CMAPTM TWO

LITERATURE REVIEW

2.1 halysis of Ra in fa l l Data:

Usually, t h e primary r a i n f a l l datia which are of i n t e r e s t

inc lude t h e ' r a i n f a l l amowt and t h e r a i n f a l l dura t ion and i n

some cases , t h e i n t e n s i t y - dist ;r ibution,

A c o l l a t i o n of t h e r a i n f a l l magnit;ude measured i n m i l l i -

~ n e t e r s over a 24 hour period y i e l d s tho d a i l y amount. A

f u r t h e r cw$nulation of t h e da i ly values w i l l y i e l d t h e weekly,

monthl.~, seasonal and t h e annual values.

The mean values of t h e above values inc luding t h e

i n t e n s i t y provide a rough est imate of t h e quan t i ty of water

genera l ly a v a i l a b l e frorn r a i n f a l l dprirng a given period,

However, they do not fiupply information on tho i n t r i n s i c o r

s p e c i f i c c h a r a c t e r i s t i c of ind iv idua l event o r groups of events ,

t h e i r d i s t r i b u t i o n and i n t e r r e l a t i o n ~ h i p s over a given area o r

t h e i r r e l a t i v e f e a t u r e s with reGpect t o a given circumstance,

'

In order t o have a n i n s i g h t t o the above, u t a t i s t i c a l

methods-have been employed i n r a i n f a l l analysis. Such methods

a s frequency and p robab i l i ty a n a l y ~ i s have been used t o 1, ,

determine t h e l ike l ihood of a given event reoccurring over a

given range o r period of time, usual ly ranging between 5 and 100

yews. However, low ranges of between I and years may be ugeful

i n some circumr;t;ances,

2.1,1 Frequency Analysis:

TLic conunon frequency parameter i n ~ a i n f a l l a n a l y s i s is t h e

r e t u r n pe r iod otherwise lcnown as t h e reoccurrence i n t e r v a l

which is def ined by Schwab e t a1 (1981) afi tithe average per iod

of t ime wi th in which t h e depth of r a i n f a l l f o r a given du ra t ion

w i l l be equa l l ed o r exceeded once on t h e average."

The Gumbel (1954) equat ion remains t h e most common equat ion

f o r determining t h e frequency o r r e t u r n per iod of a given

ra in fa l l magnitude and is given as fol lows:

where T = reoccurrence i n t e r v a l o r retu.rn per iod

n = number of y e a r s of r eco rd

m = rank of event = 1 f o r h ighes t event.

Due t o l a r g e s i z e of da t a involved i n ana lyses i ~ l v o l v i n g

r a i n f a l l o r o t h e r hydrologic event , and a l s o due t o t h e

c lo seness od t h e data values , i t is usua:Ll;y common t o

sc loc t t h e da t a range t h a t w i l l ' s a t i s f y t h e ob jec t ive

of t h e a.nalysis, Normally e i t h e r t h e aruiual s e r i e s o r . I.

t h e p a r t i a l du ra t ion s e r i e s is adop,l;ed. The annual s e r i e s

involves .the s e l e c t i o n of t h e l a r g e s t s i n g l e event

f o r each year while t h e p a r t i a l du ra t ion ~ e r i e s involves t h e ,

se lec t ion . of all data values above a given base i r respec t ive

of t he r~umber of data available.

Onukwugha (1986) used tho annual s e r i e s i n determining t h e

50 year d e s i p storm from a 15 year (1971 - 7985) r a i n f a l l

record a t Nsukka f o r the purpose of designing a non-recording

rzringuage, Similar mcthod could be adopted i n tho design of

o ther hydrologic s t r uc tu r e s and equipments.

.However, f o r t he purpose of f i e l d crop production such

l a r g e values may not be necessar i ly re levant , Uhattacharaya and

Sarkar '(1982) contend t ha t s ince d i f f erelit crops have d i f fe ren t

degrees of tolerance t o water logging (and water s t r e s s ) , it is

not wise t o u ~ e t he common drainage coef f i c ien t based on storm

peak flow fo r the design of drainagd system of a gi.ven f i e l d

plot. I n t h e i r work, they s t a t e d t h a t i n order t o determine

the quanti ty and r a t e of drainable water i n a f i d d corr&onding

t o the type and water to lerance of each crop, frequency ana lys i s

should be ca r r i ed out spec i f i c a l l y with r a i n f a l l records from

the months having well d i s t r ibu ted and high r a i n f a l l values,

Also, tHe data should be delineated i n t o days of consecutive

r a i n f a l l ,events.

p r inc ip le behind

i ,. This is more or l e s s r e l a t ed t o the

the p a r t i a l duration s e r i e s ,

2.1.2 Probab i l i ty Analysis:

'Probabi l i ty ana lys i s in

and Mackichan (1987) as "the

event i n a l a rge sequenceV1'

hydrology ie described by Hammer

r e l a t i v e frequency of a pa r t i cu l a r

!Phe object ive of probabi l i ty

ana lys i s i n hydrology and water resources development is t o

make the most poss ible forecas t of events of unknown timing

and magnitude i n order t o formulate decisions t o control and

manage the natural occurrences.

Mathematically, an expression fo r the probabi l i ty of any sequence

of ev in t s i~ approximately similar t o the reciprocal of t he

expression fo r the frequency diot r ibut ion. The Weibulls p l o t t i n g

pos i t ion formular according t o Chow (1951, 1954) remains the

most common expression and is giveri ac;

where,

Fa 5 Plo t t i ng Posi t ion

m = Tiank nyrnber

n = Total number of observatione.

0' I

By p lo t t i ng the values of given events agains t t h e i r

corresponding p robab i l i t i e s on a log-normal paper, t he l ikel ihood

of tho occurrence of a given event, o r the expected value of an

event a t a given probabil.ity p n . be determined. Such information

may be useful i n making decisions i n t h e design of water management

system arid a l s o i n the planning of agr: icultural production program

as well as i n t he predic t ion of the a v a i l a b i l i t y o r s ca r c i t y of

water accruable from r a in f a l l .

S h o o e t a1 (1985) ca r r i ed out a p r o b b i l i t y ana lys i s of

27 years of weekly r a i n f a l l and evaporation data f o r the design

of a r i c e i r r i g a t i o n system a t Centrd. Rice Research I n s t i t u t e

i n ~ u t t a c k , . ~ Orissa, India, By e~nployirlg r a i n f a l l d i s t r i bu t i on

at 7Qd and 4% probab i l i t i e s , they were ab le t o est imate the

expected cost and benef i ts of an in tegra ted i r r i g a t i o n and

clrainage plan, Using the r a i n f a l l d i s t r i bu t i on a t M$$ probabi l i ty

and employing t he Bhattachraya and SarLrar (1982) pr inc ip le and

asourning t h a t 5% of t h e excess rainfal .1 f o r m the runoff , the

drainage c a p c i t y of f i e l d drains and t he water removal r a t e t h a t

corresponds t o t he water to lerance cha rac t e r i s t i c s of a pa r t i -

cu l a r crop can be obsi ly determined,

Malik and Agwwal (1982) ca r r i ed c u t a probabi l i ty n n d y s i s

of 31 years .o f r a i n f a l l and 17 years of' evaporation data a t

Hissar, Haryana, India using the Weibull 18 formula. !they were

a b l e t o e s t ab l i sh functional re la t ionshipo between the

cummulative r a i n f a l l d e f i c i t s and time using two growth models.

This i h f o r m t i o n according t o them "can g r ea t l y help i n determining . the optimal re leases from a rese rvo i r i n accordance with demand"

f o r d i f f e r e n t areas and p e r i o h .

Sharrna e t u l (1982) s t a t i s t i c a l l y analysed A 17 year

r a i n f a l l record at PantnagEir,iJaJ.nital !rarui region India t o

e s t a b l i s h a crop planning programme f o r t h e region. From t h e i r

'

probab i l i ty nnd s t a t i s t i c a l . analysis, they found out t h a t weekly

r a i n f a l l da ta a r e more useful f o r planning of crop programme

as well a s 8 w a t o r management p r a c t i c e s than monthly, seasonal

o r annual data.

P robab i l i ty ana lys i s , may a l s o be useful i n o ther a spec t s

of hydrologic. a n a l y s i s t h a t hay have 1~e2ated importance t o

a g r i c u l t u r a l and r a t e r rurfige~nent oyston. For inr;t;ance, it may

be useful i n t h e determination of the adequacy of length

of record u t i l i z e d i n any hydrological analys is . l'his is t o

ensure t h e r e l i a b i l i t y of t h e est iwtec ' l information from t h e record.

Schwab e t a1 (1981). Mockus (1960) proposed an equation f o r

es t imat ing the adequacy o! the length of record f o r a given

l e v e l of s ign i f i cance as:

where, Y = minimuin acceptable y e w s of period

t = s tudunts s t a t i s t i c a l value a t the 9Oah . . . l e v e l of s ign i f i cance with (Y - 6 )

d.egrees of freedom,

R = Rat io of magnitude of t h e 100-year event

t o %year event.

According t o Bhat tacharaya and Sarkar (1982), t h e use

of t h e above r e l a t i o n s h i p which invo lves t h e s t u d e n t s ' I t "

can only g ive a r e l i a b l e r e s u l t i f t h e bas i c da t a a r e

d i s t r i b u t e d ' normally and independent ly, otherwise, t h e data

shou ld .be broken down i n t o blocks of l e s s e r number of yea r s

before t h e ana lys i s .

Water Requirements of Crops:

Crop water requirement is def ined as t h e q u a n t i t y of

water r e g a r d l e s s of its source , r equ i r ed by a c r o p o r d i v e r s i f i e d

p a t t e r n of c rops i n a g iven per iod of t ime f o r its n o r k l growth

under f i e l d cond i t i ons a t a p l ace ( ~ i c h a e l , 1985). Thi s

comprises t h e l o s s e s due t o evaporation., losf ies due t o

t r a n s p i r a t i o n , l o s s e s dur ing a p p l i c a t i o n of i r r i g a t i o n water i n

form oi! r u n o f r ; deep pe rco la t ion , seepage and in t e r f lows , and

water r equ i r ed f o r o the r a g r i c u l t u r a l ~ ~ p e r a t i o n o such as l and

p repa ra t ion , t r a n s p l a n t i n g , leaching e t c ,

I n view of t h e above d e f i n i t i o n , t h e ' water requirement

o i a c rop could be expressed mathematically as followrj: .

WR = E T + L E L + L S ~ - - - 4

where, WH = Uater requirement (mm)

ET = Evapot ranspi ra t ion

15

Ln = Application Losses

Al ternat ive ly , t h e water requiramc?nl;s of a crop may be

' expressed in term of the rmny f o r m o r avenues through which

water is contr ibuted t o the crop f ie ld , , Among such source8 are

predominantly i r r i g a t i o n water (IN), Effec t ive r a i n f a l l (ER)

and S o i l p r o f i l e con t r ibu t ion ( s ) (Michael. ,1985). Assuming

t h a t each of these sources con t r ibu te water simultenously,

the water requirement of a crop may then be expresiwi as

follows :

2.2.1 Ectimati.on of Water Requj.rernent~, of Crops :

I n most cases, t h e determination of the water requirement

of a crop commences with the evapotmnspira t ion or the

consumptive use. The various methob. commonly used i n the . determination of crop conswuptive ufie o r evapotranspirat ion are

I' I

as follows:

'i, Weighing and Non-Weighing lys imeters

ii. F i e l d experimental p l o t s

, . iii. Clirnatologicul da ta

iv, Evaporation records,

2.2.2 Enlpperical Mc thods of Evapotranspiration De t ermina t i on :

Nwotite (1786) c a r r i e d out a stud;y of consumptive w e of

~m&nnthus hybridus using the lysirnat e:r method. The emperical

methods according t o Nwotite (1986)~ genera l ly employ a pr inc ip le

of d i f f e r e n t i a t i o n between c l i m t o and crop which i n t h e long

run has r e s u l t e d i n none of them having a n absolute comparative

advantage over t h e otherc, This i s due t o the f a c t t h a t each

of t h e methods predic t evapotranspirat ion from l o c a l metero-

l o g i c a l condition, The impl ica t ion of t h i s is t h a t a n emperical

method can only be applied with g rea te r confidence i n n l o c a l i t y

a f t e r it has been adapted o r readjus ted with the l o c a l c l imatological

da ta and t e s t e d over a period which t h e p o t e n t i a l evapotranspirat ion

averages are most r e l i ab le . . For ins tance , t h e Penman (1948) equation which was developed

.,I , b a ~ e d on t h e theory t h a t evapotran6pir;ntion is d i r e c t l y r e l a t e d t o

t h e incoming ~ o l a r energy has been found t o have a l o t of

a p p l i c a b i l i t y problems, The nlajor problem with the equation i 6

" its dependence on numerous metereological parameters which a r e

~eldorn s u f f i c i e n t i n many s'tf&tions. . M,oreover, it involvos

tediously complex computations (Duru a:nd Adewwni 19801, a n d

approximations, though at tempts have been made t o produce

c h a r t s and s impl i f i ed version of the e.quation O@chae l 1985) , ( Doorenbos and P r u i t , 1975).

17

Similar problems are inherent i n t h e o ther popular evapo-

t r ansp i ra t ion equations such as t h e Rlaney-Criddle ( I g p ) , the

Dlanoy-Moriq ( 1942) and the Blaney-Morin-Nigeria (Duru, 1982)

equations e tc ,

The lane^-Criddle and t h e Blane y-Morin equations which are

both developed b a ~ e d on t h e theory t h a t the r a t e s of water use

by crops i n a growing s e w o n a r e d i r e c t l y r e l a t e d t o cl i lnatological

parameters of r e l a t i v e humidity, and temperature, as well as day-

l i g h t hour6 have been found t o be unsuccessful i n t h e t r o p i c a l

regions because of t h e i r overdependence on these parameters, Duru

and Yusuf (19801, Nwotite (1986)~ Anielwe (1989). Doorenbos and

P r u i t (1975) have found out t h a t the Dlmney-Criddle

equation is s p e c i f i c a l l y not appropr ia te f o r es t imat ing t h e mean

da i ly p o t e n t i a l evapotranspirat ion f o r :periods l e s s than one I

month,

The Blaney-Morin-Nigeria equation (Duru, 1982) which was

developed as an adapta t ion of the Blaney-Morin (1942) Torrnula

td t h e Nigerian c l imatological c,ondition, has been t e s t e d ac ross

the d i f f e r e n t ecological zonea :in the. c ~ x c t r y and found t o be

comparatively appropriate. However, it still has t h e general

problem of loca l i zed va r ia t ions (Nwotite ,1986 ; Aniekwe 1989).

An approach known a s the Standard di f ference (SDF) method

proposed by Aniekwe (1983) as an a l t e r r u t i v e t o the o r i g i n a l

Blaney-Morin Niger ia formula however, f a i l e d t o produce a

u n i y e r s a l s o l u t i o n t o t h e v a r i a t i o n s i n l o c a l i z e d r e s u l t s from

t h e e a r l i e r equation.

I n view of t h e above observa t ions , it is obvious t h a t it

w i l l cont inue t o remain i ,nappropr ia te t o e s t ima te t h e water

requirements of c rops us ing t h e vurious evapont ranspi ra t ion

equat ions o r models h igh l igh ted above without t h e adequate

c l i m a t o l o g i c a l da t a u n l e s s r i go rous and ex tens ive r e sea rches

a r e c a r r i e d out t o a u t h e n t i c a t e t h e s e equat ions. ~ a d u b u i k e

(19871, i n p ioneer ing such venture , by c a r r y i n g out a s e n s i v i t y

a n a l y s i s of some evapo t r ansp i r a t ion models h a s observed t h a t

such models w i l l perform a t t h e i r upt.iroum c a p a b i l i t y when t h e i r . very s e n s i t i v e pa ran~e te r s m e sys te rna t icn l ly i d e n t i f i e d and

'. /

given very c a r e f u l a t t e n t i o n during t h e i r measuremexlt i n every

loca t ion .

However, s i n c e t h e e s t ima t ion of c rop water requirements . a r e i nd i spensab le i n i r r i g a t i o n and dr inage systems design and

'

cons ider ing t h a t t h e achievenlent of th:is ob jec t ive i n t h e country

h a s been e l u s i v e due t o l a c k of t h e bas i c information, i t is

impor ta ,n t t h e r e f o r e t h a t a r e l a t i v e l y r e l i a b l e and a l t e r n a t i v e

method should be adopted meanwhile. The " induct ive approachtf

which involves t h e co l l . ec t ion and a n a l y s i s of da t a from a c t u a l

exper iences and e s t a b l i s h i n g r e l a t i o n s h i p s between t h e s e experiences

has been widely used i n 1n&a and o ther developing coun t r i e s of

F'ar-Ut3t such as M a l y s i ~ and the Phi l ip ines . &vaporation and

'data. form the b a s i s of crop water requirement6 and water

rer;ources rnanaaernent systems determinations i n these p laces and

t h e i r uses hnve'recorded successes and a r e still being vigorously

2.2.3 Estimation of Evapotranspirat ion Using t h e Evaporation Index:

Uperimentnl evidences have shown that t he re e x i s t s a c l o s e

co r re lu t ion bet;weon t h o r a t e of plant; uva,potrunripirution mid the

r a t e of evaporation (Michael. 1985; Sahoo st a l , 1982). Linsley

e t a1 (1995) have observed t h a t open water evaporation is t h e

numerical equivalent of p o t e n t i a l evapotranspirat ion. A mathc- ,

matica l expression r e l a t i n g p lan t evapotr imspirat ion and

evaporation as proposed by Linsley ( 1975) ;S&oo e t a1 (1982),

Michfiel (1985) is given as follows:- . ,

where, ET = Ekapotranspirat ion

, xo = Pan evaporation

F = Crop factor*

A s t rong point i n favour of the use of evaporation index as

a means of determining evapotranspi ra t ion is bas ica l ly the f a c t t h a t

i t is easy and quick t o determine and uti:Liee within shor t periods

during the crop growing season where the crop f a c t o r s of t h e

p r t i c u l u r c r o p a r e a l ready known. #

2 2 Estimation of Drainage Requirements:

Drainage requirement of a crop is viewed i n terms of t h e

quan t i ty a n d . t h e r a t e a t which excess water is removed dron

the crop f i e l d , Generally, tho rate of removal of excesG water

i c c a l l e d drainage c o e f f i c i e n t and it :is defined by Michael

(1985) as t h e depth of water t h a t is tl3 be removed i n 24 hour

per iod from t h e drainage area,

Sahoo e t a1 (1982) pointed out t h a t it is not wise t o

use peak events t o determine t h e drainage water requirements.

They c a r r i e d out a weekly p robab i l i ty m a l y s i s of r a i n f a l l

da ta t o determine t h e water d e f i c i t and excess per iods a n d . . ' ,

hence t h e i r r i g a t i o n and drainage requfirements at 7w and

40$ l e v e l s respecti.vely, The periods of d e f i c i t and excess

wFre determined by computing the f a c t o r ( R - ET) on weekly , ,

basis; t hus i.f -

and

where,

R = r a i n f a l l

ET = evapotranspi ra t ion

From tho ubovo r e l a t i o n s h i p s , the averago quant i ty of #

dra inable water i n a f i e l d can be estimated as wel l ac t h e

average ybant i ty of water required t o satisfy. the i r r i g a t i o n

needs of t h e crop i n the f i e ld .

The quant i ty of dra inable water in, a f i e l d does not

necessa r i ly provide the information for draining f i e l d s i n

r a i n y a r e a s (~ha t t acharaya and Sarkar , 1382). This is because

t h e peak values of t h e r a i n f a l l excesses do not serve adequately

i n determining t h e r a t e of removal of drainage water a ~ d the

s i z e o r capaci ty of t h e tiyatem(,Wmo et ul 1982). . Rather, they pointed out t h a t adequate removal of exceqy ra in-

wate r should t*e i n t o considerat ion the number of consecutive

days of r a i n f a l l i t takes f o r a given value of r a i n f a l l excess

t o accumulate. 1%us they obtaiped r a i n f a l l magnitudes a t rr

!%year r e t u r n periods f o r I - 5 days ccnsecutive r a i n f a l l events

using da i ly point r a i n f a l l s records of t h e months t h a t have

most r a i n f a l l s . By ascurning that; t h e surp3us water is about

50% of t h e r a i n f a l l , the design drainage coef f i c ien t was

ca lcu la ted as :-

where,

11 = r a i n f a l l (nun)

t = Tolerance pariod of crops (3 days max)

C = Drainage coef f i c ien t (mm/day)

3.1 Data Col lec t ion :

3.1.1 Location and Descr ip t ion o f t h e Study Area:'

The s tudy a r e a f o r t h i s p r o j e c t c o n s t i t u t e whole catchment

covered by t h e Univers i ty of Niger ia metero logica l s t a t i o n .

I n o the r words, i t covers t h e whole o,f Nsukka a g r i c u l t u r a l zone

and en;irons.

The Univers i ty of Niger ia rneterolc~gical. s t a t i o n is loca t ed

at about l a t i t u d e 6'52 North, longitude: 7'24-' &st and a l t i t u d e

3~ - 500 metres above sea l e v e l ( f i p r e 7) .

. . ,

3,-1.2 T ~ p c s of Datar

E s s e n t i a l l y two major t y p e s of d a t a were c o l l e c t e d f o r ,

t h e purpose of t h i s work. The f i r s t s e t of d a t a were t h e

metero logica l d a t a from t h e Univers i ty of Niger ia , Msulcha

Meterological s t a t i o n , while t h e second da t a s e t s were t h e

consumptive use , t h e P o t e n t i a l e v a p o t r m s p i r a t i on and crop

c o e f f i c i e n t s determined a t Nsukkn us ing t h e Penman, t h e

Bianey Cr idd le , and t h e Blaney-Morin-Nigeria models.

3.1.2.1 M e t e r o l o ~ i c n l Data:

The metero logica l d a t a compr ims 20 y e a r s (1977 - 1990)

d a i l y poillt r a i n f a l l r eco rd meamred with a r eco rd ing rainguage

- ( S t u d y A r a c l ) --.--- -- , , 4 4

B E N U E STATE

and 18 years (1971 - 1388) of da i ly evaporation record measured

with a United S t a t e s Water Bureau Class A Pan,

3.1.2.2 Crop Consumptive Use and Crop Coefficients:

The consumptive crop water use of African Spinnch(Amaranthus

hybridus) as determined by ~ w o t i t e (1986) using lysimeter method,

the Blaney Griddle and Dlaney Morin Ni,geria models respectively *

were col lected and presented as shown i n Appendix A. A s imi la r 1. I

data for cassava hybrid (Manihot &cden taCran t z ) as determined

by Aniekwe (1991) using t he Penman method was col lected and

p-esented i n Appendix A.

3.2.1 Monthly And Annual Rai.cfal1. - and Evaporat i on:

The 20 years and 18 years daily evaporation data were col la ted

and presented i n the format a s shown in Tables I and 2

respectively.

Table I: 20 Year-Monthly Rainfal.1 Data (1971 - 1990) From the

University of Nigeria Nsukka Meterolo~ical Sta t ion (mm)

Table 2: 18 Years of Monthly and Annua:L 1Waporation Data (7971 - 1988) From the Nsukka Meterolo[;icul S t a t i o n

Year 3an Feb March Apr May Jun

1971 266.00 187.90 183.60 14ti.60 111.80 74.80

Table 2 (Con t inued) : 18 Year:; of Monthly ttnd Annual LVwporation Data (1371 - 1988) From the Universi ty of Nig.erj a, Nsukka Me t e r o l o ~ i c n l Station (mu) -

Year C* - act: Nov Dec Annual

Total 1076.4 986.4 966.60 1236m60 ;3IG06O 4265.64 28821.60

Mean 59.80 54.80 53.70 68.70 128.70 236.98 1601.20

From t h e format, the mean monthly and the annual d i s t r i b u t i o n s

of both r a i n f a l l and evaporation values ware determined and #

shown in Tables 3, and 4, respectively and i n g igure r2 - 5,

Table 3: Mean Monthly Hainfal Distribution f o r Nsukka

January

February

March

Apri l

June

J u l y

August

September

October

November

December

Mean Ra in fa l l (mm)

Table 4: Annual Rainfa l l Distribution For Nsukka

A n n u ~ l Total Mecln (mm) (nun)

Y ERRS

F i g. 2 ANNUAL R A I N F A L L O I S T R I B U T I O N HISTOGRf lH FOR NSUKKA

J F M H M J J- A S

MOMTHS

Fig.3 MEAN MONTHLY RRINFALL D I S T R I B U T I O N FOR NSUKKA

YEARS

F I G - 4 RNNURL EVRPDRRTION flT NSUKKfl (1971 -19881

MAR. QCT . J UL.

MONTHS

FIG.5 MERN MONTHLY EVAPORATION AT NSUKKR

3.2.2~ l i a in fa l l EZ-equency Analysis :

Ucing the p r i n c i p l e of annual s e r i a s , t h e fnuximum s i n g l e

r a i n f a l l event f o r each of t h e 20 years of record was selected.

The r e ~ u l t a n t data were so r t ed (by meqnfi of a co~nputor prob:rum,

appendix B) i n descending order of magcitude.

By means 'of the Gunibel equation (equation I) t h e r e t u r n

p r i o d of each event was determined. Table 5 shows the r e t u r n

of the 20-year r a i n f a l l records and Figure 6 shows

t h e p lo t of t h e re lu t ionshlps .

For tho determination of frequency parameters f o r drainage

systems design i n accordance with I3hattacharaya and Sarkar (1982),

t h e r a i n f a l l events from Apri l t o September represent ing the major

rainfall producing months were chosen f o r t h o una lyds . 'Tho data .

were s o r t e d i n t o d i f f e r e n t blocks corresporlding t o 1 - 7 days of

consecutive r a i n f a l l . Here, an N days of c,onsccutive r t i i n f a l l

means t h e number of days during which t h e r e occurred n continous

r a i n f a l l without a break of more than o r equal t o 24 hours,

The data i n each block was arranged i n descending order of

magnitude m d t h e f i r s t 20 highes t values corresponding t o t h e

number of yea r s of record were used fo? c a l c u l a t i n g t h e r e t u r n

per iods a s 'shown i n Tables 6 and '7.

Table 5: R~:furn Period of the 20-Year Ntiulika Rainfal.1 Usin& - t h e Armuul Ser ies

-

R a i n f a l l (mm) Rank Heturn Period (years)

Table 6: Return Per iod of t h e 20-Year NsuMca Rainfall For 1 - 5 W y s Consecutivc I tn in fa l l

- , Return b i n f a l l Depth For D i f f - Consecutive Days (mm)

Xank Per iod 1 2 3 4 5

Table 7: Retwn Perid of the 20-Year Nsukka Rainfal l for 6 and 7 -- Days Consecutive Rain fal.16

Rank Return Period Ruin:fall Depth For Different (Yrti) Consccutive Days (mm)

39

This w a s accomplished by means of a computer programs i n Appendix B.

3.2.3 Izainfall and Evaporation Probab i l i ty Analysis:

The 20 years (1971 - 1990) d a i l y point r a i n f a l l and the 18

years (1971 - 88) d a i l y evaporation data were transformed i n t o

corresponding weekly d a t a of 52 standard weeks s t a r t i n g from January

1st t o 7 t h and ending at December 24th t o 318t a s suggested by #

Malik and Agarwnl (1982)-

The weekly values of r a i n f a l l and evaporution were arranged

i n descending order of magnitude, Those were then ranked, with

rank No.? assigned t o t h e h ighes t values of r a i n f a l l and rank

No.20 t o the lowest value. S imi lar ly rank No.? was assigned t o

t h e h ighes t value of evaporation and ranic No 18 t o the lowest

value, The impl ica t ion ifi t h a t , f o r a given p robab i l i ty o r percent

'chance of occurrence, the r a i n f a l l and evaporation i n a given

we& w i l l be equal t o the ind ica ted value o r higher, ,The same

ranking process was c a r r i e d out f o r both the r ~ i n i u l l and ,the

evaporation records on monthly and annual ' b a s i s ,

, Using the Weibull's p l o t t i n g pos i t ion formula (equation 2) ,

t h e p robab i l i ty d i s t r i b u t i o n of each weekly, monthly and the

annual events w a s determined,

. evaporation were p lo t t ed on a

a smooth regress ion curve was

The values of Fa versus r a i n f a l l o r

log-normal p robab i l i ty paper and

drawn. 1ihe ,values of weekly, monthly

and annual r a i n f a l l 6 o r evaporations a t p robab i l i ty l e v e l s of 4041

40

t o 10% were determined from the curve. f~ computer program was

developed t o accomplish the objec t ives involved i n the probability

as shown in appendix C.

The results of the analyses are shown in tables 8 - 11 and

f igursf i 7 - 9-

Table 8: Weekly Expected R a i n f a l l (mm) a t Dif ferent Chances f o r N s u k l c a

N A I N E ' A Y , DEPTHS AT DIFFEXKNT 31 CHANCES

Week 4W 50% 605 700r: 80s 9@ .

4 2 TABLE 8: Continued -

-

42.60

43040 54.00

48-80

58.80

86-90

75-90 68-50

59. 'to

62.50

52-50

34-20

31 -70 16-30

11.80

3.30 1.40

2.Go

7.20

3.60

' 9.60

1.70

Table 9: Weekly 1kpected Evaporation (nun) at Different % Chances f o r N s d h

Evaporation Values at, Different % Chances Week 4% 5M 60% 7e6 8W 9%

Table 9 Contj .nuted

27 74.80 74.20 13.60 13.20 12.80 12.40

28 13-60 I~.IO 12.70 12.30 12.00 11-70

29 12.70 12.10 11.60 11,20 10.80 10.50

30 13.1 12.4 ll.,8Q 11,30 71,QO 10~60 3 1 13.00 12.40 12.00 11.60 11.20 11,oo 32 12.20 11.70 11.30 11.00 10.70 10.50

33 12-10 11.60 11.20 10.80 10.50 10.30

34 12.30 , 11.50 10.90. 10.30 3-90 9-50

' 35 12-30 11.50 10.90 10.40 10.00 9-60

3G 10.80 10.50 10.20 9-90 9-70 9-50

37 12.00 11.60 11.30 11.00 10.80 10.60

Table 10: Monthly and Annual Ekpected Ra.infal1 (mm) at Different % Chances for Nr;uklm

Rainfall Depths A t Different 91 Chances Month 40k 5& 60% 7% 8M 90%

Jan

Feb

Mar

*P'

M w Jun

Jul

A%

Sept

oc t

N ov

Dec

Annual

Table 11: Monthly and Annual Expected LVaporation (mm) at . -, D i f f e r e n t $ Chances for Ntjulcka

hkaporation Values at Different $ Chances

Month 4% 5m 6011 '7(2-?7 80% 9%

Jan

Feb

Mar

A P ~

May

Jun

Jul

Au6

Sept

Oc t

N ov . Dee . Annual

1 3 5 3 9 1 1 1315171921 232527B31 3335373341 4345474951

WEEKS

FIG.7 NSUKKfl WEEKLY RAINFRLL OiSiRi0UTN AT 401 - 801 CHflNCES

WEEKS

MONTHS ( J R N . - DEC2

FIG. B NSUKKR # O N HLY RRINFRLL ZISTRISUTF4 9T 43-801 CHRBCES

F i g . l D LOG-PROBRBILITY OF RNNURL RRINFALL R T NSUKKR

1 10 100 Prohab l l I t y lX?

F16.11 LOG-PROBABILITY OF flNNUflL EVAPORATION AT NSUKKA

5 2

9.2.4 Determination of 'Miniruurn Acceptable Lcngth of Records:

l ' he annual r a i n f u l l and evaporation p robab i l i ty va lues

were on log-normal graph papers as shown i n f i g u r e s

Frocn the graph, the r a i n f a l l and evaporation values at

7% and 5C$ chances corresponding t o 2 years and 100 years

of r a i n f a l l r e spec t ive ly were e s t i k t e d .

Using e q ~ m t i o n ( 6 ) ,

From f igure 10, Rg = 2441. T W g G =

Uy t r i a l and. e r r o r , Y - 6 years a t 30% l e v e l of s ign i f i cance

was determined as equals t o 4 degrees of freedom having a

corresponding student tttl' value of 2.132,

. (4.30 x 2.132 x loglO 1 .655)~ + 6 = 110:~2

Y = j0.02 yea r s == 10 yearo

y here fore t h e minimum acceptable years of r a i n f a l l record

for t h i s a n a l y s i s is I 0 yews.

S imi la r ly , from f igure 11,

From s t a t i s t i c a l . t a b l e Y - 6 equals 3.5 degree^ of freedom

through i n t e r p o l a t i o n and tttll = 2.21t3.

8

Therefore the minimum acceptable years of evaporation data

fo r the a n a l y ~ i ~ is 9.67 years which is approximately equal

t o 10 years,

3.25 Predic t ion of Rainfa l l Def ic i t s and Surpluses:

The weekly evaporation values at 4-0$ t o 9@ chances were

subst racted from the corresponding weekly r a i n f a l l values.

Cases where the evaporation value was g rea te r than the

corresponding r a i n f a l l value, the di f ference was termed

d e f i c i t , Conversely, the di f ference between evaporation

and r a i n f a l l was termed surplus i n cases where t h e r a i n f a l l

value was grea te r than the evaporation value,

me c lmmula t i~e r a i n f a l l defj.ci ts and surpluses at the

different l e v e l s of probabi l i ty o r percent churlca~ of occurrence

over tkie 52. standard weeks a r e prusented i n Tabloo Dl and D2

i n Appendix D.

54 'IJsing l x o growth models ( t h e Gompertz and t h e Logis t ic

' ,

models) f u r t h e r t o Malik and Agarwal (11382), a funct ional

was es tabl ished between r a i n f a l l d e f i c i t s and

surpluses with time s o as t o obta in t h e necessary p a r m e t e r s

f o r the predic t ion of cwnrnulativu r a i n f a l l d e f i c i t s and

s ~ p l u s e s ,

The growth models according t o Ma1:ik and Agarwal (1982)

are as follows:

(i) Gompertz Model === Y = abCX .a. 13

( i i ) Logis t ic Model === X = a + bc ... 14

where Y* = Predicted CwnmuLative r a i n f a l l d e f i c i t ( surplus

X = Standard week from 1 t o 52and,a, b, c = Constants,

A computer program was developed (appendix E) t o p red ic t t h e

d e f i c i t s and surpluses a t d i f f e r e n t l e v e l s of p r o b a b i l i t i e s

using the two models above. The program divides t h e r a i n f a l l

d e f i c i t s and surpluses chronoLogically i n t o th ree equal segments

i n t h e manner suggested by Agarwal and IYalik (1982). For the

Gompertz model, the s u b t o t a l of t h e Logarithms of individual

ob8ervation was determined. S imi la r ly , t h e sub- to ta l of t h e

r ec ip roca l s of individual observation i . n each segment was

obtained f a r t h e Logis t ic model,

The s u b t o t a l s were then represented by S, , S2 and S 3

chronologically. The d i f fe rence between S and S i,e. 1 2 S2 - Sl #

,

'and S and S i. e S 2 3 3 - s2

were represented' by d and d2 1

lbe number of observati.ons i n each segment was

represented by n,

Using t h e above parameters, the values of a , ' b and c ,

for each of the two models were computed using the procedure

develoIjed by Mill's (1955). The t ab l e for M i l l ' s Computational

procedure is presented below.

Table 12: M i l l ' s Computational Procedure f o r Constants of the Gompert z and L%itit;ic ~ o d x s : -

Constants Gornpertz Model Logist ic Model

Source: Malik and A g ~ w a l (l982).

The r e s u l t s of the predicted surpluses and d e f i c i t s a r e shown i n

appendix D. Also, the values of a , b ,and c , a r e shown in tTab l c s

13 - 14.

Logistic Model

Logistic Gompertz Model

A statistical analysis was carried out on the pedi'ctod

results with the corrasponding calculated value for purpose of

. comparisons and determination of the efficiency of each model.

Tables 15 and 16 show the values of the coeff ic ients of

determination and the standard deviation& obtained from the

statistical analysic,

m U3 C' Zk

'rn VI t

,Table 16: 1Jalues of S t a t i s t i c a l P a r a e t e r s of Cumulative % i n f a l l D e f i c i t s and t h e i r P red ic t ed ~ J a l u e s :

C 2 = Coeffc ieo t of Determination

S = Fercent Average Absolute de-siat ion

3.2.6 Determination of ECvapotrancpiration and Crop Factors

The wqekly evaporation over the 52 standard weeks were arranged i n

ascending order so t h a t f o r u given p robab i l i ty , t h e weekly I

evaporation w i l l be equal t o the ind ica ted value or lower as

suCgested by Sahoo e t a 1 (1982). The evaporation values at

d i f f e r e n t l e v e l s of p robab i l i ty were determined w i n g t h e computer . program i n appendix C.

FVom the r e ~ u l t s , t h e weekly e v a ~ o r a t i o n values at 7(%

chance (Ev 70) wert. determined. These value& represent t h e

p o t e n t i a l evapotranspirat ion i n the given week tis suggested by

I s rae l son and Mansen (1962). Sahoo e t a1 (1932),

Using t h e values of a c t u a l (Lyeimeter ) evapotranspirat ion

determined by Nwoti t e (1986) ; appendix A: Crop c o e f f i c i e n t of

Amaranthus hybridus were ca lcu la ted a6 shown i n l 'ables 17 and 18

below, r )

Table 17:. Potential Evaportranspirat ion and Crop Factors of ( h f r i c r ~ n Spinach (~~naranthus ~ybridus) For t h e 70% Proh"bi.lity E"vaporation Index (March - May)

I ,

Week

/ . March I7 - 23 12 45.80 75-30 0- 334

March 24.30 13 42.40. 1 1 .40 0.269

March 31 - April 6 14 41.60 1 0.60 0.255

April 7 - 13 15 41 .OO 11.80 0.288

April 14-20 16 39.00 18.10 0.362

Apr. 21 - 27 17 36.00 18.00. 0.500

Table 18 ; P o t e n t i a l hVapotrans p i r a t i o n and Crop Factors of Afr ican Spinach ( h m n a r a ~ l u s Hybridus) For The ' ' ;7& P r o b a b i l i t y Evnporation Index (0ct - ~ e c )

Date

The crop fac to r of Cassava (Manibot Ksculenta Crnntz) f o r

t h e 70"7 evaporation index were similarly determined u6ing t h e

ac tua l evapotriincpir.ation va lucc ( ~ ~ c r o ~ ) as determined by

~ n i e k w c (1931) u s ing t h e Penrnnn equn-tion as shown i n appendix

A. The r e s u l t is presented i n Table 13 below;

Table 12: P o t e n t i a l Et, and Crop Fastor ( f ) of Cassava - ( ~ n r ~ i h o t Ksculenta C m n t z ) For ttie ' Prok)abil.i t y ( ~ ~ 7 0 ) Kvapur*o 7"TAu~. t ion Index - J u l z )

Month

A u p s t

September

October

November

December

January

February

March

A p r i l

May

June

J u l y

~t Crop (rm Jciay:

3.2.7 Determination of Dri~i.nage coefficient:^: .-.. The r a i n f a l l magnitudes and t h e corresponding recur rence

in t e rva l from t h e 1-7 days consecut ive r a i n l ' a l l s determined with

r a i n f a l l even t s of A p r i l t o September (Tables 6 and 7)

were p l o t t e d as shown i n figures 12 and '13.

/ *-

U 4 daus m 6 dogs / *- .-. ..-,a 2 ..-

*- _ _ _ - - - - - - .-' /? /-*#C*Z

./---- -*--m ,J - ---*:- _- . . - - - -* - -

- * ,A, # __.*-- -*- '<--,m------"-- - - -..*--

3- $.. -O ----,--------- -------------*-n P- ,$ . .. - -

," .. .

m,>J- - .m- - - - - ----- /-- m-nnzn~ = :+- ,u- -'J ,,,,LA 9 ,-o--- /-

! 3 .&\I -.,--+-< >-0 .Ah

:x; .... :<peV ... -

l n n n ~ l r r n ~ \ LIPI I I / M ~ n ~ w n i I F i g -12 FREBUENCY OF LO-YEFIR L nr nlL - JET I . J I ' I J U ~ ~ nAlw-nLL

[FUR 1 - 5 CONSECUTIVE RRIN DRYS?

5 1 D 20 RETURN PERIOD ( Y E ~ s 1

~ ' j ~ . l 3 FREBUENCY OF LO-yEflR {flpRIL - SEPT. j ) jSUj(MR R n I ~ F f l i i {FOR 8 - 7 DHYS CONSECUTIVE RRiN DRYS)

The r a i n f a l l magnitudes at 5 - 20 year recur rence i n t e r v a l s

were i n t e r p o l a t e d from the graphs and the va lucs are g iven i n

Table 20. These va lues a r e termed " t rue meansu for f u t u r e analysis

hat tacharaya and Sarkilr , 1982)-

Table 20: Return Per iods and Magnitude of Nsuklra R a i n f a l l Using 1-7 days consecut ive R a i n f a l l s (Apr i l - September)

R a i n f a l l (mm) Recurrence I n t e r v a l (Yeare) I Consecutive Days

The des ign drainage c o e f f i c i e n t s of a given c rop can then be

determined with r e f e rence t o t h e t a b l e above: and i n ocons idera t ion

of t h e c r o p ' s t o l e r ance t o excess water,

&'or i nl;tunco, i f a c rop har; only throe tiuy~; t o l w u n c o t o oxcc~io

water, we can then determine t h e drainage c o e f f i c i e n t . By us ing

(9) and usau#ling a f ive-year r e t u r n pe r iod ; Then f rou t h e

The various drainage coefficient;^ carreeponding t o the crop

tolerance periods and the recurrence intervals were similarly

calculated and presented i n Table 21 bdow and i n figure 20,

Table 21: Drainage coefficients for Nsukka Tropical Climate

Recurrence I -

Drinage Coefficients ( ~ i t r e a / ~ / h a )

Interval I I Crop Tolerance Period Day6 ) 2 6 (years) 2 . 4 5 7

IIGULTS AND DISCUSSIOI4S - 4.1 Reoults:

The r e s u l t s o f t h e ana lyses and p r e d i c t i o n s i n t h e ,

p rev ious chap te r have been shown i n t h e va r ious t a b l e s and

f i g u r e s as a l r e a d y presented.

Fu r the r d i scuss ions s h a l l then be c a r r i e d out i n t h i s

chapter based on t h e f ind ings from t h e i m l y s e s ,

4.2.1 I i a in fa l l and Idvaporation C h a r u c t e r i s t i c s of t h e Nsulcka ~ r o n i c a l Clirniite':

The r e s u l t s ; as shown i n f i g u r e s . , 2 - 5 and t a b l e s I - 4

show t h a t t h e monthly r a i n f a l l cha ra ; ; t e r i s t i c s at Nsulcka

e x h i b i t e d n unimodal d i s t r i b u t i o n wi th peak i n September

and minimum values i n January and December. I!he mean annual

r a i n f a l l a t NsuWca h a s a va lue of approxirnate1.y equal t o

1533mm. S i m i l a r l y , maximum evapora t ion occurred i n January

,whi le t h e minimuni evaporat ion occurred in September. Tho mean

annual evaporat ion at Nsulcka h a s u v.alue of 1601.20rnrn.

4.22 Frequency Anal~5i . s :

. E'rorn t h e p l o t of r e t u r n per iod versus $ a h f a l l m g n i t u d e

i n F igure 6, t h e r a i n f a l l magnitudes at r e t u r n period6 of 5 yea r s

arid 20 yeara were Illmrn and IPjmm respoot ive ly , Cornpared with

the r e s u l t s obtained from us ing I - 7 c,onsocutive r a i n f a l l days

as r o p r o ~ e n t i n g p a r t i a l du ra t ion days, ( ~ i g u r o s 12 - 13, Table

&7, ) , i t was obmrved that 7 - I+ consccrrtive r n i n f u l l day6

produced lower r a i n f a l l tnugnitudes whereus 5 - 7 consecut ive

r a i n f a l l days produced h ighe r r a i n f a l l mnagnitudes at correspondine;

r e t u r n pe r iods r e spec t ive ly ,

Therefore, t h e p a r t i a l du ra t ion s e r i e s e x h i b i t more ,,, ,

v a r i a b i l i t y i n e s t ima t ing t h e frequency of occurrence of a

r a i n f a l l event ,

, 4.2.3 P r o b a b i l i t y Analysis:

From t h e r e s u l t s obtained in t h e annual p r o b a b i l i t y of

~ c c u r r e n c e of both r a i n f a l l and evaporat ion, 10 yea r s was

determined a c t h e minimum leng th of rcxcrd t h a t may be accep tab le

f o r t h e ana lyses c a r r i e d out i n t h i s p r o j e c t and f o r f u t u r e

ana lys i s . Therefore, it impl i e s t h a t th.e 18 yours of evapora t ion

r eco rd and 20 years of r a i n f a l l r eco rd were adequate.

. Considering t h e weekly r a i n f a l l i n Table 8; r a i n f a l l va lues

of on ly 0.4nun and 0 , I m m a r e expected i n the first week of January

a t 403 and 5% p r o b a b i l i t i e s r e spec t ive ly . Y'hcre were no r a i n f a l l

even t s a t o t h e r l e v e l s of p r o b a b i l i t y u n t i l t h e f i r s t week of

plarch. Ililgl r a i n f a l l mcqnitude of ubovo ltOmrn is expoctod i n tho

f ir& week of May a t 40% p r o b a b i l i t y ; i n t he last week of May

at probab i l i ty and i n the f i r & week of September at 6& - 90%

probab i l i t i e s . This implies t h a t r a i n f ~ l l l events a t 6M - 90% chances

of occurrence a r e low magnitude r a i n f a l l s which w e very s u i t a b l e

f o r crop production planning,

I n view of the above, t h e pcriod between t h e l a s t week of

March and t h e f i r s t week of Apri l i s very convenient f o r land

preparat ion while t h e actual. c rop plant ing f o r r a in fed . a g r i c u l t u r e should be done between t h e second and t h i r d weeks

. 8.

of April. F i r s t weeding and probably f e : r t i l i z e r app l i ca t ion

should be done during t h e t h i r d week of May,

During t h e f i r s t week of Oc$ober, r a i n f a l l magnitude is "

about 35cm which is enough f o r p lant ing of shor t durat ion crops

such a s vegetables s o t h a t they can make w e of rainwater with

l i t t l e o r no supplemental i r r i g a t i o n . Supplemental i r r i g a t i o n

of crops is expected during t h e period t h a t l i e s between t h e last

week of October and f i r f i t week of November, Otherwise, t h e crops

should be scheduled f o r harveeting during t h i s period i f : no

supplemental i r r i g a t i o n is desired.

Dry season i r r i g a t e d crops should be planted as e a r l y us

t h e second week of November s o t h a t they can depend on s o i l d

moisture from r a i n f a l l ; btored i n the root zone f o r some1;ime

before f u l l i r r i g a t i o n s t a r t s .

Crop planning cun s t i l l be done at 40% - 6& l e v e l s of

probabi l i ty , bu t t h e s e ranges a r e t h e minimum l i m i t f o r t;&ing

ri&s i n c rop planning n e c e s s i t a t i n g t h e need f o r more carefu lnecs ,

4.2.4 P r e d i c t i o n of R a i n f a l l Def ic i ts and Surpluses:

R a i n f a l l d e f i c i t s were c o n s i s t e n t l y observed from f i r s t

we& of January t o t h e last wcek of A p r i l asid from last week of

~ovcnlbcr t i l l and of December a t ltC% - 60% l evc l t j of p . robabi l i ty ,

I n o the r words, t h e per iod between October 29 and Apr i l 29 i c a

r a i n f a l l d e f i c i t per iod a t 40% t o 6W l e v e l s of p robab i l i t y ,

~ l s o , the per iod between October 15 and May 6 is a r a i n f a l l

d e f i c i t per iod at 70% - 80% p r o b a b i l i t i e s , The r a i n f a l l d e f i c i t

p e r ' i ~ d at p r o b a b i l i t y starts i n October 15 and ends i n

June 10 except during May 21 - 28'whexi t h e r e was a surp lus ,

R a i n f a l l su rp luses predominantly occurred from May 7 - 10

October 28 (F igure 21).

Fro111 Table 22 below, t h e annual, d e f i c i t is lowest a 5007

p r o b a b i l i t y , implying t h a t i r r i g a t i i n planning can be s a f e l y

made at p r o b a b i l i t y l e v e l , !This observa t ion ag rees with

t h e r e s u l t s ob ta ined by Malik and Agarwal (1982).

I I t t I I I I 1 I I I ' B

Oc t I J D J F M A M J J A 6

- - - - - Deficit Period

.- Surplus Period

Figure 21: Chart Showing Rainfall Deficit and Surplus Per iods a t Nsukku

Table 22: Annual r a i n f a l l D e f i c i t s at Di f f e ren t Percent Chances at; Nsuldca

P r o b a b i l i t y (%)*

50 "

Go.

~unirnulut i i c D e f i c i t

(mm)

Cu~mulat i v o Surp lus

(nm> Annual Deficit

(nun)

I n eva lua t ing t h e two p r e d i c t i o n models, t h e c o n s t a n t s

f o r both t h e Log i s t i c and t h e Gornpertz models a r e shown i n

Tables 13 and 14, Also, t h e value6 of Coe f f i c i en t of de te rmina t ion

and percent abso lu t e average dcviati .on f o r both models a r e

-presented i n Tables 15 and 16.

Higher C o e f f i c i e n t s of de te rmina t ion and lower pecent average

a b s o l u t e dev ia t ion i n d i c a t e s a b e t t e r p red ic t ion , Therefore, t h e

Gompertz model p red ic t ed b e t t e r surpluses at a l l l u v e l s of p r o b a b i l i t y

except at 5% where the L o g i s t i c model performed b e t t e r , The *

l o g i s t i c model p red ic t ed b e t t e r d e f i c i t s at 80% and 90y: l e v e l s of

probab i l i ty while the Gompertz model predicted b e t t e r d e f i c i t s

at 409& - 7% l e v e l s of probabi l i ty .

Therefore, it is recommended t h a t t h e Gompertz model be

used f o r t h e predic t ion of r a i n f a l l surpluoei while t h e Logis t ic

model be use fo r predic t ion of r a i n f a l l d e f i c i t s i n the N~ukka

t r o p i c a l c l ima t i c amndit ions.

4.2.5 Determination of W a p o t r a n ~ ~ i r a t i o n and C s Coef f i c i en t s / l l ac to r~

Figure6 14 and 15 show the p o t e n t i a l evapotranspira' t ion

prddicted by means of the evaporation index a t 7096 l e v e l of

p robab i l i ty and its performance r e l a t i v e t o t h e evapotranspi ra t ion

predic ted by rrroans of the Ultiriey Cridd3.u and the 13lansy-Morin - Nigeria models respectively.

From f i p e 14, t h e EV7O index predic ted higher evapo- ,

t r a n s p i r a t i o n values than t h e o the r two models u n t i l t h e middle

of 16th week of the year (Apri l 20 - 27) when t h e EV7O index

s t a r t e d p red ic t ing lower evapotranspirat ion than the Blmey Criddle '

model, On the same vein , t h e EV7O index c t a r t e d p red ic t ing lower

below t h e Blaney- M0ri.n-Nigeria mode at the

middle of t h e ' 18th week (May 4 - 11 ).

I n f igure 15, the EV70 index predic ted higher evapotranspirat ion

va lues ' than the Blaney Criddle and tho Planey-Morin-Nigeria models,

However, i t maintains the same p a t t e r n with t h e Blaney-Morin-Nigeria

EV70 BLRNEY CRIDOLE

X BLR-1EY MURIN NIGERIR

12 13 14 16 16 17 18 19 20 GROWTH PERIOD CWEEK 11-10>

F ig . l 4 THE POTENTIRL ET . S PREOICTED BY THE THREE iiODEiS CMWW - bNY)

EV70 BLANEY CR I DOLE e\- 3 BLFINE'r' MORIN NIGERIH /

a

43 43 45 40 47 48 4.9 51 52 53 GROWTH PERIOD {WEEKS 43 - 523

F i g. 15 THE POTENTIRL ET . S PREDICTED BY THE THREE MOOELS CCI!~T--DEC- 3

u I 2 3 4 6 B 7 8 g 1 i l 1 1 1 2 i 3 RUG GROWTH PERIOD (RUG - JUL.1 J UL .

FIG. 16 MONTHLY POTENTIHL ET. OF CASSAVA AT NSUKKA

BLANEY CRIDDLE

0 . 8 1 o BLANEY MORIN NIGERIR

0.7

11 12 13 14 15 18 . 17 18 18 20 GROWTH PERIOD C12TH -1BTH YEEKI

F i g . 1 7 CROP COEFFICIENTS OF Rnaranihus Hybridus DETERMINED WITH THE THEE MODELS [ MHRCH - MHY I

% EV70

+ BLANEY MORIN NIFERIR

F i g . 1 S CROP FHCTORS OF CASSSAYA FOR THE PENMAN HNO EV7U MODEL

model which tend t o predic t h i b e r evapotranspirat ion value&

during dry and hot periods,

A similar predic t ion p a t t e r n is exhibiked i n f igure 16

where it was observed t h a t t h e EV7O index predicted very high

values between the months of November and

March which corresponds ~ i t h the periodri of dry season.

The crop f a c t o r s of the crops determined with the EV70

index and t h e i r comparisons with t h e crop c o e f f i c i e n t s predicted

with t h e o ther models a r e ~hown i n f igures I7 - 19,

One i n t e r e s t i n g observation nmde from t h e evaporation

predicted with the EV70 i.s tha t i t tends t o predic t high evapo-

t r a n s p i r a t i o n values during hot and dry periods and a lower

evapotranspirat ion value during cold and wet periods. I n other

words it tends t o simulate the water use of crops. i n a ssoc ia t ion

with the weather condit ion r a t h e r than tihe s t age of growth of

crops..

Determination of Drairlnge Coefficients: - Table 2q and Figure 20 show the decign drainage c o e f f i c i e n t s

corresponding t o various Crop max imurn tc~lerarice period t o excess

water at d i f f e r e n t r e t u r n periods f o r the Nsukka climate. Except

at 6.days maximum tolerance period and corresponding 5 year

r e t u r h period, a l l the drainage coef f i c ien t values a r e l a r g e r

o L 0 1 2 3 4 E; 8 7 8

WX. CROP TOLERi?KE TO EXCESS MHTEH cDRYS',

F i g .20 CHART OF ORAINAGE COEFFICIENTS FOR NSUKKR

than t h e usual ly adopted value of l . v3 l i t r e s / ~ f i a (70 ~ u s e c s /

C P ~ , mile). . -

However, if only one day r a i n f a l l is considered as i u usual ly

done, and is divided by the number of days of crop maximum

to le rance t o excecs water ( u s u a l l y ' 3 days) , t he value of the

r e su l t an t drainage coe f f i c i en t w i l l be appreciably c lose t o the

value, This implies t h a t t h e crop physiological

tol'erance t o excess wa.ter plays a v i t : d role i n t h e determination

of design drainage coe f f i c i en t . ' ,

On the other hand, t h e a c t u a l percentage of r a i n f a l l

t h a t becomes su rp lus water pliiys a major part i n ectirnating the

drainage coe f f i c i en t and its determination i.s a m j o r problem.

This ic becauce, the production of excess water dependti on a l o t

of f a c t o r s which include the s a t u r a t i o n s t a t e of the s o i l , t h e

s o i l physical and chemical p roper t i e s , vegeta t ion , and topography

e tc , Therefore when the a b s t r a c t i o n from r a i n f a l l a r e computed

giving considerat ion t o those condi t ions , a more r e a l i s t i c and

adequate valu&s of drainage coe f f i c i en t can be estimated as &bted;by

Bhat tacharaya and Sarkar ( 1 982 ) .

CONCLUSIONS AND RIGOMMKNDATIONS - 5=l Conclusions :

Essent i i i l ly , . t h e purpose of t h i s p ro j ec t was t o c a r r y out

a d e t a i l e d s t a t i s t i c a l . a n a l y s i s of t h e Nsukka r a i n f a l l and

da t a f o r t h e purpose of determiiring t h e necessary

hydro log ica l parameters t h a t w i l l a i d t 'he cr1~;irieering design

of water n~anagernerit systems i n t h e area, 'Also, t h e r e s u l t s

may a i d s c i e n t i f i c r e sea rch and. hydro logica l fo recas t i n t h e

Nsukka t r o p i c a l c l imate,

I n t h e f i r s t part of t h i s work, a genera l a n a l y s i s of t h e

r a i n f a l l and evaporat ion d a t a hi16 bcen done,to dctcrrnine t h e i r - .

monthly and annual c h a r a c t e r i s t i c s , Ylle r c s u l t s have fihown t h a t

Nsukl~a r a i n f a l l exh ib i tud unirnodal d i s t r i b u t i o n with peak i n

septernber and Mi.nimurn va lues i n January and December, wi,th a

mean annual value of 1533mrn. S i m i l a r l y , t h e Nsukka evapora t ion

h a s a rnaxirnum value i n January corresponding to t h e peak harmattan

pei.iod while t h e mj.ni.rnum value occurred i n September corresponding

t o the per iod .of maximum r a i n f a l l ,

a t ~ ~ ~ ~ k k l l ~ L L G il valuc of ?GOl,%On~rn,

I n t h e second part, a s p e c i f i c

The mean annual evapora t ion

type of s t n t i s t i c t i l a n a l y s i s

4

85

determine the sequcnce of water gc:neration through r a i n f a l l and

water l o s s through evaporat ion on pe r iod ic busis . The

p r o b a b i l i t i e s o r percent chances of occurrence of an event o r

h ighe r event occurr ing dur ing a given week, month o r year were

determined. E'roro t h e s e , t h e r a t e of water genera t ion o r l o s s

over t h e

' d e f i c i t s

i n t o t h e

d e f i c i t s

52 s tandard weeks i n a year were de l inea t ed i n t o

and surpluses . Two s t a t i s t i c a l models were f i t t e d

r e s u l t s t o e s t a b l i s h a peridoc func t ion r e l a t i n g t h e

and su rp luses t o a time se r i e s , , The cons t an t s o r

c o e f f i c i e n t s of t h e two models were' de t s rn~ ined s p e c i a l l y f o r t h e

Nsuldca t r o p i c a l c l ima te and a comparison of t h e models showed

t h a t while t h e Log i s t i c model p red ic t ed b e t t e r d e f i c i t s , t h e

Gompertz model pred ic ted b e t t e r surp luses . A f u r t h e r a p p l i c a t i o n

of t h e p r o b a b i l i t y a n a l y s i s was made t o p red ic t pe r iods of

va luable a g r i c u l t u r a l planning program as well as t h e minimum

number of y e a r s of r a i n f a l l and evapora t ion d a t a t h a t may provide

adequate r e s u l t s f o r hydro logica l a n a l y s i s i n t h e Nsukka rea.

T h i r a l y , t h e f e a s i b i l i t y of using evaporat iou da t a only

t o p r e d i c t t h e p o t e n t i a l e ~ a p o t r a n s p i r a t ~ i o n of c rops was

inves t iga ted . 'l'he r e s u l t s showed t h a t t h e Nsukka evaporat ion

at 7V$ p r o w b i l i t y l e v e l ( ~ ~ 7 0 ) p r o v i d e s , a good index of p r e d i c t i n g

p o t e n t i a l e ~ a ~ o t r a c s p i r a t i o n i n t h e Nsukka men. However, a

comparison of ' the EV?0 index with o the r models showed t h a t i t

p r e d i c t s higher evapotranspi ra t ion during hot and dry periods and

lower evapotranspirat ion dur in & cold and wet periods, F'urther

t o t h i s , t he EV70 index was used t o determine the crop f a c t o r s of

African s p i m c h

, ~ b r c h - May and

crop f a c t o r s of

f o r the growing

year ).,

(Amaranthus ~ l y b r i d u s ) f o r t h e periods between

'October - December reupectivaly. Also the

Caswva (Manihot Fkculenta Crantz) was'determined

period of 12 months (August - J u l y of t h e following

F ina l ly , the r a i n f a l l event6 of April t o September,

representing rnonths t h a t produce most r t t i n f a l l i n Nsukka was

used t o determine the design drainage c o e f f i c i e n t s i n the a r e a

based on t h e p r inc ip le of consecutive r a i n f a l l days. From the

r e s u l t , it w a s concluded t h a t consecutive duy r a i n f a l l a n a l y s i s

ic appropr ia te f o r t h e design of ugricul.tura1 land d rn imge i n

t h e IJsukka a r e a and should the re fo re be u t i l i z e d i n a r e a s where

a g r i c u l t u r a l drainage systems a r e t o be i n s t a l l e d ,

5.,2 Jecomnendations :

Basica l ly , t h i s work has gone as far a s poss ib le i n

achieving t h e objcc-Lives t h a t were s e t o.ut i n t h i s projec t .

o ther h indered t h e completion of t h i s work t o the des i red l eve l ,

of these l i m i t a t i o n s include th'e problem of inadequate

record a t t h e n~eteorologica l s t a t i o n which necess i t a t ed soma

ext rapola t ions and,approximatiors i n the est imation of missing

data. Moreover, the problem of time c o ~ i s t r a i n t s coupled with

t h e absence of r a i n f a l l dura t ion da ta defeated t h e aim of

es t imat ing the r a i n f a l l i n t e n s i t i e s , T t l i ~ would have a ided i n

, estimatinl*; the r a i n f a l l surpluses i n for-m of run-off and deep

p r c o l a t i o n l o s s e s f o r the purpose of dcttermining the i r r i g a t i o n

requirement of crops. Another l - imi ta t ion a rea is the absence of

year sound p r a c t i c a l consumptive use data f o r a de ta i l ed

evaluat ion of t h e EV7O evapotranspi ra t ion index, .Also absent

is a r e ~ e r v o i r o r pond f r m which dutu could huvo boon obtained

t o t e s t t h e predi-ction models,

I n view of tho above, i t is t he re fo re recornended t h a t

t h i s work shoulrl be extcnded t o accommodate the above l imi ta t ions .

F i r s t l y , ra i .nfa l1 and evaporatiou record^ from other

meteorologica l s t a t i o n s should be used t o compare and a d j u s t

the da ta a v a i l a b l e at t h e Nsukka ineteoro1o~;ical s t a t ion .

Moreoyer, f i e l d da ta & o d d be co l l ec ted s o as t o est imate

t h e e f fec t ivk r a i n f a l l s t o enable t.he determination of a c t u a l

quan t i ty of rai .nfal1 excess f o r the calcul.ut;ion of drainage

c d e f f i c i e n t s and i r r i e t i o n requirements of crops,

For the t evaluat ion of t h e EV70 index; it is a l s o

recommended t h a t crops should be p lanted through the whole year

to comprehensively determine the potential evapotranspirations

and crop factors of various crops.

Finally, actual reservoir evaporation losses may be

obtained to test. the prediction models,

hneke, D.0. ( 1985) Predicting Deep ' Percola t ion l o s s e s i n Small Drained Agricultural . Catchments, Proc, NSAE Vol. 9 (63 - 71).

Aneke, D.0, and J,Oo Duru (1985)- Designing F i e l d Engineering S t ruc tu res with Scanty EIydrological Data, IJroc, NSAE Vol, 9 (72 - 8210

.ekwe, D,C, ( 1 9 8 9 ) ~ LWuluution, Anal.ysis and Modification of t h e Blaney-Morin-Nigeria (BMN) Evapotranspirat ion Model, Unpubliched M.-, Pro jec t Report, Departrnont of Agr icul tura l Engineering p n i v e r s i t y of Nigeria Nsukkn.

Aniekwe, H.L. ( 1 9 9 1 ) ~ Ef fec t s of Plant Population, Supplementary I r r i g a t i o n and Black Plus t i c Mulch on Selected v a r i e t i e s of Cassava (Manihot Esculenta C r u n t ~ ) ~ Unpublished M.Sc. Projec t Report, Fticulty of Agriculture, Universi ty of Nigeria, Nsukka.

Anyadike, R.N.C (1987). The Linacre Evaporation Forniula Tested and Conpared t o o the r s i n various Climates Over West Africa. Agric. and Forest Met,; 39: I l l - 119.

' Bhattn charilya, A.K. and T.K. S a r k a r (1982). Analysio of Ra in fa l l Data f o r Agr icu l tu ra l Land Drinage Design, Journal of Agr icul tura l Engineering Vol, xix Noel (15 - 25).

Blaney, 1I.F. and W.13. Criddle (1950). Determining Water Rkqqhirernents i n I r r i g a t e d Areas from Climatological and I r r i g a t i o n Data, USDA - SCS, T.P. '96,

Blaney, H,F. and K.V, Morin ( 1942). Evaporation and Consumptive Use of Water: Ernpericnl Yormulas, Trans, Am, Geophysical Union, 23 (pa r t 1 ) 76 - 83).

Chow, V,T, (I951 1. General Formula f o r Hydrologic Frequency Analysis. Am. Geo$yaical Union Trans. 32 ( 3 1 - 2371, April ,

Chow, V.T, (1954). The Log-ProUability Law and its Engineering Applications, Am, Socie ty of C i v i l Engineers (Separate No. 576) 80, Novem'ber,

Doorenbos, J. and W.C. P r u i t (1975). Guidelines f o r P red ic t ing Crop Wiltcr Rcquircmcn,Lo, I r r . ig . and I)ruini~gc Paper 24, FA0 Rome 197p.

Duru, J.0, 1982. Modified Blaney-Mor:in El1. ~ o d e l f o r Selec ted Climatic Cond.itiom i n Nigeria NSAE Vol,6 pg. 103 - 119.

Biru , J.O. and Adewusi ( 1984). Consum~tivc use Coeff ic ient f o r Selcc t e d Crops I n Sarnaru , Northern Nigeria. Nig. Journal of Engineering. Vol. 2 No, 1,

Duru, J,O. and A. Yusuf (1980). P o t e n t i a l of Temperature - based Evapotranspirat.ion Estimate f o r f i rming i n u Paper: Fourth Annual Coriference of NSAE, Universi ty of Ibadan, Ni.g,

Gurnbel, 6.J. (1954). S L u t i s t i c u l 'l'heory of Extreme Vdues and Some P r a c t i c a l Appl'icat ion^. U.S. Bureau Standards. Applied Plathematical S e r i e s 33.

Hammer, M.J. and K.A. Mackichan (1981 1, Hydrology and Quali ty of Water Resources. John Wil-ley and Sons, Inc. New York,

I s rae l son , O.W. and V,E. Iimsen. (3962 1, I r r i g a t i o n , P r i n c i p l e s and Pract ice . Third Edit ion, John Wiley and Sons Inc. New York.

Linsley, R.L; M.A. Kohler and J.L.H. Paulhus (1975). Hydrology f o r Engineers, 2nd Edit ion, McGrawhill Book Company Inc, New York,

Madubuike , CON. (1987). The S e n s i t i v i t y of hbaporation Models .

t o Errors i n Mearjured Parameters. Proc, NSAE Vol. 11 (330 - 340).

Malik, R.K. and M.C. Agarwal (1982): Predic t ion of Curnn~ulative Rainfa l l Deficitxi Using Growth Models. Journal of Agric, Engineering, Vol. xix, No.? Page I - 5 ,

blichael, A.M. (1985). I r r iga t ion : Theory and Prac t i ce V i k a s Publishing House. Put, Ltd, New Delhi India,

Mockus, V. ( lg60), Selec t ing a Flood Frequency Method, An, Soc. of Agric. Engineers, Trans, 3, 4.8 - 51, 9.

Nwotite GOO, (1986). Design and Construction of Non-Weighing Ly~irnctcr and Consumptive Use Studiou on Amaranthus IIybriduo. Unpublished M.Eng. Project Report. Department of Agric. Engineering, Un'iversity of Nigeria Nsukka. 11tOp.

Onukwugha, ROE, (1986). Design and Ccnstruction of a Non-Recording R a i n p g e . Unpublished B.Eng, P r l j o c t Report, Department of Agric. Engineering Univeroity of Nigeria, Nsukka, 48p,

Penman, H,L, (1948). Natural Evaporation from Open Water, Bre S o i l and Grass. Proc. of t h e Royal Society, Se r ies A. 1948.

Sahoo, N ; J. .Sin& and H.K. P'ande (1982). Planning a n In tegra ted Drainage and I r r i g a t i o n System i n Humid Ilice Farming - A cucse study. Jouxrlnl of A ~ r i c , Engineering Vol. x i x No.3 (37 - 471,

S a s t r i , AoSmRoA. .S; lZamu Krishna and C,S, Rhandri (1982). Agro-Climatological Analysis f o r Crop Planning i n Gubiya Catchment, Journal of Agric, Engineering, Vol, x ix No.2 (15 - 19).

Sh'araa, H.C; H.S, Chauhan and S.Rarn (7979). ProWbi l i ty Analysis of llainftill for Crop Plannin .. Journal of Agric. a Engineering Vol; XVI NO, 3 ( 2 - 951,

ih S,F; L.H. Allefi; L,C, Hammond; J.W. Jones; J.S, Rogers; and A.G. Smujstrla (19831, Basin Water Requirement Estimation i n Southern Florida. .Trans ASAE 2. (760 - 766).

S o i l Conservution Service (1976). I r r i ga t i on Water Requirements: Technical Release No,21; USDA S o i l Conservation Service, b i n e e r i n g Division,

Sonuga, J.O. (1990). Hydralogic, Decision-Making for Dusign of Water Resources Systesm. Paper Presented a t the F i r s t Biennal Hydrology Symposium, Nigerian National Committee fo r UNESCO RIP, Maiduguiri 26 -- 28th w c h .

, A P P E N D I C E S

A P P E N D I X A

Table A f : Crop Evapotranspiration (EXp), And Crop Coefficierlts (Kc) of The African Sdnnch (Armranthus Hvbr idu~; ) U ~ i n e the Blanev , - - . - . - - - " - - - . - - - - ..

C r i ddle Formula :

D A T E

act, 29 - NOV. 4

NOV. 5 - 11 NOV. 12 - 18 NOV, 19 25

Nov. 26 - D m , 2 Dee, 3 - 9 '

Dec, I0 - 16 Dec. 17 - 23 Dec, 24 - 30

Correspondent Week (PI

(March 1'

Actual ET

Source: Nwotite (1986) -

'I. ,

Table A 2 : Crop Evapotranspiration ( ~ 2 ) ~ A.nd Crop Coefficients ( K ~ ) Of The African Spinach (~rriarar~thus Hybridus) UsinR Blaney-Criddlc Formula (March 17 - 11)

D A T E

March 17 -"23

March 24 - 30 March 31 - April 6

April 7 - 13 Apri,l 14 - 20 '

April 21 - 27 April 28 Nay 4 -

May 5 - 1 1

Source: Nwotite (1986) -

Corresponding Week

Actual ET (m1)

15.30

11.40

10.60

11.80

14.10

18.0

10.2

7.30

Potential ET (f

l'ablc Ag: Evapotrancpiruti.on ( E T ~ ) And Crop coefficient^ (KC) ' - O f The African Spinuch ( A m r a n t h ~ s 1Iybridus) Using

The nlaney Morin Nir:cria Formula

D A T E

M U C ~ 17 - 23

March 2'1 - 30 March 31 - April 6

April 7 - 13 April 14 - 20

April 21 - 27

April 28 - May 4 '

May 5 - 11 .

source: Nwotite (19%)

Table A 14 : Evapotranspirat ion (m) Anti CropCoefficients (Kc) O f The African Spinach maran an thus Hybridus) U s i n 6 The Blaney Morin Nigeria Formula

D A T E

- - -

act. 27 - NOV. 4

NOV, 5 -11

NOV. 12 - 18

NOV. 19 - 25

N o v . 2G - D e c , '2

Dec. 3 - 9,

Dec. 17 - 23

Dec, 24 - 30

/-act: 29 - Week

44

45

46

47

48

49

5 1

52

Table A5: Potential Evapotranspiration (EIo) consumptive Uoe ( m p ) Arid Crop Coeff ic ients of Cussava (14anihot E s c u l e n t a Crantz) us in^ The Pemmn Forrnula

Month

August

September

October

November

December

January

February

March

April

May

June

a J u l y I

Source: Aniekwe (1991 ) -

EIo (mm/day)

1.96

2.62

2.78

5.88

4-07

5.50

7.30

7.10

7-60

5-50

3-75

3.00

ETp l:rnm/day)

01, 69

0,32

a 9 8

3,,23

3.25

5-78

7870

7e50

7*98

5.79

2,.81

2.24

Kc

0.35

0035

0.35

0-55

0.80

1.05

1.05

1.05

1.05

7-05

0.75

0.75

APPENDIX C

# : [-j ~;f; ~1 rd,f7,pl[:: 1 :] 13 1. i.:) I-.l(', (j [$I:. < ri'.;[::)l; :::. .. '{

f:

. ,a 1;. lwl (.;[;I.. ., 1\11. Jpl i.jf;{ /":li:.:i ,/ pl[::;[q(" ./ i;ii:;> ,' 7 C j I ( 5 $;

!, . , I::,.(. \ . [)I-- f::s. 1 - ()\;;I::< ;[ (,:; " 1;rqc; 1 I\\[? ,) \,.I I\,! pd . ......... ........ . I .,,,,) ....... -. - ......... " ............................................................................................. ,."'",'. ,..",' ,",. ..... ."" ........ '.." ....... ............... ." ........-....... ............... .................... ..... ..... .............................................. ..... ....................................................... ...............

9 ,..-. "". ,.", ..", "-. *.., -.,. ".- ,-.. .-.. ,.,-...,. --.".."-. ..- .-,~*-*., ..-s ....

' , l t - j fil:;: " 1 1 1 ,[ <'; [;si <()(:,,;(,, ,!'!ll%l [::; ~ ! l f ~ ( [ ~ 1: [!!: tzi (:!I l','[; (::J r;!(.:jE; :]: I,,,, :[ "r "f /,$~~{!ll,,,~ 'f 5 1 !,:; (:)I :[ i\lf.-{.il,,,,i,,,, DVAp , ,, ; f.(l.: l . . ~ ~ ~ " ' ~ 2 . j f i ij::; [.'h ' 1 1, I#, '1" (YJ ;I, (;~(:)*l, 1,. l:!:(/f.! I,,, t:; [,J$:; :[ [:,'; "l"t../E$; (;;bni[::]W E:,('.){, [{.\'I- 1 (Jjq

, . , 1 .. 1- $ 1 .... .: .. ..: . :..:. ..;: ::1. . :.: ::::; :: :: ::::: ::::: :::.. ::::; :-: :::; ::::: .::; 2:: .::: :.::::::: i:!: :::.: ii.3 .::;:.::. .;.:. .:.;: :::: ::::. :::: :;:: 2: ..:; i:::: :;::: ::: ::::: ::..: :...: :::: =: ..:; ::;:: ;z ::: :.I: ::r ..:; ::.: :; ..: ..:: :1:: =:: :.:: :;::: ..:::

; ,,') ~:,y-q 1,ji;:: li,'.I {)I < r:; (.:l/~~:;,'!,'f t::' ' ' ',' "' , , .. ,.., 1. i I.::. t ,, 1 ( 1 "pq 1"' ,.:'!l';l", I,,.! # I I,' I 1 '! [ 1 , :I ' ["f pl,, I"] ' [ ' p,.jc; 1' "1 '1: ,-]I\,l

Table Dl : C a l c a a t e d C u m d a t i v e Dezic i ts and PrecEcted C u m u l a t i v e Def ic i t s Using the Gonpertz and Logist ic Xodels a t 4% - 9C% Chances of Occurrence (dm)

-. ---

w I m r 6% 4

S/?lo Calculated

49

Calculated Calculated

55 11 2

I

Predicted ,

Gompert z Logis t ic

122 112 157 . 136

z 1 # 181 143

P r e a c t ed

I 2

Gompert z

138 178

6 1 124

1 222 i 182 162 1 196 1 163

Logis t ic

126 152 I : I

268 21 6 4 5 6 7 8

21 8 299 356 404 449

238 375 255 .

I I 94

9 I c 11 12 13 14 15

491 532 569 595 619 627 049

259

494 533 569 6C2

16 17 I 8 1 9 20 2 I 22 23 24 25. 26

( s

450 489 525 558 589 617 642 665 666 704 720 735 743 759 769 778 785 792

362 4c8 452

446 499 551 602

658 661 665 679 7& 739 774 808 862 908 970

A-

i yi 244 28 I

# 482 51 9 545

29 2 336

229 324 36s

572 58 5 6c8 622 630 637 654 679 710 744 777 829 876 939

298 345

. 395 408 1 423

532 659 083 3 4 . 723 740 754. 767

' 779 788 797 804 81 I 816

259 31 2

31 2 358 401

458 509 558 6C6 651 693 730

650 694 735

. 771 803 830 854 873 890 go4 915 925 933 939

41 o

458 4% 523 553 569 594 61 1

359 379

768 792 817 838 856 871 , 884 894 902 909

623 633 653 677 705 737 768 816 86 7 919

t - O 7

Table D? (Continued)

Predic ted

L o g i s t i c Calculated

L o g i s t i c

) 3 ~ c x 3 c 0 - 4 - 4 C h V l V l k * w w w h , n,h,h, -A 2J-r W a * ~ m ~ m \ D N < W 9 a \ W * m - c - o m u N O ~ w- r ~ - d c r , O N O \ - - r 0 3 N U l w 4 0 > 0 ~ u 3 N O W CV1u3 \L ) rn18W 4 2

APPENDIX E

109