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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
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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
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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
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!Phis work is for: Mum and the Girls: #
Gera ld ine , Uche.ma, Odiraa and
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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 ,
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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TABLE OF CONTlQ4TS (CONTD. ) - xiv
P A Ci E
4,2.6 Determination of Drainage Coefficients - - - - CHAPTm FIVE: CONCLUSIONS AND RECOMMmDATIONS - - - -
REFERENCES
APPEXlDICES
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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
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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
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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- .
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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).
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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
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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 .
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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 ,
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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,
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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 ,
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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 ,
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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
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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"
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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,
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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
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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,
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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).
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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
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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
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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. #
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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
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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)
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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
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- ( S t u d y A r a c l ) --.--- -- , , 4 4
B E N U E STATE
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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.
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Table I: 20 Year-Monthly Rainfal.1 Data (1971 - 1990) From the
University of Nigeria Nsukka Meterolo~ical Sta t ion (mm)
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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
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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
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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)
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Table 4: Annual Rainfa l l Distribution For Nsukka
A n n u ~ l Total Mecln (mm) (nun)
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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
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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
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YEARS
F I G - 4 RNNURL EVRPDRRTION flT NSUKKfl (1971 -19881
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MAR. QCT . J UL.
MONTHS
FIG.5 MERN MONTHLY EVAPORATION AT NSUKKR
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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.
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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)
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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
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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)
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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
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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-
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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@ .
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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
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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%
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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
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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
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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
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1 3 5 3 9 1 1 1315171921 232527B31 3335373341 4345474951
WEEKS
FIG.7 NSUKKfl WEEKLY RAINFRLL OiSiRi0UTN AT 401 - 801 CHflNCES
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WEEKS
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MONTHS ( J R N . - DEC2
FIG. B NSUKKR # O N HLY RRINFRLL ZISTRISUTF4 9T 43-801 CHRBCES
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F i g . l D LOG-PROBRBILITY OF RNNURL RRINFALL R T NSUKKR
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1 10 100 Prohab l l I t y lX?
F16.11 LOG-PROBABILITY OF flNNUflL EVAPORATION AT NSUKKA
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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.
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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.
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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 #
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,
'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.
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Logistic Model
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Logistic Gompertz Model
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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,
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m U3 C' Zk
'rn VI t
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,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
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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 )
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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
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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;
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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.
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/ *-
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?
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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)
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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
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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
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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
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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
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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 .
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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).
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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
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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
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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
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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)
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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
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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
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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
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% EV70
+ BLANEY MORIN NIFERIR
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F i g . 1 S CROP FHCTORS OF CASSSAYA FOR THE PENMAN HNO EV7U MODEL
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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
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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
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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 ) .
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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
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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
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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
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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
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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,
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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).
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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,
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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).
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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 .
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, 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. ,
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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
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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%)
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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
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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
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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
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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
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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
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) 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
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APPENDIX E
109
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