3--“-U, wol Qd3 9? influerrcs of Fer ion...
3--“-U,
wol Qd3 9?
influerrcs of Fer
ion Nonuniformity on Crop Response 83 Kc7
/S/D /
I,*
and R. S. Yost*
ABSTRACT
Geostatistical concepts and mcthods of studying two-
and thrce-dimensiona vari;rtion in soi1 properties
!RY& of nonuniformity in K fertiliser application were
es nb-
provide new ways to quantify nutrient content and
lished in a field cxperiment on a K deficient soil. Measures of It ni-
formity of fertiliser distribution (UCF) were cnlculated from tbe
variability and may be useful for estimating rates of
<V
fertilizer application rnore precisely.
coefficienr
of vurintion (CV) of K npplicrtion (UCV -= 1 J 0’.
The objectives of this study were to (i) test the use-
The slructure of spatial dependencr of exchangenble soi1 K wps
s e d
fulness of geostatistical methods as tools for estimat-
to estimate the proportion of a given expetimental plot which i
sh, uld
ing rates of fertilizer application, (ii) investigate trop
hc bclun a tpecified threshold of exchwngeable K. Fertilizer req
irr-
response to nonuniform K application using cabbage
ment5 were estimuted on the bas& of the proportion of the re
i o n
as an indicator trop.
that H~S dcficient.
If ddicirnt areas werc icientified
in the F i e l d , h e n
variable rufes of fertilizati,m could be applied.
The respons of
MATERIALS AND METHODS
chinete c?bbrge
(Brass;~a oleracea
L. Chinensis) to K applic tira
HBS strongly
affected by the uniformity of fertilizer distribu
ion.
i
3laxitnum yield decreased 9.5% with nonuniformity of fertilizeridis-
Thc study was conducted on a 9:!- by 42-m fallow field at
tributimx Amounts of K associnted
nith 95% maximum yield Acre
the 1.: liversity of Hawaii Volcano Research Station on the
97, J 13, ami 444 kg K ha-’ for UC% values of 1.0, 0.42, and -
.OZ,
islan d of Hawaii. The expcrimcntal site was located at 1200
respe< tively. Correspcnding tissue K concentrations assuciated
d ,ith
m elcvation with a mean annual rainfall of 3000 mm and
95% riauimum yield were 3.5, 3.8, and 4.0%. Increased variati
n ir,
mcan annual temperature of 14 “(1. The soil was a media1
e\\rhrngetihle K from CV = 44.lY0 to CV = 96.6% result
over thixotropic, isomesic, Typic Hydrandept (Puaulu se-
% i n
critical levels of soi1 K of 0.28 and 0.73 cmol, ha-*, respective1
ries). The Puaulu series consists of well-draincd
soils devel-
{*
oped in geologically recent volcanic ash (Ikawa et al., 1985).
l
The subsoils are smeary and dry irreversibly.
l
I.J
Spatial Structural Analysis qfSoil Potassium
‘NIFr)Kb? APPL I C ATI ON O F FERTJLIZERS iS ~SU’ lly
considered essential for maximum yield. Ex4ess
In order to assess thc magnitude of soi1 K spatial’varia-
iMli7er ir: some spots within a field may decrqase
bility. 161 samples of field soi1 from 0- to 15-cm depth were
yic!d ami profit. Investigations Lhat describe relatibn-
taken with a 7.5-cm diam. auger at 2-m intervals afang four
ships hetwecn nonuniform fertilizer application nd
transects (N-S, E-W, NE-SW, SE-NW). Exchangeab!e K
C~O~I yL!d are rare, however. Nonuniform
i
fertil zer
was extracted from field-moist soi1 samples with 1 M
,Ippl:rariçn cari occur because of faulty machin hry,
NH,OAc pH 7.0. Potassium in NH,OAc extracts was de-
faulty =;Chine opetation or because of ferti$zer p If,op-
termined by atomic absorption spectrophotometry. Semi-
erticj wllich adversely affect the performance of ~the
variograms were computed to investigate the degree of spa-
tial dependence of exchangeable K (Yost et al., 1986).
machine. .4ccording !o Green et al. (1968) equip
cnt
Semivariograms were computed from log-tmnsformed
data
shouid be r:ipabic of applying fertilizers to
4
meet ag-
since exchangeable K uas lognormally distributed. The
ronomic standards. They pro;;cse d that “Fertiljzer
semivariance is defined by
shall bc applied so that when the application rate is
rneauured (:i: art-as not less than 1 foot by I foot nd
y(h) = 1/2 #!qZ(x + h) - z(x)]*.
t11
net greater than 1.5 fret by 1.5 feet, tFc meas
An unbiased estimatc of semivariance is obtained by
4rcd
variation from the mean rate shali be such that it an
N(W
,e gilaranteed that on 95% of the total area the F.
van-
y (h) = g(h) 2 [2(x,) -Z(Xi + h)12
PI
atioik from the mean rate Will not exceed :1:20% on
i- I
hi&-valuc crops and & 30% on low-value crops:
ver
where E dcnotes expectation, h’(Iz) is the number of pairs of
thc ~vhole area the variation from the mcan
9
appl’ca-
values 2(x,), 2(x-, -I- h) separated by a distance h. Aniso-
lion rate shall not excced $JO% and + 45% for igh
troplc variation of exchangeable K was evaluared by cal-
and low cr’ops, respectively.” Even hand applica ion
culating semivariograms of four directions (45, 90, 135, and
of s~llic: tèrtilizer in cxperirnental plots may not n\\ cet
I go”), cach subtending an arc of 45” (?z 22.5”). lsotropic
thcsr standards.
semivariograms, considering all samples taker? in all direc-
1 R.IICS of fertilizer application are usually d ‘ter-
tions (90” -t 90”), were also calculated.
mrn8.rd hy comparing soi1 lest values with a cri ical
,v;iItiz appropriate for the nutrient and situation u der
A Giwstatislical.4pproach
to rhc Drtermination
of JWnssiwn Application Rate
study. Although nutrient vai-iability across a field
ay
rcducc yicld and rcsu!t in wasteful application, sp’ tial
The fitted isotropic semivariogram of exchangeable K was
v;irl.~hility of the soi1 nutrient is seldom considc cd.
used to estimate thc averagc lcvcl of cxchangeablc K of 8-
.__-~_--
- - - - - -
by 4-m blocks using block kriging. These blocks were later
1.P lidlaye. ISRA. CRA Saint-Louis, B.P. 240,
used as cxperimental plots. Given a lognormal distribution
i
Sain\\-Louis. enc-
g,tl; and R.S Yost, Dep. Agron. and Suil S-i., Univ. Hawaii. 1910
of soi1 K test vaiues, the cumulative probability density
F.ast-p.‘est
RoaC, Honolulu. HI 96812. Joint contribution H waii
function of soi1 K is given by Eq. [3) (Matheron, 1955).
Inst. I;rr .fruplcal Agric. and tiuman Rcsources and \\he Af‘ican
&x - p)’
.Imt:~lcan !nmturc. Rcccived 15 M:!r. 1988. *Corrcspondingau ! hor,
o2
[31
Puhlshcd 111 %!II Ci. Soc. Am. J. 53:1X7?- i878 (I’?!(9).
1877
L
N[)IAYE & y~yf’: FEKllL.I%EK
At’I’I.l(.‘:~‘rI,I )N NONI~NIH~Khll’l
Y .ANI> (‘KOI’ KESPONSE
1873
whCrC’ 9 IS thc mcdian of thc distribution. Thc mcan of {hc
Thc lcvcl of cxch;ingcablc K in the delicicnt zone of the
tognolJIlal ( I n ) distribution crin lx cstirriatcd hq’ kl. 141
spwificd arca was cstimatcd
by dividing thc amount of nu-
(hlathcron, 1955)
trient in thc dclicicnt zone by thc sizc of thc zone
l
a2
m = p P- .
41
7
t
Kcarrînglng
Eq. [4] yields
In p = In rn -- $,
51
and lct
z _ In x - Inv
161
The amount of K necessary to bring 0, 25, 50, and 100%
u
.
of the deficient”area
up to the critical level was determined.
*
This yielded four rates of K application (0, 70. 140, and 280
e -2Jl
kg K ha-l). An additional rate, 560 kg K ha-‘, was added to
I
cnsure sufficient K was added.
T‘hc value of the integral G’(z) = ’ 2a
d% cari bc
found in standard statistical tables.
Experimentai
Design and Fertilizcr Application
‘I’h(bn substituting Eq. [S] into Eq. [6) yiclds
A 3$X 5 factorial arrangement of treatments with three
replications was laid out in a split-plot design with three
indices of fertilizer distribution as main plots and five rates
of K as subplots. The index of fertilizer distribution was
(jivcn a critical level (X,.) of exchangeable K, thc proportIon
defined as thc ratio of the area fertilized in each experimen-
of eac:h block above that threshold is givcn by Eq. [8]
tal plot to the total area and was determined as follows: a
l- by I-m grid was superimposed over each 8- by 4-m plot.
‘bl
The percentage of grid cells randomly selected to receive K
fcrtilizcr applications was 100, 75, or 50. This resulted in
three indices of fertilizer distribution (1.0, 0.75. 0.50) and
For tlle lognormal case Eq. (81 becomes (David, 1977:
cnnscquently,
three uniformity coefficients of fertilizer ap-
plication.
Each experimental plot received a uniform fertiIizer and
[91
lime application which consisted of 120 kg N ha-l as
(NH&SO,, 235 kg P ha-’ as treble superphosphate, 15 kg
whew .\\‘, =- critical level of cxchangeable K and is CO ;id-
ha-’ each of Ca and Zn as sulfate, 15 kg B ha-l as borax,
ercd .IS a random variable with a spatial component
i ., a
and dolomite at 2 t ha-‘, all incorporated into the soi1 with
regionalized variable, G = cumulative normal distribl
ion
a rototiller. Potassium fcrtilizer was then applied by hand
function, PI, = mcan of exchangeable K (kriged valuc)
md
in grid cells and rototilled into the soil. Two weeks afier
a 7 square root of the estimation variante. Thc var
nce
fertilizer application the same l- by l-m moving grid used
term, commonly known as the dispersion variancc or I 3ck
for fcrtilizer application was superimposed over each plot.
yariance, is unique to the geostatistical approach. 1 de-
Soil samples were taken from the O- to 15-cm depth from
scribes the way in which exchangeable K varies withl
a n
the tenter of each cell with a 7.1%cm diam. auger. Exchange-
area +3f specitïed dimensions.
able K was extracted with 1 M NH,OAc pH 7. Seedlings of
From Eq. [8] the proportion of the area below the cr Ical
chinese cabbage were transplanted
into experimental plots
level (0.8 cmolJkg) was calculated as follows
3 wk after fertilizer application at a spacing of 90 by 40 cm.
Four weeks afier transplanting a top dressing of 120 kg N
101
ha-l as urea was applied. Cabbage heads were individually
harvested and weighed in the field. Cabbage leaf samples
were taken, dried at 60 “C, and nutrient contents were de-
The amount of” exchangeable K above ,Y,, expressed
s a
termincd.
proportion to the total amount is given by Eq. [ 1 l] (D {id,
1977)
RESULTS AND DISCUSSION
Standard Statistical Analysis
1’1
Distribution function of exchangeable K was eval-
uatcd using a probability plot and the Kolmogorov-
Smirnoff D statistic (Barr et al., 1979). The results in-
dicated that exchangeable K could be approximated
For 2 lognormal distribution Eq. [I I] bccomes (David, 1 77)
to a lognormal probability distribution. The mean of
log-transformed exchangeable K re-expresscd in terms
121
of the original data (Haan, 1977) was 0.2 cmol, kg-’
with a standard deviation of 0.025 and a coefficient
From Eq. [ 121 thc amount of cxchangeablc K in thc deti
of variation (CV) of 12.6%. The variability of
ent
zone. cxprrsscd as
exchangeable K was influcnced by thc support size
(soi1 tore). This is the classical volume-variante re-
lationship-(Froidevcaux; 1982)--which states that--ihe ----.
131
averagc values of large samplcs Will bc Icss dispersed
__-
-._
18:-t
SOIl. S’C’I. SOC‘. AM. .l., VO _, 53. NoVEMHEK-I)E(‘EMHEK 1989
(small~ variability) than thc average values of small
0 . 0 2 4
oncs. l-lencc, thc overall variability of the proper y
u~ldcr study Will depend to a grcat extent on the si e
oi‘ thc soi1 cote. Thc numbcr of samples nccessary to
c‘stimatc rhc mean value with a given level ofcertain y
was calculatcd by Eq. [ 151
:
v.hcrc t is thc two-tailcd studcnt’s I with infinitc d -
grec of“frcedom at the confidence level Q. d is tl e
allo~ablc crror (precision required within the giv n
limits of the truc mean), and Sz is the sample va i-
0 . 0 0 4 -
ance. Thc results of such calculations showed that s x
sampl~:s would be requircd to estimate the truc me 1n
0, , ,
I ,
I
I
I
1
1
1
m
7
ofesc:tangeable K to within 10% of thc sample me n
2
6
10
14
18
22
26
at 0.05 probability.
Dlatonce, m
While this information is useful, it is only a porti n
Fig. 1. Experimental (stars) and theoretical (solid line) semivario-
of thc knowledge required to efficiently sample n
grams of exchangeable K.
arca: !t is also nccessary to estimate the minimu
j
distance for spacing the samples. The geostatistic 1
analysis provides an estimate of the minimum sa1-
and the average rate of Kapplication respectively. The
pling interval.
uniformity coefficient provides an overall indication
of the evenness of fertilizer application. The UCF val-
Spatial Analysis of Soi1 Potassium
ues were calculated for.each of the three levels of uni-
formity. However, for the case where 100% of the grid
fhe rssults of the analysis of directional semivar-
cells in each plot received the same amount of K fer-
iograrls suggested that exchangeable K varied isb-
tilizer a UCF value of 1 was assumed.
tropically. The isotropic semivariogram of exchan e-
f
Thc relationship between cabbage yield and K ap-
ablc K is shown in Fig. 1. It indicated the presence of
plication is shown in Fig. 2 for the various uniformity
a !:ng: nuggct effczt. The nugget variante account d
coefficients. Cabbage yields decreased with increasing
f:)r Zi’Yo of the variancc of exchangeable K. The ran e
nonuniformity of fertilizer application. The spatial
(of spatial dependencc was about 17 m. The range in-
variability of soil properties across the field also sig-
tlicates a zone of influence of a sample and is an s-
nificantly influenced yields. This cari be seen from the
+imatc~ of the minimum distance required for spaci g
differences in yield with no K application.
of inclcpcndent samplcs. Samples farther apart th n
TO quantify the relationship between yield and rates
rhe rznge are cnnsidcred to be independent of l
ea h
of K application the data were fitted to a Mitscherlich
other. Hcgionalized variable theory cari be applied to
mode1
rlugm:nt thc classical approach which assumes t at
= A - Bexp (-CQ)
clcviations about the mcan have a random geograp ic
Y(Q)
il81
distribution. lising the range, the number
1
of samp es
wher: Ytu> = yield (Mg ha-‘), .,l = maximum yield,
rcquircd in Eq. [ 151 cari be de!ermined SO that t ey
B and C are fitted coefficients, and Q = amount of K
are spntially indcpendent.
1
applicd. The amount of K rcquired to attain 95% of
The spherical mode1 weightcd for the number lof
maximum yield was calculated from Eq. [IS] as fol-
pairs in cach lag was ftted to the experimental se i-
lows
x,,ario,;rarn using the SAS noniinear algorithm (Bar et
%
KRqS = (In B - In :1 -- In O.Oj)/C.
1191
al.. 1079) to obtain semivariogram parameters
~
i Il
113
Values of KR,, for the three lcvels of variability were:
y(h) = C,., + C 1 .S- - 0.5- for /r <: n
i,
a
a’ 1
KRVS = 97 kg K ha-’ for UCF = 1.0.
y(h) = CO + C’ for h > a
1(61
KRq5 = 113 kg K ha-’ for UCF = 0.42, and
KR,, = 446 kg K ha-’ for UCF = -0.02.
r\\hcrc (’ - spatial covariance; a = rang of spatial de
n-
.itilce; !I =: lag dislance.
The geostatistical techniqnes employed earlier to
determine rates of fertilizer application indicated that
Yield Response ta Nonuniform Potassium t,
the application of 97 kg K ha-’ would bring 35% of
Application
the deficient area up to the critical level of 0.8 cmol,
ha-‘. If a critical level of 0.5 cmol, ha-i were selected,
Thc uniformity coefficient of fertilizer applicat on
however, 97 kg K ha-i would adjust 70% of the deli-
for c;lch plot was defined as
tient area to the critical. In this mariner the relation-
l
ship of critical level to the proportion of each plot
[JC’F = 1 - 2
I~l 71
below the threshold’can Ix estimated and, in turn, IX
-Q
used to determine rates of K application. (ieostatist-
whcre IJCF is the uniformity coefficient of fertililzcr
ical methods provide relativcly precise estimatcs of K
application, and S and Q arc the standard deviatfon
content;--R~tesof-K-appTicatiorr-can- be-obtained-by-----
NDIAYE & YCIST: FERTILIZER AfWXA7
IN NONLINIFORMITY AND CKOP RESPONSE
1875
1985). Geostatistical techniques described in this pa-
per provide an optimal method to develop such maps
from soi1 sample data.
Predicting Yield frOm Potassium Application
.
and Nonuniformity
Because variation of K application significantly af-
fected yield, and a relationship between yield per unit
area and the application rate was established, it was
useful to develop an expression for yield as a function
of application rate and nonuniformity. Neglecting ge-
netic factors, trop yield cari be assumed to depend on
17 -
both the average rate of K application over the area
24 -
I
I
,
-7
and the spatial deviations from that average (Zaslav-
Il
ZOO
400
M O
sky and Mokady, 1967). The relevant expression is
K Applled, k g h o - ’
(Zaslavsky and Mokady)
--
i
P
4, -
(Q)
%Q>
WI
.
4 ’ 1
UCF - 0.42
where
is the spatial average trop yield, Y,,, is the
y(Q)
5 SS-
/
+
+
yield that would have been obtained with perfectly
uniform application (Q - (2, i.e., no fluctuation in Q),
and
is the spatial variante of fertilizer application
qQ)
(Q), and. is also called the fluctuation index (FI). The
is called the response index (RI),, The
product of FI and RI is the fluctuation response Index
(FRI) and this expresses changes in average yield due
to fluctuations in the level of applied nutrient.
In order to calculate the effects of nonuniformity of
24
K fertilizer application on cabbagé yield Eq. [ 181 was
0
200
400
SO0
K Appllsd, k g h o - ’
substituted into Eq. [20] to obtain
7
- R e x p ( - C Q ) -t- +
T(Q)=A
1211
4s 1
4, -
Rearranging Eq. [17] and substituting for s2 in Eq.
[21] one obtains
SI -
Y(,) = A -
-.
B exp( - CQ)
J7 -
34 -
“+ [ $$ILQc1 - ucn]‘.
SS -
Because yields of cabbage on no-K treatments vaxied
Jl -
due to inherent variability in soi1 properties, the yield-
2 1 -
fertilizer function obtained with UCF - 1.0 could not
be considered as Y,
in Eq. [20]. An estimate of Y
27 -i /
Y
was obtained by poo mg the data from the entire ex-
25 1
1
I
8
periment and fitting Eq. [ 181. Therefore the fitting pa-
0
200
400
400
rameters A, B, and C in Eq. {22] are those estimated
K Applied, k g h o - ’
from the pooled data with A = 39.98, B - 10.17, and
Fig. 2. Relationship between cabbage yield and rates of K applicat
1
C- 0.0172. Using Eq. [22], cabbage yield was pre-
for various levels of uniformity of K fertilizer application.
dicted for UCF values of 1 .O, 0.42, and -0.02 and for
different rates of K application. A plot of predicted
methods described in Eq. [ 131 if the semivariogn
yield against observed yield is shown in Fig. 3. A sig-
of soi1 K is known, and if an adequate number
1
nificant (P < 0.05) correlation coefficient (r) of 0.89
samples are available. Fertilizer rates cari then
was found between observcd and predicted cabbage
based on the proportion of the deficient area belov I
yield.
standard. If the deficient zones are large and cent
Expressing yielti as relative yicld (Y, = ~~c,,/~t, with
uous, they cari be identified and fertilized separau I
A = 39.98), curves of relative yield as a function of
..-
!
Another method of applying fertilizer to nonunifoi 1
the nonuniformity-of fertilizcr application wcre drawn
soils is possible with variable rate fertilizer spreadc ,
in Fig. 4 using Eq. [22]. It cari be seen from this figure
which use maps of nutrient levels as a guide (L.uellt
that the decrease in relative yield with decrease in uni-
_,-_-
.--
1476
NIL Xl. SOC’. AM. J.. ’ )L.. 53. NOV~M~~&DECEMBER 1989
M
>
.-
0
-
-
70 kg/ho
5
a
---. 140 kg/ha
,’
,’
/
-
210 kg/ha
i’
- 6 - ./
-
280 kg/h.
r
- 7 1
4
0.0
0.2
0 . 4
0.0
0.1
1.1
is
Uniformity Coafflclent, UCF
Fig. 5. Calculated relative fluctuation response index (FRI) as a
- 1
function of uniformity coefficient of K fertilizer application for 4
Obsarvod Yisld, tonnea ha
.
.
ratejof K apphcatron.
Fig. 2’. Comparison of predicted and observed cabbage yield.
*
*
ucel.0
A
UCS=O.U
M
27 -
:
?
?????????
????
?
?
? ?
??
?
?
?
? ?
??? ?
?
3.2
3.4
3.6
J.0
4.0
4.2
4.4
4.6
4.9
0.0
0.2
0.4
0.6
0.1
Uniformity Coefficient, UCF
Leaf K Concentration, 9;
Fig. ,t. C’alculated relative yield of cabbage as a function
Fig. 6. Relationship bctween cabbage yield and K in dry matter as
formity coefficient of K fertilizer application for four
afl’ccted by uniformity of K application.
apt>licalion.
zone volume, such as plant species, population den-
formity coefficient was most pronounced at app ica-
sity and row width, Will probably influence the size of
tion rates 5140 kg K ha-‘. This is also shown in 1 Fig.
area that is sufflcicntly nonuniform to affect yields.
5 b> the relationship between relative fluctuatiod re-
Increasing the uniformity of fertilizer application in
sponse index and uniformity coefficient. These ‘cal-
ordcr to improvc trop yield must be viewed critically.
culations showed that the decrease in relative
RI
Under certain conditions ensuring uniform fertilizer
witP increase in UCF was much steeper for lower r tes
application may be expensive without commensurate
of fi:rtilizer application.
1
increase in yield. Under other conditions, however,
There are some limitations on the use of data f om
yield may be greatly increased through uniforrn ap-
experiments which measure trop response to no un-
plication of fertilizer.
.
iform application of fertilizers. If areas of non ni-
formity are sufficiently small, the nonuniformity
ay
Yield-Tissue Potassium Concentration Relationship
not be important because individual plants may i
raw
nutrients from areas receiving both high and low dates
as Affected by Nonuniformity of Potassium
Application
of fcrtilizer. In this way, individual plants
age nonuniformity in fertilizer application rate.
The relationship between yield and K concentration
information is available on the minimum area
in cabbage leaf is shown in Fig. 6a, b, and c for UCF
which nonuniformity of application should
values of 1.0, 0.42 and -0.02, respectively. The re-
ereçl. Prummel and Datema (1962)
sults are in agreement with the general relationships
ineclualities in rate of application
reported in the literature between plant nutrient status
when the areas of fertilizcd and unfcrtilized
and trop performance (Dow and Roberts, 1982).
. _ . . -__-
tlon were greater than 0.5 m. Factors which
~oowever;-1-he~-scattering~‘of points along each curvë .‘_
.
l
--__-
-
._.
‘--
4 NONIINIFORMITY
AND C‘ROP RESPONSE
1877
Cabbage Yield as Affected by Spatial Variability
of Soil Potassium
-t
1.0 -
*
*
D.0
The effectivqness of a soi1 K test is usually measured
*
cv = 44.1% LC
by its accuracy in predictipg trop response to applied
-ü
+
-6
K. The goal of such a têst is to.measure the quantlty
‘Y
*
of plant-available K. and. therefore the test is nega-
<D.z
tively related to responsiveness and amount of K re-
ôz
quired to make up the deficit. Figures 7a, b, and c
ûi
show the relationship between relative yield and
exchangeable K for various coefficient of variation
(CV) of soi1 K. The general form of the relationship
was
1 ,
,
(
(
,
,
,
,
Y=a$bx
[231
0
0.2
0.4
0.6
0.6
1.0
1.2
-i-
1.
E x c h o n g a a b l e K. cmolc kg-’
where Y = relative yield, x = exchangeable K, and a
and h are constants. The levcl of exchangeable K as-
+-
sociatd with 90% maximum relative yield incrcascd
with increasing CV: 0.28 cmol, ha-’ for CV - 44.1%.
0.31 crnol, ha-’ for 67 =- 67.0%, and 0.73 cmol, ha-’
for CV = 96.6%. A critical level of 0.28 cmol, ha-’ is
suggested by Boyer (1972) for tropical agriculture.
Thc range in nonuniformity in this study is within
the ranges of nonuniformity reported in several stud-
ies. A CV value of 44.1% is consistent witli values
reported by Beckett and Webster (197 l), and Courtin
et al. ( 1983). However, Trangmar (1984) found a CV
value of 105% in a study area of about 0.1 ha in Si-
tiung, Indonesia. He attributed this high heterogeneity
to differences between burn sites, areas of exposed
subsoil, and intermediate areas of surrounding soil.
0
,
1
,
,
,
0.2
0 . 4
I
0.6
a.,
0.8
,
1.0
.
.
1.2
,
1:4
The results obtained in this study suggest that an av-
Excharrgoabls
K , cmol, kg-’
erage soi1 K test value may be misleading if the spatial
variability K is not considered.
1.0 -
*
6’
6’
* *
CONCLUSIONS
CY = 96.6X
0:f
0.9
*
The response of chinese cabbage to K application
was strongly dependent on the uniformity of fertilizer
F
distribution. Different maximum yields were obtained
‘-0 0.6
with different levels of nonuniformity of K. With a
<L?L
uniformity coefficient of -0.02, the K requirement
0.7 -
was four times greater than that for more uniform
conditions.
The decrease in yield due to nonuniform applica-
0.6 -
tion of fertilizer was quantitatively described by the
fluctuation response index., The fluctuation response
0.3
0.3!‘,
,
index value decreased with increasing rates of K ap-
0
0.2
0.4
0.6
0.1
1.0
1.2
1.4
plicaiion suggesting that at higher rates of application
E x c h a n g e a b l s K , cmolc k g - ’
the areal uniformity of fertilizer application became a
Fig. 7. Relationship between relative yield of cabbage and excha
less important influence on overall yield.
ge-
ahlrb K as at7ected by spatial variability of soi1 K.
The geostatistical approach used to determine rates
of K fertilizer is a promising technique for determin-
indicates thc difficulty of
ing fertilizer quantities needed to adjust fertility to a
centage as the critical
given critical levef and for estimating the statistical
Graphical determination
distribution of nutrient in trop fields. Variable rates
max:mum yield gave 3.6, 3.
of fcrtilization cari be applied if deficient zones have
values of 1 .O, 4.2, and -0.02
been identified in the field. The level of exchangeable
less the variation about the
K associated with 90% of maximum relative yield in-
the contention that a narra
creased from 0.28 cmol, ha-l for a CV of 44.1% to
rathcr than a sirrgle valuc seemsmore a
0.73 cmol,.h.a-.l_for.a.CV.of 96.6%~.The.results.suggest ..___ _-
evaluating nutrient status of crops (Dow an
that an average soi1 K test value may be misleading
1082 ).
if the spatial variability of soi1 K is not considered.
_. . .
SOIL SC’I. SOC‘. AM. J.. $0~. 53. NOvEMBER-DECEMHER 1989
REFERENCES
Haan, C.T. 1977. Staristical methods in hydrology. The Iowa Slatc
Univ. Press, Ames.
Harr. A.J.. J.tI. Goodnighr. J.P. Sall. W.H. Blair, and D.H. C iko.
IkgWa. H., H.H. .%ro. A.K.S. Chavg, S. Nakamura, E. Robellor, Jr.,
l WC). SAS user’!, guidc 1979 cdiiion. SAS Insl.. Inc.. Raleigh NC.
an<j S.P. Periaswamy. 198s. So~ls of rhe Hawall Agrlcultural Ex-
tIcck:Ii. P.1V.T.. and R. Wcbslcr. 197 1. Soil vnriahiliiy: A re;1. ICW.
periment Station, University of Hawaii: Soi1 ,survey ,laboratory
Sht Fert. 31:1-15.
dala. and soi1 description. Bcnchmark Soils ProJect Tech.
Bovcr. J. 1972. Soi1 ootassium. D. 102-135. I~I Soi)s
1
of the h mld
Report 4.
Luellen, W.R. 1985. Fine-tuncd fcrtilily. Tomorrow’s technolopy
(‘ourun, P.. M.C. Felier, and K. Klinka. 1983. Lateral variabil ty in
M:;;;“a& Corp .Solls !8: 18-22.
%)~ne propcrties of drsturhcd forest soils in Southwestern B itish
1955 Apphcallon des methodcs statistiques rleval-
Cclumbia. Can. J. Soi1 Sci. 63:529-539.
ualion ces &ements. Ann. Mines 7:50-75.
David. M. 1977. Geostatistical ore rescrve estimation. Elsevie Sci.
!
Prummei J., and P. Datema. 1962. The evenntss of distribution
Puhl. CO.
by fertilizer distributors and its effects on trop yield. Land-
Dow. A.].. and S. Robens. 1982. Proposa[: Critical nutrient r nges
bouwmechanisatia 13:742.
fol, trop diagnosis. Agron. J. 74:401-403.
Trangmar, B.B. 1984. Spatial variability of soi1 properties in Sitiung,
Froideveaux. R. 1982. Gcostatistics and ore reserve classifie tion.
West Sumatra, Indonesia. Ph.D. diss. Univ. of Hawaii, Manoa.
CIM Bulletin. 75:77-83.
l
Yost, R., B.B. Trangmar, and J.P. Ndiayc. 1986. Geostatisticrl com-
Green. T.L., C. Eng.. and E.A. Mech. 1968. Achieving the
isrri-
putation software for microcomputcrs. 1. Scmivariograms. Rc-
hution requiremcnts of solid fertilizers. J. Proc. Inst. Agric. Eng.
search
Extension Scrics 074, College
of Tropical Agric, rnd Hu-
?3:125-137.
p
man Rcsour.,
Univ. of Hawaii.
l
Optimum Application Parameters f@ Point Injection of Nitrogen in Winter Wheat
a
H. H. Jan en* and C. W. Lindwall
ABSTRACT
doway, 1977; Christeison and Meints, 1982; Fowler,
1982). The efficiency of top-dressed N, however, may
Prtint injection may enhance N fertilizer use efficiency in
inter
be limited by volatile losses (Keller and Mengel, 1986;
McInnes et al., 1986), biological immobiiization in
surface residues (Fredrickson et al., 1982; Sharpe et
al., 1988), and inaccessibility to wheat roots in dry soi1
conditions (Harapiak et al., 1986).
An approach which may circumvent some limita-
tions of conventional application methods for winter
wheat is point injection of fluid N fertilizer, a method
developed for fcrtilization of row crops (Baker et al.,
1983). If adapted for winter wheat production, this
method could facilitate effective N placement in
spring without appreciable disturbance of the growing
trop and thereby increase fertilizer use efficiency.
Other potential advantages of this proposed method
from 40 tu 60 cm. Adoption of smaller injection intervals i
include compatibility with conservation tillage sys-
dimensions,
while not jeopardizing fertilizer use efficiency,
tems because of minimal soi1 disruption, and reduced
energy consumption because of ver-y low draft require-
deptb was observed to be approximately 10 cm. Grnitn yield res~ponse
ments relative to conventional banding methods.
and fertilizer N recovery in the trop increased four- and thre
The first step in the effective exploitation of point
rcspectively, when injection depth was increased from 2.5 to
injection for the enhancement of fertilizer use effi-
I’hi!; effect was attributed to the inaccessibility of fertilizer N
ciency in winter wheat is the identification of opti-
ing in dry surface soil. Injection of fcrtilizer at tS cm rathe
10 cm demonstrated no additionnl ndvantnge.
mum application parameters. Two of the most im-
portant variables are the geometrical spacing of
injection points and the depth of injection. Optimi-
zation of these variables is prerequisite to the mean-
ingful comparison of pain; injection with conven-
tional application methods.
The objective of this study, thercfore, was to deter-
mine the optimum spatial arrangement and injection
depths for point injection of N in wintcr wheat. This
objective was addressed under field conditions using
15N tracer techniques to quantify N distribution from
injection points and determine fertilizer uptake cfli-
ciency as a function of injection interval and depth.
MATERIAU AND METHODS
Kçcri\\ed 7 Scpl. 1988. ‘Corresponding
author.
.-.Three. fielb.experiments.werc conducted.In..south~n.AL- ---.- -. - -
I’ubllçhcd in fioil Sci. Soc. Am. J. 53: 1878-1883 (1989).
berta, Canada, during 1985 and 1986 to determine distri-
wol Qd3 9?
influerrcs of Fer
ion Nonuniformity on Crop Response 83 Kc7
/S/D /
I,*
and R. S. Yost*
ABSTRACT
Geostatistical concepts and mcthods of studying two-
and thrce-dimensiona vari;rtion in soi1 properties
!RY& of nonuniformity in K fertiliser application were
es nb-
provide new ways to quantify nutrient content and
lished in a field cxperiment on a K deficient soil. Measures of It ni-
formity of fertiliser distribution (UCF) were cnlculated from tbe
variability and may be useful for estimating rates of
<V
fertilizer application rnore precisely.
coefficienr
of vurintion (CV) of K npplicrtion (UCV -= 1 J 0’.
The objectives of this study were to (i) test the use-
The slructure of spatial dependencr of exchangenble soi1 K wps
s e d
fulness of geostatistical methods as tools for estimat-
to estimate the proportion of a given expetimental plot which i
sh, uld
ing rates of fertilizer application, (ii) investigate trop
hc bclun a tpecified threshold of exchwngeable K. Fertilizer req
irr-
response to nonuniform K application using cabbage
ment5 were estimuted on the bas& of the proportion of the re
i o n
as an indicator trop.
that H~S dcficient.
If ddicirnt areas werc icientified
in the F i e l d , h e n
variable rufes of fertilizati,m could be applied.
The respons of
MATERIALS AND METHODS
chinete c?bbrge
(Brass;~a oleracea
L. Chinensis) to K applic tira
HBS strongly
affected by the uniformity of fertilizer distribu
ion.
i
3laxitnum yield decreased 9.5% with nonuniformity of fertilizeridis-
Thc study was conducted on a 9:!- by 42-m fallow field at
tributimx Amounts of K associnted
nith 95% maximum yield Acre
the 1.: liversity of Hawaii Volcano Research Station on the
97, J 13, ami 444 kg K ha-’ for UC% values of 1.0, 0.42, and -
.OZ,
islan d of Hawaii. The expcrimcntal site was located at 1200
respe< tively. Correspcnding tissue K concentrations assuciated
d ,ith
m elcvation with a mean annual rainfall of 3000 mm and
95% riauimum yield were 3.5, 3.8, and 4.0%. Increased variati
n ir,
mcan annual temperature of 14 “(1. The soil was a media1
e\\rhrngetihle K from CV = 44.lY0 to CV = 96.6% result
over thixotropic, isomesic, Typic Hydrandept (Puaulu se-
% i n
critical levels of soi1 K of 0.28 and 0.73 cmol, ha-*, respective1
ries). The Puaulu series consists of well-draincd
soils devel-
{*
oped in geologically recent volcanic ash (Ikawa et al., 1985).
l
The subsoils are smeary and dry irreversibly.
l
I.J
Spatial Structural Analysis qfSoil Potassium
‘NIFr)Kb? APPL I C ATI ON O F FERTJLIZERS iS ~SU’ lly
considered essential for maximum yield. Ex4ess
In order to assess thc magnitude of soi1 K spatial’varia-
iMli7er ir: some spots within a field may decrqase
bility. 161 samples of field soi1 from 0- to 15-cm depth were
yic!d ami profit. Investigations Lhat describe relatibn-
taken with a 7.5-cm diam. auger at 2-m intervals afang four
ships hetwecn nonuniform fertilizer application nd
transects (N-S, E-W, NE-SW, SE-NW). Exchangeab!e K
C~O~I yL!d are rare, however. Nonuniform
i
fertil zer
was extracted from field-moist soi1 samples with 1 M
,Ippl:rariçn cari occur because of faulty machin hry,
NH,OAc pH 7.0. Potassium in NH,OAc extracts was de-
faulty =;Chine opetation or because of ferti$zer p If,op-
termined by atomic absorption spectrophotometry. Semi-
erticj wllich adversely affect the performance of ~the
variograms were computed to investigate the degree of spa-
tial dependence of exchangeable K (Yost et al., 1986).
machine. .4ccording !o Green et al. (1968) equip
cnt
Semivariograms were computed from log-tmnsformed
data
shouid be r:ipabic of applying fertilizers to
4
meet ag-
since exchangeable K uas lognormally distributed. The
ronomic standards. They pro;;cse d that “Fertiljzer
semivariance is defined by
shall bc applied so that when the application rate is
rneauured (:i: art-as not less than 1 foot by I foot nd
y(h) = 1/2 #!qZ(x + h) - z(x)]*.
t11
net greater than 1.5 fret by 1.5 feet, tFc meas
An unbiased estimatc of semivariance is obtained by
4rcd
variation from the mean rate shali be such that it an
N(W
,e gilaranteed that on 95% of the total area the F.
van-
y (h) = g(h) 2 [2(x,) -Z(Xi + h)12
PI
atioik from the mean rate Will not exceed :1:20% on
i- I
hi&-valuc crops and & 30% on low-value crops:
ver
where E dcnotes expectation, h’(Iz) is the number of pairs of
thc ~vhole area the variation from the mcan
9
appl’ca-
values 2(x,), 2(x-, -I- h) separated by a distance h. Aniso-
lion rate shall not excced $JO% and + 45% for igh
troplc variation of exchangeable K was evaluared by cal-
and low cr’ops, respectively.” Even hand applica ion
culating semivariograms of four directions (45, 90, 135, and
of s~llic: tèrtilizer in cxperirnental plots may not n\\ cet
I go”), cach subtending an arc of 45” (?z 22.5”). lsotropic
thcsr standards.
semivariograms, considering all samples taker? in all direc-
1 R.IICS of fertilizer application are usually d ‘ter-
tions (90” -t 90”), were also calculated.
mrn8.rd hy comparing soi1 lest values with a cri ical
,v;iItiz appropriate for the nutrient and situation u der
A Giwstatislical.4pproach
to rhc Drtermination
of JWnssiwn Application Rate
study. Although nutrient vai-iability across a field
ay
rcducc yicld and rcsu!t in wasteful application, sp’ tial
The fitted isotropic semivariogram of exchangeable K was
v;irl.~hility of the soi1 nutrient is seldom considc cd.
used to estimate thc averagc lcvcl of cxchangeablc K of 8-
.__-~_--
- - - - - -
by 4-m blocks using block kriging. These blocks were later
1.P lidlaye. ISRA. CRA Saint-Louis, B.P. 240,
used as cxperimental plots. Given a lognormal distribution
i
Sain\\-Louis. enc-
g,tl; and R.S Yost, Dep. Agron. and Suil S-i., Univ. Hawaii. 1910
of soi1 K test vaiues, the cumulative probability density
F.ast-p.‘est
RoaC, Honolulu. HI 96812. Joint contribution H waii
function of soi1 K is given by Eq. [3) (Matheron, 1955).
Inst. I;rr .fruplcal Agric. and tiuman Rcsources and \\he Af‘ican
&x - p)’
.Imt:~lcan !nmturc. Rcccived 15 M:!r. 1988. *Corrcspondingau ! hor,
o2
[31
Puhlshcd 111 %!II Ci. Soc. Am. J. 53:1X7?- i878 (I’?!(9).
1877
L
N[)IAYE & y~yf’: FEKllL.I%EK
At’I’I.l(.‘:~‘rI,I )N NONI~NIH~Khll’l
Y .ANI> (‘KOI’ KESPONSE
1873
whCrC’ 9 IS thc mcdian of thc distribution. Thc mcan of {hc
Thc lcvcl of cxch;ingcablc K in the delicicnt zone of the
tognolJIlal ( I n ) distribution crin lx cstirriatcd hq’ kl. 141
spwificd arca was cstimatcd
by dividing thc amount of nu-
(hlathcron, 1955)
trient in thc dclicicnt zone by thc sizc of thc zone
l
a2
m = p P- .
41
7
t
Kcarrînglng
Eq. [4] yields
In p = In rn -- $,
51
and lct
z _ In x - Inv
161
The amount of K necessary to bring 0, 25, 50, and 100%
u
.
of the deficient”area
up to the critical level was determined.
*
This yielded four rates of K application (0, 70. 140, and 280
e -2Jl
kg K ha-l). An additional rate, 560 kg K ha-‘, was added to
I
cnsure sufficient K was added.
T‘hc value of the integral G’(z) = ’ 2a
d% cari bc
found in standard statistical tables.
Experimentai
Design and Fertilizcr Application
‘I’h(bn substituting Eq. [S] into Eq. [6) yiclds
A 3$X 5 factorial arrangement of treatments with three
replications was laid out in a split-plot design with three
indices of fertilizer distribution as main plots and five rates
of K as subplots. The index of fertilizer distribution was
(jivcn a critical level (X,.) of exchangeable K, thc proportIon
defined as thc ratio of the area fertilized in each experimen-
of eac:h block above that threshold is givcn by Eq. [8]
tal plot to the total area and was determined as follows: a
l- by I-m grid was superimposed over each 8- by 4-m plot.
‘bl
The percentage of grid cells randomly selected to receive K
fcrtilizcr applications was 100, 75, or 50. This resulted in
three indices of fertilizer distribution (1.0, 0.75. 0.50) and
For tlle lognormal case Eq. (81 becomes (David, 1977:
cnnscquently,
three uniformity coefficients of fertilizer ap-
plication.
Each experimental plot received a uniform fertiIizer and
[91
lime application which consisted of 120 kg N ha-l as
(NH&SO,, 235 kg P ha-’ as treble superphosphate, 15 kg
whew .\\‘, =- critical level of cxchangeable K and is CO ;id-
ha-’ each of Ca and Zn as sulfate, 15 kg B ha-l as borax,
ercd .IS a random variable with a spatial component
i ., a
and dolomite at 2 t ha-‘, all incorporated into the soi1 with
regionalized variable, G = cumulative normal distribl
ion
a rototiller. Potassium fcrtilizer was then applied by hand
function, PI, = mcan of exchangeable K (kriged valuc)
md
in grid cells and rototilled into the soil. Two weeks afier
a 7 square root of the estimation variante. Thc var
nce
fertilizer application the same l- by l-m moving grid used
term, commonly known as the dispersion variancc or I 3ck
for fcrtilizer application was superimposed over each plot.
yariance, is unique to the geostatistical approach. 1 de-
Soil samples were taken from the O- to 15-cm depth from
scribes the way in which exchangeable K varies withl
a n
the tenter of each cell with a 7.1%cm diam. auger. Exchange-
area +3f specitïed dimensions.
able K was extracted with 1 M NH,OAc pH 7. Seedlings of
From Eq. [8] the proportion of the area below the cr Ical
chinese cabbage were transplanted
into experimental plots
level (0.8 cmolJkg) was calculated as follows
3 wk after fertilizer application at a spacing of 90 by 40 cm.
Four weeks afier transplanting a top dressing of 120 kg N
101
ha-l as urea was applied. Cabbage heads were individually
harvested and weighed in the field. Cabbage leaf samples
were taken, dried at 60 “C, and nutrient contents were de-
The amount of” exchangeable K above ,Y,, expressed
s a
termincd.
proportion to the total amount is given by Eq. [ 1 l] (D {id,
1977)
RESULTS AND DISCUSSION
Standard Statistical Analysis
1’1
Distribution function of exchangeable K was eval-
uatcd using a probability plot and the Kolmogorov-
Smirnoff D statistic (Barr et al., 1979). The results in-
dicated that exchangeable K could be approximated
For 2 lognormal distribution Eq. [I I] bccomes (David, 1 77)
to a lognormal probability distribution. The mean of
log-transformed exchangeable K re-expresscd in terms
121
of the original data (Haan, 1977) was 0.2 cmol, kg-’
with a standard deviation of 0.025 and a coefficient
From Eq. [ 121 thc amount of cxchangeablc K in thc deti
of variation (CV) of 12.6%. The variability of
ent
zone. cxprrsscd as
exchangeable K was influcnced by thc support size
(soi1 tore). This is the classical volume-variante re-
lationship-(Froidevcaux; 1982)--which states that--ihe ----.
131
averagc values of large samplcs Will bc Icss dispersed
__-
-._
18:-t
SOIl. S’C’I. SOC‘. AM. .l., VO _, 53. NoVEMHEK-I)E(‘EMHEK 1989
(small~ variability) than thc average values of small
0 . 0 2 4
oncs. l-lencc, thc overall variability of the proper y
u~ldcr study Will depend to a grcat extent on the si e
oi‘ thc soi1 cote. Thc numbcr of samples nccessary to
c‘stimatc rhc mean value with a given level ofcertain y
was calculatcd by Eq. [ 151
:
v.hcrc t is thc two-tailcd studcnt’s I with infinitc d -
grec of“frcedom at the confidence level Q. d is tl e
allo~ablc crror (precision required within the giv n
limits of the truc mean), and Sz is the sample va i-
0 . 0 0 4 -
ance. Thc results of such calculations showed that s x
sampl~:s would be requircd to estimate the truc me 1n
0, , ,
I ,
I
I
I
1
1
1
m
7
ofesc:tangeable K to within 10% of thc sample me n
2
6
10
14
18
22
26
at 0.05 probability.
Dlatonce, m
While this information is useful, it is only a porti n
Fig. 1. Experimental (stars) and theoretical (solid line) semivario-
of thc knowledge required to efficiently sample n
grams of exchangeable K.
arca: !t is also nccessary to estimate the minimu
j
distance for spacing the samples. The geostatistic 1
analysis provides an estimate of the minimum sa1-
and the average rate of Kapplication respectively. The
pling interval.
uniformity coefficient provides an overall indication
of the evenness of fertilizer application. The UCF val-
Spatial Analysis of Soi1 Potassium
ues were calculated for.each of the three levels of uni-
formity. However, for the case where 100% of the grid
fhe rssults of the analysis of directional semivar-
cells in each plot received the same amount of K fer-
iograrls suggested that exchangeable K varied isb-
tilizer a UCF value of 1 was assumed.
tropically. The isotropic semivariogram of exchan e-
f
Thc relationship between cabbage yield and K ap-
ablc K is shown in Fig. 1. It indicated the presence of
plication is shown in Fig. 2 for the various uniformity
a !:ng: nuggct effczt. The nugget variante account d
coefficients. Cabbage yields decreased with increasing
f:)r Zi’Yo of the variancc of exchangeable K. The ran e
nonuniformity of fertilizer application. The spatial
(of spatial dependencc was about 17 m. The range in-
variability of soil properties across the field also sig-
tlicates a zone of influence of a sample and is an s-
nificantly influenced yields. This cari be seen from the
+imatc~ of the minimum distance required for spaci g
differences in yield with no K application.
of inclcpcndent samplcs. Samples farther apart th n
TO quantify the relationship between yield and rates
rhe rznge are cnnsidcred to be independent of l
ea h
of K application the data were fitted to a Mitscherlich
other. Hcgionalized variable theory cari be applied to
mode1
rlugm:nt thc classical approach which assumes t at
= A - Bexp (-CQ)
clcviations about the mcan have a random geograp ic
Y(Q)
il81
distribution. lising the range, the number
1
of samp es
wher: Ytu> = yield (Mg ha-‘), .,l = maximum yield,
rcquircd in Eq. [ 151 cari be de!ermined SO that t ey
B and C are fitted coefficients, and Q = amount of K
are spntially indcpendent.
1
applicd. The amount of K rcquired to attain 95% of
The spherical mode1 weightcd for the number lof
maximum yield was calculated from Eq. [IS] as fol-
pairs in cach lag was ftted to the experimental se i-
lows
x,,ario,;rarn using the SAS noniinear algorithm (Bar et
%
KRqS = (In B - In :1 -- In O.Oj)/C.
1191
al.. 1079) to obtain semivariogram parameters
~
i Il
113
Values of KR,, for the three lcvels of variability were:
y(h) = C,., + C 1 .S- - 0.5- for /r <: n
i,
a
a’ 1
KRVS = 97 kg K ha-’ for UCF = 1.0.
y(h) = CO + C’ for h > a
1(61
KRq5 = 113 kg K ha-’ for UCF = 0.42, and
KR,, = 446 kg K ha-’ for UCF = -0.02.
r\\hcrc (’ - spatial covariance; a = rang of spatial de
n-
.itilce; !I =: lag dislance.
The geostatistical techniqnes employed earlier to
determine rates of fertilizer application indicated that
Yield Response ta Nonuniform Potassium t,
the application of 97 kg K ha-’ would bring 35% of
Application
the deficient area up to the critical level of 0.8 cmol,
ha-‘. If a critical level of 0.5 cmol, ha-i were selected,
Thc uniformity coefficient of fertilizer applicat on
however, 97 kg K ha-i would adjust 70% of the deli-
for c;lch plot was defined as
tient area to the critical. In this mariner the relation-
l
ship of critical level to the proportion of each plot
[JC’F = 1 - 2
I~l 71
below the threshold’can Ix estimated and, in turn, IX
-Q
used to determine rates of K application. (ieostatist-
whcre IJCF is the uniformity coefficient of fertililzcr
ical methods provide relativcly precise estimatcs of K
application, and S and Q arc the standard deviatfon
content;--R~tesof-K-appTicatiorr-can- be-obtained-by-----
NDIAYE & YCIST: FERTILIZER AfWXA7
IN NONLINIFORMITY AND CKOP RESPONSE
1875
1985). Geostatistical techniques described in this pa-
per provide an optimal method to develop such maps
from soi1 sample data.
Predicting Yield frOm Potassium Application
.
and Nonuniformity
Because variation of K application significantly af-
fected yield, and a relationship between yield per unit
area and the application rate was established, it was
useful to develop an expression for yield as a function
of application rate and nonuniformity. Neglecting ge-
netic factors, trop yield cari be assumed to depend on
17 -
both the average rate of K application over the area
24 -
I
I
,
-7
and the spatial deviations from that average (Zaslav-
Il
ZOO
400
M O
sky and Mokady, 1967). The relevant expression is
K Applled, k g h o - ’
(Zaslavsky and Mokady)
--
i
P
4, -
(Q)
%Q>
WI
.
4 ’ 1
UCF - 0.42
where
is the spatial average trop yield, Y,,, is the
y(Q)
5 SS-
/
+
+
yield that would have been obtained with perfectly
uniform application (Q - (2, i.e., no fluctuation in Q),
and
is the spatial variante of fertilizer application
qQ)
(Q), and. is also called the fluctuation index (FI). The
is called the response index (RI),, The
product of FI and RI is the fluctuation response Index
(FRI) and this expresses changes in average yield due
to fluctuations in the level of applied nutrient.
In order to calculate the effects of nonuniformity of
24
K fertilizer application on cabbagé yield Eq. [ 181 was
0
200
400
SO0
K Appllsd, k g h o - ’
substituted into Eq. [20] to obtain
7
- R e x p ( - C Q ) -t- +
T(Q)=A
1211
4s 1
4, -
Rearranging Eq. [17] and substituting for s2 in Eq.
[21] one obtains
SI -
Y(,) = A -
-.
B exp( - CQ)
J7 -
34 -
“+ [ $$ILQc1 - ucn]‘.
SS -
Because yields of cabbage on no-K treatments vaxied
Jl -
due to inherent variability in soi1 properties, the yield-
2 1 -
fertilizer function obtained with UCF - 1.0 could not
be considered as Y,
in Eq. [20]. An estimate of Y
27 -i /
Y
was obtained by poo mg the data from the entire ex-
25 1
1
I
8
periment and fitting Eq. [ 181. Therefore the fitting pa-
0
200
400
400
rameters A, B, and C in Eq. {22] are those estimated
K Applied, k g h o - ’
from the pooled data with A = 39.98, B - 10.17, and
Fig. 2. Relationship between cabbage yield and rates of K applicat
1
C- 0.0172. Using Eq. [22], cabbage yield was pre-
for various levels of uniformity of K fertilizer application.
dicted for UCF values of 1 .O, 0.42, and -0.02 and for
different rates of K application. A plot of predicted
methods described in Eq. [ 131 if the semivariogn
yield against observed yield is shown in Fig. 3. A sig-
of soi1 K is known, and if an adequate number
1
nificant (P < 0.05) correlation coefficient (r) of 0.89
samples are available. Fertilizer rates cari then
was found between observcd and predicted cabbage
based on the proportion of the deficient area belov I
yield.
standard. If the deficient zones are large and cent
Expressing yielti as relative yicld (Y, = ~~c,,/~t, with
uous, they cari be identified and fertilized separau I
A = 39.98), curves of relative yield as a function of
..-
!
Another method of applying fertilizer to nonunifoi 1
the nonuniformity-of fertilizcr application wcre drawn
soils is possible with variable rate fertilizer spreadc ,
in Fig. 4 using Eq. [22]. It cari be seen from this figure
which use maps of nutrient levels as a guide (L.uellt
that the decrease in relative yield with decrease in uni-
_,-_-
.--
1476
NIL Xl. SOC’. AM. J.. ’ )L.. 53. NOV~M~~&DECEMBER 1989
M
>
.-
0
-
-
70 kg/ho
5
a
---. 140 kg/ha
,’
,’
/
-
210 kg/ha
i’
- 6 - ./
-
280 kg/h.
r
- 7 1
4
0.0
0.2
0 . 4
0.0
0.1
1.1
is
Uniformity Coafflclent, UCF
Fig. 5. Calculated relative fluctuation response index (FRI) as a
- 1
function of uniformity coefficient of K fertilizer application for 4
Obsarvod Yisld, tonnea ha
.
.
ratejof K apphcatron.
Fig. 2’. Comparison of predicted and observed cabbage yield.
*
*
ucel.0
A
UCS=O.U
M
27 -
:
?
?????????
????
?
?
? ?
??
?
?
?
? ?
??? ?
?
3.2
3.4
3.6
J.0
4.0
4.2
4.4
4.6
4.9
0.0
0.2
0.4
0.6
0.1
Uniformity Coefficient, UCF
Leaf K Concentration, 9;
Fig. ,t. C’alculated relative yield of cabbage as a function
Fig. 6. Relationship bctween cabbage yield and K in dry matter as
formity coefficient of K fertilizer application for four
afl’ccted by uniformity of K application.
apt>licalion.
zone volume, such as plant species, population den-
formity coefficient was most pronounced at app ica-
sity and row width, Will probably influence the size of
tion rates 5140 kg K ha-‘. This is also shown in 1 Fig.
area that is sufflcicntly nonuniform to affect yields.
5 b> the relationship between relative fluctuatiod re-
Increasing the uniformity of fertilizer application in
sponse index and uniformity coefficient. These ‘cal-
ordcr to improvc trop yield must be viewed critically.
culations showed that the decrease in relative
RI
Under certain conditions ensuring uniform fertilizer
witP increase in UCF was much steeper for lower r tes
application may be expensive without commensurate
of fi:rtilizer application.
1
increase in yield. Under other conditions, however,
There are some limitations on the use of data f om
yield may be greatly increased through uniforrn ap-
experiments which measure trop response to no un-
plication of fertilizer.
.
iform application of fertilizers. If areas of non ni-
formity are sufficiently small, the nonuniformity
ay
Yield-Tissue Potassium Concentration Relationship
not be important because individual plants may i
raw
nutrients from areas receiving both high and low dates
as Affected by Nonuniformity of Potassium
Application
of fcrtilizer. In this way, individual plants
age nonuniformity in fertilizer application rate.
The relationship between yield and K concentration
information is available on the minimum area
in cabbage leaf is shown in Fig. 6a, b, and c for UCF
which nonuniformity of application should
values of 1.0, 0.42 and -0.02, respectively. The re-
ereçl. Prummel and Datema (1962)
sults are in agreement with the general relationships
ineclualities in rate of application
reported in the literature between plant nutrient status
when the areas of fertilizcd and unfcrtilized
and trop performance (Dow and Roberts, 1982).
. _ . . -__-
tlon were greater than 0.5 m. Factors which
~oowever;-1-he~-scattering~‘of points along each curvë .‘_
.
l
--__-
-
._.
‘--
4 NONIINIFORMITY
AND C‘ROP RESPONSE
1877
Cabbage Yield as Affected by Spatial Variability
of Soil Potassium
-t
1.0 -
*
*
D.0
The effectivqness of a soi1 K test is usually measured
*
cv = 44.1% LC
by its accuracy in predictipg trop response to applied
-ü
+
-6
K. The goal of such a têst is to.measure the quantlty
‘Y
*
of plant-available K. and. therefore the test is nega-
<D.z
tively related to responsiveness and amount of K re-
ôz
quired to make up the deficit. Figures 7a, b, and c
ûi
show the relationship between relative yield and
exchangeable K for various coefficient of variation
(CV) of soi1 K. The general form of the relationship
was
1 ,
,
(
(
,
,
,
,
Y=a$bx
[231
0
0.2
0.4
0.6
0.6
1.0
1.2
-i-
1.
E x c h o n g a a b l e K. cmolc kg-’
where Y = relative yield, x = exchangeable K, and a
and h are constants. The levcl of exchangeable K as-
+-
sociatd with 90% maximum relative yield incrcascd
with increasing CV: 0.28 cmol, ha-’ for CV - 44.1%.
0.31 crnol, ha-’ for 67 =- 67.0%, and 0.73 cmol, ha-’
for CV = 96.6%. A critical level of 0.28 cmol, ha-’ is
suggested by Boyer (1972) for tropical agriculture.
Thc range in nonuniformity in this study is within
the ranges of nonuniformity reported in several stud-
ies. A CV value of 44.1% is consistent witli values
reported by Beckett and Webster (197 l), and Courtin
et al. ( 1983). However, Trangmar (1984) found a CV
value of 105% in a study area of about 0.1 ha in Si-
tiung, Indonesia. He attributed this high heterogeneity
to differences between burn sites, areas of exposed
subsoil, and intermediate areas of surrounding soil.
0
,
1
,
,
,
0.2
0 . 4
I
0.6
a.,
0.8
,
1.0
.
.
1.2
,
1:4
The results obtained in this study suggest that an av-
Excharrgoabls
K , cmol, kg-’
erage soi1 K test value may be misleading if the spatial
variability K is not considered.
1.0 -
*
6’
6’
* *
CONCLUSIONS
CY = 96.6X
0:f
0.9
*
The response of chinese cabbage to K application
was strongly dependent on the uniformity of fertilizer
F
distribution. Different maximum yields were obtained
‘-0 0.6
with different levels of nonuniformity of K. With a
<L?L
uniformity coefficient of -0.02, the K requirement
0.7 -
was four times greater than that for more uniform
conditions.
The decrease in yield due to nonuniform applica-
0.6 -
tion of fertilizer was quantitatively described by the
fluctuation response index., The fluctuation response
0.3
0.3!‘,
,
index value decreased with increasing rates of K ap-
0
0.2
0.4
0.6
0.1
1.0
1.2
1.4
plicaiion suggesting that at higher rates of application
E x c h a n g e a b l s K , cmolc k g - ’
the areal uniformity of fertilizer application became a
Fig. 7. Relationship between relative yield of cabbage and excha
less important influence on overall yield.
ge-
ahlrb K as at7ected by spatial variability of soi1 K.
The geostatistical approach used to determine rates
of K fertilizer is a promising technique for determin-
indicates thc difficulty of
ing fertilizer quantities needed to adjust fertility to a
centage as the critical
given critical levef and for estimating the statistical
Graphical determination
distribution of nutrient in trop fields. Variable rates
max:mum yield gave 3.6, 3.
of fcrtilization cari be applied if deficient zones have
values of 1 .O, 4.2, and -0.02
been identified in the field. The level of exchangeable
less the variation about the
K associated with 90% of maximum relative yield in-
the contention that a narra
creased from 0.28 cmol, ha-l for a CV of 44.1% to
rathcr than a sirrgle valuc seemsmore a
0.73 cmol,.h.a-.l_for.a.CV.of 96.6%~.The.results.suggest ..___ _-
evaluating nutrient status of crops (Dow an
that an average soi1 K test value may be misleading
1082 ).
if the spatial variability of soi1 K is not considered.
_. . .
SOIL SC’I. SOC‘. AM. J.. $0~. 53. NOvEMBER-DECEMHER 1989
REFERENCES
Haan, C.T. 1977. Staristical methods in hydrology. The Iowa Slatc
Univ. Press, Ames.
Harr. A.J.. J.tI. Goodnighr. J.P. Sall. W.H. Blair, and D.H. C iko.
IkgWa. H., H.H. .%ro. A.K.S. Chavg, S. Nakamura, E. Robellor, Jr.,
l WC). SAS user’!, guidc 1979 cdiiion. SAS Insl.. Inc.. Raleigh NC.
an<j S.P. Periaswamy. 198s. So~ls of rhe Hawall Agrlcultural Ex-
tIcck:Ii. P.1V.T.. and R. Wcbslcr. 197 1. Soil vnriahiliiy: A re;1. ICW.
periment Station, University of Hawaii: Soi1 ,survey ,laboratory
Sht Fert. 31:1-15.
dala. and soi1 description. Bcnchmark Soils ProJect Tech.
Bovcr. J. 1972. Soi1 ootassium. D. 102-135. I~I Soi)s
1
of the h mld
Report 4.
Luellen, W.R. 1985. Fine-tuncd fcrtilily. Tomorrow’s technolopy
(‘ourun, P.. M.C. Felier, and K. Klinka. 1983. Lateral variabil ty in
M:;;;“a& Corp .Solls !8: 18-22.
%)~ne propcrties of drsturhcd forest soils in Southwestern B itish
1955 Apphcallon des methodcs statistiques rleval-
Cclumbia. Can. J. Soi1 Sci. 63:529-539.
ualion ces &ements. Ann. Mines 7:50-75.
David. M. 1977. Geostatistical ore rescrve estimation. Elsevie Sci.
!
Prummei J., and P. Datema. 1962. The evenntss of distribution
Puhl. CO.
by fertilizer distributors and its effects on trop yield. Land-
Dow. A.].. and S. Robens. 1982. Proposa[: Critical nutrient r nges
bouwmechanisatia 13:742.
fol, trop diagnosis. Agron. J. 74:401-403.
Trangmar, B.B. 1984. Spatial variability of soi1 properties in Sitiung,
Froideveaux. R. 1982. Gcostatistics and ore reserve classifie tion.
West Sumatra, Indonesia. Ph.D. diss. Univ. of Hawaii, Manoa.
CIM Bulletin. 75:77-83.
l
Yost, R., B.B. Trangmar, and J.P. Ndiayc. 1986. Geostatisticrl com-
Green. T.L., C. Eng.. and E.A. Mech. 1968. Achieving the
isrri-
putation software for microcomputcrs. 1. Scmivariograms. Rc-
hution requiremcnts of solid fertilizers. J. Proc. Inst. Agric. Eng.
search
Extension Scrics 074, College
of Tropical Agric, rnd Hu-
?3:125-137.
p
man Rcsour.,
Univ. of Hawaii.
l
Optimum Application Parameters f@ Point Injection of Nitrogen in Winter Wheat
a
H. H. Jan en* and C. W. Lindwall
ABSTRACT
doway, 1977; Christeison and Meints, 1982; Fowler,
1982). The efficiency of top-dressed N, however, may
Prtint injection may enhance N fertilizer use efficiency in
inter
be limited by volatile losses (Keller and Mengel, 1986;
McInnes et al., 1986), biological immobiiization in
surface residues (Fredrickson et al., 1982; Sharpe et
al., 1988), and inaccessibility to wheat roots in dry soi1
conditions (Harapiak et al., 1986).
An approach which may circumvent some limita-
tions of conventional application methods for winter
wheat is point injection of fluid N fertilizer, a method
developed for fcrtilization of row crops (Baker et al.,
1983). If adapted for winter wheat production, this
method could facilitate effective N placement in
spring without appreciable disturbance of the growing
trop and thereby increase fertilizer use efficiency.
Other potential advantages of this proposed method
from 40 tu 60 cm. Adoption of smaller injection intervals i
include compatibility with conservation tillage sys-
dimensions,
while not jeopardizing fertilizer use efficiency,
tems because of minimal soi1 disruption, and reduced
energy consumption because of ver-y low draft require-
deptb was observed to be approximately 10 cm. Grnitn yield res~ponse
ments relative to conventional banding methods.
and fertilizer N recovery in the trop increased four- and thre
The first step in the effective exploitation of point
rcspectively, when injection depth was increased from 2.5 to
injection for the enhancement of fertilizer use effi-
I’hi!; effect was attributed to the inaccessibility of fertilizer N
ciency in winter wheat is the identification of opti-
ing in dry surface soil. Injection of fcrtilizer at tS cm rathe
10 cm demonstrated no additionnl ndvantnge.
mum application parameters. Two of the most im-
portant variables are the geometrical spacing of
injection points and the depth of injection. Optimi-
zation of these variables is prerequisite to the mean-
ingful comparison of pain; injection with conven-
tional application methods.
The objective of this study, thercfore, was to deter-
mine the optimum spatial arrangement and injection
depths for point injection of N in wintcr wheat. This
objective was addressed under field conditions using
15N tracer techniques to quantify N distribution from
injection points and determine fertilizer uptake cfli-
ciency as a function of injection interval and depth.
MATERIAU AND METHODS
Kçcri\\ed 7 Scpl. 1988. ‘Corresponding
author.
.-.Three. fielb.experiments.werc conducted.In..south~n.AL- ---.- -. - -
I’ubllçhcd in fioil Sci. Soc. Am. J. 53: 1878-1883 (1989).
berta, Canada, during 1985 and 1986 to determine distri-