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Agricultural Systems 63 (2000) 123±140
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Dynamics of spatial variability of millet
growth and yields at three sites in Niger, West
Africa and implications for precision
agriculture research
M. Gandah a,b,*, A. Stein b, J. Brouwer c, J. Bouma b
a
INRAN, B.P. 429, Niamey, Niger
Department of Environmental Sciences, Wageningen University, PO Box 37, NL-6700 AA Wageningen,
Netherlands
c
Wildekamp 32, 6721 JD Bennekom, Netherlands

b

Received 29 January 1999; received in revised form 25 November 1999; accepted 13 December 1999

Abstract
This paper focuses on possibilities for using a simple scoring technique to make estimates of

millet yield. Estimates are intended to be used for de®ning application rates of manure in the
context of low-tech precision agriculture. Yields from 1995 and 1996 at three locations were
related to scoring, soil data and elevation. Kriging was used to interpolate point data to areas.
Several procedures for pattern comparison were applied. Because scoring data were available
at a much higher density than yield data a sensitivity analysis was made to compare scoring
and yield. Correlations between scoring and yield ranged from 0.42 to 0.91. During a separate
experiment the optimal time for scoring turned out to be approximately 3 months after seeding for the local varieties of 120 days, but 2 months is convenient for farmers to locally apply
chemical fertilizer. R2 values ranging from 0.15 to 0.60 were observed for soil data and yield,
subject to local conditions and changes in weather. We conclude that scoring is a cheap and
reliable procedure to identify ®eld patterns which can form the basis for precision agriculture.
# 2000 Elsevier Science Ltd. All rights reserved.
Keywords: Spatial variability; West Africa; Precision agriculture

* Corresponding author.
0308-521X/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S0308-521X(99)00076-1

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M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

1. Introduction
Crop production in the semi-arid tropics of West Africa, also called the Sahel,
depends upon highly variable weather and soil conditions. At the beginning of the
planting season, distribution of rainfall and its amounts are irregular. Millet is
the major cereal crop for the region with a production zone that is increasingly
moving to drier areas, normally used as pasture land (McIntire et al., 1989; FAO,
1996). Soils have been cropped for decades without a proper nutrient renewal,
leading to nutrient mining and poor land. Consequently, high variability of crop
growth and yield within ®elds is typical in these production systems. In the past 10
years, researchers have studied variability to identify its causes in experimental plots
and in farmer's ®elds (Mutsaers et al., 1986). Almekinders et al. (1995) used the term
agrodiversity for variation in agro-systems as a result of abiotic environmental variation, biotic environmental variation, and interaction between the two.
In this study we distinguish between within ®eld variation and variation between
®elds. Variation within ®elds in plant growth occurs at a scale varying from 1 or 2
meters to tens of meters. The processes by which yield variability occurs are
observed as soon as seedlings emerge. Sand blasting and burial of young seedlings
are responsible for high levels of variability in early millet stands (Gaze, 1996). To
protect against sand movement, Klaij (1994) proposed a technique of ridging. This
improved crop stands, but required additional labor and tools. Buerkert et al.

(1995) observed 18% higher soil mechanical resistance in low productivity areas
compared to high productivity areas. Later in the season, chemical and physical soil
factors including soil moisture may cause large within-®eld yield variation, singly or
jointly. In ®elds in western Niger, variation coecients of yields may exceed 50%,
and poor correlations between soil properties and grain yields have been found
(Brouwer and Bouma 1997; Gandah et al., 1998). Wendt (1986), on the other hand,
on similar soils in western Niger, found that poor millet growth correlated well with
pH values below 5 and with aluminum and hydrogen saturation rates of the
exchange complex above 45%. With low bu€ering capacity and low nutrient content of these soils, a small change in soil nutrient status can thus cause large changes
in plant growth.
Variation between ®elds and, at a higher scale, between geomorphological units
can be caused by moisture redistribution and di€erences in chemical fertility as well
as by variation in management by di€erent farmers (Wilding and Daniels, 1989).
In recent studies we observed that crop growth patterns correlate well with soil
properties patterns, but this relation was not linear and di€ered between years (Stein
et al., 1997). These patterns, though, are available only after harvest, whereas in
precision agriculture a preliminary yield estimate may target application of scarce
manure and fertilizer. Yield patterns, however, may vary during successive years
whereas for farming practices it is important to know at an early stage the amount
and pattern of yield that a farmer may expect. For that reason, attention recently

focused on scoring (Buerkert, 1997). Scoring patterns are easily obtained on an
individual hill basis during the growing season. In this study, geostatistical upscaling relates these to soil and yield patterns.

M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

125

The objective of this study was: (1) to characterize variability in crop growth
(expressed by measured hill scores), yield (grain) and soil characteristics within and
between three sites in Niger; and (2) to explore implications for precision agriculture. We focused on two successive years (1995 and 1996) to have an impression
of changes in variation between various years caused by varying environmental and
®eld conditions. In a separate experiment we analyzed the optimal time for scoring.
These served, therefore, to evaluate the eciency of scoring as a tool to predict the
stability of poor crop growth areas for use in precision agriculture practices among
years.

2. Materials and methods
2.1. Experimental sites and sampling procedures
During the rainy seasons of 1995 and 1996, experimental ®elds at research stations in Ouallam, Sadore and Tara were selected in western Niger and planted with
millet (Pennisetum americanum). The three sites are located in a north/south gradient which also represents a rainfall gradient from dry to wet. At Ouallam, two

®elds of 2275 and 2700 m2 were selected, whereas ®eld sizes were 6750 m2 at SadoreÂ
and 2125 m2 at Tara, respectively. To evaluate time of scoring, a further test site
was selected at Tchigo Tagui where we selected 20 on-farm ®elds with sizes ranging
from 1 to 10 ha. Plots with a size of 55 m were laid out inside the ®elds, without
dividing alleys, yielding 91 and 108 plots of 55 m at the two Ouallam ®elds, 270 at
Sadore and 85 at Tara, respectively. At each site, the local millet variety adapted to
the local soil type was planted. Planting density was 11m (25 hills per plot) and
stands were thinned to three plants per hill during the ®rst weeding. Field sites and
management activities at each site have been described elsewhere (Gandah et al.,
1998). At Tchigo Tagui, three plots with a size of 1010 m were laid in each ®eld.
Scoring was done 30, 64 and 91 days after sowing (DAS). Planting was in rows and
without a uniform distance between rows and between hills as is common in farmers' ®elds. Millet was harvested manually at maturity. Millet heads from each plot
were air dried during 2 weeks before threshing and residual millet straw was harvested and dried in the ®eld during 2±3 weeks before weighing. Final weight was
obtained by correcting for moisture, using oven-dried samples. Grain yield, number
of hills, number of harvested heads and head yield per plot were measured. No
fertilizer or organic matter was applied nor was there any land preparation other
than the removal of shrubs and old millet plants from the previous crop to comply
with local practices restricted by inputs. At Tara, by tradition, farmers plow their
land before planting as the soil is more structured and the longer season favors this
practice. In this experiment, the ®eld was not plowed during both years to allow a

better comparison among the sites. When necessary, weeding was done manually
with a hoe.
To study the relation between measured plant data and soil properties, a soil survey was done in each ®eld after harvest in 1995 using a 0.08-m-diameter auger.

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M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

Sampling depths of 0±0.1, 0.1±0.2, and 0.2±0.4 m were chosen according to millet
rooting patterns as 80±90% of roots occur within these depths, although roots occur
as well beyond 1.50 m. Moreover, changes in the amount of soil nutrients predominantly occur in the upper 0.4 m soil layer (Bationo, personal communication,
1997). Finally, the top layer explains most of the soil chemical in¯uence on millet
yield (Geiger et al., 1992; Hafner, 1992). Soils at all three sites are classi®ed as
psammentic paleustalfs (Anonymous, 1994).
Soil samples were taken at 1010-m grid nodes, and in addition at the center of a
limited number of the plots. At SadoreÂ, for example, 63 samples were taken at grid
nodes and 20 samples were taken at the center of 20 plots (Fig. 1). In total, more
than 600 soil samples were analyzed for pH, e€ective cation exchange capacity

Fig. 1. The plot layout at SadoreÂ, showing soil samples at the 1010-m grid and delineated 55-m plots

for yield measurements.

M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

127

(ECEC) (calcium, magnesium, sodium, potassium, aluminum, hydrogen), available
phosphorus (PBray1), organic matter and texture, according to the standard procedures used at ICRISAT Sahelian Center (Van Reeuwijk, 1992).
Old shrub sites, termite mounds and waterlogged areas were identi®ed in the
®elds and mapped (Fig. 1). We took elevation readings with a level at the four
corners of each 55-m plot to obtain detrended elevation that characterizes microtopography. We identi®ed plots with water ponding for a few hours after heavy
rains.
Daily rainfall was recorded at all three sites. Rainfall did not follow the north±
south gradient, as Ouallam received more rain than Sadore over fewer wet days.
Tara, in the south had the highest rainfall for both years and the highest number of
wet days in 1996.
2.2. Scoring
Scoring is a simple, `low-tech' method used in this study to measure spatial
variability in crop growth during the growing season. Scoring is based on the
observation that, at a given time, the millet hills present various development stages

due to the reaction of the plant to its environment and to the variability in that
environment (soil, climate, pests, human action). In a uniformly planted ®eld without any fertility management practices, development of crop will mainly be in¯uenced by soil and climate. The latter is considered to be uniform over ®elds of the
size used in this experiment (Sivakumar et al., 1993). With this hypothesis and no
observed pest damage, variability in millet growth should then be explained by variation in soil physical and chemical characteristics and by topography.
Scoring is done by touring each ®eld and visually evaluating the development of
millet hills or hills vigor (Buerkert et al., 1995). A scale of hill vigor is set, being an
estimate of the above-ground development on the basis of a combination of plant
height and biomass. Scoring assigns class values to performance of plants in individual hills. Classes of hill development have been identi®ed with an increasing step
size ranging from 0 (no millet plant present) to 8 (best millet hill in the ®eld).
Reference hills are tagged to allow comparison during scoring. The same scale has
been used at all sites, although a score of 8 at Tara in 1995, for example, corresponds to a higher hill development than the same score at Ouallam. Collected data
are geo-referenced by x- and y-coordinates of each hill. Hill scoring in 1996 was
done at about the same number of days after sowing as in 1995 at all sites. At
Tchigo Tagui, scoring was done similarly as in the other three sites, but at three
dates: 3±5 July, 7±8 August, and 3±4 September 1997.
2.3. Scales of observation
Multi-scale measurements of ®eld variability allow to consider a range of
exploratory factors. Choice for any scale is based upon simplicity of measurement,
labor and ®nancial cost. In this study, scales of measurement vary from individual
hill, via plot and aggregated plots, to entire ®elds. Easily obtained data such as

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M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

scoring were measured at a ®ne scale (11 m). Yields were measured at the plot
scale (55 m) to save labor costs. Soil was sampled at the aggregated plot scale
(1010 m) to limit costs for sample analysis. The plot scale served as the matching
scale between yield and scoring, where we used the median scoring value observed
within the plot to make comparisons. The aggregated plot scale served for a comparison between yield and soil patterns, yield data were upscaled to this scale using
block-kriging (Cressie, 1993).
2.4. Pattern comparison
We applied various procedures to quantitatively compare observed yield patterns
with scoring data and with measured soil properties.
1. A global analysis by means of summary statistics and stepwise regression
related millet grain yield with measured soil properties and scoring. The statistical package SPSS version 7.5 (Anonymous, 1988) was used for the statistical analyses.
2. The taxonomic distance method (Davis, 1986) relates patterns of grain yield
with median scores. For this method data are interpolated with ordinary kriging towards a 4052 grid (Van U€elen et al., 1997). The taxonomic distance
method compares standardized values
z;xy ˆ

v;xy ÿ v
;
s

…1†

at the nodes of a grid mesh where v and s are mean and standard deviation
of the original values in pattern p. Corresponding pattern portions are viewed
by a window of a ®xed size. An optimal window size of 25 nodes was determined in this study and has been used at each of the three sites.
Next, a polynomial function is ®tted within the windows to each of the two
patterns. A third-degree polynomial is sucient to detect the most important
changes (Van U€elen et al., 1997) and has the form:
z ˆ b;0 ‡ b;1  x ‡ b;2  y ‡ b;3  x2 ‡ b;4  y2 ‡ b;5  y ‡ b;6
 x3 ‡ b;7  y3 ‡ b;8  x2 y ‡ b;9  xy2 :

…2†

Coecients b,0 to b,9 are obtained by a least square regression ®t. Two sets of
coecients for two patterns are compared by way of the taxonomic distance d

(Davis, 1986) de®ned as:
v
u pÿ1 ÿ


uX b1;i ÿ b2;i 2
t
;
dˆ
p
iˆ0

…3†

M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

129

where p is the number of polynomials (p=10) and leading indices (1 and 2)
denote the two compared patterns. The result is stored as similarities between
the two patterns, and the window is moved to a new position while keeping
points from the former windows (20 points out of 25).
A weighted equivalent applies a weight to the taxonomic distance with wi
equal to the range along the z-axis of the polynomial term i (Verhagen, 1997):

v
 ÿ
u

2 
uX
pÿ1 wi b1;i ÿ b2;i
u
dw ˆ u
u
pÿ1
P
t iˆ0
wi

…4†

iÿ0

Taxonomic distance maps are drawn to show similarities and dissimilarities
between yield and scoring maps.
3. Cross-correlograms were used to analyze lagged patterns, i.e. to compare shift
in patterns (Stein et al., 1997). The cross-correlogram between two patterns i
and j is de®ned as:
Cij …h†
ij …h† ˆ q 2 ‰ÿ1; ‡1Š;
i2ÿh  j2‡h

…5†

where Cij(h) is the covariance function (Cressie, 1993) and s2iÿh and s2j+h are the
variance of the ith and the jth variable, respectively, for those points involved
in calculating Cij(h).
From the patterns obtained for the numerous soil and plant data (all soil
chemical and physical characteristics, plant grain yields, scores and microtopography), only those identi®ed in step (1) were considered in the crosscorrelation analysis. For the yieldsoil cross-correlation functions, a 95%
con®dence interval was determined using tabulated values for the correlation
coecient.
2.5. Sensitivity analysis
A sensitivity analysis of modeling the relation between scoring and yield was
done by calculating the plot speci®c mean mP and the standard deviation sP of
the 25 scoring measurements. A random, plot-speci®c value was drawn from
the normal distribution with parameters mP and sP. This was done for all
plots. With values thus obtained, the cross-correlation function was re-calculated. The procedure of drawing random values and re-estimating the crosscorrelation function was repeated 200 times. At each lag distance the interval
between the third and the 197th cross-correlation value served as the 95%
con®dence interval.

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M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

3. Results and discussion
3.1. Descriptive statistics
Descriptive statistics are given in Table 1. As concerns notation we will use standard chemical symbols, and abbreviations Csa (for coarse sand) and Clay (for clay
content). Grain yields are followed by the year of harvest and Elev denotes elevation. Mean yields were low at all sites for both years, except at Tara in 1996 where
531 kg haÿ1 was harvested. This was probably caused by a nutrient release as the
®eld was fallowed prior to 1995. Average yield at Ouallam remained below
the threshold level of 250 kg haÿ1 during both years, indicating the marginal state of
this site for agriculture. Standard deviations were in general lower at Ouallam than
at the two other sites for both years. This site, therefore, has low and stable yields.
An example of the scoring data is given in Fig. 2, showing clear variability, but
some pattern as well. For example, the termite mound at the center left of Fig. 1
appears as a low scoring sub-area in Fig. 1. Scores for 1995 had a distribution close to
normal at Ouallam, Sadore and Tara and for 1996 at Sadore and Tara. Score distribution in 1996 at Ouallam was skewed to the right distribution in 1996 (Table 1).
This di€erence between the two years may have resulted from the rainfall amounts
received in July and August, with 1995 showing a relatively good rainfall distribution
over time, producing more uniform crop growth and subsequent grain yields.
Results of a stepwise regression of soil factors and detrended elevation are given in
Table 2 for the three sites. At Ouallam, the most important explanatory variables
for both ®elds combined are pH40, Al40, H20, Na40, and Mg40 in 1995. In 1996, the
variables included in the model were K10, Al10 and the texture properties Csa20 and
Table 1
Statistics of grain yields and scoring in 1995 and 1996 at the three experiment sitesa
Sites

Grain yield (kg haÿ1)




Score values

Correlation yield x
mean score r

Skew





Skew

Ouallam
Field 1
Field 2

1995

109
125

72
80

0.90
1.15

4.6
4.9

2.05
2.05

ÿ0.61
ÿ0.78

Ouallam
Field 1
Field 2

1996

141
83

133
111

0.98
1.96

1.7
1.1

1.92
1.63

0.93
1.71

0.91
0.87

SadoreÂ

1995
1996

379
301

208
177

1.11
1.1

2.9
2.5

1.78
1.52

0.44
0.59

0.89
0.88

Tara

1995

332

177

0.59

2.6

2.26

0.41

0.44

Tara

1996

531

197

0.9

4.7

1.50

ÿ0.53

0.42

a

, Mean; , standard deviation; Skew, skewness.

ÿ0.013
0.51

M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

131

Fig. 2. Individual scoring observations at SadoreÂ, 1995.

Clay40. In SadoreÂ, the explanatory variables with the highest signi®cance were Al10,
Elev, and Clay10 in 1995, and the chemical variables Al10, K40, Mg40 and P20 in
1996. At Tara, no explanatory variable was included in the model at the 10% level
for 1995 although the site was under fallow for 4 years, whereas in 1996, it included
P20. These di€erences could be due to di€erent tillage management practices applied
in Tara.
As in previous studies, the coecient of determination (R2) is about 30±40%,
except at Ouallam, ®eld 1 (Table 2). The soil factors included in the models vary
between years, but Al, H, pH are more common to both years. Correlation between
yield and mean score for the two years is from 0.01 and 0.91 (Table 2) with the best
relationship for years with poor yields.
The range of micro-elevation was divided into ®ve classes at SadoreÂ. Signi®cance
testing using a standard t-test shows clear di€erences in yields between elevation
class 1 and classes 2±5, and also between classes 2±3 and class 5. No signi®cance

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M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

Table 2
Regression of millet yields and soil chemical and physical factors at Ouallam, Sadore and Tara
Sites
Ouallam

Field 1

Field 2

SadoreÂ

Tara

Regression equationa

Signi®cance

Coecient

Grain95 = 685.4 ÿ 99.1pH40 ÿ 473
H20 + 1556Mg40
Grain96 = 614.8 ÿ 47
Clay40 ÿ 4972K10
Grain95 = 284 ÿ 4159
Na40 ÿ 212Al40
Grain96 = ÿ66.8 ÿ 6.6
Csa20 ÿ 164Al10
Grain95 = 394 ÿ 509Al10 + 279
Elev + 14Clay10
Grain96 = 456 ÿ 488Al10 ÿ62
P20 + 1653K40 ÿ 632Mg40
Grain95 = no relationship obtained
with variables used
Grain96 = 360 +820P20

p=0.01

R2=0.49

p=0.01

R2=0.60

p=0.04

R2=0.43

p=0.04

R2=0.46

p=0.03

R2=0.33

p=0.00

R2=0.35

p=0.04

R2=0.15

a
Elev, detrended elevation; pH, soil pH; Csa, coarse sand. Subscripts: 10=0±0.1 m;, 20=0.1±0.2 m;
40=0.2±0.4 m below the soil surface; 95 and 96=1995 and 1996, respectively.

occurs between classes 2, 3 and 4, and class 4 is intermediate between classes 2, 3 and
5 (Table 3). This indicates that at SadoreÂ, a di€erence in elevation of 1.2 m causes a
signi®cant yield di€erence. This also applies between less di€erent elevation classes,
such as between classes 2, 3 and 5. Ponding of water on plots also has an e€ect on
grain yield (Table 3). Yield at ponded plots reduced with 50%.
Best hill scoring times were tested at Tchigo Tagui (Table 4). Variability of hill
scores is expressed as coecient of variation (CV), correlation coecient and R2. An
increase in variability with time occurs, as plants grow with more variation between
hills. The relationship between grain yield and mean score expressed by the correlation coecient indicates that the third scoring date is the best time of scoring
because at this time the highest R2 value is observed. Implications for precision
farming could vary according to objectives:
Table 3
Grains yields as a function of elevation classes and observed water logging at SadoreÂ
Elevation (m)/moisture status

Elevation class

Grain yield (1995 and 1996)
(kg haÿ1)a

>240.30
239.90±240.30
239.50±239.90
239.10±239.50
238.70±239.10
No ponding
Ponding

1
2
3
4
5

965.9 a
427.38 b
405.4 b
328.31 bc
202.81 c
356.90 a
182.30 b

a

Mean grain yields followed by the same letter are not signi®cantly di€erent at 5% signi®cance level.

M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

133

Table 4
Coecient of variation of millet hill scores in 60 plots at Tchigo Taguia
Level of scoring

DAS

CV (%)

Correlation coecient,
between grain yield and mean score

R2

First scoring
Second scoring
Third scoring

30
64
91

36.2
51.5
44.27

0.35
0.50
0.73

0.12
0.25
0.54

a

DAS, days after sowing; CV, coecient of variation.

1. the second date of scoring (64 DAS) best supports decision making for application of corrective treatments during the season (e.g. chemical fertilizer); and
2. the third scoring date (91 DAS) best predicts grain yields and obtains the best
®eld information to apply corrective measure the following cropping season.
Both conclusions are based on a single data set, and are tentative and approximate
only.
3.2. Taxonomic distance
Taxonomic distance maps comparing grain yields and median score are plotted
(Fig. 3a±h). Dark shading shows the ®eld areas with a good pattern similarity
between yield and score. The percentage of ®eld area with similar patterns is given in
Table 5. The procedure slightly overestimates the similar patterns, as there is a band
around the edges always identi®ed as similar due to edge e€ects. Highest percentage
of similarity occurs at SadoreÂ. A similar concordance of yield and score is illustrated
in Fig. 4a±h where high yields correspond with high scores.
3.3. Cross-correlation
Cross-correlation analysis of grain yield with soil factors and detrended elevation
are presented in Fig. 5a±g. Clear di€erences emerge between the di€erent plots.
At Ouallam, a negative correlation between grain95 with pH40 (and H20) in ®eld 1
was signi®cant only at very small distances, whereas a positive correlation with Mg40
was signi®cant up to approximately 20 m. In 1996, Clay40 was signi®cantly correlated with grain up to 20 m. This strong relation with clay is not observed at SadoreÂ
under similar weather conditions. It could be a major determining factor in yield
variation with implications for precision agriculture. Also, di€erences occur as a
consequence to di€erences in rainfall distribution during the critical months of July
and August. In ®eld 2, 1995, a signi®cant negative correlation between grain and
Na40 exists for distances up to 21 m. Notice as well the negative, but not signi®cant, correlation with Al40. In 1996, however, Al10 shows a signi®cant positive correlation at shorter distances with grain yield. Although it cannot be explained on
soil chemical considerations, rainfall possibly was the most limiting factor. Any
management practice related to Al of the soil should, therefore, be subject to the
occurring weather conditions.

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M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

Fig. 3. Taxonomic distance maps of grain yield and score at Ouallam, SadoreÂ, and Tara.

At SadoreÂ, grain95 is spatially correlated at distances up to 15 m with both Elev
and with Al10, although correlation is positive with Elev and negative with Al10. This
emphasizes the high Al values in low areas in the ®eld. A deviating correlation
occurs for Clay10, showing signi®cance beyond 10 m. Both could have been caused
by erosion as described previously, where the highest yields are obtained at some
distance from places with high clay contents, due to local crusting (Stein et al.,

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M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

Table 5
Summary of taxonomic distance maps: percentage of ®eld area with good correlation between yield and
scores
Sites

Field area covered by similar patterns (in %)
1995

1996

57
54

56
57.2

SadoreÂ

65

63.5

Tara

56.4

56.2

Ouallam

Field 1
Field 2

1997). Further, grain96 is highly correlated for short distances (up to 10±15 m)
with both K40 and Al10 (negatively) and with K40 (positively). Also, a signi®cant
cross-correlation with Mg40 exists, but for distances up to 10 m. Di€erences in distribution of rainfall probably have caused these di€erences in variables. A selection
of chemical variables is much more important in conditions of frequent rain (1996).
As in previous studies (Stein et al., 1997), the importance of erosion in explaining
grain yield variation in this area is important in 1995, whereas in 1996 no such e€ect
appears to exist.
For the southern site Tara, the single soil element well correlated with grain yield
was, in 1996, P20. It is successively positive and negative at various distances but
never signi®cantly di€erent from zero. The variation is, therefore, still too erratic,
possibly due to tillage practices to show any spatial structure and the ®eld may need
to be cropped for some years to develop some type of distinct pattern.
3.4. Sensitivity analysis
The sensitivity analysis of the scoring method produced plots of the cross-correlation between grain yield and mean score for all three sites and two years. The 95%
con®dence interval of the 200 random sample plots and the actual data are indicated
in Fig. 6a±h. In Ouallam, ®eld 1, cross-correlation ®ts within the con®dence interval
and decreases with distance, with no correlation beyond 20 m in 1995. In 1996, the
same declining trend with distance is observed, but with much less variability. In
®eld 2, cross-correlation is very broad at shorter distances, and decreases to zero at
about 15 m. At SadoreÂ, the two years had a similar trend of a good correlation over
a short distance, with no correlation for distances exceeding 15 m. For Tara, there is
a high degree of scattering at short distances in both years, although the shapes are
di€erent for the two years.

4. Conclusions
From this study, we conclude that soil variables correlate di€erently with millet
grain yield depending upon site and year. Soil pH, H and Al, basic indicators of soil

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M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

Fig. 4. Yield and scoring maps for Ouallam, SadoreÂ, and Tara.

M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

137

Fig. 5. Cross-correlation between grain yield and soil factors at the three study sites. Dashed lines are
95% con®dence limits obtained by standard intervals for the correlation coecient. Distance scaling is in
meters.

acidity, are all included in the regression models at Ouallam and Sadore during both
years. For the southern Tara site, P was the single nutrient well correlated with yield.
Micro-topography was important in the ®nal yield at Sadore where it caused 50%
yield decrease due to water ponding. Patterns of ponded areas vary from 50 to 150
m2 which represent units large enough for precision agriculture treatments. For
research, this information is also useful in deciding the layout of experimental
plots. Cross-correlation between soil and topography variables usually extends to

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M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

Fig. 6. Cross-correlation between scoring and yield. Dashed lines are 95% con®dence limits obtained by
resampling of the original scoring data, indicating spatial con®dence of the curves. Distance scaling is in meters.

distances up to 10±15 m. This value may, therefore, serve as a guidance for di€erences in management: uniform inorganic nutrients and manure amounts may apply
to areas of this size, whereas modi®cations may be necessary beyond such distances.

M. Gandah et al. / Agricultural Systems 63 (2000) 123±140

139

The 60 DAS scoring time, with a correlation between score and yield of 0.5, can be
used as the best time to perform precision farming involving such as application
of mineral fertilizer. However, the 90 DAS should be considered in the context of
West African agriculture where manure and other sources of nutrients are gathered
during the long dry season and applied to the ®elds just before planting the crops.
This second alternative gives a better prediction of grain yield and provide information on ®eld areas where corrective measures will be used the following cropping
season.
Acknowledgments
The authors would like to thank the ICRISAT Sahelian Center (Niger) for its
support, the INRAN station managers and ®eld technicians at Ouallam and Tara.
They express their appreciation to Mr. J.W. Van Groenigen and N. van Duivenbooden for their comments and suggestions. Field research activities were funded
by the World Bank Project PNRA.
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