978-1-4577-1591-4/11/$26.00 ©2011 IEEE
Infrastructure for Data-Driven Agriculture:
Identifying Management Zones for Cotton using Statistical Modeling
and Machine Learning Techniques
Edmund W. Schuster, Sumeet Kumar,
Sanjay E. Sarma
Field Intelligence Lab
Massachusetts Institute of Technology
Cambridge, MA USA
[email protected], [email protected],
[email protected]
Jeffrey L. Willers
Genetics and Precision Agriculture Research Unit
United States Department of Agriculture, Agricultural
Research Service
Mississippi State, MS USA
[email protected]
George A. Milliken
Professor Emeritus, Department of Statistics,
Kansas State University, Manhattan, Kansas
[email protected]
Abstract— Advances in many areas of sensing technologies and
the widespread use and greater accuracy of global positioning
systems offer the prospect of improving agricultural productivity
through the intensive use of data. By nature, agriculture is a
spatial science characterized by significant variability in terms of
yield and concentration of pests and plant diseases.
Consequently, precision agriculture seeks to improve the
effectiveness of various types of sensing information to give the
grower more data and the ability to design the specific treatments
for site-specific management of inputs and outputs. The intensive
use of data in agriculture is at a relatively early stage and there
remains much opportunity to refine modeling approaches and to
build information infrastructure. With the overall goal of
optimizing inputs to achieve the maximum output in terms of
yield, this paper focuses on the application of a clustering
algorithm to field data with the goal to identify management
zones. We employ two sets of attributes, first yield and second
field properties like slope and electrical conductivity to delineate
the management zones. By definition, a management zone is a
contiguous area defined by one or more features and may take on
many different shapes. Building on the established machine
learning approach of k-means clustering, we successfully identify
a near optimal number of management zones for a cotton field.
Keywords - precision agriculture, management zones, k-means,
unsupervised learning
I. INTRODUCTION
Author and investor Jim Rogers recently mentioned as part
of an interview with the Wall Street Journal that America has
underinvested in agricultural infrastructure during much of the
post WWII period [1]. Consequently, since 2005 many
agricultural commodities have steadily gained in price,
reflecting tightening constraints due to higher energy costs,
global supply for inputs to produce food and fiber, and global
demand for these resources. Complicating things, according to
some estimates the increase in world population to around 9
billion people by 2030, along with rising disposable income,
will require a 100 percent increase in food production [2]. For
all areas of the world, especially in Asia, constraints on land
and water availability will make this goal challenging to
achieve. Already, food price inflation is a major issue in China
and India and has potential to cause wide ranging civil unrest.
Our vision for Precision Agriculture (PA) involves the
sophisticated formulation and use of mathematical models for
ongoing analysis of spatial data along with Internet computing
to rapidly connect models to data resident on farm computers
[3]. In this way, PA will become a control system where data
feedback from various sensors facilitates optimization of
inputs.
II. ELEMENTS OF PRECISION AGRICULTURE
Representing a change from established philosophies, the
essential concept of PA puts forth that crops undergo spatial
variation during the growth cycle. For example, physical
attributes of the field such as slope, drainage, soil type, and
fertility will inherently cause variation in yields over space. As
such, PA involves: ‘‘Matching resource application and
agronomic practices with soil and crop requirements as they
vary in space and time within a field. [4].’’
A. Sensing
From an equipment standpoint, advances in the yield
monitors mounted on harvest machinery have greatly improved
the amount and quality of spatial data. These sensors measure
the weight of the harvest per area. For example, in grain crops,
the methodology involves a load sensor placed under a
conveyer belt on the harvest machine, along with Global
Positioning System (GPS) coordinates for the location in the
field.
Other data acquisition is possible through remote sensing.
In particular, the use of multi-spectral imaging provides data
over large spaces and at different resolutions. The Normalized
Difference Vegetation Index (NDVI) is a type of raw data
calculated from multi-spectral images.978-1-4577-1591-4/11/$26.00 ©2011 IEEE
B. Control
For inputs such as fertilizer and pesticide, Variable Rate
Application Technology (VRT) is now available for most
agricultural machines such as sprayers. This allows for the
application of chemicals to vary over space. However, the
precision of VRT is such that change in application amount is
not instantaneous. This limits the number of rate changes
possible within a given area. For example, switching the
application amount every few meters is not possible with
current technology.
C. Calculating the Prescription through Induction
Given sensing data for spatial yield and the capabilities of
VRT, it is possible to increase the level of precision for
managing agriculture inputs over space. However, few if any
deductive approaches exist to calculate the exact pattern of
inputs (termed a prescription) needed to maximize yield.
Rather, foundational research in PA describes what amounts to
a process of induction. The following quote represents a
typical viewpoint from the agricultural research community:
“Early scientific endeavor employed Baconian principles in
experimental designs which involved the construction of
scenarios and the collection of response observations in the
hope of distilling an answer. [5]”
By these means, it is possible to calculate the prescription
needed to maximize yield. In turn, the prescription provides
the information to implement the VRT.
D. Management Zones
With improved sensing and control capabilities, the
current high priority issue for PA involves using mathematical
models to rapidly analyze the field data and to determine the
best course of action to optimize spatial yield. Specifically, the
research contained in this paper explores the use of machine
learning to identify management zones in a field where the
combination (and interaction) of physical and variable inputs
comprise homogeneous areas that identify similar spatial crop
yield responses. Management zones are typically irregular in
size, shape, and patterns of interspersion, which make them
difficult to identify because of the complexities of the sets of
spatial inputs and their interactions with field topography.
III. LITERATURE REVIEW
In cotton production, various researchers have established
diverse criteria to define different management zones within a
field. For instance, Landsat Thematic Mapper imagery for 11
consecutive years from the same cotton field was studied as a
technique to establish temporally stable regions of similarity
[6]. Another group of researchers examined the effect of
landscape position and soil series on cotton phosphorous
utilization [7]. Using soil electrical conductivity (ECa)
measurements, researchers have observed significant
correlations with several soil properties such as leaching
fraction, pH, plant-available water, and salinity with cotton
yield, and provided valuable information for site-specific
management [8]. Others have developed software that used a
fuzzy c-means unsupervised classification algorithm to
apportion field information into management zones [9]. In the
pest management of the tarnished plant bug in cotton,
unsupervised classification techniques of normalized difference
vegetation index (NDVI) values derived from imagery to
determine different growth phenology classes [10].
In crops such as grain, there are other techniques for
management zone delineation [11]. These include quadratic
discriminant analysis (QDA) and k-nearest neighbor
discriminant analysis (KNN) [12], fuzzy k-means clustering
algorithm along with fuzzy performance index (FPI) modified
partition entropy (MPE) to determine the optimum number of
clusters [13]; the spatial contiguous k-means clustering
algorithm (SC-KM) [14], and the watershed algorithm [15].
Arguably, cotton is different as compared to grain crops.
For example, we did not find a strong correlation between
NDVI and yield. One reason is that our analyses did not
include the treatment structure attributes [16] for nitrogen rates
applied to strip plots, which were part of the original
experiment that generated the data. A second reason is that the
relationship between NDVI and yield is not simple [17].
Further experimentation with this data set will potentially
discover other causes (i.e., estimates of effects of nematode
stress) for the absence of a strong correlation between NDVI
and yield.
IV. DATA
The data for this research study comes from a cotton field
located near Saint Joseph, Louisiana, and is referred to as the
“Helena fertility trial.” Besides geodetic information, there are
several classes of available data for determining management
zones when calculating input-output responses. The first class,
representing dependent variables include two measures of
yield, bales of cotton per acre and biomass flow.
The second class, representing geo-referenced field
topographical characteristics, includes NDVI, obtained from
multi-spectral imaging of the crop on 5 August 2005 (several
weeks before harvest) using airborne sensors. Other measures
include apparent soil electrical conductivity (ECa) readings that
are useful for soil texture mapping. These data were collected
using a Veris® model 3100 sensor cart (Veris Technologies,
Salina, Kansas). The Veris® 3100 cart was used in conjunction
with a sub-meter accurate Global Positioning System (GPS)
receiver, and collected geo-referenced data of shallow and deep
soil resistivities at one second intervals. The standard operating
width across fields was 40 feet. The soil electrical conductivity
data derived from the Veris® system was analyzed using
SSToolbox®, an agriculture-oriented geographic information
system (GIS), and then converted into a surface utilizing
Surfer® for data interpolation.
A Real-Time Kinematic (RTK) GPS system with cm
accuracy in topographic measurements was used to collect
elevation data [18]. This system consisted of a GPS receiver
(the rover antenna), a RTK base station, with a data radio link
between the two GPS antennas.
Other physical characteristics of the field are slope, soil
series type, and some operational variables that are part of the
treatment structure, like the type of irrigation, seed variety, and
chemical treatments (such as amounts of nitrogen) (see
Appendix).978-1-4577-1591-4/11/$26.00 ©2011 IEEE
The data set used in this research was assembled using
GIS and statistical processing methods as described in [19]. In
general, various information layers (themes) were registered to
earth coordinates and obtained by selected remote and
proximal sensing systems. This information, along with the
yield monitor data, provided descriptions of the fields’
topology and topography. GIS processing attached data from
all spatial layers to the yield monitor coordinates to produce the
database table used in this research.
The data set represents a single year of observations. As
such, it does not allow for temporal analysis. However, if
properly identified, management zones change little over time.
A data set from a single year is a good start toward
development of an algorithm to aid in the identification of
management zones before the planting of the crop and
imposition of agricultural management practices. The fact of
limited data sets will possibly be routine for first time analyses
of commercial production fields.
V. METHODOLOGY
In this paper, we employ a two-step k-means clustering
algorithm to identify management zones (MZ). One of the
critical factors in using k-means is identifying the best
attributes/variables for management zone delineation. In the
past, researchers have explored using yield [20], NDVI [21] or
soil properties like slope, elevation, and electrical conductivity
[22]. Researchers have hypothesized that NDVI is correlated
with yield [23].
In our data set we have two estimates of yield, bales of
cotton per acre (Y1) and biomass flow (Y2). We observed that
the correlation between yield and NDVI (Y3) is low, i.e. ρ(Y1
,Y3) = 0.5629 and ρ(Y2 ,Y3) = 0.4874 where ρ is the Pearson
Correlation coefficient. Hence, we do not consider NDVI as an
informative variable to delineate management zones. Our first
set of attributes is Y1 and Y2.
In addition, we consider another set of attributes that are
fixed independent variables, which describe field topography.
These include slope, electrical conductivity measured at deep,
electrical conductivity measured at shallow and the ratio of
deep to shallow electrical conductivity (all obtained from the
VERIS® cart).
The k-means algorithm is a popular clustering method
used extensively for unsupervised learning and identifying
structure in dataset. We denote the dataset of attributes by FN×d
that includes N samples of d features/attributes. We normalize
every column (attribute) of the dataset in the range [0 1] to
remove any scale bias. The algorithm implements clustering by
minimizing an objective function in a heuristic manner, which
is usually the sum of the square of distance of every point from
the corresponding cluster centroid, i.e.
€
O(K) = || f j − f i ||2
f j ∈Ci
∑
i=1
K∑
, (1)
where K is the number of clusters, Ci’s is the i’th cluster
and the centroid of every cluster is represented by
€
fi = f j
f j ∈Ci
∑ NCi and
€
NC
i
is the number of points in cluster
Ci. Note that fj’s can represent a vector (d > 1) and ||.|| denotes
L2 norm.
A critical aspect of management zone delineation is
ensuring contiguity of the zones by taking into account spatial
autocorrelation. When dividing points into clusters both the
geographical proximity and attribute values should be
considered. In some scenarios, when the k-means is used
without considering a proximity metric for the point, the
resulting clusters may not be contiguous (Fig. 1).
The aforementioned issue is addressed by including spatial
information of the points apart from the attribute values in the
k-means algorithm. We augment the dataset by including the
normalized geographic spatial information (x, y coordinates) of
the points. Furthermore, a two-step k-means algorithm is
implemented as described below (Note: Matlab® notation has
been used to represent vectors and matrices):
1. Augment the dataset to D1 = [w0x w0y F]N×(d+2), where
x and y are the spatial coordinates of the samples and
w0 is a weighting factor, chosen to be less than 1 (e.g.
w0 = 0.2).
2. Implement k-means on D1 with large number of
clusters K0 (~200). In the first step, we aim at
segmenting the domain into a large number of clusters
where a higher weight is given to dissimilarity among
attributes compared to spatial proximity. From the kmeans algorithm, we obtain the centroids of K0
clusters as Q0.
3. Create the data set for the second step as D2 =
[w1Q0(:,1) w1Q0(:,2) Q0(:,3:d+2)], where w1 is a
weighting factor, chosen to be greater than 1 (e.g. w1 =
10).
4. Implement k-means on D2 with a small number of
clusters K1 (~15). In this step, the aim is to merge the
clusters previously formed into a smaller number of
clusters. The overall weight of spatial coordinates at
this step is w0w1. The domain has already been
segmented into smaller clusters (K0) where each
cluster represents segments of the domain with
homogenous attribute values. These clusters are now
merged into K1 clusters where both spatial proximity
and similarity between attributes are considered.
It is worth noting that the Helena fertility trial data has
undergone previous analysis to determine the management
zones needed for the optimal nitrogen prescription through the
approach of design of experiments (DOE) described briefly in
Section VIII. As part of the next section, we compare the
results of the two-step k-means approach with the results from
the DOE analysis.
VI. RESULTS AND DISCUSSION
The algorithm described involves four different parameters
w0, w1, K0 and K1. Generally, delineating management zones
involves maximizing homogeneity of every zone in terms of
attribute values and contiguity. These two objectives may be978-1-4577-1591-4/11/$26.00 ©2011 IEEE
of conflicting nature as seen in Fig. 1 when similar attributes
are scattered all across the domain. We ran simulations with
the following values of the parameters and identified the one
that gave the smallest objective O(K1) involving only the yield
features (Eqn. 2 with [Y1 Y2] and K = K1): K0 = 200, K1 =
(2:2:20)’, w0 = [0.05 0.1 0.25 0.5 0.75 1 2]’, w1 = [0.5 1 1.5 2 3
4 5 10]’. We found that K1 = 18, w0 = 0.1 and w1 = 10 gave the
minimum O(K1).
Intuitively, as the weights are increased the importance of
spatial proximity increases and for high weights the
management zones are more contiguous but contain higher
attribute variance within cluster. Hence, there is a tradeoff
between contiguity and homogeneity of management zones.
The number of management zones (K1) is an important
parameter. A higher K1 will lead to a lower within zone
variance but may be impractical from VRT perspective. The
issue here is at least twofold. First, the problem is if the VRT
controller has the precision to deliver the required inputs to
have a useful distinction for a higher number of zones. Second,
as indicated in Fig. 1 and 3, the edges of contrast among zones
is quite irregular and sometimes includes a gradient of
interspersion.
Fig. 2 plots the variation in the objective O(K1) and its
derivative with the number of clusters for the two sets of
attributes. We use the following parameters for the simulations:
K0 = 200, w0 = 0.1, w1 = 10. After K1 = 15, marginal decreases
were observed in the objective function O(K1) and hence K1 =
15 is a good choice for number of management zones.
Figure 1. Delineation of management zones through k-means considering
only attribute variables with the number of clusters = 15; (a) yield (Y1 and Y2)
(b) fixed independent variables. The axes are the normalized (x,y) cooridinate
values derived from the original Universal Transverse Mercator Easting and
Northing coordinate values (m).
Figure 2. Variation of the objective (a) and its derivative (b) with the final
number of clusters (K1). The objective considered here is the sum of the
square of the distance of every feature from its centroid feature and was
evaluated for both sets of attributes as descibed Section V.
Additional simulations where ran, setting w0 = 0.5, w1 = 4,
K0 = 200 and K1 = 15, to identify the different management
zones by our two-step clustering algorithm (Fig. 3). Compared
to clustering without considering the spatial information (Fig.
1) the two-step algorithm delineates more contiguous
management zones. With these conditions, the ratio of O(K1) to
O(1) (where O(1) represents the total variability of attributes
across the domain) was O(K1)/O(1) = 0.5462 for the yield
attributes and was O(K1)/O(1) = 0.0807 for the topography
attributes. Hence, there is a significant reduction in variability
for both types of attributes when grouped into management
zones compared to the overall variability in the domain.
A comparison of the DOE management zone predictions
to the k-means approach shows similarities and differences.
Both the single step cluster method and the DOE approaches
depict more variability in the upper halves (northeast) of each
east-west field portion compared to more homogeneity and
greater areal extent of the zones derived for the lower halves
(southwest) (Fig. 1 and 4). The single step cluster method,
using the two yield measures, also recovered information on
the effects of the nitrogen rates applied to the strip plots (Fig.
1a).978-1-4577-1591-4/11/$26.00 ©2011 IEEE
Figure 3. Fifteen management zones delineated through the two-step
clustering algorithm for (a) yield attributes and (b) fixed independent
attributes.
On the other hand, the two-step cluster method clearly
shows more equitable apportionment of the field and removal
of the nitrogen treatment effects (Fig. 3a). The DOE approach
is somewhat similar, since once the relationship between the
amount of nitrogen applied and the topographic characteristics
was modeled by Eqn. 2, refinements to this covariance model
could be derived to predict what amount of nitrogen should be
applied at which location with or without irrigation (Fig. 4).
The next reasonable step is to consider implementation of the
clusters mapped by the two-step approach to simply, with the
DOE methodology, the number of terms that involve the
topographical characteristics, Xgijklmn.
This type of investigation could lead to innovative
solutions for better automation of data processing techniques to
handle the copious quantities of geographical information
involved with PA.
VII. CONCLUSION AND FUTURE WORK
While the machine learning approach outlined in this
paper successfully delineates management zones for cotton, an
important issue continues to exist. It involves introduction of
VRT constraints (rate of change of the application) directly into
the machine-learning algorithm. Such a change would increase
the performance of machine learning to match real world
operational conditions.
In addition, farming equipment travels in parallel paths
following the directions of the crop row. These application
paths are spaced at a distance that relates to the size of the
sprayer boom (or tool bar width) of the application equipment.
Thus, the geographical intersections of the characteristics of
VRT equipment and the edges of the zone are spatially
complex and are not symmetrical. Therefore, how much of a
beneficial increase in yield is required to recover the costs
involved with optimal delineation of management zones versus
the cost and operational characteristics of the VRT equipment
are a topic for more research.
Figure 4. Management zones derived from a mixed, analysis of covariance
model which indicates different management for rates of nitrogen with
irrigation (a) or without irrigation (b).
Finally, the concept of using machine learning for
identifying management zones does not just apply to yield. For
an agricultural field, other phenomena tend to cluster. A good
example is cool air during the fall season for harvesting grapes
in the Northern part of the US. The cool air tends to cluster in
low-lying areas causing fruit to freeze [24]. Identifying these
areas through temperature sensing technology and machine
learning algorithms represents another new application for the
research in this paper.
VIII. APPENDIX
This data set has been previously analyzed using methods
equivalent to [25] and [26]. Generally, the intersecting
geometries of the various topography zones and farm
equipment characteristics defined the design structure of the
original experiment. The blanket or site-specific management
(SSM) practices applied to the field by the producer/researcher
described the treatment structure. These design and treatment
structures were put together to build a general, linear, mixed
analysis of covariance model for an analysis. For the Helena978-1-4577-1591-4/11/$26.00 ©2011 IEEE
fertility study, the statistical model that describes seed cotton
yield monitor data as functions of equipment geometry, several
nitrogen rates (applied as either 2 types of blanket or 3 types of
SSM tactics), several site characteristics (or topography
variables, Xgijklmn), and the randomized, complete block design
structure imposed in the experiment is:
yijklmn = µ + φirijkl+φr2ijkl +
1
G
g=
∑ βgiXgijklmn + BLKk +
BLKk×TRT_IDik + H_group(BLK TRT_ID)m(ik) + εijklmn (2)
where yijklmn is the yield value of the nth yield monitor reading
(or site) in the mth harvest group (H_group, or paired harvest
passes within each strip plot) within the lth asymmetrical
experimental unit (EU) of the kth block (or block_id) in the jth
strip plot (labeled by a plot_id) assigned the ith nitrogen
treatment tactic. (The EUs are the spatial intersections of the
strip plot boundaries and fertility management zones derived
from the ECa data.) The variable r is a regressor, not a class,
variable representing the nitrogen rates (r = 60, 75, 90, 105,
120, 135, and 150 lbs/ac) applied to all (or various) locations
within the strip plots according to the treatment (trt_id)
assigned to them. The term µ is the mean seed cotton yield of
the field and error eijklmn is the effect of the nth yield monitor
observation (the harvesting unit or yield point) within the mth
harvest group within the lth EU in the kth block in the jth strip
plot for the ith treatment. Other terms are BLKk, or the effect of
the kth block, the BLKk×TRT_IDik interaction, and the harvest
group nested within (BLK TRT)m(ik). Keep in mind that the
BLKk×TRT_IDik term is nested within block_id and is an alias
for the plot_id .
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