Download Agronomic Spatial Variability and Resolution 2001, 1st Lecture

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Spatial Variability
and Resolution
What is it?
How do we describe it?
What does it imply for
Agronomic Variability
• Fundament assumption of precision
• Agronomic factors vary spatially
within a field
• If these factors can be measured
then crop yield and/or net economic
returns can be optimize
Agronomic Variables
• Soils
Organic matter
Water holding
• Topography
– Slope
– Aspect
• Fertility
Other nutrients
• Plant available
• Crop Cultivar
Agronomic Variables
• Temperature
• Rainfall
• Weeds
– Species
– Population
• Insects
– Species
– Feeding patterns
• Tillage Practices
• Diseases
– Macro and micro
• Crop Stand
• Method and
Uniformity of
– Fertilizers
– Crop protectants
What is variability
• Variability - difference in the
magnitude of measurements of
– Values can change randomly because
of error in the sensor
– Values can change because of changes
in the underlying factor
• As time changes
• As location changes
Why statistically describe
• Raw data sets are too large to
understand or interpret
• Statistics provide a means of
summarizing data and can be readily
interpreted for making management
• Statistics can define relationships
among variables
Statistical Analyses Commonly
Used In Precision Agriculture
• Descriptive Statistics
– Measures of Central Tendency
• Mean
• Median
– Measures of Dispersion
• Range
• Standard Deviation
• Coefficient of Variation
• Regression
• Geostatistics - Semivariance Analysis
Measures of Central Tendency
• When a factor, such as crop yield, is
measured at different locations
within a field, values vary greatly
• This variation can appear to be
• The set of these measurements is a
• A value exists that is the central or
usual value of the population
Measures of Central Tendency
• This is important because the current
practices in precision farming treat
the field or region in the field based
on the average of the measurements
Mean or Average Value
• Most common measure of central
• Definition:
For n measurements X1,X2,X3,…,Xn
X 1 + X 2 +...+ X n
X =
i =1
Mean or Average
• The mean value is useful if the
measured value is normally
distributed (Bell Curve)
– Most biological processes are normally
– Spatially distributed measurements are
often not normally distributed
• To calculated the mean in Excel
= Average (Col Row : Col Row)
The Median Value
• For skewed distributions, is the
better predictor of the expected or
central value
• Calculated by ranking the values
from high to low
– For an odd number of measurements,
the median is middle value
– For an even number of measurements,
the median is average of the two middle
The Median Value
• In Excel, the median is calculated
using the following formula:
= Median (Col Row: Col Rows)
Measures of Dispersion
• Measures of dispersion describe the
distribution of the set of
Range of the Sample Set
• Difference between the maximum
and minimum values of the
• Calculated in Excel by the following
= Max (Col Row : Col Row)
- Min (Col Row : Col Row)
Standard Deviation
• The standard deviation of a normally
distributed sample set is 1/2 of the
“range” of 66 %values for the
 (X
i =1
-X )
n -1
Standard Deviation
• For a normal distribution (Bell Curve)
95% of the samples from a
population will lie in the interval
X - 1.96s  Z  X + 1.96s
• The standard deviation is calculated
in Excel using the following formual:
= Stdev (Col Row : Col Row)
Coefficient of Variation
• The magnitudes of the differences
between large values and their
means tend to be large. The
differences between small values
and there means tend to be small.
• Consequently, a high yielding field
is likely to have a higher standard
deviation than a low yielding field,
even if the variability is lower in the
high yield field.
Coefficient of Variation
• Thus, variation about two means of
different magnitudes cannot easily
be compared.
• Comparisons can be made by
calculating the relative variation, or
the normalized standard deviation.
• This measurement is called the
Coefficient of Variation.
Coefficient of Variation
• The Coefficient of Variation or C.V. is
calculated by dividing the standard
deviation of the data set by its mean.
Often that value is multiplied by 100
and the C.V. is expressed as a
• Experience with similar data set is
required to determine if the C.V. is
unusually large.
• One objective of precision farming is
to alter the level of one variable (e.g.
soil nitrate) to change the response
of another variable (e.g. grain yield).
• There are other confounding factors
affecting grain yield such as weed
competition or pH, which cannot
always be accounted for.
• The practitioner still needs to
determine the degree to which the
two variables vary together.
• The correlation coefficient indicates
is that measure.
• The correlation coefficient, r, lies
between -1 and 1. Positive values
indicate that X and Y tend to increase
or decrease together.
• Values of r near 0 indicate that there is
little or no relationship between the two
• The coefficient of determination, r2, is
important in precision farming because,
when the samples are collected by
location in the field, it indicates the
percentage of the variability in the
dependent variable explained by the
independent variable.
• For example, if the r2 of soil N and grain
yield is 90% then 90% of the variability
across the field can be explained by soil
nitrate. Spatially varying the N fertilizer
rate based on the nitrate level in the soil
should have a large effect on grain yield.
• In Excel, correlation is calculate by the
= Correl (Col Row : Col Row, Col Row:
Col Row)
Small-scale spatial variability