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I. INTRODUCTION

The major limiting factor in terms of mass adoption of precision agriculture practices has been cost and timeliness of data collection. The ease and cost of operation of unmanned aerial vehicles are quickly making precision agriculture more accessible to grow operations of all sizes. The spearheads of precision agriculture are various indices that give the grower a comprehensive overview of the crop’s overall health. The two most promising precision agriculture indices are Normalized Difference Vegetation Index (NDVI), and Crop Water Stress Index (CWSI).

II. HISTORY OF NDVI

“Landsat 1 was launched on July 23, 1972; at that time the satellite was known as the Earth Resources Technology Satellite (ERTS). It was the first Earth-observing satellite to be launched with the express intent to study and monitor our planet’s landmasses.” [1] Landsat1 carried 2 Camera Systems: The Return Beam Vidcon(RBV) and the Multispectral Scanner(MSS) [1]. MSS recorded data in four spectral bands: Red, Green, and two infrared bands. [1].The MSS provided so much seemingly useful data that NASA funded a number of studies to develop ways to interpret the multispectral data. One such study was the Great Plains Corridor project:

“The Landsat-1 Great Plains Corridor project… was designed to evaluate Landsat capability for quantitatively monitoring the progression of phenological development from South Texas northward through North Dakota.” [2]

Then PhD. Student Donald Deering and his advisor Dr. Robert Hass developed a correlation between the spectral response seen on channels 5-7 on landsat 1 (Red, and the two NIR bands) and volume of Green biomass. They called this model the Normalized Difference.

III. NDVINormalized Difference Vegetative Index is a Vegetative Index model that describes the relative “greenness” of the inspected area. Photosynthetic organisms absorb light between 400nm and 700nm for photosynthesis. More specifically, leaf cells, while simultaneously absorbing 490nm-690nm light [3] will reflect near-Infrared light (>700nm) that will cause the cells to overheat [4]. Thus comparing the amount of Red light absorbed to the amount of Near-IR light reflected is a reliable indicator of photosynthetic activity [2].

Fig 1. Absorption spectrum of Chlorophyll [3]

The NDVI equation as formulated by Deering and Hass is [2] :

A Survey of Normalized Deference Vegetative Index (NDVI) and Crop water Stress Index

(CWSI)Meinrad A. Charles

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NDVI=Near IR−RedNear IR+Red (1)

Where Near IR is define as the reflectance of Near Infrared light (>700nm), and Red is define as the reflectance of Red Light (650-700nm). This equation will result in NDVI values form 0 to 1 with bare soil typically resulting in a value of 0.1 and dense vegetation resulting in a value of 0.9.

The reflectance values are calculated using the formula:

Reflectance= RadianceIrradiance (2)

Where Radiance is defined as the amount of light the sensor sees in the specific color band, and Irradiance is defined as the amount of light, in the respective color band, emitted by the light source. Equation (2) implies that the Near IR and Red values used in equation (1) will have to be calibrated to the amount of incident light, typically form the Sun, on the crops at the time of data acquisition.

There are two approaches to collecting reflectance data:

True NDVI Relative NDVI

A. True NDVI

The conventional method, known as True NDVI, involves recording both radiance and Irradiance values and calculating the reflectance values using equation (2). While recording radiance values is fairly straightforward, the irradiance values may be recorded by using reflective panels that reflect ~100% of the incident light or using a purpose-built incident light sensor that synchronously records irradiance with radiance. Both approaches to recording irradiance values have benefits and pitfalls. While, it is relatively expensive to install and maintain reflective panels in the field, one may justify the cost as opposed to increasing the complexity and weight of the payload by installing an incident light sensor.

B. Relative NDVI

Relative NDVI is seeing larger adoption in industrial and consumer applications of NDVI due to the relatively simplistic payload needed. Relative NDVI eliminates the need to reflective

panels, calibration images, and incident light sensors by statistically determining the irradiance values from the radiance values. The general method with which this is accomplished involves capturing just the radiance values of the crop, stitching the individual images together to obtain a comprehensive view of the area of inspection and then applying probability models to statistically determine what the irradiance values most likely were at the time of data acquisition. A survey of the statistical methods employed to determine these irradiance values is outside the scope of this paper.

There are pros and cons to both approaches to acquiring NDVI data:

True NDVI Relative NDVI• High

confidence level for data

• Expensive to install and maintain reflective panels in the field

• Compromise: capture “calibration” image before flying field

• Medium confidence level for data (good enough)

• Cheaper to implement, no maintenance cost

• Eliminates extra step in processing data

Table 1. Comparison of benefits and pitfalls of True NDVI vs. relative NDVI

IV. CONSTRUCTION OF NDVI CAPTURING DEVICE

Imaging sensors in modern digital cameras are capable of recording light in the near infrared region. However, manufacturers typically install filters that block out such radiation. Construction of a camera capable of acquiring NDVI data typically starts with dismantling an existing camera, such as a webcam, and removing the infrared filter. The next step is to install a notch filter that blocks out green or blue light while allowing red and near infrared light to pass to the imaging sensor.

Post processing of the captured data involves only reading values from the red and blue or green

Fig 2. Public Labs NIR Camera conversion kit [8]

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channel, depending on the filters used, and then applying equation (2) to both channels and then using the results compute the NDVI value described in equation (1).

V. HISTORY OF CWSI [5]

French biologist Rameaux was the first scientist to attempt to record the temperature of the leaves of a plant in 1843. Considered to be crude by today’s standards, Rameaux simple stacked leaves upon each other and wrapped the stacked around a mercury thermometer; however, this experiment can be considered the beginning of research into a correlation between leaf temperature and water stress. A little under a century later, Miller and Saunders used thermocouples to measure the temperature of the canopy of a crop in Kansas and recorded an average temperature difference of 1⁰C. It was not until 1981 that Idso and Jackson developed a formal relation between canopy temperature and crop water stress, leading to the CWSI expression detailed below.

VI. CWSI

Crop water Stress Index is a vegetative index that describes the water stress level of a crop by proxy of the difference between air temperature and canopy temperature. The Equation for CWSI is describes as [6]:

CWSI=dT−dT l

dT u−dT l (3)

Where dT is the difference between the air and canopy temperature, dTl is the lower limit of the difference between air and canopy temperature and dTu is the upper limit of the difference between air and canopy temperature. Idso et al. developed a method to estimate the upper and lower limits of the temperature variance by taking the vapor deficit into account [6]:

dT l=b+m∙ VPD(Ta) (4)

dT u=b+m [VP sat (T a )−VPsat (T a+b )] (5)

Where b and m are the empirically determined intercepts and slopes, respectively, for the crop of interest, VPD(Ta) is the recorded vapor pressure

deficit at the air temperature, VPsat(Ta) is the saturation vapor deficit at the temperature of recorded air temperature, and VPsat(Ta+b) is the saturation vapor pressure deficit of the air temperature and the intercept. Furthermore, Vapor pressure deficit is calculated using the formula [7]:

VPsat (T )=0.6108 ∙ e17.27 ∙TT +265.5 (6)

VPD (T )=VPsat (T )−(0.6108∙ e17.27 ∙T d

Td +237.3) (7)

Where temperatures are in degrees Celsius, and Td is the dew point.

Combining and simplifying expressions 3 through 7 results in the following equation:

CWSI=(T a−T c)−(b+0.6108 m∙ (e

17.27 ∙T a

T a+265.5−e17.27 ∙T d

T d+237.3 ))0.6108 m∙(e

17.27 ∙T a

T a+237.3−e17.27 ∙( Ta+ b)T a+b+265.5 )

(8)

An example of the slope and intercept values for Soybeans is given below, followed by values for

various other crops:

Fig 3. Example Vapor Pressure deficit Baseline for Soybeans [6]

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  Crop   Intercept (b)   Slope (m)Alfalfa 0.51 -1.92

Barley (pre-heading) 2.01 -2.25

Barley (post-heading) 1.72 -1.23

Bean 2.91 -2.35Beet 5.16 -2.3Corn (no tassels) 3.11 -1.97

Cotton 1.49 -2.09Cowpea 1.32 -1.84Cucumber 4.88 -2.52Lettuce, leaf 4.18 -2.96Potato 1.17 -1.83Soybean 1.44 -1.34Tomato 2.86 -1.96

Wheat (pre-heading) 3.38 -3.25

Wheat (post-heading) 2.88 -2.11

Table 2. Intercept and Slope values for various crops[6]

VII. CONSTRUCTION OF CWSI CAPTURING DEVICE

CWSI is a little more complicated to implement due to the number of variables need perform the calculation. The sensors needed to calculate CWSI are:

Thermal Imaging camera capable of providing reliable thermographic data

Temperature sensor for air temperature readings

Humidity Sensor or access to reliable localized dew point data.

Two possible approaches to implementing CWSI are either having all the instruments built into a single package, or having a localized weather station record Air temperature and humidity data with timestamps that are synchronized with the timestamps of the thermal images. Post processing for either data collection approach will be as simple as applying the required formula for the crop of choice.

VIII. INTEGRATING NDVI AND CWSI WITH EXISTING FARM MANAGEMENT SOFTWARE.

The key to having successful adoption of a system in any grow operation is seamless integration. Any system that requires intensive interpretation or file type conversion for integration into farm management software will be a hard sell for the grower. The workflow from flight planning to data acquisition to the end-product of ready-to-import-maps needs to be as hands off as possible. As Such the key attributes that growers look for in any Precision Ag system are:

Intuitive flight planning Automated flight and data collection Easily generated orthomosaic maps in the

shape file format

The ability to generate orthomosaic maps with minimal input for the user is a highly desired feature due to the relative complexity of the operation. Furthermore, the most widely used Farm management software packages all require the imported Geographic Information System (GIS) data to conform to the shapefile convention, developed and regulated by ESRI. Successfully integrating NDVI and CWSI data into farm management software hinges on the processing software’s ability to export results in the shapefile format.

IX. INTERPRETING NDVI AND CWSI DATA

The core of Precision Agriculture is accurate, timely field data. For years, the major limiting factor in adopting precision agriculture practices is the relative cost of data collection. Unmanned aerial systems are the much needed bridge between data acquisition and variable rate applications of nutrient, pesticide and water resources. NDVI has been used in a number of different ways:

Assisting growers in focusing tissue sampling tests to only the areas that are stressed

Writing variable rate nitrogen prescription in wheat

Yield estimates from stand count information

Weather damage assessment Determining field water drainage issues Used in conjunction with CWSI, only the

areas of the field with crop cover can be irrigated

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While a number of farms possess the ability to implement variable rate water applications, reliable and cost effective CWSI data acquisition has been difficult. Thermal images from UAS platforms, in conjunction with weather station data bridges this gap. CWSI may also be used in quality control and estimation in crops where access to water directly affect the quality of the crop such as, grapes, oranges, and tomatoes. Other applications for CWSI is being actively researched by USDA.

REFERENCES

[1] NASA, "Landsat Science," NASA, 19 August 2015. [Online]. Available: http://landsat.gsfc.nasa.gov/?p=3172. [Accessed 22 August 2015].

[2] D. Deering and R. H. Hass, "Using Landsat Digital Data for Estimating Green Biomass," NASA, Greenbelt, MD, 1980.

[3] J. Whitmarsch and Govindjee, "The Photosynthetic Process," 1995. [Online]. Available: http://www.life.illinois.edu/govindjee/paper/gov.html#52. [Accessed 22 August 2015].

[4] D. M. Gates, Biophysical Ecology, New York: Springer-Verlag, 1980.

[5] Public Labs, "Near Infrared Camera," Public Labs, JUne 2015. [Online]. Available: http://publiclab.org/wiki/near-infrared-camera. [Accessed 25 August 2015].

[6] R. D. W. P. K. a. B. J. C. Jackson, "A reexamination of the crop water stress index.," Irrigation Science, vol. 9, no. 4, pp. 309-317, 1988.

[7] USDA agricultural Research Service, "Crop water Stress Detection," USDA, 15 december 2005. [Online]. Available: http://www.ars.usda.gov/Main/docs.htm?docid=9715&pf=1. [Accessed 24 August 2015].

[8] K. P. U. R.L. Snyder, "Measuring Vapor Pressure Deficit in the Field," Regents of the University of California, 6 January 2006. [Online]. Available:

http://biomet.ucdavis.edu/biomet/VPD/vpd.htm. [Accessed 24 August 2015].