# Overview

WorldView is a commercial earth observation satellite. Details about the sensor are provided at Digital Globe's [1].

## Availability (Sample Data)

• Search for commercial satellite image providers in the internet.

## Modules overview

### Outside of GRASS

Satellite imagery can be managed and, at some extent, pre-processed with various GDAL utilities.

### Inside GRASS GIS

GRASS GIS features a complete set of modules and various add-ons enabling pre- and post-processing of IKONOS satellite imagery. The following lists offer an overview of related modules and add-ons.

## Pre-Processing

### Overview

Typically, multispectral satellite data are converted into physical quantities such as Radiance or Reflectance before they are subjected in multispectral analysis techniques (image interpretation, band arithmetic, vegetation indices, matrix transformations, etc.). The latter can be differentiated in Top of Atmosphere Reflectance (ToAR) which does not account for atmospheric effects (absorption or scattering) and in Top of Canopy Reflectance (ToCR) which introduces a "correction" for atmospheric effects.

In order to derive Reflectance values, likewise as with remotely sensed data acquired by other sensors, WorldView raw image digital numbers (DNs) need to be converted to at-sensor spectral Radiance values. At-sensor spectral Radiance values are an important input for the equation to derive Reflectance values. Note, Spectal Radiance is the measure of the quantity of radiation that hits the sensor and typically expressed in ${\displaystyle {\frac {W}{m^{2}*sr*nm}}}$, that is watts per unit source area, per unit solid angle, and per unit wavelength.

• Converting DNs to at-sensor Radiance can be done by using the following equation:
${\displaystyle L\lambda ={\frac {10^{4}*DN\lambda }{CalCoef\lambda *Bandwidth\lambda }}}$
• Converting to Top of Atmosphere Reflectance, also referred to as Planetary Reflectance, can be done by using the following equation:
${\displaystyle \rho _{p}={\frac {\pi *L\lambda *d^{2}}{ESUN\lambda *cos(\Theta _{S})}}}$
where:
• ${\displaystyle \rho }$ - Unitless Planetary Reflectance
• ${\displaystyle \pi }$ - mathematical constant (3.14159265358)
• ${\displaystyle L\lambda }$ spectral Radiance at the sensor's aperture, from equation... ToADD
• ${\displaystyle d}$ - Earth-Sun distance in astronomical units, interpolated values
• ${\displaystyle Esun}$ - Mean solar exoatmospheric irradiance(s) (W/m2/μm), interpolated values
• ${\displaystyle cos(\theta _{s})}$ - Solar_zenith_angle from the image acquisition's metadata

### Importing data

#### Importing

• Location creation based on georeferenced data

Once inside a Location that is defined by the spatial reference system in which the bands of interest are projected, they can be imported with the r.in.gdal module.

For example, GeoTIFF files can be imported by looping r.in.gdal over all of them

for TIF in echo *.tif; do r.in.gdal in=${TIF} out=${TIF%%.*}; done

To keep the raw material untouched, we create another Mapset inside the same Location and copy over the bands giving, optionally at the same time, a new name for each.

### Deriving Physical Quantities

ToCleanUp

Converting Digital Numbers to Radiance/Reflectance requires knowledge about the sensor's specific spectral band parameters. In the following listed paramters (see below), the Effective Bandwidths and the Band-Averaged Solar Spectral Irradiances are extracted from the document Radiometric Use of WorldView-2 Imagery, Technical Note (2010) by Todd Updike and Chris Comp. The Absolute Calibration Factors are extracted from a WorldView-2 product, specifically from an image metadata file (extension .IMD).

Note, however, as stated in the above document,

The absolute radiometric calibration factor is dependent on the specific band, as well as the TDI exposure level, line rate, pixel aggregration, and bit depth of the product. Based on these parameters, the appropriate value is provided in the .IMD file. For this reason, care should be taken not to mix absolute radiometric calibration factors between products that might have different collection conditions.

Pan_CalCoef=0.05678345		;	Pan_Width=0.2846000			;	Pan_Esun=1580.8140
Coastal_CalCoef=0.009295654	;	Coastal_CalCoef=0.04730000	;	Coastal_Esun=1758.2229
Blue_CalCoef=0.01260825		;	Blue_Width=0.05430000		;	Blue_Esun=1974.2416
Green_CalCoef=0.009713071	;	Green_Width=0.06300000		;	Green_Esun=1856.4104
Yellow_CalCoef=0.005829815	;	Yellow_Width=0.03740000		;	Yellow_Esun=1738.4791
Red_CalCoef=0.01103623		;	Red_Width=0.05740000		;	Red_Esun=1559.4555
RedEdge_CalCoef=0.005188136	;	RedEdge_Width=0.03930000	;	Red_Edge_Esun=1342.0695
NIR1_CalCoef=0.01224380		;	NIR1_Width=0.09890000		;	NIR_Esun=1069.7302
NIR2_CalCoef=0.009042234	;	NIR2_Width=0.09960000		;	NIR2_Esun=861.2866

The following examples exemplify the conversion of raw Blue band digital numbers into Radiance and Reflectance.

Converting a Blue Band (Digital Numbers) in to Spectral at-sensor Radiance in the correct units to be further used for the conversion in to unitless Reflectance:

# set the region
g.region rast=Blue_DNs -p

# convert DNs to spectral Radiance values
r.mapcalc "Blue_Radiance = ( (10000 * WorldView_Blue_DNs) / (... * ...) )"

#### Planetary Reflectance

The equation to derive Reflectance values incorporates in addition:

• The mathematical constant Pi PI=3.14159265358.
• The Earth-Sun distance in astronomical units which depends on the acquisition's day of year (DOY -- also referred to as Julian day, Ordinal_date) and can be retrieved from the following spreadsheet <http://landsathandbook.gsfc.nasa.gov/excel_docs/d.xls>.
• The mean solar exoatmospheric irradiance in ${\displaystyle {\frac {W}{m^{2}*\mu m}}}$. See 3rd column of (interplated) values given above.
• The cosine of the Solar Zenith Angle (SZA) at the time of the acquisition. The SZA can be calculated from its complementary Solar Elevation Angle (SEA) given in the image acquisition's metadata.

In the following example we accept as the acquisition's DOY=... and SEA=.... Hence, we get the Earth-Sun distance ESD=... and SZA = ... deg.

Converting the in-Blue spectral band at-sensor Radiance in to Planerary Reflectance:

PI=...; ESD=...; BAND_Esun=...; SZA=...
r.mapcalc "Blue_Reflectance = ( ${PI} * Blue_Radiance *${ESD}^2 ) / ( ${BAND_Esun} * cos(${SZA}) )"

#### Automatising Conversions

The conversion process can be scripted to avoid repeating the same steps for each band separately. In bash, such a script might be as the following example. Note, however, in this example script constants, band parameters and acquisition related metadata are hard-coded!

#!/bin/bash

Pan_CalCoef=		;	Pan_Width=		;	Pan_Esun=

# set constants, band parameters and acquisition related metadata here!

# Pi, first 11 decimals
PI=3.14159265358

# Acquisition's Day of Year and estimated Earth-Sun Distance
DOY=...; ESD=...

# Sun Zenith Angle based on the acquisition's Sun Elevation Angle
SEA=... ; SZA=$(echo "90 -${SEA}" | bc )

...

## Post-Processing

Having beforehand satellite image data expressed in physical quantities (radiance or reflectance) is preferred to follow-up with digital image analysis techniques. A few common post-processing practices are Contrast-Enhancement, Pan-Sharpening and creating Pseudo- or True-Color Composites. Other well known enhancing manipualtions to support the analyses of satellite imagery, include deriving Vegetation Indices, transforming multi-spectral data based on PCA and Segmenting images.

### Pan-Sharpening

Pan-Sharpening / Fusion is the process of merging high-resolution panchromatic and lower resolution multi-spectral imagery. GRASS 7 holds a dedicated pan-sharpening module, i.pansharpen which features three techniques for sharpening, namely the Brovey transformation, the classical IHS method and one that is based on Principal Components Analysis (PCA).

One approach inside GRASS-GIS to get an acceptable color-balanced composite image after Pan-sharpening 11-bit IKONOS spectral bands comprises the following steps

1. rescale the 11-bit WorldView spectral bands to 8-bit ranging in [0, 255] (r.rescale)
2. pan-sharpen with any of the featured methods (Brovey, IHS, PCA) (i.pansharpen)
3. color-balance by using the i.landsat.rgb module or manually adjusting the color tables of the bands of interest
4. create a composite image by using the r.compose module

#### Automatising Sharpening & RGB Composition

An experimental bash script to automatise the sharpening/fusion and RGB composition process is demonstrated here. The script uses the Spectral Reflectance values (double precision values), gained from previous steps (see above), and produces Pan-sharpened images by applying all of the three methods that Template:Addon offers. In addition, it attempts to produce True-Color composite images, without and with re-balancing the color tables by using the i.landsat.rgb module.

Initial tests indicate that at least one of the three sharpening methods, combined with re-balancing, produces very clear and balanced True-Color composites. Note, there is no 100% confidence that it will produce nice looking True-Color composites. Some of the methods might simply work, others might deliver fancy-colored images. As usual, some manual action might be required to get the re-balancing to work as best as possible.

The script can be expanded in terms of using more inputs by utilising bash's positional parameters. However, care has to be taken to alter the instruction that concerns the conversion from double precision values to 8-bit integers.

...