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Algorithms

.. toctree::
    :maxdepth: 2

This page documents all implemented algorithms in two ways. First, we show the mathematical structure of the algorithm as documented in Pelkey (2007). Second, we show a usage example that can be copied to a command line.

Algorithms are broadly split into two categories as per Pelkey et. al (2007)[1]. We have implemented the surface algorithms for MRDR products. These are map projected, mosaiced TRR3 images that have band to wavelength mapping in the header. We have also supplied the SW lookup tables and code to allow for band to wavelength mappings for TRR3 files. Currently, TRR3 files are not supported due to issues reading the label.

In the algorithm formulations below we indicate the reflectance of a band using $R$ and the wavelength of the band using $wv$. Note that $wv$ is the nearest wavelength, not the absolute wavelength. This is because the lookup tables can undergo modification such that hard coded values would not be possible.

Warning

The detector used to capture an image dictates which wavelengths the image contains. Since all TRR3 images ship with an identical number of bands, we check the detector label (from the header). Note that algorithms not designed to run on IR data will still process a VNIR image, but the results will not be as expected.

Warning

The VNIR detector (S) supports, Reflectance 770nm, Red / Blue Ratio, Band Depth 530nm, Shoulder Height 600nm, Band Depth 640nm, Band Depth 860nm, Band Depth 920nm, RPeak1, Integrated Band Depth 1nm Visible, Reflectance 440nm, and IR Ratio 800nm / 1020nm.

Warning

The IR detector (L) supports, Integrated Band Depth 1000nm IR, 1.3µm reflectance, Olivine Index, LCP Index, HCP Index, Spectral Variance, ISlope1, Band Depth 1435nm, Band Depth 1500nm, Ice 1, Ice 2, Band Depth 1750, Band Depth 1900, Integrated Band Depth 2µm, Band Depth 2100nm, Band Deoth 2210nm, Band Depth 2290nm, 2.3µm Drop, 2.33µm & 2.53µm Band Depth, Band Depth 3000nm, Band Depth 3100nm, Band Depth 3200nm, Band Depth 3400nm, Band Depth 1270µmO2, 3.9µm Gauge, Band Depth 1400nm H20,Band Depth 2000nm CO2, Band Depth 2350, Band Depth 2600, IR Ratio 2, Reflectance 2700nm, Band Depth 2700, IR Ratio 3.

Note

Do to compatibility issues between the GDAL PDS driver and the TRR3 data product, we rewrite a label, appended with '_fixed.lbl' for each input image. Additionally, we derive an ENVI .hdr file. These workarounds allow GDAL to support the TRR3 data files without changes to the label files supplied by the team.

Warning

If an output with the same name already exists, the new output overwrites the old output. That is, if you run the script twice without supplying a file name, the new output will overwrite your old output.

Surface

Reflectance at 770µm

Rationale : rock / dust

Algorithm : R770

Code Snippet:

$ python csas.py --R770 input.IMG output.tif

Red / Blue Ratio

Rationale : rock / dust

Algorithm : \frac{R770}{R440}

Code Snippet:

$ python csas.py --RBR input.IMG output.tif

Band Depth at 530nm

Rationale : Crystalline ferric minerals

Algorithm : $\begin{aligned} & a = \frac{wv530 - wv440}{wv709 - wv440} \nonumber\\ & b = 1.0 - a \nonumber\\ & bd530 = \frac{R530}{(a*R709)+(b*R440)} \end{aligned}$

Code Snippet:

$ python csas.py --BD530 input.IMG output.tif

Shoulder 600nm

Rationale : Select ferric minerals

Algorithm : $\begin{aligned} & a = \frac{wv600 - wv533}{wv710 - wv533} \nonumber\\ & b = 1.0 - a \nonumber\\ & bd600 = \frac{R600}{(a*R530)+(b*R709)} \end{aligned}$

Code Snippet:

$ python csas.py --SH600 input.IMG output.tif

Band Depth 640nm

Rationale : Select ferric minerals, especially maghemite

Algorithm : $\begin{aligned} & a = \frac{wv648 - wv600}{wv709 - wv600} \nonumber\\ & b = 1.0 - a \nonumber\\ & bd640 = \frac{R600}{(b*R600)+(a*R709)} \end{aligned}$

Code Snippet:

$ python csas.py --BD640 input.IMG output.tif

Band Depth 860

Rationale : Select ferric minerals ('hematite band')

Algorithm : $\begin{aligned} & a = \frac{wv860 - wv800}{wv984 - wv800} \nonumber\\ & b = 1.0 - a \nonumber\\ & bd860 = \frac{R860}{(a*R800)+(b*R984)} \end{aligned}$

Code Snippet:

$ python csas.py --BD860 input.IMG output.tif

Band Depth 920

Rationale : Select ferric minerals ('Pseudo BDI1000 VIS')

Algorithm : $\begin{aligned} & a = \frac{wv920 - wv800}{wv984 - wv800} \nonumber\\ & b = 1.0 - a \nonumber\\ & bd920 = \frac{R920}{(b*R800)+(a*R984)} \end{aligned}$

Code Snippet:

$ python csas.py --BD920 input.IMG output.tif

RPeak 1

Rationale : Fe mineralogy

Algorithm : Wavelength where 1st derivative=0 of 5th order polynomial fit to R600, R648, R680, R710, R740, R770, R800, R830

Code Snippet:

$ python csas.py --RPEAK1 input.IMG output.tif

Warning

This is computationally expensive, and a slow implementation. Expect runtimes between 15 and 30 minutes for a 1GB image.

Integrated Band Depth 1µm Visible

Rationale : Crystalline Fe+2 or Fe+3 minerals

Algorithm : Divide R830, R860, R890, R915 by RPEAK1 then
integrate over (1 - normalized radiances)

Code Snippet:

$ python csas.py ----BDI1000VIS input.IMG output.tif

Warning

This algorithm must first run RPeak1 (15 - 30 minutes) and then integrate again over 4 bands. This is computationally expensive and will require 35+ minutes.

Integrated Band Depth 1000 IR

Rationale : Crystalline Fe+2 minerals; corrected for overlying aerosol induced slope

Algorithm : Divide R1030, R1050, R1080, R1150 by linear fit from peak R between 1.3 - 1.87 microns to R2530 extrapolated backwards, then integrate over (1 - normalized radiances)

Code Snippet:

$ python csas.py ----BDI1000IR input.IMG output.tif

Warning

Not yet implemented.

1.3µm Reflectance (IR Albedo)

Rationale : IR Albedo

Algorithm : R1330

Code Snippet:

$ python csas.py --IRAlbedo input.IMG output.tif

Olivine Index

Rationale : Olivine will be strongly +; based on fayalite

Algorithm : \frac{R1695}{(0.1*R1080)+(0.1*R1210)+(0.4*R1330)+(0.4R1470)}-1

Code Snippet:

$ python csas.py --OlIndex input.IMG output.tif

Olivine Index 2

Rationale : Olivine Index for TRDR v3

Algorithm : Unknown

Warning

Not yet implemented by the CAT team.

HCP Index

Rationale : Pyroxene is strongly +; favors high-Ca pyroxene

Algorithm : 100 * (\frac{R1470-R1080}{R1470+R1080} / \frac{R1470-R2067}{R1470+R2067})

Code Snippet:

$ python csas.py --HCP input.IMG output.tif

Note

Algorithm differs from published - coded as per CAT

LCP Index

Rationale : Pyroxene is strongly +; favors low-Ca pyroxene

Algorithm : 100 * (\frac{R1330-R1080}{R1330+R1080} / \frac{R1330-R1815}{R1330+R1815})

Code Snippet:

$ python csas.py --LCP input.IMG output.tif

Note

Algorithm differs from published - coded as per CAT

Spectral Variance

Rationale : Ol & Px will have high values; Type 2 areas will have low values

Algorithm : Variance of observed data from a line fit from 1.0 - 2.3µm

Code Snippet:

$ python csas.py --VAR input.IMG output.tif

Warning

Not yet implemented.

ISlope1

Rationale : Ferric coating on dark rock

Algorithm : \frac{R1815-R2530}{wv2530 - wv1815}

Code Snippet:

$ python csas.py --ISLOPE1 input.IMG output.tif

Band Depth 1435nm

Rationale : CO2 surface ice

Algorithm : $\begin{aligned} & a = \frac{wv1430 - wv1370}{wv1470 - wv1370} \nonumber\\ & b = 1.0 - a \nonumber\\ & bd1435 = \frac{R1470}{(b*R1370)+(a*R1470)} \end{aligned}$

Code Snippet:

$ python csas.py --BD1435 input.IMG output.tif

Band Depth 1500mn

Rationale : H2O surface ice

Algorithm : 1.0 - (\frac{R1558 + R1505}{R1808 + R1367})

Code Snippet:

$ python csas.py --BD1500 input.IMG output.tif

Note

Algorithm differs from published - coded as per CAT (reduced instrument noise)

ICER1

Rationale : CO2, H20 ice mixtures

Algorithm : \frac{R1430}{R1510}

Code Snippet:

$ python csas.py --ICER1 input.IMG output.tif

Band Depth 1750

Rationale : Gypsum

Algorithm : $\begin{aligned} & a = \frac{wv1750 - wv1557}{wv1815 - wv1557} \nonumber\\ & b = 1.0 - a \nonumber\\ & bd1750 = \frac{R1750}{(b*R1557)+(a*R1815)} \end{aligned}$

Code Snippet:

$ python csas.py --BD1750 input.IMG output.tif

Band Depth 1900

Rationale : H2O, chemically bound or adsorbed

Algorithm : 1.0 - (\frac{R1972 + R1927}{R2006 + R1874})

Code Snippet:

$ python csas.py --BD1900 input.IMG output.tif

Note

Algorithm differs from published - coded as per CAT (reduced instrument noise)

Integrated Band Depth 2µm

Rationale : Pyroxene abundance and particle size

Algorithm : divide R1660, R1815, R2140, R2210, R2250, R2290, R2330, R2350, R2390, R2430, R2460 by linear fit from peak R between 1.3 - 1.87 microns to R2530, then integrate over (1 - normalized radiances)

Code Snippet:

$ python csas.py --BDI2000 input.IMG output.tif

Warning

Not yet implemented.

Band Depth 2100

Rationale : Monohydrated minerals

Algorithm : $\begin{aligned} & a = \frac{((wv2120 - wv2140)/2)-wv1930}{wv2250 - wv1930} \nonumber\\ & b = 1.0 - a \nonumber\\ & bd2100 = 1.0 - (\frac{(R2120 + R2140)*0.5}{(b*R1930)+(a*R2250)}) \end{aligned}$

Code Snippet:

$ python csas.py --BD2100 input.IMG output.tif

Band Depth 2210

Rationale : Al-OH minerals: monohydrated minerals

Algorithm : $\begin{aligned} & a = \frac{wv2210 - wv2140}{wv2250 - wv2140} \nonumber\\ & b = 1.0 - a \nonumber\\ & bd2210 = 1.0 - (\frac{(R2210}{(b*R2140)+(a*R2250)}) \end{aligned}$

Code Snippet:

$ python csas.py --BD2210 input.IMG output.tif

Band Depth 2290

Rationale : Mg,Fe-OH minerals (at 2.3); also CO2 ice (at 2.292 microns)

Algorithm : $\begin{aligned} & a = \frac{wv2290 - wv2250}{wv2350 - wv2250} \nonumber\\ & b = 1.0 - a \nonumber\\ & bd2290 = 1.0 - (\frac{(R2290}{(b*R2250)+(a*R2350)}) \end{aligned}$

Code Snippet:

$ python csas.py --BD2290 input.IMG output.tif

2.3µm Drop

Rationale : Hydrated minerals; particularly clays

Algorithm : $\begin{aligned} & slope = \frac{band2530 - band1815}{wv2530 - wv1815}\nonumber\\ & cr2290 = R1815 + slope * (wv2290 - wv1815)\nonumber\\ & cr2320 = R1815 + slope * (wv2320 - wv1815)\nonumber\\ & cr2330 = R1815 + slope * (wv2330 - wv1815)\nonumber\\ & cr2120 = R1815 + slope * (wv2120 - wv1815)\nonumber\\ & cr2170 = R1815 + slope * (wv2170 - wv1815)\nonumber\\ & cr2210 = R1815 + slope * (wv2210 - wv1815)\nonumber\\ & drop = 1.0 - (\frac{\frac{R2290}{cr2290}+\frac{R2320}{cr2330}+\frac{R2330}{cr2330}}{\frac{R2120}{cr2120}+\frac{R2170}{cr2170}+\frac{R2210}{cr2210}}) \end{aligned}$

Code Snippet:

$ python csas.py --D2300 input.IMG output.tif

SIndex

Rationale : Hydrated minerals; particularly sulfates

Algorithm : 1.0 - (\frac{R2100 + R2400}{2 * R2290})

Code Snippet:

$ python csas.py --SINDEX input.IMG output.tif

ICER2

Rationale : CO2 ice will be >>1, H2O ice and soil will be about 1

Algorithm : \frac{R2530}{R2600}

Code Snippet:

$ python csas.py --ICER2 input.IMG output.tif

BDCarb

Rationale : Carbonate overtones

Algorithm : $\begin{aligned} & a = \frac{(0.5(wv2330+wv2120))-wv2230}{wv2390-wv2230}\nonumber\\ & b = 1.0 -a \nonumber\\ & c = \frac{(0.5(wv2530+wv2120))-wv2390}{wv2600-wv2390}\nonumber\\ & d = 1.0 - c\nonumber\\ & BDCarb = 1.0 - (\sqrt{\frac{R2330}{(b*R2230)+(a*R2390)}*\frac{R2530}{(d*R2230)+(c*R2600)}}) \end{aligned}$

Code Snippet:

$ python csas.py --BDCARB input.IMG output.tif

BD3000

Rationale : H2O, chemically bound or adsorbed

Algorithm : 1.0 - (\frac{R3000}{R2530 * \frac{R2530}{R2210}})

Code Snippet:

$ python csas.py --SINDEX input.IMG output.tif

Band Depth 3100

Rationale : H2O ice

Algorithm : $\begin{aligned} & a = \frac{wv3120 - wv3000}{wv3250 - wv3000} \nonumber\\ & b = 1.0 - a \nonumber\\ & bd3100 = 1.0 - (\frac{(R3120}{(b*R3000)+(a*R3250)}) \end{aligned}$

Code Snippet:

$ python csas.py --BD3100 input.IMG output.tif

Band Depth 3200

Rationale : CO2 ice

Algorithm : $\begin{aligned} & a = \frac{wv3320 - wv3250}{wv3390 - wv3250} \nonumber\\ & b = 1.0 - a \nonumber\\ & bd3200 = 1.0 - \frac{(R3320}{(b*R3250)+(a*R3390)} \end{aligned}$

Code Snippet:

$ python csas.py --BD3200 input.IMG output.tif

BD3400

Rationale : Carbonates; organics

Algorithm : $\begin{aligned} & c = \frac{(0.5(wv3390+wv3500))-wv3250}{wv3630-wv3250}\nonumber\\ & d = 1.0 - c\nonumber\\ & BD3400 = 1.0 - \frac{(R3390 + R3500)*0.5}{(d*R3250)+(c*R3630)} \end{aligned}$

Code Snippet:

$ python csas.py --BD3400 input.IMG output.tif

CINDEX

Rationale : Carbonates

Algorithm : \frac{R3750 + (R3750 - R3630)}{(wv3750 - wv3630)*(wv3920 - wv3750)} / (R3920 - 1)

Code Snippet:

$ python csas.py --BD3400 input.IMG output.tif

Note

Algorithm differs from published - coded as per CAT

[1]Pelkey, S.M. et al. (2007). CRISM multispectral summary products: Parameterizing minearl diversity on Mars for reflectance. Journal of Geophysical Research, v.112.