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Calculating NDVI from Landsat 8 USGS Tiles

PeterWilson

I'm busy writing a Python module to calculate the NDVI (Normalized Difference Vegetation Index) based on the following post: Using Python to calculate NDVI with multiband imagery. According to the USGS background data on Landsat 8 Product, the tiles are provided as Digitial Numbers 16-bit unsigned integer format. The current examples (tutorials and reference material) that I've found to calculate NDVI use Landsat 5 + 7 which is stored as 8-bit unsigned integer format. Can I still use the same formula to calculate NDVI for Landsat 8 that is now stored as 16-bit unsigned integer format. The formula that I'm using is found in: Making Spatial Decisions Using GIS and Remote Sensing: A Workbook

NDVI = (IR-R)/(IR+R)

ArcGIS: USGS Landsat 8 GeoTIFF (Bands 4 + 5)

ArcGIS: scale range of Landsat 8 Bands 4 + 5

USGS: Using the USGS Landsat 8 Product

USGS EarthExplorer: Landsat 8 Dataset Selection

USGS EarthExplorer: Landsat 8 Download Options

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Accepted answers

DanPatterson_Retired

Peter, if you are checking the script for whether it is working, run it manually and compare results.

Your only other alternative is to generate 'images' that have a known patterns of values from which you could calculate NDVI. This can be done in numpy

ir <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">64</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">128</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="number token">128</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">192</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">255</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="number token">255</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">128</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN>&nbsp; <SPAN class="comment token"># I have left 0's out for now</SPAN>

r <SPAN class="operator token">=</SPAN> np<SPAN class="punctuation token">.</SPAN>swapaxes<SPAN class="punctuation token">(</SPAN>ir<SPAN class="punctuation token">,</SPAN> <SPAN class="number token">1</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">)</SPAN>

r 
array<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">[</SPAN>&nbsp; <SPAN class="number token">1</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">128</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">255</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="punctuation token">[</SPAN> <SPAN class="number token">64</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">192</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">128</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="punctuation token">[</SPAN><SPAN class="number token">128</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="number token">255</SPAN><SPAN class="punctuation token">,</SPAN>&nbsp;&nbsp; <SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN>

np<SPAN class="punctuation token">.</SPAN>divide<SPAN class="punctuation token">(</SPAN>ir <SPAN class="operator token">-</SPAN> r<SPAN class="punctuation token">,</SPAN> ir <SPAN class="operator token">+</SPAN> r<SPAN class="punctuation token">)</SPAN>&nbsp; <SPAN class="comment token"># or whatever</SPAN>
 
array<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">[</SPAN> <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="punctuation token">,</SPAN> <SPAN class="operator token">-</SPAN><SPAN class="number token">0.33333333</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="operator token">-</SPAN><SPAN class="number token">0.33159269</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="punctuation token">[</SPAN> <SPAN class="number token">0.33333333</SPAN><SPAN class="punctuation token">,</SPAN>&nbsp; <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="punctuation token">,</SPAN>&nbsp; <SPAN class="number token">0.33159269</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="punctuation token">[</SPAN> <SPAN class="number token">0.33159269</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="operator token">-</SPAN><SPAN class="number token">0.33159269</SPAN><SPAN class="punctuation token">,</SPAN>&nbsp; <SPAN class="number token">0</SPAN><SPAN class="punctuation token">.</SPAN>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="line-numbers-rows"><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN><SPAN>‍</SPAN></SPAN>

Obviously, the only catch is to use masked arrays to mask 0 values to prevent division by zero errors. (hope I got stuff right... scale the input ranges to suit)

All comments

DanPatterson_Retired

not sure I follow... 16 bit isn't 0-255 https://en.wikipedia.org/wiki/16-bit 8-bit is https://en.wikipedia.org/wiki/8-bit

PeterWilson

Hi Dan

I found the following on ResearchGate:

Based on the following I presume that I should be able to calculate the NDVI using same formula, its just that the Landsat 8 is being stored in 16-bit and not 8-bit.

Cody Benkelman

Peter

Agreed with Dan, you should be using the full 16 bit range, not scaling to 8 bit. The simple difference ratio equation you show
NDVI = (IR-R)/(IR+R)
IS the equation for NDVI. It does not have any requirement to be 8 bit (0-255) so you should use the full range of values available in the data.
Second, unless this is purely an exercise for you to learn more Python, why start from scratch? ArcGIS can immediately calculate NDVI for you - let us know which version you have (ArcGIS Pro 2.0.1? ArcMap?) and we can advise for how to do it. Note the NDVI tools within ArcGIS may automatically apply a color ramp, but you'll presumably want the "scientific" version which outputs the raw floating point values.
NOTE - this will give you pixel values from -1.0 to +1.0, and you'll presumably need to rescale/convert those for VIEWING the data - but if you're attempting any quantitative analysis, you'll want to do that work with the floating point values for best accuracy

PeterWilson

Hi Cody

Thanks for the response. I'd like to determine the NDVI for the dry and wet season for my study area and then determine the difference between the two. I'm currently still using ArcGIS 10.3.1, unfortunately no ArcGIS Pro. The link that I provided in my initial post is a blog post by ESRI Australia: Using Python to calculate NDVI with multiband imagery, that has a Python script for determing the NDVI. If you are able to assist in the approach I need to following once I've determined the NDVI for say (i.e. 2017 Feb (Wet) and 2017 Oct (Dry)) ,how I can show the difference in NDVI between the wet and dry season. I'd like to be able to code the following in Python as its part of a larger water project that I'm busy with.

DanPatterson_Retired

a difference is sa.Minus

PeterWilson

Hi Dan

I completed writing my Python module to automatically generate NDVI rasters from Landsat 8 tiles (Downloaded from USGS EarthExplorer) with TOA Reflectance and Sun Angle correction.

NDVI: With TOA Reflectance and Sun Angle correction

NDVI: Value range (between 1 and -1)

<SPAN class="string token">'''
Created on 23 Sep 2017

Create NDVI Rasters

with TOA Reflectance

and Sun Angle

correction

@author: PeterW
'''</SPAN>
<SPAN class="comment token"># import site-packages and modules</SPAN>
<SPAN class="keyword token">import</SPAN> re
<SPAN class="keyword token">import</SPAN> argparse
<SPAN class="keyword token">from</SPAN> pathlib <SPAN class="keyword token">import</SPAN> Path
<SPAN class="keyword token">import</SPAN> arcpy
<SPAN class="keyword token">from</SPAN> arcpy<SPAN class="punctuation token">.</SPAN>sa <SPAN class="keyword token">import</SPAN> <SPAN class="operator token">*</SPAN>


<SPAN class="keyword token">def</SPAN> <SPAN class="token function">list_landsat_tiles</SPAN><SPAN class="punctuation token">(</SPAN>landsat_dir<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="string token">"""
&nbsp;&nbsp;&nbsp; Create a list of Landsat 8
&nbsp;&nbsp;&nbsp; tiles bands 4 & 5.
&nbsp;&nbsp;&nbsp; """</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="comment token"># Determine how to prevent nested loops - Big 0 Notation</SPAN>
&nbsp;&nbsp;&nbsp; landsat_tiles <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">{</SPAN><SPAN class="punctuation token">}</SPAN>
&nbsp;&nbsp;&nbsp; ndvi_bands <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="string token">'_B4.TIF'</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="string token">'_B5.TIF'</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="string token">'_MTL.txt'</SPAN><SPAN class="punctuation token">]</SPAN>
&nbsp;&nbsp;&nbsp; p <SPAN class="operator token">=</SPAN> Path<SPAN class="punctuation token">(</SPAN>landsat_dir<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">for</SPAN> directory <SPAN class="keyword token">in</SPAN> p<SPAN class="punctuation token">.</SPAN>iterdir<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="comment token"># add error handling to validate its subdirectories</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">for</SPAN> band <SPAN class="keyword token">in</SPAN> ndvi_bands<SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; match <SPAN class="operator token">=</SPAN> <SPAN class="string token">'*{0}'</SPAN><SPAN class="punctuation token">.</SPAN>format<SPAN class="punctuation token">(</SPAN>band<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; landsat_tile <SPAN class="operator token">=</SPAN> str<SPAN class="punctuation token">(</SPAN>directory<SPAN class="punctuation token">.</SPAN>glob<SPAN class="punctuation token">(</SPAN>match<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">.</SPAN>next<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; landsat_name <SPAN class="operator token">=</SPAN> str<SPAN class="punctuation token">(</SPAN>directory<SPAN class="punctuation token">.</SPAN>stem<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; landsat_key <SPAN class="operator token">=</SPAN> re<SPAN class="punctuation token">.</SPAN>findall<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'_(\d{6})_\d{8}_(\d{8})'</SPAN><SPAN class="punctuation token">,</SPAN> landsat_name<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; landsat_tiles<SPAN class="punctuation token">.</SPAN>setdefault<SPAN class="punctuation token">(</SPAN>landsat_key<SPAN class="punctuation token">,</SPAN> <SPAN class="punctuation token">[</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">.</SPAN>append<SPAN class="punctuation token">(</SPAN>landsat_tile<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">return</SPAN> landsat_tiles


<SPAN class="keyword token">def</SPAN> <SPAN class="token function">remove_zero_values</SPAN><SPAN class="punctuation token">(</SPAN>landsat_tiles<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="string token">"""
&nbsp;&nbsp;&nbsp; Convert zero cell values
&nbsp;&nbsp;&nbsp; to NoData.
&nbsp;&nbsp;&nbsp; """</SPAN>
&nbsp;&nbsp;&nbsp; arcpy<SPAN class="punctuation token">.</SPAN>CheckOutExtension<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'Spatial'</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">for</SPAN> k<SPAN class="punctuation token">,</SPAN> v <SPAN class="keyword token">in</SPAN> landsat_tiles<SPAN class="punctuation token">.</SPAN>iteritems<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; red_band <SPAN class="operator token">=</SPAN> SetNull<SPAN class="punctuation token">(</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="string token">'value=0'</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; NIR_band <SPAN class="operator token">=</SPAN> SetNull<SPAN class="punctuation token">(</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">,</SPAN> <SPAN class="string token">'value=0'</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="operator token">=</SPAN> red_band
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="operator token">=</SPAN> NIR_band
&nbsp;&nbsp;&nbsp; arcpy<SPAN class="punctuation token">.</SPAN>CheckInExtension<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'Spatial'</SPAN><SPAN class="punctuation token">)</SPAN>


<SPAN class="keyword token">def</SPAN> <SPAN class="token function">extract_reflectance_coefficients</SPAN><SPAN class="punctuation token">(</SPAN>landsat_tiles<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="string token">"""
&nbsp;&nbsp;&nbsp; Extract the reflectance
&nbsp;&nbsp;&nbsp; coefficients from metadata
&nbsp;&nbsp;&nbsp; txt file.
&nbsp;&nbsp;&nbsp; """</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">for</SPAN> k<SPAN class="punctuation token">,</SPAN> v <SPAN class="keyword token">in</SPAN> landsat_tiles<SPAN class="punctuation token">.</SPAN>iteritems<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">with</SPAN> open<SPAN class="punctuation token">(</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">2</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN> <SPAN class="keyword token">as</SPAN> mlt<SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; lines <SPAN class="operator token">=</SPAN> mlt<SPAN class="punctuation token">.</SPAN>read<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">.</SPAN>splitlines<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; reflect_mult <SPAN class="operator token">=</SPAN> float<SPAN class="punctuation token">(</SPAN>lines<SPAN class="punctuation token">[</SPAN><SPAN class="number token">187</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">.</SPAN>split<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'='</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">2</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="operator token">=</SPAN> reflect_mult
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; reflect_add <SPAN class="operator token">=</SPAN> float<SPAN class="punctuation token">(</SPAN>lines<SPAN class="punctuation token">[</SPAN><SPAN class="number token">196</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">.</SPAN>split<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'='</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; v<SPAN class="punctuation token">.</SPAN>append<SPAN class="punctuation token">(</SPAN>reflect_add<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; sun_elev <SPAN class="operator token">=</SPAN> float<SPAN class="punctuation token">(</SPAN>lines<SPAN class="punctuation token">[</SPAN><SPAN class="number token">76</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">.</SPAN>split<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'='</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; v<SPAN class="punctuation token">.</SPAN>append<SPAN class="punctuation token">(</SPAN>sun_elev<SPAN class="punctuation token">)</SPAN>


<SPAN class="keyword token">def</SPAN> <SPAN class="token function">toa_reflectance_correction</SPAN><SPAN class="punctuation token">(</SPAN>landsat_tiles<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="string token">"""
&nbsp;&nbsp;&nbsp; Correct landsat 8
&nbsp;&nbsp;&nbsp; bands 4 & 5
&nbsp;&nbsp;&nbsp; for TOA reflectance
&nbsp;&nbsp;&nbsp; """</SPAN>
&nbsp;&nbsp;&nbsp; arcpy<SPAN class="punctuation token">.</SPAN>CheckOutExtension<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'Spatial'</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">for</SPAN> k<SPAN class="punctuation token">,</SPAN> v <SPAN class="keyword token">in</SPAN> landsat_tiles<SPAN class="punctuation token">.</SPAN>iteritems<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; reflect4 <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">(</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">2</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="operator token">*</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="operator token">+</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">3</SPAN><SPAN class="punctuation token">]</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="operator token">=</SPAN> reflect4
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; reflect5 <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">(</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">2</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="operator token">*</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="operator token">+</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">3</SPAN><SPAN class="punctuation token">]</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="operator token">=</SPAN> reflect5
&nbsp;&nbsp;&nbsp; arcpy<SPAN class="punctuation token">.</SPAN>CheckInExtension<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'Spatial'</SPAN><SPAN class="punctuation token">)</SPAN>


<SPAN class="keyword token">def</SPAN> <SPAN class="token function">sun_angle_correction</SPAN><SPAN class="punctuation token">(</SPAN>landsat_tiles<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="string token">"""
&nbsp;&nbsp;&nbsp; Correct Landsat 8
&nbsp;&nbsp;&nbsp; bands 4 & 5
&nbsp;&nbsp;&nbsp; for sun angle
&nbsp;&nbsp;&nbsp; """</SPAN>
&nbsp;&nbsp;&nbsp; arcpy<SPAN class="punctuation token">.</SPAN>CheckOutExtension<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'Spatial'</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">for</SPAN> k<SPAN class="punctuation token">,</SPAN> v <SPAN class="keyword token">in</SPAN> landsat_tiles<SPAN class="punctuation token">.</SPAN>iteritems<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; sun4 <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">(</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="operator token">/</SPAN><SPAN class="punctuation token">(</SPAN>Sin<SPAN class="punctuation token">(</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">4</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="operator token">=</SPAN> sun4
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; sun5 <SPAN class="operator token">=</SPAN> <SPAN class="punctuation token">(</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="operator token">/</SPAN><SPAN class="punctuation token">(</SPAN>Sin<SPAN class="punctuation token">(</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">4</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="operator token">=</SPAN> sun5
&nbsp;&nbsp;&nbsp; arcpy<SPAN class="punctuation token">.</SPAN>CheckInExtension<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'Spatial'</SPAN><SPAN class="punctuation token">)</SPAN>


<SPAN class="keyword token">def</SPAN> <SPAN class="token function">calculate_ndvi</SPAN><SPAN class="punctuation token">(</SPAN>landsat_tiles<SPAN class="punctuation token">,</SPAN> output_dir<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="string token">"""
&nbsp;&nbsp;&nbsp; Generate NDVI from
&nbsp;&nbsp;&nbsp; preprocessed
&nbsp;&nbsp;&nbsp; landsat 8 bands 4 & 5
&nbsp;&nbsp;&nbsp; """</SPAN>
&nbsp;&nbsp;&nbsp; arcpy<SPAN class="punctuation token">.</SPAN>env<SPAN class="punctuation token">.</SPAN>overwriteOutput <SPAN class="operator token">=</SPAN> <SPAN class="token boolean">True</SPAN>
&nbsp;&nbsp;&nbsp; arcpy<SPAN class="punctuation token">.</SPAN>CheckOutExtension<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'Spatial'</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="keyword token">for</SPAN> f<SPAN class="punctuation token">,</SPAN> v <SPAN class="keyword token">in</SPAN> landsat_tiles<SPAN class="punctuation token">.</SPAN>iteritems<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; NDVI_name <SPAN class="operator token">=</SPAN> <SPAN class="string token">'_'</SPAN><SPAN class="punctuation token">.</SPAN>join<SPAN class="punctuation token">(</SPAN>f<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; arcpy<SPAN class="punctuation token">.</SPAN>AddMessage<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'Processing {0}.tif NDVI'</SPAN><SPAN class="punctuation token">.</SPAN>format<SPAN class="punctuation token">(</SPAN>NDVI_name<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Num <SPAN class="operator token">=</SPAN> Float<SPAN class="punctuation token">(</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="operator token">-</SPAN> v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Denom <SPAN class="operator token">=</SPAN> Float<SPAN class="punctuation token">(</SPAN>v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">1</SPAN><SPAN class="punctuation token">]</SPAN> <SPAN class="operator token">+</SPAN> v<SPAN class="punctuation token">[</SPAN><SPAN class="number token">0</SPAN><SPAN class="punctuation token">]</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; NDVI_raster <SPAN class="operator token">=</SPAN> Divide<SPAN class="punctuation token">(</SPAN>Num<SPAN class="punctuation token">,</SPAN> Denom<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; NDVI_output <SPAN class="operator token">=</SPAN> <SPAN class="string token">'{0}\\{1}.tif'</SPAN><SPAN class="punctuation token">.</SPAN>format<SPAN class="punctuation token">(</SPAN>output_dir<SPAN class="punctuation token">,</SPAN> NDVI_name<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; NDVI_raster<SPAN class="punctuation token">.</SPAN>save<SPAN class="punctuation token">(</SPAN>NDVI_output<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; arcpy<SPAN class="punctuation token">.</SPAN>CheckInExtension<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'Spatial'</SPAN><SPAN class="punctuation token">)</SPAN>


<SPAN class="keyword token">def</SPAN> <SPAN class="token function">main</SPAN><SPAN class="punctuation token">(</SPAN>landsat_dir<SPAN class="punctuation token">,</SPAN> output_dir<SPAN class="punctuation token">)</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp; <SPAN class="string token">"""
&nbsp;&nbsp;&nbsp; Determine NDVI for
&nbsp;&nbsp;&nbsp; each Landsat tile.
&nbsp;&nbsp;&nbsp; """</SPAN>
&nbsp;&nbsp;&nbsp; landsat_tiles <SPAN class="operator token">=</SPAN> list_landsat_tiles<SPAN class="punctuation token">(</SPAN>landsat_dir<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; remove_zero_values<SPAN class="punctuation token">(</SPAN>landsat_tiles<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; extract_reflectance_coefficients<SPAN class="punctuation token">(</SPAN>landsat_tiles<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; toa_reflectance_correction<SPAN class="punctuation token">(</SPAN>landsat_tiles<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; sun_angle_correction<SPAN class="punctuation token">(</SPAN>landsat_tiles<SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; calculate_ndvi<SPAN class="punctuation token">(</SPAN>landsat_tiles<SPAN class="punctuation token">,</SPAN> output_dir<SPAN class="punctuation token">)</SPAN>


<SPAN class="keyword token">if</SPAN> __name__ <SPAN class="operator token">==</SPAN> <SPAN class="string token">'__main__'</SPAN><SPAN class="punctuation token">:</SPAN>
&nbsp;&nbsp;&nbsp; parser <SPAN class="operator token">=</SPAN> argparse<SPAN class="punctuation token">.</SPAN>ArgumentParser<SPAN class="punctuation token">(</SPAN>description<SPAN class="operator token">=</SPAN><SPAN class="string token">'Calculate the NDVI for Landsat 8 tiles'</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; parser<SPAN class="punctuation token">.</SPAN>add_argument<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'--landsat_dir'</SPAN><SPAN class="punctuation token">,</SPAN> metavar<SPAN class="operator token">=</SPAN><SPAN class="string token">'path'</SPAN><SPAN class="punctuation token">,</SPAN> required<SPAN class="operator token">=</SPAN><SPAN class="token boolean">True</SPAN><SPAN class="punctuation token">,</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; help<SPAN class="operator token">=</SPAN><SPAN class="string token">'Input Landsat 8 tile directory'</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; parser<SPAN class="punctuation token">.</SPAN>add_argument<SPAN class="punctuation token">(</SPAN><SPAN class="string token">'--output_dir'</SPAN><SPAN class="punctuation token">,</SPAN> metavar<SPAN class="operator token">=</SPAN><SPAN class="string token">'path'</SPAN><SPAN class="punctuation token">,</SPAN> required<SPAN class="operator token">=</SPAN><SPAN class="token boolean">True</SPAN><SPAN class="punctuation token">,</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; help<SPAN class="operator token">=</SPAN><SPAN class="string token">'Output NDVI directory'</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; args <SPAN class="operator token">=</SPAN> parser<SPAN class="punctuation token">.</SPAN>parse_args<SPAN class="punctuation token">(</SPAN><SPAN class="punctuation token">)</SPAN>
&nbsp;&nbsp;&nbsp; main<SPAN class="punctuation token">(</SPAN>landsat_dir<SPAN class="operator token">=</SPAN>args<SPAN class="punctuation token">.</SPAN>landsat_dir<SPAN class="punctuation token">,</SPAN>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; output_dir<SPAN class="operator token">=</SPAN>args<SPAN class="punctuation token">.</SPAN>output_dir<SPAN class="punctuation token">)</SPAN>
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The only question that I have is that my output raster is between 1 and -1 but is not represented as 1 to -1 is that because of the actual values within my tile or is there a problem with my calculation?

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