I have collected data (spectral bands) from Landsat 4-5 and Landsat 8. I was calculating NDVI when I noticed that the two Landsats have different band numbers designated as Red and Near Infra Red (needed for NDVI calculation). When I checked the wavelengths associated with these bands here Landsat Band Description I noticed that the wavelengths also differ a bit. For example I used bands 3 and 4 (Red & Near Infra Red) from Landsat 4-5 and bands 4 and 5 (Red and Near Infra Red) from Landsat 8 for NDVI calculation, but the wavelength range of band 3 in Landsat 4-5 is not exactly the same as of band 4 in Landsat 8. Is there any way to convert things so that they are same and comparable. I got big variances between NDVI values from the two satellites that's why the confusion.
where ̅, RMSD, and ̅ are the mean difference, the root mean square deviation, and the mean relative difference respectively between corresponding Landsat-8 OLI (viOLI) and Landsat-4/5 ETM + (viETM +) values (TOA or surface spectral reflectance or NDVI) for n pixel values
Assume that TM bands respond linearly within 0-255 for spectral reflectances of 0-100%, then the change rate is 0.39% reflectance unit per DN unit.
For e.g., DN = 100, the actual DN values can be 99.5-100.5 as a result of truncation. That is, the reflectance error due to 8-bit quantization is half 0.39% (~0.20%). When correcting for solar effects, the reflectance should be divided by cos(SZA). At a large solar zenith angle (SZA), the reflectance error can be amplified. For SZA=60°, the error is 0.39%. This value is larger than that of OLI, but is still acceptable compared to other uncertainties, such as the 5% sensor calibration uncertainty.
SOURCES:https://www.sciencedirect.com/science/article/pii/S0034425715302455 and researchgate.
The results using bands 3/4 and 4/5 should be similar and comparable, but they cannot be converted to identical ones due to the difference in wavelengths. The difference in NDVI results between the two sensors is expected and normal, since you are comparing values from different dates (it is impossible to have similar dates from TM and 8 since Landsat 5TM was decommissioned before the release of Landsat 8): the results vary lesser due to sensor differences and more due to changes in vegetation health & cover and atmospheric effects. NDVI results can be different even between a short time, or even from the same sensor and date if you use correction on your data (TOA, surface reflectance etx).
The variety of NDVI across time(and not it's absolute values) is of interest in the use of NDVI (and other related vegetation indices) since it enables us in the interpretation of vegetation health, status and cover.