Der Sujai,

You are absolutely right in being skeptical about using NDVI, not only because there is no vegetation on ice but also because that is anyway a poor and obsolete indicator of vegetation itself.

The main reason an "external" indicator is needed to assess the emissivity of surface components in the thermal domain is that emissivity is wavelength-dependent and potentially quite variable over heterogeneous land surfaces. However, ice and snow are relatively simple targets, compared to typical terrestrial environments, so you will be better off using a fixed value, as determined in the laboratory or from field studies. I found one publication (Advanced Concepts and Techniques in the Study of Snow and Ice Resources, edited by Henry S. Santeford, James LeRoy Smith, page 488) that reports an emissivity value of 0.985 for glacier ice, but you may probably find multiple sources on the Web.

Lastly, you may need to assess the sensitivity of your results to the value of the emissivity, and compare that to your expectations in terms of accuracy: you should invest considerable effort in defining the most appropriate value for your snow and ice surfaces only if an error in emissivity would result in unacceptable uncertainties in your products.

Best regards, Michel.

there is another problem while dealing with temperatures in landsat and that is both melting snow and cold water usually fall into one reflectance value and it is very difficult to differentiate between then as the classification might be narrow

If you want to calculate from thermal band of optical remote sensing like Landsat 8 or from previous years (Landsat 4-5) than you can use split window algorithm and spectral radiance model. plz follow the link below:

 https://www.researchgate.net/publication/301797360_Analyzing_land_surface_temperature_distribution_in_response_to_land_useland_cover_change_using_split_window_algorithm_and_spectral_radiance_model_in_Sundarban_Biosphere_Reserve_India#feedback/470802

Article Analyzing land surface temperature distribution in response ...

Hi Sujai,

Good to know you are working on Glaciers.

Regarding LST estimation of glaciers based on Landsat images, I agree with your assessment. NDVI based emissivity is a very crude method. Many use this method to estimate LST because this is the easiest way. Sobrino et al. (2004) uses average emissivity values of soils and vegetation from the list of samples present in the JPL ASTER Spectral library. I'm not sure if Snow & Ice were ever considered in their paper. However, as Prof. Michel suggested you can use one of the reported emissivity values of snow and ice from literature. The most crucial questions that you need to ask regarding this research was very well summed up by Prof. Michel's last paragraph. Therefore, please pay attention to what are the acceptable levels of uncertainties. LST itself comes with uncertainties, e.g., the algorithm used, the sensor used, atmospheric corrections, stray light effect (Landsat 8 TIRS) etc.

Having said that, I would suggest you to take a look at the ASTER derived emissivities for your study area. AST_05 is an on demand product that you can order for free. You may want to download as many ASTER derived emissivity images and study the values, compare it with values based on literature and come up with the most appropriate emissivity values for your study area. The reference links are attached.

https://lpdaac.usgs.gov/dataset_discovery/aster/aster_products_table/ast_05

www.mdpi.com/2072-4292/6/11/11244/pdf