I am using MODIS NDVI product (MOD13Q1) for the vegetation changes study. I want to remove cloudy or bad pixel from MODIS NDVI data. I am not getting any suitable method or software or any program to do this task.
Although it requires signing up for an account, you can do this through Google Earth Engine's API quite easily. They give comprehensive tutorials and scripts for how to do so, as well as the data products you are asking for. You can remove the cloudy/bad pixels from the NDVI product by adjusting the script of this tutorial for the data layers you'd like to use: https://developers.google.com/earth-engine/ic_composite_mosaic
As I know, there is a QA band in MOD13Q1 product. you can check on this link It indicate whether the pixel is covered by snow or cloud.
This group at the University of Colorado monitors storm surges and flooding globally using MODIS. You might look at their publications for some insight on their dealings with clouds... I know that they use multiple days worth of images from both Terra and Aqua to produce their products.