There are multiple drought indexes developed in USA to evaluate the drought effects. You can check them in this link: http://www.ncdc.noaa.gov/temp-and-precip/drought/drought-tools.php

Just using seasonal vegetation index (VI) from remote sensing may not be enough for evaluating the drought effect. You may want to use climatology data and long-term remote sensing VIs to find the anomaly of the vegetation. Besides VI, soil moisture, surface temperature observed from satellite can also be used for drought monitoring. But they will require more complex processing, usually with models.

Drought leads the rangeland become dry due to water sacristy and hence, it lost the vegetation (grazing/grass and others). Such kind of study you can carry out from the satellite remote sensing. However, you should keep in your mind that different seasonal variation also brings the area become dry for example summer.

You can try for NDVI, TVI, VHI studies from satellite images and compare with the precipitation and weather data for further analysis.

Further, given the information of how can use the remote sensing technology for rangeland studies.

Remote sensing technology for rangeland management applications by Paul T Tueller (https://journals.uair.arizona.edu/index.php/jrm/article/viewFile/8418/8030).

Improving Rangeland Monitoring and Assessment: Integrating Remote Sensing, GIS, and Unmanned Aerial Vehicle Systems. By Robert P. Breckenridge (The INL is a U.S. Department of Energy National Laboratory operated by Battelle Energy Alliance)

There are multiple drought indexes developed in USA to evaluate the drought effects. You can check them in this link: http://www.ncdc.noaa.gov/temp-and-precip/drought/drought-tools.php

Just using seasonal vegetation index (VI) from remote sensing may not be enough for evaluating the drought effect. You may want to use climatology data and long-term remote sensing VIs to find the anomaly of the vegetation. Besides VI, soil moisture, surface temperature observed from satellite can also be used for drought monitoring. But they will require more complex processing, usually with models.

Drought in rangelands results in lower vegetation production (or greenness as measured by a vegetation index) than during times of ample precipitation, especially for annual vegetation. You can use one of the many vegetation indexes, like the normalized difference vegetation index (NDVI), and compare growing-season greenness during a dry period with growing-season greenness during a wet period.

Depending on type of the vegetation and period of extreme drought or heat wave you can also analyze the different shape of the annual profile of NDVI, For example, when summer heat occurred, the second peak of the curve does not occurred in  temporal grasslands.

I guess everyone agrees that vagetation indices can be estimated using satellite data and can be used as measure for vegetation production. Also integration of TRMM with such datasets can give a good estimate of the actual precipitation in the area and further using different models (SWAT and others) the actual recharge can be precisely estimated. Alll thsi will help in understanding the effect of drought on rangeland.

Regarding to the remotely sensed methods for drought monitoring, I would suggest you to try this indices: the Perpendicular Drought Index (PDI) and Modified Perpendicular Drought Index (MPDI) in this paper below.

https://www.researchgate.net/publication/257129063_Drought_monitoring_in_Iran_using_the_perpendicular_drought_indices?ev=prf_pub

Article Drought monitoring in Iran using the perpendicular drought indices

You can monitor the draught estimating the evapotranspiration over time using remote sensing. There are several methods, including using thermal bands that allow to calculate ET from energy balance.

Drought effects the quality and quantity of grass in range lands.As the range lands are highly adapted to drought and arid climates,effects of drought are not that severe as in other crop areas.The range lands occupying large area and being not easily accessible,remote sensing is the best way to study the effect of drought  .There are so many indices to study the effect of drought on rage lands.NDVI  is one of the indices used for remotely understanding the drought effect.Scientists of ICARDA are reporting a lot on range lands.You can get some useful information from their studies.

The common methods for drought assessment and monitoring are the indices derived from freely remote sensing data such as AVHRR and MODIS. These indices like a  normalized difference vegetation index (NDVI), vegetation condition index (VCI). In addition, evapotranspiration as a good indicator for drought can be estimated from remote sensing data. 

You can assess drought of vegetation through a combination of band in a satellite image. The Landsat images, bands 2,3 and 4 are the most commonly used to assess the state of the vegetation, including the moisture content even at ground level.

Dianna you are right.

Dear friend,

The image analysis of red and infrared spectrum band value for mapping the range vegetation indices may reflect the real situation of the rangeland, and make available to the analysis with vegetation indices average value of NDVI for 30 years could be provided the datum of base line for mapping rangeland. However, it is perfectly alright when the analysis added with rainfall, LST, soil moisture for minimum of 30 years, soil depth and porosity, chemical components of the soils, land covers including vegetation types, etc. 

Take a look at VegDRI products, developed by the US Geological Survey. They integrate NDVI, precipitation, and other factors to estimate drought stress. It is generally able to capture dynamics on rangelands.

http://vegdri.cr.usgs.gov/overview.php

So many indices based on remote sensing are available for assessment of drought effect on crops and range lands.One has to relate different indices with productivity of different grass types to identify the better index for his/her region.Integration of remote sensing products with rainfall,soil moisture etc will also help in understanding the impacts on range lands.