I am looking for the value of the HDI, that it would be possible to separate USGS gauges to non-urbanized, semi-urbanized and urbanized watersheds based on that. As I am working in the ArcGIS, I need quantitative values for this index.
Many, perhaps most, of USGS gauges are located to provide a baseline of streamflow, and typically avoid heavily urbanized areas. There is some instances that urban areas fund stream gauging stations to quantify flows for their area, and of course many instances where urban areas may be included as portions of a hydrologic unit. The information of each station usually includes an approximation of land uses, such as forest, agriculture, urban. One may exist, but I know of no HDI breakup into categories, but in GIS, you have substantial ability to select and change values to suit your purpose.
Due to the potential effects are substantial on the functioning of a watershed and streams, I would suggest these categories for your consideration, and see how they might match up with others. Non-urbanized could be looked at as zero, but you may allow up to 5%, as zero may be difficult. Test using zero first, see how many you find, and then make a decision at being a little more inclusive up to a max of 5%. Even at 5%, there are some potential effects, so this category should have a really low value. I think semi-urbanized may include up to 25% urban, and urbanized over 25% urban.
Another way that I have sometimes used to classify might be using forest and grasslands as primarily undisturbed to low disturbance frequency, and then comparing to cultivated lands and urban areas as disturbed, even though the urbanization including roads is typically the biggest impact.
Since you mentioned the acronym HDI, perhaps there is some official classification to consider, and if I find something, I will send to you.
You may be looking for this, and attached a paper on various aspects of selecting watersheds in another study. There are other efforts at categorizing disturbance, the HDI by Falcone et al, 2010 is quite complex beyond considering urbanization, and has apparently caught some attention and repeated use or consideration.
Using watershed metrics like Effective Impervious Area has been successfully used to evaluate stream impairment. This might work well to classify urban, and suburban areas rather than general land cover metrics. Given your background in GIS, I recommend using EIA or similar classifications of the watershed land to develop thresholds. This literature is well developed in past decade. One threshold you could use is 10% EIA that has shown to have a shift in nature of impacts from rural to suburban conditions. Indices like HDI could help but using it to classify the type of land use impact on hydrograph is not straightforward.
Thank you very much for your valuable answers and comments and sorry for being late in replying here.
My research is to find the different impacts of urbanization on the streams in various climates and I was looking for the USGS gauges with the trace of the urbanization. In this regard, first I used HDI to filter some of the gauges. After that, I checked the upstream region of the gauges to see a: the drainage area of each one (smaller areas had more priority because they are more sensitive to urbanization) and b: the urbanized area (to be sure that a part of high HDI is because of the urbanized elements).