A typical solution to the frozen water problem is to use a "Water Year" instead of a calendar year. This time-shifts all frozen water at the end of one year to the beginning of the next year. A similar approach is to use a "Hydro-Ecological Year." Both of those methods time-shift the frozen water. My own approach, the "Locally Relevant Water Year" yields similar results in semi-arid lands in subtropical climates that are not subject to prolonged freezing. One additional approach is to limit your analysis to the growing season. I have mentioned several different approaches because it really depends on what type of drought you are trying to identify. Meteorological drought? Hydrological drought? Physiological drought?

Definitely consider Dr. Kamps response. If you have long term record, do you know of actual drought periods. I have not experienced what I would call a drought because of severe cold, frozen water and soils. I believe I can see your point, but the standard definitions of drought typically mention lack of rain as the precursor. Could a glacier under severe cold be in a drought? If water is flowing under thick ice, or hyporheic flow with a frozen channel be drought? I don’t know, but certainly streams can slow or stop flowing, even if full, under severe cold. If drought effects are limited to growing season, and the growing season turns ice cold, the plant is not going to be growing. Interesting!

Ray H. Kamps William F. Hansen Thank you so much. Yes, it is necessary to considerate Water Year or Eco-hydrological year. Because the relative lower flow caused by frozen in winter is not the actual hydrological drought, even there are lots of rainfall or solid precipitation. Is it possible to define a hydrological drought flee from frozen season? Or define a hydrological drought regarding meteorological drought?

Concerning flow duration curve and years of record, how many days would you consider drought? Perhaps you might have dryness drought periods (meteorological drought), and frozen water (such as solid hydrological drought). The frequency percentage over for example 50 years of flow data, would be the sum of days with no or minimal flow due to lack of rain, and sum of days of no or minimal flow from frozen soils and channels, divided by the number of days in 50 years. When you select 90%, that effectively says you expect on average 36.5 days a year to be in some form of drought. if freezing is a common problem each year, you will have days with zero flow if the stream gauging equipment is functional. In this instance, functional means the stream is frozen, and the water flowing recorded is zero. Maybe if you use a manometer, the bubbles cannot escape, I don’t know. Those should be easy to pick out.

Yanfeng Wu , I think that William F. Hansen and I are both trying to pick your brain for more information. The research target species or end-user is important for defining drought. I have been in situations of a "drought" when it has been raining every day for a week because the target or end-user of the water was humans, and a week of rain was insufficient to fill the reservoirs. I've also been in the situation of no rain for 3 months, but the trees were not suffering because they were phreatophytes and had access to deep ground water. It is axiomatic that ecosystems are adapted to their climate, so 50 cm of rain/year would be an incredibly wet year in one ecosystem, and a devastating drought in another.

Based only on the information that you've given us, I would say that you need to develop an algorithm to estimate storage and an algorithm to estimate evapotranspiration, and then develop some criteria for when a drought is occurring based on supply and demand. As William F. Hansen pointed out, plants will not be demanding water when the temperature is freezing. (This is also the basis for defining a Hydro-Ecological Year.)

With a long historical record, you have the advantage to be able to work backwards because if streamflow is higher than normal when the temperatures rise, then you can attribute that to greater frozen precipitation in the previous months, and so you can estimate storage. However, it is a lot of estimates and guesswork. Or, as we say in the business, "modelling."

Ray H. Kamps William F. Hansen Thank you for your valuable response. When considering froze, it is complex. However, according to you discussion above, I think I can try to define a drought with respect to precipitation, evapotranspiration and storage in a drainage watershed. For example, the SPEI have been widely used for defining meteorological droughts. But for daily hydrological drought, there are some different because flow are relevant to more factors. In fact, I finished modeling the hydrological processes in this watershed. But the hydrological model I am using excessively generalize ecological water demand. Hope you can give more suggestions. I really appreciate it.