The question is not very clear. If you are interested in how to differentiate upstream, midstream and downstream of a river, upstream is the direction towards the source or mouth of a river or stream. Downstream is the direction the river flows towards while midstream is the portion between the upstream and downstream of the river.
If your interest is in pollution monitoring of the river, then the physical, chemical and biological indicators of the river water quality can be monitored from designated sampling points which can be represented as upstream, midstream and downstream of the river. The upstream represents the control point.
I need to classify the a few water quality monitoring stations in one river stretch. Is there any method to classify 1 station located downstream or middle stream?
The upstream of the river is defined as the upper portion of the river where it is started, then the medium portion will be the middle portion of the river, and finally the downstream of one river will be the lower portion where it is moving into the sea or ocean or of a bigger river.
Apart from specific definitions that may be used in a particular discipline, the terms upstream and downstream can be best viewed as the direction of water flow relative to a position on a stream, such as a sampling site or monitoring station. So of course, stating the obvious, upstream will be the direction against the flow towards the source and downstream with the flow towards the river mouth and any delta that may exist. In general I would use midstream as the location midway between the headwaters and mouth (this could be measured rectilinearly or along the course traversed by the stream, talweg - read on); it could also be defined as the point of median flow rate or velocity along the stream.
This may help in terms of identifying sampling sites that are upstream or downstream of the midpoint by whichever definition is applicable to your study.
In other instances interest may be in lateral profile of the stream in which case the talweg of thalweg is the midpoint, although I would not refer to this as midstream. The definition of talweg used by fluvial gemorphologists is the lowest elevation within the valley in which a stream flows and is the curvi-linear line that is used to measure the stream length and so the midstream point will lie on the talwag regardless of whether you choose to use distance or stream velocity/flow rate (remembering that stream velocity will vary transversely across the stream profile).
Others may offer other definitions relevant to their field of study, as per the suggestion about using riparian or stream basin vegetation (cover abundance, floristic composition, or physiognomic structure), but it is up to you to decide which one best suits your research or monitoring. If you are using these terms in a scientific publication or technical report then make sure that you clearly define them in the text.
I think what you may be looking for is termed a typology of rivers. Of course, rivers have been classified in lots of different ways, depending on the purpose of the classification. Appropriate definitions will also depend on the region and geography of where the rivers occur. A system like the Amazon or the Mississippi would need a very different classification from the local river where I live. Common descriptions for the sections of the river would be headwaters, upland reaches, lowland reaches, alluvial plains and estuarine sections.
Note that the links below are not necessarily the best available; they are just what I could find with a quick online search, and they will give you ideas for further searches! ;)
A long-standing method is to classify the stream order, as in the following descriptions:
The River Continuum Concept also classifies rivers, with a system based on the nature of the river in various sections with regard to the physical and biological characteristics.
The EU European Water Framework Directive has developed a physical typology for rivers and lakes. This paper discusses its development and application.
Article A new broad typology for rivers and lakes in Europe: Develop...
You may find that none of the "official" classifications suit your purpose, and you will have to define your own. However, these links may give you some ideas on appropriate characteristics to be looking at.
I will add one more region to what you have given.
Upstream= After leaving the water source, its flow is fast. The bed is narrow and curved forward. It is rich in oxygen. It is clear and cold. Trout are generally found in this region. The bottom of the bed is stony and gravelly. May beetle larvae are seen. Aquatic plants are either absent or not very developed.
Middle stream= Water flow rate has decreased. Its bed is enlarged and relatively flattened. Aquatic plants begin to increase on the coasts. The base is sandy and gravelly. The water temperature has increased a few degrees, the oxygen has decreased a little. Gammarus are seen on the water floor. Whiskered fish such as Barbus species are seen.
Downstream= The flow rate of the water has decreased considerably. The bed has expanded, the depth has decreased. High aquatic plants have increased on the coasts and in the water. The color of the water has changed due to turbidity and plankton. The temperature of the water increased and the amount of dissolved oxygen decreased. The water floor is generally sandy-muddy. Cyprinidae species live in this region. Fish species diversity has increased.
Dead zone-water region: It is the region where the stream meets the sea. The bed expands. The water flow rate has almost stopped. In most cases there is a blurry- muddy water appearance. Marine fish species are also found. Water is very rich in nutrients. However, not many aquatic plants are seen.