Relatively short distances with no added tributaries or water diversions should have little change in discharge between sections.  That being said, sections can sometimes have water inflow or outlet that can only be measured with data collected.  If your inflow is down to bedrock section, and for example, lower stream sections are dominated by deep cobbles and gravel, you can have substantial hyporeic (in channel substrate) flow that would not normally be measured as surface flow.  Geologic fissures or porous contacts have potential to serve as inflow or outflow, depending on circumstance.  These are not typical, but possible.  If your inflow and outflow discharge values are about the same, the assumption is probably all discharges are the same.  It is not unusual to have somewhat more discharge as you go downstream, due to increased watershed size, so if small increase in outlet flow, that is probably the answer, as each cross section from the inlet toward outlet has a slightly larger watershed area.

Thank you a lot  for your response. I see the point. However I need to know if there is any statistical method how to calculate/ interpolate discharge in the ungauged sections.

What is the input value and output value?  What is the change in wateshed size for input and output?  

You may want to normalize flow by watershed area.  Determine the inflow cubic meters per second per square kilometer, and the outflow the same units.  If they are close to the same, then use that or just prorate the change as watershed size increases as you move to the downstream cross sections as an estimate.  Statistics involves collecting more than inflow and outflow data.   

Discharge measures are typically not exact anyway, and +- 10% considered good.  So if you measured discharge during a stable flow day, at all the cross sections, there would probably some measurement error to consider, along with the change in watershed size from inflow to,outflow.  Statistics often enters when you replicate masurement data at each site.  At best, you might estimate flow from interpretation, based on assumptions.  To use statistics, you cannot estimate or interpret data. 

It is not unusual for stream gauging agencies to move slightly upstream or downstream, based on flow level, to get a better cross section, especially if trying to gauge low flows.  On small streams, low flow can sometimes disappear (hyporheic) for a distance, then reappear.  If you have a gaining stream, some periods of flow will have adjacent water,table and/or groundwater influx.  If loosing stream, there may be some losses.  If important for the study, more data at some of the other cross sections should be considered to,help validate some of the assumptions made.

If you know the inflow at upstream and want to know the discharge downstream somewhere then flood routing is the useful technique. 

Even you can use HEC-HMS and HEC-RAS package. 

We have often used discharge from an adjacent or nearby similarly-sized gauged catchment to estimate the ungauged discharge. We use the simple assumption that the discharge is proportional to catchment area for similar catchments. We also have used similar assumption to estimate the added discharge between the most downstream gauge point on a stream, and the discharge as is enters a lake. Others have assumed non-linear relationships, but we found the simple area proportionality assumption is adequate. We discussed estimating total freshwater discharge to Lake Pontchartrain (Louisiana, USA) in this publication

https://www.researchgate.net/publication/269705794_Annual_salinity_and_nutrient_budget_of_Lake_Pontchartrain_and_impact_of_the_proposed_Bonnet_Carre_Diversion

Conference Paper Annual salinity and nutrient budget of Lake Pontchartrain an...

Hi

you need  a profile or river section and measuring the velocity of water pass the cross section of river(you need field measurements and survey works)

best wishes

you can use HEC program to interpolate cross section and find the discharge

Dr. William and Dr. Michael have very clearly explained on the topic. Thank you both for the same. First of all 'statistics' is all about analysing the data sets, and if you don't have the data, what type of statistical analysis you can do ??

Only approach to your problem is extrapolation technique, for this you have to find out an identical watershed (in terms of shape, drainage pattern, topography and even landuse) where inflow and outflow data are available and extrapolate the same to the ungauged watershed according to its size. You have to understand that this is an approximate measure. The discharge from a watershed can be less or even more than the inflow depending on the interaction of groundwater with the surface water along the river course.

Dr. Prasad, I think getting a statistical sense of the uncertainty of the method you finally select is possible. Apply the estimation method to a similar stream where there are existing discharge measurements. Comparison of measured to estimated discharge could then be assumed to have similar uncertainty to that in the un-gauged stream. 

Dr. Prasad,

IF you have the other model input data sets, you can use distributed models. Take the X,Y,Z coordinate of each cross section point and force your model to use this points as an outlet. Then you will have that number of sub-catchments one routed to the next.

William F. Hansen answer is good.

Following

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