If taken during the same event and vacinity, stream A is smallest, C is largest, unless there is significant orographic differences such as rain shadow.  Typically stage is plotted as x axis, discharge is y axis, and relationship is curvalinear.  My guess is the data is made up or really unusual channel form to get a perfectly linear form, although C could be curvalinear shape if that one flow rate with two markedly different stages had one point removed.  Both stream cross section and mean velocity typically increase with stage, resulting in a curvalinear plot of data.  Are you plotting culvert data?  Since I have concerns about data, there is really no point in speculating further, and it is always best to actually visit the sites where data is collected, than try to speculate on channel type and watershed function from a small amount of stream data with no other information.  If you do not have any examples of what data form to expect and how data is commonly plotted, I can send you an example from the Blue Ridge Mountains.  I am not in my computer.

I would like to add, if you have increasing stage and cross section, the only way to keep a linear relationship is reducing mean velocity, and this could be caused in some circumstances as increased roughness or velocity impact such as from boulders or markedly dense vegetation increasingly blocking flow as stage increases.  Normally, this is not a place selected to measure flow.

Hello William

I like your suggestion, and would like to say that, I often visit my watershed and these are data from streams not culvert. How can I really correlate my data with the roughness.

While taking the stage and discharge care has been taken as prescribed in manual and guideline.

OK, I am sending an example of a stream gauged at one stage, the readings are in English units of feet, feet per second, cubic feet per second.  If you send me an example of one of your measurements, or one at high stage and one at low stage, and perhaps a picture of the site, perhaps I can look over what you  have and offer more discussion.  With stream stage, the velocity and cross section typically increases.  If this is a braided stream network or some other unusual channel form that I am not used to seeing, perhaps that could explain.  When the stream goes onto the floodplain, the mean velocity can decrease due to the added roughness.  I have an example of a stage discharge relationship in the mountains, but did not have it loaded in this computer or external hard drive.    

I think you know the main hydraulic relationships governing stage discharge function.

You have:

1. a discrete relationship wetted area [Aw] as a function af stage [FWL = free water level]

2. a discrete relationship wetted perimeter [Pw] as a function of FWL

3. The speed equation: V = C*sqrt(R*So), where So is the hydraulic slope or, for lower enough stages, channel slope; R = hydraulic radius [Aw/Pw], Chezy's coefficient.

4. If your data (mainly Q) are derived from Q=Aw*V, (and I supose that is your data, because you rise the problem of rougness)  where V was measured, then C=  V/sqrt(R*So).

5. Knowing that C=power(R,1/6)/n, where n is Manning coefficient of roughness, is very simple to obtain it.

For the mountainous catchments you can use some usefull relationships for roughness, as Jarrett (1984), Thorne et Zevenbergen (1985), Bathurst (2002), Ugarte et Madrid-Aris (1994), Comiti et al (2007), Rickenmann (1990, 1991, 1994, 1996), Alonso et Fernandez (2003), Madrid – Aris (1992). Having the cross section geometry elements, and some granulometry samples, you can obtain theoretical values of roughness and compare with those resulted from your data.

If you have some patience to translate from Romanian, you can find a lot of answers about your question in my paper https://www.researchgate.net/publication/264420090_RELATII_DE_AJUSTARE_A_GEOMETRIEI_HIDRAULICE_A_ALBIILOR_MONTANE_IN_BAZINE_HIDROGRAFICE_MICI_PREDOMINANT_FORESTIERE_thesis_chapter. 

And pay attention at the stage - discharge relationship, as Mr. Hansen said. Usualy it is power function, as it results from an analysis of Q = Aw*V relationship. So you can use a log - log linear fitting instead a simply linear adjustment. More, you can ad 1 to all data (Q and FWL) and then apply log function. In that manner you can surprise also the point of zero stage and zero discharge.

An other aspect you must take into account is that of lack of coincidence of discharge at the same stage, between rising and descending parts of the hydrograph.

Thesis RELAŢII DE AJUSTARE A GEOMETRIEI HIDRAULICE A ALBIILOR MONTA...