Could you give more details on how you calculated the uncertainty and how were the rating curves developed?

Nonetheless, the uncertainty in this curves is usually linked to the methods used to estimate or measure discharge (or measure velocity), which do have large uncertainties easily above 20% of the estimated discharge. Assuming that the measurements in different watersheds were taken in exactly the same manner (which is of course imposible, but nevertheless), it could happen that uncertainty in velocity measurments (with the Area - Velocity method as the most usual means of estimating discharge) is favored by a complex hydraulic geometry.

If your area interest are different catchment area, you may got the different uncertainity level and can not not correlated. The factors and parameters to developed rating curve are different and unique for each catchment area, such as river morfometri, hydraullic of suface water level, rainfall intensity, soil hydrology group and lanc cover. Even though you can develop correlation the uncertainity and hydrologic phenomenan for each parameters or factors for unique catchment area only.

Thanks for your response.

Vikram, Don't know if it would answer your question, but pl have a look at this paper, and the approach we followed for uncertainty analysis. Best,

Article Estimation of Columbia River Virgin Flow: 1879 to 1928

Conference Paper Estimation of the Columbia River virgin flow.

The reason could be the different hydraulic characteristics for each hydrometric station and also the measurement technique used for flow measurement, this includes the frequency of measurements also.

Article Uncertainty regarding instantaneous discharge obtained from ...

The uncertainty in the rating curve is driven by two factors: the quality of the measurements and the complexity of the rating curve. The quality of the measurements includes the uncertainty in the individual discharge measurements, the number of discharge measurements, and how these are distributed with stage height. The complexity of the rating curve is determined from the structure of the cross section: low complexity for a v-notch weir (at least until the water level exceeds the top of the structure); high for natural structures. The more complex the rating curve, the more observations are needed to achieve the same level of precision. There is also the issue of the condition of the control (e.g. has there been excessive plant growth, sedimentation, erosion) which can lead to an increase in the uncertainty in the rating curve as the rating curve will vary in time (hence limiting the number of observations used for estimating the rating curve at any particular time.

A note concerning the individual flow measurements: these are made by multiple measures of the flow velocity at different points in the cross section. Under the assumption that the cross section has been well sampled, the estimated average flow velocity will be reliable. However, what is generally missed is that by using the average of a number of observations, we should also consider the standard deviation as the standard error in the mean is given by the standard deviation divided by the square root of the number of independent observations. Assuming each observation is independent (calibration errors will be correlated between observations), the standard error will give us a lower bound on the uncertainty in the estimated flow velocity, and hence in the estimated discharge.

@Barry:Thanks for your answer.

I have calculated the error now and would like to know, how do we know weather the error either is because of  incorrect measurement in stage or discharge?

Any methodology for this?

Mainly, you need to know details about how the stage measurements were taken (what instruments were used (including limit of reading and precision), what calibrations were done (including frequency, and size of error on before recalibration) and details about the structure used, Without this information it will be difficult to distinguish between the error in the stage and the rating curve.

If you have very high resolution stage data (near minute resolution), then you could look at the stage height data to try to understand the limit of reading and precision without information about the instrument, but if you only have longer term average values (e.g. daily), then this is not possible.

If you can get information about how the measurements were made, then you can estimate the error in the stage height and compare this to the scatter in the data used to derive the rating curve. To do this compare the projection of the uncertainty in the stage height onto discharge using the fitted rating curve, and compare this to the uncertainty in the discharge due to the uncertainty in the rating curve. If you consider the stage height and rating curve uncertainties as being uncorrelated (generally a good assumption), then they will combine as the sum of squares:

overall uncertainty = sqrt(a2+b2)

where a is the uncertainty in the stage height measurements, and b is the uncertainty from the rating curve. If there is a significant difference between a and b then you only need to consider the larger value.

Dear Barry

Thanks for informative knowledge. Will try this but would like to request you can you please provide me any literature in support of above theory.

As far as stage measurement is concern, I have measured it manually and validated it with the recording sensor which is also there. The time when I measured discharge at same time I also measured stage from fixed location.

 And discharge is being measured by salt dilution method as it works better for mountainous catchment rather than current meter.

Hi You assume there would a close to constant uncertainty for all rating tables. It really depends on how did you start with. Did you just use mathmatics to match the observation curve? Then the uncertainty or say the error is merely factored in how good your fit is. If you embeded some principles in your model, such as a standard process/technic in fitting, then the differences in the uncertainty may indicate whether the gauge is behaving 'irregularly'. 

As an environmental engineer, I always check the on-site conditions rather than relying on pure mathmatics. Obvisouly you need to make sure this difference doesn't come from mathmatics or measurements. 

The 'environmantal reasons' for a variation in uncertainty involve:

-High flow flutuations

-Local water whirlpools(high Re number turblent flow)

-Rocky river bed(causing water not flowing at a surface)

@Liao:

Hello I would like to mention that I have used some spastics principles followed by published literature.  

Onsite consideration has been taken care while measuring depth and it influences discharge.

Hi Vikram, Sure then you would have understood my points in previous response. I just listed some possible hydrological phenomenons for you to considerate. If you want to cooperate high level theoretical reasoning, you should certainly follow my supervisor Barry Croke's instruction. However he is not easy to understand, so I just suggest you to argue the possiblity of my mentioned hydrological conditions to form a good thesis.

Our team is able to reach NSE=0.99 for rating table modelling, which converts to a  neglectable uncertainty. Wish you would support our finding when I publish related paper. Thank you.

i agree with Rafael Anleu