Stage-Discharge Relationship

Using the data of stage and discharge collected for a stream, we can develop its stage-discharge relationship and describe it using a rating equation. Where the relationship is expected to stay consistent over time, it is said to be under permanent control.

A rating equation consists of three important parameters, namely Cr, beta and a. a is the value of stage associated with zero discharge. It is a hypothetical value that can only be determined using either Running’s method or empirical formula.

Cr and beta are both rating curve constants that are calculated using least-square error method. First, we need to convert the rating equation into a linear equation. Logarithmic operation is required for this. Then, we can simply apply the respective formula and determine them. Correlation coefficient is usually calculated together to describe how well the stage and discharge are correlated with each other. Positive value of the coefficient denotes the parameters are positively correlated. Value greater than 0.6 means the parameters are already in good correlation, and unity shows they are perfectly correlated.

The following show some information regarding the development of stage-discharge relationship. Watch the video above for full details.

Field measurement for stage and discharge
Permanent control and shifting control
Determination of rating curve parameter a using Running's method
Determination of rating curve parameter using formula
Arithmetic plot for stage-discharge relationship
Determination of rating curve constants Cr and beta
Example - determination of rating curve parameter a using Running's method
Example - determination of rating curve parameter a using formula
Solution for stage-discharge relationship
Solution for stage-discharge relationship

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