Fitting of rating curve
HYMOS includes following options to fit stage-discharge data by a rating curve:
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A graph of the stage-discharge data can be shown by pressing the <Graph> button. The data points in this graph are linked with the spreadsheet of the 'Fitting of Rating Curves' form, therefore it is easy to select outliers and flag them to zero. All data with a flag set to '0' are not taken into the rating curve computation. By clicking a point in the graph a label with the number of the stage-discharge data will be shown in the graph next to the selected point. By clicking the point in the graph again the label will disappear. By holding the shift key pressed on the keyboard and selecting the point in the graph the flag of the selected point will be set to zero in the spreadsheet. When a flag of a stage-discharge data is set to zero the point will be removed from the graph. The same can be achieved by changing the flag number to '0' in the spreadsheet. When the flag of a stage-discharge data is set to 1 again the point will be shown again in the graph with stage-discharge data.
Simple rating curve
When unsteady flow and backwater effects are negligibly small the stage-discharge data can be fitted by a single channel relationship, valid for a given period of time and water level range.
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where:
t = Student t-value at 95% probability
P = value dependent on type of equation
with: P = h~i~ for parabolic equation
P = ln(h~i~ + a~2~ ) for power equation
= variance of P
Compound channel rating curve (for power equation only)
The compound channel rating curve option has been introduced to avoid large values for the b-parameter and extremely low values for the c-parameter in the power equation for compound cross-sections (river+flood plain).
For this new option the last interval of water levels given will be treated as flood plain water levels. River discharge Qr will be computed for this last interval using the parameters computed for the one but last interval. A temporary floodplain discharge Qf is then computed by subtracting Qr from the observed discharge Qobs for the last water level interval: Qf = Qobs - Qr. Discharge Qf will be used to compute the parameters for a rating curve for the flood plain separately. These parameters together with the one(s) of the rating curve(s) for the other interval(s) will be stored.
Rating curve with unsteady flow correction
If the rate of change of the water level is high the stage-discharge relation will not be unique but it will show loopings for the rising and falling stages. Omitting the acceleration terms in de dynamic flow equation the relation between the unsteady discharge Q~m~ and steady discharge Q~c~ , see also Figure, is given by the Jones equation:
with:
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The factor 1/S~0~ v~w~ \[day/m\] varies with the water level. This factor is fitted by a parabolic function of h:
!02 Rating curves^image020.gif! _for h > h_ _~min~_
with:
_h_ _~min~_ ~~ = the lowest water level for which the Jones correction has to be applied. |
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In addition to h~min~ a maximum value for 1/S~0~ v~w~ has to be entered as well to avoid that unacceptably high values of 1/S~0~ v~w~ take part in the fit of equation. Remember that 1/S~0~ v~w~ is expressed in \[day/m\]!! |
Rating curve with backwater correction
Stage-fall-discharge or the twin gauge station fall-discharge methods are used to include backwater effects on stage-discharge ratings. hymosincludes:
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In these methods the fall F between the water level at the discharge measuring site and a downstream station is considered as an additional parameter, to account for the effect of water surface slope on discharge. Both methods are based on the following equation:
where:
Q~m~ = backwater affected discharge
Q~r~ = reference discharge
F~m~ = measured fall
F~r~ = reference fall
p = power, with: 0.4 £p £0.6
Constant-fall method
In this method the reference fall F~r~ is taken as a constant. A special case of the constant-fall method is the unit-fall method, where F~r~ = 1 m is applied.
In the computational procedure a value for F~r~ is assumed. Then a rating curve is fitted to the values:
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In the plot the fit of Q~r~ to the rating curve is shown, whereas in the error analysis the measured discharge Q~m~ is compared with the computed discharge according to the above equation.
Normal-fall method
In this method the reference fall F~r~ is modelled as a function of the water level: F~r~ = f(h). This function is represented by a parabola:
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- computation of the backwater free rating curve to represent reference discharge Q~r~
- fitting of normal fall equation to the reference falls.
Backwater free rating curve
To isolate the backwater free data from the rest of the measurements a data flag = 2 has to be added to the data. This is done by editing the spreadsheet column <Flag> from the screen and replacement of flag = 1 by 2 where applicable. Then to all backwater free data a rating curve is fitted analogous to the single channel rating curve procedure described in the previous section. Note that sufficient backwater free data have to be available for a proper fit, else data have to be added (temporarily) to shape the rating curve.
Reference fall
Next all remaining data above h~min~ with flag =1 are used to fit a parabola to the reference fall computed as:
where Q~r~ is the reference discharge Q~r~ = f(h) computed from the backwater free stage-discharge data. The parameter p is optimised between 0.4 and 0.6.
Application
To execute the <Fitting of Rating Curve> function the following selections must be made.
Station Codes
Select a station by clicking the checkbox in the stations list. HYMOSwill extract all Stage-Discharge data for this station within the specified period from the database and place them in the spreadsheet on the form. The specified period is the processing period defined in the <Time> tab of the HYMOS main window.
Graph
From the data in the spreadsheet a graph can be made by pressing the <Graph> button on the <Fitting of Rating Curve> form. All water levels and discharges on dates with a 'flag' not equal to zero will be presented in the graph. In the graph window the user can select to view the data on a linear or logarithmic scale. There is also the possibility to subtract a fixed value from all the water levels, for example the gauge zero value. This allows the user to better analyse the stage-discharge data on a logarithmic scale when the water levels have a reference which is much below the measured values. By clicking a point in the graph a label with the number of the stage-discharge data will be shown in the graph next to the selected point. By clicking the point in the graph again the label will disappear. By holding the shift key pressed on the keyboard and selecting the point in the graph the flag of the selected point will be set to zero in the spreadsheet.To exit this graph window press the <Close> button.
Rating Curve option
Select a Rating curve function by selecting the function in the list box. The special options will be enabled when selecting the function.
Function curve and Function intervals
Select what kind of function you want to fit and enter the number of interval levels with their minimum and maximum values.
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