03 With rating curve

Stage-discharge transformation

Water level series can be transformed in discharge series by use of a stage-discharge relation of one of the following forms:
1. single channel rating curve
2. compound channel rating curve
3. rating curve with unsteady flow correction
4. rating curve with constant fall backwater correction
5. rating curve with normal fall backwater correction
6. user structure equation
7. measuring structure relations.
The first five transformations will be dealt with in this section. The options 6 and 7 are presented in the sections about structure and measurement structure transformation.
For a particular station the combination of water level(s) and discharge series, cross-sections and structure parameters required to transform stages into discharges can be stored in the database to facilitate the transformation at subsequent occasions.

Single and compound channel rating curve

If a single channel rating curve is used the stage-discharge transformation reads:
(parabolic)
or:
(power)
where:
Q_t = discharge at time t (m³ /s)
h_t = water level at time t
a₁ ,b₁ ,c₁ = parameters of parabolic equation
a₂ ,b₂ ,c₂ = parameters of power-equation
i = index for water level interval for which the parameters are valid (1£i£3)
When compound channel rating is selected, the discharge for the flood plain interval will be computed by adding the discharge computed for the river-section up to the maximum flood plain level using the parameters for the one but last interval, and the discharge computed for the flood plain section for the last interval: Qfp = Qr + Qfc.

Rating curve with unsteady flow correction

If a rating curve is used with the Jones correction for unsteady flow, the stage-discharge transformation reads:

where:

• Q_ct is computed by equation of the simple rating curve
• 
  with
  a₃ ,b₃ ,c_{3 {}} = parameters
  h_min = the lowest water level for which the Jones correction is applied
• the rate of change of the water level in time is determined from:
  
  with:
  Dt = time interval between two successive observations. If h_t+1 or h_t-1 does not exist, its value is replaced by h_t and the denominator by Dt.
  The required entries are similar to the entries for the single channel rating curve transformation.
  

  Rating curve with constant fall backwater correction

  If a rating curve is used with the constant fall backwater correction procedure, the stage-discharge transformation reads:
  
  where:
• Q_rt is computed by the simple rating curve equation with h_t replaced by h_1t
• the fall F_t is computed from:
• F_t = h_1t - h_2t
  with:
• h_1t = upstream station water level series
• h_2t = downstream station water level series
• the reference fall F_r and power p are parameters.
  

  Rating curve with normal fall backwater correction

  If a rating curve is used with the normal fall backwater correction procedure, the stage-discharge transformation reads:
  for h_t >h_min or F_t <F_rt
  or:
  Q_t = Q_rt for h_t £h_min or F_t ³F_rt
  where:
• Q_rt is computed by the simple rating curve equations
• F_t is computed by equation for constant fall
• The reference fall follows from:
  for h_t > h_min
  with:
• a₄ ,b₄ ,c₄ = parameters
• the power p in the equation is read from the database.
  The required entries are similar to the entries for the constant fall backwater correction procedure.
  

  Application

  Select the function <Stage-Discharge Transformation> from the Flow Measurements functions map.
  

  Series Codes

  Select a water level series by highlighting the series in the series list and pressing <Select> after the water level series textbox. HYMOSwill extract all Stage-Discharge relations for this station within the specified period from the database and place them in the spreadsheet on the form.
  When the checkbox "Original discharge series" is activated, the computed discharge values can be compared with an original or earlier computed discharge series.
  

  Rating curve

  If more than one rating curve exists within the selected time period, select the relation by clicking on the appropriate spreadsheet tab. The values of each rating curve can be changed for calculation by editing the cells of the spreadsheet.
  After you made your selections press <Execute> and analyse the results as a graph, table or report. To show the graph on screen select <Graph> from the functions tab. To analyse the report press <Report> from the functions tab.
  You can also Save the generated series by pressing the <Save> button or exporting the series by selecting <Export>.
  Non-equidistant water level time series data can be used. The available water level within the requested discharge time interval will be converted to discharge.
  and multiplied by the number of minutes till next water level within the time interval, etc. Summing up these volumes and dividing the sum by the total minutes in the time interval gives the discharge.
  Example
  
• Discharge time interval: day.
• First water level at 8 hours and 22 min, converted to discharge = 14 m3/s.
• Next water level, same day, at 15 hours and 30 min, converted = 16 m3/s.
• Let's assume the last value of the previous day = 12 m3/s (ignored at start of period).
• The result will be: ((8 * 60 + 22) * 12 + (15 * 60 + 30 - (8 * 60 + 22)) * 14 +(24 * 60 - (15 * 60 + 30)) * 16) / 1440
  The value of a previous day is always taken into account, even when days ago, unless a value for missing data is entered for the water level, in which case a new start is assumed.