HydPy-WQ (base model)

The HydPy-WQ base model provides features to implement small function-like submodels for calculating discharge based on information like the current water level.

Method Features

class hydpy.models.wq.wq_model.Model

Bases: AdHocModel, SubmodelInterface

HydPy-WQ (base model).

The following interface methods are available to main models using the defined model as a submodel:

• Calculate_Discharge_V1 Calculate the discharge based on the water depth given in m according to Brauer et al. (2014) and return it in mm/T.

• Set_WaterDepth_V1 Set the water depth in m.

• Set_WaterLevel_V1 Set the water level in m.

• Set_WettedArea_V1 Set the wetted area in m².

• Use_WaterDepth_V1 Set the water depth in m and use it to calculate all other properties.

• Use_WaterDepth_V2 Set the water depth in m and use it to calculate all other properties.

• Use_WaterLevel_V1 Set the water level in m and use it to calculate all other properties.

• Use_WaterLevel_V2 Set the water level in m and use it to calculate all other properties.

• Use_WettedArea_V1 Set the wetted area in m² and use it to calculate all other properties.

• Get_WaterDepth_V1 Get the water depth in m.

• Get_WaterLevel_V1 Get the water level in m.

• Get_WettedArea_V1 Get the wetted area in m².

• Get_WettedPerimeter_V1 Get the wetted perimeter in m.

• Get_SurfaceWidth_V1 Get the surface width in m.

• Get_Discharge_V1 Get the discharge in m³/s.

• Get_Celerity_V1 Get the wave celerity in m/s.

The following “additional methods” might be called by one or more of the other methods or are meant to be directly called by the user:

• Calc_WaterDepth_V1 Calculate the water depth based on the current water level.

• Calc_WaterDepth_V2 Calculate the water depth based on the current wetted area.

• Calc_WaterLevel_V1 Calculate the water level based on the current water depth.

• Calc_WettedAreas_V1 Calculate the wetted area for each trapeze range.

• Calc_WettedArea_V1 Sum up the individual trapeze ranges’ wetted areas.

• Calc_WettedPerimeters_V1 Calculate the wetted perimeter for each trapeze range.

• Calc_WettedPerimeter_V1 Sum up the individual trapeze ranges’ wetted perimeters.

• Calc_WettedPerimeterDerivatives_V1 Calculate the change in the wetted perimeter of each trapeze range with respect to the water level increase.

• Calc_SurfaceWidths_V1 Calculate the surface width for each trapeze range.

• Calc_SurfaceWidth_V1 Sum the individual trapeze ranges’ surface widths.

• Calc_Discharges_V1 Calculate the discharge for each trapeze range.

• Calc_Discharge_V2 Sum the individual trapeze ranges’ discharges.

• Calc_DischargeDerivatives_V1 Calculate the discharge change for each trapeze range with respect to a water level increase.

• Calc_DischargeDerivative_V1 Sum the individual trapeze ranges’ discharge derivatives.

• Calc_Celerity_V1 Calculate the kinematic wave celerity.

DOCNAME: DocName = ('WQ', 'base model')

REUSABLE_METHODS: ClassVar[tuple[type[ReusableMethod], ...]] = ()

class hydpy.models.wq.wq_model.Calculate_Discharge_V1

Bases: Method

Calculate the discharge based on the water depth given in m according to Brauer et al. (2014) and return it in mm/T.

Requires the control parameters:

ChannelDepth CrestHeight BankfullDischarge DischargeExponent

Requires the derived parameter:

CrestHeightRegularisation

Basic equation (discontinuous):

\[\begin{split}q = q_{max} \cdot \left( \frac{max(h-h_{max}, \ 0)}{h_{max}-h_{min}} \right)^x \\ \\ q = Discharge \\ q_{max} = BankfullDischarge \\ h = waterdepth \\ h_{max} = ChannelDepth \\ h_{min} = CrestHeight \\ x = DischargeExponent\end{split}\]

Examples:

>>> from hydpy.models.wq_walrus import *
>>> simulationstep("12h")
>>> parameterstep("1d")
>>> channeldepth(5.0)
>>> crestheight(2.0)
>>> bankfulldischarge(2.0)
>>> dischargeexponent(2.0)
>>> from hydpy import round_
>>> hs = 1.0, 1.9, 2.0, 2.1, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0

Without smoothing:

>>> crestheighttolerance(0.0)
>>> derived.crestheightregularisation.update()
>>> for h in hs:
...     round_([h, model.calculate_discharge_v1(h)])
1.0, 0.0
1.9, 0.0
2.0, 0.0
2.1, 0.001111
3.0, 0.111111
4.0, 0.444444
5.0, 1.0
6.0, 1.777778
7.0, 2.777778
8.0, 4.0

Without smooting:

>>> crestheighttolerance(0.1)
>>> derived.crestheightregularisation.update()
>>> for h in hs:
...     round_([h, model.calculate_discharge_v1(h)])
1.0, 0.0
1.9, 0.0
2.0, 0.00001
2.1, 0.001111
3.0, 0.111111
4.0, 0.444444
5.0, 1.0
6.0, 1.777778
7.0, 2.777778
8.0, 4.0

class hydpy.models.wq.wq_model.Calc_WaterDepth_V1

Bases: Method

Calculate the water depth based on the current water level.

Required by the methods:

Use_WaterLevel_V1 Use_WaterLevel_V2

Requires the control parameter:

BottomLevels

Requires the factor sequence:

WaterLevel

Calculates the factor sequence:

WaterDepth

Basic equation:

\[WaterDepth = max(WaterLevel - BottomLevels_{\,0}, \ 0)\]

Examples:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(2)
>>> bottomlevels(2.0, 3.0)
>>> factors.waterlevel(6.0)
>>> model.calc_waterdepth_v1()
>>> factors.waterdepth
waterdepth(4.0)

>>> factors.waterlevel(1.0)
>>> model.calc_waterdepth_v1()
>>> factors.waterdepth
waterdepth(0.0)

class hydpy.models.wq.wq_model.Calc_WaterDepth_V2

Bases: Method

Calculate the water depth based on the current wetted area.

Required by the method:

Use_WettedArea_V1

Requires the control parameters:

NmbTrapezes BottomWidths SideSlopes

Requires the derived parameters:

TrapezeHeights SlopeWidths TrapezeAreas

Requires the factor sequence:

WettedArea

Calculates the factor sequence:

WaterDepth

Basic equation:

\[\begin{split}WaterDepth = \begin{cases} a / w &|\ s = 0 \\ \left( \sqrt{4 \cdot s \cdot a + w^2} - w \right) / (2 \cdot s) &|\ s > 0 \\ \end{cases} \\ a = WettedArea \\ w = BottomWidth \\ s = SideSlope\end{split}\]

Examples:

One can understand Calc_WaterDepth_V2 as an inverse method of Calc_WettedAreas_V1 (and Calc_WettedArea_V1). Hence, the following convenience function allows the creation of examples that are directly comparable to those on method Calc_WettedAreas_V1:

>>> from hydpy import print_vector, round_
>>> def test(*wettedareas):
...     derived.trapezeheights.update()
...     derived.slopewidths.update()
...     derived.trapezeareas.update()
...     for a in wettedareas:
...         factors.wettedarea = a
...         model.calc_waterdepth_v2()
...         print_vector([a, factors.waterdepth.value])

The first example deals with identical rectangular trapezes. We pass different wetted areas to the test function. These are the sums of the wetted areas of the different trapeze ranges calculated in the first example on method Calc_WettedAreas_V1. As expected, method Calc_WaterDepth_V2 finds the water depths used as input data for this example. However, note that negative wetted areas result in zero water depths:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(3)
>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(2.0)
>>> sideslopes(0.0)
>>> factors.wettedarea = 0.0
>>> test(-0.5, 0.0, 1.0, 2.0, 4.0, 6.0, 9.0, 12.0, 15.0, 18.0)
-0.5, 0.0
0.0, 0.0
1.0, 0.5
2.0, 1.0
4.0, 1.5
6.0, 2.0
9.0, 2.5
12.0, 3.0
15.0, 3.5
18.0, 4.0

The second example deals with identical triangular trapezes and corresponds to the second example on method Calc_WettedAreas_V1:

>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(0.0)
>>> sideslopes(2.0)
>>> test(-0.5, 0.0, 0.5, 2.0, 4.5, 8.0, 12.5, 18.0, 24.5, 32.0)
-0.5, 0.0
0.0, 0.0
0.5, 0.5
2.0, 1.0
4.5, 1.5
8.0, 2.0
12.5, 2.5
18.0, 3.0
24.5, 3.5
32.0, 4.0

The third example deals with identical “complete” trapezes and corresponds to the third example on method Calc_WettedAreas_V1:

>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(2.0)
>>> sideslopes(2.0)
>>> test(-0.5, 0.0, 1.5, 4.0, 8.5, 14.0, 21.5, 30.0, 39.5, 50.0)
-0.5, 0.0
0.0, 0.0
1.5, 0.5
4.0, 1.0
8.5, 1.5
14.0, 2.0
21.5, 2.5
30.0, 3.0
39.5, 3.5
50.0, 4.0

The fourth example mixes three different geometries and corresponds to the fourth example on method Calc_WettedAreas_V1:

>>> bottomlevels(1.0, 3.0, 4.0)
>>> bottomwidths(2.0, 0.0, 2.0)
>>> sideslopes(0.0, 2.0, 2.0)
>>> test(-0.5, 0.0, 1.0, 2.0, 3.0, 4.0, 5.5, 8.0, 12.5, 18.0)
-0.5, 0.0
0.0, 0.0
1.0, 0.5
2.0, 1.0
3.0, 1.5
4.0, 2.0
5.5, 2.5
8.0, 3.0
12.5, 3.5
18.0, 4.0

class hydpy.models.wq.wq_model.Calc_WaterLevel_V1

Bases: Method

Calculate the water level based on the current water depth.

Required by the methods:

Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WettedArea_V1

Requires the control parameter:

BottomLevels

Requires the factor sequence:

WaterDepth

Calculates the factor sequence:

WaterLevel

Basic equation:

\[WaterLevel = WaterDepth + BottomLevels_{\,0}\]

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(2)
>>> bottomlevels(2.0, 3.0)
>>> factors.waterdepth(4.0)
>>> model.calc_waterlevel_v1()
>>> factors.waterlevel
waterlevel(6.0)

class hydpy.models.wq.wq_model.Calc_WettedAreas_V1

Bases: Method

Calculate the wetted area for each trapeze range.

Required by the methods:

Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

Requires the control parameters:

NmbTrapezes BottomWidths SideSlopes

Requires the derived parameters:

BottomDepths TrapezeHeights SlopeWidths

Requires the factor sequence:

WaterDepth

Calculates the factor sequence:

WettedAreas

Basic equation:

\[\begin{split}WettedAreas_i = \begin{cases} 0 &|\ d < 0 \\ (W_B + S_S\cdot d) \cdot d &|\ 0 \leq d < H_T \\ (W_B + W_S / 2) \cdot H_T + (W_B + W_S) \cdot (d - H_T) &|\ H_T \leq d \\ \end{cases} \\ \\ d = WaterDepth - BottomDepth_i \\ H_T = TrapezeHeights_i \\ W_B = BottomWidths_i \\ S_S = SideSlopes_i \\ W_S = SlopeWidths_i\end{split}\]

Examples:

The following convenience function executes Calc_WettedAreas_V1 for different water depths and prints the resulting wetted areas:

>>> from hydpy import print_vector, round_
>>> def test():
...     derived.bottomdepths.update()
...     derived.trapezeheights.update()
...     derived.slopewidths.update()
...     for d in [0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0]:
...         factors.waterdepth = d
...         model.calc_wettedareas_v1()
...         round_(d, end=": ")
...         print_vector(factors.wettedareas.values)

The first example deals with identical rectangular trapezes. There are no differences except those due to the different bottom levels:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(3)
>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(2.0)
>>> sideslopes(0.0)
>>> test()
0.0: 0.0, 0.0, 0.0
0.5: 1.0, 0.0, 0.0
1.0: 2.0, 0.0, 0.0
1.5: 3.0, 1.0, 0.0
2.0: 4.0, 2.0, 0.0
2.5: 5.0, 3.0, 1.0
3.0: 6.0, 4.0, 2.0
3.5: 7.0, 5.0, 3.0
4.0: 8.0, 6.0, 4.0

The second example deals with identical triangular trapezes. Here, the heights of the individual trapezes also matter because they mark where the triangular shape switches to a rectangular shape:

>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(0.0)
>>> sideslopes(2.0)
>>> test()
0.0: 0.0, 0.0, 0.0
0.5: 0.5, 0.0, 0.0
1.0: 2.0, 0.0, 0.0
1.5: 4.0, 0.5, 0.0
2.0: 6.0, 2.0, 0.0
2.5: 8.0, 4.0, 0.5
3.0: 10.0, 6.0, 2.0
3.5: 12.0, 8.0, 4.5
4.0: 14.0, 10.0, 8.0

The third example deals with identical “complete” trapezes by combining the first two geometries:

>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(2.0)
>>> sideslopes(2.0)
>>> test()
0.0: 0.0, 0.0, 0.0
0.5: 1.5, 0.0, 0.0
1.0: 4.0, 0.0, 0.0
1.5: 7.0, 1.5, 0.0
2.0: 10.0, 4.0, 0.0
2.5: 13.0, 7.0, 1.5
3.0: 16.0, 10.0, 4.0
3.5: 19.0, 13.0, 7.5
4.0: 22.0, 16.0, 12.0

The fourth example mixes three different geometries:

>>> bottomlevels(1.0, 3.0, 4.0)
>>> bottomwidths(2.0, 0.0, 2.0)
>>> sideslopes(0.0, 2.0, 2.0)
>>> test()
0.0: 0.0, 0.0, 0.0
0.5: 1.0, 0.0, 0.0
1.0: 2.0, 0.0, 0.0
1.5: 3.0, 0.0, 0.0
2.0: 4.0, 0.0, 0.0
2.5: 5.0, 0.5, 0.0
3.0: 6.0, 2.0, 0.0
3.5: 7.0, 4.0, 1.5
4.0: 8.0, 6.0, 4.0

class hydpy.models.wq.wq_model.Calc_WettedArea_V1

Bases: Method

Sum up the individual trapeze ranges’ wetted areas.

Required by the methods:

Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

Requires the control parameter:

NmbTrapezes

Requires the factor sequence:

WettedAreas

Calculates the factor sequence:

WettedArea

Basic equation:

\(WettedArea = \sum_{i=1}^{NmbTrapezes} WettedAreas_i\)

Examples:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(3)
>>> factors.wettedareas(2.0, 3.0, 1.0)
>>> model.calc_wettedarea_v1()
>>> factors.wettedarea
wettedarea(6.0)

class hydpy.models.wq.wq_model.Calc_WettedPerimeters_V1

Bases: Method

Calculate the wetted perimeter for each trapeze range.

Required by the methods:

Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

Requires the control parameters:

NmbTrapezes BottomWidths SideSlopes

Requires the derived parameters:

BottomDepths TrapezeHeights

Requires the factor sequence:

WaterDepth

Calculates the factor sequence:

WettedPerimeters

Basic equation:

\[\begin{split}WettedPerimeters_i = \begin{cases} 0 &|\ d < 0 \\ W_B + 2 \cdot d \cdot \sqrt{S_S^2 + 1} &|\ 0 \leq d < H_T \\ W_B + 2 \cdot H_T \cdot \sqrt{S_S^2 + 1} + 2 \cdot (d - H_T) &|\ H_T \leq d \\ \end{cases} \\ \\ d = WaterDepth - BottomDepth_i \\ H_T = TrapezeHeights_i \\ W_B = BottomWidths_i \\ S_S = SideSlopes_i\end{split}\]

Examples:

The following convenience function executes Calc_WettedPerimeters_V1 for different water depths and prints the resulting wetted perimeters:

>>> from hydpy import print_vector, round_
>>> def test():
...     derived.bottomdepths.update()
...     derived.trapezeheights.update()
...     for d in [0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0]:
...         factors.waterdepth = d
...         model.calc_wettedperimeters_v1()
...         round_(d, end=": ")
...         print_vector(factors.wettedperimeters.values)

The first example deals with identical rectangular trapezes. Note that method Calc_WettedPerimeters_V1 adds the contact surface between two adjacent trapeze ranges only to the wetted perimeter of the inner one:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(3)
>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(2.0)
>>> sideslopes(0.0)
>>> test()
0.0: 2.0, 0.0, 0.0
0.5: 3.0, 0.0, 0.0
1.0: 4.0, 2.0, 0.0
1.5: 5.0, 3.0, 0.0
2.0: 6.0, 4.0, 2.0
2.5: 7.0, 5.0, 3.0
3.0: 8.0, 6.0, 4.0
3.5: 9.0, 7.0, 5.0
4.0: 10.0, 8.0, 6.0

The second example deals with identical triangular trapezes. Here, the heights of the individual trapezes also matter because they mark where the triangular shape switches to a rectangular shape:

>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(0.0)
>>> sideslopes(2.0)
>>> test()
0.0: 0.0, 0.0, 0.0
0.5: 2.236068, 0.0, 0.0
1.0: 4.472136, 0.0, 0.0
1.5: 5.472136, 2.236068, 0.0
2.0: 6.472136, 4.472136, 0.0
2.5: 7.472136, 5.472136, 2.236068
3.0: 8.472136, 6.472136, 4.472136
3.5: 9.472136, 7.472136, 6.708204
4.0: 10.472136, 8.472136, 8.944272

The third example deals with identical “complete” trapezes by combining the first two geometries:

>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(2.0)
>>> sideslopes(2.0)
>>> test()
0.0: 2.0, 0.0, 0.0
0.5: 4.236068, 0.0, 0.0
1.0: 6.472136, 2.0, 0.0
1.5: 7.472136, 4.236068, 0.0
2.0: 8.472136, 6.472136, 2.0
2.5: 9.472136, 7.472136, 4.236068
3.0: 10.472136, 8.472136, 6.472136
3.5: 11.472136, 9.472136, 8.708204
4.0: 12.472136, 10.472136, 10.944272

The fourth example mixes three different geometries:

>>> bottomlevels(1.0, 3.0, 4.0)
>>> bottomwidths(2.0, 0.0, 2.0)
>>> sideslopes(0.0, 2.0, 2.0)
>>> test()
0.0: 2.0, 0.0, 0.0
0.5: 3.0, 0.0, 0.0
1.0: 4.0, 0.0, 0.0
1.5: 5.0, 0.0, 0.0
2.0: 6.0, 0.0, 0.0
2.5: 7.0, 2.236068, 0.0
3.0: 8.0, 4.472136, 2.0
3.5: 9.0, 5.472136, 4.236068
4.0: 10.0, 6.472136, 6.472136

class hydpy.models.wq.wq_model.Calc_WettedPerimeter_V1

Bases: Method

Sum up the individual trapeze ranges’ wetted perimeters.

Required by the methods:

Use_WaterDepth_V2 Use_WaterLevel_V2 Use_WettedArea_V1

Requires the control parameter:

NmbTrapezes

Requires the factor sequence:

WettedPerimeters

Calculates the factor sequence:

WettedPerimeter

Basic equation:

\(WettedPerimeter = \sum_{i=1}^{NmbTrapezes} WettedPerimeters_i\)

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(3)
>>> factors.wettedperimeters(2.0, 3.0, 1.0)
>>> model.calc_wettedperimeter_v1()
>>> factors.wettedperimeter
wettedperimeter(6.0)

class hydpy.models.wq.wq_model.Calc_WettedPerimeterDerivatives_V1

Bases: Method

Calculate the change in the wetted perimeter of each trapeze range with respect to the water level increase.

Required by the methods:

Use_WaterDepth_V1 Use_WaterLevel_V1

Requires the control parameter:

NmbTrapezes

Requires the derived parameters:

BottomDepths TrapezeHeights PerimeterDerivatives

Requires the factor sequence:

WaterDepth

Calculates the factor sequence:

WettedPerimeterDerivatives

Basic equation:

\[\begin{split}WettedPerimeterDerivatives_i = \begin{cases} 0 &|\ d < 0 \\ P' &|\ 0 \leq d < H_T \\ 2 &|\ H_T \leq d \\ \end{cases} \\ \\ d = WaterDepth - BottomDepth_i \\ H_T = TrapezeHeights_i \\ P' = PerimeterDerivatives_i\end{split}\]

Examples:

The following convenience function executes Calc_WettedPerimeterDerivatives_V1 for different water depths and prints the resulting wetted perimeters:

>>> from hydpy import print_vector, round_
>>> def test():
...     derived.bottomdepths.update()
...     derived.trapezeheights.update()
...     derived.perimeterderivatives.update()
...     for d in [0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0]:
...         factors.waterdepth = d
...         model.calc_wettedperimeterderivatives_v1()
...         round_(d, end=": ")
...         print_vector(factors.wettedperimeterderivatives.values)

The first example deals with identical rectangular trapezes. Note that method Calc_WettedPerimeterDerivatives_V1 adds the contact surface increase between two adjacent trapeze ranges only to the wetted perimeter derivative of the inner one:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(3)
>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(2.0)
>>> sideslopes(0.0)
>>> test()
0.0: 2.0, 0.0, 0.0
0.5: 2.0, 0.0, 0.0
1.0: 2.0, 2.0, 0.0
1.5: 2.0, 2.0, 0.0
2.0: 2.0, 2.0, 2.0
2.5: 2.0, 2.0, 2.0
3.0: 2.0, 2.0, 2.0
3.5: 2.0, 2.0, 2.0
4.0: 2.0, 2.0, 2.0

The second example deals with identical triangular trapezes. Here, the heights of the individual trapezes also matter because they mark where the triangular shape switches to a rectangular shape:

>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(0.0)
>>> sideslopes(2.0)
>>> test()
0.0: 4.472136, 0.0, 0.0
0.5: 4.472136, 0.0, 0.0
1.0: 2.0, 4.472136, 0.0
1.5: 2.0, 4.472136, 0.0
2.0: 2.0, 2.0, 4.472136
2.5: 2.0, 2.0, 4.472136
3.0: 2.0, 2.0, 4.472136
3.5: 2.0, 2.0, 4.472136
4.0: 2.0, 2.0, 4.472136

The third example deals with identical “complete” trapezes by combining the first two geometries:

>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(2.0)
>>> sideslopes(2.0)
>>> test()
0.0: 4.472136, 0.0, 0.0
0.5: 4.472136, 0.0, 0.0
1.0: 2.0, 4.472136, 0.0
1.5: 2.0, 4.472136, 0.0
2.0: 2.0, 2.0, 4.472136
2.5: 2.0, 2.0, 4.472136
3.0: 2.0, 2.0, 4.472136
3.5: 2.0, 2.0, 4.472136
4.0: 2.0, 2.0, 4.472136

The fourth example mixes three different geometries:

>>> bottomlevels(1.0, 3.0, 4.0)
>>> bottomwidths(2.0, 0.0, 2.0)
>>> sideslopes(0.0, 2.0, 2.0)
>>> test()
0.0: 2.0, 0.0, 0.0
0.5: 2.0, 0.0, 0.0
1.0: 2.0, 0.0, 0.0
1.5: 2.0, 0.0, 0.0
2.0: 2.0, 4.472136, 0.0
2.5: 2.0, 4.472136, 0.0
3.0: 2.0, 2.0, 4.472136
3.5: 2.0, 2.0, 4.472136
4.0: 2.0, 2.0, 4.472136

class hydpy.models.wq.wq_model.Calc_SurfaceWidths_V1

Bases: Method

Calculate the surface width for each trapeze range.

Required by the methods:

Use_WaterDepth_V1 Use_WaterLevel_V1

Requires the control parameters:

NmbTrapezes BottomWidths SideSlopes

Requires the derived parameters:

BottomDepths TrapezeHeights SlopeWidths

Requires the factor sequence:

WaterDepth

Calculates the factor sequence:

SurfaceWidths

Basic equation:

\[\begin{split}SurfaceWidths_i = \begin{cases} 0 &|\ d < 0 \\ W_B + 2 \cdot S_S \cdot d &|\ 0 \leq d < H_T \\ W_B + W_S &|\ H_T \leq d \\ \end{cases} \\ \\ d = WaterDepth - BottomDepth_i \\ H_T = TrapezeHeights_i \\ W_B = BottomWidths_i \\ S_S = SideSlopes_i \\ W_S = SlopeWidth_i\end{split}\]

Example:

The following convenience function executes Calc_SurfaceWidths_V1 for different water depths and prints the surface widths:

>>> from hydpy import print_vector, round_
>>> def test():
...     derived.bottomdepths.update()
...     derived.trapezeheights.update()
...     derived.slopewidths.update()
...     for d in [0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0]:
...         factors.waterdepth = d
...         model.calc_surfacewidths_v1()
...         round_(d, end=": ")
...         print_vector(factors.surfacewidths.values)

The first example deals with identical rectangular trapezes. There are no differences except those due to the different bottom levels:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(3)
>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(2.0)
>>> sideslopes(0.0)
>>> test()
0.0: 2.0, 0.0, 0.0
0.5: 2.0, 0.0, 0.0
1.0: 2.0, 2.0, 0.0
1.5: 2.0, 2.0, 0.0
2.0: 2.0, 2.0, 2.0
2.5: 2.0, 2.0, 2.0
3.0: 2.0, 2.0, 2.0
3.5: 2.0, 2.0, 2.0
4.0: 2.0, 2.0, 2.0

The second example deals with identical triangular trapezes. Here, the heights of the individual trapezes also matter because they mark where the triangular shape switches to a rectangular shape:

>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(0.0)
>>> sideslopes(2.0)
>>> test()
0.0: 0.0, 0.0, 0.0
0.5: 2.0, 0.0, 0.0
1.0: 4.0, 0.0, 0.0
1.5: 4.0, 2.0, 0.0
2.0: 4.0, 4.0, 0.0
2.5: 4.0, 4.0, 2.0
3.0: 4.0, 4.0, 4.0
3.5: 4.0, 4.0, 6.0
4.0: 4.0, 4.0, 8.0

The third example deals with identical “complete” trapezes by combining the first two geometries:

>>> bottomlevels(1.0, 2.0, 3.0)
>>> bottomwidths(2.0)
>>> sideslopes(2.0)
>>> test()
0.0: 2.0, 0.0, 0.0
0.5: 4.0, 0.0, 0.0
1.0: 6.0, 2.0, 0.0
1.5: 6.0, 4.0, 0.0
2.0: 6.0, 6.0, 2.0
2.5: 6.0, 6.0, 4.0
3.0: 6.0, 6.0, 6.0
3.5: 6.0, 6.0, 8.0
4.0: 6.0, 6.0, 10.0

The fourth example mixes three different geometries:

>>> bottomlevels(1.0, 3.0, 4.0)
>>> bottomwidths(2.0, 0.0, 2.0)
>>> sideslopes(0.0, 2.0, 2.0)
>>> test()
0.0: 2.0, 0.0, 0.0
0.5: 2.0, 0.0, 0.0
1.0: 2.0, 0.0, 0.0
1.5: 2.0, 0.0, 0.0
2.0: 2.0, 0.0, 0.0
2.5: 2.0, 2.0, 0.0
3.0: 2.0, 4.0, 2.0
3.5: 2.0, 4.0, 4.0
4.0: 2.0, 4.0, 6.0

class hydpy.models.wq.wq_model.Calc_SurfaceWidth_V1

Bases: Method

Sum the individual trapeze ranges’ surface widths.

Required by the methods:

Use_WaterDepth_V1 Use_WaterLevel_V1

Requires the control parameter:

NmbTrapezes

Requires the factor sequence:

SurfaceWidths

Calculates the factor sequence:

SurfaceWidth

Basic equation:

\(SurfaceWidth = \sum_{i=1}^{NmbTrapezes} SurfaceWidths_i\)

Examples:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(3)
>>> bottomslope(0.01)
>>> factors.surfacewidths(2.0, 3.0, 1.0)
>>> model.calc_surfacewidth_v1()
>>> factors.surfacewidth
surfacewidth(6.0)

class hydpy.models.wq.wq_model.Calc_Discharges_V1

Bases: Method

Calculate the discharge for each trapeze range.

Required by the methods:

Use_WaterDepth_V1 Use_WaterLevel_V1

Requires the control parameters:

NmbTrapezes BottomSlope StricklerCoefficients

Requires the derived parameter:

BottomDepths

Requires the factor sequences:

WaterDepth WettedAreas WettedPerimeters

Calculates the flux sequence:

Discharges

Basic equation:

\[\begin{split}Discharges_i = \begin{cases} 0 &|\ d < 0 \\ C \cdot A^{5/3} \cdot P^{-2/3} \cdot \sqrt{S_B} &|\ 0 \leq d \end{cases} \\ \\ d = WaterDepth - BottomDepth_i \\ C = StricklerCoefficient_i \\ A = WettedAreas_i \\ P = WettedPerimeters_i \\ S_B = BottomSlope\end{split}\]

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(4)
>>> bottomslope(0.01)
>>> stricklercoefficients(20.0, 40.0, 60.0, 80.0)
>>> derived.bottomdepths = 1.0, 2.0, 3.0, 4.0
>>> factors.wettedareas = 1.0, 4.0, 8.0, 16.0
>>> factors.wettedperimeters = 2.0, 4.0, 6.0, 8.0
>>> factors.waterdepth = 4.0
>>> model.calc_discharges_v1()
>>> fluxes.discharges
discharges(1.259921, 16.0, 58.147859, 0.0)

class hydpy.models.wq.wq_model.Calc_Discharge_V2

Bases: Method

Sum the individual trapeze ranges’ discharges.

Required by the methods:

Use_WaterDepth_V1 Use_WaterLevel_V1

Requires the control parameter:

NmbTrapezes

Requires the flux sequence:

Discharges

Calculates the flux sequence:

Discharge

Basic equation:

\(Discharge = \sum_{i=1}^{NmbTrapezes} Discharges_i\)

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(3)
>>> bottomslope(0.01)
>>> fluxes.discharges(2.0, 3.0, 1.0)
>>> model.calc_discharge_v2()
>>> fluxes.discharge
discharge(6.0)

class hydpy.models.wq.wq_model.Calc_DischargeDerivatives_V1

Bases: Method

Calculate the discharge change for each trapeze range with respect to a water level increase.

Required by the methods:

Use_WaterDepth_V1 Use_WaterLevel_V1

Requires the control parameters:

NmbTrapezes BottomSlope StricklerCoefficients

Requires the derived parameter:

BottomDepths

Requires the factor sequences:

WaterDepth WettedAreas WettedPerimeters WettedPerimeterDerivatives SurfaceWidths

Calculates the factor sequence:

DischargeDerivatives

Basic equation:

\[\begin{split}DischargeDerivatives_i = \begin{cases} 0 &|\ d < 0 \\ C \cdot (A / P)^{5/3} \cdot \frac{5 \cdot P \cdot A' - 2 \cdot A \cdot P'}{3 \cdot P} \cdot \sqrt{S_B} &|\ 0 \leq d \end{cases} \\ \\ d = WaterDepth - BottomDepth_i \\ C = StricklerCoefficient_i \\ A = WettedAreas_i \\ A' = SurfaceWidth_i \\ P = WettedPerimeters_i \\ P' = WettedPerimeterDerivatives_i \\ S_B = BottomSlope\end{split}\]

Example:

The given basic equation assumes that the wetted area, the wetted perimeter, and their derivatives are calculated via methods Calc_WettedAreas_V1, Calc_SurfaceWidths_V1, Calc_WettedPerimeters_V1, and Calc_WettedPerimeterDerivatives_V1. Hence, we apply these methods and check that, after also executing Calc_DischargeDerivatives_V1, the results are sufficiently similar to the numerical approximations gained when applying NumericalDifferentiator to the mentioned methods and method Calc_Discharges_V1:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(4)
>>> bottomlevels(1.0, 3.0, 4.0, 5.0)
>>> bottomwidths(2.0, 0.0, 2.0, 2.0)
>>> sideslopes(0.0, 2.0, 2.0, 2.0)
>>> bottomslope(0.01)
>>> stricklercoefficients(20.0, 40.0, 60.0, 60.0)
>>> factors.waterdepth = 3.5
>>> derived.bottomdepths.update()
>>> derived.trapezeheights.update()
>>> derived.slopewidths.update()
>>> derived.perimeterderivatives.update()
>>> model.calc_wettedareas_v1()
>>> model.calc_surfacewidths_v1()
>>> model.calc_wettedperimeters_v1()
>>> model.calc_wettedperimeterderivatives_v1()
>>> model.calc_dischargederivatives_v1()
>>> factors.dischargederivatives
dischargederivatives(3.884141, 18.475494, 16.850223, 0.0)

>>> from hydpy import NumericalDifferentiator, pub
>>> numdiff = NumericalDifferentiator(
...     xsequence=factors.waterdepth,
...     ysequences=[fluxes.discharges],
...     methods=[model.calc_wettedareas_v1,
...              model.calc_surfacewidths_v1,
...              model.calc_wettedperimeters_v1,
...              model.calc_wettedperimeterderivatives_v1,
...              model.calc_discharges_v1],
...     dx=1e-8)
>>> with pub.options.reprdigits(5):
...     numdiff()
d_discharges/d_waterdepth: 3.88414, 18.47549, 16.85022, 0.0

class hydpy.models.wq.wq_model.Calc_DischargeDerivative_V1

Bases: Method

Sum the individual trapeze ranges’ discharge derivatives.

Required by the methods:

Use_WaterDepth_V1 Use_WaterLevel_V1

Requires the control parameter:

NmbTrapezes

Requires the factor sequence:

DischargeDerivatives

Calculates the factor sequence:

DischargeDerivative

Basic equation:

\(DischargeDerivative = \sum_{i=1}^{NmbTrapezes} DischargeDerivatives_i\)

Examples:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(3)
>>> bottomslope(0.01)
>>> factors.dischargederivatives(2.0, 3.0, 1.0)
>>> model.calc_dischargederivative_v1()
>>> factors.dischargederivative
dischargederivative(6.0)

class hydpy.models.wq.wq_model.Calc_Celerity_V1

Bases: Method

Calculate the kinematic wave celerity.

Required by the methods:

Use_WaterDepth_V1 Use_WaterLevel_V1

Requires the factor sequences:

DischargeDerivative SurfaceWidth

Calculates the factor sequence:

Celerity

Basic equation:

\(Celerity = \frac{DischargeDerivative}{SurfaceWidth}\)

Examples:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> factors.dischargederivative = 6.0
>>> factors.surfacewidth = 2.0
>>> model.calc_celerity_v1()
>>> factors.celerity
celerity(3.0)

>>> factors.surfacewidth = 0.0
>>> model.calc_celerity_v1()
>>> factors.celerity
celerity(nan)

class hydpy.models.wq.wq_model.Set_WaterDepth_V1

Bases: Method

Set the water depth in m.

Required by the methods:

Use_WaterDepth_V1 Use_WaterDepth_V2

Calculates the factor sequence:

WaterDepth

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> model.set_waterdepth_v1(2.0)
>>> factors.waterdepth
waterdepth(2.0)

class hydpy.models.wq.wq_model.Set_WaterLevel_V1

Bases: Method

Set the water level in m.

Required by the methods:

Use_WaterLevel_V1 Use_WaterLevel_V2

Calculates the factor sequence:

WaterLevel

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> model.set_waterlevel_v1(2.0)
>>> factors.waterlevel
waterlevel(2.0)

class hydpy.models.wq.wq_model.Set_WettedArea_V1

Bases: Method

Set the wetted area in m².

Required by the method:

Use_WettedArea_V1

Calculates the factor sequence:

WettedArea

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> model.set_wettedarea_v1(2.0)
>>> factors.wettedarea
wettedarea(2.0)

class hydpy.models.wq.wq_model.Use_WaterDepth_V1

Bases: SetAutoMethod

Set the water depth in m and use it to calculate all other properties.

Required submethods:

Set_WaterDepth_V1 Calc_WaterLevel_V1 Calc_WettedAreas_V1 Calc_WettedArea_V1 Calc_WettedPerimeters_V1 Calc_WettedPerimeterDerivatives_V1 Calc_SurfaceWidths_V1 Calc_SurfaceWidth_V1 Calc_Discharges_V1 Calc_Discharge_V2 Calc_DischargeDerivatives_V1 Calc_DischargeDerivative_V1 Calc_Celerity_V1

Requires the control parameters:

NmbTrapezes BottomLevels BottomWidths SideSlopes StricklerCoefficients BottomSlope

Requires the derived parameters:

BottomDepths TrapezeHeights SlopeWidths PerimeterDerivatives

Calculates the factor sequences:

WaterDepth WaterLevel WettedAreas WettedArea WettedPerimeters WettedPerimeterDerivatives SurfaceWidths SurfaceWidth DischargeDerivatives DischargeDerivative Celerity

Calculates the flux sequences:

Discharges Discharge

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(2)
>>> bottomlevels(1.0, 3.0)
>>> bottomwidths(2.0, 2.0)
>>> sideslopes(0.0, 0.0)
>>> bottomslope(0.01)
>>> stricklercoefficients(20.0, 40.0)
>>> derived.bottomdepths.update()
>>> derived.trapezeheights.update()
>>> derived.slopewidths.update()
>>> derived.perimeterderivatives.update()
>>> model.use_waterdepth_v1(3.0)
>>> factors.waterdepth
waterdepth(3.0)
>>> factors.waterlevel
waterlevel(4.0)
>>> factors.wettedarea
wettedarea(8.0)
>>> fluxes.discharge
discharge(14.945466)
>>> factors.celerity
celerity(2.642957)

class hydpy.models.wq.wq_model.Use_WaterDepth_V2

Bases: SetAutoMethod

Set the water depth in m and use it to calculate all other properties.

Required submethods:

Set_WaterDepth_V1 Calc_WaterLevel_V1 Calc_WettedAreas_V1 Calc_WettedArea_V1 Calc_WettedPerimeters_V1 Calc_WettedPerimeter_V1

Requires the control parameters:

NmbTrapezes BottomLevels BottomWidths SideSlopes

Requires the derived parameters:

BottomDepths TrapezeHeights SlopeWidths

Calculates the factor sequences:

WaterDepth WaterLevel WettedAreas WettedArea WettedPerimeters WettedPerimeter

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(2)
>>> bottomlevels(1.0, 3.0)
>>> bottomwidths(2.0, 2.0)
>>> sideslopes(0.0, 0.0)
>>> derived.bottomdepths.update()
>>> derived.trapezeheights.update()
>>> derived.slopewidths.update()
>>> model.use_waterdepth_v2(3.0)
>>> factors.waterdepth
waterdepth(3.0)
>>> factors.waterlevel
waterlevel(4.0)
>>> factors.wettedarea
wettedarea(8.0)
>>> factors.wettedperimeter
wettedperimeter(12.0)

class hydpy.models.wq.wq_model.Use_WaterLevel_V1

Bases: SetAutoMethod

Set the water level in m and use it to calculate all other properties.

Required submethods:

Set_WaterLevel_V1 Calc_WaterDepth_V1 Calc_WettedAreas_V1 Calc_WettedArea_V1 Calc_WettedPerimeters_V1 Calc_WettedPerimeterDerivatives_V1 Calc_SurfaceWidths_V1 Calc_SurfaceWidth_V1 Calc_Discharges_V1 Calc_Discharge_V2 Calc_DischargeDerivatives_V1 Calc_DischargeDerivative_V1 Calc_Celerity_V1

Requires the control parameters:

NmbTrapezes BottomLevels BottomWidths SideSlopes StricklerCoefficients BottomSlope

Requires the derived parameters:

BottomDepths TrapezeHeights SlopeWidths PerimeterDerivatives

Calculates the factor sequences:

WaterLevel WaterDepth WettedAreas WettedArea WettedPerimeters WettedPerimeterDerivatives SurfaceWidths SurfaceWidth DischargeDerivatives DischargeDerivative Celerity

Calculates the flux sequences:

Discharges Discharge

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(2)
>>> bottomlevels(1.0, 3.0)
>>> bottomwidths(2.0, 2.0)
>>> sideslopes(0.0, 0.0)
>>> bottomslope(0.01)
>>> stricklercoefficients(20.0, 40.0)
>>> derived.bottomdepths.update()
>>> derived.trapezeheights.update()
>>> derived.slopewidths.update()
>>> derived.perimeterderivatives.update()
>>> model.use_waterlevel_v1(4.0)
>>> factors.waterdepth
waterdepth(3.0)
>>> factors.waterlevel
waterlevel(4.0)
>>> factors.wettedarea
wettedarea(8.0)
>>> fluxes.discharge
discharge(14.945466)
>>> factors.celerity
celerity(2.642957)

class hydpy.models.wq.wq_model.Use_WaterLevel_V2

Bases: SetAutoMethod

Set the water level in m and use it to calculate all other properties.

Required submethods:

Set_WaterLevel_V1 Calc_WaterDepth_V1 Calc_WettedAreas_V1 Calc_WettedArea_V1 Calc_WettedPerimeters_V1 Calc_WettedPerimeter_V1

Requires the control parameters:

NmbTrapezes BottomLevels BottomWidths SideSlopes

Requires the derived parameters:

BottomDepths TrapezeHeights SlopeWidths

Calculates the factor sequences:

WaterDepth WaterLevel WettedAreas WettedArea WettedPerimeters WettedPerimeter

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(2)
>>> bottomlevels(1.0, 3.0)
>>> bottomwidths(2.0, 2.0)
>>> sideslopes(0.0, 0.0)
>>> derived.bottomdepths.update()
>>> derived.trapezeheights.update()
>>> derived.slopewidths.update()
>>> model.use_waterlevel_v2(4.0)
>>> factors.waterdepth
waterdepth(3.0)
>>> factors.waterlevel
waterlevel(4.0)
>>> factors.wettedarea
wettedarea(8.0)
>>> factors.wettedperimeter
wettedperimeter(12.0)

class hydpy.models.wq.wq_model.Use_WettedArea_V1

Bases: SetAutoMethod

Set the wetted area in m² and use it to calculate all other properties.

Required submethods:

Set_WettedArea_V1 Calc_WaterDepth_V2 Calc_WaterLevel_V1 Calc_WettedAreas_V1 Calc_WettedArea_V1 Calc_WettedPerimeters_V1 Calc_WettedPerimeter_V1

Requires the control parameters:

NmbTrapezes BottomLevels BottomWidths SideSlopes

Requires the derived parameters:

BottomDepths TrapezeHeights SlopeWidths TrapezeAreas

Calculates the factor sequences:

WaterDepth WaterLevel WettedAreas WettedArea WettedPerimeters WettedPerimeter

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(2)
>>> bottomlevels(1.0, 3.0)
>>> bottomwidths(2.0, 2.0)
>>> sideslopes(0.0, 0.0)
>>> derived.bottomdepths.update()
>>> derived.trapezeheights.update()
>>> derived.slopewidths.update()
>>> derived.trapezeareas.update()
>>> model.use_wettedarea_v1(8.0)
>>> factors.waterdepth
waterdepth(3.0)
>>> factors.waterlevel
waterlevel(4.0)
>>> factors.wettedarea
wettedarea(8.0)
>>> factors.wettedperimeter
wettedperimeter(12.0)

class hydpy.models.wq.wq_model.Get_WaterDepth_V1

Bases: Method

Get the water depth in m.

Requires the factor sequence:

WaterDepth

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> factors.waterdepth = 2.0
>>> model.get_waterdepth_v1()
2.0

class hydpy.models.wq.wq_model.Get_WaterLevel_V1

Bases: Method

Get the water level in m.

Requires the factor sequence:

WaterLevel

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> factors.waterlevel = 2.0
>>> model.get_waterlevel_v1()
2.0

class hydpy.models.wq.wq_model.Get_WettedArea_V1

Bases: Method

Get the wetted area in m².

Requires the factor sequence:

WettedArea

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> factors.wettedarea = 2.0
>>> model.get_wettedarea_v1()
2.0

class hydpy.models.wq.wq_model.Get_WettedPerimeter_V1

Bases: Method

Get the wetted perimeter in m.

Requires the factor sequence:

WettedPerimeter

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> factors.wettedperimeter = 2.0
>>> model.get_wettedperimeter_v1()
2.0

class hydpy.models.wq.wq_model.Get_SurfaceWidth_V1

Bases: Method

Get the surface width in m.

Requires the factor sequence:

SurfaceWidth

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> factors.surfacewidth = 2.0
>>> model.get_surfacewidth_v1()
2.0

class hydpy.models.wq.wq_model.Get_Discharge_V1

Bases: Method

Get the discharge in m³/s.

Requires the flux sequence:

Discharge

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> fluxes.discharge = 2.0
>>> model.get_discharge_v1()
2.0

class hydpy.models.wq.wq_model.Get_Celerity_V1

Bases: Method

Get the wave celerity in m/s.

Requires the factor sequence:

Celerity

Example:

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> factors.celerity = 2.0
>>> model.get_celerity_v1()
2.0

class hydpy.models.wq.wq_model.TrapezeModel

Bases: AdHocModel

Base class for HydPy-WQ models that rely on trapezoidal geometries.

plot(*, ymax: float | None = None, color: str | None = None, label: bool | str = False) → Figure

Plot the channel profile.

See the main documentation of application model wq_trapeze for more information.

REUSABLE_METHODS: ClassVar[tuple[type[ReusableMethod], ...]] = ()

class hydpy.models.wq.wq_model.Base_DischargeModel_V2

Bases: DischargeModel_V2

Base class for HydPy-WQ models that comply with the DischargeModel_V2 submodel interface.

prepare_channeldepth

Set the channel depth in m.

>>> from hydpy.models.wq_walrus import *
>>> parameterstep()
>>> model.prepare_channeldepth(2.0)
>>> channeldepth
channeldepth(2.0)

prepare_tolerance

Set the depth-related smoothing parameter in m.

>>> from hydpy.models.wq_walrus import *
>>> parameterstep()
>>> model.prepare_tolerance(2.0)
>>> crestheighttolerance
crestheighttolerance(2.0)

REUSABLE_METHODS: ClassVar[tuple[type[ReusableMethod], ...]] = ()

preparemethod2arguments: dict[str, tuple[tuple[Any, ...], dict[str, Any]]]

cymodel: CyModelProtocol | None

parameters: parametertools.Parameters

sequences: sequencetools.Sequences

masks: masktools.Masks

METHOD_GROUPS: ClassVar[tuple[str, ...]]

DOCNAME: DocName

Parameter Features

Control parameters

class hydpy.models.wq.ControlParameters(master: Parameters, cls_fastaccess: type[FastAccessParameter] | None = None, cymodel: CyModelProtocol | None = None)

Bases: SubParameters

Control parameters of model wq.

The following classes are selected:

• NmbTrapezes() Number of trapezes defining the cross section [-].

• BottomLevels() The bottom level for each trapeze [m].

• BottomWidths() The bottom width for each trapeze [m].

• SideSlopes() The side slope for each trapeze[-].

• StricklerCoefficients() Manning-Strickler coefficient for each trapeze [m^(1/3)/s].

• BottomSlope() Bottom slope [-].

• ChannelDepth() Channel depth [m].

• CrestHeight() The height of the weir’s crest above the channel bottom [m].

• CrestHeightTolerance() Smoothing parameter related to the difference between the water depth and the crest height [m].

• BankfullDischarge() Bankfull discharge [mm/T].

• DischargeExponent() Exponent of the water depth-discharge relation [-].

class hydpy.models.wq.wq_control.NmbTrapezes(subvars: SubParameters)

Bases: Parameter

Number of trapezes defining the cross section [-].

Required by the methods:

Calc_DischargeDerivative_V1 Calc_DischargeDerivatives_V1 Calc_Discharge_V2 Calc_Discharges_V1 Calc_SurfaceWidth_V1 Calc_SurfaceWidths_V1 Calc_WaterDepth_V2 Calc_WettedArea_V1 Calc_WettedAreas_V1 Calc_WettedPerimeterDerivatives_V1 Calc_WettedPerimeter_V1 Calc_WettedPerimeters_V1 Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

NDIM: int = 0

TYPE

alias of int

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (1, None)

name: str = 'nmbtrapezes'

Name of the variable in lowercase letters.

unit: str = '-'

Unit of the variable.

class hydpy.models.wq.wq_control.BottomLevels(subvars: SubParameters)

Bases: Parameter

The bottom level for each trapeze [m].

Required by the methods:

Calc_WaterDepth_V1 Calc_WaterLevel_V1 Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

If water levels are essential, we encourage using the sea level as a reference. If not (as for common hydrological routing approaches), one could also set the lowest trapeze’s bottom level to zero.

NDIM: int = 1

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (None, None)

name: str = 'bottomlevels'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

class hydpy.models.wq.wq_control.BottomWidths(subvars: SubParameters)

Bases: Parameter

The bottom width for each trapeze [m].

Required by the methods:

Calc_SurfaceWidths_V1 Calc_WaterDepth_V2 Calc_WettedAreas_V1 Calc_WettedPerimeters_V1 Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

For example, when dealing with the second trapeze, the corresponding value of BottomWidths represents the sum of the trapeze’s partial bottoms on the left and right sides of the first trapeze.

NDIM: int = 1

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'bottomwidths'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

class hydpy.models.wq.wq_control.SideSlopes(subvars: SubParameters)

Bases: Parameter

The side slope for each trapeze[-].

Required by the methods:

Calc_SurfaceWidths_V1 Calc_WaterDepth_V2 Calc_WettedAreas_V1 Calc_WettedPerimeters_V1 Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

A value of zero corresponds to a rectangular shape. A value of two corresponds to a half-meter elevation increase for each additional meter distance from the trapeze’s centre.

NDIM: int = 1

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'sideslopes'

Name of the variable in lowercase letters.

unit: str = '-'

Unit of the variable.

class hydpy.models.wq.wq_control.StricklerCoefficients(subvars: SubParameters)

Bases: Parameter

Manning-Strickler coefficient for each trapeze [m^(1/3)/s].

Required by the methods:

Calc_DischargeDerivatives_V1 Calc_Discharges_V1 Use_WaterDepth_V1 Use_WaterLevel_V1

The higher the coefficient’s value, the higher the calculated discharge. Typical values range from 20 to 80.

NDIM: int = 1

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'stricklercoefficients'

Name of the variable in lowercase letters.

unit: str = 'm^(1/3)/s'

Unit of the variable.

class hydpy.models.wq.wq_control.BottomSlope(subvars: SubParameters)

Bases: Parameter

Bottom slope [-].

Required by the methods:

Calc_DischargeDerivatives_V1 Calc_Discharges_V1 Use_WaterDepth_V1 Use_WaterLevel_V1

\(BottomSlope = \frac{elevation_{start} - elevation_{end}}{length}\)

NDIM: int = 0

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'bottomslope'

Name of the variable in lowercase letters.

unit: str = '-'

Unit of the variable.

class hydpy.models.wq.wq_control.ChannelDepth(subvars: SubParameters)

Bases: Parameter

Channel depth [m].

Required by the method:

Calculate_Discharge_V1

NDIM: int = 0

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'channeldepth'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

class hydpy.models.wq.wq_control.CrestHeight(subvars: SubParameters)

Bases: Parameter

The height of the weir’s crest above the channel bottom [m].

Required by the method:

Calculate_Discharge_V1

Set CrestHeight to zero for channels without weirs.

NDIM: int = 0

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'crestheight'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

class hydpy.models.wq.wq_control.CrestHeightTolerance(subvars: SubParameters)

Bases: Parameter

Smoothing parameter related to the difference between the water depth and the crest height [m].

NDIM: int = 0

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'crestheighttolerance'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

class hydpy.models.wq.wq_control.BankfullDischarge(subvars: SubParameters)

Bases: Parameter

Bankfull discharge [mm/T].

Required by the method:

Calculate_Discharge_V1

NDIM: int = 0

TYPE

alias of float

TIME: bool | None = True

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'bankfulldischarge'

Name of the variable in lowercase letters.

unit: str = 'mm/T'

Unit of the variable.

class hydpy.models.wq.wq_control.DischargeExponent(subvars: SubParameters)

Bases: Parameter

Exponent of the water depth-discharge relation [-].

Required by the method:

Calculate_Discharge_V1

NDIM: int = 0

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

INIT: int | float | bool | None = 1.5

name: str = 'dischargeexponent'

Name of the variable in lowercase letters.

unit: str = '-'

Unit of the variable.

Derived parameters

class hydpy.models.wq.DerivedParameters(master: Parameters, cls_fastaccess: type[FastAccessParameter] | None = None, cymodel: CyModelProtocol | None = None)

Bases: SubParameters

Derived parameters of model wq.

The following classes are selected:

• BottomDepths() The cumulated depth of a trapeze and its lower neighbours [m].

• TrapezeHeights() The individual height of each trapeze [m].

• SlopeWidths() The tatal width of both side slopes of each trapeze.

• TrapezeAreas() The individual area of each trapeze [m].

• PerimeterDerivatives() Change of the perimeter of each trapeze relative to a water level increase within the trapeze’s range [-].

• CrestHeightRegularisation() Regularisation parameter related to the difference between the water depth and the crest height [m].

class hydpy.models.wq.wq_derived.BottomDepths(subvars: SubParameters)

Bases: Parameter

The cumulated depth of a trapeze and its lower neighbours [m].

Required by the methods:

Calc_DischargeDerivatives_V1 Calc_Discharges_V1 Calc_SurfaceWidths_V1 Calc_WettedAreas_V1 Calc_WettedPerimeterDerivatives_V1 Calc_WettedPerimeters_V1 Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

NDIM: int = 1

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

update()

Calculate the depth values based on \(BottomDepths_i = BottomLevels_i - BottomLevels_0\).

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(3)
>>> bottomlevels(1.0, 4.0, 6.0)
>>> derived.bottomdepths.update()
>>> derived.bottomdepths
bottomdepths(0.0, 3.0, 5.0)

name: str = 'bottomdepths'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

class hydpy.models.wq.wq_derived.TrapezeHeights(subvars: SubParameters)

Bases: Parameter

The individual height of each trapeze [m].

Required by the methods:

Calc_SurfaceWidths_V1 Calc_WaterDepth_V2 Calc_WettedAreas_V1 Calc_WettedPerimeterDerivatives_V1 Calc_WettedPerimeters_V1 Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

The highest trapeze has no upper neighbour and is thus infinitely high.

NDIM: int = 1

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

update()

Calculate the height values based on \(TrapezeHeights_i = BottomLevels_{i+1} - BottomLevels_i\).

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(3)
>>> bottomlevels(1.0, 4.0, 6.0)
>>> derived.trapezeheights.update()
>>> derived.trapezeheights
trapezeheights(3.0, 2.0, inf)

name: str = 'trapezeheights'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

class hydpy.models.wq.wq_derived.SlopeWidths(subvars: SubParameters)

Bases: Parameter

The tatal width of both side slopes of each trapeze.

Required by the methods:

Calc_SurfaceWidths_V1 Calc_WaterDepth_V2 Calc_WettedAreas_V1 Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

The highest trapeze has no upper neighbour and is thus infinitely high and potentially infinitely wide.

NDIM: int = 1

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

update()

Calculate the slope width values based on \(SlopeWidths = 2 \cdot SideSlopes \cdot TrapezeHeights\).

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(3)
>>> sideslopes(0.0, 2.0, 2.0)
>>> derived.trapezeheights(2.0, 3.0, inf)
>>> derived.slopewidths.update()
>>> derived.slopewidths
slopewidths(0.0, 12.0, inf)

name: str = 'slopewidths'

Name of the variable in lowercase letters.

unit: str = '?'

Unit of the variable.

class hydpy.models.wq.wq_derived.TrapezeAreas(subvars: SubParameters)

Bases: Parameter

The individual area of each trapeze [m].

Required by the methods:

Calc_WaterDepth_V2 Use_WettedArea_V1

The highest trapeze has no upper neighbour and is thus infinitely large.

NDIM: int = 1

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

update()

Calculate the perimeter derivatives based on \((BottomWidths + SlopeWidths / 2) \cdot TrapezeHeights\).

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(4)
>>> bottomlevels(1.0, 3.0, 4.0, 5.0)
>>> bottomwidths(2.0, 0.0, 2.0, 2.0)
>>> sideslopes(0.0, 2.0, 2.0, 2.0)
>>> derived.trapezeheights.update()
>>> derived.slopewidths.update()
>>> derived.trapezeareas.update()
>>> derived.trapezeareas
trapezeareas(4.0, 4.0, 10.0, inf)

name: str = 'trapezeareas'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

class hydpy.models.wq.wq_derived.PerimeterDerivatives(subvars: SubParameters)

Bases: Parameter

Change of the perimeter of each trapeze relative to a water level increase within the trapeze’s range [-].

Required by the methods:

Calc_WettedPerimeterDerivatives_V1 Use_WaterDepth_V1 Use_WaterLevel_V1

NDIM: int = 1

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

update()

Calculate the perimeter derivatives based on \(2 \cdot \sqrt{1 + SideSlopes^2}\).

>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbtrapezes(2)
>>> sideslopes(0.0, 2.0)
>>> derived.perimeterderivatives.update()
>>> derived.perimeterderivatives
perimeterderivatives(2.0, 4.472136)

name: str = 'perimeterderivatives'

Name of the variable in lowercase letters.

unit: str = '-'

Unit of the variable.

class hydpy.models.wq.wq_derived.CrestHeightRegularisation(subvars: SubParameters)

Bases: Parameter

Regularisation parameter related to the difference between the water depth and the crest height [m].

Required by the method:

Calculate_Discharge_V1

NDIM: int = 0

TYPE

alias of float

TIME: bool | None = None

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

update()

Calculate the smoothing parameter value.

The documentation on module smoothtools explains the following example in some detail:

>>> from hydpy.models.wq import *
>>> from hydpy.cythons.smoothutils import smooth_logistic2
>>> from hydpy import round_
>>> parameterstep()
>>> crestheighttolerance(0.0)
>>> derived.crestheightregularisation.update()
>>> round_(smooth_logistic2(0.0, derived.crestheightregularisation))
0.0
>>> crestheighttolerance(0.0025)
>>> derived.crestheightregularisation.update()
>>> round_(smooth_logistic2(0.0025, derived.crestheightregularisation))
0.00251

name: str = 'crestheightregularisation'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

Sequence Features

Factor sequences

class hydpy.models.wq.FactorSequences(master: Sequences, cls_fastaccess: type[TypeFastAccess_co] | None = None, cymodel: CyModelProtocol | None = None)

Bases: FactorSequences

Factor sequences of model wq.

The following classes are selected:

• WaterDepth() Water depth [m].

• WaterLevel() Water level [m].

• WettedAreas() Wetted area of each trapeze range [m²].

• WettedArea() Total wetted area [m²].

• WettedPerimeters() Wetted perimeter of each trapeze range [m].

• WettedPerimeter() Total wetted perimeter [m].

• WettedPerimeterDerivatives() Change in the wetted perimeter of each trapeze range with respect to a water level increase [-].

• SurfaceWidths() Surface width of each trapeze range [m].

• SurfaceWidth() Total surface width [m].

• DischargeDerivatives() Discharge change of each trapeze range with respect to a water level increase [m²/s].

• DischargeDerivative() Total discharge change with respect to a water level increase [m²/s].

• Celerity() Kinematic celerity (wave speed) [m/s].

class hydpy.models.wq.wq_factors.WaterDepth(subvars: ModelSequences[ModelSequence, FastAccess])

Bases: FactorSequence

Water depth [m].

Calculated by the methods:

Calc_WaterDepth_V1 Calc_WaterDepth_V2 Set_WaterDepth_V1 Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

Required by the methods:

Calc_DischargeDerivatives_V1 Calc_Discharges_V1 Calc_SurfaceWidths_V1 Calc_WaterLevel_V1 Calc_WettedAreas_V1 Calc_WettedPerimeterDerivatives_V1 Calc_WettedPerimeters_V1 Get_WaterDepth_V1

NDIM: int = 0

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'waterdepth'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

class hydpy.models.wq.wq_factors.WaterLevel(subvars: ModelSequences[ModelSequence, FastAccess])

Bases: FactorSequence

Water level [m].

Calculated by the methods:

Calc_WaterLevel_V1 Set_WaterLevel_V1 Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

Required by the methods:

Calc_WaterDepth_V1 Get_WaterLevel_V1

NDIM: int = 0

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (None, None)

name: str = 'waterlevel'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

class hydpy.models.wq.wq_factors.WettedAreas(subvars: ModelSequences[ModelSequence, FastAccess])

Bases: FactorSequence

Wetted area of each trapeze range [m²].

Calculated by the methods:

Calc_WettedAreas_V1 Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

Required by the methods:

Calc_DischargeDerivatives_V1 Calc_Discharges_V1 Calc_WettedArea_V1

NDIM: int = 1

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'wettedareas'

Name of the variable in lowercase letters.

unit: str = 'm²'

Unit of the variable.

class hydpy.models.wq.wq_factors.WettedArea(subvars: ModelSequences[ModelSequence, FastAccess])

Bases: FactorSequence

Total wetted area [m²].

Calculated by the methods:

Calc_WettedArea_V1 Set_WettedArea_V1 Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

Required by the methods:

Calc_WaterDepth_V2 Get_WettedArea_V1

NDIM: int = 0

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'wettedarea'

Name of the variable in lowercase letters.

unit: str = 'm²'

Unit of the variable.

class hydpy.models.wq.wq_factors.WettedPerimeters(subvars: ModelSequences[ModelSequence, FastAccess])

Bases: FactorSequence

Wetted perimeter of each trapeze range [m].

Calculated by the methods:

Calc_WettedPerimeters_V1 Use_WaterDepth_V1 Use_WaterDepth_V2 Use_WaterLevel_V1 Use_WaterLevel_V2 Use_WettedArea_V1

Required by the methods:

Calc_DischargeDerivatives_V1 Calc_Discharges_V1 Calc_WettedPerimeter_V1

NDIM: int = 1

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'wettedperimeters'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

class hydpy.models.wq.wq_factors.WettedPerimeter(subvars: ModelSequences[ModelSequence, FastAccess])

Bases: FactorSequence

Total wetted perimeter [m].

Calculated by the methods:

Calc_WettedPerimeter_V1 Use_WaterDepth_V2 Use_WaterLevel_V2 Use_WettedArea_V1

Required by the method:

Get_WettedPerimeter_V1

NDIM: int = 0

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'wettedperimeter'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

class hydpy.models.wq.wq_factors.WettedPerimeterDerivatives(subvars: ModelSequences[ModelSequence, FastAccess])

Bases: FactorSequence

Change in the wetted perimeter of each trapeze range with respect to a water level increase [-].

Calculated by the methods:

Calc_WettedPerimeterDerivatives_V1 Use_WaterDepth_V1 Use_WaterLevel_V1

Required by the method:

Calc_DischargeDerivatives_V1

NDIM: int = 1

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'wettedperimeterderivatives'

Name of the variable in lowercase letters.

unit: str = '-'

Unit of the variable.

class hydpy.models.wq.wq_factors.SurfaceWidths(subvars: ModelSequences[ModelSequence, FastAccess])

Bases: FactorSequence

Surface width of each trapeze range [m].

Calculated by the methods:

Calc_SurfaceWidths_V1 Use_WaterDepth_V1 Use_WaterLevel_V1

Required by the methods:

Calc_DischargeDerivatives_V1 Calc_SurfaceWidth_V1

NDIM: int = 1

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'surfacewidths'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

class hydpy.models.wq.wq_factors.SurfaceWidth(subvars: ModelSequences[ModelSequence, FastAccess])

Bases: FactorSequence

Total surface width [m].

Calculated by the methods:

Calc_SurfaceWidth_V1 Use_WaterDepth_V1 Use_WaterLevel_V1

Required by the methods:

Calc_Celerity_V1 Get_SurfaceWidth_V1

NDIM: int = 0

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (0.0, None)

name: str = 'surfacewidth'

Name of the variable in lowercase letters.

unit: str = 'm'

Unit of the variable.

class hydpy.models.wq.wq_factors.DischargeDerivatives(subvars: ModelSequences[ModelSequence, FastAccess])

Bases: FactorSequence

Discharge change of each trapeze range with respect to a water level increase [m²/s].

Calculated by the methods:

Calc_DischargeDerivatives_V1 Use_WaterDepth_V1 Use_WaterLevel_V1

Required by the method:

Calc_DischargeDerivative_V1

NDIM: int = 1

NUMERIC: bool = False

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (None, None)

name: str = 'dischargederivatives'

Name of the variable in lowercase letters.

unit: str = 'm²/s'

Unit of the variable.

class hydpy.models.wq.wq_factors.DischargeDerivative(subvars: ModelSequences[ModelSequence, FastAccess])

Bases: FactorSequence

Total discharge change with respect to a water level increase [m²/s].

Calculated by the methods:

Calc_DischargeDerivative_V1 Use_WaterDepth_V1 Use_WaterLevel_V1

Required by the method:

Calc_Celerity_V1

NDIM: int = 0

NUMERIC: bool = False

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (None, None)

name: str = 'dischargederivative'

Name of the variable in lowercase letters.

unit: str = 'm²/s'

Unit of the variable.

class hydpy.models.wq.wq_factors.Celerity(subvars: ModelSequences[ModelSequence, FastAccess])

Bases: FactorSequence

Kinematic celerity (wave speed) [m/s].

Calculated by the methods:

Calc_Celerity_V1 Use_WaterDepth_V1 Use_WaterLevel_V1

Required by the method:

Get_Celerity_V1

NDIM: int = 0

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (None, None)

name: str = 'celerity'

Name of the variable in lowercase letters.

unit: str = 'm/s'

Unit of the variable.

Flux sequences

class hydpy.models.wq.FluxSequences(master: Sequences, cls_fastaccess: type[TypeFastAccess_co] | None = None, cymodel: CyModelProtocol | None = None)

Bases: FluxSequences

Flux sequences of model wq.

The following classes are selected:

• Discharges() The discharge of each trapeze range [m³/s].

• Discharge() Total discharge [m³/s].

class hydpy.models.wq.wq_fluxes.Discharges(subvars: ModelSequences[ModelSequence, FastAccess])

Bases: FluxSequence

The discharge of each trapeze range [m³/s].

Calculated by the methods:

Calc_Discharges_V1 Use_WaterDepth_V1 Use_WaterLevel_V1

Required by the method:

Calc_Discharge_V2

NDIM: int = 1

NUMERIC: bool = False

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (None, None)

name: str = 'discharges'

Name of the variable in lowercase letters.

unit: str = 'm³/s'

Unit of the variable.

class hydpy.models.wq.wq_fluxes.Discharge(subvars: ModelSequences[ModelSequence, FastAccess])

Bases: FluxSequence

Total discharge [m³/s].

Calculated by the methods:

Calc_Discharge_V2 Use_WaterDepth_V1 Use_WaterLevel_V1

Required by the method:

Get_Discharge_V1

NDIM: int = 0

NUMERIC: bool = False

SPAN: tuple[int | float | bool | None, int | float | bool | None] = (None, None)

name: str = 'discharge'

Name of the variable in lowercase letters.

unit: str = 'm³/s'

Unit of the variable.

class hydpy.models.wq.ControlParameters(master: Parameters, cls_fastaccess: type[FastAccessParameter] | None = None, cymodel: CyModelProtocol | None = None)

Bases: SubParameters

Control parameters of model wq.

The following classes are selected:

• NmbTrapezes() Number of trapezes defining the cross section [-].

• BottomLevels() The bottom level for each trapeze [m].

• BottomWidths() The bottom width for each trapeze [m].

• SideSlopes() The side slope for each trapeze[-].

• StricklerCoefficients() Manning-Strickler coefficient for each trapeze [m^(1/3)/s].

• BottomSlope() Bottom slope [-].

• ChannelDepth() Channel depth [m].

• CrestHeight() The height of the weir’s crest above the channel bottom [m].

• CrestHeightTolerance() Smoothing parameter related to the difference between the water depth and the crest height [m].

• BankfullDischarge() Bankfull discharge [mm/T].

• DischargeExponent() Exponent of the water depth-discharge relation [-].

class hydpy.models.wq.DerivedParameters(master: Parameters, cls_fastaccess: type[FastAccessParameter] | None = None, cymodel: CyModelProtocol | None = None)

Bases: SubParameters

Derived parameters of model wq.

The following classes are selected:

• BottomDepths() The cumulated depth of a trapeze and its lower neighbours [m].

• TrapezeHeights() The individual height of each trapeze [m].

• SlopeWidths() The tatal width of both side slopes of each trapeze.

• TrapezeAreas() The individual area of each trapeze [m].

• PerimeterDerivatives() Change of the perimeter of each trapeze relative to a water level increase within the trapeze’s range [-].

• CrestHeightRegularisation() Regularisation parameter related to the difference between the water depth and the crest height [m].

class hydpy.models.wq.FactorSequences(master: Sequences, cls_fastaccess: type[TypeFastAccess_co] | None = None, cymodel: CyModelProtocol | None = None)

Bases: FactorSequences

Factor sequences of model wq.

The following classes are selected:

• WaterDepth() Water depth [m].

• WaterLevel() Water level [m].

• WettedAreas() Wetted area of each trapeze range [m²].

• WettedArea() Total wetted area [m²].

• WettedPerimeters() Wetted perimeter of each trapeze range [m].

• WettedPerimeter() Total wetted perimeter [m].

• WettedPerimeterDerivatives() Change in the wetted perimeter of each trapeze range with respect to a water level increase [-].

• SurfaceWidths() Surface width of each trapeze range [m].

• SurfaceWidth() Total surface width [m].

• DischargeDerivatives() Discharge change of each trapeze range with respect to a water level increase [m²/s].

• DischargeDerivative() Total discharge change with respect to a water level increase [m²/s].

• Celerity() Kinematic celerity (wave speed) [m/s].

class hydpy.models.wq.FluxSequences(master: Sequences, cls_fastaccess: type[TypeFastAccess_co] | None = None, cymodel: CyModelProtocol | None = None)

Bases: FluxSequences

Flux sequences of model wq.

The following classes are selected:

• Discharges() The discharge of each trapeze range [m³/s].

• Discharge() Total discharge [m³/s].