# pylint: disable=missing-module-docstring
import itertools
import math
import numpy
from hydpy.core import parametertools
from hydpy.core.typingtools import *
from hydpy.auxs import smoothtools
from hydpy.models.wq import wq_control
from hydpy.models.wq import wq_variables
[docs]
class BottomDepths(wq_variables.MixinTrapezes, parametertools.Parameter):
"""The cumulated depth of a trapezium and its lower neighbours [m]."""
NDIM: Final[Literal[1]] = 1
TYPE: Final = float
SPAN = (0.0, None)
CONTROLPARAMETERS = (wq_control.BottomLevels,)
[docs]
def update(self) -> None:
r"""Calculate the depth values based on
:math:`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)
"""
bottomlevels = self.subpars.pars.control.bottomlevels.values
self.values = bottomlevels - bottomlevels[0]
[docs]
class TrapezeHeights(wq_variables.MixinTrapezes, parametertools.Parameter):
"""The individual height of each trapezium [m].
The highest trapezium has no upper neighbour and is thus infinitely high.
"""
NDIM: Final[Literal[1]] = 1
TYPE: Final = float
SPAN = (0.0, None)
CONTROLPARAMETERS = (wq_control.BottomLevels,)
[docs]
def update(self) -> None:
r"""Calculate the height values based on
:math:`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)
"""
self.values = numpy.inf
self.values[:-1] = numpy.diff(self.subpars.pars.control.bottomlevels.values)
[docs]
class SlopeWidths(wq_variables.MixinTrapezes, parametertools.Parameter):
"""The total width of both side slopes of each trapezium.
The highest trapezium has no upper neighbour and is thus infinitely high and
potentially infinitely wide.
"""
NDIM: Final[Literal[1]] = 1
TYPE: Final = float
SPAN = (0.0, None)
CONTROLPARAMETERS = (wq_control.SideSlopes,)
DERIVEDPARAMETERS = (TrapezeHeights,)
[docs]
def update(self) -> None:
r"""Calculate the slope width values based on
:math:`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)
"""
sideslopes = self.subpars.pars.control.sideslopes.values
trapezeheights = self.subpars.trapezeheights.values
self.values = numpy.inf
self.values[:-1] = 2.0 * sideslopes[:-1] * trapezeheights[:-1]
[docs]
class TrapezeAreas(wq_variables.MixinTrapezes, parametertools.Parameter):
"""The individual area of each trapezium [m].
The highest trapezium has no upper neighbour and is thus infinitely large.
"""
NDIM: Final[Literal[1]] = 1
TYPE: Final = float
SPAN = (0.0, None)
CONTROLPARAMETERS = (wq_control.BottomWidths,)
DERIVEDPARAMETERS = (TrapezeHeights, SlopeWidths)
[docs]
def update(self) -> None:
r"""Calculate the perimeter derivatives based on
:math:`(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)
"""
wb = self.subpars.pars.control.bottomwidths.values
ht = self.subpars.trapezeheights.values
ws = self.subpars.slopewidths.values
self.values = (wb + ws / 2.0) * ht
w = numpy.cumsum(wb + ws)
self.values[1:] += w[:-1] * ht[1:]
[docs]
class PerimeterDerivatives(wq_variables.MixinTrapezes, parametertools.Parameter):
"""Change of the perimeter of each trapezium relative to a water level increase
within the trapezoidal's range [-].
"""
NDIM: Final[Literal[1]] = 1
TYPE: Final = float
SPAN = (0.0, None)
CONTROLPARAMETERS = (wq_control.SideSlopes,)
[docs]
def update(self) -> None:
r"""Calculate the perimeter derivatives based on
:math:`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)
"""
sideslopes = self.subpars.pars.control.sideslopes.value
self.values = 2.0 * (1.0 + sideslopes**2.0) ** 0.5
class _SectorWidths(wq_variables.MixinSectorsAndWidths, parametertools.Parameter):
TYPE: Final = float
SPAN = (0.0, None)
def _update(self, widths: wq_control.FlowWidths | wq_control.TotalWidths) -> None:
control = self.subpars.pars.control
n = control.nmbsectors.value
t = control.transitions.values
w = widths.values
self.values = 0.0
s = self.values
for i in range(n):
w0 = 0.0 if i == 0 else w[t[i - 1]]
w1 = w[-1] if i + 1 == n else w[t[i]]
s[i, :] = numpy.clip(w - w0, 0.0, w1 - w0)
[docs]
class SectorFlowWidths(_SectorWidths):
"""The sector-specific widths of those subareas of the cross section involved in
water routing [m]."""
CONTROLPARAMETERS = (
wq_control.NmbSectors,
wq_control.Transitions,
wq_control.Heights,
wq_control.FlowWidths,
)
[docs]
def update(self) -> None:
"""Allocate the |wq_control.FlowWidths| parts to the respective cross-section
sectors.
>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbwidths(9)
>>> nmbsectors(4)
>>> heights(1.0, 3.0, 4.0, 4.0, 4.0, 5.0, 6.0, 7.0, 8.0)
>>> flowwidths(2.0, 4.0, 6.0, 14.0, 18.0, 18.0, 24.0, 28.0, 30.0)
>>> transitions(2, 3, 5)
>>> derived.sectorflowwidths.update()
>>> derived.sectorflowwidths
sectorflowwidths([[2.0, 4.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0],
[0.0, 0.0, 0.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0],
[0.0, 0.0, 0.0, 0.0, 4.0, 4.0, 4.0, 4.0, 4.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 6.0, 10.0, 12.0]])
"""
flowwidths = self.subpars.pars.control.flowwidths
self._update(flowwidths)
[docs]
class SectorTotalWidths(_SectorWidths):
"""The sector-specific widths of the total cross section [m]."""
CONTROLPARAMETERS = (
wq_control.NmbSectors,
wq_control.Transitions,
wq_control.Heights,
wq_control.TotalWidths,
)
[docs]
def update(self) -> None:
"""Allocate the |wq_control.TotalWidths| parts to the respective cross-section
sectors.
>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbwidths(9)
>>> nmbsectors(4)
>>> heights(1.0, 3.0, 4.0, 4.0, 4.0, 5.0, 6.0, 7.0, 8.0)
>>> totalwidths(2.0, 4.0, 6.0, 14.0, 18.0, 18.0, 24.0, 28.0, 30.0)
>>> transitions(2, 3, 5)
>>> derived.sectortotalwidths.update()
>>> derived.sectortotalwidths
sectortotalwidths([[2.0, 4.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0],
[0.0, 0.0, 0.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0],
[0.0, 0.0, 0.0, 0.0, 4.0, 4.0, 4.0, 4.0, 4.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 6.0, 10.0, 12.0]])
"""
totalwidths = self.subpars.pars.control.totalwidths
self._update(totalwidths)
class _SectorAreasFromWidths(
wq_variables.MixinSectorsAndWidths, parametertools.Parameter
):
def _update(self, widths: SectorFlowWidths | SectorTotalWidths) -> None:
h = self.subpars.pars.control.heights.values
w = widths.values
h_diff = numpy.diff(h)
w_mean = (w[:, :-1] + w[:, 1:]) / 2.0
self.values = 0.0
self.values[:, 1:] = numpy.cumsum(h_diff * w_mean, axis=1)
[docs]
class SectorFlowAreasFromWidths(_SectorAreasFromWidths):
"""The sector-specific wetted areas of those subareas of the cross section
involved in water routing [m²]."""
TYPE: Final = float
SPAN = (0.0, None)
CONTROLPARAMETERS = (wq_control.Heights,)
DERIVEDPARAMETERS = (SectorFlowWidths,)
[docs]
def update(self) -> None:
"""Calculate the cumulative sum of the individual trapezoidal areas defined by
the height-width pairs of the individual sectors.
>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbwidths(9)
>>> nmbsectors(4)
>>> heights(1.0, 3.0, 4.0, 4.0, 4.0, 5.0, 6.0, 7.0, 8.0)
>>> flowwidths(2.0, 4.0, 6.0, 14.0, 18.0, 18.0, 24.0, 28.0, 30.0)
>>> transitions(2, 3, 5)
>>> derived.sectorflowwidths.update()
>>> derived.sectorflowareasfromwidths.update()
>>> derived.sectorflowareasfromwidths
sectorflowareasfromwidths([[0.0, 6.0, 11.0, 11.0, 11.0, 17.0, 23.0,
29.0, 35.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 8.0, 16.0, 24.0,
32.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 8.0, 12.0,
16.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 3.0, 11.0,
22.0]])
"""
sectorflowwidths = self.subpars.sectorflowwidths
self._update(sectorflowwidths)
[docs]
class SectorTotalAreasFromWidths(_SectorAreasFromWidths):
"""The sector-specific wetted areas of the total cross section [m²]."""
TYPE: Final = float
SPAN = (0.0, None)
CONTROLPARAMETERS = (wq_control.Heights,)
DERIVEDPARAMETERS = (SectorTotalWidths,)
[docs]
def update(self) -> None:
"""Calculate the cumulative sum of the individual trapezoidal areas defined by
the height-width pairs of the individual sectors.
>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbwidths(9)
>>> nmbsectors(4)
>>> heights(1.0, 3.0, 4.0, 4.0, 4.0, 5.0, 6.0, 7.0, 8.0)
>>> totalwidths(2.0, 4.0, 6.0, 14.0, 18.0, 18.0, 24.0, 28.0, 30.0)
>>> transitions(2, 3, 5)
>>> derived.sectortotalwidths.update()
>>> derived.sectortotalareasfromwidths.update()
>>> derived.sectortotalareasfromwidths
sectortotalareasfromwidths([[0.0, 6.0, 11.0, 11.0, 11.0, 17.0, 23.0,
29.0, 35.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 8.0, 16.0, 24.0,
32.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 8.0, 12.0,
16.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 3.0, 11.0,
22.0]])
"""
sectortotalwidths = self.subpars.sectortotalwidths
self._update(sectortotalwidths)
class _SectorAreasFromTable(
wq_variables.MixinSectorsAndWidths, parametertools.Parameter
):
def _update(self, *, widths: VectorFloat, areas: VectorFloat) -> None:
control = self.subpars.pars.control
nw = control.nmbwidths.value
ns = control.nmbsectors.value
ts = control.transitions.values
hs = control.heights.values
self.values = 0.0
vs = self.values
for i in range(ns):
t = (nw - 1) if (i == ns - 1) else ts[i]
vs[i, : t + 1] = areas[: t + 1]
vs[i, t + 1 :] = areas[t] + numpy.cumsum(widths[t] * numpy.diff(hs[t:]))
if i > 0:
vs[i, :] -= numpy.sum(vs[:i, :], axis=0)
[docs]
class SectorFlowAreasFromTable(_SectorAreasFromTable):
"""The sector-specific wetted areas of those subareas of the cross section involved
in water routing [m²]."""
TYPE: Final = float
CONTROLPARAMETERS = (
wq_control.NmbWidths,
wq_control.NmbSectors,
wq_control.Transitions,
wq_control.Heights,
wq_control.FlowWidths,
wq_control.FlowAreas,
)
[docs]
def update(self) -> None:
"""Divide the routing-relevant wetted areas of the complete cross section into
the individual sections.
We perform the following test calculation using geometric input data, assuming
a pattern of stacked trapezoids for simplicity:
>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbwidths(7)
>>> nmbsectors(4)
>>> transitions(2, 3, 5)
>>> heights(1.0, 3.0, 4.0, 6.0, 6.0, 9.0, 10.0)
>>> flowwidths(2.0, 4.0, 4.0, 6.0, 8.0, 8.0, 12.0)
>>> flowareas.approximate()
>>> flowareas
flowareas(0.0, 6.0, 10.0, 20.0, 20.0, 44.0, 54.0)
>>> derived.sectorflowareasfromtable.update()
>>> derived.sectorflowareasfromtable
sectorflowareasfromtable([[0.0, 6.0, 10.0, 18.0, 18.0, 30.0, 34.0],
[0.0, 0.0, 0.0, 2.0, 2.0, 8.0, 10.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 6.0, 8.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0]])
>>> assert numpy.array_equal(
... numpy.sum(derived.sectorflowareasfromtable.values, axis=0),
... flowareas.values,
... )
"""
control = self.subpars.pars.control
self._update(widths=control.flowwidths.values, areas=control.flowareas.values)
[docs]
class SectorTotalAreasFromTable(_SectorAreasFromTable):
"""The sector-specific wetted areas of the total cross section [m²]."""
TYPE: Final = float
CONTROLPARAMETERS = (
wq_control.NmbWidths,
wq_control.NmbSectors,
wq_control.Transitions,
wq_control.Heights,
wq_control.TotalWidths,
wq_control.TotalAreas,
)
[docs]
def update(self) -> None:
"""Divide the total wetted areas of the complete cross section into the
individual sections.
We perform the following test calculation using geometric input data, assuming
a pattern of stacked trapezoids for simplicity:
>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbwidths(7)
>>> nmbsectors(4)
>>> transitions(2, 3, 5)
>>> heights(1.0, 3.0, 4.0, 6.0, 6.0, 9.0, 10.0)
>>> totalwidths(2.0, 4.0, 4.0, 6.0, 8.0, 8.0, 12.0)
>>> totalareas.approximate()
>>> totalareas
totalareas(0.0, 6.0, 10.0, 20.0, 20.0, 44.0, 54.0)
>>> derived.sectortotalareasfromtable.update()
>>> derived.sectortotalareasfromtable
sectortotalareasfromtable([[0.0, 6.0, 10.0, 18.0, 18.0, 30.0, 34.0],
[0.0, 0.0, 0.0, 2.0, 2.0, 8.0, 10.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 6.0, 8.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0]])
>>> assert numpy.array_equal(
... numpy.sum(derived.sectortotalareasfromtable.values, axis=0),
... totalareas.values,
... )
"""
control = self.subpars.pars.control
self._update(widths=control.totalwidths.values, areas=control.totalareas.values)
class _AreaAdjustments(wq_variables.MixinSectorsAndWidths, parametertools.Parameter):
def _update(self, *, widths: MatrixFloat, areas: MatrixFloat) -> None:
control = self.subpars.pars.control
nw = control.nmbwidths.value
ns = control.nmbsectors.value
ts = control.transitions.values
hs = control.heights.values
self.values = 1.0
vs = self.values
for i in range(ns):
t1 = nw - 1 if i == ns - 1 else ts[i]
t0 = 0 if i == 0 else ts[i - 1]
dhs = numpy.diff(hs[t0 : t1 + 1])
das_trapezoid = dhs * (widths[i, t0:t1] + widths[i, t0 + 1 : t1 + 1]) / 2.0
das_data = numpy.diff(areas[i, t0 : t1 + 1])
sel = dhs > 0.0
vs[i, t0:t1][sel] = das_data[sel] / das_trapezoid[sel]
self.trim()
[docs]
class FlowAreaAdjustments(_AreaAdjustments):
"""Factors for adjusting flow areas calculated by assuming trapezoidal geometries
to externally defined flow areas [-]."""
TYPE: Final = float
SPAN = (0.0, 2.0)
CONTROLPARAMETERS = (
wq_control.NmbWidths,
wq_control.NmbSectors,
wq_control.Transitions,
wq_control.Heights,
)
DERIVEDPARAMETERS = (SectorFlowWidths, SectorFlowAreasFromTable)
[docs]
def update(self) -> None:
"""Divide externally defined flow areas by flow areas calculated assuming
trapezoidal geometries.
For the first test calculation, we calculate the "externally defined" areas
based on trapezoidal geometries. Hence, all adjustment factors are one:
>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbwidths(7)
>>> nmbsectors(4)
>>> transitions(2, 3, 5)
>>> heights(1.0, 3.0, 4.0, 6.0, 6.0, 9.0, 10.0)
>>> flowwidths(2.0, 4.0, 4.0, 6.0, 8.0, 8.0, 12.0)
>>> flowareas.approximate()
>>> flowareas
flowareas(0.0, 6.0, 10.0, 20.0, 20.0, 44.0, 54.0)
>>> derived.sectorflowwidths.update()
>>> derived.sectorflowareasfromtable.update()
>>> derived.flowareaadjustments.update()
>>> derived.flowareaadjustments
flowareaadjustments(1.0)
After setting "non-trapezoidal" areas, the individual adjustment factors should
usually lie between zero and two (in the extrapolation range, all factors are
one):
>>> flowareas(0.0, 8.0, 10.0, 22.0, 22.0, 42.0, 53.0)
>>> derived.sectorflowareasfromtable.update()
>>> derived.flowareaadjustments.update()
>>> derived.flowareaadjustments
flowareaadjustments([[1.333333, 0.5, 1.0, 1.0, 1.0, 1.0, 1.0],
[1.0, 1.0, 2.0, 1.0, 1.0, 1.0, 1.0],
[1.0, 1.0, 1.0, 1.0, 0.333333, 1.0, 1.0],
[1.0, 1.0, 1.0, 1.0, 1.0, 1.5, 1.0]])
Unplausible adjustment factors are trimmed to the acceptable interval:
>>> flowareas(0.0, 8.0, 10.0, 22.0, 22.0, 39.0, 53.0)
>>> derived.sectorflowareasfromtable.update()
>>> derived.flowareaadjustments.update()
>>> derived.flowareaadjustments
flowareaadjustments([[1.333333, 0.5, 1.0, 1.0, 1.0, 1.0, 1.0],
[1.0, 1.0, 2.0, 1.0, 1.0, 1.0, 1.0],
[1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0],
[1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 1.0]])
"""
derived = self.subpars
self._update(
widths=derived.sectorflowwidths.values,
areas=derived.sectorflowareasfromtable.values,
)
[docs]
class TotalAreaAdjustments(_AreaAdjustments):
"""Factors for adjusting total wetted areas calculated by assuming trapezoidal
geometries to externally defined total wetted areas [-]."""
TYPE: Final = float
SPAN = (0.0, 2.0)
CONTROLPARAMETERS = (
wq_control.NmbWidths,
wq_control.NmbSectors,
wq_control.Transitions,
wq_control.Heights,
)
DERIVEDPARAMETERS = (SectorTotalWidths, SectorTotalAreasFromTable)
[docs]
def update(self) -> None:
"""Divide externally defined flow areas by flow areas calculated assuming
trapezoidal geometries.
For the first test calculation, we calculate the "externally defined" areas
based on trapezoidal geometries. Hence, all adjustment factors are one:
>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbwidths(7)
>>> nmbsectors(4)
>>> transitions(2, 3, 5)
>>> heights(1.0, 3.0, 4.0, 6.0, 6.0, 9.0, 10.0)
>>> totalwidths(2.0, 4.0, 4.0, 6.0, 8.0, 8.0, 12.0)
>>> totalareas.approximate()
>>> totalareas
totalareas(0.0, 6.0, 10.0, 20.0, 20.0, 44.0, 54.0)
>>> derived.sectortotalwidths.update()
>>> derived.sectortotalareasfromtable.update()
>>> derived.totalareaadjustments.update()
>>> derived.totalareaadjustments
totalareaadjustments(1.0)
After setting "non-trapezoidal" areas, the individual adjustment factors should
usually lie between zero and two (in the extrapolation range, all factors are
one):
>>> totalareas(0.0, 8.0, 10.0, 22.0, 22.0, 42.0, 53.0)
>>> derived.sectortotalareasfromtable.update()
>>> derived.totalareaadjustments.update()
>>> derived.totalareaadjustments
totalareaadjustments([[1.333333, 0.5, 1.0, 1.0, 1.0, 1.0, 1.0],
[1.0, 1.0, 2.0, 1.0, 1.0, 1.0, 1.0],
[1.0, 1.0, 1.0, 1.0, 0.333333, 1.0, 1.0],
[1.0, 1.0, 1.0, 1.0, 1.0, 1.5, 1.0]])
Unplausible adjustment factors are trimmed to the acceptable interval:
>>> totalareas(0.0, 8.0, 10.0, 22.0, 22.0, 39.0, 53.0)
>>> derived.sectortotalareasfromtable.update()
>>> derived.totalareaadjustments.update()
>>> derived.totalareaadjustments
totalareaadjustments([[1.333333, 0.5, 1.0, 1.0, 1.0, 1.0, 1.0],
[1.0, 1.0, 2.0, 1.0, 1.0, 1.0, 1.0],
[1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0],
[1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 1.0]])
"""
derived = self.subpars
self._update(
widths=derived.sectortotalwidths.values,
areas=derived.sectortotalareasfromtable.values,
)
[docs]
class SectorFlowPerimetersFromWidths(
wq_variables.MixinSectorsAndWidths, parametertools.Parameter
):
"""The sector-specific wetted perimeters of those subareas of the cross section
involved in water routing [m]."""
TYPE: Final = float
SPAN = (0.0, None)
CONTROLPARAMETERS = (wq_control.Heights,)
DERIVEDPARAMETERS = (SectorFlowWidths,)
[docs]
def update(self) -> None:
"""Calculate the total wetted perimeters of the individual sections.
>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbwidths(9)
>>> nmbsectors(4)
>>> heights(1.0, 3.0, 4.0, 4.0, 4.0, 5.0, 6.0, 7.0, 8.0)
>>> flowwidths(2.0, 4.0, 6.0, 14.0, 18.0, 18.0, 24.0, 28.0, 30.0)
>>> transitions(2, 3, 5)
>>> derived.sectorflowwidths.update()
>>> derived.sectorflowperimetersfromwidths.update()
>>> derived.sectorflowperimetersfromwidths
sectorflowperimetersfromwidths([[2.0, 6.472136, 9.300563, 9.300563,
9.300563, 11.300563, 13.300563,
15.300563, 17.300563],
[0.0, 0.0, 0.0, 8.0, 8.0, 10.0, 12.0,
14.0, 16.0],
[0.0, 0.0, 0.0, 0.0, 4.0, 6.0, 8.0,
10.0, 12.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 6.324555,
10.796691, 13.625118]])
"""
control = self.subpars.pars.control
h = control.heights.values
w = self.subpars.sectorflowwidths.values
dh = numpy.diff(h)
dw = numpy.diff(w)
p = numpy.sqrt(numpy.square(2.0 * dh) + numpy.square(dw))
self.values = 0.0
for i, t in enumerate(
itertools.chain([numpy.int64(0)], control.transitions.values)
):
self.values[i, t:] = w[i, t]
self.values[i, t + 1 :] += numpy.cumsum(p[i, t:])
[docs]
class SectorFlowPerimetersFromTable(
wq_variables.MixinSectorsAndWidths, parametertools.Parameter
):
"""The sector-specific wetted perimeters of those subareas of the cross section
involved in water routing [m]."""
TYPE: Final = float
SPAN = (0.0, None)
CONTROLPARAMETERS = (
wq_control.NmbWidths,
wq_control.NmbSectors,
wq_control.Transitions,
wq_control.Heights,
wq_control.FlowWidths,
wq_control.FlowPerimeters,
)
[docs]
def update(self) -> None:
"""Divide the total wetted perimeters of the complete cross section into the
individual sections.
>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbwidths(7)
>>> nmbsectors(4)
>>> transitions(2, 3, 5)
>>> heights(1.0, 3.0, 4.0, 6.0, 6.0, 9.0, 10.0)
>>> flowwidths(2.0, 4.0, 4.0, 6.0, 8.0, 8.0, 12.0)
>>> flowperimeters.approximate()
>>> flowperimeters
flowperimeters(2.0, 6.472136, 8.472136, 12.944272, 14.944272, 20.944272,
25.416408)
>>> derived.sectorflowperimetersfromtable.update()
>>> derived.sectorflowperimetersfromtable
sectorflowperimetersfromtable([[2.0, 6.472136, 8.472136, 12.472136,
12.472136, 18.472136, 20.472136],
[0.0, 0.0, 0.0, 4.472136, 4.472136,
10.472136, 12.472136],
[0.0, 0.0, 0.0, 0.0, 2.0, 8.0, 10.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.472136]])
"""
control = self.subpars.pars.control
nw = control.nmbwidths.value
ns = control.nmbsectors.value
ts = control.transitions.values
hs = control.heights.values
ps = control.flowperimeters.values
self.values = 0.0
vs = self.values
for i in range(ns):
t1 = (nw - 1) if (i == ns - 1) else ts[i]
if i == 0:
vs[i, : t1 + 1] = ps[: t1 + 1]
else:
t0 = ts[i - 1]
vs[i, t0 + 1 : t1 + 1] = ps[t0 + 1 : t1 + 1] - ps[t0]
vs[i, t1 + 1 :] = vs[i, t1] + numpy.cumsum(2.0 * numpy.diff(hs[t1:]))
[docs]
class SectorFlowPerimeterDerivativesFromWidths(
wq_variables.MixinSectorsAndWidths, parametertools.Parameter
):
"""Sector-specific changes in the wetted perimeters of the subareas of the cross
section involved in water routing with respect to water-level increases [m]."""
TYPE: Final = float
SPAN = (0.0, None)
CONTROLPARAMETERS = (wq_control.Heights,)
DERIVEDPARAMETERS = (SectorFlowWidths,)
[docs]
def update(self) -> None:
r"""Calculate the flow perimeter derivatives based on
:math:`2 \cdot \sqrt{1 + (dw / dh / 2)^2}`.
>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbwidths(9)
>>> nmbsectors(4)
>>> heights(1.0, 3.0, 4.0, 4.0, 4.0, 5.0, 6.0, 7.0, 8.0)
>>> flowwidths(2.0, 4.0, 6.0, 14.0, 18.0, 18.0, 24.0, 28.0, 30.0)
>>> transitions(2, 3, 5)
>>> derived.sectorflowwidths.update()
>>> derived.sectorflowperimeterderivativesfromwidths.update()
>>> derived.sectorflowperimeterderivativesfromwidths
sectorflowperimeterderivativesfromwidths([[2.236068, 2.828427, 2.0, 2.0,
2.0, 2.0, 2.0, 2.0, 2.0],
[nan, nan, 2.0, 2.0, 2.0, 2.0,
2.0, 2.0, 2.0],
[nan, nan, nan, 2.0, 2.0, 2.0,
2.0, 2.0, 2.0],
[nan, nan, nan, nan, nan,
6.324555, 4.472136, 2.828427,
2.0]])
"""
control = self.subpars.pars.control
n = control.nmbwidths.value
dh = numpy.diff(control.heights.values)
dw = numpy.diff(self.subpars.sectorflowwidths.values)
self.values = numpy.nan
v = self.values
v[:, -1] = 2.0
for i, t in enumerate(
itertools.chain([numpy.int64(0)], control.transitions.values)
):
d = 2.0
for j in range(n - 2, t - 1, -1):
if dh[j] > 0.0:
d = 2.0 * math.sqrt(1.0 + math.pow(dw[i, j] / dh[j] / 2.0, 2.0))
v[i, j] = d
[docs]
class SectorFlowPerimeterDerivativesFromTable(
wq_variables.MixinSectorsAndWidths, parametertools.Parameter
):
"""Sector-specific changes in the wetted perimeters of the subareas of the cross
section involved in water routing with respect to water-level increases [m]."""
TYPE: Final = float
SPAN = (0.0, None)
CONTROLPARAMETERS = (
wq_control.NmbSectors,
wq_control.Transitions,
wq_control.Heights,
)
DERIVEDPARAMETERS = (SectorFlowPerimetersFromTable,)
[docs]
def update(self) -> None:
r"""Approximate the derivatives of the sector-specific flow perimeter based on
simple difference quotients between subsequent measurement heights.
>>> from hydpy.models.wq import *
>>> parameterstep()
>>> nmbwidths(7)
>>> nmbsectors(4)
>>> heights(1.0, 3.0, 4.0, 6.0, 6.0, 9.0, 10.0)
>>> flowwidths(2.0, 4.0, 4.0, 6.0, 8.0, 8.0, 12.0)
>>> flowperimeters.approximate()
>>> transitions(2, 3, 5)
>>> derived.sectorflowwidths.update()
>>> derived.sectorflowperimetersfromtable.update()
>>> derived.sectorflowperimeterderivativesfromtable.update()
>>> derived.sectorflowperimeterderivativesfromtable
sectorflowperimeterderivativesfromtable([[2.236068, 2.0, 2.0, 2.0, 2.0,
2.0, 2.0],
[nan, nan, 2.236068, 2.0, 2.0,
2.0, 2.0],
[nan, nan, nan, 2.0, 2.0, 2.0,
2.0],
[nan, nan, nan, nan, nan,
4.472136, 2.0]])
"""
derived = self.subpars
control = derived.pars.control
ns = control.nmbsectors.value
ts = control.transitions.values
dh = numpy.diff(control.heights.values)
dp = numpy.diff(derived.sectorflowperimetersfromtable.values, axis=1)
self.values = numpy.nan
vs = self.values
for i in range(ns):
t = 0 if i == 0 else ts[i - 1]
sel = dh[t:] > 0.0
vs[i, t:-1][sel] = dp[i, t:][sel] / dh[t:][sel]
vs[i, t:-1][~sel] = 2.0
self.values[:, -1] = 2.0
[docs]
class CrestHeightRegularisation(parametertools.Parameter):
"""Regularisation parameter related to the difference between the water depth and
the crest height [m]."""
NDIM: Final[Literal[0]] = 0
TYPE: Final = float
SPAN = (0.0, None)
CONTROLPARAMETERS = (wq_control.CrestHeightTolerance,)
[docs]
def update(self) -> None:
"""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
"""
metapar = self.subpars.pars.control.crestheighttolerance.value
self(smoothtools.calc_smoothpar_logistic2(1000.0 * metapar) / 1000.0)
