A TabulatedRatingCurve determines outflow from a Basin by looking up the flow rate that corresponds to the current upstream level from a rating curve. The TabulatedRatingCurve takes a rating curve as input. Use it for instance to model flow over a weir.
1 Tables
1.1 Static
column
type
unit
restriction
node_id
Int32

sorted
control_state
String

(optional) sorted per node_id
active
Bool

(optional, default true)
max_downstream_level
Float64
\(\text{m}\)
(optional)
level
Float64
\(\text{m}\)
sorted per control_state, unique
flow_rate
Float64
\(\text{m}^3/\text{s}\)
start at 0, increasing
Thus a single rating curve can be given by the following table:
node_id
flow_rate
level
2
0.0
0.10
2
0.0001
0.09
2
0.01
0.29
2
0.9
20.09
Below the lowest given level of 0.10, the flow rate is kept at 0. Between given levels the flow rate is interpolated linearly. Above the maximum given level of 20.09, the flow rate keeps increases linearly according to the slope of the last segment.
1.1.1 Interpolation
The \(Q(h)\) relationship of a tabulated rating curve is defined as a linear interpolation.
Here it is validated that the flow starts at \(0\) and is nondecreasing. The flow is extrapolated as \(0\) backward and linearly forward.
1.2 Time
This table is the transient form of the TabulatedRatingCurve table. The only difference is that a time column is added. The table must by sorted by time, and per time it must be sorted by node_id. With this the rating curves can be updated over time. Note that a node_id can be either in this table or in the static one, but not both.
column
type
unit
restriction
node_id
Int32

sorted
time
DateTime

sorted per node_id
level
Float64
\(\text{m}\)
sorted per node_id per time
flow_rate
Float64
\(\text{m}^3/\text{s}\)
nonnegative
max_downstream_level
Float64
\(\text{m}\)
(optional)
2 Equations
The TabulatedRatingCurve is a tabulation of a Basin’s discharge behavior. It describes a piecewise linear relationship between the Basin’s level and its discharge. It can be understood as an empirical description of a Basin’s properties. This can include a weir, but also the lumped hydraulic behavior of the upstream channels.
\[
Q = \phi f(h)
\]
Where:
\(h\) is the upstream water level
\(f\) is a piecewise linear function describing the given rating curve \(Q(h)\)
\(\phi\) is the reduction factor, which smoothly reduces flow based on all of these criteria:
The upstream volume is below \(10 m^3\).
The upstream level is less than \(0.02 m\) above the downstream level.
The downstream level is above max_downstream_level  \(0.02 m\)