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Welcome to the next generation MIKE+ Documentation

General parameters

The general parameter definition covers

  • Specification of the method used to assimilate observation data into the simulation. Currently only 'Updating with weighting function' is available. The computational engine behind MIKE+ (MIKE 1D) has an experimental implementation of the Ensemble Kalman filter (EnKF), which may become available in future versions of MIKE+.
  • Specification of the simulation range that the updating is applied to (from 'First updating time step' to 'Time of forecast').

Note

Model setups with DA are constrained to run with fixed time step. This is partly due to some specifications given in "number of time steps" (as e.g. the above mentioned 'First updating time step') and partly due to the error correction model, where the coefficients are interpreted (and estimated) in terms of the size of the time step.

Mode selection

In the current version, only the mode 'Updating with weighting function' is available. This approach updates the state variables in the vicinity of each observation based on a user-defined weighting function. The weighting function specifies how large a fraction of the deviation to the observation that should be applied as correction, and how the correction is distributed to the neighboring points in the computational grid.

In the 'Update with weighting function' method, an observation only exerts correction of states of the same kind as itself, which means that the not-updated states will only receive an indirect update, which is the result of advancing the updated states to the next time step.

The statement about the weighting function method only correcting states of the same kind as the measurement comes with a twist:

  • A water level measurement corrects water level grid points inside the update range, not the discharge grid points.
  • A discharge measurement corrects discharge, but the correction is made indirectly, in that the calculated discharge correction is injected as lateral flows to the water level grid points inside the update range - so a discharge measurement does not directly manipulate the values of discharge grid points.

Computationally, 'Update with weighting function' is only marginally more expensive than running an ordinary simulation, because it is a 'single-simulation approach'.

The weighting function can be viewed as a simplified version of the "gain" of a Kalman filter. The weighting function is stationary (the weights do not vary over time) and the user decides both the size and distribution in space of the weights.

In comparison, the Ensemble Kalman filter (EnKF) calculates a gain function from an ensemble of model simulations. This results in a gain function, which varies in space and time with the model dynamics. EnKF quantifies the correlation between grid points of different types, and therefore a water level measurement causes a joint update of both water level grid points and discharge grid points.

Basic parameters

First updating time step: The time step number at which the model starts to be updated. A value of 0 corresponds to the first time step of the simulation and e.g. a value of 100 corresponds to running the simulation without update for the first 100 time steps. The weighting function method has no requirement of a "warm-up" phase before the updating starts, so the first updating time step can safely be set to 0.

Forecast

Time of forecast: Date and time at which the model at latest switches from updating to forecasting without correction.

For operational systems, the updating goes on as long as the measurement time series contains values. This will at most be up to time of forecast, and in many cases the last time stamp is before time of forecast, because the system needs some time to retrieve and process the sensor data before issuing the forecast. Note that each measurement corrects the model state independently of the other measurements, so all the measurement time series need not have the last time stamp in common. The correction continues until the last time stamp of the measurement.

For hindcast applications and emulation of operational systems, the last update happens at time of forecast, even though the measurement series contains time stamps beyond that point in time.