This section presents a twin experiment aimed for getting more understanding about the data assimilation under an idealized situation. In reality, model noise as well as the true state of a system is unknown. One needs to make certain assumptions in order to apply a data assimilation technique. A twin experiment allows us to study the effect of various assumptions on the behaviour of a data assimilation system. The goal of this first twin experiment is to check if the data assimilation can improve the estimate of all model state variables for the Yeongsan EFDC model in an ideal case where all error statistics are known.
Data assimilation setting
Model state
The following variables are included in the definition of the state vector, being updated directly by the filter:
- Algal Cyanobacteria
- Algal Diatom
- Algal Green
- Refractory PO Carbon
- Labile PO Carbon
- Dissolved Phosphorus
- Phosphate
- Refractory PO Nitrogen
- Labile PONitrogen
- DissolvedONitrogen
- Ammonia
- Nitrate
- Dissolved Oxygen
Noise model
In this experiment, the model uncertainty is assumed to come from the a number of model input parameters at four locations (see red circles on the figure below). The noise processes for each parameter at each location are assumed additive, indepent from each other, and modelled by an AR(1) process with the following statistics:
- Algal Diatom: standard deviation 0.5 μg/L, correlation time 72 hours
- Algal Cyanobacteria: standard deviation 0.2 μg/L, correlation time 72 hours
- Algal Green Algae: standard deviation 0.2 μg/L, correlation time 72 hours
- Phosphate: standard deviation 0.05 μg/L, correlation time 72 hours
- Discharge: standard deviation 1.0 m3/s, correlation time 72 hours
- Global Radiation: standard deviation 10.0 W/m2, correlation time 24 hours
The above statistics apply for all the four locations.
Observation station
Synthetic observations are generated by running a stochastic model with the above mentioned noise specifications. One assimilation location is used (circled on the figure below) with four observed parameters: Algal Cyanobacteria, Algal Diatom, Algal Green, and Phosphate. When generating the synthetic observations, we assume that the observation is perfect. However, in the Kalman filter setting, a standard deviation of 0.1 μg/L is assigned to each of the four observed parameters. To be close to reality, we sample the synthetic observations with a period of seven days.
Results
At assimilation station
Discussion points:
- Algal Cyanobacteria and Algal Green: the truth is non zero even in the winter. Is this realistic? This is the result of modelling the error as additive to the input variable. Perhaps modelling the error with "ln" operation, i.e. the noise process determines the fraction of the input that is noisy; the perturbed input is computed according to: input = input * exp(noise) ≈ input * (1+noise) ?
At validation stations
The accuracy at all assimilation and validation stations is presented in term of RMSE and shown in the figures below. At the x-axes, the locations are arranged from upstream to downstream. The assimilation station is location 5004A10.
Discussion points:
- For all the four assimilated parameters, accuracy at the downstream locations is improved. The accuracy of Phosphate estimate at the assimilation station is however deteriorated. Perhaps this is due to the interaction between Phosphate and the other assimilated parameters? Suggestion: perform a twin experiment where only Phosphate is assimilated. Suggestion from NIER (tele-discussion, 24-11-2016): the observational standard deviation of Phosphate is too large, hence try a smaller standard deviation.
- At upstream locations, the accuracy of Algal Cyanobacteria estimate of the deterministic run is high, but it deteriorates at assimilation stations. Perhaps because the noise the input location just upstream of the assimilation stations happens to be larger than the others. Still needs to be checked.
- Water temperature is affected by the noise although it is not included in the state vector definition. Assimilating the four water quality parameters doesn't help improve the accuracy of water temperature estimates.
