A two-stage inflation method in parameter estimation to compensate for constant parameter evolution in Community Earth System Model
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Abstract: Parameter estimation is defined as the process to adjust or optimize the model parameter using observations. A long-term problem in ensemble-based parameter estimation methods is that the parameters are assumed to be constant during model integration. This assumption will cause underestimation of parameter ensemble spread, such that the parameter ensemble tends to collapse before an optimal solution is found. In this work, a two-stage inflation method is developed for parameter estimation, which can address the collapse of parameter ensemble due to the constant evolution of parameters. In the first stage, adaptive inflation is applied to the augmented states, in which the global scalar parameter is transformed to fields with spatial dependence. In the second stage, extra multiplicative inflation is used to inflate the scalar parameter ensemble to compensate for constant parameter evolution, where the inflation factor is determined according to the spread growth ratio of model states. The observation system simulation experiment with Community Earth System Model (CESM) shows that the second stage of the inflation scheme plays a crucial role in successful parameter estimation. With proper multiplicative inflation factors, the parameter estimation can effectively reduce the parameter biases, providing more accurate analyses.
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Key words:
- parameter estimation /
- data assimilation /
- inflation /
- CESM /
- EnKF
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Figure 1. Flow diagram of OSSE for state and parameter estimation. The unit of bckgrnd-vdc is cm2/s.
Figure 2. TS profile locations (a) and depths (b) of the period from January 1, 2010 to January 10, 2010. For a better display, only the depths of the first 500 observations are shown in b.
Figure 3. SST spread (left) and SSS spread (right) of the 1st (a, b), 4th (c, d), 7th (e, f), 10th (g, h) month from the parameter sensitivity experiment.
Figure 4. RMSEs of prior and posterior innovations of the temperature (left) and salinity (right) for depths 10 m (a, b), 50 m (c, d), 200 m (e, f), and 1 000 m (g, h).
Figure 5. RMSE of SST (a,b), SSS (c,d), and SSH (e,f) from control run (left) and state estimation (right) of the first 6 months.
Figure 6. The ratio of posterior error standard deviation to prior error standard deviation of the parameter ensemble (a); the posterior ensemble member 1–3 (b–d). The quantities are computed for the first parameter estimation step.
Figure 7. The spatial varying inflation values for temperature (left) and salinity (right) in 5 m (a, b), 100 m (c, d) and 200 m (e, f) depth; the inflation values for the two-dimensional parameter field for the first analysis step (g).
Figure 8. The evolution of the parameter mean (red solid line) plus/minus one standard deviation (red dotted lines) over the data assimilation period (a); the parameter error (red line) and ensemble spread (green line) over the data assimilation period (b).
Figure 9. The global mean temperature (left) and salinity (right) spread in each data assimilation step at the depth 5 m (a, b), 50 m (c, d), and 200 m (e, f), each dashed line connects the posterior of the previous step and the prior of the current step. And the temperature (g) and salinity (h) spread growth ratio at the first step.
Figure 10. The evolution of the parameter mean (red solid line) and spread (red dotted lines) over the data assimilation period using extra parameter inflation with
$ \mathrm{\alpha }=1.1 $ (a), 1.2 (b), 1.3 (c), and 1.5 (d), respectively.
Figure 11. The temperature (upper) and salinity (bottom) RMSE for the last 6 months of the 2nd year using the data assimilation results from parameter estimation and pure state estimation, respectively.
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