The results show that the spin-up period of the state estimation is approximately 2 years.

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The principles of the twin experiment are introduced in section 3, where the assimilation model is assimilated with the "observation" field to retrieve the analysis solution. In this section, the ef-. Here, the RMSE is calculated on the first day of each month in the first year simulations for the assimilation red and non-assimilation blue experiments. In this section, we first check the time series of the RMSEs of several key variables. The RMSE here for each grid is calculated as follows:. For the zonal t anomaly, the maximum RMSEs are located in the central equatorial Pacific, with values of 0.

Similar results are obtained for the meridional t anomaly Figs. The reason is the fact that only the "observations" of the SST anomaly are assimilated in Expt. Thus, the assimilation process has a direct effect on the SST anomaly field and thereby on the t anomaly field. In contrast, the SL and Te fields are indirectly impacted by the SST anomaly assimilation through the model physical processes. These results demonstrate that the 4D-Var method can effectively reduce the error in the initial conditions, thereby leading to.

Here, the RMSE is calculated from results obtained for the first year simulations for the assimilation left panels and non-assimilation right panels experiments. Thirdly, we check the temporal evolution of the SST and t anomalies. It can be seen that the ENSO period, spatial structure and phase transition are well. Excluding the spin-up period of 4D-Var, Expt.

For Expt. For example, the amplitude of the modeled SST anomaly exhibits. Contour interval: 0.

Additionally, the phase transition time of the SST anomaly also differs from the "truth" value. Similar to Fig. The spatiotemporal structure and amplitude of the zonal t anomaly produced by Expt. The ocean subsurface fields play an important role in the development of the ENSO events. Figure 8 shows the longitude-time sections of Te anomalies along the equator for the "truth" fields, Expt.

Through the model adjustment achieved by assimilating "observations" of the SST anomaly, the spatiotemporal evolution of Te produced by Expt.

Figure 9a shows the time series of the Nino3. It can be seen that Expt. For clarity, the time series of the absolute errors of the Nino3. It is evident that the absolute error produced by Expt. Furthermore, the absolute error produced by Expt. Thus, the high level of agreement between the assimilation results and the "truth" value can provide a better initialization for ENSO prediction.

In general, a better prediction of ENSO events is a strict test for model simulation and analysis through data assimilation. Therefore, improved prediction accuracy is an important indicator for assessing the quality of the 4D-Var data assimilation approach. As in Fig.

Time series of the Nino3. Figure 10 presents the time series of the Nino3. The Nino3. The correlation coefficient between the "truth" and the predicted Nino3. The results are likely idealized to a certain extent because they are evaluated in a twin experiment, but these experiments provide us with important information about the way the 4D-Var data assimilation approach can effectively improve the model state estimation and prediction of ENSO events using the ICM. Data assimilation is an effective way to improve the accuracy of model simulations and analyses for weather and climate through an optimal combination of model solutions and observations.

In particular, the advanced 4D-Var data assimilation method is more dynamically and mathematically consistent in constraining numerical models with observations to achieve the optimal initialization for ENSO analysis and prediction. In this study, we implement the 4D-Var method based on an improved ICM that has been routinely used for. The construction of the 4D-Var assimilation system includes the tangent linear model and adjoint model of the ICM and a minimization procedure.

Strict testing justifies the accuracy of the adjoint model and the effectiveness of the 4D-Var in constraining dynamical models with observations. The impacts of the optimal initialization produced by 4D-Var on ENSO analysis and prediction are evaluated through a biased twin experiment. In this study, only "observations" of the SST anomaly are assimilated into the model to optimize the initial conditions. Results show that, compared with the non-assimilation case, the assimilation results are more consistent with the "truth" value, and the RMSEs of the anomalies for the SST, t, SL and Te fields are much smaller especially for the SST and t fields.

Additionally, the prediction accuracy is improved by optimizing the initial conditions. The results obtained in this study provide some insight into the way in which ENSO prediction can be improved with the 4D-Var algorithm. Further modeling studies using the 4D-Var are underway. In this application, however, no sophisticated data assimilation is applied in the ICM; instead, a simple initialization method is currently taken for the model forecast, as follows: The observed interannual SST anomalies are the only field used in the prediction initialization Zhang et al.

In real-time practice, experimental predictions are typically conducted near the middle of each month, when the monthly mean SST fields from the previous month and the weekly mean SST fields from the first week of the current month are available from NOAA's Environment Modeling Center Reynolds et al. Then, the observed SST anomalies are used to derive interannual Tinter fields using the empirical t model.

The derived Tinter fields are taken to force the ocean model to produce an initial ocean state for the first day of each month, from which predictions are made. Additionally, as part of the initialization procedure, the observed SST anomalies are directly inserted into the ICM when making predictions. Additionally, even without data assimilation, the forecasts using the ICM show a fairly high level of skill Fig. This is attributed to the fact that stochastic atmospheric wind forcing is not included in the ICM Zhang et al.

In a more realistic global coupled climate model, however, the forecast skill of Nino 3. In the future, we plan to assess the impact of the 4D-Var data. Furthermore, the 4D-Var method can also be used to optimize the model parameters, as demonstrated by the ensemble Kalman filter Wu et al. In addition, the oceanic subsurface state has a considerable effect on SST in the tropical Pacific; thus, in addition to assimilating the observed SST field, observed subsurface thermal fields need to be assimilated into the ICM.

In addition to the assimilation of oceanic fields, that of atmospheric data can also be considered. Note that during the 4D-Var assimilation process the forward and backward time integrations of the model and its adjoint model , t anomalies are internally determined using its anomaly model from the corresponding SST anomalies. Thus, the ICM with the 4D-Var has already taken into account the coupling between the ocean and atmosphere. So, the observed t anomaly field can be introduced into the 4D-Var assimilation processes in a fairly straightforward way that is, the coupled data assimilation.

### Objectives

Taking all these together, it can ultimately be expected that real-time ENSO forecasting using the ICM can be improved through optimal initialization and parameter optimization using the 4D-Var data assimilation method. The authors wish to thank the two anonymous reviewers for their comments, which helped to improve the original manuscript. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.

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Balmaseda, M. Anderson, and M. Davey, ENSO prediction using a dynamical ocean model coupled to statistical atmospheres. Tellus A, 46 4 , Barnett, T. Graham, S. Pazan, W. White, M. Latif, and M. Part I: Prediction of equatorial Pacific sea surface temperature with. Bjerknes, J. Cane, M. Zebiak, and S. Dolan, Experimental forecasts of El Nino. Nature, , Chen, D. Zebiak , A. Busalacchi, and Cane, M. Science, , Derber, J. Rosati, A global oceanic data assimilation system. Dommenget, D. Climate, 17 22 , Evensen, G. Galanti, E. Tziperman, M. Harrison, A.

Rosati, and Z. Sirkes, A study of ENSO prediction using a hybrid coupled model and the adjoint method for data assimilation. Rev, 11 , Han, G. Li, Z. He, K. Liu, and J. Wu, S. Zhang, Z. Liu, I. Navon, and W.

## Ebook Four Dimensional Model Assimilation Of Data A Strategy For The Earth System Sciences

Advances in Meteorology, , doi: Houtekamer, P. Mitchell, Data assimilation using an ensemble Kalman filter technique. Kalnay, E. Cambridge University Press, pp. Keenlyside, N. Kleeman, Annual cycle of equatorial zonal currents in the Pacific. Latif, M. Botzet, J. Jungclaus, and U. Schulzweida, A coupled method for initializing El Nino Southern Oscillation forecasts using sea surface temperature. Tellus A, 57 3 , Kirtman, B. Zebiak, ENSO simulation and prediction with a hybrid coupled model. Kleeman, R. Moore, and N. Smith, Assimilation of subsurface thermal data into a simple ocean model for the initialization of an intermediate tropical coupled ocean-atmosphere forecast model.

Klinker, E. Rabier, G. Kelly, and J. III: experimental results and diagnostics with operational configuration. Kumar, A. Wang, Y. Xue, and W. Wang, How much of monthly subsurface temperature variability in the equatorial Pacific can be recovered by the specification of sea surface temperatures?. Climate, 27, Liu, D. Mathematical Programming, 45, For information on how to request permission to translate our work and for any other rights related query please click here. For questions about using the Copyright. Finding similar items Read Online. View Cover.

Login or Register. E-mail this page Embed book widget. What is an eBook? Why is an eBook better than a PDF? Where do I get eBook files? Overview Contents Rights Stats. There is an immediate need to assimilate all available atmospheric and oceanic data with a state-of-the-art assimilation model, so as to produce a best-to-date interpretation of the available data record, particularly for study of climate and global change. Such analysis of long records from the past will require the marshaling of financial and manpower resources at the national and even international levels.

The immediate goals of this report are to review the current status of data assimilation and the application of model-assimilated data sets for both operational prediction and scientific research. The panel's recommendations are aimed at ensuring the availability of assimilated data sets for broad national needs in the coming decades.

As a starting point for action, the report emphasizes the need for an integrated national effort for the generation, archiving, and service-oriented publication of model-assimilated data sets that will serve a broad range of operational and research programs in atmospheric, oceanographic, and earth sciences. To ensure that the needs of the coming decades are met, the panel includes in this report a recommendation that an integrated national program be developed to provide the focus for and implementation of the full range of effort needed to meet these needs.

This volume explores and evaluates the development, multiple applications, and usefulness of four-dimensional space and time model assimilations of data in the atmospheric and oceanographic sciences and projects their applicability to the earth sciences as a whole. Using the predictive power of geophysical laws incorporated in the general circulation model to produce a background field for comparison with incoming raw observations, the model assimilation process synthesizes diverse, temporarily inconsistent, and spatially incomplete observations from worldwide land, sea, and space data acquisition systems into a coherent representation of an evolving earth system.

The book concludes that this subdiscipline is fundamental to the geophysical sciences and presents a basic strategy to extend the application of this subdiscipline to the earth sciences as a whole. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website. Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

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## Inferring causation from time series in Earth system sciences

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