Using machine learning techniques to generate analog ensembles for data assimilation

<p>We propose to use analogs of the forecast mean to generate an ensemble of perturbations for use in ensemble optimal interpolation (EnOI) or ensemble variational (EnVar) methods.  In addition to finding analogs from a library, we propose a new method of constructing analogs using autoencoders (a machine learning method).  To extend the scalability of constructed analogs for use in data assimilation on geophysical models, we propose using patching schemes to divide the global spatial domain into digestable chunks.  Using patches makes training the generative models possible and has the added benefit of being able to exploit parallel computing powers.  The resulting analog methods using analogs from a catalog (AnEnOI), constructed analogs (cAnEnOI), and patched constructed analogs (p-cAnEnOI) are tested in the context of a multiscale Lorenz-`96 model, with standard EnOI and an ensemble square root filter for comparison.  The use of analogs from a modestly-sized catalog is shown to improve the performance of EnOI, with limited marginal improvements resulting from increases in the catalog size.  The method using constructed analogs is found to perform as well as a full ensemble square root filter, and to be robust over a wide range of tuning parameters.  Lastly, we find that p-cAnENOI with larger patches produces the best data assimilation performance despite having larger reconstruction errors.  All patch variants except for the variant that uses the smallest patch size outperform cAnEnOI as well as some traditional data assimilation methods such as the ensemble square root filter.</p>

Model-driven optimization of coastal sea observatories through data assimilation in a finite element hydrodynamic model (SHYFEM v. 7_5_65)

Monitoring networks aims at capturing the spatial and temporal variability of one or several environmental variables in a specific environment. The optimal placement of sensors in an ocean or coastal observatory should maximize the amount of collected information and minimize the development and operational costs for the whole monitoring network. In this study, the problem of the design and optimization of ocean monitoring networks is tackled throughout the implementation of data assimilation techniques in the Shallow water HYdrodynamic Finite Element Model (SHYFEM). Two data assimilation methods – nudging and ensemble square root filter – have been applied and tested in the Lagoon of Venice (Italy), where an extensive water level monitoring network exists. A total of 29 tide gauge stations were available, and the assimilation of the observations results in an improvement of the performance of the SHYFEM model, which went from an initial root mean square error (RMSE) on the water level of 5.8 cm to a final value of about 2.1 and 3.2 cm for each of the two data assimilation methods. In the monitoring network optimization procedure, by excluding just one tide gauge at a time and always the station that contributes less to the improvement of the RMSE, a minimum number of tide gauges can be found that still allow for a successful description of the water level variability. Both data assimilation methods allow identifying the number of stations and their distribution that correctly represent the state variable in the investigated system. However, the more advanced ensemble square root filter has the benefit of keeping a physically and mass-conservative solution of the governing equations, which results in a better reproduction of the hydrodynamics over the whole system. In the case of the Lagoon of Venice, we found that, with the help of a process-based and observation-driven numerical model, two-thirds of the monitoring network can be dismissed. In this way, if some of the stations must be decommissioned due to a lack of funding, an a priori choice can be made, and the importance of a single monitoring site can be evaluated. The developed procedure may also be applied to the continuous monitoring of other ocean variables, like sea temperature and salinity.

Model-driven optimization of coastal sea observatories through data assimilation in a finite element hydrodynamic model (SHYFEM v.7_5_65)

Monitoring networks aims at capturing the spatial and temporal variability of one or several environmental variables in a specific environment. The optimal placement of sensors in an ocean or coastal observatory should maximize the amount of collected information and minimize the development and operational costs for the whole monitoring network. In this study, the problem of the design and optimization of ocean monitoring networks is tackled throughout the implementation of data assimilation techniques in the Shallow water Hydrodynamic Finite Element Model (SHYFEM). Two data assimilation methods – Nudging and Ensemble Square Root Filter – have been applied and tested in the Lagoon of Venice (Italy), where an extensive water level monitoring network exists. A total of 29 tide gauge stations were available and the assimilation of the observations result in an improvement of the performance of the SHYFEM model that went from an initial root mean square error (RMSE) on the water level of 5.8 cm to a final value of about 2.1 and 3.2 cm for the two data assimilation methods, respectively. In the monitoring network optimization procedure, by excluding just one tide gauge at a time, and always the station that contributes less to the improvement of the RMSE, a minimum number of tide gauges can be found that still allow for a successful description of the water level variability. Both data assimilation methods allow identifying the number of stations and their distribution that correctly represent the state variable in the investigated system. However, the more advanced Ensemble Square Root Filter has the benefit of keeping a physically and mass conservative solution of the governing equations, which results in a better reproduction of the hydrodynamics over the whole system. In the case of the Lagoon of Venice, we found that, with the help of a process-based and observation-driven numerical model, two-thirds of the monitoring network can be dismissed. In this way, if some of the stations must be decommissioned due to a lack of funding, an a-priori choice can be made, and the importance of the single monitoring site can be evaluated. The developed procedure may also be applied to the continuous monitoring of other ocean variables, like sea temperature and salinity.

An Ensemble Square Root Filter for the joint assimilation of surface soil moiture and leaf area index within LDAS-Monde: application over the Euro-Mediterranean region

This paper introduces an Ensemble Square Root Filter (EnSRF), a deterministic Ensemble Kalman Filter, to the context of assimilating jointly observations of surface soil moisture (SSM) and leaf area index (LAI) in the Land Data Assimilation System LDAS-Monde. By ingesting those satellite-derived products, LDAS-Monde constrains the Interaction between Soil, Biosphere and Atmosphere (ISBA) land surface model (LSM), coupled with the CNRM (Centre National de Recherches Météorologiques) version of the Total Runoff Integrating Pathways (CTRIP), to improve the reanalysis of land surface variables (LSVs). To evaluate its ability to produce improved LSVs reanalyses, the EnSRF is compared with the Simplified Extended Kalman, which has been routinely operated in LDAS-Monde, in a real case over the well-studied Euro-Mediterranean region at a 0.25° spatial resolution between 2008 and 2017. Both data assimilation approaches provide a positive impact on SSM and LAI estimates with respect to the model alone, putting them closer to assimilated observations. SEKF and EnSRF have a similar behaviour for LAI showing performances that are influenced by the vegetation type. For SSM, EnSRF estimates tend to be closer to observations than SEKF. The impact of assimilating SSM and LAI is also assessed on unobserved soil moisture in the other layers of soil. Unobserved control variables are updated in the EnSRF through covariances and correlations sampled from the ensemble linking them to observed control variables. In our context, a strong correlation between SSM and soil moisture in deeper soil layers is exhibited, as expected, showing seasonal patterns that vary geographically. Moderate correlation and anti-correlations are also noticed between LAI and soil moisture in spring, summer and autumn, their absolute value tending to be larger for soil moisture in root-zone areas, showing that assimilating LAI can have an influence on soil moisture. Finally an independent evaluation of both assimilation approaches is conducted using satellite estimates of evapotranspiration and gross primary production (GPP) as well as measures of river discharges from gauging stations. The EnSRF shows a systematic albeit moderate improvement for evapotranspiration and GPP and a highly positive impact on river discharges, while the SEKF exhibits a more contrasting performance.