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GHOSH v1.0.0: a novel Gauss-Hermite High-Order Sampling Hybrid filter for computationally efficient data assimilation in geosciencesSpada, S., Teruzzi, A., Maset, S., Salon, S., Solidoro, C., and Cossarini, G. 2023. Geoscientific Model Development Discussions, 1–43,,
Abstract: Data assimilation is used in a number of geophysical applications to optimally integrate observations and model knowledge. Providing an estimation of both state and uncertainty, ensemble algorithms are one of the most successful data assimilation approaches. Since the estimation quality depends on the ensemble, the sampling method is a crucial step in ensemble data assimilation. Among other options to improve the capability of generating an effective ensemble, a sampling method featuring a higher polynomial order of approximation represents a novelty. Indeed, the order of the most widespread ensemble algorithms is usually equal to or lower than 2. We propose a novel hybrid ensemble algorithm, the Gauss-Hermite High-Order Sampling Hybrid (GHOSH) filter, version 1.0.0, which we apply in a twin experiment (based on Lorenz96) and in a realistic geophysical application. In the most error components, the GHOSH sampling method can achieve a higher order of approximation than in other ensemble based filters. To evaluate the benefits of the higher approximation order, a set of thousands twin experiments of Lorenz96 simulations has been carried out using the GHOSH filter and a second order ensemble Kalman filter (SEIK; singular evolutive interpolated Kalman filter). The comparison between the GHOSH and the SEIK filter has been done by varying a number of data assimilation settings: ensemble size, inflation, assimilated observations, and initial conditions. The twin-experiment results show that GHOSH outperforms SEIK in most of the assimilation settings up to a 69 % reduction of the root mean square error on assimilated and non-assimilated variables. A parallel implementation of the GHOSH filter has been coupled with a realistic geophysical application: a physical-biogeochemical model of the Mediterranean Sea with assimilation of surface satellite chlorophyll. The simulation results are validated using both semi-independent (satellite chlorophyll) and independent (nutrient concentrations from an in-situ climatology) observations. Results show the feasibility of GHOSH implementation in a realistic three-dimensional application. The GHOSH assimilation algorithm improves the agreement between forecasts and observations without producing unrealistic effects on the non-assimilated variables. Furthermore, the sensitivity analysis on GHOSH setup indicates that the use of a higher order of convergence substantially improves the performance of the assimilation with respect to nitrate (i.e., one of the non-assimilated variables). In view of potential implementation of the GHOSH filter in operational applications, it should be noted that GHOSH and SEIK filters have not shown significant differences in terms of time to solution, since, as in all ensemble-like Kalman filters, the model integration is by far more computationally expensive than the assimilation scheme.

Marine ecosystem models of realistic complexity rarely exhibits significant endogenous non-stationary dynamics, Occhipinti, G., Solidoro, C., Grimaudo, R., Valenti, D., & Lazzari, P. (2023). Chaos, Solitons & Fractals175, 113961.

Abstract: Despite the observation of cyclic and chaotic dynamics in nature, it is still not clear whether this behaviour is inherent to ecological systems or caused by external forcings. Here we explored a set of approximately 210,000 simulations to assess how often a model of realistic complexity exhibits non-stationary dynamics when external perturbations are excluded. Remarkably, less than one third of the population shown non-stationary dynamics and, even when present, fluctuations were rather small. The inherent stability of plankton communities showed to be related to the presence of multiple feedbacks in the food web structure, omnivory, low centre of gravity, and supports the conclusion that food webs of realistic complexity rarely exhibit significant endogenous non-stationary dynamics. Finally, we computed Lyapunov exponents for the non-stationary trajectories, in order to assess in which proportion they were periodic or chaotic, and we concluded that less than 10% of the non-stationary trajectories (3% of the total) showed sensitivities to initial conditions. This further supports the conclusion that complex topology mainly damps endogenous fluctuations in the food web.

Chromophoric dissolved organic matter dynamics revealed through the optimization of an optical-biogeochemical model in the NW Mediterranean Sea, Álvarez, Eva et al, 2023. Biogeosciences, 15. DOI 10.5194/bg-2023-48

Abstract. Chromophoric dissolved organic matter (CDOM) significantly contributes to the non-water absorption budget in the Mediterranean Sea. The absorption coefficient of CDOM, αCDOM(λ), is measurable in situ and remotely from different platforms and can be used as an indicator of the concentration of other relevant biogeochemical variables, e.g., dissolved organic carbon. However, our ability to model the biogeochemical processes that determine CDOM concentrations is still limited. Here we propose a novel parametrisation of the CDOM cycle that accounts for the interplay between the light- and nutrient-dependent dynamics of local CDOM production and degradation, as well as its vertical transport. The parameterization is included in a one-dimensional (1D) configuration of the Biogeochemical Flux Model (BFM), which is here coupled to the General Ocean Turbulence Model (GOTM) through the Framework for Aquatic Biogeochemical Models (FABM). Here BFM is augmented with a bio-optical component that revolves spectrally the underwater light transmission. We did run this new GOTM-FABM-BFM configuration to simulate the seasonal αCDOM(λ) cycle at the deep-water site of the BOUSSOLE project in the North-Western Mediterranean Sea. Our results show that accounting for both nutrient and light dependence of CDOM production improves the simulation of the seasonal and vertical dynamics of αCDOM(λ), including a subsurface maximum that forms in spring and progressively intensifies in summer. Furthermore, the model consistently reproduces the higher-than-average concentrations of CDOM per unit chlorophyll concentration observed at BOUSSOLE. The configuration, outputs and sensitivity analyses from this 1D model application will be instrumental for future applications of BFM to the entire Mediterranean Sea in a 3D configuration.

Biogeochemical Modelling, Bertino, L., Brasseur, P., Ciavatta, S., Cossarini, G., Fennel, K., Ford, D., Grégoire, M., Lavoie, D., and Lehodey, P. In Implementing Operational Ocean Monitoring and Forecasting Systems Chapter 9, (pp. 249 – 306). ETOOFS. E. Alvarez Fanjul, S. Ciliberti & P. Bahurel (Eds.), 2022. DOI:​ 

The guide aims to promote the development of new marine forecasting systems around the globe; along with the improvement of the existing ones. Indeed, it provides an overview of the value chain of an operational ocean forecasting system (OOFS) as well as international standards and best practices for setting up such a service.

A solution for autonomous, adaptive monitoring of coastal ocean ecosystems: Integrating ocean robots and operational forecasts. 2022. Front. Mar. Sci., Sec. Ocean Observation. Ford D, Grossberg S, Rinaldi G, Menon P, Palmer M, Skakala J,  Smyth T, Wiliams C, Lorenzon Lopez A and Ciavatta S.

Abstract: This study presents a proof-of-concept for a fully automated and adaptive observing system for coastal ocean ecosystems. Such systems present a viable future observational framework for oceanography, reducing the cost and carbon footprint of marine research. An autonomous ocean robot (an ocean glider) was deployed for 11 weeks in the western English Channel and navigated by exchanging information with operational forecasting models. It aimed to track the onset and development of the spring phytoplankton bloom in 2021. A stochastic prediction model combined the real-time glider data with forecasts from an operational numerical model, which in turn assimilated the glider observations and other environmental data, to create high-resolution probabilistic predictions of phytoplankton and its chlorophyll signature. A series of waypoints were calculated at regular time intervals, to navigate the glider to where the phytoplankton bloom was most likely to be found. The glider successfully tracked the spring bloom at unprecedented temporal resolution, and the adaptive sampling strategy was shown to be feasible in an operational context. Assimilating the real-time glider data clearly improved operational biogeochemical forecasts when validated against independent observations at a nearby time series station, with a smaller impact at a more distant neighboring station. Remaining issues to be addressed were identified, for instance relating to quality control of near-real time data, accounting for differences between remote sensing and in situ observations, and extension to larger geographic domains. Based on these, recommendations are made for the development of future smart observing systems.

Biogeochemical Model Optimization by Using Satellite-Derived Phytoplankton Functional Type Data and BGC-Argo Observations in the Northern South China Sea. 2022. Remote Sens. 14, 1297. Shu C, Xiu P, Xing X, Qiu G, Ma W, Brewin R and Ciavatta S.
Abstract: Marine biogeochemical models have been widely used to understand ecosystem dynamics and biogeochemical cycles. To resolve more processes, models typically increase in complexity, and require optimization of more parameters. Data assimilation is an essential tool for parameter optimization, which can reduce model uncertainty and improve model predictability. At present, model parameters are often adjusted using sporadic in-situ measurements or satellite-derived total chlorophyll-a concentration at sea surface. However, new ocean datasets and satellite products have become available, providing a unique opportunity to further constrain ecosystem models. Biogeochemical-Argo (BGC-Argo) floats are able to observe the ocean interior continuously and satellite phytoplankton functional type (PFT) data has the potential to optimize biogeochemical models with multiple phytoplankton species. In this study, we assess the value of assimilating BGC-Argo measurements and satellite-derived PFT data in a biogeochemical model in the northern South China Sea (SCS) by using a genetic algorithm. The assimilation of the satellite-derived PFT data was found to improve not only the modeled total chlorophyll-a concentration, but also the individual phytoplankton groups at surface. The improvement of simulated surface diatom provided a better representation of subsurface particulate organic carbon (POC). However, using satellite data alone did not improve vertical distributions of chlorophyll-a and POC. Instead, these distributions were improved by combining the satellite data with BGC-Argo data. As the dominant variability of phytoplankton in the northern SCS is at the seasonal timescale, we find that utilizing monthly averaged BGC-Argo profiles provides an optimal fit between model outputs and measurements in the region, better than using high-frequency measurements. 

The impact of ocean biogeochemistry on physics and its consequences for modelling shelf seas.  Ocean Modelling Volume 172, April 2022, 101976. Skalala J et al. Doi: 10.1016/j.ocemod.2022.101976

Abstract: We use modelling and assimilation tools to explore the impact of biogeochemistry on physics in the shelf sea environment, using North-West European Shelf (NWES) as a case study. We demonstrate that such impact is significant: the attenuation of light by biogeochemical substances heats up the upper 20 m of the ocean by up to 1 °C and by a similar margin cools down the ocean within the 20–200 m range of depths. We demonstrate that these changes to sea temperature influence mixing in the upper ocean and feed back into marine biology by influencing the timing of the phytoplankton bloom, as suggested by the critical turbulence hypothesis. We compare different light schemes representing the impact of biogeochemistry on physics, and show that the physics is sensitive to both the spectral resolution of radiances and the represented optically active constituents. We introduce a new development into the research version of the operational model for the NWES, in which we calculate the heat fluxes based on the spectrally resolved attenuation by the simulated biogeochemical tracers, establishing a two-way coupling between biogeochemistry and physics. We demonstrate that in the late spring–summer the two-way coupled model increases heating in the upper oceanic layer compared to the existing model and improves by 1–3 days the timing of the simulated phytoplankton bloom. This improvement is relatively small compared with the existing model bias in bloom timing, but is sufficient to have a visible impact on model skill in the free run. We also validate the skill of the two-way coupling in the context of the weakly coupled physical–biogeochemical assimilation currently used for operational forecasting of the NWES. We show that the change to the skill is negligible for analyses, but it remains to be seen how much it differs for the forecasts.

Reanalysis in Earth System Science: Toward Terrestrial Ecosystem Reanalysis.  July 2021.  Reviews of Geophysics. Baatz R et al 
 Abstract: A reanalysis is a physically consistent set of optimally merged simulated model states and historical observational data, using data assimilation. High computational costs for modeled processes and assimilation algorithms has led to Earth system specific reanalysis products for the atmosphere, the ocean and the land separately. Recent developments include the advanced uncertainty quantification and the generation of biogeochemical reanalysis for land and ocean. Here, we review atmospheric and oceanic reanalyzes, and more in detail biogeochemical ocean and terrestrial reanalyzes. In particular, we identify land surface, hydrologic and carbon cycle reanalyzes which are nowadays produced in targeted projects for very specific purposes. Although a future joint reanalysis of land surface, hydrologic, and carbon processes represents an analysis of important ecosystem variables, biotic ecosystem variables are assimilated only to a very limited extent. Continuous data sets of ecosystem variables are needed to explore biotic-abiotic interactions and the response of ecosystems to global change. Based on the review of existing achievements, we identify five major steps required to develop terrestrial ecosystem reanalysis to deliver continuous data streams on ecosystem dynamics.

Towards a Multi-Platform Assimilative System for North Sea Biogeochemistry. 2021. JGR Oceans. Skakala J et al. 
Abstract: Oceanography has entered an era of new observing platforms, such as biogeochemical-Argo floats and gliders, some of which will provide three-dimensional maps of essential ecosystem variables on the North-West European (NWE) Shelf. In a foreseeable future operational centers will use multi-platform assimilation to integrate those valuable data into ecosystem reanalysis and forecast systems. Here we address some important questions related to glider biogeochemical data assimilation (DA) and introduce multi-platform DA in a preoperational model of the NWE Shelf sea ecosystem. We test the impact of the different multi-platform system components (glider vs. satellite, physical vs. biogeochemical) on the simulated biogeochemical variables. To characterize the model performance, we focus on the period around the phytoplankton spring bloom, since the bloom is a major ecosystem driver on the NWE Shelf. We found that the timing and magnitude of the phytoplankton bloom is insensitive to the physical DA, which is explained in the study. To correct the simulated phytoplankton bloom one needs to assimilate chlorophyll observations from glider or satellite Ocean Color (OC) into the model. Although outperformed by the glider chlorophyll assimilation, we show that OC assimilation has mostly desirable impact on the sub-surface chlorophyll. Since the OC assimilation updates chlorophyll only in the mixed layer, the impact on the sub-surface chlorophyll is the result of the model dynamical response to the assimilation. We demonstrate that the multi-platform assimilation combines the advantages of its components and always performs comparably to its best performing component.