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years of use increased beyond the target   available, such as ice thickness and concen-                          data assimilation methods extract the best   the initial condition. The smaller the initial
               value of 0.01 psu, reaching more than 0.05   tration, carbon dioxide concentration and                           information from these sources and com-  condition error, the greater the probabili-
               psu (K. Sato, 8th OceanPredict OS-Eval-TT   pH. In ecosystem models, in addition to all                          bine them to produce the valuable objec-  ty of producing accurate predictions (e.g.,
               Meeting, April 28, 2021). This fact moved   these quantities, nutrients, chlorophyll, and                        tive analyses, which are employed both for   DERBER and ROSATI, 1989; KALNAY, 2003;
               the scientific community to remove data   a myriad of parameters of the trophic chain                            scientific studies and for the practice of op-  EVENSEN, 2006; DAVIDSON , 2019).
               bias and identify the impacts of these data   must be considered. The models therefore                           erational ocean forecasting.             Observing the right scales for
               on the scientific results derived from them.   offer a spatio-temporal representation of                         Data assimilation                        assimilation
               In addition to the instrumentation error,   oceanic processes, the biogeochemical cy-
               there is also the sampling error, associated   cle and ecosystems that serve or can serve                           In order to extract the maximum infor-   The ability of assimilation to constrain
               with the fact that it is often not possible to   diverse applications, including the conser-                     mation from the observed data and reduce   or correct the numerical model solution in
               collect data with the frequency necessary   vation of the marine environment, and a                              the errors of numerical models, data assim-  the direction of observations is limited by
               to characterize the variability of the natural   wide range of users of oceanographic in-                        ilation methods are used. They improve the   the  quality  and quantity of  observations.
               phenomenon. Some frequencies of variabili-  formation, specialists or not. However, the                          representation of circulation and the physi-  In relatively low-resolution global models,
               ty obtained from the observed data are erro-  models also have limitations.                                      cal state of the system of interest produced   with grid spacing of 20 km or greater, the
               neous projections of the natural frequency.   In order to obtain a solution, nonlinear                           by numerical models by correcting the mod-  global SST and SSH fields available today
               Therefore, great care must always be taken   numerical models undergo a series of ap-                            el fields in the direction of observations and   with  resolutions,  respectively,  of  approxi-
               when using observed data to study process-  proximations and have systematic or ran-                             extrapolating observational information into   mately 5 km and 25 km, together with the
               es, as both instrumentation and representa-  dom errors in all their quantities. The mod-                        model space (DALEY, 1991; KALNAY et al.,   T/S profiles obtained by the Argo profilers
               tiveness errors have to be considered.   el equations, after being approximated                                  1996; EVENSEN, 1996; EVENSEN,  2003).    and  other equipment,  offer  good quali-
                                                        with numerical methods and mathemat-                                    The assimilation methods optimally or sub   ty and quantity to effectively correct the
               Models
                                                        ical approximations, still face difficulties                            optimally combine in a mathematical sense,   models. However, when considering re-
                 Numerical models of the oceans, as well   with the spatial and temporal resolutions                            model fields with observed data and produce   gional or even global models with high res-
               as those of the atmosphere and the Earth   used to discretize the space-time, consid-                            new fields, objective analyses, with smaller   olution (2 km or smaller), the observational
               system, are fundamental tools for society   ering that the increase in resolution impos-                         errors than those of the models. They con-  systems available today are no longer ef-
               today.  They  reflect  much  of  the  scientific   es more computational costs, not only in                      sider observed data errors and model errors,   fective. This challenge requires the design
               knowledge gained to date in oceanogra-   processing but also in in the storage of the                            observed data and model fields that will be   and implementation of new high-resolu-
               phy and meteorology considering nonlin-  outputs. This prevents models from solving                              corrected. When model errors are large rela-  tion observational systems to meet a new
               ear equations that translate momentum,   processes with small spatial scale and/or                               tive to observations errors, the analysis relies   stage in the evolution of predictive systems
               mass,  and  energy  balances  (FOX-KEMPER   high frequency. Another source of model                              more on observations. When the opposite   for features with high frequency variability
               et al., 2019). Unlike observations, model   errors is the so-called physical parameter-                          happens, the analysis relies more on the of   at spatial scales of less than 2 km, in the
               fields are produced across the three-di-  izations, which are not universal, that is,                            the model fields.                        so-called submesoscale.
               mensional domain of interest, which can   they often do not work in the same way                                    Despite the diverse and relevant ap-  The international scientific community
               be global or regional. These fields include   in different regions and are built to provide                      plications, the use of analysis as an initial   involved in operational oceanography
               fluxes of heat, salt, and momentum, in   relationships between quantities in specific                            condition of the forecasting system was
               addition to the primitive quantities of sea   ranges of values. Finally, there are sources                       and still is the main motivation for the de-  Considering the need to develop op-
               surface height, velocity, temperature, sa-  of model errors associated with boundary                             velopment of data assimilation methods in   erational oceanography, in 1998 a major
               linity, and density or pressure, in the case   conditions, whether in bathymetry, in the                         meteorology  and  oceanography.  Like  the   international effort was initiated through
               of a purely ocean circulation model. If the   kinematic conditions of the boundaries,                            atmosphere, oceans, and climate and Earth   the Global Ocean Data Assimilation Ex-
               model includes sea ice and biogeochemical   or in atmospheric forcing. Considering the                           systems are chaotic, and part of the system   periment (GODAE) project (CHASSIGNET
               cycle quantities, other quantities are also   limitations  of  models  and  observations,                        predictability depends on the quality of   and VERRON, 2006; BELL  et al., 2009).



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