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A profile from the Argo ocean observation array is a sequence of three‐dimensional vectors composed of pressure, salinity, and temperature, appearing as a continuous curve in three‐dimensional space. The shape of this curve is faithfully represented by a path signature, which is a collection of all the iterated integrals. Moreover, the product of two terms of the signature of a path can be expressed as the sum of higher‐order terms. As a result of this algebraic property, a nonlinear function of the profile shape can always be represented by a weighted linear combination of the iterated integrals, which enables machine learning of a complicated function of the profile shape. In this study, we performed supervised learning for existing Argo data with quality control flags by using the signature method and demonstrated the estimation performance by cross validation. Unlike rule‐based approaches, which require several complicated and possibly subjective rules, this method is simple and objective in nature because it relies only on past knowledge regarding the shape of profiles. This technique is critical for realizing automatic quality control for Argo profile data. Key Points We transformed each vertical sequence of Argo observation into the signature Then, it becomes easy to express the nonlinear function of the profile shape We took advantage of this mathematical property for assigning quality control flags

Energy dissipation rates are an important characteristic of turbulence; however, their magnitude in observational profiles can be incorrectly determined owing to their irregular appearance during vertical evolution. By analysing the data obtained from oceanic turbulence measurements, we demonstrate that the vertical sequences of energy dissipation rates exhibit a scaling property. Utilising this property, we propose a method to estimate the population mean for a profile. For scaling in the observed profiles, we demonstrate that our data exhibit a statistical property consistent with that exhibited by the universal multifractal model. Meanwhile, the population mean and its uncertainty can be estimated by inverting the probability distribution obtained by Monte Carlo simulations of a cascade model; to this end, observational constraints from several moments are imposed over each vertical sequence. This approach enables us to determine, to some extent, whether a profile shows an occasionally large mean or whether the population mean itself is large. Thus, it will contribute to the refinement of the regional estimation of the ocean energy budget, where only a small amount of turbulence observation data is available.

An observation operator in data assimilation was formalized based on the signatures extracted from the integral quantities contained within observed vertical profiles in the ocean. A four-dimensional variational global ocean data assimilation system, founded on this observation operator, was developed and utilized to conduct preliminary data assimilation experiments over a ten-year assimilation window, comparing the proposed method, namely profile-by-profile matching, with the traditional method, namely point-by-point matching. The proposed method not only demonstrated a point-by-point skill comparable to the traditional method but also provided superior analysis fields in terms of profile shapes on the temperature-salinity plane. This is an indication of a well-balanced analysis field, in contrast to the traditional method, which can produce extremely poor relative errors for certain metrics. Additionally, signatures were shown to successfully represent properties of the water column, such as steric height, and serve as an effective new diagnostic tool. The top-down, or macro–micro, viewpoint in this method is fundamental to the extent that it can offer an alternative view of how we comprehend ocean observations, holding significant implications for the advancement of data assimilation.

An optimization experiment was conducted to reproduce the climatological distribution of water properties with an ocean general circulation model in which interior vertical mixing below the surface mixed layer is represented by tidally induced near- and far-field vertical-mixing schemes. Globally constant parameters in the tidally induced mixing schemes along with other physical parameters are optimally estimated based on the Green’s function method. The optimized model performs reasonably well in reproducing the deep-water properties of the Pacific Ocean, suggesting that the combination of tidally induced vertical-mixing schemes is useful in providing a reliable simulation of the deep-ocean state, consistent with both observed broad-scale hydrographic characteristics and recent knowledge of mixing. Adjustment of the parameters in the near-field mixing scheme was effective in improving simulation of the deep-ocean state. These results suggest that the adjustment of a small number of globally constant parameters in tidally induced and other mixing schemes based on recent knowledge of mixing through data assimilation may enable improvements in ocean state estimation throughout the entire water column, including the deep ocean.

Decadal-scale climate variations over the Pacific Ocean and its surroundings are strongly related to the so-called Pacific decadal oscillation (PDO) which is coherent with wintertime climate over North America and Asian monsoon, and have important impacts on marine ecosystems and fisheries. In a near-term climate prediction covering the period up to 2030, we require knowledge of the future state of internal variations in the climate system such as the PDO as well as the global warming signal. We perform sets of ensemble hindcast and forecast experiments using a coupled atmosphere-ocean climate model to examine the predictability of internal variations on decadal timescales, in addition to the response to external forcing due to changes in concentrations of greenhouse gases and aerosols, volcanic activity, and solar cycle variations. Our results highlight that an initialization of the upper-ocean state using historical observations is effective for successful hindcasts of the PDO and has a great impact on future predictions. Ensemble hindcasts for the 20th century demonstrate a predictive skill in the upper-ocean temperature over almost a decade, particularly around the Kuroshio-Oyashio extension (KOE) and subtropical oceanic frontal regions where the PDO signals are observed strongest. A negative tendency of the predicted PDO phase in the coming decade will enhance the rising trend in surface air-temperature (SAT) over east Asia and over the KOE region, and suppress it along the west coasts of North and South America and over the equatorial Pacific. This suppression will contribute to a slowing down of the global-mean SAT rise.

Recent observational surveys have shown significant oceanic bottom-water warming. However, the mechanisms causing such warming remain poorly understood, and their time scales are uncertain. Here, we report computer simulations that reveal a fast teleconnection between changes in the surface air-sea heat flux off the Adélie Coast of Antarctica and the bottom-water warming in the North Pacific. In contrast to conventional estimates of a multicentennial time scale, this link is established over only four decades through the action of internal waves. Changes in the heat content of the deep ocean are thus far more sensitive to the air-sea thermal interchanges than previously considered. Our findings require a reassessment of the role of the Southern Ocean in determining the impact of atmospheric warming on deep oceanic waters.

We investigated the impact of assimilating a mapped dataset of subsurface ocean currents into an ocean state estimation. We carried out two global ocean state estimations from 2000 to 2007 using the K7 four-dimensional variational data synthesis system, one of which included an additional map of climatological geostrophic currents estimated from the global set of Argo floats. We assessed the representativeness of the volume transport in the two exercises. The assimilation of Argo ocean current data at only one level, 1000 dbar depth, had subtle impacts on the estimated volume transports, which were strongest in the subtropical North Pacific. The corrections at 10°N, where the impact was most notable, arose through the nearly complete offset of wind stress curl by the data synthesis system in conjunction with the first mode baroclinic Rossby wave adjustment. Our results imply that subsurface current data can be effective for improving the estimation of global oceanic circulation by a data synthesis.

By using a four‐dimensional variational data assimilation system capable of estimating physical and biogeochemical variables for the global ocean, we investigated multidecadal changes in the dissolved inorganic carbon (DIC) in the ocean. The system was newly constructed with a pelagic ecosystem model and an oceanic general circulation model to integrate available ocean observations obtained with a wide range of observation tools. The distribution of estimated DIC was by and large consistent with previous reports. We validated the changes in DIC along the World Ocean Circulation Experiment (WOCE) Hydrographic Program sections. The correlation coefficients of the modeled versus observed decadal difference patterns of DIC ranged from 0.25 to 0.51 in the Pacific Ocean, from 0.36 to 0.62 in the Atlantic Ocean, and from 0.23 to 0.57 in the Indian Ocean, and were significant at the 95% confidence level. Thus, at basin scale, the reproducibility of long‐term climate change was similar. Estimation of vertical DIC fluxes in each basin showed that the fluxes changed on a multidecadal time scale in our system. These changes were possibly due to changes in the dynamical state of CO2 absorption and to changes in ocean circulation. Our integrated data set on the basis of a dynamically self‐consistent ocean state is a promising tool for examining long‐term changes in the ocean carbon cycle. Key Points: The multidecadal ocean state, including DIC distribution, was estimated Parameters for biological variables were optimized by Green's function approach Multidecadal change in the dissolved inorganic carbon was identified

We carry out the first attempt to apply an adjoint method to a coupled general circulation model (CGCM) toward enhancing a skill in seasonal climate modeling. Focusing on 10‐day mean errors of a CGCM output, we optimize the oceanic initial conditions together with the bulk adjustment factors by employing a four‐dimensional variational data assimilation approach. We perform 9‐month‐long assimilation experiments independently every 6 months between January 1990 and March 2000. When using the optimized values for the initial conditions and the adjustment factors, a set of 9‐month‐long, 10‐member ensemble simulation always displays realistic seasonal cycle and its interannual modulations over the tropical Indian Ocean (e.g., growing, mature, and decaying phases of the Indian Ocean Dipole Mode events). The optimized values of the bulk adjustment factors primarily reduce the model biases in climatological fields, while the optimization of the oceanic initial conditions largely contributes to a realistic representation of the interannual modulations of seasonal cycle. In the overlapped seasons (i.e., January–March and July–September), the ensemble mean states derived from two experiments show only slight differences in seasonal climate variations over most of the Indian Ocean. These results validate that our assimilation approach is generally effective for advancing a seasonal climate modeling and for obtaining a realistic analysis that is compatible between atmosphere and ocean.

We analyze the results of 4‐dimensional variational data assimilation experiments using a coupled general circulation model and identify signals from a possible extratropical oceanic feedback relating to the North Atlantic Sea Surface Temperature (SST) tripole. Examination of the optimized control variables (coupling parameters) and the resultant climate fields reveals that the model errors in the North Atlantic climate variations are very sensitive to the intensity of the extratropical air‐sea thermal coupling. This results in the enhancement of the atmospheric responses to SST changes particularly around 40°N, 50°W, when the model errors are most effectively corrected. Since an adjoint approach enables us to detect the sensitivity to fluctuations in the model variables, our results suggest that this oceanic thermal feedback in the extratropics is a key physical process influencing the North Atlantic Oscillation and the associated North Atlantic SST tripole.