Data-Interpolating Variational Analysis Research Articles

Developing a New Oxygen Atlas of the World’s Oceans Using Data Interpolating Variational Analysis

Abstract We present a new global oxygen atlas. This atlas uses all of the available full water column profiles of oxygen, salinity, and temperature available as part of the World Ocean Database released in 2018. Instead of optimal interpolation, we use the Data Interpolating Variational Analysis (DIVA) approach to map the available profiles onto 108 depth levels between the surface and 6800 m, covering more than 99% of ocean volume. This 1/2° × 1/2° atlas covers the period 1955–2018 in 1-yr intervals. The DIVA method has significant benefits over traditional optimal interpolation. It allows the explicit inclusion of advection and boundary constraints, thus offering improvements in the representations of oxygen, salinity, and temperature in regions of strong flow and near coastal boundaries. We demonstrate these benefits of this mapping approach with some examples from this atlas. We can explore the regional and temporal variations of oxygen in the global oceans. Preliminary analyses confirm earlier analyses that the oxygen minimum zone in the eastern Pacific Ocean has expanded and intensified. Oxygen inventory changes between 1970 and 2010 are assessed and compared against prior studies. We find that the full ocean oxygen inventory decreased by 0.84% ± 0.42%. For this period, temperature-driven solubility changes explain about 21% of the oxygen decline over the full water column; in the upper 100 m, solubility changes can explain all of the oxygen decrease; for the 100–600 m depth range, it can explain only 29%, 19% between 600 and 1000 m, and just 11% in the deep ocean. Significance Statement The purpose of this study is to create a new oxygen atlas of the world’s oceans using a technique that better represents the effects of ocean currents and topographic boundaries, and to investigate how oxygen in the ocean has changed over recent decades. We find the total quantity of oxygen in the world’s oceans has decreased by 0.84% since 1970, similar to previous studies. We also examine how much of this change can be explained by changes in water temperature; we find that this can explain all the changes in the upper 100 m but only 21% of the oxygen decline over the whole water column.

Sea surface height anomaly and geostrophic current velocity from altimetry measurements over the Arctic Ocean (2011–2020)

Abstract. Satellite altimetry missions flying over the ice-covered Arctic Ocean have opened the possibility of further understanding changes in the ocean beneath the sea ice. This requires complex processing of satellite signals emerging from the sea surface in leads within the sea ice, with efforts to generate consistent Arctic-wide datasets of sea surface height ongoing. The aim of this paper is to provide and assess a novel gridded dataset of sea surface height anomaly and geostrophic velocity, which incorporates both the ice-covered and open ocean areas of the Arctic. Data from the CryoSat-2 mission in the period 2011–2020 were gridded at monthly intervals, up to 88∘ N, using the Data-Interpolating Variational Analysis (DIVA) method. To examine the robustness of our results, we compare our dataset to independent satellite data, mooring time series and Arctic-wide hydrographic observations. We find that our dataset is well correlated with independent satellite data at monthly timescales. Comparisons to in situ ocean observations show that our dataset provides reliable information on the variability of sea surface height and surface geostrophic currents over geographically diverse regions of the Arctic Ocean and different dynamical regimes and sea ice states. At all comparison sites we find agreement with in situ observed variability at seasonal to interannual timescales. Furthermore, we find that our geostrophic velocity fields can resolve the variability of boundary currents wider than about 50 km, a result relevant for studies of Arctic Ocean circulation. Additionally, large-scale seasonal features emerge. Sea surface height exhibits a wintertime Arctic-wide maximum, with the highest amplitude over the shelves. Also, we find a basin-wide seasonal acceleration of Arctic slope currents in winter. We suggest that this dataset can be used to study not only the large-scale sea surface height and circulation, but also the regionally confined boundary currents. The dataset is available in netCDF format from PANGAEA at https://doi.org/10.1594/PANGAEA.931869 (Doglioni et al., 2021d).

On spreading of Antarctic Bottom Water in fracture zones of the Mid-Atlantic Ridge at 7–8°N

A Data-Interpolating Variational Analysis in n-dimensions was used to describe a potential temperature distribution in the bottom layer of the fracture zones of the Mid-Atlantic Ridge at 7–8°N. This analysis was based on a new digital terrain model obtained by supplementing the STRM15+ bathymetry data with multibeam echo sounding data from the 33rd cruise of the research vessel
 Akademik Nikolaj Strakhov (2016) and oceanological data from the World Ocean Database, supplemented with CTD profiles and reversing thermometer data measured in scientific cruises of the Shirshov Institute of Oceanology, Russian Academy of Sciences in 2014–2016. A 2D model of near-bottom potential temperature distribution in the study area was calculated based on the analysis. The model allows us to propose the Antarctic Bottom Water propagation pattern through the Doldrums, Vernadsky, and Pushcharovsky fracture zones. It is shown that bottom water warms up when passing fracture zones from 1.4°C in Pushcharovsky Fracture Zone up to 1.6–1.7°C in Vernadsky Fracture Zone. Bottom water from Pushcharovsky and Vernadsky fractures propagates in two directions. Northernly, it propagates to the Doldrums Fracture Zone, where its temperature reaches about 1.9–2.0°C. Easterly, it flows along Pushcharovsky Fracture Zone and raising the temperature up to 1.8–2.0°C. We propose the absence of Antarctic Bottom Water's overflow with a temperature less than 1.8°C to the East Atlantic in the study area.

Generation and Assessment of ARGO Sea Surface Temperature Climatology for the Indian Ocean Region

ARGO program was conceived with an aim to generate near real-time ocean observations as the primary in-situ sources for use in operational oceanography studies. Two decades-long ARGO near-surface temperature data set was used for generating monthly gridded ARGO sea surface temperature (ASST) product on a climatological scale. Data interpolating variational analysis (DIVA) method was employed for generating the product with a spatial resolution of 0.25° x 0.25° for the Tropical Indian Ocean. This monthly ASST product was evaluated using five different climatological SST products derived from in-situ and satellite measurements. Various statistics such as BIAS, RMSE, coefficient of correlation, and skill scores were generated to evaluate the reliability of the ASST product. Further, the ASST product was validated with climatological in-situ SST obtained from RAMA and OMNI moorings deployed in the Indian Ocean. Statistical comparisons showed low BIAS and RMSE, and high correlation and skill scores with most of the buoys locations and the gridded SST products. Results concluded that the near-surface temperature data from ARGO can be used along with other SST data sets in the generation of high-resolution blended SST products.

DISTRIBUTION OF SALINITY AND TEMPERATURE IN MUSI ESTUARY: USING VERTICAL SALINITY GRADIENT FOR ESTUARY CLASSIFICATION ZONE

Musi estuary is the mouth of the Telang and Musi rivers directly adjacent to the Bangka Strait. During flood (ebb) we see the distribution of salinity increases (decreases) which is known through the vertical distribution using CTD. The TS diagram is used to see the water mass characteristics the study area. Data-Interpolating Variational Analysis (DIVA) method is used to interpolate and visualize data from vertical and spatial temperature, salinity and density data. The classification of the Musi estuary zone is identified based on the value of the distribution of salinity, which considers the exchange of circulating salinity at flood and ebb. The density of the water mass is significantly affected by the proven graded salinity. While the temperature distribution does not change significantly with depth, the spatial distribution indicates that the temperature in the estuary is lower than in the upstream and ocean areas. The spatial distribution of salinity indicates that high salinity enters the estuary towards the river further at flood than at ebb. Salinity distribution ranges from 0.5 to 30 psu and temperatures between 29 and 33 oC from horizontal and vertical sections. The pattern of salinity distribution in the Musi river estuary was identified, consisting of three zones representing salinity conditions in the study area, namely the Polyhaline, Mesohaline, and Olygohaline zones.

A global climatology of the ocean surface during the Last Glacial Maximum mapped on a regular grid (GLOMAP)

Abstract. We present a climatology of the near-sea-surface temperature (NSST) anomaly and the sea-ice extent during the Last Glacial Maximum (LGM, 23 000–19 000 years before present) mapped on a global regular 1∘×1∘ grid. It is an extension of the Glacial Atlantic Ocean Mapping (GLAMAP) reconstruction of the Atlantic NSST based on the faunal and floral assemblage data of the Multiproxy Approach for the Reconstruction of the Glacial Ocean Surface (MARGO) project and several recent estimates of the LGM sea-ice extent. Such a gridded climatology is highly useful for the visualization of the LGM climate, calculation of global and regional NSST averages, and estimation of the equilibrium climate sensitivity, as well as a boundary condition for atmospheric general circulation models. The gridding of the sparse NSST reconstruction was done in an optimal way using the Data-Interpolating Variational Analysis (DIVA) software, which takes into account the uncertainty in the reconstruction and includes the calculation of an error field. The resulting Glacial Ocean Map (GLOMAP) confirms the previous findings by the MARGO project regarding longitudinal and meridional NSST differences that were greater than today in all oceans. Taken at face value, the estimated global and tropical cooling would imply an equilibrium climate sensitivity at the lower end of the currently accepted range. However, because of anticipated changes in the seasonality and thermal structure of the upper ocean during the LGM as well as uneven spatial sampling, the estimated cooling and implied climate sensitivity are likely to be biased towards lower values.

Variational interpolation of high-frequency radar surface currents using DIVAnd

DIVAnd (Data-Interpolating Variational Analysis, in n-dimensions) is a tool to interpolate observations on a regular grid using the variational inverse method. We have extended DIVAnd to include additional dynamic constraints relevant to surface currents, including imposing a zero normal velocity at the coastline, imposing a low horizontal divergence of the surface currents, temporal coherence and simplified dynamics based on the Coriolis force, and the possibility of including a surface pressure gradient. The impact of these constraints is evaluated by cross-validation using the HF (high-frequency) radar surface current observations in the Ibiza Channel from the Balearic Islands Coastal Ocean Observing and Forecasting System (SOCIB). A small fraction of the radial current observations are set aside to validate the velocity reconstruction. The remaining radial currents from the two radar sites are combined to derive total surface currents using DIVAnd and then compared to the cross-validation dataset and to drifter observations. The benefit of the dynamic constraints is shown relative to a variational interpolation without these dynamical constraints. The best results were obtained using the Coriolis force and the surface pressure gradient as a constraint which are able to improve the reconstruction from the Open-boundary Modal Analysis, a quite commonly used method to interpolate HF radar observations, once multiple time instances are considered together.

A volumetric census of the Barents Sea in a changing climate

Abstract. The Barents Sea, located between the Norwegian Sea and the Arctic Ocean, is one of the main pathways of the Atlantic Meridional Overturning Circulation. Changes in the water mass transformations in the Barents Sea potentially affect the thermohaline circulation through the alteration of the dense water formation process. In order to investigate such changes, we present here a seasonal atlas of the Barents Sea including both temperature and salinity for the period 1965–2016. The atlas is built as a compilation of datasets from the World Ocean Database, the Polar Branch of the Russian Federal Research Institute of Fisheries and Oceanography and the Norwegian Polar Institute using the Data-Interpolating Variational Analysis (DIVA) tool. DIVA allows for a minimization of the expected error with respect to the true field. The atlas is used to provide a volumetric analysis of water mass characteristics and an estimation of the ocean heat and freshwater contents. The results show a recent “Atlantification” of the Barents Sea, that is a general increase in both temperature and salinity, while its density remains stable. The atlas is made freely accessible as user-friendly NetCDF files to encourage further research in the Barents Sea physics (https://doi.org/10.21335/NMDC-2058021735, Watelet et al., 2020).

Dissolved oxygen variability in the Mediterranean Sea

Abstract The interannual variability and the mechanisms controlling the dissolved oxygen concentration in the Mediterranean Sea were investigated through generating gridded fields of dissolved oxygen, salinity and potential temperature. The Data-Interpolating Variational Analysis (DIVA) software was used to produce a gridded dataset for the time period 1960–2011. High oxygen concentrations for the upper and bottom layers, separated by an oxygen minimum zone at intermediate layers, are a typical structure of the dissolved oxygen in the Eastern and the Western Mediterranean sub-basins. Although an oxygen minimum zone is observed in both sub-basins, its vertical positions are different; in the Eastern Mediterranean at between 600 and 1200 m depth and in the Western Mediterranean at between 400 and 600 m. The vertical distribution of dissolved oxygen shows significant differences between the two sub-basins and their temporal evolution reveals large interannual to decadal variability. A negative correlation was observed between dissolved oxygen and surface potential temperature due to solubility changes over the whole period. However, the positive correlation between the dissolved oxygen and potential temperature in the Eastern Mediterranean deep layers is an indication that the dynamical processes are dominant and are involved in the dissolved oxygen interannual variability. The dissolved oxygen variability presents shifts with a multi-decadal signal, rather than trends as observed in the global ocean, associated with mixing processes and decadal oscillations that influence the dense water formation or biological activity.

Observed spatiotemporal variation of three-dimensional structure and heat/salt transport of anticyclonic mesoscale eddy in Northwest Pacific

As in-situ observations are sparse, targeted observations of a specific mesoscale eddy are rare. Therefore, it is difficult to study the three-dimensional structure of moving mesoscale eddies. From April to September 2014, an anticyclonic eddy located at 135°E–155°E, 26°N–42°N was observed using 17 rapid-sampling Argo floats, and the spatiotemporal variations in the three-dimensional structure were studied. The results are as follows: (1) the eddy was identified and tracked using satellite altimeter data. It had a lifetime of 269 days and an average radius of 91.5 km. The lifetime of the eddy can be divided into three phases, i.e., the initiation, maturity, and termination phases. The depth of its influence reached 1 000 m; (2) the Argo profiles were divided into seven periods (approximately 20 days in each) for composite analysis, and the composite Argo profiles and CARS2009 (CSIRO Atlas of Regional Seas) climatology data were merged following the data-interpolating variational analysis (DIVA) method to reconstruct the three-dimensional structure. The temperature and salinity anomaly cores of the anticyclonic mesoscale eddy are located from 500 to 600 m. From 800 to 900 m, there is an area of low salinity at the center of the eddy. A high concentration anomaly of dissolved oxygen was located at approximately 250 m; (3) to better understand the features of the eddy and its interaction with the surroundings, we calculated the anomalous velocity of the geostrophic flow and the heat, salt, dissolved oxygen transport anomaly, and discussed the eddy’s origin and its adjustments to topography. The maximum heat, salt, and oxygen transport caused by eddy were 9.37×1011 W, 3.08×103 kg/s, and 2.70×102 kg/s, which all occurred during the termination phase. This study highlights the applicability of using Argo floats to understand the three-dimensional structure thermohaline features of eddies in the North Pacific.

Observed subsurface eddies near the Vietnam coast of the South China Sea

In this study, subsurface eddies near the Vietnam coast of the South China Sea were observed with in situ observations, including Argo, CTD, XBT and some processed and quality controlled data. Based on temperature profiles from four Argo floats near the coast of Vietnam, a subsurface warm eddy was identified in spring and summer. The multi-year Argo and Global Temperature and Salinity Profile Programme (GTSPP) data were merged on a seasonal basis based on the data interpolating variational analysis (DIVA) method to reconstruct the three-dimensional temperature structure. There is a warm eddy in the central subsurface at 12.5°N, 111°E below 300 m depth in spring, which does not exist in autumn and is weak in winter and summer. From CSIRO Atlas of Regional Seas (CARS) and Generalized Digital Environment Model (GDEM) reanalysis data, this subsurface warm eddy is also verified in spring.

Mediterranean Sea Hydrographic Atlas: towards optimal data analysis by including time-dependent statistical parameters

Abstract. The goal of the present work is to provide the scientific community with a high-resolution atlas of temperature and salinity for the Mediterranean Sea based on the most recent datasets available and contribute to the studies of the long-term variability in the region. Data from the pan-European marine data infrastructure SeaDataNet were used, the most complete and, to our best knowledge, best quality dataset for the Mediterranean Sea as of today. The dataset is based on in situ measurements acquired between 1900 and 2015. The atlas consists of horizontal gridded fields produced by the Data-Interpolating Variational Analysis, in which unevenly spatial distributed measurements were interpolated onto a 1∕8° × 1∕8° regular grid on 31 depth levels. Seven different types of climatological fields were prepared with different temporal integration of observations. Monthly, seasonal and annual climatological fields have been calculated for all the available years, seasonal to annual climatologies for overlapping decades and specific periods. The seasonal and decadal time frames have been chosen in accordance with the regional variability and in coherence with atmospheric indices. The decadal and specific-period analysis was not extended to monthly resolution due to the lack of data, especially for the salinity. The Data-Interpolating Variational Analysis software has been used in the Mediterranean region for the SeaDataNet and its predecessor Medar/Medatlas Climatologies. In the present study, a more advanced optimization of the analysis parameters was performed in order to produce more detailed results. The past and present states of the Mediterranean region have been extensively studied and documented in a series of publications. The purpose of this atlas is to contribute to these climatological studies and get a better understanding of the variability on timescales from months to decades and longer. Our gridded fields provide a valuable complementary source of knowledge in regions where measurements are scarce, especially in critical areas of interest such as the Marine Strategy Framework Directive (MSFD) regions and subregions. The dataset used for the preparation of the atlas is available from https://doi.org/10.12770/8c3bd19b-9687-429c-a232-48b10478581c.The climatologies in netCDF are available at the following sources: annual climatology (https://doi.org/10.5281/zenodo.1146976), seasonal climatology for 57 running decades (https://doi.org/10.5281/zenodo.1146938), seasonal climatology (https://doi.org/10.5281/zenodo.1146953), annual climatology for 57 running decades (https://doi.org/10.5281/zenodo.1146957), seasonal climatology for six periods (https://doi.org/10.5281/zenodo.1146966), annual climatology for six periods (https://doi.org/10.5281/zenodo.1146970), monthly climatology (https://doi.org/10.5281/zenodo.1146974).

Validation of global sea‐level pressure fields calculated from Oceansat‐2 scatterometer wind data using the UWPBL model

Sea level pressure fields were estimated from the Oceansat‐2 scatterometer (OSCAT) wind measurements using the University of Washington Planetary Boundary Layer (UWPBL) model, and the estimations were evaluated for the year 2011. The Data Interpolating Variational Analysis (DIVA) technique was used for the generation of daily global composites from the along‐track pressure field values. The sea level pressure field data were compared with in‐situ pressure observations (of which there were 220 818 in total) over the global oceans. Scatterometer‐derived pressure fields are in good agreement with the in‐situ measurements, with a bias of 0.31hPa, a correlation coefficient of 0.918 and a standard deviation ratio of 0.398. The accuracy of the estimations shows that global pressure fields calculated using OSCAT winds are suitable for use in synoptic studies/global oceanographic studies.

Reconstruction of the Gulf Stream from 1940 to the Present and Correlation with the North Atlantic Oscillation

AbstractIn this study, the Gulf Stream (GS)’s response to the North Atlantic Oscillation (NAO) is investigated by generating an observation-based reconstruction of the GS path between 70° and 50°W since 1940. Using in situ data from the World Ocean Database (WOD), SeaDataNet, International Council for the Exploration of the Sea (ICES), Hydrobase3, and Argo floats, a harmonized database of more than 40 million entries is created. A variational inverse method implemented in the software Data Interpolating Variational Analysis (DIVA) allows the production of time series of monthly analyses of temperature and salinity over the North Atlantic (NA). These time series are used to derive two GS indices: the GS north wall (GSNW) index for position and the GS delta (GSD) index as a proxy of its transport. This study finds a significant correlation (0.37) between the GSNW and the NAO at a lag of 1 year (NAO preceding GS) since 1940 and significant correlations (0.50 and 0.43) between the GSD and the NAO at lags of 0 and 2 years between 1960 and 2014. The authors suggest this 2-yr lag is due to Rossby waves, generated by NAO variability, that propagate westward from the center of the NA. This is the first reconstruction of GS indices over a 75-yr period based on an objective method using the largest in situ dataset so far.

A new global interior ocean mapped climatology: the 1° × 1° GLODAP version 2

Abstract. We present a mapped climatology (GLODAPv2.2016b) of ocean biogeochemical variables based on the new GLODAP version 2 data product (Olsen et al., 2016; Key et al., 2015), which covers all ocean basins over the years 1972 to 2013. The quality-controlled and internally consistent GLODAPv2 was used to create global 1° × 1° mapped climatologies of salinity, temperature, oxygen, nitrate, phosphate, silicate, total dissolved inorganic carbon (TCO2), total alkalinity (TAlk), pH, and CaCO3 saturation states using the Data-Interpolating Variational Analysis (DIVA) mapping method. Improving on maps based on an earlier but similar dataset, GLODAPv1.1, this climatology also covers the Arctic Ocean. Climatologies were created for 33 standard depth surfaces. The conceivably confounding temporal trends in TCO2 and pH due to anthropogenic influence were removed prior to mapping by normalizing these data to the year 2002 using first-order calculations of anthropogenic carbon accumulation rates. We additionally provide maps of accumulated anthropogenic carbon in the year 2002 and of preindustrial TCO2. For all parameters, all data from the full 1972–2013 period were used, including data that did not receive full secondary quality control. The GLODAPv2.2016b global 1° × 1° mapped climatologies, including error fields and ancillary information, are available at the GLODAPv2 web page at the Carbon Dioxide Information Analysis Center (CDIAC; doi:10.3334/CDIAC/OTG.NDP093_GLODAPv2).

Generation and Validation of two Day Composite Wind Fields from Oceansat-2 Scatterometer

The Oceansat-2 scatterometer (OSCAT) of the Indian Space Research Organization (ISRO), provides surface wind speed and direction with a spatial resolution of 50 km × 50 km. With a revisit time of 2 days it had provided ocean surface wind vectors over the global oceans. In the present work, an attempt has been made to generate two day composite of OSCAT wind vectors using Data-Interpolating Variational Analysis (DIVA) and compare them with daily composite winds to check how better is the two day composites in comparison to daily composites. The daily and two days composite wind vectors of zonal (U) and meridional (V) components have been validated with wind measurements from in situ buoys and Advanced Scatterometer (ASCAT) for the year 2012 over the tropical Indian Ocean region. The statistical comparison with the in situ measurements and ASCAT has shown that the two-day OSCAT wind composites are slightly better than the daily composite winds. The improvement in the statistics can be attributed to the use of ascending and descending passes pertaining to two days which results in fewer gaps between passes, thereby reducing the interpolation errors.

Qualified temperature, salinity and dissolved oxygen climatologies in a changing Adriatic Sea

Abstract. An updated climatology, based on a comprehensive data set (1911–2009) of temperature, salinity and dissolved oxygen, has been produced for the whole Adriatic Sea with the variational inverse method using the DIVA (Data-Interpolating Variational Analysis) software. Climatological maps were produced at 26 levels and validated with ordinary cross-validation and with a real vs. synthetic temperature–salinity diagram intercomparison. The concept of climatology–observation misfit (COM) has been introduced as an estimate of the physical variability associated with the climatological structures. In order to verify the temporal stability of the climatology, long-term variability has been investigated in the Middle Adriatic and the South Adriatic pits, regarded as the most suitable records of possible long-term changes. Compared with previous climatologies, this study allows a clear identification of the seasonal dynamic of the southern Adriatic, where a clear oxygen minimum is typically observed in the centre of the South Adriatic Gyre. New and better resolved features emerged from this analysis: (1) below 100 m all properties profoundly differ between the central and the southern Adriatic and seem characterized by different biogeochemical dynamics; (2) the South Adriatic Pit clearly shows the remote effects of the Eastern Mediterranean Transient, while no effect is observed in the Middle Adriatic Pit; (3) the deepest part of the southern Adriatic seems now to be significantly saltier (+0.18 psu since the period 1910–1914, with an increase of +0.018 decade−1 since the late 1940s) and warmer (+0.54 °C since 1910–1914) even though a long-term temperature trend could not be statistically demonstrated; (4) the Middle Adriatic Pit shows a long-term increase in apparent oxygen utilization (+0.77 mL L−1 since 1910–1914, with a constant increase of +0.2 mL L−1 decade−1 after the 1970s).

Daily composite wind fields from Oceansat-2 scatterometer

Oceansat-2 scatterometer (OSCAT) is an active microwave sensor, intended to provide ocean surface wind vectors over the global oceans. In the present work, an attempt has been made to generate daily composites of OSCAT Level-3 (L3) wind vectors using Data-Interpolating Variational Analysis (DIVA) method from ascending and descending passes over the Indian Ocean region. This could be useful for operational purposes and in generating value-added products like wind stress and curl of wind stress. The daily composite wind vectors of zonal (U) and meridional (V) components have been validated by comparing with Advanced Scatterometer (ASCAT) and wind from in situ buoys for the year 2012. Wind composites thus generated using DIVA are found to match well with in situ, and ASCAT wind products. Minor deviations are observed with respect to ASCAT wind, which could be attributed to the difference in interpolation techniques used for the two scatterometer products. Given that the repeat period of ASCAT is 5 days and that of OSCAT is only 2 days, OSCAT wind products could be conveniently used for real-time met-ocean studies.

Approximate and Efficient Methods to Assess Error Fields in Spatial Gridding with Data Interpolating Variational Analysis (DIVA)

Abstract This paper presents new approximate methods to provide error fields for the spatial analysis tool Data Interpolating Variational Analysis (DIVA). The first method shows how to replace the costly analysis of a large number of covariance functions with a single analysis for quick error computations. Then another method is presented where the error is only calculated in a small number of locations, and from there the spatial error field itself is interpolated by the analysis tool. The efficiency of the methods is illustrated on simple schematic test cases and a real application in the Mediterranean Sea. These examples show that with these methods, one has the possibility for quick masking of regions void of sufficient data and the production of “exact” error fields at reasonable cost. The error-calculation methods can also be generalized for use with other analysis methods such as three-dimensional variational data assimilation (3DVAR) and are therefore potentially interesting for other implementations.

Untangling spatial and temporal trends in the variability of the Black Sea Cold Intermediate Layer and mixed Layer Depth using the DIVA detrending procedure

Current spatial interpolation products may be biased by uneven distribution of measurements in time. This manuscript presents a detrending method that recognizes and eliminates this bias. The method estimates temporal trend components in addition to the spatial structure and has been implemented within the Data Interpolating Variational Analysis (DIVA) analysis tool. The assets of this new detrending method are illustrated by producing monthly and annual climatologies of two vertical properties of the Black Sea while recognizing their seasonal and interannual variabilities : the mixed layer depth and the cold content of its cold intermediate layer (CIL). The temporal trends, given as by-products of the method, are used to analyze the seasonal and interannual variability of these variables over the past decades (1955–2011). In particular, the CIL interannual variability is related to the cumulated winter air temperature anomalies, explaining 88 % of its variation.