Validation of satellite-based sea surface temperature products against in situ observations off the western coast of Sumatra

This study validated the sea surface temperature (SST) datasets from the Group for High-Resolution SST Multi Product Ensemble (GMPE), National Oceanic and Atmospheric Administration (NOAA) Optimal Interpolation (OI) SST version 2 and 2.1 (OIv2 and OIv2.1), and Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2) in the area off the western coast of Sumatra against in situ observations. Furthermore, the root mean square differences (RMSDs) of OIv2, OIv2.1, and ECCO2 were investigated with respect to GMPE, whose small RMSD < 0.2 K against in situ observations confirmed its suitability as a reference. Although OIv2 showed a large RMSD (1–1.5 K) with a significant negative bias, OIv2.1 (RMSD < 0.4 K) improved remarkably. In the average SST distributions for December 2017, the differences among the 4 datasets were significant in the areas off the western coast of Sumatra, along the southern coast of Java, and in the Indonesian inland sea. These results were consistent with the ensemble spread distribution obtained with GMPE. The large RMSDs of OIv2 corresponded to high clouds, and it was suggested that the change in the satellites used for SST estimation contributed to the improvement in OIv2.1.

Changes in Alpine Butterfly Communities during the Last 40 Years

Our work aims to assess how butterfly communities in the Italian Maritime Alps changed over the past 40 years, in parallel with altitudinal shifts occurring in plant communities. In 2019, we sampled butterflies at 7 grassland sites, between 1300–1900 m, previously investigated in 2009 and 1978, by semi-quantitative linear transects. Fine-scale temperature and precipitation data elaborated by optimal interpolation techniques were used to quantify climate changes. The changes in the vegetation cover and main habitat alterations were assessed by inspection of aerial photographs (1978–2018/1978–2006–2015). The vegetation structure showed a marked decrease of grassland habitats and an increase of woods (1978–2009). Plant physiognomy has remained stable in recent years (2009–2019) with some local exceptions due to geomorphic disturbance. We observed butterfly ‘species substitution’ indicating a general loss in the more specialised and a general gain in more tolerant elements. We did not observe any decrease in species richness, but rather a change in guild compositions, with (i) an overall increased abundance in some widespread and common lowland species and (ii) the disappearance (or strong decrease) of some alpine (high elevation) species, so that ‘resilience’ could be just delusive. Changes in butterfly community composition were consistent with predicted impacts of local warming.

Next generation of Bluelink ocean reanalysis with multiscale data assimilation: BRAN2020

BRAN2020 (2020 version of the Bluelink ReANalysis) is an ocean reanalysis that combines observations with an eddy-resolving, near-global ocean general circulation model to produce a four-dimensional estimate of the ocean state. The data assimilation system employed is ensemble optimal interpolation, implemented with a new multiscale approach that constrains the broad-scale ocean properties and the mesoscale circulation in two steps. There is a separation in the scales that are corrected in the two steps: the high-resolution step corrects the mesoscale dynamics in the same way as previous versions of BRAN, while the extra coarse step is effective at correcting biases that develop at large scales. The reanalysis currently spans January 1993 to December 2019 and assimilates observations of in situ temperature and salinity, as well as of satellite sea-level anomaly and sea surface temperature. BRAN2020 is planned to be updated to within months of real time after this initial release, until an updated version of BRAN is available. Reanalysed fields from BRAN2020 generally show much closer agreement to observations than all previous versions with misfits between reanalysed and observed fields reduced by over 30 % for some variables, for subsurface temperature and salinity in particular. The BRAN2020 dataset is comprised of daily averaged fields of temperature, salinity, velocity, mixed-layer depth and sea level. Reanalysed fields realistically represent all of the major current systems within 75∘ S and 75∘ N, excluding processes relating to sea ice but including boundary currents, equatorial circulation, Southern Ocean variability and mesoscale eddies. BRAN2020 is publicly available at https://doi.org/10.25914/6009627c7af03 (Chamberlain et al., 2021b) and is intended for use by the research community.

Arctic sea surface height maps from multi-altimeter combination

We present a new Arctic sea level anomaly dataset based on the combination of three altimeter missions using an optimal interpolation scheme. Measurements from SARAL/AltiKa, CryoSat-2 and Sentinel-3A are blended together, providing an unprecedented resolution for this type of product. Such high-resolution products are necessary to tackle some contemporaneous science questions in the basin. We use the adaptive retracker to process both open ocean and lead echoes on SARAL/AltiKa, thus removing the need to estimate a bias between open ocean and ice-covered areas. The usual processing approach, involving an empirical retracking algorithm on specular echoes, is applied on CryoSat-2 and Sentinel-3A synthetic aperture radar (SAR) mode echoes. SARAL/AltiKa also provides the baseline for the cross-calibration of CryoSat-2 and Sentinel-3A data. The final gridded fields cover all latitudes north of 50∘ N, on a 25 km EASE2 grid, with one grid every 3 d over 3 years from July 2016 to April 2019. When compared to tide gauge measurements available in the Arctic Ocean, the combined product exhibits a much better performance than mono-mission datasets with a mean correlation of 0.78 and a mean root-mean-square deviation (RMSd) of 5 cm. The effective temporal resolution of the combined product is 3 times better than a single mission analysis. This dataset can be downloaded from https://doi.org/10.24400/527896/a01-2020.001 (Prandi, 2020).

Экстремальная функция интерполяционных формул в пространстве W2(2,0)

One of the main problems of computational mathematics is the optimization of computational methods in functional spaces. Optimization of computational methods are well demonstrated in the problems of the theory of interpolation formulas. In this paper, we study the problem of constructing an optimal interpolation formula in a Hilbert space. Here, using the Sobolev method, the first part of the problem is solved, i.e., an explicit expression of the square of the norm of the error functional of the optimal interpolation formulas in the Hilbert space W2(2,0) is found. Одна из основных проблем вычислительной математики — оптимизация вычислительных методов в функциональных пространствах. Оптимизация вычислительных методов хорошо проявляется в задачах теории интерполяционных формул. В данной статье исследуется проблема построения оптимальной интерполяционной формулы в гильбертовом пространстве. Здесь с помощью метода Соболева решается первая часть задачи — явное выражение квадрата нормы функционала погрешности оптимальных интерполяционных формул в гильбертовом пространстве W2(2,0) .

Estimating Mean Surface Backscatter from GPM Surface Backscatter Observations

The radar on the Global Precipitation Measurement (GPM) mission observes precipitation at 13.6 GHz (Ku-band) and 35.6 GHz (Ka-band) and also receives echoes from the earth’s surface. Statistics of surface measurements for non-raining conditions are saved in a database for later use in estimating the precipitation path-integrated attenuation. Previous work by Meneghini and Jones (2011) showed that while averaging over larger latitude/longitude bins increase the number of samples, it can also increase sample variance due to spatial inhomogeneity in the data. As a result, Meneghini and Kim (2017) proposed a new, adaptive method of database construction, in which the number of measurements averaged depends on the spatial homogeneity. The purpose of this work is to re-visit previous, single-frequency results using dual-frequency data and optimal interpolation (kriging). Results include that (1) temporal inhomogeneity can create similar results as spatial, (2) Ka-band behavior is similar to Ku-band, (3) the Ku-/Ka-band difference has less spatial inhomogeneity than either band by itself, and (4) kriging and the adaptive method can reduce the sample variance. The author concludes that finer spatial and temporal resolution is necessary in constructing the database for single frequencies but less so for the Ku-/Ka-band difference. The adaptive approach reduces sample standard deviation with a relatively modest computational increase.

Generalized Kalman Filter and Ensemble Optimal Interpolation, Their Comparison and Application to the Hybrid Coordinate Ocean Model

In this paper, we consider a recently developed data assimilation method, the Generalized Kalman Filter (GKF), which is a generalization of the widely-used Ensemble Optimal Interpolation (EnOI) method. Both methods are applied for modeling the Atlantic Ocean circulation using the known Hybrid Coordinate Ocean Model. The along-track altimetry data taken from the Archiving, Validating and Interpolating Satellite Oceanography Data (AVISO) were used for data assimilation and other data from independent archives of observations; particularly, the temperature and salinity data from the Pilot Research Array in the Tropical Atlantic were used for independent comparison. Several numerical experiments were performed with their results discussed and analyzed. It is shown that values of the ocean state variables obtained in the calculations using the GKF method are closer to the observations in terms of standard metrics in comparison with the calculations using the standard data assimilation method EnOI. Furthermore, the GKF method requires less computational effort compared to the EnOI method.

A data assimilation framework that uses the Kullback-Leibler divergence

The process of integrating observations into a numerical model of an evolving dynamical system, known as data assimilation, has become an essential tool in computational science. These methods, however, are computationally expensive as they typically involve large matrix multiplication and inversion. Furthermore, it is challenging to incorporate a constraint into the procedure, such as requiring a positive state vector. Here we introduce an entirely new approach to data assimilation, one that satisfies an information measure and uses the unnormalized Kullback-Leibler divergence, rather than the standard choice of Euclidean distance. Two sequential data assimilation algorithms are presented within this framework and are demonstrated numerically. These new methods are solved iteratively and do not require an adjoint. We find them to be computationally more efficient than Optimal Interpolation (3D-Var solution) and the Kalman filter whilst maintaining similar accuracy. Furthermore, these Kullback-Leibler data assimilation (KL-DA) methods naturally embed constraints, unlike Kalman filter approaches. They are ideally suited to systems that require positive valued solutions as the KL-DA guarantees this without need of transformations, projections, or any additional steps. This Kullback-Leibler framework presents an interesting new direction of development in data assimilation theory. The new techniques introduced here could be developed further and may hold potential for applications in the many disciplines that utilize data assimilation, especially where there is a need to evolve variables of large-scale systems that must obey physical constraints.