Optimal Spectral Decomposition Research Articles

Temporal and Spatial Variability of Global Upper Ocean Freshwater Content

Observational salinity data from the Global Temperature and Salinity Profile Program (GTSPP) are used to identify temporal and spatial variability of the upper ocean freshwater content (FWC). First, the optimal spectral decomposition (OSD) is used to build up monthly synoptic temperature and salinity data set from January 1990 to December 2009 on 1oA—1o grids and the same 33 vertical levels as the World Ocean Atlas 2005. Then, the monthly varying upper layer FWC fields (F) with four different layer thicknesses (surface to 50, 100, 300, and 700 m depths) are obtained.

Spatial and temporal variability of the California Current identified from the synoptic monthly gridded World Ocean Database (WOD)

The synoptic monthly gridded (SMG) world ocean database (WOD) were constructed with 1° × 1° horizontal resolution and 28 standard vertical levels from the surface to 3000 m deep using the optimal spectral decomposition technique. Monthly acceleration potential (AP) relative to 1000-dbar is calculated for the isopycnal surface 26.4 kg m−3 from January 1960 to December 2014 to investigate the spatial and temporal variability of the California Current. A composite analysis was conducted to obtain the total-time mean AP field and the climatological monthly mean AP variability, which is two orders of magnitude smaller than the total-time mean. Residual data were used to examine interannual variations of the AP field. An empirical orthogonal function (EOF) analysis was conducted to analyze the AP anomaly data. The EOF-1 (40% variance) represents strengthening/weakening of the North Pacific Gyre and California Current. EOF-2 (20% variance) represents onshore/offshore geostrophic flow. The first principal component was negatively correlated with the PDO; the second principal component was negatively correlated with both the PDO and ENSO, which implied that the AP anomaly contains climate variability signals.

Synoptic monthly gridded global and regional four‐dimensional World Ocean Database and Global Temperature and Salinity Profile Programme (T, S, u, v) fields with the optimal spectral decomposition and P‐vector methods

Synoptic monthly gridded (SMG) world ocean temperature (T) and salinity (S) fields with (1° × 1°) horizontal resolution and 28 standard vertical levels from the ocean surface to 3000 m deep have been established from the observational (T, S) profiles from the NOAA National Centers for Environmental Information (NCEI) World Ocean Database (WOD) from January 1945 to December 2014 and the Global Temperature and Salinity Profile Programme (GTSPP) from January 1990 to December 2009 using the optimal spectral decomposition (OSD) method. The world ocean abstract geostrophic currents (u, v) are calculated from the 4D SMG‐WOD and SMG‐GTSPP (T, S) data using the P‐vector inverse method. The SMG‐WOD (T, S, u, v) and SMG‐GTSPP (T, S, u, v) fields with a higher horizontal resolution (0.25° × 0.25°) have also been produced for the Mediterranean Sea, the Japan/East Sea, and the Gulf of Mexico.

Spectral Decomposition Using the CEEMD Method: a Case Study from the Carpathian Foredeep

The purpose of this work is to select the optimal spectral decomposition (SD) method for channel detection in the Miocene strata of the Carpathian Fordeep, SE Poland. For analysis, two spectral decomposition algorithms were tested on 3D seismic data: the first, based on Fast Fourier Transform (FFT), and second, on Complete Ensemble Empirical Mode Decomposition (CEEMD). Additionally the results of instantaneous frequency (IF) were compared with the results of peak frequency (PF) computed after the CEEMD. Both algorithms of SD enabled us to interpret channels, but the results are marginally different, i.e. the FFT shows more coarse, linear structures, that are desirable for channel interpretation, whereas the CEEMD does not highlight these structures as clearly and shows more, what the authors believe to be, noise.

Ocean spectral data assimilation without background error covariance matrix

Predetermination of background error covariance matrix B is challenging in existing ocean data assimilation schemes such as the optimal interpolation (OI). An optimal spectral decomposition (OSD) has been developed to overcome such difficulty without using the B matrix. The basis functions are eigenvectors of the horizontal Laplacian operator, pre-calculated on the base of ocean topography, and independent on any observational data and background fields. Minimization of analysis error variance is achieved by optimal selection of the spectral coefficients. Optimal mode truncation is dependent on the observational data and observational error variance and determined using the steep-descending method. Analytical 2D fields of large and small mesoscale eddies with white Gaussian noises inside a domain with four rigid and curved boundaries are used to demonstrate the capability of the OSD method. The overall error reduction using the OSD is evident in comparison to the OI scheme. Synoptic monthly gridded world ocean temperature, salinity, and absolute geostrophic velocity datasets produced with the OSD method and quality controlled by the NOAA National Centers for Environmental Information (NCEI) are also presented.

Optimal Spectral Decomposition (OSD) for Ocean Data Assimilation

AbstractOptimal spectral decomposition (OSD) is applied to ocean data assimilation with variable (temperature, salinity, or velocity) anomalies (relative to background or modeled values) decomposed into generalized Fourier series, such that any anomaly is represented by a linear combination of products of basis functions and corresponding spectral coefficients. It has three steps: 1) determination of the basis functions, 2) optimal mode truncation, and 3) update of the spectral coefficients from innovation (observational increment). The basis functions, depending only on the topography of the ocean basin, are the eigenvectors of the Laplacian operator with the same lateral boundary conditions as the assimilated variable anomalies. The Vapnik–Chervonkis dimension is used to determine the optimal mode truncation. After that, the model field updates due to innovation through solving a set of a linear algebraic equations of the spectral coefficients. The strength and weakness of the OSD method are demonstrated through a twin experiment using the Parallel Ocean Program (POP) model.

Global upper ocean heat content and climate variability

Observational data from the Global Temperature and Salinity Profile Program were used to calculate the upper ocean heat content (OHC) anomaly. The thickness of the upper layer is taken as 300 m for the Pacific/Atlantic Ocean and 150 m for the Indian Ocean since the Indian Ocean has shallower thermoclines. First, the optimal spectral decomposition scheme was used to build up monthly synoptic temperature and salinity dataset for January 1990 to December 2009 on 1° × 1° grids and the same 33 vertical levels as the World Ocean Atlas. Then, the monthly varying upper layer OHC field (H) was obtained. Second, a composite analysis was conducted to obtain the total-time mean OHC field (\( \bar{\bar{H}} \)) and the monthly mean OHC variability (\( \widetilde{\text{H}} \)), which is found an order of magnitude smaller than \( \widehat{\text{H}} \). Third, an empirical orthogonal function (EOF) method is conducted on the residue data (\( \widehat{\text{H}} \)), deviating from \( \widetilde{\text{H}} \) + \( \widetilde{\text{H}} \), in order to obtain interannual variations of the OHC fields for the three oceans. In the Pacific Ocean, the first two EOF modes account for 51.46% and 13.71% of the variance, representing canonical El Nino/La Nina (EOF-1) and pseudo-El Nino/La Nina (i.e., El Nino Modoki; EOF-2) events. In the Indian Ocean, the first two EOF modes account for 24.27% and 20.94% of the variance, representing basin-scale cooling/warming (EOF-1) and Indian Ocean Dipole (EOF-2) events. In the Atlantic Ocean, the first EOF mode accounts for 49.26% of the variance, representing a basin-scale cooling/warming (EOF-1) event. The second EOF mode accounts for 8.83% of the variance. Different from the Pacific and Indian Oceans, there is no zonal dipole mode in the tropical Atlantic Ocean. Fourth, evident lag correlation coefficients are found between the first principal component of the Pacific Ocean and the Southern Oscillation Index with a maximum correlation coefficient (0.68) at 1-month lead of the EOF-1 and between the second principal component of the Indian Ocean and the Dipole Mode Index with maximum values (around 0.53) at 1–2-month advance of the EOF-2. It implies that OHC anomaly contains climate variability signals.

Seasonal variability of the Black Sea chlorophyll- a concentration

The optimal spectral decomposition (OSD) method is used to reconstruct seasonal variability of the Black Sea horizontally averaged chlorophyll- a concentration from data collected during the NATO SfP-971818 Black Sea Project in 1980–1995. During the reconstruction, quality control is conducted to reduce errors caused by measurement accuracy, sampling strategy, and irregular data distribution in space and time. A bi-modal structure with winter/spring (February–March) and fall (September–October) blooms is uniquely detected and accurately documented. The chlorophyll- a enriched zone rises to 15 m depth in winter and June, and deepens to 40 m in April and 35 m in August. The June rise of the chlorophyll- a enriched zone is accompanying by near-continuous reduction of upper layer maximum chlorophyll- a concentration.