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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

Scott, James R.↗
DOE OSTI2024

Improving the precision of forces in real-space pseudopotential density functional theory

The high-order finite difference real-space pseudopotential density functional theory (DFT) approach is a valuable method for large-scale, massively parallel DFT calculations. A significant challenge in the approach is the oscillating “egg-box” error introduced by aliasing associated with a coarse grid spacing. To address this issue while minimizing computational cost, we developed a finite difference interpolation (FDI) scheme [Roller et al., J. Chem. Theory Comput. 19, 3889 (2023)] as a means of exploiting the high resolution of the pseudopotential to reduce egg-box effects systematically. Here, we show an implementation of this method in the PARSEC code and examine the practical utility of the combination of FDI with additional methods for improving force precision and/or reducing its computational cost, including orbital-based forces, compensating charges (namely, adding and subtracting a judiciously chosen charge density such that the total density is unaltered), and a modified spatial domain in which the real-space grid is defined. Using selected small molecules, as well as metallic Li, as test cases, we show that a combination of all four aspects leads to a significant reduction in computational cost while retaining a high level of precision that supports accurate structures and vibrational spectra, as well as stable and accurate molecular dynamics runs.

Chemistry↗
NASA NTRS2021

Weekly Mapping of Sea Ice Freeboard in the Ross Sea from ICESat-2

NASA’s ICESat-2 has been providing sea ice freeboard measurements across the polar regions since October 2018. In spite of the outstanding spatial resolution and precision of ICESat-2, the spatial sparsity of the data can be a critical issue for sea ice monitoring. This study employs a geostatistical approach (i.e., ordinary kriging) to characterize the spatial autocorrelation of the ICESat-2 freeboard measurements (ATL10) to estimate weekly freeboard variations in 2019 for the entire Ross Sea area, including where ICESat-2 tracks are not directly available. Three variogram models (exponential, Gaussian, and spherical) are compared in this study. According to the cross-validation results, the kriging-estimated freeboards show correlation coefficients of 0.56–0.57, root mean square error (RMSE) of ~0.12 m, and mean absolute error (MAE) of ~0.07 m with the actual ATL10 freeboard measurements. In addition, the estimated errors of the kriging interpolation are low in autumn and high in winter to spring, and low in southern regions and high in northern regions of the Ross Sea. The effective ranges of the variograms are 5–10 km and the results from the three variogram models do not show significant differences with each other. The southwest (SW) sector of the Ross Sea shows low and consistent freeboard over the entire year because of the frequent opening of wide polynya areas generating new ice in this sector. However, the southeast (SE) sector shows large variations in freeboard, which demonstrates the advection of thick multiyear ice from the Amundsen Sea into the Ross Sea. Thus, this kriging-based interpolation of ICESat-2 freeboard can be used in the future to estimate accurate sea ice production over the Ross Sea by incorporating other remote sensing data.

Satellite altimeter↗
NASA NTRS1982

Discrete Fourier transforms of nonuniformly spaced data

Time series or spatial series of measurements taken with nonuniform spacings have failed to yield fully to analysis using the Discrete Fourier Transform (DFT). This is due to the fact that the formal DFT is the convolution of the transform of the signal with the transform of the nonuniform spacings. Two original methods are presented for deconvolving such transforms for signals containing significant noise. The first method solves a set of linear equations relating the observed data to values defined at uniform grid points, and then obtains the desired transform as the DFT of the uniform interpolates. The second method solves a set of linear equations relating the real and imaginary components of the formal DFT directly to those of the desired transform. The results of numerical experiments with noisy data are presented in order to demonstrate the capabilities and limitations of the methods.

Swan, P. R.↗
NASA NTRS1981

A Quasi-Parabolic technique for computation of three-dimensional viscous flows

A computational technique is presented for obtaining flowfield solutions to a parabolic form of the Navier-Stokes equations. The point of departure is the General Interpolant Method (GIM) which provides a discretization for partial differential equations on arbitrary three-dimensional geometries. The new scheme, termed Quasi-Parabolic, treats the parabolized equations but with 'time-like' terms appended. Addition of these extra terms, which are relaxed by iteration, avoid many of the singularities inherent in classical parabolic Navier-Stokes methods. Streamwise derivatives are approximated by three-point backward differences and the cross plane operators use an alternating forward-backward sweep. A two-step sequence is used to implement the difference scheme in the spatial dimensions and a time-like relaxation converges the quasi-parabolic procedure at each plane. Solutions are presented for flows in two and three dimensions. Inviscid flows are solved for internal and external applications and viscous flows in boundary layers and free shear layers are also computed with the GIM/Quasi-Parabolic scheme.

Spradley, L. W.↗
NASA NTRS1994

Blocking reduction of Landsat Thematic Mapper JPEG browse images using optimal PSNR estimated spectra adaptive postfiltering

Two representative sample images of Band 4 of the Landsat Thematic Mapper are compressed with the JPEG algorithm at 8:1, 16:1 and 24:1 Compression Ratios for experimental browsing purposes. We then apply the Optimal PSNR Estimated Spectra Adaptive Postfiltering (ESAP) algorithm to reduce the DCT blocking distortion. ESAP reduces the blocking distortion while preserving most of the image's edge information by adaptively postfiltering the decoded image using the block's spectral information already obtainable from each block's DCT coefficients. The algorithm iteratively applied a one dimensional log-sigmoid weighting function to the separable interpolated local block estimated spectra of the decoded image until it converges to the optimal PSNR with respect to the original using a 2-D steepest ascent search. Convergence is obtained in a few iterations for integer parameters. The optimal logsig parameters are transmitted to the decoder as a negligible byte of overhead data. A unique maxima is guaranteed due to the 2-D asymptotic exponential overshoot shape of the surface generated by the algorithm. ESAP is based on a DFT analysis of the DCT basis functions. It is implemented with pixel-by-pixel spatially adaptive separable FIR postfilters. PSNR objective improvements between 0.4 to 0.8 dB are shown together with their corresponding optimal PSNR adaptive postfiltered images.

Linares, Irving↗
DOE OSTI2020

The effect of geographic sampling on evaluation of extreme precipitation in high-resolution climate models

Traditional approaches for comparing global climate models and observational data products typically fail to account for the geographic location of the underlying weather station data. For modern global high-resolution models with a horizontal resolution of tens of kilometers, this is an oversight since there are likely grid cells where the physical output of a climate model is compared with a statistically interpolated quantity instead of actual measurements of the climate system. In this paper, we quantify the impact of geographic sampling on the relative performance of high-resolution climate model representations of precipitation extremes in boreal winter (December–January–February) over the contiguous United States (CONUS), comparing model output from five early submissions to the HighResMIP subproject of the CMIP6 experiment. We find that properly accounting for the geographic sampling of weather stations can significantly change the assessment of model performance. Across the models considered, failing to account for sampling impacts the different metrics (extreme bias, spatial pattern correlation, and spatial variability) in different ways (both increasing and decreasing). We argue that the geographic sampling of weather stations should be accounted for in order to yield a more straightforward and appropriate comparison between models and observational data sets, particularly for high-resolution models with a horizontal resolution of tens of kilometers. While we focus on the CONUS in this paper, our results have important implications for other global land regions where the sampling problem is more severe.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRSDate not supplied

Interannual to Decadal Variability in Subarctic Atlantic Ocean Primary Productivity Historical Variability, Dynamics, and Response to Warming

Phytoplankton primary productivity in the Subarctic Atlantic Ocean sustains valuable fisheries and exports anthropogenic atmospheric carbon dioxide, but multiple Earth system models show that this productivity declines substantially in 21st century global warming scenarios. Prior studies have investigated the spatial and temporal dynamics of the seasonal cycle of the phytoplankton, which exhibit a prominent but spatially variable spring bloom that is caused by the closely related seasonal cycles in solar radiation and vertical mixing that modulate both phytoplankton growth and loss rates. However, recent work indicates that multi-decade declines in this spring bloom with global warming in multiple Earth system models are driven by reductions in circulation of nutrients from the subtropical and tropical thermocline, rather than local changes in vertical mixing or shortwave radiation in the Subarctic. It is unclear if current models of how phytoplankton productivity varies seasonally or over a century in global warming can be interpolated to explain the interannual to decadal variability. In this poster, I will quantify the interannual to decadal variability of phytoplankton chlorophyll using historical satellite ocean color observations and model simulations with the Community Earth System Model. I will then use the observations and model simulations to elucidate the mechanisms of interannual to decadal variability and how that variability is restructured in 21st century global warming scenarios.

nterannual↗
DOE OSTI2017

Evaluation of a data fusion approach to estimate daily PM{sub 2.5} levels in North China

PM{sub 2.5} air pollution has been a growing concern worldwide. Previous studies have conducted several techniques to estimate PM{sub 2.5} exposure spatiotemporally in China, but all these have limitations. This study was to develop a data fusion approach and compare it with kriging and Chemistry Module. Two techniques were applied to create daily spatial cover of PM{sub 2.5} in grid cells with a resolution of 10 km in North China in 2013, respectively, which was kriging with an external drift (KED) and Weather Research and Forecast Model with Chemistry Module (WRF-Chem). A data fusion technique was developed by fusing PM{sub 2.5} concentration predicted by KED and WRF-Chem, accounting for the distance from the central of grid cell to the nearest ground observations and daily spatial correlations between WRF-Chem and observations. Model performances were evaluated by comparing them with ground observations and the spatial prediction errors. KED and data fusion performed better at monitoring sites with a daily model R{sup 2} of 0.95 and 0.94, respectively and PM{sub 2.5} was overestimated by WRF-Chem (R{sup 2}=0.51). KED and data fusion performed better around the ground monitors, WRF-Chem performed relative worse with high prediction errors in the central of study domain. In our study, both KED and data fusion technique provided highly accurate PM{sub 2.5}. Current monitoring network in North China was dense enough to provide a reliable PM{sub 2.5} prediction by interpolation technique. - Highlights: • KED and data fusion model predicted daily PM{sub 2.5} with high accuracy. • WRF-Chem performed worse in PM{sub 2.5} prediction compared with KED and data fusion. • The PM{sub 2.5} monitoring network in North China was able to support reliable PM{sub 2.5} interpolation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Phase-field model of alloy solidification far from chemical equilibrium at the solid-liquid interface

We further develop a recently introduced phase-field model of far-from-equilibrium alloy solidification under additive manufacturing conditions [K. Ji et al., Phys. Rev. Lett. 130, 026203 (2023)]. This model utilizes enhanced solute diffusivity within the spatially diffuse interface region to quantitatively capture solute trapping with a larger interface width, thereby making simulations on experimentally relevant length and timescales computationally feasible. The main developments presented here include testing the robustness of different variational formulations, extending the model to concentrated alloys by incorporating solid and liquid free energies from thermodynamic databases, as illustrated for hypoeutectic Al-Ag alloys with CALPHAD, extending convergence tests as a function of interface width to 3D, and carrying out simulations in both 2D and 3D to examine existing theories of microstructure development. Our results indicate that the simplest variational formulation that interpolates the bulk free-energy density between its solid and liquid forms is the most robust. Remarkably, for hypoeutectic Al-Ag alloys, this formulation yields a high-velocity nonequilibrium phase diagram that is independent of interface width, thereby demonstrating that the framework of enhanced solute diffusivity can be nontrivially extended to concentrated alloys. Other variational formulations have restricted ranges of materials or processing parameters that can be reliably modeled. We use 2D simulations to construct high-velocity microstructure selection maps for dilute Al-Cu alloys. The results validate the important role of latent heat rejection at the interface and extend the limited predictions of linear stability analysis [A. Karma and A. Sarkissian, Phys. Rev. E 47, 513 (1993)] and sharp-interface 1D simulations to fully nonlinear regimes. Furthermore, 3D simulations, carried out using a computationally tractable axisymmetric cellular/dendritic interface shape, demonstrate a good convergence similar to that observed in 2D as a function of interface width. Full 3D simulations, in turn, reveal that the standard theory of absolute stability is a good predictor of the upper critical velocity beyond which steady-state growth becomes unstable, despite the different morphological manifestations of this instability in 2D and 3D.

36 MATERIALS SCIENCE↗
NASA NTRS1978

Two-dimensional computer code for design assessment of SRM aft closure environment

A general interpolants method for constructing numerical analogs of the partial differential equations of continuum mechanics and which combines the best features of both finite element and finite difference methods was used in a two dimensional axisymmetric analysis of the space shuttle solid motor aft closure region flowfield. The numerical technique used is discussed as well as the results of the analysis. A steady state solution for the submerged nozzle nose region indicates the development of an area gas flow recirculation near the propellant burning surface boundary and in the region of the underside of the nozzle nose. This recirculation region remains spatially fixed for successive iterations (greater than 800) of the solution.

Freeman, J. A.↗
NASA NTRS2022

Estimating groundwater use and demand in arid Kenya through assimilation of satellite data and in-situ sensors with machine learning toward drought early action

Groundwater is an important source of water for people, livestock, and agriculture during drought in the Horn of Africa. In this work, areas of high groundwater use and demand in drought-prone Kenya were identified and forecasted prior to the dry season. Estimates of groundwater use were extended from a sentinel network of 69 in-situ sensored mechanical boreholes to the region with satellite data and a machine learning model. The sensors contributed 756 site-month observations from June 2017 to September 2021 for model building and validation at a density of approximately one sensor per 3700 sq.km. An ensemble of 19 parameterized algorithms was informed by features including satellite-derived precipitation, surface water availability, vegetation indices, hydrologic land surface modeling, and site characteristics to dichotomize high groundwater pump utilization. Three operational definitions of high demand on groundwater infrastructure were considered: 1) mechanical runtime of pumps greater than a quarter of a day (6+ hr) and daily per capita volume extractions indicative of 2) domestic water needs (35+ L), and 3) intermediate needs including livestock (75+ L). Gridded interpolation of localized groundwater use and demand was provided from 2017 to 2020 and forecasted for the 2021 dry season, June–September 2021. Cross-validated skill for contemporary estimates of daily pump runtime and daily volume extraction to meet domestic and intermediate water needs was 68%, 69%, and 75%, respectively. Forecasts were externally validated with an accuracy of at least 56%, 70%, or 72% for each groundwater use definition. The groundwater maps are accessible to stakeholders including the Kenya National Drought Management Authority (NDMA) and the Famine Early Warning Systems Network (FEWS NET). These maps represent the first operational spatially-explicit sub-seasonal to seasonal (S2S) estimates of groundwater use and demand in the literature. Knowledge of historical and forecasted groundwater use is anticipated to improve decision-making and resource allocation for a range of early warning early action applications.

Katie Fankhauser↗
DOE OSTI2025

Enhanced MPM framework with multipatch isogeometric analysis for geotechnical applications

Achieving stable stress solutions at large strains using the Material Point Method (MPM) is challenging due to the accumulation of errors associated with geometry discretization, cell-crossing noise, and volumetric locking. Several simplified attempts exist in the literature to mitigate these errors, including higher-order frameworks. However, the stability of the MPM solution in such frameworks has been limited to simple geometries and the single-phase formulation (i.e., neglecting pore fluid). Although never explored, multipatch isogeometric analysis offers desirable qualities to simulate complex geometries while mitigating errors in the MPM. The degree of required high-order spatial integration has also never been investigated to infer a minimum limit for the stability of the stress solution in MPM. This paper presents a general-purpose numerical framework for simulating stable stresses in porous media, capturing both near incompressibility and multiphase interactions. First, the numerical framework is presented considering Non-Uniform Rational B-splines (NURBS) to perform isogeometric analysis (IGA) in MPM. Additionally, a volumetric strain smoothing algorithm is used to alleviate errors associated with volumetric locking. Second, the manifestation of cell-crossing errors is assessed via a series of problems with orders ranging from linear to cubic interpolation functions. Third, the use of NURBS is investigated and verified for problems with circular geometries. Finally, multipatch analysis is deployed to simulate plane strain and 3D penetration in soils, considering nearly incompressible elastoplastic (total stress) analysis and fully-coupled hydro-mechanical (effective stress) analysis. The stability of the solution is also analyzed for different constitutive models. From the results, it can be concluded that the framework using cubic interpolation functions with strain smoothing is the most convenient, presenting stable stress solutions for a broad range of multiphase geotechnical applications.

58 GEOSCIENCES↗
NASA NTRS2018

Linking Improvements in Sulfur Dioxide Emissions to Decreasing Sulfate Wet Deposition by Combining Satellite and Surface Observations with Trajectory Analysis

Sulfur dioxide (SO2), a criteria pollutant, and sulfate (SO42) deposition are major environmental concerns in the eastern U.S. and both have been on the decline for two decades. In this study, we use satellite column SO2 data from the Ozone Monitoring Instrument (OMI), and SO42 wet deposition data from the NADP (National Atmospheric Deposition Program) to investigate the temporal and spatial relationship between trends in SO2 emissions and the downward sulfate wet deposition over the eastern U.S. from 2005 to 2015. To establish the relationship between SO2 emission sources and receptor sites, we conducted a Potential Source Contribution Function (PSCF) analysis using HYSPLIT back trajectories for five selected Air Quality System (AQS) sites - (Hackney, OH, Akron, OH, South Fayette, PA, Wilmington, DE, and Beltsville, MD) - in close proximity to NADP sites with large downward SO42 trends since 2005. Back trajectories were run for three summers (JJA) and three winters (DJF) and used to generate seasonal climatology PSCFs for each site. The OMI SO2 and interpolated NADP sulfate deposition trends were normalized and overlapped with the PSCF, to identify the areas that had the highest contribution to the observed drop. The results suggest that emission reductions along the Ohio River Valley have led to decreases in sulfate deposition in eastern OH and western PA (Hackney, Akron and South Fayette). Farther to the east, emission reductions in southeast PA resulted in improvements in sulfate deposition at Wilmington, DE, while for Beltsville, reductions in both the Ohio River Valley and nearby favorably impacted sulfate deposition. For Beltsville, sources closer than 300km from the site contribute roughly 56% observed deposition trends in winter, and 82% in summer, reflecting seasonal changes in transport pattern as well as faster oxidation and washout of sulfur in summer. This suggests that emissions and wet deposition are linked through not only the location of sources relative to the observing sites, but also to photochemistry and the weather patterns characteristic to the region, as evidenced by a west to east shift in the contribution between winter and summer. The method developed here is applicable to other regions with significant trends such as China and India, and can be used to estimate the potential benefits of emission reduction in those areas.

Acid depostion↗
NASA NTRS2018

Linking Improvements in Sulfur Dioxide Emissions to Decreasing Sulfate Wet Deposition By Combining Satellite and Surface Observations With Trajectory Analysis

Sulfur dioxide (SO2), a criteria pollutant, and sulfate (SO42−) deposition are major environmental concerns in the eastern U.S. and both have been on the decline for two decades. In this study, we use satellite column SO2 data from the Ozone Monitoring Instrument (OMI), and SO42− wet deposition data from the NADP (National Atmospheric Deposition Program) to investigate the temporal and spatial relationship between trends in SO2 emissions and the downward sulfate wet deposition over the eastern U.S. from 2005 to 2015. To establish the relationship between SO2 emission sources and receptor sites, we conducted a Potential Source Contribution Function (PSCF) analysis using HYSPLIT back trajectories for five selected Air Quality System (AQS) sites - (Hackney, OH, Akron, OH, South Fayette, PA, Wilmington, DE, and Beltsville, MD) - in close proximity to NADP sites with large downward SO42− trends since 2005. Back trajectories were run for three summers (JJA) and three winters (DJF) and used to generate seasonal climatology PSCFs for each site. The OMI SO2 and interpolated NADP sulfate deposition trends were normalized and overlapped with the PSCF, to identify the areas that had the highest contribution to the observed drop. The results suggest that emission reductions along the Ohio River Valley have led to decreases in sulfate deposition in eastern OH and western PA (Hackney, Akron and South Fayette). Farther to the east, emission reductions in southeast PA resulted in improvements in sulfate deposition at Wilmington, DE, while for Beltsville, reductions in both the Ohio River Valley and nearby favorably impacted sulfate deposition. For Beltsville, sources closer than 300 km from the site contribute roughly 56% observed deposition trends in winter, and 82% in summer, reflecting seasonal changes in transport pattern as well as faster oxidation and washout of sulfur in summer. This suggests that emissions and wet deposition are linked through not only the location of sources relative to the observing sites, but also to photochemistry and the weather patterns characteristic to the region, as evidenced by a west to east shift in the contribution between winter and summer. The method developed here is applicable to other regions with significant trends such as China and India, and can be used to estimate the potential benefits of emission reduction in those areas.

sulfur dioxide emissions↗
NASA NTRS2006

Constraining Numerical Geodynamo Modeling with Surface Observations

Numerical dynamo solutions have traditionally been generated entirely by a set of self-consistent differential equations that govern the spatial-temporal variation of the magnetic field, velocity field and other fields related to dynamo processes. In particular, those solutions are obtained with parameters very different from those appropriate for the Earth s core. Geophysical application of the numerical results therefore depends on correct understanding of the differences (errors) between the model outputs and the true states (truth) in the outer core. Part of the truth can be observed at the surface in the form of poloidal magnetic field. To understand these differences, or errors, we generate new initial model state (analysis) by assimilating sequentially the model outputs with the surface geomagnetic observations using an optimal interpolation scheme. The time evolution of the core state is then controlled by our MoSST core dynamics model. The final outputs (forecasts) are then compared with the surface observations as a means to test the success of the assimilation. We use the surface geomagnetic data back to year 1900 for our studies, with 5-year forecast and 20-year analysis periods. We intend to use the result; to understand time variation of the errors with the assimilation sequences, and the impact of the assimilation on other unobservable quantities, such as the toroidal field and the fluid velocity in the core.

Kuang, Weijia↗
DOE OSTI2022

Parametric dynamic mode decomposition for reduced order modeling

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by singular value decomposition of the temporal data sets. For parameter-dependent models, as found in many multi-query applications such as uncertainty quantification or design optimization, the only parametric DMD technique developed was a stacked approach, with data sets at multiple parameter values were aggregated together, increasing the computational work needed to devise low-rank dynamical reduced-order models. Here in this paper, we present two novel approach to carry out parametric DMD: one based on the interpolation of the reduced-order DMD eigen-pair and the other based on the interpolation of the reduced DMD (Koopman) operator. Numerical results are presented for diffusion-dominated nonlinear dynamical problems, including a multiphysics radiative transfer example. All three parametric DMD approaches are compared.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Assimilation of TOPEX Sea Level Measurements with a Reduced-Gravity, Shallow Water Model of the Tropical Pacific Ocean

Sea surface height variability measured by TOPEX is analyzed in the tropical Pacific Ocean by way of assimilation into a wind-driven, reduced-gravity, shallow water model using an approximate Kalman filter and smoother. The analysis results in an optimal fit of the dynamic model to the observations, providing it dynamically consistent interpolation of sea level and estimation of the circulation. Nearly 80% of the expected signal variance is accounted for by the model within 20 deg of the equator, and estimation uncertainty is substantially reduced by the voluminous observation. Notable features resolved by the analysis include seasonal changes associated with the North Equatorial Countercurrent and equatorial Kelvin and Rossby waves. Significant discrepancies are also found between the estimate and TOPEX measurements, especially near the eastern boundary. Improvements in the estimate made by the assimilation are validated by comparisons with independent tide gauge and current meter observations. The employed filter and smoother are based on approximately computed estimation error covariance matrices, utilizing a spatial transformation and an symptotic approximation. The analysis demonstrates the practical utility of a quasi-optimal filter and smoother.

Fukumori, Ichiro↗