Engineering topics

Tangborn, Andrew

Publications and source records attributed to Tangborn, Andrew.

15 records

NASA NTRS2017

Impact of Archeomagnetic Field Model Data on Modern Era Geomagnetic Forecasts

A series of geomagnetic data assimilation experiments have been carried out to demonstrate the impact of assimilating archeomagnetic data via the CALS3k.4 geomagnetic field model from the period between 10 and 1590 CE. The assimilation continues with the gufm1 model from 1590 to 1990 and CM4 model from 1990 to 2000 as observations, and comparisons between these models and the geomagnetic forecasts are used to determine an optimal maximum degree for the archeomagnetic observations, and to independently estimate errors for these observations. These are compared with an assimilation experiment that uses the uncertainties provided with CALS3k.4. Optimal 20 year forecasts in 1990 are found when the Gauss coefficients up to degree 3 are assimilated. In addition we demonstrate how a forecast and observation bias correction scheme could be used to reduce bias in modern era forecasts. Initial experiments show that this approach can reduce modern era forecast biases by as much as 50 percent.

Tangborn, Andrew↗

NASA NTRS2014

Dynamic Responses of the Earth's Outer Core to Assimilation of Observed Geomagnetic Secular Variation

Assimilation of surface geomagnetic observations and geodynamo models has advanced very quickly in recent years. However, compared to advanced data assimilation systems in meteorology, geomagnetic data assimilation (GDAS) is still in an early stage. Among many challenges ranging from data to models is the disparity between the short observation records and the long time scales of the core dynamics. To better utilize available observational information, we have made an effort in this study to directly assimilate the Gauss coefficients of both the core field and its secular variation (SV) obtained via global geomagnetic field modeling, aiming at understanding the dynamical responses of the core fluid to these additional observational constraints. Our studies show that the SV assimilation helps significantly to shorten the dynamo model spin-up process. The flow beneath the core-mantle boundary (CMB) responds significantly to the observed field and its SV. The strongest responses occur in the relatively small scale flow (of the degrees L is approx. 30 in spherical harmonic expansions). This part of the flow includes the axisymmetric toroidal flow (of order m = 0) and non-axisymmetric poloidal flow with m (is) greater than 5. These responses can be used to better understand the core flow and, in particular, to improve accuracies of predicting geomagnetic variability in future.

secular variation↗

NASA NTRS2011

Geomagnetic Secular Variation Prediction with Thermal Heterogeneous Boundary Conditions

It has long been conjectured that thermal heterogeneity at the core-mantle boundary (CMB) affects the geodynamo substantially. The observed two pairs of steady and strong magnetic flux lobes near the Polar Regions and the low secular variation in the Pacific over the past 400 years (and perhaps longer) are likely the consequences of this CMB thermal heterogeneity. There are several studies on the impact of the thermal heterogeneity with numerical geodynamo simulations. However, direct correlation between the numerical results and the observations is found very difficult, except qualitative comparisons of certain features in the radial component of the magnetic field at the CMB. This makes it difficult to assess accurately the impact of thermal heterogeneity on the geodynamo and the geomagnetic secular variation. We revisit this problem with our MoSST_DAS system in which geomagnetic data are assimilated with our geodynamo model to predict geomagnetic secular variations. In this study, we implement a heterogeneous heat flux across the CMB that is chosen based on the seismic tomography of the lowermost mantle. The amplitude of the heat flux (relative to the mean heat flux across the CMB) varies in the simulation. With these assimilation studies, we will examine the influences of the heterogeneity on the forecast accuracies, e.g. the accuracies as functions of the heterogeneity amplitude. With these, we could be able to assess the model errors to the true core state, and thus the thermal heterogeneity in geodynamo modeling.

Kuang, Weijia↗

NASA NTRS2011

MoSST DAS: The First Working Geomagnetic Data Assimilation System

The Earth possesses an internal magnetic field (geomagnetic field) generated by convection in the outer core (geodynamo). Previous efforts have been focused along two distinct paths: (1) numerical geodynamo modeling to understand the origin of the geomagnetic field, and the mechanisms of geomagnetic secular variations (SV); and (2) geomagnetic field modeling to map the spatial/temporal variations of the field from geomagnetic data, and to derive core properties, e.g. inversion of core flow near the core-mantle boundary (CMB). Geomagnetic data assimilation is a new approach emerged over the past 5 years: surface observations are assimilated with geodynamo models for better understanding of the core dynamical state, and accurately prediction of SV. In collaboration with several geomagnetic research groups, we have developed the first working geomagnetic data assimilation system, Modular, Scalable, Self-consistent, and Three-dimensional (MoSST) DAS, that includes the MoSST numerical dynamo model; 7000 years of geomagnetic field maps from several field models utilizing satellite and ground observatory data, historical magnetic records and archeo/paleo magnetic data; and an ensemble based optimal interpolation (01) assimilation algorithm. With this system, we have demonstrated clearly that the assimilated core dynamical state is substantially different from those of pure geodynamo simulations. Ensemble assimilation runs also show the convergence of the assimilated solutions inside the core, suggesting that the simulation state is pulled closer to the truth via data assimilation. The forecasts from this system are also very accurate: the 5-year forecast of the geomagnetic field agrees very well with the observations; and the 5-year secular variation forecast is more accurate than the IGRF SV forecast models in the past. Using geomagnetic records up to 2009, we have made an SV forecast for the period from 2010-2015, and is a candidate SV model for IGRF-11.

Kuang, Weijia↗

NASA NTRS2011

Effect of Cross-Correlation on Geomagnetic Forecast Accuracies

Surface geomagnetic observation can determine up to degree L = 14 time-varying spherical harmonic coefficients of the poloidal magnetic field. Assimilation of these coefficients to numerical dynamo simulation could help us understand better the dynamical processes in the Earth's outer core, and to provide more accurate forecast of geomagnetic secular variations (SV). In our previous assimilation studies, only the poloidal magnetic field in the core is corrected by the observations in the analysis. Unobservable core state variables (the toroidal magnetic field and the core velocity field) are corrected via the dynamical equations of the geodynamo. Our assimilation experiments show that the assimilated core state converges near the CMB, implying that the dynamo state is strongly constrained by surface geomagnetic observations, and is pulled closer to the truth by the data. We are now carrying out an ensemble of assimilation runs with 1000 years of geomagnetic and archeo/paleo magnetic record. In these runs the cross correlation between the toroidal and the poloidal magnetic fields is incorporated into the analysis. This correlation is derived from the physical boundary conditions of the toroidal field at the core-mantle boundary (CMB). The assimilation results are then compared with those of the ensemble runs without the cross-correlation, aiming at understanding two fundamental issues: the effect of the crosscorrelation on (1) the convergence of the core state, and (2) the SV prediction accuracies. The constrained dynamo solutions will provide valuable insights on interpreting the observed SV, e.g. the near-equator magnetic flux patches, the core-mantle interactions, and possibly other geodynamic observables.

Kuang, Weijia↗

NASA NTRS2009

Chemical Source Inversion using Assimilated Constituent Observations in an Idealized Two-dimensional System

We present a source inversion technique for chemical constituents that uses assimilated constituent observations rather than directly using the observations. The method is tested with a simple model problem, which is a two-dimensional Fourier-Galerkin transport model combined with a Kalman filter for data assimilation. Inversion is carried out using a Green's function method and observations are simulated from a true state with added Gaussian noise. The forecast state uses the same spectral spectral model, but differs by an unbiased Gaussian model error, and emissions models with constant errors. The numerical experiments employ both simulated in situ and satellite observation networks. Source inversion was carried out by either direct use of synthetically generated observations with added noise, or by first assimilating the observations and using the analyses to extract observations. We have conducted 20 identical twin experiments for each set of source and observation configurations, and find that in the limiting cases of a very few localized observations, or an extremely large observation network there is little advantage to carrying out assimilation first. However, in intermediate observation densities, there decreases in source inversion error standard deviation using the Kalman filter algorithm followed by Green's function inversion by 50% to 95%.

Tangborn, Andrew↗

NASA NTRS2008

Assimilation of SCIAMACHY Total Column CO Observations: Regional Analysis of Data Impact

Carbon monoxide (CO) total column observations from the SCanning Imaging Absorption SpectroMeter for Atmospheric CHartography (SCIAMACHY) on board ENVISAT are assimilated into the Global Modeling and Assimilation Office (GMAO) constituent assimilation system for the period July 18-October 31, 2004. This is the first assimilation of CO observations from a near infrared sounder. The impact of the assimilation on CO distribution is evaluated using independent Measurement of Ozone and Water vapor by Airbus In-service Aircraft (MOZAIC) in-situ CO profiles. Assimilation of satellite data improves agreement with MOZAIC CO globally, especially in the upper troposphere.

Tangborn, Andrew↗

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↗

NASA NTRS2004

On the Possibilities of Predicting Geomagnetic Secular Variation with Geodynamo Modeling

We use our MoSST core dynamics model and geomagnetic field at the core-mantle boundary (CMB) continued downward from surface observations to investigate possibilities of geomagnetic data assimilation, so that model results and current geomagnetic observations can be used to predict geomagnetic secular variation in future. As the first attempt, we apply data insertion technique to examine evolution of the model solution that is modified by geomagnetic input. Our study demonstrate that, with a single data insertion, large-scale poloidal magnetic field obtained from subsequent numerical simulation evolves similarly to the observed geomagnetic variation, regardless of the initial choice of the model solution (so long it is a well developed numerical solution). The model solution diverges on the time scales on the order of 60 years, similar to the time scales of the torsional oscillations in the Earth's core. Our numerical test shows that geomagnetic data assimilation is promising with our MoSST model.

Kuang, Wei-Jia↗

NASA NTRS2004

Torque Balances on the Taylor Cylinders in the Geomagnetic Data Assimilation

In this presentation we report on our continuing effort in geomagnetic data assimilation, aiming at understanding and predicting geomagnetic secular variation on decadal time scales. In particular, we focus on the effect of the torque balances on the cylindrical surfaces in the core co-axial with the Earth's rotation axis (the Taylor cylinders) on the time evolution of assimilated solutions. We use our MoSST core dynamics,model and observed geomagnetic field at the Earth's surface derived via Comprehensive Field Model (CFM) for the geomagnetic data assimilation. In our earlier studies, a model solution is selected randomly from our numerical database. It is then assimilated with the observations such that the poloidal field possesses the same field tomography on the core-mantel boundary (CMB) continued downward from surface observations. This tomography change is assumed to be effective through out the outer core. While this approach allows rapid convergence between model solutions and the observations, it also generates sevee numerical instabilities: the delicate balance between weak fluid inertia and the magnetic torques on the Taylor cylinders are completely altered. Consequently, the assimilated solution diverges quickly (in approximately 10% of the magnetic free-decay time in the core). To improve the assimilation, we propose a partial penetration of the assimilation from the CMB: The full-scale modification at the CMB decreases linearly and vanish at an interior radius r(sub a). We shall examine from our assimilation tests possible relationships between the convergence rate of the model solutions to observations and the cut-off radius r(sub a). A better assimilation shall serve our nudging tests in near future.

Kuang, Weijia↗

NASA NTRS2003

Prospect of Using Numerical Dynamo Model for Prediction of Geomagnetic Secular Variation

Modeling of the Earth's core has reached a level of maturity to where the incorporation of observations into the simulations through data assimilation has become feasible. Data assimilation is a method by which observations of a system are combined with a model output (or forecast) to obtain a best guess of the state of the system, called the analysis. The analysis is then used as an initial condition for the next forecast. By doing assimilation, not only we shall be able to predict partially secular variation of the core field, we could also use observations to further our understanding of dynamical states in the Earth's core. One of the first steps in the development of an assimilation system is a comparison between the observations and the model solution. The highly turbulent nature of core dynamics, along with the absence of any regular external forcing and constraint (which occurs in atmospheric dynamics, for example) means that short time comparisons (approx. 1000 years) cannot be made between model and observations. In order to make sensible comparisons, a direct insertion assimilation method has been implemented. In this approach, magnetic field observations at the Earth's surface have been substituted into the numerical model, such that the ratio of the multiple components and the dipole component from observation is adjusted at the core-mantle boundary and extended to the interior of the core, while the total magnetic energy remains unchanged. This adjusted magnetic field is then used as the initial field for a new simulation. In this way, a time tugged simulation is created which can then be compared directly with observations. We present numerical solutions with and without data insertion and discuss their implications for the development of a more rigorous assimilation system.

Kuang, Weijia↗

NASA NTRS2003

A Wavelet based Suboptimal Kalman Filter for Assimilation of Stratospheric Chemical Tracer Observations

A suboptimal Kalman filter system which evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. This scheme projects the discretized covariance propagation equations and covariance matrix onto an orthogonal set of compactly supported wavelets. Wavelet representation is localized in both location and scale, which allows for efficient representation of the inherently anisotropic structure of the error covariances. The truncation is carried out in such a way that the resolution of the error covariance is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments which last 24 days, and used different degrees of truncation were carried out. These reduced the covariance size by 90, 97 and 99 % and the computational cost of covariance propagation by 80, 93 and 96 % respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period were found to be not growing in the first case, and growing relatively slowly in the later two cases. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients in the constituent field. This results indicate that propagation of error covariances for a global two-dimensional data assimilation system are currently feasible. Recommendations for further reduction in computational cost are made with the goal of extending this technique to three-dimensional global assimilation systems.

Tangborn, Andrew↗

NASA NTRS2002

Wavelet Approximation in Data Assimilation

Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.

Tangborn, Andrew↗

NASA NTRS2002

A Wavelet Based Suboptimal Kalman Filter for Assimilation of Stratospheric Chemical Tracer Observations

A suboptimal Kalman filter system which evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. The truncation is carried out in such a way that the resolution of the error covariance, is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments which last 24 days, and used different degrees of truncation were carried out. These reduced the covariance, by 90, 97 and 99 % and the computational cost of covariance propagation by 80, 93 and 96 % respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period were found to be not growing in the first case, and a growing relatively slowly in the later two cases. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients in the tracer field.

Auger, Ludovic↗

NASA NTRS2001

Bias Correction and Random Error Characterization for the Assimilation of HRDI Line-of-Sight Wind Measurements

A new approach to the analysis of systematic and random observation errors is presented in which the error statistics are obtained using forecast data rather than observations from a different instrument type. The analysis is carried out at an intermediate retrieval level, instead of the more typical state variable space. This method is carried out on measurements made by the High Resolution Doppler Imager (HRDI) on board the Upper Atmosphere Research Satellite (UARS). HRDI, a limb sounder, is the only satellite instrument measuring winds in the stratosphere, and the only instrument of any kind making global wind measurements in the upper atmosphere. HRDI measures doppler shifts in the two different O2 absorption bands (alpha and B) and the retrieved products are tangent point Line-of-Sight wind component (level 2 retrieval) and UV winds (level 3 retrieval). This analysis is carried out on a level 1.9 retrieval, in which the contributions from different points along the line-of-sight have not been removed. Biases are calculated from O-F (observed minus forecast) LOS wind components and are separated into a measurement parameter space consisting of 16 different values. The bias dependence on these parameters (plus an altitude dependence) is used to create a bias correction scheme carried out on the level 1.9 retrieval. The random error component is analyzed by separating the gamma and B band observations and locating observation pairs where both bands are very nearly looking at the same location at the same time. It is shown that the two observation streams are uncorrelated and that this allows the forecast error variance to be estimated. The bias correction is found to cut the effective observation error variance in half.

Tangborn, Andrew↗