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DOE OSTI2021

An uncertainty-focused database approach to extract spatiotemporal trends from qualitative and discontinuous lake-status histories

Changes in lake status are often interpreted as palaeoclimate indicators due to their dependence on precipitation and evaporation. The Global Lake Status Database (GLSDB) has since long provided a standardised synopsis of qualitative lake status over the last 30,000 14C years. Potential sources of uncertainty however are not recorded in the GLSDB. Here we present an updated and improved relational-database framework that incorporates uncertainty in both chronology and the interpretation of palaeoenvironmental data. The database uses peer-reviewed palaeolimnological studies to produce a consensus on qualitative lake-status histories, whose chronologies are revised and standardized through the recalibration of radiocarbon dates and the application of Bayesian age-depth modelling for stratigraphic archives. Quantitative information on absolute water-level elevation is preserved if available from geomorphological sources. We also propose a new probabilistic analytical framework that accounts for these uncertainties to reconstruct synoptic, integrated environmental signals. The process is based on a Monte Carlo algorithm that iteratively samples individual lake-status histories within the limits of their uncertainties to produce many possible scenarios. We then use Recursively-Subtracted Empirical Orthogonal Function analysis to extract dominant patterns of lake-status variability from these scenarios. As a proof of concept, we apply this framework to 67 sites in eastern and southern Africa whose lake-status histories cover part of the late Pleistocene and/or Holocene. We show that, despite the sometimes large temporal and interpretation uncertainties, and the inclusion of highly discontinuous lake-status time series, identifying the major known millennial-scale climatic phases during the last 20,000 years is possible. Our framework was also able to identify an antiphased response between the lake basins in eastern and interior southern Africa to these changes. Here, we propose that our new database and methodology framework serves as a template for efficient lake-status data synthesis, encourages the incorporation of lake-status data in palaeoclimate syntheses, and expands the possibilities for the use of such data in the evaluation of climate models.

58 GEOSCIENCES↗

DOE OSTI2022

Assessment of Crustal Leg Uncertainties for RSTT Path-dependent Uncertainty

The Regional Seismic Travel Time (RSTT) model and software were recently updated to allow for path-dependent uncertainty (PDU) estimates for travel-time (Begnaud et al. 2021; Begnaud et al. 2020). Begnaud et al. (2021) describes the process of improving the current distance-dependent uncertainty parameterization for RSTT using a random effects model (REM) to estimate slowness (inverse velocity) uncertainty as a mean squared error for each model parameter. The REM separates the error between observed slowness and model predicted slowness into bias and random components. The PDU is calculated by integrating these mean squared errors along a seismic-phase ray path.

58 GEOSCIENCES↗

DOE OSTI2021

The utility of Bayesian data reconciliation for separations

Data reconciliation methods for separation processes typically rely on classical statistical approaches to generate estimates of true mass flow rates from measurements. Knowledge regarding the uncertainty of these estimates has value in decision making, but is often not acquired. Bayesian approaches intrinsically quantify uncertainty; however, literature for Bayesian data reconciliation of separation processes is scarce. This publication outlines two Bayesian data reconciliation models and provides details for how the models were implemented for the BayesMassBal (V 1.0.0) software package written in R. To demonstrate the advantages of this approach for data reconciliation, the models were first applied to simulated data and then compared to a classical model through a Monte Carlo experiment. In this example, the Bayesian models were found to provide more accurate estimates of the simulated data, while also providing quantitative information on the estimate uncertainty. To demonstrate the use of the technique in a practical problem, the models were also applied to real data collected from a pilot-scale rare earth solvent extraction process. Here, this publication provides a small window into how Bayesian methods can be used for data reconciliation, but findings suggest Bayesian data reconciliation models for separation processes have distinct advantages over classical alternatives.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2017

Nested polynomial trends for the improvement of Gaussian process-based predictors

The role of simulation keeps increasing for the sensitivity analysis and the uncertainty quantification of complex systems. Such numerical procedures are generally based on the processing of a huge amount of code evaluations. When the computational cost associated with one particular evaluation of the code is high, such direct approaches based on the computer code only, are not affordable. Surrogate models have therefore to be introduced to interpolate the information given by a fixed set of code evaluations to the whole input space. When confronted to deterministic mappings, the Gaussian process regression (GPR), or kriging, presents a good compromise between complexity, efficiency and error control. Such a method considers the quantity of interest of the system as a particular realization of a Gaussian stochastic process, whose mean and covariance functions have to be identified from the available code evaluations. In this context, this work proposes an innovative parametrization of this mean function, which is based on the composition of two polynomials. This approach is particularly relevant for the approximation of strongly non linear quantities of interest from very little information. After presenting the theoretical basis of this method, this work compares its efficiency to alternative approaches on a series of examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

WIND Toolkit Long-Term Ensemble Dataset

WIND Toolkit Long-term Ensemble Dataset (WTK-LED), an updated version of the meteorological WIND Toolkit, is a meteorological dataset providing high-resolution time series, including interannual variability and model uncertainty of wind speed at every modeling grid point to indicate ranges of possible wind speeds. The data were produced using the Weather Research and Forecasting Model (WRF). The vertical grid used in WTK-LED includes many vertical layers in the atmospheric boundary layer to provide information of atmospheric quantities across the rotor layer of utility scale and distributed wind turbines. The WTK-LED includes: (1) Numerical simulations of wind speed and other meteorological variables covering the contiguous United States (CONUS) and Alaska, with high-resolution (5-minute [min], 2-kilometer [km]) data for 3 years (2018-2020): WTK-LED CONUS, WTK-LED Alaska. (2) Climate simulations from Argonne National Laboratory covering North America, including Alaska, Canada, and most of Mexico and the Caribbean islands. These simulations complement the new WTK-LED to offer a 4-km, hourly dataset covering 20 years (2001-2020): WTK-LED Climate. (3) Specific long-term, high-resolution offshore simulations have been conducted separately for the U.S. coasts, Hawaii, and the Great Lakes, leading to the 2023 National Offshore Wind dataset: NOW-23. The data for Hawaii include land-based data and are part of WTK-LED Hawaii. Because the accuracy of simulations from a mesoscale model, such as WRF, varies depending on the location and weather situation, and can reach up to several m/s for wind speed, we provide simulated wind speed uncertainty estimates to the community to be used in conjunction with the deterministic model simulations. This dataset was developed to satisfy a wide group of stakeholders across various wind energy disciplines, including but not limited to stakeholders in the distributed and utility scale wind industry, the new emerging airborne wind energy field, grid integration, power systems modeling, environmental modeling, and researchers in academia, and to close some of the gaps that current public datasets have. Based on our validation results to date, we suggest use cases and applications for each dataset of the WTK-LED as shown in "WTK-LED Use Cases" resource below.

Array↗

DOE OSTI2016

CRADA FINAL REPORT FOR CRADA NO. CR-08-001 CEMENTITIOUS BARRIERS PARTNERSHIPS

The Cementitious Barriers Partnership (CBP), led by the Savannah River National Laboratory, has achieved its ultimate purpose to support progress in final treatment and disposal of legacy waste and closure of High-Level Waste (HLW) tanks in the DOE complex. The CBP achieved its goal by developing experimental programs with results that supported the development of a reasonable and credible set of software tools to improve understanding and prediction of the structural, hydraulic and chemical performance of cementitious barriers and waste forms used in nuclear applications. These experimental data and software tools are and will continue to reduce the uncertainties in the current methodologies for assessing cementitious barrier performance and increase the consistency and transparency of the assessment process. The CBP has made a significant impact in reducing risk and uncertainties in the performance assessments that directly impact U.S. Department of Energy (DOE) environmental cleanup and closure programs. The CBP has developed an experimentally-based, integrated modeling tool that serves as a screening tool known as the CBP Software Toolbox, Version 3.0. The CBP products reduce the uncertainties of current methodologies for assessing cementitious barrier performance and increasing the consistency and transparency of the DOE assessment process. This CBP Software Toolbox predicts the hydraulic properties and chemical stability of cement matrix phases and release fluxes of constituents, in response to variable boundary conditions. Therefore, the CBP tools are reducing the uncertainty by coupling multiscale and multi-physics processes, including physical-chemical evolution and transport phenomena applied to heterogeneous materials with changing boundary conditions. In addition, the CBP Experimental and Characterization Program has provided test data to support chemical and physical degradation mechanisms for cementitious barriers. These tools have application to low activity waste forms, high level waste tank closure, D&D and entombment of major nuclear facilities, landfill waste acceptance criteria, and in-situ grouting and immobilization of vadose zone contamination. The CBP also provided: 1) a forum for DOE-NRC technical exchange, 2) material characterization to support performance assessment (PA) predictions, 3) uncertainty reduction in PA predictions, 4) base case performance to improve PA predictions, and 5) improvement in understanding and quantification of moisture and contaminant transport used in PAs. Additional CBP accomplishments include: sponsorship of a national test bed workshop to obtain collaboration in establishing the path forward to obtain actual data supporting future predictions of cementitious barrier performance, and participation in an International Atomic Energy Agency (IAEA) Cooperative Research Project on the use of cementitious barriers for low-level radioactive waste treatment and disposal.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Restoration Strategy for Active Distribution Systems Considering Endogenous Uncertainty in Cold Load Pickup

Cold load pickup (CLPU) phenomenon is identified as the persistent power inrush upon a sudden load pickup after an outage. Under the active distribution system (ADS) paradigm, where distributed energy resources (DERs) are extensively installed, the decreased outage duration can induce a strong interdependence between CLPU pattern and load pickup decisions. In this paper, we propose a novel modelling technique to tractably capture the decision-dependent uncertainty (DDU) inherent in the CLPU process. Subsequently, a two-stage stochastic decision-dependent service restoration (SDDSR) model is constructed, where first stage searches for the optimal switching sequences to decide step-wise network topology, and the second stage optimizes the detailed generation schedule of DERs as well as the energization of switchable loads. Further, to tackle the computational burdens introduced by mixed-integer recourse, the progressive hedging algorithm (PHA) is utilized to decompose the original model into scenario-wise subproblems that can be solved in parallel. The numerical test on modified IEEE 123-node test feeders has verified the efficiency of our proposed SDDSR model and provided fresh insights into the monetary and secure values of DDU quantification.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2013

On quantum Rényi entropies: A new generalization and some properties

The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data-processing inequalities, a duality relation, and an entropic uncertainty relation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Validation of the Community Land Model Version 5 over the Contiguous United States (CONUS) using in situ and remote sensing data sets

The Community Land Model (CLM) is an effective tool to simulate the biophysical and biogeochemical processes and their interactions with the atmosphere. Although CLM Version 5 (CLM5) constitutes various updates in these processes, its performance in simulating energy, water and carbon cycles over the Contiguous United States (CONUS) at scales which land surface changes and hydrometeorological and hydroclimatological applications are more locally relevant is yet to be assessed. In this study, we conducted three simulations at 0.125? during 1979-2018 over the CONUS using different configurations of CLM, namely CLM5-biogeochemistry (CLM5BGC), CLM4.5BGC, and CLM5-satellite phenology (CLM5SP). We validated and compared their simulations against multiple remote-sensed and in-situ datasets. Overall, the parametric and structural updates (e.g., carbon cost for nitrogen uptake, variable soil thickness, dry surface layer) in CLM5 improve its ability in capturing terrestrial biogeochemical dynamics. The low evapotranspiration in CLM5BGC is associated with biases in simulating vegetation phenological characteristics rather than soil water limitations. The mismatch between CLM5BGC-simulated peak leaf area index and reference data can be attributed to CLM5BGC's inability in simulating phenology of trees and grasses. The differences between CLM-simulated irrigation and reference estimates can be attributed to differences between processes represented in models and in reality, and uncertainties in input and validation datasets. Evaluation against observations at small catchments suggest that hydrologic parameters needed to be calibrated to improve simulations of runoff, especially subsurface runoff. Additional efforts are needed to incorporate spatially-distributed plant phenology and physiology parameters and regional-specific agricultural management practices (e.g., planting, harvest).

Cheng, Yanyan↗

DOE OSTI2023

Sister Rod Destructive Examinations (FY23) Appendix F3: Uncertainty and Conservative Bias in the Cyclic Integrated Reversible-Bending Fatigue Test

The development and application of the Cyclic Integrated Reversible-Bending Fatigue Tester (CIRFT) has been documented over the past 10 years. The CIRFT system was developed in collaboration with the U.S. Nuclear Regulatory Commission (NRC) to address the concern that high-burnup fuel rod fatigue performance was degraded compared to cladding-only behavior. Fatigue data measured by CIRFT on high-burnup fuel rods were then used by the NRC to develop a fatigue response curve for pressurized water reactor fuel rods with Zircaloy-4 cladding in NUREG-2224. Subsequently, CIRFT has been used in the sister rod project to test whether reoriented hydrides associated with vacuum drying influenced the fatigue lifetime, to extend the fatigue testing database to include fuel rods with ZIRLO cladding, and to add to the experience on both Zircaloy-4 and M5 cladding. These data will be used as a reference for subsequent characterization of fuel rods removed from the high-burnup demonstration cask to better understand the effects of long-term dry storage, which can be thought of as a multiyear elevated temperature anneal. The objective of fatigue testing is to provide data that can be used to develop a best-estimate fatigue curve and a conservative fatigue design curve that accounts for uncertainty and can be compared with actual transportation conditions. The process for defining a design fatigue curve for commercial used fuel rods was developed by Oak Ridge National Laboratory (ORNL) in FY22. One issue noted in the fatigue evaluation was that the calculated combined uncertainty in the strain amplitude values determined from the measured data was large. It was proposed then to directly measure the uncertainty in the strain amplitude to either validate the calculated combined uncertainty or update the uncertainty based on the measurement data. Thus, the purpose of this appendix is to document the measured uncertainty in the strain amplitude data. In the process, it was determined that there has been a conservative bias in the calculated strain amplitude that is small enough to be within the measurement uncertainty. This observation is discussed herein, and a case is made to continue to include the conservative bias in the data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Can machine learning accelerate process understanding and decision‐relevant predictions of river water quality?

Abstract The global decline of water quality in rivers and streams has resulted in a pressing need to design new watershed management strategies. Water quality can be affected by multiple stressors including population growth, land use change, global warming, and extreme events, with repercussions on human and ecosystem health. A scientific understanding of factors affecting riverine water quality and predictions at local to regional scales, and at sub‐daily to decadal timescales are needed for optimal management of watersheds and river basins. Here, we discuss how machine learning (ML) can enable development of more accurate, computationally tractable, and scalable models for analysis and predictions of river water quality. We review relevant state‐of‐the art applications of ML for water quality models and discuss opportunities to improve the use of ML with emerging computational and mathematical methods for model selection, hyperparameter optimization, incorporating process knowledge into ML models, improving explainablity, uncertainty quantification, and model‐data integration. We then present considerations for using ML to address water quality problems given their scale and complexity, available data and computational resources, and stakeholder needs. When combined with decades of process understanding, interdisciplinary advances in knowledge‐guided ML, information theory, data integration, and analytics can help address fundamental science questions and enable decision‐relevant predictions of riverine water quality.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2004

NASA GEOS-3/TRMM Re-analysis: Capturing Observed Tropical Rainfall Variability in Global Analysis for Climate Research

Understanding climate variability over a wide range of space-time scales requires a comprehensive description of the earth system. Global analyses produced by a fixed assimilation system (i.e., re-analyses) - as their quality continues to improve - have the potential of providing a vital tool for meeting this challenge. But at the present time, the usefulness of re-analyses is limited by uncertainties in such basic fields as clouds, precipitation, and evaporation - especially in the tropics, where observations are relatively sparse. Analyses of the tropics have long been shown to be sensitive to. the treatment of cloud precipitation processes, which remains a major source of uncertainty in current models. Yet, for many climate studies it is crucial that analyses can accurately reproduce the observed rainfall intensity and variability since a small error of 1 mm/d in surface rain translates into an error of approx. 30 W/sq m in energy (latent heat) flux. Currently, discrepancies between the observed and analyzed monthly-mean rain rates averaged to 100 km x 100 km resolution can exceed 4 mm/d (or 120 W/sq m ), compared to uncertainties in surface radiative fluxes of approx. 10-20 W/sq m . Improving precipitation in analyses would reduce a major source of uncertainty in the global energy budget. Uncertainties in tropical precipitation have also been a major impediment in understanding how the tropics interact with other regions, including the remote response to El Nino/Southern Oscillation (ENSO) variability on interannual time scales, the influence of Madden-Julian Oscillation (MJO) and monsoons on intraseasonal time scales. A global analysis that can replicate the observed precipitation variability together with physically consistent estimates of other atmospheric variables provides the key to breaking this roadblock. NASA Goddard Space Flight Center has been exploring the use of satellite-based microwave rainfall measurements in improving global analyses and has recently produced a multi-year, 1 x 1 TRMM re-analysis , which assimilates 6-hourly TMI and SSM/I surface rain rates over tropical oceans using a ID variational continuous assimilation (VCA) procedure in the GEOS-3 global data assimilation system. The analysis period extends from 1 November 1997 through 3 1 December 2002. The goal is to produce a multi-year global analysis that is dynamically consistent with available tropical precipitation observations for the community to assess its utility in climate applications and identify areas for further improvements. A distinct feature of the GEOS-3RRMh4 re-analysis is that its precipitation analysis is not derived from a short-term forecast (as done in most operational systems) but is given by a time- continuous model integration constrained by precipitation observations within a 6-h analysis window, while the wind, temperature, and pressure fields are allowed to directly respond to the improved precipitation and associated latent heating structures within the same analysis window. In this talk, I will assess the impact VCA precipitation assimilation on analyses of climate signals ranging from a few weeks to interannual time scales and compare results against other operational and reanalysis products.

Hou, Arthur Y.↗

NASA NTRS2014

Uncertainty in Agricultural Impact Assessment

This chapter considers issues concerning uncertainty associated with modeling and its use within agricultural impact assessments. Information about uncertainty is important for those who develop assessment methods, since that information indicates the need for, and the possibility of, improvement of the methods and databases. Such information also allows one to compare alternative methods. Information about the sources of uncertainties is an aid in prioritizing further work on the impact assessment method. Uncertainty information is also necessary for those who apply assessment methods, e.g., for projecting climate change impacts on agricultural production and for stakeholders who want to use the results as part of a decision-making process (e.g., for adaptation planning). For them, uncertainty information indicates the degree of confidence they can place in the simulated results. Quantification of uncertainty also provides stakeholders with an important guideline for making decisions that are robust across the known uncertainties. Thus, uncertainty information is important for any decision based on impact assessment. Ultimately, we are interested in knowledge about uncertainty so that information can be used to achieve positive outcomes from agricultural modeling and impact assessment.

damage assessment↗

DOE OSTI2020

Electron ionization via dark matter-electron scattering and the Migdal effect

There are currently several existing and proposed experiments designed to probe sub-GeV dark matter (DM) using electron ionization in various materials. The projected signal rates for these experiments assume that this ionization yield arises only from DM scattering directly off electron targets, ignoring secondary ionization contributions from DM scattering off nuclear targets. We investigate the validity of this assumption and show that if sub-GeV DM couples with comparable strength to both protons and electrons, as would be the case for a dark photon mediator, the ionization signal from atomic scattering via the Migdal effect scales with the atomic number Z and 3-momentum transfer q as Z 2 q 2 . The result is that the Migdal effect is always subdominant to electron scattering when the mediator is light, but that Migdal-induced ionization can dominate over electron scattering for heavy mediators and DM masses in the hundreds of MeV range. We put these two ionization processes on identical theoretical footing, address some theoretical uncertainties in the choice of atomic wave functions used to compute rates, and discuss the implications for DM scenarios where the Migdal process dominates, including for XENON10, XENON100, and the recent XENON1T results on light DM scattering.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Assessing variability of wind speed: comparison and validation of 27 methodologies

Because wind resources vary from year to year, the intermonthly and interannual variability (IAV) of wind speed is a key component of the overall uncertainty in the wind resource assessment process, thereby creating challenges for wind farm operators and owners. We present a critical assessment of several common approaches for calculating variability by applying each of the methods to the same 37-year monthly wind-speed and energy-production time series to highlight the differences between these methods. We then assess the accuracy of the variability calculations by correlating the wind-speed variability estimates to the variabilities of actual wind farm energy production. We recommend the robust coefficient of variation (RCoV) for systematically estimating variability, and we underscore its advantages as well as the importance of using a statistically robust and resistant method. Using normalized spread metrics, including RCoV, high variability of monthly mean wind speeds at a location effectively denotes strong fluctuations of monthly total energy generation, and vice versa. Meanwhile, the wind-speed IAVs computed with annual-mean data fail to adequately represent energy-production IAVs of wind farms. Finally, we find that estimates of energy-generation variability require 10±3 years of monthly mean wind-speed records to achieve a 90 % statistical confidence. This paper also provides guidance on the spatial distribution of wind-speed RCoV.

17 WIND ENERGY↗

DOE OSTI2014

Computational solution verification and validation applied to a thermal model of a ruggedized instrumentation package

This study details a methodology for quantification of errors and uncertainties of a finite element heat transfer model applied to a Ruggedized Instrumentation Package (RIP). The proposed verification and validation (V&V) process includes solution verification to examine errors associated with the code's solution techniques, and model validation to assess the model's predictive capability for quantities of interest. The model was subjected to mesh resolution and numerical parameters sensitivity studies to determine reasonable parameter values and to understand how they change the overall model response and performance criteria. To facilitate quantification of the uncertainty associated with the mesh, automatic meshing and mesh refining/coarsening algorithms were created and implemented on the complex geometry of the RIP. Automated software to vary model inputs was also developed to determine the solution’s sensitivity to numerical and physical parameters. The model was compared with an experiment to demonstrate its accuracy and determine the importance of both modelled and unmodelled physics in quantifying the results' uncertainty. An emphasis is placed on automating the V&V process to enable uncertainty quantification within tight development schedules.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

Survival of carbon grains in shocks

Supernova shocks play a significant part in the life of an interstellar grain. In a typical 10 to the 9th power year lifetime, a grain will be hit by an average of 10 shocks of 100 km s(sup -1) or greater velocity, and even more shocks of lower velocity. Evaluation of the results of this frequent shock processing is complicated by a number of uncertainties, but seems to give about 10 percent destruction of silicate grains and about half that for graphite grains. Because of the frequency of shocking, the mineralogy and sizes of the grain population is predominately determined by shock processing effects, and not by the initial grain nucleation and growth environment. One consequence of the significant role played by interstellar shocks is that a certain fraction (up to 5 percent) of the carbon should be transformed into the diamond phase. Diamond transformation is observed in the laboratory at threshold shock pressures easily obtainable in grain-grain collisions in supernova shocks. Yields for transforming graphite, amorphous carbon, glassy carbon, and other nearly pure carbon solids into diamond are quite high. Impurities up to at least the 10 percent level (for oxygen) are tolerated in the process. The typical size diamond expected from shock transformation agrees well with the observed sizes in the Lewis et al. findings in meteoritic material. Isotropic anomalies already contained in the grain are likely to be retained through the conversion process, while others may be implanted by the shock if the grain is close to the supernova. The meteoritic diamonds are likely to be the results of transformation of carbon grains in grain-grain collisions in supernova shock waves.

Seab, C. Gregory↗

NASA NTRSDate not supplied

From Formal Errors Towards Realistic Uncertainties

Evaluation of uncertainties of geodetic parameter estimates is the problem that is not yet solved in a satisfactory way. A direct evaluation of the uncertainties derived from a least square solution is labeled "formal" and is usually biased, sometimes up to an order of magnitude. Customary, the use of formal errors for scientific analysis is discouraged. We claim that the root of the problem is neglecting off-diagonal elements in the variance-covariance matrix of the noise in the data. A careful reconstruction of the full variance-covariance matrix, including the off-diagonal terms greatly improves realism of uncertainty estimates derived from least squares. We processed the dataset of VLBI group delays and built a prior variance-covariance of the atmosphere-driven noise based on analysis of the output of NASA high-resolution numerical weather models. We found that the uncertainties of parameter estimates derived from this least square solution that uses such variance-covariance matrices become much closer to realistic errors. We consider approaches for implementation of this method in routine data analysis of space geodesy data.

Leonid Petrov↗