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DOE OSTI2021

Developing High-Resolution Constrained Variational Analysis of Vertical Velocity and Advective Tendencies within the Range of ARM Scanning Radars at the SGP

Research progress has been made in two areas. One is about the incorporation of the ARM variationally constrained objective analysis method into the WRF GSI data assimilation system. The other is the development of high resolution ARM data and its applications. Specially, we developed a new data assimilation algorithm by adding dynamical constraints to the WRF GSI data assimilation system using hybrid ensemble variational system to derive 3-D fields of atmospheric dynamics and thermodynamics over the ARM SGP sites. We also developed 4x4 km high-resolution constrained variational analysis data over the SGP during the PECAN and made them available to the community. Details are in the attached report.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Development of a Framework for Data Integration, Assimilation, and Learning for Geological Carbon Sequestration (DIAL-GCS) (Final Report)

This project aimed to develop and demonstrate a Data Integration, Assimilation, and Learning framework for geologic carbon sequestration projects (DIAL-GCS). DIAL-GCS is an intelligence monitoring system (IMS) for automating GCS closed-loop management by leveraging recent developments in machine learning technologies, complex event processing (CEP), and reduced-order modeling. The safe and efficient operation of GCS repositories requires integrated monitoring to track the injected CO¬2 as it moves within a storage reservoir. GCS projects are data intensive, as a result of proliferation of digital instrumentation and smart-sensing technologies. GCS projects are also resource intensive, often requiring multidisciplinary teams performing different monitoring, verification, accounting (MVA) tasks throughout the lifecycle of a project to ensure secure containment of injected CO2. The success of GCS thus depends in a large part on our ability to access, assimilate, and analyze heterogeneous data and information sources in a timely manner. This project included a number of meaningful and necessary tasks to transform the human domain knowledge into machine-interpretable rules for automating knowledge extraction and discovery in GCS. The specific technical objectives of the proposed DIAL-GCS project were to develop an ontology-driven GCS data management module for storing, querying, and exchanging GCS data (both historic and live sensor data) from multiple sources and in heterogeneous formats. Incorporate a CEP engine for detecting abnormal situations by seamlessly combining expert knowledge, rule-based reasoning, and machine learning. Enable uncertainty quantification and predictive analytics using a combination of coupled-process modeling, AI/ML methods, and reduced-order modeling, and integrate and demonstrate the system’s capabilities with both real and simulated data. As far as we know, this is one of the first projects aimed to develop intelligent monitoring systems (IMS) targeting the GCS. Under this project, the team had developed a large number of web applications and scientific algorithms that contribute the main theme of intelligent monitoring. The team has published more than a dozen peer reviewed papers and disseminated the research results at multiple technical meetings.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2025

Preliminary Results on Bayesian Inverse UQ for OECD/NEA WPNCS Subgroup 14 Benchmark Exercise for Error Recovery and Experimental Coverage

The Organization for Economic Cooperation and Development (OECD) Working Party on Nucelar Criticality Safety (WPNCS) has proposed a benchmark exercise representative of neutronic behavior in criticality experiments. Here, the goal is to develop confidence in data assimilation techniques used to adjust nuclear data. Participants are given synthetic experimental models with associated measured data and asked to estimate the model parameters given the model and measurements as well as provide predictions for separate application models. In this work, we performed data assimilation using Bayesian inverse Uncertainty Quantification (UQ) with machine learning surrogate models to produce posterior parameter distributions for the requested parameters and posterior predictive distributions for the requested responses. Several experimental models are shown to insufficiently inform the posterior parameter distributions for the applications involved. However, given sufficient experimental data, posterior parameter estimates yielded reduced uncertainty in the response predictions of interest while covering the experimental data.

Bayesian Inference↗

NASA NTRS2004

Inner Radiation Belt Representation of the Energetic Electron Environment: Model and Data Synthesis Using the Salammbo Radiation Belt Transport Code and Los Alamos Geosynchronous and GPS Energetic Particle Data

The highly energetic electron environment in the inner magnetosphere (GEO inward) has received a lot of research attention in resent years, as the dynamics of relativistic electron acceleration and transport are not yet fully understood. These electrons can cause deep dielectric charging in any space hardware in the MEO to GEO region. We use a new and novel approach to obtain a global representation of the inner magnetospheric energetic electron environment, which can reproduce the absolute environment (flux) for any spacecraft orbit in that region to within a factor of 2 for the energy range of 100 KeV to 5 MeV electrons, for any levels of magnetospheric activity. We combine the extensive set of inner magnetospheric energetic electron observations available at Los Alamos with the physics based Salammbo transport code, using the data assimilation technique of "nudging". This in effect input in-situ data into the code and allows the diffusion mechanisms in the code to interpolate the data into regions and times of no data availability. We present here details of the methods used, both in the data assimilation process and in the necessary inter-calibration of the input data used. We will present sample runs of the model/data code and compare the results to test spacecraft data not used in the data assimilation process.

Friedel, R. H. W.↗

NASA NTRS1998

Comparison of Surface Ground Temperature from Satellite Observations and the Off-Line Land Surface GEOS Assimilation System

The surface ground temperature (Tg) is an important meteorological variable, because it represents an integrated thermal state of the land surface determined by a complex surface energy budget. Furthermore, Tg affects both the surface sensible and latent heat fluxes. Through these fluxes. the surface budget is coupled with the atmosphere above. Accurate Tg data are useful for estimating the surface radiation budget and fluxes, as well as soil moisture. Tg is not included in conventional synoptical weather station reports. Currently, satellites provide Tg estimates globally. It is necessary to carefully consider appropriate methods of using these satellite data in a data assimilation system. Recently, an Off-line Land surface GEOS Assimilation (OLGA) system was implemented at the Data Assimilation Office at NASA-GSFC. One of the goals of OLGA is to assimilate satellite-derived Tg data. Prior to the Tg assimilation, a thorough investigation of satellite- and model-derived Tg, including error estimates, is required. In this study we examine the Tg from the n Project (ISCCP DI) data and the OLGA simulations. The ISCCP data used here are 3-hourly DI data (2.5x2.5 degree resolution) for 1992 summer months (June, July, and August) and winter months (January and February). The model Tg for the same periods were generated by OLGA. The forcing data for this OLGA 1992 simulation were generated from the GEOS-1 Data Assimilation System (DAS) at Data Assimilation Office NASA-GSFC. We examine the discrepancies between ISCCP and OLGA Tg with a focus on its spatial and temporal characteristics, particularly on the diurnal cycle. The error statistics in both data sets, including bias, will be estimated. The impact of surface properties, including vegetation cover and type, topography, etc, on the discrepancies will be addressed.

Yang, R.↗

NASA NTRS1998

Variations in Atmospheric Water Vapor as Seen in Satellite Data and Model Reanalysis Fields

New data sets used to describe components of the hydrologic and energy cycles of the Earth system are currently being produced and disseminated through the NASA EOS DAACs and several data assimilation centers supported by such organizations as NASA and NOAA. These data sets incorporate hybrid data analysis schemes and portray satellite and radiosonde data combined in a diagnostic sense and in a forecast mode. There is a need to develop a better understanding of the accuracy and utility of these global, relatively long-term, datasets to describe components of the hydrologic cycle and to understand atmospheric moisture variability and its relation to climatological significant events Much progress has been made in the last ten years in the development of global atmospheric models and analysis of satellite data for global studies. The atmospheric models have improved in their ability to predict both short term and longer term weather events. This has been possible through better understanding of atmosphere dynamics and very rapid advances in computer technology. Over the same period, data assimilation methods have advanced and unconventional data sources such as aircraft and satellite data, drifting buoys, etc., can be assimilated at non-synaptic times. As a result of these improvements, comprehensive global atmospheric fields based on four-dimensional data assimilation methods now provide one of the most reliable methods for studying dynamical and physical behavior in the atmosphere.

Jedlovec, Gary J.↗

NASA NTRS2001

The Impact of British Airways Wind Observations on the Goddard Earth Observing System Analyses and Forecasts

British Airways flight data recorders can provide valuable meteorological information, but they are not available in real-time on the Global Telecommunication System. Information from the flight recorders was used in the Global Aircraft Data Set (GADS) experiment as independent observations to estimate errors in wind analyses produced by major operational centers. The GADS impact on the Goddard Earth Observing System Data Assimilation System (GEOS DAS) analyses was investigated using GEOS-1 DAS version. Recently, a new Data Assimilation System (fvDAS) has been developed at the Data Assimilation Office, NASA Goddard. Using fvDAS , the, GADS impact on analyses and forecasts was investigated. It was shown the GADS data intensify wind speed analyses of jet streams for some cases. Five-day forecast anomaly correlations and root mean squares were calculated for 300, 500 hPa and SLP for six different areas: Northern and Southern Hemispheres, North America, Europe, Asia, USA These scores were obtained as averages over 21 forecasts from January 1998. Comparisons with scores for control experiments without GADS showed a positive impact of the GADS data on forecasts beyond 2-3 days for all levels at the most areas.

Rukhovets, Leonid↗

NASA NTRS2017

Early Estimation of Solar Activity Cycle: Potential Capability and Limits

The variable solar magnetic activity known as the 11-year solar cycle has the longest history of solar observations. These cycles dramatically affect conditions in the heliosphere and the Earth's space environment. Our current understanding of the physical processes that make up global solar dynamics and the dynamo that generates the magnetic fields is sketchy, resulting in unrealistic descriptions in theoretical and numerical models of the solar cycles. The absence of long-term observations of solar interior dynamics and photospheric magnetic fields hinders development of accurate dynamo models and their calibration. In such situations, mathematical data assimilation methods provide an optimal approach for combining the available observational data and their uncertainties with theoretical models in order to estimate the state of the solar dynamo and predict future cycles. In this presentation, we will discuss the implementation and performance of an Ensemble Kalman Filter data assimilation method based on the Parker migratory dynamo model, complemented by the equation of magnetic helicity conservation and longterm sunspot data series. This approach has allowed us to reproduce the general properties of solar cycles and has already demonstrated a good predictive capability for the current cycle, 24. We will discuss further development of this approach, which includes a more sophisticated dynamo model, synoptic magnetogram data, and employs the DART Data Assimilation Research Testbed.

Kitiashvili, Irina N.↗

NASA NTRS2023

Assimilation of Blended Satellite Soil Moisture Data Products to Further Improve Noah-MP Model Skills

Microwave satellite remote sensing has enabled observations of soil moisture (SM) at the global scale, and multiple SM data products have been developed in the past decades. However, single-sensor-based measurements are insufficient for continuous spatiotemporal coverage. In the context of its climate program, the Climate Change Initiative, the European Space Agency (ESA) has developed robust, long term, global scale, multi instrument satellite derived time series of climate data record for key component of the climate system, including soil moisture (CCI), while the Soil Moisture Operational Product System (SMOPS) was specifically developed by National Oceanic and Atmospheric Administration (NOAA) to offer the real time blended SM datasets through merging all available individual products. Before combining, all individual SM data ingested into both SMOPS and CCI blended products are scaled to Global Land Data Assimilation System (GLDAS) 0-10 cm SM climatology. Benefiting from land surface model evolution and the availability of high-quality forcing data, GLDAS has become more comprehensive to track SM changes and dynamic trends. The development of GLDAS and the scaling procedure in CCI and SMOPS leave an open scientific and operational question: do the blended satellite SM data products have added value comparing to the GLDAS product? This study clearly reveals that both CCI and SMOPS can provide the reliable SM observations with independent information, although their climatology matches well with GLDAS. Relative to assimilation of GLDAS 0-10 cm SM data, Noah-MP model can be further improved by assimilating the blended satellite SM observations with respect to the quality-controlled in situ measurements. The strong consistency of results presented in this paper proves that the blended satellite SM data products are more useful than the GLDAS product in terms of improving Noah-MP model performance.

Jifu Yin↗

NASA NTRS2015

Explore GPM IMERG and Other Global Precipitation Products with GES DISC GIOVANNI

New features and capabilities in the newly released GIOVANNI allow exploring GPM IMERG (Integrated Multi-satelliE Retrievals for GPM) Early, Late and Final Run global half-hourly and monthly precipitation products as well as other precipitation products distributed by the GES DISC such as TRMM Multi-Satellite Precipitation Analysis (TMPA), MERRA (Modern Era Retrospective-Analysis for Research and Applications), NLDAS (North American Land Data Assimilation Systems), GLDAS (Global Land Data Assimilation Systems), etc. GIOVANNI is a web-based tool developed by the GES DISC (Goddard Earth Sciences and Data Information Services Center) to visualize and analyze Earth science data without having to download data and software. The new interface in GIOVANNI allows searching and filtering precipitation products from different NASA missions and projects and expands the capabilities to inter-compare different precipitation products in one interface. Knowing differences in precipitation products is important to identify issues in retrieval algorithms, biases, uncertainties, etc. Due to different formats, data structures, units and so on, it is not easy to inter-compare precipitation products. Newly added features and capabilities (unit conversion, regridding, etc.) in GIOVANNI make inter-comparisons possible. In this presentation, we will describe these new features and capabilities along with examples.

Giovanni↗

NASA NTRS2018

An Overview of the TROPICS NASA Earth Venture Mission

The Time-Resolved Observations of Precipitation structure and storm Intensity with a Constellation of Smallsats (TROPICS) mission was selected by NASA as part of the Earth Venture-Instrument (EVI-3) program. The overarching goal for TROPICS is to provide nearly all-weather observations of 3D temperature and humidity, as well as cloud ice and precipitation horizontal structure, at high temporal resolution to conduct high-value science investigations of tropical cyclones. TROPICS will provide rapid-refresh microwave measurements (median refresh rate better than 60 min for the baseline mission) which can be used to observe the thermodynamics of the troposphere and precipitation structure for storm systems at the mesoscale and synoptic scale over the entire storm life cycle. TROPICS comprises six Cube-Sats in three low-Earth orbital planes. Each CubeSat will host a high-performance radiometer to provide temperature profiles using seven channels near the 118.75 GHz oxygen absorption line, water vapour profiles using three channels near the 183 GHz water vapour absorption line, imagery in a single channel near 90 GHz for precipitation measurements (when combined with higher-resolution water vapour channels), and a single channel near 205 GHz which is more sensitive to precipitation-sized ice particles. This observing system offers an unprecedented combination of horizontal and temporal resolution to measure environmental and inner-core conditions for tropical cyclones on a nearly global scale and is a major leap forward in the temporal resolution of several key parameters needed for assimilation into advanced data assimilation systems capable of utilizing rapid-update radiance or retrieval data.Launch readiness is currently projected for late 2019.

TROPICS↗

NASA NTRS1999

Impact of TRMM and SSM/I-derived Precipitation and Moisture Data on the GEOS Global Analysis

Current global analyses contain significant errors in primary hydrological fields such as precipitation, evaporation, and related cloud and moisture in the tropics. The Data Assimilation Office at NASA's Goddard Space Flight Center has been exploring the use of space-based rainfall and total precipitable water (TPW) estimates to constrain these hydrological parameters in the Goddard Earth Observing System (GEOS) global data assimilation system. We present results showing that assimilating the 6-hour averaged rain rates and TPW estimates from the Tropical Rainfall Measuring Mission (TRMM) and Special Sensor Microwave/Imager (SSM/I) instruments improves not only the precipitation and moisture estimates but also reduce state-dependent systematic errors in key climate parameters directly linked to convection such as the outgoing longwave radiation, clouds, and the large-scale circulation. The improved analysis also improves short-range forecasts beyond 1 day, but the impact is relatively modest compared with improvements in the time-averaged analysis. The study shows that, in the presence of biases and other errors of the forecast model, improving the short-range forecast is not necessarily prerequisite for improving the assimilation as a climate data set. The full impact of a given type of observation on the assimilated data set should not be measured solely in terms of forecast skills.

Hou, Arthur Y.↗

NASA NTRSDate not supplied

Early Comparison of Ocean Analyses Using JEDI/SOCA 3 DVar vs. GEOS-S2S- 3 ODAS LETKF

At NASA’s Global Modeling and Assimilation Office (GMAO), data assimilation (DA) for the next-generation Goddard Earth Observing System Subseasonal-to-Seasonal (GEOS-S 2 S) coupled-model forecast system will transition to the Joint Effort for DA Integration (JEDI) system, which includes the marine DA component SOCA (Sea ice, Ocean, and Coupled Assimilation). It is envisioned that incorporating SOCA into GMAO Earth System Modeling will allow a more systematic approach to assimilating new data types (e.g., SWOT KaRIn), increasing resolution (e.g., 1/12°), and facilitating weakly (and eventually strongly) coupled DA (air-sea-ice, etc.). To prepare for this transition, testing is underway to compare SOCA results at high ocean resolution against the current GEOS-S 2 S Version 3 Ocean DA System (ODAS) 1 using similar initial conditions and observations.

David Russell↗

NASA NTRS2012

Inferring Land Surface Model Parameters for the Assimilation of Satellite-Based L-Band Brightness Temperature Observations into a Soil Moisture Analysis System

The Soil Moisture and Ocean Salinity (SMOS) satellite mission provides global measurements of L-band brightness temperatures at horizontal and vertical polarization and a variety of incidence angles that are sensitive to moisture and temperature conditions in the top few centimeters of the soil. These L-band observations can therefore be assimilated into a land surface model to obtain surface and root zone soil moisture estimates. As part of the observation operator, such an assimilation system requires a radiative transfer model (RTM) that converts geophysical fields (including soil moisture and soil temperature) into modeled L-band brightness temperatures. At the global scale, the RTM parameters and the climatological soil moisture conditions are still poorly known. Using look-up tables from the literature to estimate the RTM parameters usually results in modeled L-band brightness temperatures that are strongly biased against the SMOS observations, with biases varying regionally and seasonally. Such biases must be addressed within the land data assimilation system. In this presentation, the estimation of the RTM parameters is discussed for the NASA GEOS-5 land data assimilation system, which is based on the ensemble Kalman filter (EnKF) and the Catchment land surface model. In the GEOS-5 land data assimilation system, soil moisture and brightness temperature biases are addressed in three stages. First, the global soil properties and soil hydraulic parameters that are used in the Catchment model were revised to minimize the bias in the modeled soil moisture, as verified against available in situ soil moisture measurements. Second, key parameters of the "tau-omega" RTM were calibrated prior to data assimilation using an objective function that minimizes the climatological differences between the modeled L-band brightness temperatures and the corresponding SMOS observations. Calibrated parameters include soil roughness parameters, vegetation structure parameters, and the single scattering albedo. After this climatological calibration, the modeling system can provide L-band brightness temperatures with a global mean absolute bias of less than 10K against SMOS observations, across multiple incidence angles and for horizontal and vertical polarization. Third, seasonal and regional variations in the residual biases are addressed by estimating the vegetation optical depth through state augmentation during the assimilation of the L-band brightness temperatures. This strategy, tested here with SMOS data, is part of the baseline approach for the Level 4 Surface and Root Zone Soil Moisture data product from the planned Soil Moisture Active Passive (SMAP) satellite mission.

Reichle, Rolf H.↗

NASA NTRS2013

Assessment and Applications of NASA Ozone Data Products Derived from Aura OMI-MLS Satellite Measurements in Context of the GMI Chemical Transport Model

Measurements from the Ozone Monitoring Instrument (OMI) and Microwave Limb Sounder (MLS), both onboard the Aura spacecraft, have been used to produce daily global maps of column and profile ozone since August 2004. Here we compare and evaluate three strategies to obtain daily maps of tropospheric and stratospheric ozone from OMI and MLS measurements: trajectory mapping, direct profile retrieval, and data assimilation. Evaluation is based upon an assessment that includes validation using ozonesondes and comparisons with the Global Modeling Initiative (GMI) chemical transport model (CTM). We investigate applications of the three ozone data products from near-decadal and inter-annual timescales to day-to-day case studies. Zonally averaged inter-annual changes in tropospheric ozone from all of the products in any latitude range are of the order 1-2 Dobson Units while changes (increases) over the 8-year Aura record investigated http://eospso.gsfc.nasa.gov/atbd-category/49 vary approximately 2-4 Dobson Units. It is demonstrated that all of the ozone products can measure and monitor exceptional tropospheric ozone events including major forest fire and pollution transport events. Stratospheric ozone during the Aura record has several anomalous inter-annual events including stratospheric warming split events in the Northern Hemisphere extra-tropics that are well captured using the data assimilation ozone profile product. Data assimilation with continuous daily global coverage and vertical ozone profile information is the best of the three strategies at generating a global tropospheric and stratospheric ozone product for science applications.

GMI↗

NASA NTRS2004

Multivariate Error Covariance Estimates by Monte-Carlo Simulation for Assimilation Studies in the Pacific Ocean

One of the most difficult aspects of ocean state estimation is the prescription of the model forecast error covariances. The paucity of ocean observations limits our ability to estimate the covariance structures from model-observation differences. In most practical applications, simple covariances are usually prescribed. Rarely are cross-covariances between different model variables used. Here a comparison is made between a univariate Optimal Interpolation (UOI) scheme and a multivariate OI algorithm (MvOI) in the assimilation of ocean temperature. In the UOI case only temperature is updated using a Gaussian covariance function and in the MvOI salinity, zonal and meridional velocities as well as temperature, are updated using an empirically estimated multivariate covariance matrix. Earlier studies have shown that a univariate OI has a detrimental effect on the salinity and velocity fields of the model. Apparently, in a sequential framework it is important to analyze temperature and salinity together. For the MvOI an estimation of the model error statistics is made by Monte-Carlo techniques from an ensemble of model integrations. An important advantage of using an ensemble of ocean states is that it provides a natural way to estimate cross-covariances between the fields of different physical variables constituting the model state vector, at the same time incorporating the model's dynamical and thermodynamical constraints as well as the effects of physical boundaries. Only temperature observations from the Tropical Atmosphere-Ocean array have been assimilated in this study. In order to investigate the efficacy of the multivariate scheme two data assimilation experiments are validated with a large independent set of recently published subsurface observations of salinity, zonal velocity and temperature. For reference, a third control run with no data assimilation is used to check how the data assimilation affects systematic model errors. While the performance of the UOI and MvOI is similar with respect to the temperature field, the salinity and velocity fields are greatly improved when multivariate correction is used, as evident from the analyses of the rms differences of these fields and independent observations. The MvOI assimilation is found to improve upon the control run in generating the water masses with properties close to the observed, while the UOI failed to maintain the temperature and salinity structure.

Borovikov, Anna↗

NASA NTRS2000

The Global Precipitation Mission

The Global Precipitation Mission (GPM), expected to begin around 2006, is a follow-up to the Tropical Rainfall Measuring Mission (TRMM). Unlike TRMM, which primarily samples the tropics, GPM will sample both the tropics and mid-latitudes. The primary, or core, satellite will be a single, enhanced TRMM satellite that can quantify the 3-D spatial distributions of precipitation and its associated latent heat release. The core satellite will be complemented by a constellation of very small and inexpensive drones with passive microwave instruments that will sample the rainfall with sufficient frequency to be not only of climate interest, but also have local, short-term impacts by providing global rainfall coverage at approx. 3 h intervals. The data is expected to have substantial impact upon quantitative precipitation estimation/forecasting and data assimilation into global and mesoscale numerical models. Based upon previous studies of rainfall data assimilation, GPM is expected to lead to significant improvements in forecasts of extratropical and tropical cyclones. For example, GPM rainfall data can provide improved initialization of frontal systems over the Pacific and Atlantic Oceans. The purpose of this talk is to provide information about GPM to the USWRP (U.S. Weather Research Program) community and to discuss impacts on quantitative precipitation estimation/forecasting and data assimilation.

Braun, Scott↗

DOE OSTI2022

Physics Informed Neural Networks as Computational Physics Emulators

This report is a brief overview and evaluation of Physics Informed Neural Networks (PINNs). Karniadakis and co-workers, e.g., Karniadakis et al. (2021) assert that the PINNs approach integrates seamlessly both data and mathematical physics models, even in partially understood, uncertain and high-dimensional contexts. They further claim that PINNs are effective and efficient for ill-posed and inverse problems, and when combined with domain decomposition, are scalable to large problems and a tool to discover hidden physics. While they demonstrate the capabilities in specific academic instances, their overarching claims about PINNs seem to be an overstatement, at least at the current time. We have briefly considered a few of the limitations of PINNs in this investigation. It is not clear to us if the PINNs approach can ever be competitive with approaches that use specialized algorithms to achieve high-accuracy solutions of governing equations and other techniques that can combine observational data with such solutions. As an example of the latter, consistent with the principles of Bayesian inference, data assimilation, or more generally data-model fusion, is a process that fuses observational data typically with a computational model that respects certain constraints such as conservation laws. For example, improvements in observational network combined with data assimilation have been key in improving weather predictions over the past four decades Kalnay (2003).

97 MATHEMATICS AND COMPUTING↗