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Improving Boundary Layer Data Assimilation Using Observation Data from Multiple Observing Systems in the NASA GEOS System

The Planetary Boundary Layer (PBL) is a complex interface that mediates energy and moisture exchanges between the Earth’s surface and atmosphere. Accurate simulation and observation of PBL characteristics, such as PBL height and thermodynamic structure, have proven to be a challenge. In our latest efforts, we have focused on improving PBL thermodynamic structure using data from multiple observing systems in the Goddard Earth Observing System (GEOS), developed by the NASA Global Modeling and Assimilation Office (GMAO). We present strategies and results from assimilating PBL height data derived from radiosondes, GNSS radio occultation, space-based lidar (CALIPSO, CATS, IceSat-2), ground-based lidar (MPLNET), and radar wind profilers, including a novel global PBL height analysis dataset. We also discuss the impacts of better representing capping inversions by using PBL height data together with other observations in GEOS through adjustments to the background error covariance. Long-term statistics of the impact of assimilating and utilizing PBL height data in GEOS are presented. In addition, we explore an innovative approach to assimilate GNSS-RO refractivity data in the lower troposphere.

Eun-Gyeong Yang↗
DOE OSTI2024

A Scalable Real-Time Data Assimilation Framework for Predicting Turbulent Atmosphere Dynamics

AI-based foundation models like FourCastNet, GraphCast are revolutionizing weather and climate predictions but are not yet ready for operational use. Their limitation lies in the absence of a data assimilation system to incorporate real-time Earth system observations, crucial for accurately forecasting events like tropical cyclones. To overcome these obstacles, we introduce a generic real-time data assimilation framework and demonstrate its end-to-end performance on the Frontier supercomputer. This framework comprises two primary modules: an ensemble score filter (EnSF), which significantly outperforms the state-of-the-art data assimilation method, and a vision transformer-based surrogate capable of real-time adaptation through the integration of observational data. We demonstrate both the strong and weak scaling of our framework up to 1024 GPUs on the Exascale supercomputer, Frontier. Our results not only illustrate the framework's exceptional scalability on high-performance computing systems, but also demonstrate the importance of supercomputers in real-time data assimilation for weather and climate predictions.

Lu, Dan↗
DOE OSTI2016

Ring current pressure estimation with RAM-SCB using data assimilation and Van Allen Probe flux data

Capturing and subsequently modeling the influence of tail plasma injections on the inner magnetosphere is important for understanding the formation and evolution of the ring current. In this study, the ring current distribution is estimated with the Ring Current–Atmosphere Interactions Model with Self–Consistent Magnetic field (RAM–SCB) using, for the first time, data assimilation techniques and particle flux data from the Van Allen Probes. The state of the ring current within the RAM–SCB model is corrected via an ensemble based data assimilation technique by using proton flux from one of the Van Allen Probes, to capture the enhancement of the ring current following an isolated substorm event on 18 July 2013. The results show significant improvement in the estimation of the ring current particle distributions in the RAM–SCB model, leading to better agreement with observations. Furthermore, this newly implemented data assimilation technique in the global modeling of the ring current thus provides a promising tool to improve the characterization of particle distribution in the near–Earth regions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation

We address the development of innovative algorithms designed to solve the strong-constraint Four Dimensional Variational Data Assimilation (4DVar DA) problems in large scale applications. We present a space-time decomposition approach which employs the whole domain decomposition, i.e. both along the spacial and temporal direction in the overlapping case, and the partitioning of both the solution and the operator. Starting from the global functional defined on the entire domain, we get to a sort of regularized local functionals on the set of sub domains providing the order reduction of both the predictive and the Data Assimilation models. The algorithm convergence is developed. Performance in terms of reduction of time complexity and algorithmic scalability is discussed on the Shallow Water Equations on the sphere. The number of state variables in the model, the number of observations in an assimilation cycle, as well as numerical parameters as the discretization step in time and in space domain are defined on the basis of discretization grid used by data available at repository Ocean Synthesis/Reanalysis Directory of Hamburg University.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A dynamic data-driven method for dealing with model structural error in soil moisture data assimilation

Attributing to the flexibility in considering various types of observation error and model error, data assimilation has been increasingly applied to dynamically improve soil moisture modeling in many hydrological practices. However, accurate characterization of model error, especially the part caused by defective model structure, presents a significant challenge to the successful implementation of data assimilation. Model structural error has received limited attention relative to parameter and input errors, mainly due to our poor understanding of structural inadequacy and the difficulties in parameterizing structural error. In this paper, we present a dynamic data-driven approach to estimate the model structural error in soil moisture data assimilation without the need for identifying error generation mechanism or specifying particular form for the error model. The error model is based on the Gaussian process regression and then integrated into the ensemble Kalman filter (EnKF) to form a hybrid method for dealing with multi-source model errors. Two variants of the hybrid method in terms of two different error correction manners are proposed. The effectiveness of the proposed method is tested through a suit of synthetic cases and a real-world case. Results demonstrate the potential of the proposed hybrid method for estimating model structural error and providing improved model predictions. Compared to the traditional EnKF without explicitly considering the model structural error, parameter compensation issue is obviously reduced and soil moisture retrieval is substantially improved.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Early season prediction of within-field crop yield variability by assimilating CubeSat data into a crop model

Accurate early season predictions of crop yield at the within-field scale can be used to address a range of crop production, management, and precision agricultural challenges. While the remote sensing of within-field insights has been a research goal for many years, it is only recently that observations with the required spatio-temporal resolutions, together with efficient assimilation methods to integrate these into modeling frameworks, have become available to advance yield prediction efforts. Here we explore a yield prediction approach that combines daily high-resolution CubeSat imagery with the APSIM crop model. The approach employs APSIM to train a linear regression that relates simulated yield to simulated leaf area index (LAI). That relationship is then used to identify the optimal regression date at which the LAI provides the best prediction of yield: in this case, approximately 14 weeks prior to harvest. Instead of applying the regression on satellite imagery that is coincident, or closest to, the regression date, our method implements a particle filter that integrates CubeSat-based LAI into APSIM to provide end-of-season high-resolution (3 m) yield maps weeks before the optimal regression date. The approach is demonstrated on a rainfed maize field located in Nebraska, USA, where suitable collections of both imagery and in-situ data were available for assessment. The procedure does not require in-field data to calibrate the regression model, with results showing that even with a single assimilation step, it is possible to provide yield estimates with good accuracy up to 21 days before the optimal regression date. Yield spatial variability was reproduced reasonably well, with a strong correlation to independently collected measurements (R 2 = 0.73 and rRMSE = 12%). When the field averaged yield was compared, our approach reduced yield prediction error from 1 Mg/ha (control case based on a calibrated APSIM model), to 0.5 Mg/ha (using satellite imagery alone), and then to 0.2 Mg/ha (results with assimilation up to three weeks prior to the optimal regression date). Such a capacity to provide spatially explicit yield predictions early in the season has considerable potential to enhance digital agricultural goals and improve end-of-season yield predictions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Data assimilation for combustion ignition delay time simulation using schlieren image velocimetry

This study sought to improve the accuracy of simulating spray penetration and combustion ignition delay by means of data assimilation (DA). The simulations were conducted using the Reynolds-averaged Navier–Stokes (RANS) equations and assimilating the schlieren image data. In DA, an ensemble square root filter (EnSRF) was used to build the statistical model, making the simulation results more accurate without any change in the governing equations. Recognizing that the spray-cone injection angle has a large effect on penetration, we created ensemble members with different injection angles. And we applied the two-component velocity distribution calculated via SIV and updated both velocity and temperature by using a DA statistical model derived from RANS ensemble simulations. The ignition delay time is generally known to vary even under the same experimental conditions because it is influenced by many factors. In this study, we attempted the transient DA-assisted RANS simulation to predict the ignition delay time even when the temporal resolution and accuracy of the observation data ware insufficient. Our trials offer an example of how a combination of techniques can be effectively used to assimilate experimental data obtained under restricted conditions.

Combustion simulation↗
DOE OSTI2022

Using Ensemble Data Assimilation to Estimate Transient Hydrologic Exchange Flow Under Highly Dynamic Flow Conditions

Abstract Quantifying dynamic hydrologic exchange flows (HEFs) within river corridors that experience high‐frequency flow variations caused by dam regulations is important for understanding the biogeochemical processes at the river water and groundwater interfaces. Heat has been widely used as a tracer to infer steady‐state flow velocities through analytical solutions of heat transport defined by the diurnal temperature signals. Under sub‐daily dynamic flow conditions, however, such analytical solutions are not applicable due to the violation of their fundamental assumptions. In this study, we developed a data assimilation‐based approach to estimate the sub‐daily flux under highly dynamic flow conditions using multi‐depth temperature observations at a 5‐min resolution. If the hydraulic gradient is measured, Darcy's law was used to calculate the flux with permeability estimated from temperature responses below the riverbed. Otherwise, flux was estimated directly by assimilating multi‐depth temperature data at 1‐ or 2‐hr time intervals assuming one‐dimensional flow and heat transport governing equation. By comparing estimated fluxes with model‐generated synthetic truth, we demonstrated that both schemes have robust performance in estimating fluxes under highly dynamic flow conditions. This data assimilation‐based flux estimation method was able to capture the vertical sub‐daily fluxes using multi‐depth high‐resolution temperature data alone, even in the presence of multi‐dimensional flow. This approach has been successfully applied to real field temperature data collected at the Hanford site, which experiences highly dynamic HEFs. Our study shows the promise of adopting distributed 1‐D temperature monitoring to capture spatial and temporal exchange dynamics in river corridors at a watershed scale or beyond.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Quantifying UAS Observation Error Variance Used in Data Assimilation Systems and Its Impact on Predictive Skill

Observation error determines the weights of the observations and background state used in data assimilation to generate analyses. Quantifying observation error is critical for the optimal assimilation of observational data sets. Uncrewed Aircraft System (UAS) observations have shown potential benefits in filling observational gaps in the lower atmosphere; however, characterization of their error characteristics has been limited. To optimize the use of UAS observations in numerical weather prediction, UAS observation error is estimated based on the 3‐cornered hat diagnostic approach which uses three independent estimates of the atmospheric state. This approach is applied to data from the 2018 Lower Atmospheric Profiling Studies at Elevation‐a Remotely‐piloted Aircraft Team Experiment field campaign using collocated UAS and rawinsonde observations along with output from a set of convection‐permitting model simulations. The estimated observation error values for UAS temperature, wind, and relative humidity measurements were found to be only weakly dependent on height AGL with mean values equal to 0.5°C, 0.8 m s −1 , and 3%, respectively. Only the newly estimated observation error for temperature differed from that previously used to assimilate commercial aircraft observations into global models (1.0°C). However, using this reduced temperature observation error produced more accurate mesoscale analyses and forecasts of both terrain‐driven flows and convection initiation generated by colliding outflow boundaries within the San Luis Valley of Colorado.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Data assimilation in operator algebras

We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a nonabelian operator algebra, which provides a representation of observables by multiplication operators and probability densities by density operators (quantum states). In the algebraic approach, the forecast step of data assimilation is represented by a quantum operation induced by the Koopman operator of the dynamical system. Moreover, the analysis step is described by a quantum effect, which generalizes the Bayesian observational update rule. Projecting this formulation to finite-dimensional matrix algebras leads to computational schemes that are i) automatically positivity-preserving and ii) amenable to consistent data-driven approximation using kernel methods for machine learning. Moreover, these methods are natural candidates for implementation on quantum computers. Applications to the Lorenz 96 multiscale system and the El Niño Southern Oscillation in a climate model show promising results in terms of forecast skill and uncertainty quantification.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Evaluating proxy influence in assimilated paleoclimate reconstructions – Testing the exchangeability of two ensembles of spatial processes

Climate field reconstructions (CFR) attempt to estimate spatiotemporal fields of climate variables in the past using climate proxies such as tree rings, ice cores, and corals. Data Assimilation (DA) methods are a recent and promising new means of deriving CFRs that optimally fuse climate proxies with climate model output. Despite the growing application of DA-based CFRs, little is understood about how much the assimilated proxies change the statistical properties of the climate model data. To address this question, we propose a robust and computationally efficient method, based on functional data depth, to evaluate differences in the distributions of two spatiotemporal processes. In this study, we apply our test to study global and regional proxy influence in DA-based CFRs by comparing the background and analysis states, which are treated as two samples of spatiotemporal fields. We find that the analysis states are significantly altered from the climate-model-based background states due to the assimilation of proxies. Moreover, the difference between the analysis and background states increases with the number of proxies, even in regions far beyond proxy collection sites. Our approach allows us to characterize the added value of proxies, indicating where and when the analysis states are distinct from the background states.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Convergence in simulating global soil organic carbon by structurally different models after data assimilation

Abstract Current biogeochemical models produce carbon–climate feedback projections with large uncertainties, often attributed to their structural differences when simulating soil organic carbon (SOC) dynamics worldwide. However, choices of model parameter values that quantify the strength and represent properties of different soil carbon cycle processes could also contribute to model simulation uncertainties. Here, we demonstrate the critical role of using common observational data in reducing model uncertainty in estimates of global SOC storage. Two structurally different models featuring distinctive carbon pools, decomposition kinetics, and carbon transfer pathways simulate opposite global SOC distributions with their customary parameter values yet converge to similar results after being informed by the same global SOC database using a data assimilation approach. The converged spatial SOC simulations result from similar simulations in key model components such as carbon transfer efficiency, baseline decomposition rate, and environmental effects on carbon fluxes by these two models after data assimilation. Moreover, data assimilation results suggest equally effective simulations of SOC using models following either first‐order or Michaelis–Menten kinetics at the global scale. Nevertheless, a wider range of data with high‐quality control and assurance are needed to further constrain SOC dynamics simulations and reduce unconstrained parameters. New sets of data, such as microbial genomics‐function relationships, may also suggest novel structures to account for in future model development. Overall, our results highlight the importance of observational data in informing model development and constraining model predictions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Leaf-scale carbon assimilation simulated by the multi-assumption architecture & testbed for process sensitivity analysis

Raw and processed output from the Multi-Assumption Architecture & Testbed (MAAT, https://github.com/walkeranthonyp/MAAT, tag: v1.2.1_walker2020; Walker et al., 2018). The dataset contains leaf-scale carbon assimilation data from three MAAT simulations and their post-processing and plotting scripts. Simulation 1, labelled "FvC_4proc_proc," is a four-process, process sensitivity analysis (Dai et al., 2017) of carbon assimilation based on the Farquhar et al. (1980) photosynthesis model, and its variant proposed by Collatz et al. (1991). Simulation 2, labelled "FvC_4proc_salt," is a 14 parameter sensitivity analysis (Saltelli et al., 2010) of carbon assimilation based on the Farquhar and Collatz photosynthesis models. Simulation 3, labelled "FvC," is a factorial combination of the alternative process representations and parameter values presented in those original papers across a factorial combination of incident photosynthetically active radiation (50-2000 µmol m-2 s-1, in increments of 50) and atmospheric CO2 concentration (50-1500 µmol m-2 s-1, in increments of 50). Additional scripts/functions for post-processing and plotting are part of the MAAT repository. These data were generated to evaluate and compare the Farquhar and Collatz models of leaf-scale photosynthesis across a range of CO2 and incident light conditions. Analysis of results can be found in Walker et al. (2020). This dataset is comprised of R scripts to process data and produce figures; .RDS files, a binary format specific to R and read with the 'readRDS' function, to store raw MAAT output; R and bash scripts (.bs) that help to run a MAAT simulation, .XML files that are output from MAAT describing a run, and .csv files which contain the calculated sensitivity indexes published in Walker et al. (2020).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

PyDA: A Hands-On Introduction to Dynamical Data Assimilation with Python

Dynamic data assimilation offers a suite of algorithms that merge measurement data with numerical simulations to predict accurate state trajectories. Meteorological centers rely heavily on data assimilation to achieve trustworthy weather forecast. With the advance in measurement systems, as well as the reduction in sensor prices, data assimilation (DA) techniques are applicable to various fields, other than meteorology. However, beginners usually face hardships digesting the core ideas from the available sophisticated resources requiring a steep learning curve. In this tutorial, we lay out the mathematical principles behind DA with easy-to-follow Python module implementations so that this group of newcomers can quickly feel the essence of DA algorithms. We explore a series of common variational, and sequential techniques, and highlight major differences and potential extensions. We demonstrate the presented approaches using an array of fluid flow applications with varying levels of complexity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Assimilation of citizen science data in snowpack modeling using a new snow data set: Community Snow Observations

A physically based snowpack evolution and redistribution model was used to test the effectiveness of assimilating crowd-sourced snow depth measurements collected by citizen scientists. The Community Snow Observations project gathers, stores, and distributes measurements of snow depth recorded by recreational users and snow professionals in high mountain environments. These citizen science measurements are valuable since they come from terrain that is relatively undersampled and can offer in situ snow information in locations where snow information is sparse or nonexistent. The present study investigates (1) the improvements to model performance when citizen science measurements are assimilated, and (2) the number of measurements necessary to obtain those improvements. Model performance is assessed by comparing time series of observed (snow pillow) and modeled snow water equivalent values, by comparing spatially distributed maps of observed (remotely sensed) and modeled snow depth, and by comparing fieldwork results from within the study area. The results demonstrate that few citizen science measurements are needed to obtain improvements in model performance, and these improvements are found in 62 % to 78 % of the ensemble simulations, depending on the model year. Model estimations of total water volume from a subregion of the study area also demonstrate improvements in accuracy after CSO measurements have been assimilated. These results suggest that even modest measurement efforts by citizen scientists have the potential to improve efforts to model snowpack processes in high mountain environments, with implications for water resource management and process-based snow modeling.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1996

Climate Data Assimilation on a Massively Parallel Supercomputer

We have designed and implemented a set of highly efficient and highly scalable algorithms for an unstructured computational package, the PSAS data assimilation package, as demonstrated by detailed performance analysis of systematic runs on up to 512-nodes of an Intel Paragon. The preconditioned Conjugate Gradient solver achieves a sustained 18 Gflops performance. Consequently, we achieve an unprecedented 100-fold reduction in time to solution on the Intel Paragon over a single head of a Cray C90. This not only exceeds the daily performance requirement of the Data Assimilation Office at NASA's Goddard Space Flight Center, but also makes it possible to explore much larger and challenging data assimilation problems which are unthinkable on a traditional computer platform such as the Cray C90.

supercomputer↗
NASA NTRS2004

What is data assimilation really solving, and how is the calculation actually done?

Data assimilation is a procedure in which observations are combined with models. The observations correct model errors on the one hand, and the models extrapolate the data information in space, time, and among different properties on the other. The result of assimilation is generally a more complete and more accurate description of the state of the modeled system than those obtained by either observations or model simulations alone. However, data assimilation is not a panacea for correcting every model error or for compensating all deficiencies of observations.

smoother↗