Ensemble Kalman Filter Data Assimilation Research Articles

An Enhanced Long-Term Wind Speed Prediction Using Dynamic Unified Ensemble Learning and Data Assimilation Techniques: A Case Study in Tamil Nadu, India

Reliable wind speed prediction is essential for effective grid management since wind energy is a key component of renewable energy generation. However, controlling wind speed just right is no easy feat since the wind flow changes constantly. This paper presents an innovative method for predicting wind speeds in the future. It uses state-of-the-art data assimilation methods and a dynamic unified ensemble learning model. For efficient wind energy planning and monitoring, WSP accuracy is crucial. Data from a single site limited the accuracy of WSPs in previous research. An improved accuracy of long-term wind speed predictions is achieved by the proposed model via the integration of data assimilation and ensemble learning. To increase forecast accuracy, the model uses sophisticated data assimilation methods like the Kalman filter to combine data from many sources. Specifically, the model employs the Stacked CNN + BiLSTM with Data Assimilator (SCBLSTM+DA) technique, which integrates Wind Speed (WS) data from adjacent areas with the CNN + BiLSTM-based Ensemble Learning Model (ELM) and the Four-Dimensional Variational and Ensemble Kalman Filter (4DVar/EnKF) Data Assimilation method. Using real-world wind speed data from nine meteorological stations in Tamil Nadu, India, we find that current prediction models, including both classical statistical and cutting-edge machine learning models, perform better. Further, unlike standalone models, the suggested model shows less susceptibility to changes in prediction time scales. Promising a solution to improve long-term wind speed predictions accuracy, this study has significant consequences for wind energy management and production.

Federal Algorithm Design and Numerical Experiments of Ensemble Kalman Filter Data Assimilation Analysis Process

Based on the federated Kalman filter proposed by Carlson with linear systems, we propose a federated computing scheme for the ensemble Kalman filter (EnKF) assimilation analysis process for nonlinear systems, and give an optimal information fusion estimation algorithm weighted by diagonal matrix under the linear minimum variance criterion, that is, the assimilation analysis values of each variable in the global estimation are linear combinations of the assimilation analysis values of the corresponding variables in the local estimation of sub-filters, and the calculation of the combination coefficients is given. The federated algorithm of the EnKF assimilation analysis process for nonlinear systems is verified by the Lorenz (1963) system.

Are the Noah and Noah-MP land surface models accurate for frozen soil conditions?

The accurate prediction of frozen soil conditions is a critical component of dynamic terrain characterization for engineering operations in cold regions. Currently the trusted resource for dynamic terrain within the US military uses gridded global soil conditions (i.e., temperature and moisture) generated by the Land Information System (LIS) architecture. LIS combines static terrain data with trusted surface weather information into the Noah land surface model to generate a continuous representation of the global surface conditions. Both the input weather data and the model output land surface state are adjusted to match the observed state using an advanced ensemble Kalman filter data assimilation technique to incorporate in situ and remote sensing observations. While this product has been robustly evaluated under unfrozen conditions only sporadic studies have investigated its ability to accurately simulate freeze/thaw cycles, and soil temperature and moisture under frozen conditions. Here, we present a broad comparison and evaluation of the simulated soil state against an in situ network of soil temperature and moisture distributed across the Continental United States that focuses on the winter season. This comparison includes both the Noah and the newer Noah with multi-parameterization (Noah-MP) land surface models. A comparison of the two models reveals substantial differences in simulated soil moisture, frozen content, and frozen soil strength. In general, Noah predicts colder soils with deeper frost depths, and frozen soils that are slightly stronger than Noah-MP. Initial results evaluating Noah and Noah-MP against in situ observations show that both models have significantly degraded model performance for frozen soil conditions compared to their performance for unfrozen soil. In particular, Noah has a significant and persistent cold bias of approximately −3 K when the soil temperature is below freezing. This cold bias is not present in Noah-MP and further analysis shows that this improvement was almost entirely caused by a better representation of thermal conduction through snow in Noah-MP. Specifically, we find that the bulk effective thermal conductivity of a snowpack is 2× greater in Noah, which allows for greater surface heat loss during the winter and, consequently, lower soil temperatures. This analysis reveals that the more advanced multi-layer snow model in Noah-MP substantially improves the representation of soil temperature during the cold season.

Representing uncertainty in limited-area data assimilating ocean models

A limited-area ocean prediction system is developed to acquire forecast error covariances related to uncertainty in atmospheric forcing and turbulent mixing using perturbed model parameters within an Ensemble Kalman Filter (EnKF). The system performs sequential data assimilation delivering realistic ocean state estimation and forecasts. It is initialised to observations using the EnKF, the hybrid-EnKF and Ensemble Optimal Interpolation (EnOI). It has higher resolution than the parent global model, includes tides and assimilates altimetric sea level anomaly to constrain the offshore mesoscale circulation. Dynamic ensemble spread introduced by parameter uncertainty shows agreement with error estimates obtained from forecast innovation statistics. Hybrid EnKF offers improvements to both EnKF and EnOI, having smaller analysis increments and forecast errors. The ensemble mean of the hybrid-EnKF is more accurate than any member due to the introduction of parameterised error which behaves as additive inflation in the hybrid EnKF system. This indicates the parameterisation acts as a non-linear filter for model forecast error growth. To demonstrate consistency, experiments are carried out for various regions that differ in their oceanographic situations. The hybrid EnKF data assimilation system enables practical use of dynamic ensembles that capture the flow dependent errors which are mixed with static or climatological covariances for situations where model error is systematically under-estimated.

Optimizing measurement schemes to improve indoor airflow and temperature CFD–EnKF joint simulation

An ensemble Kalman filter (EnKF) effectively rectifies simulation inaccuracies arising from uncertain flow field boundary conditions. In this methodology, measurement data plays a pivotal and indispensable role. This study investigated the requirements for observation data in joint EnKF and computational fluid dynamics (CFD) simulation models to correct errors. It established guiding principles for measurement schemes and validated them using numerical experiments on the airflow and temperature fields in a small chamber. The optimized scheme significantly reduced simulation errors, enhancing assimilation accuracy. In addition, the influence of measurement noise was considered, revealing a positive correlation between assimilation and measurement errors, thus highlighting the significance of high-precision instruments. Additionally, this study confirmed that the optimal number of measurement points corresponds to the number of uncertain boundary condition variables. Fewer measurement points hinder accurate estimation, whereas increasing their number does not significantly improve the data assimilation accuracy, regardless of measurement noise. Overall, this study provides guidelines for implementing EnKF data assimilation to ensure reliable and precise results.

A Quantile-Conserving Ensemble Filter Framework. Part II: Regression of Observation Increments in a Probit and Probability Integral Transformed Space

Abstract Traditional ensemble Kalman filter data assimilation methods make implicit assumptions of Gaussianity and linearity that are strongly violated by many important Earth system applications. For instance, bounded quantities like the amount of a tracer and sea ice fractional coverage cannot be accurately represented by a Gaussian that is unbounded by definition. Nonlinear relations between observations and model state variables abound. Examples include the relation between a remotely sensed radiance and the column of atmospheric temperatures, or the relation between cloud amount and water vapor quantity. Part I of this paper described a very general data assimilation framework for computing observation increments for non-Gaussian prior distributions and likelihoods. These methods can respect bounds and other non-Gaussian aspects of observed variables. However, these benefits can be lost when observation increments are used to update state variables using the linear regression that is part of standard ensemble Kalman filter algorithms. Here, regression of observation increments is performed in a space where variables are transformed by the probit and probability integral transforms, a specific type of Gaussian anamorphosis. This method can enforce appropriate bounds for all quantities and deal much more effectively with nonlinear relations between observations and state variables. Important enhancements like localization and inflation can be performed in the transformed space. Results are provided for idealized bivariate distributions and for cycling assimilation in a low-order dynamical system. Implications for improved data assimilation across Earth system applications are discussed.

Barents-2.5km v2.0: an operational data-assimilative coupled ocean and sea ice ensemble prediction model for the Barents Sea and Svalbard

Abstract. An operational ocean and sea ice forecast model, Barents-2.5, is implemented for short-term forecasting at the coast off northern Norway, the Barents Sea, and the waters around Svalbard. Primary forecast parameters are sea ice concentration (SIC), sea surface temperature (SST), and ocean currents. The model also provides input data for drift modeling of pollutants, icebergs, and search-and-rescue applications in the Arctic domain. Barents-2.5 has recently been upgraded to include an ensemble prediction system with 24 daily realizations of the model state. SIC, SST, and in situ hydrography are constrained through the ensemble Kalman filter (EnKF) data assimilation scheme executed in daily forecast cycles with a lead time up to 66 h. Here, we present the model setup and validation in terms of SIC, SST, in situ hydrography, and ocean and ice velocities. In addition to the model's forecast capabilities for SIC and SST, the performance of the ensemble in representing the model's uncertainty and the performance of the EnKF in constraining the model state are discussed.

A method for estimating yield of maize inbred lines by assimilating WOFOST model with Sentinel-2 satellite data.

Maize is the most widely planted food crop in China, and maize inbred lines, as the basis of maize genetic breeding and seed breeding, have a significant impact on China's seed security and food safety. Satellite remote sensing technology has been widely used for growth monitoring and yield estimation of various crops, but it is still doubtful whether the existing remote sensing monitoring means can distinguish the growth difference between maize inbred lines and hybrids and accurately estimate the yield of maize inbred lines. This paper explores a method for estimating the yield of maize inbred lines based on the assimilation of crop models and remote sensing data, initially solves the problem. At first, this paper analyzed the WOFOST(World Food Studies)model parameter sensitivity and used the MCMC(Markov Chain Monte Carlo) method to calibrate the sensitive parameters to obtain the parameter set of maize inbred lines differing from common hybrid maize; then the vegetation indices were selected to establish an empirical model with the measured LAI(Leaf Area Index) at three key development stages to obtain the remotely sensed estimated LAI; finally, the yield of maize inbred lines in the study area was estimated and mapped pixel by pixel using the EnKF(Ensemble Kalman Filter) data assimilation algorithm. Also, this paper compares a method of assimilation by setting a single parameter. Instead of the WOFOST parameter optimization process, a parameter representing the growth weakness of the inbred lines was set in WOFOST to distinguish the inbred lines from the hybrids. The results showed that the yield estimated by the two methods compared with the field measured yield data had R2: 0.56 and 0.18, and RMSE: 684.90 Kg/Ha and 949.95 Kg/Ha, respectively, which proved that the crop growth model of maize inbred lines established in this study combined with the data assimilation method could initially achieve the growth monitoring and yield estimation of maize inbred lines.

Comparison of temperature and wind observations in the Tropics in a perfect‐model, global EnKF data assimilation system

Flow‐dependent errors in tropical analyses and short‐range forecasts are analysed using global observing‐system simulation experiments assimilating only temperature, only winds, and both data types using the ensemble Kalman filter (EnKF) Data Assimilation Research Testbed (DART) and a perfect model framework. The idealised, homogeneous observation network provides profiles of wind and temperature data from the nature run for January 2018 using the National Center for Atmospheric Research (NCAR) Community Earth System Model (CESM) forced by the observed sea‐surface temperature. The results show that the assimilation of abundant wind observations in a perfect model makes the temperature data in the Tropics largely uninformative. Furthermore, the assimilation of wind data reduces the background errors in specific humidity twice as much as the assimilation of temperature observations. In all experiments, the largest analysis uncertainties and the largest short‐term forecast errors are found in regions of strong vertical and longitudinal gradients in the background wind, especially in the upper troposphere and lower stratosphere over the Indian Ocean and Maritime Continent. The horizontal error correlation scales are on average short throughout the troposphere, just several hundred km. The correlation scales of the wind variables in precipitating regions are half of those in nonprecipitating regions. In precipitating regions, the correlations are elongated vertically, especially for the wind variables. Strong positive cross‐correlations between temperature and specific humidity in the precipitating regions are explained using the Clausius–Clapeyron equation.

An Ensemble Kalman Filter Data Assimilation Method for the Sea Surface Temperature in the China Seas: Implementation and Simulation Experiments

Data assimilation refers to a method of integrating observation data in the dynamic operation of numerical models on the basis of considering the temporal and spatial distribution of data and the error of observation field and background field. The Ensemble Kalman filter (EnKF) as a technology that has been widely used in the field of atmosphere and ocean has been applied to the ROMS (the Regional Ocean Modeling System) for predicting Sea surface temperature in Yellow, and East China Seas. In order to explore the applicability and effectiveness of the EnKF method for improving the accuracy of marine numerical model, the Sea surface temperature (SST) gained from buoy were used to conduct data assimilation process with EnKF method. Twin experiments have been performed to analysis the sensitivity of this system to the ensemble size and errors in model simulation and observations and a real data assimilation scheme has been conducted to hindcast the SST at the Yellow, and East China Seas during the July of year 2014. The updated results after data assimilation indicate that the model simulation fits observation better when the forecast was updated by observations. The result show that EnKF can effectively reduce the simulation error of complex numerical marine models.

Flow-induced vibration modeling of bluff bodies with data assimilation

Vortex-induced vibration (VIV) and galloping are two typical flow-induced vibration (FIV) problems of bluff bodies, which often cause fatigue damage or destruction of structures. Therefore, the accurate and effective FIV prediction has become a requirement of the industry in order to prevent structural damage and guide design. Although the semi-empirical model (such as the wake oscillator model) is an efficient FIV prediction tool, the precision ability of existing models is constrained due to empirical parameters and unideal mathematical equations. Generally, the numerical simulation and wind tunnel experiments are relatively accurate methods, but for complex fluid–structure interaction problems, their cost is too high. As a result, a data-driven FIV prediction model is proposed to accomplish effective and high-precision prediction in this study. The Ensemble Kalman filter (ENKF) data assimilation (DA) technique is used to combine the experimental data with a semi-empirical model. First, the sensitivity of empirical parameters is analyzed, and the most sensitive ones are selected as the target parameters for data assimilation. The mean deviation of ensemble (MDE) is proposed to represent the sensitivity of parameters. Then DA-based model is used to predict the galloping and VIV of a rectangular cylinder. The results indicate that the accuracy of the DA-based model is up to 10 times greater than that of the initial semi-empirical model. With the data-driven technology, the typical ‘quasi-steady’ theory of galloping has been improved for low Scruton number values. For the wake oscillator model, assimilating the parameters of the acceleration and velocity coupled terms can improve the prediction accuracy of VIV. Also, this modeling procedure can be regarded as a new parameter identification method from forced and free vibration.

Direct Assimilation of All-Sky GOES-R ABI Radiances in GSI EnKF for the Analysis and Forecasting of a Mesoscale Convective System

Abstract In this study, all-sky GOES-R ABI infrared radiances at their native resolution are assimilated using an enhanced GSI ensemble Kalman filter (EnKF) data assimilation (DA) system, and the impacts of the data on the analysis and forecast of a mesoscale convective system (MCS) are explored. Results show that all-sky ABI BT data can correctly build up observed storms within the model and effectively remove spurious storms in model background through frequent DA cycles. Both bias and root-mean-squared innovation of the background and analysis are significantly reduced during the DA cycles, and free forecasts are improved when verified subjectively and objectively against observed ABI BTs and independent radar reflectivity observations. A horizontal localization radius of 30 km is found to produce the best results while 5-min DA cycles improve the storm analyses over 15-min cycles, but the differences in forecasts are small. Further analyses show that the clearing of spurious clouds by ABI radiance is correctly accompanied by reduction in moisture through background error cross covariance, but overdrying often occurs, which can cause spurious storm decay in the forecast. The problem is reduced when the ensemble mean of observation prior instead of observation prior of the ensemble mean state is used in the ensemble mean state update equation of EnKF. The significant difference between the two ways that the ensemble mean of observation prior is calculated when the observational operator is very nonlinear has not been recognized in earlier cloudy radiance DA studies. Significance Statement Satellite observations in cloudy regions are not used in most current operational weather prediction systems due to complex nonlinear relations between satellite-observed quantities, the radiances, and model state in such regions. The models also must predict clouds reasonably well for cloudy observations to be effectively assimilated. The latest NOAA geostationary satellites can provide radiance observations at high spatial and temporal resolutions and such data in both cloudy- and clear-air regions are assimilated using an advanced data assimilation method into a model that explicitly represents convection. Forecasts up to 4 h are improved by the assimilation while several issues associated with the assimilation are discussed. The study contributes to the eventual use of all-sky satellite radiance data in operational models.

The effects of estimating a photoionization parameter within a physics-based model using data assimilation

Data assimilation (DA) is the process of merging information from prediction models with noisy observations to produce an estimate of the state of a physical system. In ionospheric physics-based models, the solar ionizing irradiance is commonly estimated from a solar index like F10.7. The goal of this work is to provide the fundamental understanding necessary to appreciate how a DA algorithm responds to estimating an external parameter driving the model’s interpretation of this solar ionizing irradiance. Therefore, in this work we allow the DA system to find the F10.7 value that delivers the degree of photoionization that leads to a predicted electron density field that best matches the observations. To this end, we develop a heuristic model of the ionosphere along the magnetic equator that contains physics from solar forcing and recombination/plasma diffusion, which allows us to explore the impacts of strongly forced system dynamics on DA. This framework was carefully crafted to be both linear and Gaussian, which allows us to use a Kalman filter to clearly see how: (1) while recombination acts as a sink on the information in the initial condition for ionospheric field variables, recombination does not impact the information in parameter estimates in the same way, (2) when solar forcing dominates the electron density field, the prior covariance matrix becomes dominated by its leading eigenvector whose structure is directly related to that of the solar forcing, (3) estimation of parameters for forcing terms leads to a time-lag in the state estimate relative to the truth, (4) the performance of a DA system in this regime is determined by the relative dominance of solar forcing and recombination to that of the smaller-scale processes and (5) the most impactful observations on the electron density field and on the solar forcing parameter are those observations on the sunlit side of the ionosphere. These findings are then illustrated in a full physics-based ionospheric model using an ensemble Kalman filter DA scheme.

Spatiotemporal estimation of model error to improve soil moisture analysis in ensemble Kalman filter data assimilation

As a key variable in the surface hydrological cycle and energy balance, soil moisture is often analyzed using data assimilation to improve precise and high spatiotemporal resolution from multisource data. However, accurate estimation of model error in soil moisture data assimilation is not sufficient in spatial and temporal dimensions. This paper proposes a spatiotemporal error estimation method that integrates the spatial and temporal dimensions of the study area into model error estimation. The in-situ data was regarded as the “true value” for the temporal dimensions model error estimation. The triple collocation (TC) technique was used to estimate the spatial error of the model. Based on the aforementioned estimation, a linear method to construct the relationship between spatial and temporal information was proposed to fuse the spatiotemporal model error. Result from the proposed method was compared against the overall model error estimation and spatial estimation methods in ensemble Kalman filter (EnKF) data assimilation. The ERA-Interim reanalysis data and in-situ soil moisture data from Washington State in 2016 were used to evaluate the performance of EnKF data assimilation. Using statistical metrics, including the root mean square error (RMSE), the mean bias error (MBE), and the Pearson correlation coefficient (i.e., R-value), the results show that our proposed approach, which uses spatiotemporal approach to model error estimation in EnKF data assimilation, yielded more accurate soil moisture estimates. When ERA-Interim reanalysis soil moisture data was used as the reference data, compared with the overall model error estimation EnKF Data Assimilation Experiment, RMSE and MBE of spatiotemporal model error estimation EnKF Data Assimilation Experiment were reduced by 0.0062 and 0.0061 m3 / m3, respectively, and R remained basically unchanged. When using in-situ measurements as reference data, RMSE and MBE decreased by 0.0034 and 0.0038 m3 / m3, respectively, and R increased by 0.0365. Compared with the other estimation approaches in the experiments, the spatiotemporal error estimation approach greatly improved the estimation accuracy of soil moisture analysis, yielding the closest values and variation trends with the in-situ measurements. Fully considering the temporal and spatial variation of model error and improving the estimation accuracy of model error can provide more accurate model information for data assimilation. The proposed method and framework in this paper can be used in model error estimation and data assimilation, particularly in the fields of numerical weather forecasting, natural environment monitoring, and geographical environment research.

Calibration of RANS model constant based on data assimilation and accurate simulation of separated flow

To improve the prediction accuracy of separated flow based on the Reynolds Averaged Navier–Stokes model, the model constants of the baseline Reynolds stress model are calibrated by the ensemble Kalman filter data assimilation method. The separated flow in a diffuser is taken as the object, and the wall pressure coefficients of the diffuser are used as the driving data. The results show that the method that recalibrates the model constants based on data assimilation is easy to implement and is an effective method. The wall pressure coefficients and the separation regions of the diffuser predicted by the baseline Reynolds stress model with the default model constants deviate greatly from the experimental observations. By recalibrating the model constants, the prediction accuracy of separated flow based on the baseline Reynolds stress model is improved. This provides an idea for the accurate simulation of separated flow based on the Reynolds Averaged Navier–Stokes model in engineering applications.

Assimilation of wheat and soil states for improved yield prediction: The APSIM-EnKF framework

Context.Accurate prediction of within-field crop yield in response to spatial and temporal variability provides essential information for farm managers to improve productivity and ensure optimal use of inputs. Understanding yield spatial and temporal variability cannot be solely addressed by crop modelling or remote sensing but by integrating the instantaneous spatial information from remote sensing and the temporal information from crop modelling. Sequential data assimilation techniques allow wheat and soil observations to be assimilated into the crop model while it evolves and evaluate model and observational uncertainties to improve the accuracy of crop monitoring and yield prediction. ObjectivesThe objective of this study was to comprehensively explore the potential yield estimation improvement by assimilating observations of all prognostic wheat and soil states, including various repeat intervals and accuracy, allowing recommendations on implementation to be made. MethodsThis study develops an Ensemble Kalman filter (EnKF) data assimilation framework for the APSIM-Wheat model and illustrates potential improvements in wheat yield estimation through a synthetic study. Through several scenarios, assimilation of wheat and soil observations into APSIM was explored, by assimilating these variables solely or collectively, and in various phenological stages.Results and conclusions.The results showed, under the specific weather and soil conditions assumed in this study, that while open-loop (no data assimilation) provided a yield estimation with a bias of 10.1%, assimilation in the flowering to end of grain filling stage reduced the bias to 1.4%, 2.9%, 4.4%, and 1.0% when constraining with leaf area index, leaf weight, stem weight, surface soil moisture observations, respectively. When assimilating in the floral initiation to the flowering stage, the yield estimation bias was reduced to 7.1%, 9.8%, 1.1%, and 1.2% when constraining with leaf nitrogen, stem nitrogen, top-layer soil ammonium‑nitrogen and nitrate‑nitrogen, respectively. Leaf area index, biomass and surface soil moisture are recommended for data assimilation especially with observations from remote sensing. SignificanceThis study developed a data assimilation framework for the APSIM-Wheat model and can be extended to over 20 crop modules integrated with APSIM. This synthetic study provided a exhaustive data assimilation experiment for wheat and soil states that are measurable by current techniques with a rigorous justification on uncertainties. It thus provides a guide for future agricultral data assimilation practices in choosing crop and soil states for assimilation, and for planning the timing and frequency of data collection. It should also inspire researchers to develop new techniques for measuring wheat states.

Object-Based Verification of GSI EnKF and Hybrid En3DVar Radar Data Assimilation and Convection-Allowing Forecasts within a Warn-on-Forecast Framework

Abstract The Center for Analysis and Prediction of Storms has recently developed capabilities to directly assimilate radar reflectivity and radial velocity data within the GSI-based ensemble Kalman filter (EnKF) and hybrid ensemble three-dimensional variational (En3DVar) system for initializing convective-scale forecasts. To assess the performance of EnKF and hybrid En3DVar with different hybrid weights (with 100%, 20%, and 0% of static background error covariance corresponding to pure 3DVar, hybrid En3DVar, and pure En3DVar) for assimilating radar data in a Warn-on-Forecast framework, a set of data assimilation and forecast experiments using the WRF Model are conducted for six convective storm cases of May 2017. Using an object-based verification approach, forecast objects of composite reflectivity and 30-min updraft helicity swaths are verified against reflectivity and rotation track objects in Multi-Radar Multi-Sensor data on space and time scales typical of National Weather Service warnings. Forecasts initialized by En3DVar or the best performing EnKF ensemble member produce the highest object-based verification scores, while forecasts from 3DVar and the worst EnKF member produce the lowest scores. Averaged across six cases, hybrid En3DVar using 20% static background error covariance does not improve forecasts over pure En3DVar, although improvements are seen in some individual cases. The false alarm ratios of EnKF members for both composite reflectivity and updraft helicity at the initial time are lower than those from variational methods, suggesting that EnKF analysis reduces spurious reflectivity and mesocyclone objects more effectively.

Reconstructing Arctic Sea Ice over the Common Era Using Data Assimilation

Abstract Arctic sea ice decline in recent decades has been dramatic; however, few long-term records of Arctic sea ice exist to put such a decline in context. Here we employ an ensemble Kalman filter data assimilation approach to reconstruct Arctic sea ice concentration over the last two millennia by assimilating temperature-sensitive proxy records with ensembles drawn from last millennium climate model simulations. We first test the efficacy of this method using pseudoproxy experiments. Results show good agreement between the target and reconstructed total Arctic sea ice extent (R2 value and coefficient of efficiency values of 0.51 and 0.47 for perfect model experiments and 0.43 and 0.43 for imperfect model experiments). Imperfect model experiments indicate that the reconstructions inherit some bias from the model prior. We assimilate 487 temperature-sensitive proxy records with two climate model simulations to produce two gridded reconstructions of Arctic sea ice over the last two millennia. These reconstructions show good agreement with satellite observations between 1979 and 1999 CE for total Arctic sea ice extent with an R2 value and coefficient of efficiency of about 0.60 and 0.50, respectively, for both models. Regional quantities derived from these reconstructions show encouraging similarities with independent reconstructions and sea ice sensitive proxy records from the Barents Sea, Baffin Bay, and East Greenland Sea. The reconstructions show a positive trend in Arctic sea ice extent between around 750 and 1820 CE, and increases during years with large volcanic eruptions that persist for about 5 years. Trend analysis of total Arctic sea ice extent reveals that for time periods longer than 30 years, the satellite era decline in total Arctic sea ice extent is unprecedented over the last millennium. Significance Statement Areal coverage of Arctic sea ice is a critical aspect of the climate system that has been changing rapidly in recent decades. Prior to the advent of satellite observations, sparse observations of Arctic sea ice make it difficult to put the current changes in context. Here we reconstruct annual averages of Arctic sea ice coverage for the last two millennia by combining temperature-sensitive proxy records (i.e., ice cores, tree rings, and corals) with climate model simulations using a statistical technique called data assimilation. We find large interannual changes in Arctic sea ice coverage prior to 1850 that are associated with volcanic eruptions, with a steady rise in Arctic sea ice coverage between 750 and 1820 CE. The satellite-period loss of sea ice has no analog during the last millennium.

Length Scale Analyses of Background Error Covariances for EnKF and EnSRF Data Assimilation

Data assimilation (DA) combines incomplete background values obtained via chemical transport model predictions with observational information. Several 3-Dimensional variational (3DVAR) and sequential methods (e.g., ensemble Kalman filter (EnKF)) are used to define model errors and build a background error covariance (BEC) and are important factors affecting the prediction performance of DA. The BEC determines the spatial range, where observation concentration is reflected in the model when DA is applied to an air pollution transport model. However, studies investigating the characteristics of BEC using air quality models remain lacking. In this study, horizontal length scale (HLS) and vertical length scale (VLS) analyses of a BEC were applied to EnKF and ensemble square root filter (EnSRF), respectively, and two ensemble-based DA methods were performed; the characteristics were compared with those of a BEC applied to 3DVAR. The results of 6 h PM2.5 predictions performed for 42 days were evaluated for a control run without DA (CTR), 3DVAR, EnKF, and EnSRF. HLS and VLS respectively exhibited a high correlation with the ground wind speed and with the planetary boundary layer height for diurnal and daily variations; EnKF and EnSRF exhibited superior performances among all the methods. The root mean square errors were 11.9 μg m−3 and 11.7 μg m−3 for EnKF and EnSRF, respectively, while those for 3DVAR and CTR were 12.6 μg m−3 and 18.3 μg m−3, respectively. Thus, we proposed a simple method to find a Gaussian function that best described the error correlation of the BEC based on the physical distance.

Comparing Partial and Continuously Cycling Ensemble Kalman Filter Data Assimilation Systems for Convection-Allowing Ensemble Forecast Initialization

Abstract Several limited-area 80-member ensemble Kalman filter (EnKF) data assimilation systems with 15-km horizontal grid spacing were run over a computational domain spanning the conterminous United States (CONUS) for a 4-week period. One EnKF employed continuous cycling, where the prior ensemble was always the 1-h forecast initialized from the previous cycle’s analysis. In contrast, the other EnKFs used a partial cycling procedure, where limited-area states were discarded after 12 or 18 h of self-contained hourly cycles and reinitialized the next day from global model fields. “Blended” states were also constructed by combining large scales from global ensemble initial conditions (ICs) with small scales from limited-area continuously cycling EnKF analyses using a low-pass filter. Both the blended states and EnKF analysis ensembles initialized 36-h, 10-member ensemble forecasts with 3-km horizontal grid spacing. Continuously cycling EnKF analyses initialized ∼1–18-h precipitation forecasts that were comparable to or somewhat better than those with partial cycling EnKF ICs. Conversely, ∼18–36-h forecasts with partial cycling EnKF ICs were comparable to or better than those with unblended continuously cycling EnKF ICs. However, blended ICs yielded ∼18–36-h forecasts that were statistically indistinguishable from those with partial cycling ICs. ICs that more closely resembled global analysis spectral characteristics at wavelengths > 200 km, like partial cycling and blended ICs, were associated with relatively good ∼18–36-h forecasts. Ultimately, findings suggest that EnKFs employing a combination of continuous cycling and blending can potentially replace the partial cycling assimilation systems that currently initialize operational limited-area models over the CONUS without sacrificing forecast quality. SIGNIFICANCE STATEMENT Numerical weather prediction models (i.e., weather models) are initialized through a process called data assimilation, which combines real atmospheric observations with a previous short-term weather model forecast using statistical techniques. The overarching data assimilation strategy currently used to initialize operational regional weather models over the United States has several disadvantages that ultimately limit progress toward improving weather model forecasts. Thus, we suggest an alternative data assimilation strategy be adopted to initialize a next-generation, high-resolution (∼3 km) probabilistic forecast system currently being developed. This alternative approach preserves forecast quality while fostering a framework that can accelerate weather model improvements, which in turn will lead to better weather forecasts.