Data Assimilation Methodology Research Articles

20th‐Century Antarctic Sea Level Mitigation Driven by Uncertain East Antarctic Accumulation History

AbstractIncreasing snow accumulation over the Antarctic Ice Sheet may mitigate future sea level rise. However, current estimates of mitigation potential are poorly constrained due to limited records of past variability. We present an annually resolved reconstruction of Antarctic snow accumulation from 1801 to 2000 CE, employing a paleoclimate data assimilation methodology to integrate ice core records with a multi‐model ensemble of climate simulations. Our reconstruction correlates well with instrumental reanalysis, and we find that Antarctic accumulation rates increased over the 20th‐century, resulting in a modest amount (∼1 mm) of sea level mitigation. Mitigation is primarily driven by an accelerating trend since around 1970. Our results contrast with previous mitigation estimates of ∼10–12 mm; this discrepancy is due to poorly constrained baseline estimates of 19th‐century accumulation in East Antarctica. Our reconstruction suggests that the uncertainty of future sea level mitigation from increasing Antarctic accumulation has been underestimated.

A Data Assimilation Methodology to Analyze the Unsaturated Seepage of an Earth–Rockfill Dam Using Physics-Informed Neural Networks Based on Hybrid Constraints

Data assimilation for unconfined seepage analysis has faced significant challenges due to hybrid causes, such as sparse measurements, heterogeneity of porous media, and computationally expensive forward models. To address these bottlenecks, this paper introduces a physics-informed neural network (PINN) model to resolve the data assimilation problem for seepage analysis of unsaturated earth–rockfill dams. This strategy offers a solution that decreases the reliance on numerical models and enables an accurate and efficient prediction of seepage parameters for complex models in the case of sparse observational data. For the first attempt in this study, the observed values are obtained by random sampling of numerical solutions, which are then contributed to the synchronous constraints in the loss function by informing both the seepage control equations and boundary conditions. To minimize the effects of sharp gradient shifts in seepage parameters within the research domain, a residual adaptive refinement (RAR) constraint is introduced to strategically allocate training points around positions with significant residuals in partial differential equations (PDEs), which could facilitate enhancing the prediction accuracy. The model’s effectiveness and precision are evaluated by analyzing the proposed strategy against the numerical solutions. The results indicate that even with limited sparse data, the PINN model has great potential to predict seepage data and identify complex structures and anomalies inside the dam. By incorporating coupling constraints, the validity of our PINN model could lead to theoretically viable applications of hydrogeophysical inversion or multi-parameter seepage inversion. The results show that the proposed framework can predict the seepage parameters for the entire research domain with only a small amount of observation data. Furthermore, with a small amount of observation data, PINNs are able to obtain more accurate results than purely data-driven DNNs.

Paleoclimate data assimilation with CLIMBER-X: An ensemble Kalman filter for the last deglaciation.

Using the climate model CLIMBER-X, we present an efficient method for assimilating the temporal evolution of surface temperatures for the last deglaciation covering the period 22000 to 6500 years before the present. The data assimilation methodology combines the data and the underlying dynamical principles governing the climate system to provide a state estimate of the system, which is better than that which could be obtained using just the data or the model alone. In applying an ensemble Kalman filter approach, we make use of the advances in the parallel data assimilation framework (PDAF), which provides parallel data assimilation functionality with a relatively small increase in computation time. We find that the data assimilation solution depends strongly on the background evolution of the decaying ice sheets rather than the assimilated temperatures. Two different ice sheet reconstructions result in a different deglacial meltwater history, affecting the large-scale ocean circulation and, consequently, the surface temperature. We find that the influence of data assimilation is more pronounced on regional scales than on the global mean. In particular, data assimilation has a stronger effect during millennial warming and cooling phases, such as the Bølling-Allerød and Younger Dryas, especially at high latitudes with heterogeneous temperature patterns. Our approach is a step toward a comprehensive paleo-reanalysis on multi-millennial time scales, including incorporating available paleoclimate data and accounting for their uncertainties in representing regional climates.

Data assimilation to determine the electrohydrodynamic force of plasma actuator

The electrohydrodynamic (EHD) force is the main flow control mechanism of plasma actuators (PAs), and a thorough understanding of the EHD force field is important for the practical application of PAs. However, because it is difficult to directly measure the EHD force field, a methodology for determining the unobservable EHD force field is required. In this study, we developed a new methodology using a data assimilation (DA) method which utilizes both experimental data and numerical simulation. The methodology was based on computational fluid dynamics and ensemble four-dimensional variational method and enabled us to determine the unobservable EHD force field from experimentally observable flow field data. Through numerical experiments, we demonstrated that the methodology can inversely estimate the EHD force field using time-series velocity and density field data with sufficient precision. Moreover, the results show that either the velocity or density field data are sufficient to estimate the EHD force field. The proposed DA methodology provides key factors for determining the flow field, such as the maximum value, extent, and vertical position of the maximum value of the EHD force field. Our methodology that estimates EHD force fields from the experimentally observed flow field data is also useful for understanding other EHD flows, which are the phenomena involving plasma and flow.

A decadal atmospheric ammonia reanalysis product in China

Atmospheric ammonia has great environmental implications due to its important role in ecosystem and nitrogen cycle, as well as contribution to formation of secondary particles. China is recognized as a hotspot of NH3 pollution owing to agricultural and livestock intensification. In the quest to achieve a comprehensive understanding of atmospheric ammonia load and to quantify its environmental impacts in China, relying solely either on existing measurements or on model simulations falls short. Their limitations, either in spatial coverage and integrity or in data quality, fails to meet the needs. Available reanalysis products exhibit a marked deficiency in ammonia data. We therefore aim to propose an integrated ammonia reanalysis product in China, adeptly melding satellite observations from the Infrared Atmospheric Sounding Interferometer (IASI) NH3 retrievals with chemical transport model simulation, capitalizing on the robust Ensemble Kalman Filter (EnKF) data assimilation methodology. The product is validated in high quality via the comparison against independent measurements from ground monitoring stations. Spanning a decade from 2013 to 2022, our reanalysis uncovers not just the spatial intricacies of NH3 concentrations but also their temporal dynamics. Our findings pinpointed the spatial disparities in atmospheric ammonia intensities, highlighting regional hotspots in the NCP, SCB, and Northeast China, and identified annual and seasonal patterns. Our research provides crucial insights for shaping future NH3 pollution prevention and control strategies in China.

Ensemble data assimilation for open channel water level forecasting under flow disturbances: A synthetic data study

Accurate water level forecasts are essential for effective river management. Data assimilation (DA), involving real-time model correction through observational data, serves as a pivotal approach to enhance the predictive precision of model-based state forecasting. Nevertheless, prevailing DA methodologies encounter constraints in swiftly and accurately forecasting water levels amidst substantial uncertainties stemming from flow disturbances. To surmount this challenge, an innovative joint ensemble Kalman filter (EnKF) framework that facilitates concurrent estimation of flow disturbances and water levels is proposed. By incorporating the flow disturbance state variable into the EnKF framework for water level assimilation, a joint EnKF framework that effectively estimates flow disturbances at known disturbance points through assimilation techniques is established. Additionally, for scenarios where the precise location of the flow disturbance point remains unknown, the introduction of a fictitious lateral outflow in proximity to the observation point allows estimation of the flow disturbance process of this fictitious outflow. Synthetic case study results demonstrate that the incorporation of flow disturbance assimilation yields superior water level estimations compared to scenarios disregarding flow disturbances, regardless of the concordance between estimated and actual disturbance flow values. Furthermore, even when the location of the disturbance point is known, utilization of a fictitious lateral outflow and and subsequent flow correction exhibits heightened robustness and stability in comparison to direct correction of the disturbance point's flow. Therefore, in practical applications, utilizing a fictitious lateral outflow and flow correction within the joint EnKF framework emerges as a more suitable approach, irrespective of the knowledge of disturbance location. The proposed method constitutes a substantial contribution to the field of water level forecasting in river systems under conditions of uncertain flow disturbances.

A genetic particle filter scheme for univariate snow cover assimilation into Noah-MP model across snow climates

Abstract. Accurate snowpack simulations are critical for regional hydrological predictions, snow avalanche prevention, water resource management, and agricultural production, particularly during the snow ablation period. Data assimilation methodologies are increasingly being applied for operational purposes to reduce the uncertainty in snowpack simulations and to enhance their predictive capabilities. This study aims to investigate the feasibility of using a genetic particle filter (GPF) as a snow data assimilation scheme designed to assimilate ground-based snow depth (SD) measurements across different snow climates. We employed the default parameterization scheme combination within the Noah-MP (with multi-parameterization) model as the model operator in the snow data assimilation system to evolve snow variables and evaluated the assimilation performance of the GPF using observational data from sites with different snow climates. We also explored the impact of measurement frequency and particle number on the filter updating of the snowpack state at different sites and the results of generic resampling methods compared to the genetic algorithm used in the resampling process. Our results demonstrate that a GPF can be used as a snow data assimilation scheme to assimilate ground-based measurements and obtain satisfactory assimilation performance across different snow climates. We found that particle number is not crucial for the filter's performance, and 100 particles are sufficient to represent the high dimensionality of the point-scale system. The frequency of measurements can significantly affect the filter-updating performance, and dense ground-based snow observational data always dominate the accuracy of assimilation results. Compared to generic resampling methods, the genetic algorithm used to resample particles can significantly enhance the diversity of particles and prevent particle degeneration and impoverishment. Finally, we concluded that the GPF is a suitable candidate approach for snow data assimilation and is appropriate for different snow climates.

The GMAO Hybrid 4D-EnVar Observing System Simulation Experiment Framework

Abstract This work describes the extension of the Global Modeling and Assimilation Office (GMAO) observing system simulation experiment (OSSE) framework to use a hybrid four-dimensional ensemble–variational (4D-EnVar) scheme instead of 3D-Var. The original 3D-Var and hybrid 4D-EnVar OSSEs use the same version of the data assimilation system (DAS) so that a direct comparison is possible in terms of the validation with respect to their corresponding real cases. Rather than quantifying the differences between the two data assimilation methodologies, a short intercomparison of upgrading from a 3D to a 4D OSSE is provided to highlight aspects where this change matters to the OSSE community and to identify particular features of data assimilation that can only be explored in a four-dimensional OSSE framework. A short validation of the hybrid 4D-EnVar OSSE shows that conclusions from previous assessments of the 3D-Var OSSE in its ability to mimic the behavior of the real system still hold with the same caveats. Furthermore, some aspects of the ensemble configuration and behavior are discussed along with forecast sensitivity to observation impacts (FSOI). Estimates of error standard deviations are shown to be smaller in the hybrid 4D-EnVar OSSE but with little impact on the character of the error. A discussion on future work directions focuses on exploring the four-dimensional aspect such as the error distribution within the assimilation window or four-dimensional handling of high-temporal density observations.

An Evaluation of Non-Gaussian Data Assimilation Methods in Moist Convective Regimes

Abstract Obtaining a faithful probabilistic depiction of moist convection is complicated by unknown errors in subgrid-scale physical parameterization schemes, invalid assumptions made by data assimilation (DA) techniques, and high system dimensionality. As an initial step toward untangling sources of uncertainty in convective weather regimes, we evaluate a novel Bayesian data assimilation methodology based on particle filtering within a WRF ensemble analysis and forecasting system. Unlike most geophysical DA methods, the particle filter (PF) represents prior and posterior error distributions nonparametrically rather than assuming a Gaussian distribution and can accept any type of likelihood function. This approach is known to reduce bias introduced by Gaussian approximations in low-dimensional and idealized contexts. The form of PF used in this research adopts a dimension-reduction strategy, making it affordable for typical weather applications. The present study examines posterior ensemble members and forecasts for select severe weather events between 2019 and 2020, comparing results from the PF with those from an ensemble Kalman filter (EnKF). We find that assimilating with a PF produces posterior quantities for microphysical variables that are more consistent with model climatology than comparable quantities from an EnKF, which we attribute to a reduction in DA bias. These differences are significant enough to impact the dynamic evolution of convective systems via cold pool strength and propagation, with impacts to forecast verification scores depending on the particular microphysics scheme. Our findings have broad implications for future approaches to the selection of physical parameterization schemes and parameter estimation within preexisting data assimilation frameworks. Significance Statement The accurate prediction of severe storms using numerical weather models depends on effective parameterization schemes for small-scale processes and the assimilation of incomplete observational data in a manner that faithfully represents the probabilistic state of the atmosphere. Current generation methods for data assimilation typically assume a standard form for the error distributions of relevant quantities, which can introduce bias that not only hinders numerical prediction, but that can also confound the characterization of errors from the model itself. The current study performs data assimilation using a novel method that does not make such assumptions and explores characteristics of resulting model fields and forecasts that might make such a method useful for improving model parameterization schemes.

On the dual advantage of placing observations through forward sensitivity analysis

The four-dimensional variational data assimilation methodology for assimilating noisy observations into a deterministic model has been the workhorse in forecasting centres for over three decades. While this method provides a computationally efficient framework for dynamic data assimilation, it is largely silent on the important question concerning the minimum number and placement of observations. To answer this question, we demonstrate the dual advantage of placing the observations where the square of the sensitivity of the model solution with respect to the unknown control variables, called forward sensitivities, attains its maximum. By following this approach, we can force the observability Gramian to be of full rank, which in turn guarantees efficient recovery of the optimal values of the control variables, which is the first of the two advantages of this strategy. We further show that the proposed strategy of placing observations has another inherent optimality: the square of the sensitivity of the optimal estimates of the control with respect to the observations (used to obtain these estimates) attains its minimum value, a second advantage that is a direct consequence of the above strategy for placing observations. Our analytical framework and numerical experiments on linear and nonlinear systems confirm the effectiveness of our proposed strategy.

Impact of spatially-dense in-situ observations on ocean forecasts of mixed layer and thermocline depth

ABSTRACT Ocean models, such as the Navy Coastal Ocean Model (NCOM), rely on ocean observations through data assimilation to predict the evolution of ocean phenomena accurately. The accuracy is highly dependent on the type and quantity of observations available. This work attempts to examine the impact of spatially dense in-situ profile observations on the forecasts of mixed layer depth (MLD) and thermocline depth (TD), using a three-dimensional variational data assimilation algorithm. To do this, a twin data assimilation experiment is used to simulate the impact of float deployments on the forecast of MLD and TD in a specific area of interest (AOI) of the North Atlantic. It is found that during the northern hemisphere summer the model MLD is sensitive to the sea surface temperature (SST) observations rather than the profiling floats. TD is more strongly impacted by the assimilation of float observations, and the experiment with the most floats produces the best results. During the northern hemisphere winter the profiling floats have a greater impact on the model simulation of MLD. Finally, the overall lack of substantial improvement in the winter months for the highest density of profiling floats is determined to be due to the data assimilation methodology itself.

How does 4DVar data assimilation affect the vertical representation of mesoscale eddies? A case study with observing system simulation experiments (OSSEs) using ROMS v3.9

Abstract. Accurate estimates and forecasts of ocean eddies in key regions such as western boundary currents are important for weather and climate, biology, navigation, and search and rescue. The dynamic nature of mesoscale eddies requires data assimilation to produce accurate eddy timings and locations in ocean model simulations. However, data assimilating models are rarely assessed below the surface due to a paucity of observations; hence it is not clear how data assimilation impacts the subsurface eddy structure. Here, we use a suite of observing system simulation experiments to show how the subsurface representation of eddies is changed within data assimilating simulations even when assimilating nearby observations. We examine in detail two possible manifestations of how the data assimilation process impacts three-dimensional eddy structure, namely, by producing overly active baroclinic instability and through inaccurate vertical mode structure. Therefore, in DA simulations, subsurface temperature structures can be too deep and too warm, particularly in dynamic eddy features. Our analyses demonstrate the need for further basic research in ocean data assimilation methodologies to improve the representation of the subsurface ocean structure.

A Statistical Hypothesis Testing Strategy for Adaptively Blending Particle Filters and Ensemble Kalman Filters for Data Assimilation

Abstract Particle filters avoid parametric estimates for Bayesian posterior densities, which alleviates Gaussian assumptions in nonlinear regimes. These methods, however, are more sensitive to sampling errors than Gaussian-based techniques such as ensemble Kalman filters. A recent study by the authors introduced an iterative strategy for particle filters that match posterior moments—where iterations improve the filter’s ability to draw samples from non-Gaussian posterior densities. The iterations follow from a factorization of particle weights, providing a natural framework for combining particle filters with alternative filters to mitigate the impact of sampling errors. The current study introduces a novel approach to forming an adaptive hybrid data assimilation methodology, exploiting the theoretical strengths of nonparametric and parametric filters. At each data assimilation cycle, the iterative particle filter performs a sequence of updates while the prior sample distribution is non-Gaussian, then an ensemble Kalman filter provides the final adjustment when Gaussian distributions for marginal quantities are detected. The method employs the Shapiro–Wilk test to determine when to make the transition between filter algorithms, which has outstanding power for detecting departures from normality. Experiments using low-dimensional models demonstrate that the approach has a significant value, especially for nonhomogeneous observation networks and unknown model process errors. Moreover, hybrid factors are extended to consider marginals of more than one collocated variables using a test for multivariate normality. Findings from this study motivate the use of the proposed method for geophysical problems characterized by diverse observation networks and various dynamic instabilities, such as numerical weather prediction models. Significance Statement Data assimilation statistically processes observation errors and model forecast errors to provide optimal initial conditions for the forecast, playing a critical role in numerical weather forecasting. The ensemble Kalman filter, which has been widely adopted and developed in many operational centers, assumes Gaussianity of the prior distribution and solves a linear system of equations, leading to bias in strong nonlinear regimes. On the other hand, particle filters avoid many of those assumptions but are sensitive to sampling errors and are computationally expensive. We propose an adaptive hybrid strategy that combines their advantages and minimizes the disadvantages of the two methods. The hybrid particle filter–ensemble Kalman filter is achieved with the Shapiro–Wilk test to detect the Gaussianity of the ensemble members and determine the timing of the transition between these filter updates. Demonstrations in this study show that the proposed method is advantageous when observations are heterogeneous and when the model has an unknown bias. Furthermore, by extending the statistical hypothesis test to the test for multivariate normality, we consider marginals of more than one collocated variable. These results encourage further testing for real geophysical problems characterized by various dynamic instabilities, such as real numerical weather prediction models.

A data assimilation framework to predict the response of glioma cells to radiation.

We incorporate a practical data assimilation methodology into our previously established experimental-computational framework to predict the heterogeneous response of glioma cells receiving fractionated radiation treatment. Replicates of 9L and C6 glioma cells grown in 96-well plates were irradiated with six different fractionation schemes and imaged via time-resolved microscopy to yield 360- and 286-time courses for the 9L and C6 lines, respectively. These data were used to calibrate a biology-based mathematical model and then make predictions within two different scenarios. For Scenario 1, 70% of the time courses are fit to the model and the resulting parameter values are averaged. These average values, along with the initial cell number, initialize the model to predict the temporal evolution for each test time course (10% of the data). In Scenario 2, the predictions for the test cases are made with model parameters initially assigned from the training data, but then updated with new measurements every 24 hours via four versions of a data assimilation framework. We then compare the predictions made from Scenario 1 and the best version of Scenario 2 to the experimentally measured microscopy measurements using the concordance correlation coefficient (CCC). Across all fractionation schemes, Scenario 1 achieved a CCC value (mean ± standard deviation) of 0.845 ± 0.185 and 0.726 ± 0.195 for the 9L and C6 cell lines, respectively. For the best data assimilation version from Scenario 2 (validated with the last 20% of the data), the CCC values significantly increased to 0.954 ± 0.056 (p = 0.002) and 0.901 ± 0.061 (p = 8.9e-5) for the 9L and C6 cell lines, respectively. Thus, we have developed a data assimilation approach that incorporates an experimental-computational system to accurately predict the in vitro response of glioma cells to fractionated radiation therapy.

Data assimilation as a key step towards the implementation of an efficient management of dissolved oxygen in land-based aquaculture

A data assimilation (DA) methodology, e.g. the continuous-discrete Kalman filter (CD-KF), was applied to the assimilation of dissolved oxygen data, in order to obtain a dynamic estimation of the oxygen demand in a land-based aquafarm. The CD-KF was implemented on a dynamic model, which included as state variables the concentration of dissolved oxygen (DO) and fish respiration rate: the latter was considered as a non-observable stochastic variable. The model was applied to a 1-month long set of observations collected at a raceway rainbow trout farm, including (1) hourly time series of water temperature and dissolved oxygen concentration in the raceway influent and effluent and (2) a daily time series of fish number and fish weight distribution. The results show that the assimilation of DO data led to a dynamic estimate of DO demand which showed changes in the daily mean and the daily pattern: these were related to changes in the feeding regime. Furthermore, the methodology provided accurate short-term predictions of the DO concentration also in the presence of short-term fluctuations, which would be very difficult to relate to external forcings in a mechanistic model. These findings indicate that DA could be effectively used to design and implement efficient and robust control systems for optimizing the oxygen supply, thus contributing to the implementation of Precision Fish Farming in land-based aquafarms.

Simulating surface height and terminus position for marine outlet glaciers using a level set method with data assimilation

We implement a data assimilation framework for integrating ice surface and terminus position observations into a numerical ice-flow model. The model uses the well-known shallow shelf approximation (SSA) coupled to a level set method to capture ice motion and changes in the glacier geometry. The level set method explicitly tracks the evolving ice–atmosphere and ice–ocean boundaries for a marine outlet glacier. We use an Ensemble Transform Kalman Filter to assimilate observations of ice surface elevation and lateral ice extent by updating the level set function that describes the ice interface. Numerical experiments on an idealized marine-terminating glacier demonstrate the effectiveness of our data assimilation approach for tracking seasonal and multi-year glacier advance and retreat cycles. The model is also applied to simulate Helheim Glacier, a major tidewater-terminating glacier of the Greenland Ice Sheet that has experienced a recent history of rapid retreat. By assimilating observations from remotely-sensed surface elevation profiles we are able to more accurately track the migrating glacier terminus and glacier surface changes. These results support the use of data assimilation methodologies for obtaining more accurate predictions of short-term ice sheet dynamics.

Estimation for dynamical systems using a population-based Kalman filter – Applications in computational biology

Estimating dynamical systems — in particular identifying theirs parameters — involved in computational biology – for instance in pharmacology, in virology or in epidemiology – is fundamental to put in accordance the model trajectory with the measurements at hand. Unfortunately, when the sampling of data is very scarce or the data are corrupted by noise, parameters mean and variance priors must be chosen very adequately to balance our measurement distrust. Otherwise the identification procedure fails. A circumvention consists in using repeated measurements collected in configurations that share common priors – for instance with multiple population subjects in a clinical study or clusters in an epidemiology investigation. This common information is of benefit and is typically modeled in statistics by nonlinear mixed-effect models. In this paper, we introduce a data assimilation methodology compatible with such mixed-effect strategy without being strangled by the potential resulting curse of dimensionality. We define population-based estimators through maximum likelihood estimation. Then, from filtering theory, we set-up an equivalent robust large population sequential estimator that integrates the data as they are collected. Finally, we limit the computational complexity by defining a reduced-order version of this population Kalman filter clustering subpopulations of common observation background. The resulting algorithm performances are evaluated on classical pharmacokinetics benchmark. The versatility of the proposed method is finally fully challenged in a real-data epidemiology study of COVID spread in regions and departments of France.

Dense velocity, pressure and Eulerian acceleration fields from single-instant scattered velocities through Navier–Stokes-based data assimilation

In this study, a reconstruction procedure to infer full 3D instantaneous velocity and pressure fields from sparse velocity measurements is proposed, here focusing on the case of scattered data as provided by particle tracking velocimetry (PTV). A key characteristic of the present approach is that it only relies on single-instant velocity measurements, and does not require any time-resolved or acceleration information. It is based on a strong enforcement of the Navier–Stokes equations where the partial time derivative of the velocity field, namely Eulerian acceleration, is considered as a control vector to minimize the discrepancies between the single-instant measurements and the reconstructed flow. Eulerian acceleration is thus a byproduct of the present methodology in addition to the identification of the full velocity and pressure fields. The reconstruction performances of the proposed Navier–Stokes-based data-assimilation approach for single-instant velocity measurements (NS-DA-SIM) are assessed using a numerical dataset for the 3D flow past a cylinder. Comparisons with existing data assimilation methodologies allow to further illustrate the merits of the present approach. The latter is finally applied to the instantaneous reconstruction of an experimental air jet flow from volumetric PTV data, confirming its robustness and high efficacy.

Estimating Maize Yield in the Black Soil Region of Northeast China Using Land Surface Data Assimilation: Integrating a Crop Model and Remote Sensing.

Accurate yield estimation at the regional scale has always been a persistent challenge in the agricultural sector. With the vigorous emergence of remote sensing land surface observations in recent decades, data assimilation methodology has become an effective means to promote the accuracy and efficiency of yield estimation by integrating regional data and point-scale crop models. This paper focuses on the black soil area of Northeast China, a national strategic grain production base, applying the AquaCrop crop growth model to simulate the fractional vegetation cover (FVC) and maize yield from 2000 to 2020 and then forming a reliable FVC optimization dataset based on an ensemble Kalman filter (EnKF) assimilation algorithm with remote sensing products. Using the random forest model, the regression relationship between FVC and yield was established from the long-term time series data, which is crucial to achieve better yield estimation through the optimized FVC. The major findings include the following: (1) The R2 of the assimilated FVC and maize yield can reach 0.557. (2) When compared with the local statistical yield, our method reduced the mean absolute error (MAE) from 1.164 ton/ha (based on GLASS FVC products) to 1.004 ton/ha (based on the calibrated AquaCrop model) and then to 0.888 ton/ha (the result after assimilation). The above results show that we have proposed a yield estimation method to provide accurate yield estimations by combining data assimilation and machine learning. This study provided deep insights into understanding the variations in FVC and revealed the spatially explicit yield prediction ability from the time series land surface parameters, which has significant potential for optimizing water and soil resource management.

A Statistical Interpolation Code for Ocean Analysis and Forecasting

Abstract We present a data assimilation package for use with ocean circulation models in analysis, forecasting, and system evaluation applications. The basic functionality of the package is centered on a multivariate linear statistical estimation for a given predicted/background ocean state, observations, and error statistics. Novel features of the package include support for multiple covariance models, and the solution of the least squares normal equations either using the covariance matrix or its inverse—the information matrix. The main focus of this paper, however, is on the solution of the analysis equations using the information matrix, which offers several advantages for solving large problems efficiently. Details of the parameterization of the inverse covariance using Markov random fields are provided and its relationship to finite-difference discretizations of diffusion equations are pointed out. The package can assimilate a variety of observation types from both remote sensing and in situ platforms. The performance of the data assimilation methodology implemented in the package is demonstrated with a yearlong global ocean hindcast with a 1/4° ocean model. The code is implemented in modern Fortran, supports distributed memory, shared memory, multicore architectures, and uses climate and forecasts compliant Network Common Data Form for input/output. The package is freely available with an open source license from www.tendral.com/tsis/.