Operational Data Assimilation Research Articles

Toward Utilizing Similarity in Hydrologic Data Assimilation

Similarity to reality is a necessary property of models in earth sciences. Similarity information can thus possess a large potential in advancing geophysical modeling and data assimilation. We present a formalism for utilizing similarity within the existing theoretical data assimilation framework. Two examples illustrate the usefulness of utilizing similarity in data assimilation. The first, theoretical example shows changes in the accuracy of the amplitude estimate in the presence of a phase error in a sine function, where correcting the phase error prior to the assimilation reduces the degree of ill-posedness of the assimilation problem. This signifies the importance of accounting for the phase error in order to reduce the error in the amplitude estimate of the sine function. The second, real-world example illustrates that timing errors in simulated flow degrade the data assimilation performance, and that the flow gradient-informed shifting of rainfall time series improved the assimilation results with less adjusting model states. This demonstrates the benefit of utilizing streamflow gradients in shifting rainfall time series in a way to improve streamflow timing—vital information for flood early warning and preparedness planning. Finally, we discuss the implications, potential issues, and future challenges associated with utilizing similarity in hydrologic data assimilation.

Bias and multiscale correction methods for variational state estimation

Data assimilation performance can be significantly impacted by biased noise in observations, altering the signal magnitude and introducing fast oscillations or discontinuities when the system lacks smoothness. To mitigate these issues, this paper employs variational state estimation using the so-called parametrized-background data-weak method. This approach relies on a background manifold parametrized by a set of constraints, enabling the state estimation by solving a minimization problem on a reduced-order background model, subject to constraints imposed by the input measurements. The proposed formulation incorporates a novel bias correction mechanism and a manifold decomposition that handles rapid oscillations by treating them as slow-decaying modes based on a two-scale splitting of the classical reconstruction algorithm. The method is validated in different examples, including the assimilation of biased synthetic data, discontinuous signals, and Doppler ultrasound data obtained from experimental measurements.

Exploring the footprint representation of microwave radiance observations in an Arctic limited-area data assimilation system

Abstract. The microwave radiances are key observations, especially over data-sparse regions, for operational data assimilation in numerical weather prediction (NWP). An often applied simplification is that these observations are used as point measurements; however, the satellite field of view may cover many grid points of high-resolution models. Therefore, we examine a solution in high-resolution data assimilation to better account for the spatial representation of the radiance observations. This solution is based on a footprint operator implemented and tested in the variational assimilation scheme of the AROME-Arctic (Application of Research to Operations at MEsoscale – Arctic) limited-area model. In this paper, the design and technical challenges of the microwave radiance footprint operator are presented. In particular, implementation strategies, the representation of satellite field-of-view ellipses, and the emissivity retrieval inside the footprint area are discussed. Furthermore, the simulated brightness temperatures and the sub-footprint variability are analysed in a case study, indicating particular areas where the use of the footprint operator is expected to provide significant added value. For radiances measured by the Advanced Microwave Sounding Unit-A (AMSU-A) and Microwave Humidity Sounder (MHS) sensors, the standard deviation of the observation minus background (OmB) departures is computed over a short period in order to compare the statistics of the default and the implemented footprint observation operator. For all operationally used AMSU-A and MHS tropospheric channels, it is shown that the standard deviation of OmB departures is reduced when the footprint operator is applied. For AMSU-A radiances, the reduction is around 1 % for high-peaking channels and about 4 % for low-peaking channels. For MHS data, this reduction is somewhere between 1 %–2 % by the footprint observation operator.

The Met Office Forecast Ocean Assimilation Model (FOAM) using a 1/12‐degree grid for global forecasts

AbstractThe Met Office Forecast Ocean Assimilation Model (FOAM) ocean–sea‐ice analysis and forecasting operational system has been using an ORCA tripolar grid with 1/4° horizontal grid spacing since December 2008. Surface boundary forcing is provided by numerical weather prediction fields from the operational global atmosphere Met Office Unified Model. We present results from a 2‐year simulation using a 1/12° global ocean–sea‐ice model configuration while keeping a 1/4° data assimilation (DA) set‐up. We also describe recent operational data assimilation enhancements that are included in our 1/4° control and 1/12° simulations: a new bias‐correction term for sea‐level anomaly assimilation and a revised pressure correction algorithm. The primary effect of the first is to decrease the mean and variability of sea‐level anomaly increments at high latitudes, whereas the second significantly reduces the vertical velocity standard deviation in the tropical Pacific. The level of improvement achieved with the higher resolution configuration is moderate but consistently satisfactory when measured using neighbourhood verification metrics that provide fairer quantitative comparisons between gridded model fields at different spatial resolutions than traditional root‐mean‐square metrics. A comparison of the eddy kinetic energy from each configuration and an observation‐based product highlights the regions where further system developments are most needed.

Assimilation of Transformed Retrievals from IASI radiances versus direct assimilation of IASI radiances at the Met Office

AbstractSatellite radiances make up the vast majority of observations that are assimilated routinely at the Met Office and at other major numerical weather prediction (NWP) centres. Improvements in the use of these data have led to significant improvements in NWP forecast skill over the last 30 years. Since the advent of hyperspectral sensors, capable of measuring infrared radiance emerging from the atmosphere over thousands of channels, data providers and NWP centres have been facing the challenges of distributing, monitoring, and assimilating a considerable wealth of data. Forthcoming hyperspectral sensors such as the Infrared Atmospheric Sounding Interferometer New Generation (IASI‐NG) on MetOp Second Generation (Metop‐SG) and the Meteosat Third Generation Infrared Sounder (MTG‐IRS) will increase the amount of data to be considered for assimilation even further. It has been shown that Transformed Retrievals (TRs) generated from a spectrum of radiances can represent most of the information content of the radiances in a significantly reduced set of TR components. In this article we show for the first time, to our knowledge, that by assimilating TRs in an operational data assimilation system it is possible to achieve forecast skill gains similar to those when the same radiances used to generate the TRs are assimilated directly. These results pave the way to exploiting an order‐of‐magnitude larger number of channels from hyperspectral sounders for operational NWP.

Vertical Localization for Strongly Coupled Data Assimilation: Experiments in a Global Coupled Atmosphere‐Ocean Model

AbstractStrongly coupled data assimilation allows observations of one Earth system component (e.g., the ocean) to directly update another component (e.g., the atmosphere). The majority of the information transfer in strongly coupled atmosphere‐ocean systems is passed through vertical correlations between atmospheric boundary layer and ocean mixed layer fields. In this work we use correlations from a global, coupled model to study vertical observation‐space localization techniques for strongly coupled data assimilation. We generate target correlations using a bootstrapping approach from a single 24 hr forecast from a realistic global, weakly coupled atmosphere‐ocean cycling system with an 80‐member ensemble, which is the ensemble size currently used by the NOAA operational global data assimilation system. We compare data assimilation methods with different localization schemes using single‐update, offline experiments. We develop a new strategy for optimal observation space localization, called Empirical Optimal R‐localization (EORL), to give an upper bound on the improvement we can expect with any localization scheme. We then evaluate Gaspari‐Cohn localization, which is a commonly used parametric localization function and review its performance with respect to the optimal localization scheme. We investigate how the performance of these localization strategies changes with increasing ensemble sizes. Our results show that strongly coupled data assimilation has the potential to be an improvement over weakly coupled data assimilation when large ensembles are used. We also show that the Gaspari‐Cohn localization function does not appear to be a particularly good choice for cross‐fluid vertical localization.

Impacts of radar forward operator on convective-scale data assimilation and short-term forecasts

The current study utilizes the operational data assimilation system of Deutscher Wetterdienst (DWD) to investigate the impacts of improved radar forward operator. First of all, it is shown that for experiments in which both conventional and radar data are assimilated and the latent heat nudging (LHN) is applied, the one with improved operator (i.e., with improved Mie-scattering scheme and accounting for beam broadening effect and etc.) exhibits neutral impacts on short-term forecasts. However, in subsequent experiments, in which conventional data are not assimilated and the LHN is switched off, the one with improved operator not just reduces representation error during data assimilation cycles but also enhances the short-term forecast skills. In addition, it is found that the subsequent experiments result in much shorter observation error correlation length scales for radar reflectivity data, indicating that the application of the LHN or assimilation of conventional data may increase the length scales.

A neural-network-based method for generating synthetic 1.6 µm near-infrared satellite images

Abstract. In combination with observations from visible satellite channels, near-infrared channels can provide valuable additional cloud information, e.g. on cloud phase and particle sizes, which is also complementary to the information content of thermal infrared channels. Exploiting near-infrared channels for operational data assimilation and model evaluation requires a sufficiently fast and accurate forward operator. This study presents an extension to the method for fast satellite image synthesis (MFASIS) that allows for simulating reflectances of the 1.6 µm near-infrared channel based on a computationally efficient neural network with the same accuracy that has already been achieved for visible channels. For this purpose, it is important to better represent vertical variations in effective cloud particle radii, as well as mixed-phase clouds and molecular absorption in the idealized profiles used to train the neural network. A new approach employing a two-layer model of water, ice and mixed-phase clouds is described, and the relative importance of the different input parameters characterizing the idealized profiles is analysed. A comprehensive data set sampled from Integrated Forecasting System (IFS) forecasts together with different parameterizations of the effective water and ice particle radii is used for the development and evaluation of the method. Further evaluation uses a month of ICOsahedral Non-hydrostatic development based on version 2.6.1 (ICON-D2) hindcasts with effective radii directly determined by the two-moment microphysics scheme of the model. In all cases, the mean absolute reflectance error achieved is about 0.01 or smaller, which is an order of magnitude smaller than typical differences between reflectance observations and corresponding model values. The errors related to the imperfect training of the neural networks present only a small contribution to the total error, and evaluating the networks takes less than a microsecond per column on standard CPUs. The method is also applicable for many other visible and near-infrared channels with weak water vapour sensitivity.

Simulation of a clear sky satellite image in water vapor and infrared satellite M.S.G channel’s

Radiative transfer models are an important tool for the scientific community. Such models simulate the radiative transfer processes of the atmosphere at a given wavelength or spectral region for a given set of surface and atmospheric conditions. It is used to simulate the radiances and brightness temperatures of various satellite sensors. RTTOV stands for ‘Radiative Transfer for TIROS Operational Vertical Sounder’ and refers to the computational efficient algorithms that have been developed by Eumetsat within the framework of SAF to meet the requirements of the operational data assimilation system. The aim of our work is to allow a simulation of infrared image of MSG2 satellite, by the RTTOV model, starting from the temperature and humidity profiles resulting from a weather forecasting model. The results are satisfactory, the evaluation have shown that the RTTOV model is effective enough for water vapor channels, while it appears less effective for the rest of the channels.

Hyper-parameter optimization for improving the performance of localization in an iterative ensemble smoother

This work aims to help improve the performance of an iterative ensemble smoother (IES) in reservoir data assimilation problems, by introducing a data-driven procedure to optimize the choice of certain algorithmic hyper-parameters in the IES. Generally speaking, algorithmic hyper-parameters exist in various data assimilation algorithms. Taking IES as an example, localization is often useful for improving its performance, yet applying localization to an IES also introduces a certain number of algorithmic hyper-parameters, such as localization length scales, in the course of data assimilation. While different methods have been developed in the literature to address the problem of properly choosing localization length scales in various circumstances, many of them are tailored to specific problems under consideration, and may be difficult to directly extend to other problems. In addition, conventional hyper-parameter tuning methods determine the values of localization length scales based on either empirical (e.g., using experience, domain knowledge, or simply the practice of trial and error) or analytic (e.g., through statistical analyses) rules, but few of them use the information of observations to optimize the choice of hyper-parameters. The current work proposes a generic, data-driven hyper-parameter tuning strategy that has the potential to overcome the aforementioned issues. With this proposed strategy, hyper-parameter optimization is converted into a conventional parameter estimation problem, in such a way that observations are utilized to guide the choice of hyper-parameters. One noticeable feature of the proposed hyper-parameter tuning strategy is that it iteratively estimates an ensemble of hyper-parameters. In doing so, the resulting hyper-parameter tuning procedure receives some practical benefits inherent to conventional ensemble data assimilation algorithms, including the nature of being derivative-free, the ability to provide uncertainty quantification to some extent, and the capacity to handle a large number of hyper-parameters. Through 2D and 3D case studies, it is shown that when the proposed hyper-parameter tuning strategy is applied to tune a set of localization length scales (up to the order of 103) in a parameterized localization scheme, superior data assimilation performance is obtained in comparison to an alternative hyper-parameter tuning strategy without utilizing the information of observations.

Spatiotemporal estimation of analysis errors in the operational global data assimilation system at the China Meteorological Administration using a modified SAFE method

AbstractQuantification of the uncertainties in initial analyses against the real atmosphere (“reality”) provides a fundamental reference for the evaluation and development of operational data assimilation (DA) systems. Due to the unknown reality, most existing methods for analysis error estimation use reanalysis datasets or observations as a proxy for reality, which are empirical, non‐objective, and biased. Unlike these methods, our study adopted a modified Statistical Analysis and Forecast Error (SAFE) estimation method to objectively and directly quantify spatiotemporal errors in analyses compared to reality based on unbiased assumptions. In the present study, the SAFE method was first applied to estimate the annual variation and spatial distribution of analysis errors in the Global Forecast System of Global/Regional Assimilation and PrEdiction System (GRAPES_GFS) at the China Meteorological Administration (CMA) since the beginning of its operational implementation (i.e., 2016–2021). Qualitative comparison to analysis error estimations in previous studies showed that SAFE can provide more reasonable spatial‐mean analysis error profiles than can the estimation with the ERA‐5 reanalysis as a reference (the approach hereafter called “ERAv”). Moreover, ERAv overestimates (underestimates) the spatial‐mean analysis error below (above) approximately 500 hPa compared to SAFE because it neglects the uncertainties inherent in reanalysis. Overall, the SAFE estimation reveals that relative reductions of about 12.5%, 29%, and 24.5% were achieved for the spatial‐mean analysis errors of wind, temperature, and geopotential height, respectively, in the GRAPES_GFS throughout the six‐year study period. These results can largely be attributed to the DA scheme being upgraded from 3D‐Var to 4D‐Var. SAFE can also provide more reasonable and accurate pointwise analysis errors than ERAv can.

All‐sky infrared radiance assimilation of a geostationary satellite in the Japan Meteorological Agency's global system

AbstractAll‐sky assimilation of infrared (IR) radiances has been developed for water vapor bands of the geostationary satellite Himawari‐8 in the operational global data assimilation system. Cloud‐dependent quality control, bias correction, and observation error modeling are essential developments to effectively utilize the all‐sky radiances (ASRs). ASR assimilation increases the assimilated number of observations by 2.8 times and improves the coverage relative to the traditional clear‐sky radiance (CSR) assimilation. The additional observations better alleviate model dry biases in the middle and upper tropospheric humidity. ASR assimilation brings statistically significant improvements in the background (first guess) in humidity, temperature, and wind over the CSR assimilation. It also better improves short‐range forecasts of the middle and upper tropospheric temperature and humidity up to day 3 in the Tropics. A mixed impact in the stratospheric temperature is under investigation. The impacts of various aspects of the ASR assimilation configuration are evaluated with sensitivity assimilation experiments. The interband correlation and cloud‐dependent standard deviation of the observation error are crucial, whereas the cloud dependency of the correlation is not so important. Although ASRs at a single band were assimilated in many previous studies targeting severe weather using research‐based regional assimilation systems due to decreasing independent information in the presence of clouds, they are distinctly inferior to not only ASRs at multiple bands but also CSRs at multiple bands in a global data assimilation system that contains fewer cloud‐affected scenes. The cloud‐dependent bias correction predictors are essential in the presence of observation‐minus‐background bias that increases with cloud effects.

Assessing the influence of crop model structure on the performance of data assimilation for sugarcane

Process-base crop models (PBM) are important tools to describe how the agricultural system responds to environmental conditions. Sugarcane represents a major world source of sugar and ethanol and its PBMs had different levels of complexity in terms of structure, i.e. how detailed their processes were described. Yet, literature has widely demonstrated that data assimilation techniques (DA) represent a valuable option for reducing model uncertainty, but the inconsistency between PBM and the assimilated variable can significantly affect the performance of DA. Such limitation is strictly connected to model structure, and a hypothesis that arises from literature is that the use of more complex models would reduce model uncertainty after DA. We accessed the performance of using two different PBMs, one more detailed (DSSAT/SAMUCA, DS) and the other more general (WOFOST, WO), by assimilating leaf area index (LAI) retrieved from Landsat 7 ETM + and 8/OLI, using the Ensemble Kalman Filter (EnKF). Both PBMs were calibrated and evaluated with a robust database of 13 experiments and evaluated against a sugarmill database to evaluate the EnKF performance, compared with simulations without DA (Open-loop, OP). Moreover, the processes involved in LAI simulations were analyzed to assess the EnKF performance. The DS had superior performance in the calibration and evaluation step with EF = 0.907, 0.878, 0.458 for stalk dry mass, stalk fresh yield (SFY), and LAI, while WO showed EF = 0.622, 0.610, 0.417 for the same variables, respectively. The calibration step affected the OP plot simulation, with DS having higher accuracy (RMSE = 31.678 Mg ha−1) and precision (R2 = 0.509), compared with WO (RMSE = 39.593 Mg ha−1; R2 = 0.458). However, after DA, both PBM presented error inconsistency with EnKF, despite the decrease in RMSE (-44.73% and −29.58%) and increase in R2 (22.15% and 36.50%) of DS and WO, respectively. The error inconsistency diverged from each PBM: the OP simulation of DS overestimated the Landsat LAI; after DA, simulated LAI decreased resulting in SFY underestimation (Bias = -11.469 Mg ha−1); WO showed OP simulations for LAI closer to Landsat’s LAI values, despite the positive Bias in SFY estimation, and so EnKF slightly reduced the SFY overestimation (Bias = 22.944 Mg ha−1). Thus, the better descriptions of DS in terms of structure did not inhibit the error inconsistency. We suggested that new studies are required to understand how the assimilated variables impact on the other state variables of the PBM.

Estimation of CH4emission based on an advanced 4D-LETKF assimilation system

Abstract. Methane (CH4) is the second major greenhouse gas after carbon dioxide (CO2) which has substantially increased during recent decades in the atmosphere, raising serious sustainability and climate change issues. Here, we develop a data assimilation system for in situ and column-averaged concentrations using a local ensemble transform Kalman filter (LETKF) to estimate surface emissions of CH4. The data assimilation performance is tested and optimized based on idealized settings using observation system simulation experiments (OSSEs), where a known surface emission distribution (the truth) is retrieved from synthetic observations. We tested three covariance inflation methods to avoid covariance underestimation in the emission estimates, namely fixed multiplicative (FM), relaxation-to-prior spread (RTPS), and adaptive multiplicative. First, we assimilate the synthetic observations at every grid point at the surface level. In such a case of dense observational data, the normalized root mean square error (RMSE) in the analyses over global land regions is smaller by 10 %–15 % in the case of RTPS covariance inflation method compared to FM. We have shown that integrated estimated flux seasonal cycles over 15 regions using RTPS inflation are in reasonable agreement between true and estimated flux, with 0.04 global normalized annual mean bias. We then assimilated the column-averaged CH4 concentration by sampling the model simulations at Greenhouse Gases Observing Satellite (GOSAT) observation locations and time for another OSSE. Similar to the case of dense observational data, the RTPS covariance inflation method performs better than FM for GOSAT synthetic observation in terms of normalized RMSE (2 %–3 %) and integrated flux estimation comparison with the true flux. The annual mean averaged normalized RMSE (normalized mean bias) in LETKF CH4 flux estimation in the case of RTPS and FM covariance inflation is found to be 0.59 (0.18) and 0.61 (0.23), respectively. The χ2 test performed for GOSAT synthetic observations assimilation suggests high underestimation of background error covariance in both RTPS and FM covariance inflation methods; however, the underestimation is much higher (>100 % always) for FM compared to RTPS covariance inflation method.

Investigation of links between dynamical scenarios and particularly high impact of Aeolus on numerical weather prediction (NWP) forecasts

Abstract. Global wind profiles from the Aeolus satellite mission provide an important source of wind information for numerical weather prediction (NWP). Data assimilation experiments show large mean changes in the analysis and a significant reduction in forecast errors. At Deutscher Wetterdienst (DWD), a 3-month observing system experiment (OSE), from July 2020 to October 2020, was performed to evaluate the impact of the Aeolus horizontal line-of-sight (HLOS) wind observations in the operational data assimilation system of the ICOsahedral Nonhydrostatic (ICON) global model. To better understand the underlying dynamics leading to the overall beneficial impact, specific time periods and regions with a particularly high impact of Aeolus are investigated. In this study, we illustrate three examples of atmospheric phenomena that constitute dynamical scenarios for significant forecast error reduction through the assimilation of Aeolus: the phase shift of large-scale tropical circulation systems, namely the Quasi-Biennial Oscillation (QBO) and the El Niño–Southern Oscillation (ENSO), and the interaction of tropical cyclones undergoing extratropical transition (ET) with the midlatitude waveguide.

A‐CHAIM: Near‐Real‐Time Data Assimilation of the High Latitude Ionosphere With a Particle Filter

AbstractThe Assimilative Canadian High Arctic Ionospheric Model (A‐CHAIM) is an operational ionospheric data assimilation model that provides a 3D representation of the high latitude ionosphere in Near‐Real‐Time (NRT). A‐CHAIM uses low‐latency observations of slant Total Electron Content (sTEC) from ground‐based Global Navigation Satellite System (GNSS) receivers, ionosondes, and vertical TEC from the JASON‐3 altimeter satellite to produce an updated electron density model above 45° geomagnetic latitude. A‐CHAIM is the first operational use of a particle filter data assimilation for space environment modeling, to account for the nonlinear nature of sTEC observations. The large number (>104) of simultaneous observations creates significant problems with particle weight degeneracy, which is addressed by combining measurements to form new composite observables. The performance of A‐CHAIM is assessed by comparing the model outputs to unassimilated ionosonde observations, as well as to in‐situ electron density observations from the SWARM and DMSP satellites. During moderately disturbed conditions from 21 September 2021 through 29 September 2021, A‐CHAIM demonstrates a 40%–50% reduction in error relative to the background model in the F2‐layer critical frequency (foF2) at midlatitude and auroral reference stations, and little change at higher latitudes. The height of the F2‐layer (hmF2) shows a small 5%–15% improvement at all latitudes. In the topside, A‐CHAIM demonstrates a 15%–20% reduction in error for the Swarm satellites, and a 23%–28% reduction in error for the DMSP satellites. The reduction in error is distributed evenly over the assimilation region, including in data‐sparse regions.

Ensemble based methods for leapfrog integration in the simplified parameterizations, primitive‐equation dynamics model

AbstractThis paper presents efficient and practical implementations of sequential data assimilation methods for the Simplified Parameterizations, primitive‐Equation DYnamics (SPEEDY) Model, a well‐known numerical model, into the data assimilation community for climate prediction. In the SPEEDY model, the time evolution of dynamics is performed via the second‐order Leapfrog integration scheme; this time integrator relies on two steps: the position and the velocity. The computational implementation of SPEEDY blends the time integrator and the spatial discretization of dynamics to accelerate algebraic computations. Thus, there is no access to the right‐hand side function of the ordinary differential equations governing the time evolution of model dynamics. Consequently, the SPEEDY model is often treated as a black box wherein positions and velocities work as inputs and outputs. Since observations in operational data assimilation only match position states, we can exploit augmented vector states to propagate analysis innovations from positions to velocities. For this purpose, we formulate three variants of ensemble‐based filters and perform numerical experiments to assess their accuracies. We consider two scenarios for the experiments: an ideal case wherein positions and velocities can be observed and a more realistic one wherein measurements are only accessible for position states. Besides, we discuss the effects of the ensemble size on the accuracies of our formulations and, even more, the typical case in which velocities are not updated across assimilation steps. The results reveal that all filter formulations' accuracies remain the same in terms of Root‐Mean‐Square‐Error by neglecting observations from velocities (a realistic scenario) even for cases wherein the number of measurements decreases to 6% of model components. Furthermore, for all discussed filter implementations, the propagation of analysis increments from position to velocities improves up to 100% the performance of filter implementations wherein velocities are not updated, a typical operational scenario.

Reducing Biases in Thermal Infrared Surface Radiance Calculations Over Global Oceans

Thermal infrared (IR) environmental satellite data assimilation and remote sensing of the surface and lower troposphere depend on accurate specification of the spectral surface emissivity within clear-sky forward calculations. Over ocean surfaces, accurate modeling of surface-leaving radiances over the sensor scanning swaths is complicated by a quasi-specular bidirectional reflectance distribution function (BRDF). Recent findings at the Joint Center for Satellite Data Assimilation (JCSDA) have also revealed significant zonally varying systematic biases (≈ |0.5| K) on a global scale over cold ocean waters, these the result of temperature dependence in the thermal IR optical constants. This paper proposes practical solutions to these problems by modeling thermal IR “effective emissivity” in a manner that accounts for both surface emission and quasi-specular reflectance, along with temperature dependence, while meeting the latency and computational constraints of operational global data assimilation and retrieval systems. We overview the theoretical basis of the model and validate it against ship-based Marine Atmospheric Emitted Radiance Interferometer (MAERI) spectra obtained from cold and warm water ocean campaigns.

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.

Real-time thermoacoustic data assimilation

Low-order thermoacoustic models are qualitatively correct, but typically, they are quantitatively inaccurate. We propose a time-domain bias-aware method to make qualitatively low-order models quantitatively (more) accurate. First, we develop a Bayesian ensemble data assimilation method for a low-order model to self-adapt and self-correct any time that reference data become available. Second, we apply the methodology to infer the thermoacoustic states and heat-release parameters on the fly without storing data (real time). We perform twin experiments using synthetic acoustic pressure measurements to analyse the performance of data assimilation in all nonlinear thermoacoustic regimes, from limit cycles to chaos, and interpret the results physically. Third, we propose practical rules for thermoacoustic data assimilation. An increase, reject, inflate strategy is proposed to deal with the rich nonlinear behaviour; and physical time scales for assimilation are proposed in non-chaotic regimes (with the Nyquist–Shannon criterion) and in chaotic regimes (with the Lyapunov time). Fourth, we perform data assimilation using data from a higher-fidelity model. We introduce an echo state network to estimate in real time the forecast bias, which is the model error of the low-fidelity model. We show that: (i) the correct acoustic pressure, parameters, and model bias can be inferred accurately; (ii) the learning is robust as it can tackle large uncertainties in the observations (up to 50 % of the mean values); (iii) the uncertainty of the prediction and parameters is naturally part of the output; and (iv) both the time-accurate solution and statistics can be inferred successfully. Data assimilation opens up new possibility for real-time prediction of thermoacoustics by combining physical knowledge and experimental data synergistically.