Data Assimilation Studies Research Articles

Fundamental Properties of Adjoint Model and Adjoint Sensitivity Under Fully Nonlinear Hydrostatic Internal Gravity Waves

AbstractAdjoint sensitivity modeling plays an important role in inverse problems, including four‐dimensional variational data assimilation or state estimation, by providing the sensitivity of the objective (or cost) function to the model input data. Although data assimilation has become common in regional ocean modeling, and the model resolution has become high enough to resolve internal tides, it remains unclear whether physically sensible and stable adjoint sensitivity modeling is feasible in the presence of internal waves. As a first step to tackle this problem, this study investigates fundamental properties of the adjoint of a time‐dependent circulation model, and the resulting sensitivity under internal waves. The theoretical and numerical results, based on simple‐internal‐wave theory and MITgcm modeling, show that stable adjoint sensitivity modeling is feasible under fully nonlinear (but stable) hydrostatic internal waves. However, it requires a careful choice of the objective function to obtain sensitivity which has the same propagation properties as (real‐world) internal waves, because the definition primarily controls the directionality and vertical‐mode content of internal‐wave signals in the adjoint model. Also, it should be noted that the internal‐wave signals lack indirect sensitivity through the dependence of the wave‐propagation speed on the model's prognostic variables. An important implication of the results is that the standard form of the objective function, which has been used in data assimilation studies for quasi‐geostrophic flows and barotropic tides, could be problematic for internal tides.

Application of coastal acoustic tomography: calibration of open boundary conditions on a numerical ocean model for tidal currents

Coastal acoustic tomography (CAT), which measures path-averaged currents from reciprocal acoustic transmission experiments and reconstructs velocity fields from the multiple path-averaged current data, is useful for monitoring tidal currents in coastal shallow water, especially if data assimilation is employed. Previous CAT data assimilation studies have focused on state estimation problems, i.e., the reconstruction of tidal currents and following dynamical discussion. In this study, we investigate the use of path-averaged currents in a boundary control problem. Specifically, we aim to use the observed path-averaged currents to determine the parameters of a numerical ocean model, which were tidal amplitudes and phases as the open boundary conditions in this study. We investigate two methods: using the ensemble Kalman filter (EnKF) results and a linearization approach called model Green’s function method. Both calibration methods decreased the amplitudes of tidal constituents at the open boundaries. We compare the model performance between the model predictions with and without the calibration of the open boundary conditions. The model predictions with the calibrated open boundary conditions improved the agreement with the observed path-averaged current. We also implemented the sequential updates of EnKF with the two calibrated open boundary conditions. The EnKF results with the independently calibrated two open boundary conditions improved the agreement with the comparison data obtained by acoustic Doppler current profiler measurement compared with the original EnKF result with the initial open boundary conditions.

MESMAR v1: a new regional coupled climate model for downscaling, predictability, and data assimilation studies in the Mediterranean region

Abstract. Regional coupled and Earth system models are fundamental numerical tools for climate investigations, downscaling of predictions and projections, process-oriented understanding of regional extreme events, and many more applications. Here we introduce a newly developed coupled regional modeling framework for the Mediterranean region, called MESMAR (Mediterranean Earth System model at ISMAR) version 1, which is composed of the Weather Research and Forecasting (WRF) atmospheric model, the NEMO oceanic model, and the hydrological discharge (HD) model, coupled via the OASIS coupler. The model is implemented at about 1/12∘ of horizontal resolution for the ocean and river routing, while roughly twice coarser for the atmosphere, and it is targeted to long-term investigations. We focus on the evaluation of skill score metrics from several sensitivity experiments devoted to (i) understanding the best vertical physics configuration for NEMO, (ii) identifying the impact of the interactive river runoff, and (iii) choosing the best-performing physics–microphysics suite for WRF in the regional coupled system. The modeling system has been developed for downscaling reanalyses and long-range predictions, as well as coupled data assimilation experiments. We then formulate and show the performance of the system when weakly coupled data assimilation is embedded in the system (variational assimilation in the ocean and spectral nudging in the atmosphere), in particular for the representation of extreme events like intense Mediterranean cyclones (i.e., medicanes). Finally, we outline plans for future extension of the modeling framework.

Last glacial maximum cooling of 9 °C in continental Europe from a 40 kyr-long noble gas paleothermometry record

The Last Glacial Maximum (LGM; ∼26–18 kyr ago) is a time interval of great climatic interest characterized by substantial global cooling driven by radiative forcings and feedbacks associated with orbital changes, lower atmospheric CO2, and large ice sheets. However, reliable proxies of continental paleotemperatures are scarce and often qualitative, which has limited our understanding of the spatial structure of past climate changes. Here, we present a quantitative noble gas temperature (NGT) record of the last ∼40 kyr from the Albian aquifer in Eastern Paris Basin (France, ∼48°N). Our NGT data indicate that the mean annual surface temperature was ∼5 °C during the Marine Isotope Stage 3 (MIS3; ∼40–30 kyr ago), before cooling to ∼2 °C during the LGM, and warming to ∼11 °C in the Holocene, which closely matches modern ground surface temperatures in Eastern France. Combined with water stable isotope analyses, NGT data indicate δD/NGT and δ18O/NGT transfer functions of +1.6 ± 0.4‰/°C and +0.18 ± 0.04‰/°C, respectively. Our noble-gas derived LGM cooling of ∼9 °C (relative to the Holocene) is consistent with previous studies of noble gas paleothermometry in European groundwaters but larger than the low-to-mid latitude estimate of 5.8 ± 0.6 °C derived from a compilation of noble gas records, which supports the notion that continental LGM cooling was more extreme at higher latitudes. While an LGM cooling of ∼9 °C in Eastern France appears compatible with recent data assimilation studies, this value is greater than most estimates from current-generation climate model simulations of the LGM. Comparing our estimate for the temperature in Eastern France during MIS3 (6.4 ± 0.5 °C) with GCM outputs presents a promising avenue to further evaluate climate model simulations and constrain European climate evolution over the last glacial cycle.

Design and Implementation of a Low-Cost Air Quality Network for the Aburra Valley Surrounding Mountains

The densest network for measuring air pollutant concentrations in Colombia is in Medellin, where most sensors are located in the heavily polluted lower parts of the valley. Measuring stations in the higher elevations on the mountains surrounding the valley are not available, which limits our understanding of the valley’s pollutant dynamics and hinders the effectiveness of data assimilation studies using chemical transport models such as LOTOS-EUROS. To address this gap in measurements, we have designed a new network of low-cost sensors to be installed at altitudes above 2000 m.a.s.l. The network consists of custom-built, solar-powered, and remotely connected sensors. Locations were strategically selected using the LOTOS-EUROS model driven by diverse meteorology-simulated fields to explore the effects of the valley wind representation on the transport of pollutants. The sensors transmit collected data to internet gateways for posterior analysis. Various tests to verify the critical characteristics of the equipment, such as long-range transmission modeling and experiments with an R score of 0.96 for the best propagation model, energy power system autonomy, and sensor calibration procedures, besides case exposure to dust and water experiments, to ensure IP certifications. An inter-calibration procedure was performed to characterize the sensors against reference sensors and describe the observation error to provide acceptable ranges for the data assimilation algorithm (<10% nominal). The design, installation, testing, and implementation of this air quality network, oriented towards data assimilation over the Aburrá Valley, constitute an initial experience for the simulation capabilities toward the system’s operative capabilities. Our solution approach adds value by removing the disadvantages of low-cost devices and offers a viable solution from a developing country’s perspective, employing hardware explicitly designed for the situation.

Reconstruction of horizontal tidal current fields in a shallow water with model-oriented coastal acoustic tomography

Reciprocal acoustic transmission and coastal acoustic tomography (CAT) is a powerful tool for measuring tidal currents in shallow coastal water, especially if data assimilation is employed. In previous CAT data assimilation studies, the ensemble Kalman filter (EnKF) has been implemented to assimilate observed path-averaged velocity, but ad-hoc procedures called localization and inflation, which compensate for issues associated with using ensemble approximation, were not always implemented. In this study, EnKF is applied to assimilate the path-averaged currents obtained from a reciprocal acoustic transmission experiment conducted at Mihara-Seto in the Seto Inland Sea, Japan, with four acoustic stations in 2020 to reconstruct spatiotemporal variations of tidal currents at the observation site. We executed EnKF with several combinations of different values of the inflation, localization, and the number of ensemble members. The resulting data assimilated velocity reconstructions are compared with acoustic Doppler current profiling (ADCP) results. The results show that data assimilation with EnKF improved the velocity reproduction compared with the model prediction and that implementing covariance inflation contributed to additional improvements. The covariance localization did not improve the results in our case. The best result in terms of fractional error variance (FEV) between the ADCP velocity was obtained from the case with 980 ensemble members with a covariance inflation of 1.01; the FEV was 7.9%. The case of 98 ensemble members with a covariance inflation of 1.01 resulted in similar performance; the FEV value was 8.2%. Thus, with the covariance inflation, the number of ensemble member used in previous CAT studies are reasonable. In the study, we also clarified the reason for the high-frequency variation in the observed path-averaged currents in a preliminary experiment; the path-averaged currents had captured the spatiotemporal variation of vortex generation associated with island wakes. The reciprocal acoustic transmission with EnKF can capture short-period variation over a long period; thus, it can be used in studies of coastal physical processes with various time scales.

A global-scale intercomparison of Triple Collocation Analysis- and ground-based soil moisture time-variant errors derived from different rescaling techniques

Accurate specification of spatiotemporal errors of remotely sensed soil moisture (SM) data is essential for a correct assessment of their utility and optimally integrating multiple SM products or assimilating them into hydrological models. Although Triple Collocation Analysis (TCA) has been widely used to provide SM errors, the impact of rescaling technique on the TCA error estimates has not received major attention, which can lead to biased and inaccurate error estimates. Moreover, current knowledge about time-variant SM errors derived from TCA is still very limited, which hampers the advance of applying time-variant errors in data merging and data assimilation studies efficiently. Based on these considerations, this work aims to advance the use of the TCA for characterizing errors with a focus on the rescaling techniques, and validating TCA-based time-variant errors using global ground measurements in 759 grid cells. To this end, the Advanced Scatterometer (ASCAT) and four passive-based SM products, including Soil Moisture and Ocean Salinity Level-3 (SMOS-L3), SMOS INRA-CESBIO (SMOS-IC), Soil Moisture Active Passive Level-3 (SMAP-L3), and SMAP INRAE BORDEAUX (SMAP-IB) SM products, were considered. The time-variant error term here denotes an aggregate error magnitude over a 101-day moving-time-window. It is found that different selection of the rescaling technique considered in TCA led to TCA error estimates with significantly different accuracy when ground-based errors are regarded as the benchmark. The optimal combination strategy to implement TCA is applying TCA to SM anomalies and rescaling the errors by coefficients derived from the TCA model. Pearson's correlation with ground-based time-variant errors is 0.62, 0.72, 0.83, 0.89, and 0.93 for SMAP-IB, SMAP-L3, SMOS-IC, SMOS-L3, and ASCAT SM, respectively. Considering time-variant errors in applications is necessary since time-variant errors deviate from time-invariant errors by 50% when errors are rescaled by the TCA model parameters. Time-invariant errors are greater than time-variant errors when SM products are rescaled against a reference dataset while the opposite conclusion can be drawn when errors are rescaled by the TCA coefficients. TCA- and ground-based methods provide consistent evaluations in 74.7% (77.3%), 75.8% (79.8%), 79.6% (81.1%), and 78.6% (79.7%) of the analysis period on average (median) for the TCA implementations with SMAP-L3, SMAP-IB, SMOS-L3, and SMOS-IC SM, respectively. The error analysis reveals that TCA typically underestimated ASCAT errors while overestimated passive SM errors when considering ground-based evaluation as the benchmark. Moreover, TCA was found to have relatively less power to efficiently characterize SM errors in croplands when compared with other land cover types. This study validated TCA time-variant errors using ground measurements and compared TCA- and ground-based evaluation performances on a global scale. Our work arouses particular attention to the rescaling technique selection considered in TCA, which is crucial for accurately characterizing SM errors and efficiently using them in various hydrometeorological applications.

Variational parameter estimation in a two-equation turbulence model: A case study with a 3D primitive-equation ocean model

A three-dimensional and complete adjoint model of the Princeton Ocean Model with a generalized coordinate system (POMgcs) is developed to construct the 4D-Variational data assimilation (4D-Var) algorithm in this study. Uncertain parameters in the Mellor-Yamada 2.5 turbulence submodel (MY-2.5) which is enclosed in POMgcs, are tentatively estimated via the 4D-VAR algorithm within a biased model framework. Here, the control variables in the biased model are set to two uncertain wave-affected parameters (wave energy factor α and Charnock coefficient β ) in the MY-2.5 turbulence model, which play a crucial role in modulating the heat content distribution in the upper coastal sea. First of all, the ocean temperature and salinity in a typical coastal sea, Bohai Sea, are simulated by the model to validate the rationally of the MY-2.5 parameterization scheme for both constructing the “truth model” and generating the “pseudo-observations” in the data assimilation studies. Then, after thoroughly testing the ability of the 4D-Var to optimize the initial state fields of the POMgcs model, a series of parameter estimation experiments are carried out to investigate whether and to what degree the parameters embedded in high-order turbulence models can be significantly optimized. Results of parameter estimation with perfect initial fields show the two estimated parameters in the MY-2.5 submodel can successfully converge to the “truth” value. The local minimum of the cost function can be effectively and efficiently jumped out once two kinds of optimization algorithms, LBFGS and LMBM, are jointly used. In addition, the estimated parameter will converge to the optimal value rather than the truth one to compensate for the initial field error when the state-parameter are estimated simultaneously. Further, the performance of the parameter estimation is also deeply discussed when the observation samples are noised. Finally, prescribing the initial field and parameter as error source, a forecasting experiment for sea temperature is performed. The experiment results indicate that assimilating “pseudo-observations” to the model based on 4D-Var can significantly improve the sea temperature simulation. Moreover, adjusting the initial field and parameter leads to a better result than the only initial field, and this conclusion is more evident at the surface than in the deeper ocean.

Jacobians of single-scattering optical properties of super-spheroids computed using neural networks.

In atmospheric aerosol remote sensing and data assimilation studies, the Jacobians of the optical properties of non-spherical aerosol particles are required. Specifically, the partial derivatives of the extinction efficiency factor, single-scattering albedo, asymmetry factor, and scattering matrix should be obtained with respect to microphysical parameters, such as complex refractive indices, shape parameters and size parameters. When a look-up table (LUT) of optical properties of particles is available, the Jacobians traditionally can be calculated using the finite difference method (FDM), but the accuracy of the process depends on the resolution of microphysical parameters. In this paper, a deep learning scheme was proposed for computing Jacobians of the optical properties of super-spheroids, which is a flexible model of non-spherical atmospheric particles. Using the neural networks (NN), the error of the Jacobians in the FDM can be reduced by more than 60%, and the error reduction rate of the Jacobians of the scattering matrix elements can be more than 90%. We also tested the efficiency of the NN for computing the Jacobians. The computation takes 30 seconds for one million samples on a host with an NVIDIA GeForce RTX 3070 GPU. The accuracy and efficiency of the present NN scheme proves it is promising for applications in remote sensing and data assimilation studies.

Quantifying and Reducing Uncertainty in Global Carbon Cycle Predictions: Lessons and Perspectives From 15 Years of Data Assimilation Studies With the ORCHIDEE Terrestrial Biosphere Model

AbstractPredicting terrestrial carbon, C, budgets and carbon‐climate feedbacks strongly relies on our ability to accurately model interactions between vegetation, C and water cycles, and the atmosphere. However, C fluxes simulated by global, process‐based terrestrial biosphere models (TBMs) remain subject to large uncertainties, partly due to unknown or poorly calibrated parameters. This is because TBMs have not routinely been confronted against C cycle related datasets within a statistical data assimilation (DA) system. In this review, we present 15 years' development of a C cycle DA system for optimizing C cycle parameters of the ORCHIDEE TBM. We analyze the impact of assimilating multiple different C cycle related datasets on regional to global‐scale gross and net CO2 fluxes. We find that assimilating atmospheric CO2 data is crucial for improving (increasing) ORCHIDEE predictions of the terrestrial land C sink. The improvement is predominantly due to the global‐scale constraint these data provide for optimizing initial soil C stocks, which are likely in error due to inaccurate assumptions about steady state spin‐up and incomplete knowledge of land use change histories. When comparing the data‐constrained ORCHIDEE land C sink estimates to the CAMS atmospheric inversion, we show that while the two approaches agree on the global C sink magnitude, they continue to differ in how the global C sink is partitioned between the northern hemisphere and tropics. We also discuss technical challenges faced in our C cycle DA studies, in particular the difficulty in characterizing the error covariance matrix due to unknown observation biases and/or model‐data inconsistencies. We offer our perspectives on how to tackle these challenges that we hope can serve as a roadmap for other TBM groups wishing to develop C cycle DA systems.

Optimal Planning of Air Quality-Monitoring Sites for Better Depiction of PM2.5 Pollution across China.

A myriad of studies have attempted to use ground-level observations to obtain gap-free spatiotemporal variations of PM2.5, in support of air quality management and impact studies. Statistical methods (machine learning, etc.) or numerical methods by combining chemical transport modeling and observations with data assimilation techniques have been typically applied, yet the significance of site placement has not been well recognized. In this study, we apply five proper orthogonal decomposition (POD)-based sensor placement algorithms to identify optimal site locations and systematically evaluate their reconstruction ability. We demonstrate that the QR pivot is relatively more reliable in deciding optimal monitoring site locations. When the number of planned sites (sensors) is limited, using a lower number of modes would yield lower estimation errors. However, the dimension of POD modes has little impact on reconstruction quality when sufficient sensors are available. The locations of sites guided by the QR pivot algorithm are mainly located in regions where PM2.5 pollution is severe. We compare reconstructed PM2.5 pollution based on QR pivot-guided sites and existing China National Environmental Monitoring Center (CNEMC) sites and find that the QR pivot-guided sites are superior to existing sites with respect to reconstruction accuracy. The current planning of monitoring stations is likely to miss sources of pollution in less-populated regions, while our QR pivot-guided sites are planned based on the severity of PM2.5 pollution. This planning methodology has additional potentials in chemical data assimilation studies as duplicate information from current CNEMC-concentrated stations is not likely to boost performance.

Secular variation signals in magnetic field gradient tensor elements derived from satellite-based geomagnetic virtual observatories

SUMMARYWe present local time-series of the magnetic field gradient tensor elements at satellite altitude derived using a Geomagnetic Virtual Observatory (GVO) approach. Gradient element time-series are computed in 4-monthly bins on an approximately equal-area distributed worldwide network. This enables global investigations of spatio-temporal variations in the gradient tensor elements. Series are derived from data collected by the Swarm and CHAMP satellite missions, using vector field measurements and their along-track and east–west differences, when available. We find evidence for a regional secular variation impulse (jerk) event in 2017 in the first time derivative of the gradient tensor elements. This event is located at low latitudes in the Pacific region. It has a similar profile and amplitude regardless of the adopted data selection criteria and is well fit by an internal potential field. Spherical harmonic models of the internal magnetic field built from the GVO gradient series show lower scatter in near-zonal harmonics compared with models built using standard GVO vector field series. The GVO gradient element series are an effective means of compressing the spatio-temporal information gathered by low-Earth orbit satellites on geomagnetic field variations, which may prove useful for core flow inversions and in geodynamo data assimilation studies.

Data Assimilation and Comparative studies on climate change using Data Mining with statistics approaches

Data Assimilation and Comparative studies on climate change using Data Mining with statistics approaches

Geomagnetic Virtual Observatories: monitoring geomagnetic secular variation with the Swarm satellites

We present geomagnetic main field and secular variation time series, at 300 equal-area distributed locations and at 490 km altitude, derived from magnetic field measurements collected by the three Swarm satellites. These Geomagnetic Virtual Observatory (GVO) series provide a convenient means to globally monitor and analyze long-term variations of the geomagnetic field from low-Earth orbit. The series are obtained by robust fits of local Cartesian potential field models to along-track and East–West sums and differences of Swarm satellite data collected within a radius of 700 km of the GVO locations during either 1-monthly or 4-monthly time windows. We describe two GVO data products: (1) ‘Observed Field’ GVO time series, where all observed sources contribute to the estimated values, without any data selection or correction, and (2) ‘Core Field’ GVO time series, where additional data selection is carried out, then de-noising schemes and epoch-by-epoch spherical harmonic analysis are applied to reduce contamination by magnetospheric and ionospheric signals. Secular variation series are provided as annual differences of the Core Field GVOs. We present examples of the resulting Swarm GVO series, assessing their quality through comparisons with ground observatories and geomagnetic field models. In benchmark comparisons with six high-quality mid-to-low latitude ground observatories we find the secular variation of the Core Field GVO field intensities, calculated using annual differences, agrees to an rms of 1.8 nT/yr and 1.2 nT/yr for the 1-monthly and 4-monthly versions, respectively. Regular sampling in space and time, and the availability of data error estimates, makes the GVO series well suited for users wishing to perform data assimilation studies of core dynamics, or to study long-period magnetospheric and ionospheric signals and their induced counterparts. The Swarm GVO time series will be regularly updated, approximately every four months, allowing ready access to the latest secular variation data from the Swarm satellites.

A Framework for Estimating Global‐Scale River Discharge by Assimilating Satellite Altimetry

AbstractUnderstanding spatial and temporal variations in terrestrial waters is key to assessing the global hydrological cycle. The future Surface Water and Ocean Topography (SWOT) satellite mission will observe the elevation and slope of surface waters at <100 m resolution. Methods for incorporating SWOT measurements into river hydrodynamic models have been developed to generate spatially and temporally continuous discharge estimates. However, most SWOT data assimilation studies have been conducted at the local scale. We developed a novel framework for estimating river discharge at the global scale by incorporating SWOT observations into the CaMa‐Flood hydrodynamic model. The local ensemble transform Kalman filter with adaptive local patches was used to assimilate SWOT observations. We tested the framework using multimodel runoff forcing and inaccurate model parameters represented by corrupted Manning's coefficient values. Assimilation of virtual SWOT observations considerably improved river discharge estimates for continental‐scale rivers at high latitudes (>50°) and also downstream river reaches at low latitudes. High assimilation efficiency in downstream river reaches was related to both local state correction and the propagation of corrected hydrodynamic states from upstream river reaches. Accurate global river discharge estimates were obtained (Kling‐Gupta efficiency [KGE] > 0.90) in river reaches with >270 accumulated overpasses per SWOT cycle when no model error was assumed. Introducing model errors decreased this accuracy (KGE ≈ 0.85). Therefore, improved hydrodynamic models are essential for maximizing SWOT information. These synthetic experiments showed where discharge estimates could be improved using SWOT observations. Further advances are needed for global‐scale data assimilation.

A novel framework to determine the usefulness of satellite-based soil moisture data in streamflow prediction using dynamic Budyko model

Soil moisture plays an important role in partitioning rainfall into runoff and evapotranspiration. Due to advancements in remotely sensed soil moisture data acquisition techniques, many soil moisture data assimilation (SMDA) studies have been conducted to improve streamflow prediction. It is thus expected that the outcome of a SMDA exercise will be determined by the quality of soil moisture data in hand and the hydrology of the catchment. Our study begins with the hypothesis that it is possible to determine the usefulness of a satellite-based soil moisture data product for areas where paramaterizing a complex model is difficult due to availability of limited information. To this end, we use satellite-based GLDAS root-zone soil moisture data with dynamic Budyko (DB), rainfall-runoff model, to improve streamflow prediction for 60 US basins. Our results suggest that there is a reasonably good one-to-one or universal relationship between instantaneous dryness-index (φ), the key state variable of the DB model, and root-zone soil moisture (θ), which implies that the model can directly use soil moisture information for predicting streamflow. To check the robustness of the universal φ-θ relationship, we also developed basin specific φ-θ relationships. Model performance, expressed in terms of Nash-Sutcliffe efficiency (NSE), improved in 34 basins when we considered the universal φ-θ relationship and in 51 basins when we considered the basin specific relationships. Multiple linear regression (MLR) analysis reveals that change in NSE due to the use of soil moisture information is predicted quite well by certain basin characteristics. In particular, it is found that available water capacity and forest area positively influence NSE, whereas average sand, silt and clay contents, latitude, and longitude affect it negatively. A slightly stronger MLR relationship was observed while considering soil moisture deficit (the difference between saturated soil moisture and actual soil moisture) in place of soil moisture. From the stepwise MLR analysis, it is observed that the vegetation and runoff generation mechanism control the parameters of the φ-θ relationship. Overall, our study provides a framework to determine the suitability of remotely-based soil moisture data for hydrological modelling.

Artificial Neural Networks as Surrogate Models for Uncertainty Quantification and Data Assimilation in 2-D/3-D Fuel Performance Studies

This paper preliminarily investigates the use of data-driven surrogates for fuel performance codes. The objective is to develop fast-running models that can be used in the frame of uncertainty quantification and data assimilation studies. In particular, data assimilation techniques based on Monte Carlo sampling often require running several thousand, or tens of thousands of calculations. In these cases, the computational requirements can quickly become prohibitive, notably for 2-D and 3-D codes. The paper analyses the capability of artificial neural networks to model the steady-state thermal-mechanics of the nuclear fuel, assuming given released fission gases, swelling, densification and creep. An optimized and trained neural network is then employed on a data assimilation case based on the end of the first ramp of the IFPE Instrumented Fuel Assemblies 432.

Sensitivity of a data-assimilation system for reconstructing three-dimensional cardiac electrical dynamics.

Modelling of cardiac electrical behaviour has led to important mechanistic insights, but important challenges, including uncertainty in model formulations and parameter values, make it difficult to obtain quantitatively accurate results. An alternative approach is combining models with observations from experiments to produce a data-informed reconstruction of system states over time. Here, we extend our earlier data-assimilation studies using an ensemble Kalman filter to reconstruct a three-dimensional time series of states with complex spatio-temporal dynamics using only surface observations of voltage. We consider the effects of several algorithmic and model parameters on the accuracy of reconstructions of known scroll-wave truth states using synthetic observations. In particular, we study the algorithm's sensitivity to parameters governing different parts of the process and its robustness to several model-error conditions. We find that the algorithm can achieve an acceptable level of error in many cases, with the weakest performance occurring for model-error cases and more extreme parameter regimes with more complex dynamics. Analysis of the poorest-performing cases indicates an initial decrease in error followed by an increase when the ensemble spread is reduced. Our results suggest avenues for further improvement through increasing ensemble spread by incorporating additive inflation or using a parameter or multi-model ensemble. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Description of the UCAR/CU Soil Moisture Product

Currently, the ability to use remotely sensed soil moisture to investigate linkages between the water and energy cycles and for use in data assimilation studies is limited to passive microwave data whose temporal revisit time is 2–3 days or active microwave products with a much longer (>10 days) revisit time. This paper describes a dataset that provides soil moisture retrievals, which are gridded to 36 km, for the upper 5 cm of the soil surface at sparsely sampled 6-hour intervals for +/− 38 degrees latitude for 2017–present. Retrievals are derived from the Cyclone Global Navigation Satellite System (CYGNSS) constellation, which uses GNSS-Reflectometry to obtain L-band reflectivity observations over the Earth’s surface. The product was developed by calibrating CYGNSS reflectivity observations to soil moisture retrievals from NASA’s Soil Moisture Active Passive (SMAP) mission. Retrievals were validated against observations from 171 in-situ soil moisture probes, with a median unbiased root-mean-square error (ubRMSE) of 0.049 cm3 cm−3 (standard deviation = 0.026 cm3 cm−3) and median correlation coefficient of 0.4 (standard deviation = 0.27). For the same stations, the median ubRMSE between SMAP and in-situ observations was 0.045 cm3 cm−3 (standard deviation = 0.025 cm3 cm−3) and median correlation coefficient was 0.69 (standard deviation = 0.27). The UCAR/CU Soil Moisture Product is thus complementary to SMAP, albeit with a larger random noise component, providing soil moisture retrievals for applications that require faster revisit times than passive microwave remote sensing currently provides.

Retrieval of Snow Properties from the Sentinel-3 Ocean and Land Colour Instrument

The Sentinel Application Platform (SNAP) architecture facilitates Earth Observation data processing. In this work, we present results from a new Snow Processor for SNAP. We also describe physical principles behind the developed snow property retrieval technique based on the analysis of Ocean and Land Colour Instrument (OLCI) onboard Sentinel-3A/B measurements over clean and polluted snow fields. Using OLCI spectral reflectance measurements in the range 400–1020 nm, we derived important snow properties such as spectral and broadband albedo, snow specific surface area, snow extent and grain size on a spatial grid of 300 m. The algorithm also incorporated cloud screening and atmospheric correction procedures over snow surfaces. We present validation results using ground measurements from Antarctica, the Greenland ice sheet and the French Alps. We find the spectral albedo retrieved with accuracy of better than 3% on average, making our retrievals sufficient for a variety of applications. Broadband albedo is retrieved with the average accuracy of about 5% over snow. Therefore, the uncertainties of satellite retrievals are close to experimental errors of ground measurements. The retrieved surface grain size shows good agreement with ground observations. Snow specific surface area observations are also consistent with our OLCI retrievals. We present snow albedo and grain size mapping over the inland ice sheet of Greenland for areas including dry snow, melted/melting snow and impurity rich bare ice. The algorithm can be applied to OLCI Sentinel-3 measurements providing an opportunity for creation of long-term snow property records essential for climate monitoring and data assimilation studies—especially in the Arctic region, where we face rapid environmental changes including reduction of snow/ice extent and, therefore, planetary albedo.