Accurate Flux Estimation Research Articles

Optimization of an N2O Emission Flux Model Based on a Variable-Step Drosophila Algorithm

The application of intelligent process-based crop model parameter optimization algorithms can effectively improve both the model simulation accuracy and applicability. Based on measured values of soil N2O emission flux in wheat fields from 2020 to 2022, and meteorological data from 1971 to 2022, five parameters of the N2O emission flux module in the APSIM model were optimized using the variable step Fruit Fly algorithm (VSS-FOA). The optimized parameters were the soil nitrification potential, the range of concentrated KNH4 of ammonia and nitrogen at semi-maximum utilization efficiency, the proportion of nitrogen loss to N2O during the nitrification process, the denitrification coefficient, and the Power term P for calculating the denitrification water coefficient. Contrasting the optimized parameters using the VSS-FOA algorithm versus the default values supplied with the model substantially improved the goodness-of-fit to field measurements with the overall R2 increasing from 0.41 to 0.74, and a decrease in NRMSE from 17.1% to 11.4%. This work demonstrates that the VSS-FOA algorithm affords a straightforward mechanism for the optimization of parameters in models such as APSIM to enhance the accuracy of model N2O emission flux estimates.

Score-matching neural networks for improved multi-band source separation

We present the implementation of a score-matching neural network that represents a data-driven prior for non-parametric galaxy morphologies. The gradients of this prior can be incorporated in the optimization of galaxy models to aid with tasks like deconvolution, inpainting or source separation. We demonstrate this approach with modification of the multi-band modeling framework scarlet that is currently employed as deblending method in the pipelines of the HyperSuprimeCam survey and the Rubin Observatory. The addition of the prior avoids the requirement of non-differentiable constraints, which can lead to convergence failures we discovered in scarlet. We present the architecture and training details of our score-matching neural network and show with simulated Rubin-like observations that using a data-driven prior outperforms the baseline scarlet method in accuracy of total flux and morphology estimates, while maintaining excellent performance for colors. We also demonstrate significant improvements in the robustness to inaccurate initializations. The trained score models used for this analysis are publicly available at https://github.com/SampsonML/galaxygrad.

Over 100-fold improvement in the accuracy of relaxed eddy accumulation flux estimates through error diffusion

Measurements of atmosphere-surface exchange are largely limited by the availability of fast-response gas analyzers; this limitation hampers our understanding of the role of terrestrial ecosystems in atmospheric chemistry and global change. Current micrometeorological methods, compatible with slow-response gas analyzers, are difficult to implement, or rely on empirical parameters that introduce large systematic errors.Here, we develop a new micrometeorological method, optimized for slow-response gas analyzers, that directly measures exchange rates of different atmospheric constituents, with minimal requirements. The new method requires only the sampling of air at a constant rate and directing it into one of two reservoirs, depending on the direction of the vertical wind velocity. An integral component of the new technique is an error diffusion algorithm that minimizes the biases in the measured fluxes and achieves direct flux estimates.We demonstrate that the new method provides an unbiased estimate of the flux, with accuracy within 0.1% of the reference eddy covariance flux, and importantly, allows for significant enhancements in the signal-to-noise ratio of measured scalars without compromising accuracy. Our new method provides a simple and reliable way to address complex environmental questions and offers a promising avenue for advancing our understanding of ecological systems and atmospheric chemistry.

Accurate heat flux estimation in continuous casting Molds via MH-MCMC Bayesian Inverse Method

The present work focuses on accurately estimating heat flux variations on the hot faces of the billet and slab molds during continuous casting using the Metropolis Hastings–Markov Chain Monte Carlo (MH-MCMC) Bayesian inverse method and experimental data. Accurate estimation of heat flux variation is crucial for operational efficiency and ensuring high-quality steel products. The variation in the hot face heat flux (qn(y)) of the billet mold is estimated using the proposed MH-MCMC Bayesian inverse method and experimental data for various casting speeds. The study extends this methodology to the slab mold for estimating the variations in the heat fluxes (qnr(y), qw(x,y)) on the hot narrow and wide faces of the slab mold. The estimated heat fluxes for both molds are used in respective forward models to obtain temperatures. The temperatures obtained excellently match experimental temperatures and show superior accuracy in estimating the heat fluxes. From the present methodology, the errors between these simulated and experimental temperatures are much less compared with the literature. The predicted heat flux variations on the hot faces of the billet and slab molds are also compared with the heat flux obtained from the literature.This study provides valuable insights into accurately estimating heat fluxes in continuous casting molds (billet and slab) using the MH-MCMC Bayesian inverse method. The accurately estimated heat fluxes of the molds are essential for ensuring the quality, efficiency, and innovation of continuous casting processes.

An Inverse Modeling Approach for Retrieving High-Resolution Surface Fluxes of Greenhouse Gases from Measurements of Their Concentrations in the Atmospheric Boundary Layer

This study explores the potential of using Unmanned Aircraft Vehicles (UAVs) as a measurement platform for estimating greenhouse gas (GHG) fluxes over complex terrain. We proposed and tested an inverse modeling approach for retrieving GHG fluxes based on two-level measurements of GHG concentrations and airflow properties over complex terrain with high spatial resolution. Our approach is based on a three-dimensional hydrodynamic model capable of determining the airflow parameters that affect the spatial distribution of GHG concentrations within the atmospheric boundary layer. The model is primarily designed to solve the forward problem of calculating the steady-state distribution of GHG concentrations and fluxes at different levels over an inhomogeneous land surface within the model domain. The inverse problem deals with determining the unknown surface GHG fluxes by minimizing the difference between measured and modeled GHG concentrations at two selected levels above the land surface. Several numerical experiments were conducted using surrogate data that mimicked UAV observations of varying accuracies and density of GHG concentration measurements to test the robustness of the approach. Our primary modeling target was a 6 km2 forested area in the foothills of the Greater Caucasus Mountains in Russia, characterized by complex topography and mosaic vegetation. The numerical experiments show that the proposed inverse modeling approach can effectively solve the inverse problem, with the resulting flux distribution having the same spatial pattern as the required flux. However, the approach tends to overestimate the mean value of the required flux over the domain, with the maximum errors in flux estimation associated with areas of maximum steepness in the surface topography. The accuracy of flux estimates improves as the number of points and the accuracy of the concentration measurements increase. Therefore, the density of UAV measurements should be adjusted according to the complexity of the terrain to improve the accuracy of the modeling results.

Does Soil Acidification Matter? Nutrient Sustainability of Timber Harvesting in Forests on Selected Soils Developed in Sediments of the Early vs. Late Pleistocene

With this study, our aim was to estimate the nutrient fluxes relevant for assessing nutrient sustainability as accurately as possible and to calculate nutrient balances for alternative forest management scenarios. Furthermore, we tested whether mapping units from existing geologic maps can serve as a basis for forest practitioners to estimate nutrient sustainability or whether more detailed data are needed. Positive fluxes include deposition and weathering, while negative fluxes include losses due to leaching and nutrient removal through timber harvesting in the balance. Weathering and leachate losses were modeled with a geochemical model. The SwissStandSim model was used to simulate the biomass growth under different harvesting and silvicultural strategies, allowing for sustainability to be assessed for each nutrient at a given intensity of use. This assessment was made per rotation period based on two criteria: (i) nutrient supply and (ii) total stocking volume. As a result, it can be noted that the accurate estimation of individual fluxes is essential for assessing the sustainability of forestry practices and that it needs detailed site-specific data. Various influencing factors turned out to be important, particularly the assumed depth of the root zone.

Evaluation of isoprene emissions from the coupled model SURFEX–MEGANv2.1

Abstract. Isoprene, a key biogenic volatile organic compound, plays a pivotal role in atmospheric chemistry. Due to its high reactivity, this compound contributes significantly to the production of tropospheric ozone in polluted areas and to the formation of secondary organic aerosols. The assessment of biogenic emissions is of great importance for regional and global air quality evaluation. In this study, we implemented the biogenic emission model MEGANv2.1 (Model of Emissions of Gases and Aerosols from Nature, version 2.1) in the surface model SURFEXv8.1 (SURface EXternalisée in French, version 8.1). This coupling aims to improve the estimation of biogenic emissions using the detailed vegetation-type-dependent treatment included in the SURFEX vegetation ISBA (Interaction between Soil Biosphere and Atmosphere) scheme. This scheme provides vegetation-dependent parameters such as leaf area index and soil moisture to MEGAN. This approach enables a more accurate estimation of biogenic fluxes compared to the stand-alone MEGAN model, which relies on average input values for all vegetation types. The present study focuses on the assessment of the SURFEX–MEGAN model isoprene emissions. An evaluation of the coupled SURFEX–MEGAN model results was carried out by conducting a global isoprene emission simulation in 2019 and by comparing the simulation results with other MEGAN-based isoprene inventories. The coupled model estimates a total global isoprene emission of 443 Tg in 2019. The estimated isoprene is within the range of results obtained with other MEGAN-based isoprene inventories, ranging from 311 to 637 Tg. The spatial distribution of SURFEX–MEGAN isoprene is consistent with other studies, with some differences located in low-isoprene-emission regions. Several sensitivity tests were conducted to quantify the impact of different model inputs and configurations on isoprene emissions. Using different meteorological forcings resulted in a ±5 % change in isoprene emissions using MERRA (Modern-Era Retrospective analysis for Research and Applications) and IFS (Integrated Forecasting System) compared with ERA5. The impact of using different emission factor data was also investigated. The use of PFT (plant functional type) spatial coverage and PFT-dependent emission potential data resulted in a 12 % reduction compared to using the isoprene emission potential gridded map. A significant reduction of around 38 % in global isoprene emissions was observed in the third sensitivity analysis, which applied a parameterization of soil moisture deficit, particularly in certain regions of Australia, Africa, and South America. The significance of coupling the SURFEX and MEGAN models lies particularly in the ability of the coupled model to be forced with meteorological data from any period. This means, for instance, that this system can be used to predict biogenic emissions in the future. This aspect of our work is significant given the changes that biogenic organic compounds are expected to undergo as a result of changes in their climatic factors.

Sea spray emissions from the Baltic Sea: comparison of aerosol eddy covariance fluxes and chamber-simulated sea spray emissions

Abstract. To compare in situ and laboratory estimates of sea spray aerosol (SSA) production fluxes, we conducted two research campaigns in the vicinity of an eddy covariance (EC) flux tower on the island of Östergarnsholm in the Baltic Sea during May and August 2021. To accomplish this, we performed EC flux measurements for particles with diameters between 0.25 and 2.5 µm simultaneously with laboratory measurements using a plunging jet sea spray simulation chamber containing local seawater sampled close to the footprint of the flux tower. We observed a log-linear relationship between wind speed and EC-derived SSA emission fluxes, a power-law relationship between significant wave height and EC-derived SSA emission fluxes, and a linear relationship between wave Reynolds number and EC-derived SSA emission fluxes, all of which are consistent with earlier studies. Although we observed a weak negative relationship between particle production in the sea spray simulation chamber and seawater chlorophyll-α concentration and a weak positive relationship with the concentration of fluorescent dissolved organic matter in seawater, we did not observe any significant impact of dissolved oxygen on particle production in the chamber. To obtain an estimate of the size-resolved emission spectrum for particles with dry diameters between 0.015 and 10 µm, we combined the estimates of SSA particle production fluxes obtained using the EC measurements and the chamber measurements in three different ways: (1) using the traditional continuous whitecap method, (2) using air entrainment measurements, and (3) simply scaling the chamber data to the EC fluxes. In doing so, we observed that the magnitude of the EC-derived emission fluxes compared relatively well to the magnitude of the fluxes obtained using the chamber air entrainment method as well as the previous flux measurements of Nilsson et al. (2021) and the parameterizations of Mårtensson et al. (2003) and Salter et al. (2015). As a result of these measurements, we have derived a wind-speed-dependent and wave-state-dependent SSA parameterization for particles with dry diameters between 0.015 and 10 µm for low-salinity waters such as the Baltic Sea, thus providing a more accurate estimation of SSA production fluxes.

The Impact of Diurnal Variability of Sea Surface Temperature on Air–Sea Heat Flux Estimation over the Northwest Pacific Ocean

Accurate and consistent observations of diurnal variability of sea surface temperature (SST DV) and its impact on air–sea heat fluxes over large areas for extended periods are challenging due to their short time scale and wide coverage. The hourly gap-free SSTs generated from Japan Aerospace Exploration Agency-Japan Agency for Marine–Earth Science and Technology (JAXA-JAMSTEC) are input to the COARE3.5 bulk flux algorithm to investigate the impact of SST DV on air–sea heat fluxes over the Northwest Pacific Ocean (NWPO). The main results are as follows. (1) The JAXA-JAMSTEC SSTs were found to be in good agreement with the buoy observations on SST DV with a very slight negative bias of −0.007 °C and a root mean square error of 0.018 °C. (2) The case study conducted on 26 June 2020 showed that the fluxes’ diurnal amplitudes were about 30–50 W m−2, and evolution was in agreement with SST DV. (3) The average impact of SST DV on heat fluxes was 2.93 W m−2 over the subtropical NWPO, decreasing from southeast to northwest and from low to high latitudes, and showing a clear seasonal cycle during 2019–2022. This research highlights the need to consider SST DV for accurate estimation of heat fluxes, which is crucial for climate and atmospheric studies.

The impact of sea ice melt on the evolution of surface pCO2 in a polar ocean basin

The impact of sea ice melt on the evolution of surface pCO2 in a polar ocean basin

Temporal variability of air-water gas exchange of carbon dioxide in clam and fish aquaculture ponds

The growing trend of land-based aquaculture has heightened the significance of comprehensively assessing air-water carbon dioxide (CO2) gas exchange in these inland waters, given their potential impact on carbon neutral strategies. However, temporal variations of partial pressure of CO2 (pCO2) and CO2 flux in clam and fish aquaculture ponds were barely investigated. We assessed the water surface pCO2 in one to five months intervals by deploying a lab-made buoy in three clam ponds and three fishponds located in tropical and subtropical climates. Measurements were conducted over a 24 h period each time, spanning from April 2021 to June 2022, covering the stocking, middle, and harvesting stages of the culture cycle. Diurnal pCO2 variations were dominantly controlled by biologically driven changes in dissolved inorganic carbon and total alkalinity (~97 %), while temperature and salinity effects were minor (~3 %). Clam ponds acted as a sink of atmospheric CO2 during stocking stages and transitioned to a source during middle to harvesting stages. In contrast, fishponds acted as a source of atmospheric CO2 throughout culture cycles and CO2 flux strengthened when reaching harvesting stages. Overall, clam ponds acted as a weak sink for atmospheric CO2 (−2.8 ± 17.3 mmol m−2 d−1), whereas fishponds acted as a source (16.8 ± 21.7 mmol m−2 d−1). CO2 emission was stronger during daytime coinciding with higher windspeeds compared to nighttime in fishponds. We suggest incorporating high temporal resolution measurements to account for diurnal and culture-stage variations, enabling more accurate estimates of air-water CO2 flux in aquaculture ponds. Moreover, the findings of this study highlight the importance of feeding, aeration, and biological activities (photosynthesis, remineralization, and calcification) in controlling the air-water CO2 flux in aquaculture ponds and such information can be used in implementing better strategies to achieve carbon neutral goals.

Multi-annual variability of pCO2(aq) and air-water CO2 flux in the mangrove-dominated Dhamra Estuary draining into the Bay of Bengal (India).

Small estuaries often remain neglected while characterizing air-water CO2 flux dynamics. This study reports the seasonal, spatial, and multi-annual variability of carbon biogeochemistry, emphasizing air-water CO2 flux from a small tropical mangrove-dominated estuary (Dhamra Estuary) of the Bay of Bengal, based on the 9-year-long sampling survey (2013 to 2021). The sampling covered twelve pre-fixed locations of this estuary. A suite of biogeochemical parameters was kept within the purview of this study to deliniate the interrelationship between CO2 fluxes and potential factors that can regulate/govern pCO2(aq) dynamics. Air water CO2 exchange rates were calculated using five globally accepted empirical gas transfer velocity equations and varied in a range of - 832.5 to 7904 μmol m-2 h-1. The estuary was a sink for CO2 in monsoon season, having the highest average flux rates of - 380.9 ± 125.5 μmol m-2 h-1, whereas a source in pre-monsoon (38.29 ± 913.1 μmol m-2 h-1) and post-monsoon (91.81 ± 1009.8 μmol m-2 h-1). The significant factors governing pCO2 were pH, salinity, total alkalinity and dissolved inorganic carbon (DIC). This long-term seasonal study emphasizes the need to include small regional estuaries for more accurate estimates of global CO2 flux to upscale the global carbon budget and its controlling mechanism.

Dissolution-driven convection of low solubility fluids in porous media

Geological sequestration represents a promising strategy for storing CO2. In order to further elucidate this process, we simulated the dissolution-driven convection of a CO2-brine system with a free interface in a porous medium, based on a novel Darcy-Cahn-Hilliard model that accounts for the low solubility of CO2 with brine. We consider a range of unstable Rayleigh numbers Ra, and we derive a quantitative relationship for the dimensionless solute flux. This flux exhibits distinctly different behaviors during the various stages of the flow. In particular, during the free convection stage, larger Ra-values result in a moderate decrease of the solute flux, while the solute flux is approximately independent of Ra during the constant flux stage. In order to evaluate the solute flux during the shutdown stage, we employ simulations in the two-sided Rayleigh-Bénard cell configuration. With a correction factor a=0.67 to account for the damping effect of the bottom boundary, the model can reproduce the solute flux during the shutdown stage. By accounting for the effects of partial miscibility, the simulation approach developed here holds the potential to yield more accurate estimates of the solute flux in the context of CO2 sequestration and related applications.

Fetch effects on air-sea momentum transfer at very high wind speeds

ABSTRACT Accurate estimates of momentum flux through the air-sea interface at very high wind speeds are important for predicting tropical cyclone intensities. To estimate the air-sea momentum flux under the long-fetch condition (20 m fetch) at very high wind speeds using a laboratory tank, a simple momentum flux measurement method using only four water-level gauges is conducted based on the momentum budget method. The air-water momentum flux under long-fetch conditions at very high wind speeds was measured in a typhoon simulation tank at the Research Institute of Applied Mechanics, Kyushu University. The verification was performed using previous values estimated by the eddy correlation method in a typhoon simulation tank at Kyoto University, Japan. The results showed good correlation between the values of momentum flux measured by the present momentum budget method and the other methods. The drag coefficient at very high wind speeds (41 m/s) under long-fetch conditions leveled off, as well as under the short-fetch condition (4.5 m and 6.5 m fetch). Moreover, a very weak relationship was found between the drag coefficient and the fetch. Since the maximum fetch in the present laboratory experiments is 20 m, the future field observation with the longer fetch condition will be needed for applying the results to oceans.

Quantifying the Potential Contribution of Submerged Aquatic Vegetation to Coastal Carbon Capture in a Delta System from Field and Landsat 8/9-Operational Land Imager (OLI) Data with Deep Convolutional Neural Network

Submerged aquatic vegetation (SAV) are highly efficient at carbon sequestration and, despite their relatively small distribution globally, are recognized as a potentially valuable component of climate change mitigation. However, SAV mapping in tidal marshes presents a challenge due to optically complex constituents in the water. The emergence and advancement of deep learning-based techniques in the field of habitat mapping with remote sensing imagery provides an opportunity to address this challenge. In this study, an analytical framework was developed to quantify the carbon sequestration of SAV habitats in the Atchafalaya River Delta Estuary from field and remote sensing observations using deep convolutional neural network (DCNN) techniques. A U-Net-based model, Wetland-SAV Network, was trained to identify the SAV percent cover (high, medium, and low) as well as other estuarine habitat types from Landsat 8/9-OLI data. The areal extent of SAV was up to 8% of the total area (47,000 ha). The habitat areas and habitat-specific carbon fluxes were then used to quantify the net greenhouse gas (GHG) flux of the study area for with/without SAV scenarios in a carbon balance model. The total net GHG flux was in the range of −0.13 ± 0.06 to −0.86 ± 0.37 × 105 tonne CO2e y−1 and increased up to 40% (−0.23 ± 0.10 to −0.90 ± 0.39 × 105 tonne CO2e y−1) when SAV was accounted for within the calculation. At the hectare scale, the inclusion of SAV resulted in an increase of ~60% for the net GHG sink in shallow areas adjacent to the emergent marsh where SAV was abundant. This is the first attempt at remotely mapping SAV in coastal Louisiana as well as a first quantification of net GHG flux at the scale of hectares to thousands of hectares, accounting for SAV within these sub-tropical coastal delta marshes. Remote sensing and deep learning models have high potential for mapping and monitoring SAV in turbid sub-tropical coastal deltas as a component of the increasing accuracy of net GHG flux estimates at small (hectare) and large (coastal basin) scales.

Enhanced Integrator with Drift Elimination for Accurate Flux Estimation in Sensorless Controlled Interior PMSM for High-Performance Full Speed Range Hybrid Electric Vehicles Applications

Interior Permanent Magnet Synchronous Motor (IPMSM) motion-sensorless speed control necessitates precise knowledge of rotor flux, speed, and position. Due to numerous non-ideal aspects, such as converter nonlinearities, detection errors, integral initial value, and parameter mismatches, the conventional first-order integrator’s estimated rotor flux experiences a DC offset (Doff). Low-pass filters (LPF) with a constant cut-off frequency yield accurate estimates only in the medium- and high-speed range; however, at the low-speed area, both magnitude and phase estimates are inaccurate. The presented technique resolves the aforementioned issue for a broad speed range. In order to achieve precise flux estimation, this article presents an improved technique of flux estimator with two distinct drift mitigation strategies for the motion-sensorless field-oriented control (FOC) system of IPMSM. Using the orthogonality of the α- and β-axes, the proposed drift elimination system can estimate drift in different situations while maintaining a high level of dynamic performance. The stator flux linkage (SFL) computation in the synchronous coordinate is established from the estimation of the rotating shaft’s permanent magnetic flux linkage orientation and the statistical equations model of the SFL. By comparing the calculated SFL vector to the SFL vector derived from the stator winding voltage and currents integral model with a drift PI compensation loop, a feedback loop is formed to neutralize integral drift, and the rotational speed and position of an IPMSM is estimated utilizing the vector product of the two flux linkages in a phase-locked loop. Theoretical interpretation is presented, and Matlab Simulink simulations, as well as experimental outcomes, consistently demonstrate that the suggested estimation techniques can eliminate the phenomenon of flux drift.

Monitoring structural scale composite specimens in a post‐buckling regime: The integrated finite element stereo digital image correlation approach with geometrically non‐linear regularization

AbstractEven though the simulations used to describe the failure of laminates are becoming more and more predictive, complex testing under multiaxial loadings is still required to validate the design of structural parts in a wide range of industrial domains. It is thus essential to assess the actual boundary conditions to allow for an objective comparison between testing and calculations, in particular since the structural tests are complex and often leads to buckling. Therefore, accurate estimation of force and moment fluxes applied to the specimen is critical. In this context, stereo digital image correlation (SDIC) has proven to be an important measurement tool and provides very well‐resolved surface displacement fields, but the exploitation of such measurements to calculate fluxes remains problematic when testing composites. The first objective of this study is both to reduce the uncertainty associated with fluxes determination on a complex test and to simplify the extraction process with respect to existing procedures. The second objective is to make this methodology robust to geometrically non‐linear deformations. In this paper, we propose a new methodology that extracts minimal boundary conditions in the form of 3D mechanically admissible displacements fields. The approach developed uses a finite element SDIC (FE‐SDIC) method regularized by means of mechanical behaviour admissibility equations. Results show that the new methodology outputs much more accurate fluxes than classical data generated from multiple differentiations of the displacement fields. Excellent noise robustness is obtained and quantified. Numerical predictions have been satisfactorily compared with experimental data from one structural‐scale composite specimen under complex testing.

Quantifying gas emissions through vertical radial plume mapping with embedded radial basis function interpolation

The Vertical Radial Plume Mapping (VRPM) method proposed by the U.S. EPA in Other Test Method 10 (OTM-10) is widely used to measure nonpoint source emissions. However, the accuracy of the VRPM is affected by the large number of parameters relative to the measurement data and the presence of measurement noise. To improve the accuracy of flux estimation, we propose to apply evenly spaced radial basis function (RBF) interpolation to the measurement data before using the VRPM. The experiment was tested and validated under various measurement configurations. The results indicate that RBF interpolation techniques, especially Gaussian RBF (GSRBF) interpolation, reduce the mean absolute error and root mean square error of flux estimation, leading to improved flux estimation accuracy. The mean emission rate calculated after RBF interpolation is closer to the true value, indicating that this interpolation technique helps to reflect more accurately the average emission level over time. Even in the most challenging validation set, the percentage error of mean flux decreased by 3.8% after interpolation. The proposed method can be a simple and measurement-cost-effective way to improve the accuracy of VRPM measurements.

Interface flux recovery framework for constructing partitioned heterogeneous time‐integration methods

AbstractA common approach for the development of partitioned schemes employing different time integrators on different subdomains is to lag the coupling terms in time. This can lead to accuracy issues, especially in multistage methods. In this article, we present a novel framework for partitioned heterogeneous time‐integration methods, which allows the coupling of arbitrary multistage and multistep methods without reducing their order of accuracy. At the core of our approach are accurate estimates of the interface flux obtained from the Schur complement of an auxiliary monolithic system. We use these estimates to construct a polynomial‐in‐time approximation of the interface flux over the current time coupling window. This approximation provides the interface boundary conditions necessary to decouple the subdomain problems at any point within the coupling window. In so doing our framework enables a flexible choice of time‐integrators for the individual subproblems without compromising the time‐accuracy at the coupled problem level. This feature is the main distinction between our framework and other approaches. To demonstrate the framework, we construct a family of partitioned heterogeneous time‐integration methods, combining multistage and multistep methods, for a simplified tracer transport component of the coupled air‐sea system in Earth system models. We report numerical tests evaluating accuracy and flux conservation for different pairs of time‐integrators from the explicit Runge‐Kutta and Adams‐Moulton families.

Constraining the Systematics of (Acoustic) Wave Heating Estimates in the Solar Chromosphere

Acoustic wave heating is believed to contribute significantly to the missing energy input required to maintain the solar chromosphere in its observed state. We studied the propagation of waves above the acoustic cutoff in the upper photosphere into the chromosphere with ultraviolet and optical spectral observations interpreted through comparison with 3D radiative magnetohydrodynamic Bifrost models to constrain the heating contribution from acoustic waves in the solar atmosphere. Sit-and-stare observations taken with the Interface Region Imaging Spectrograph and data from the Interferometric BIdimensional Spectrograph were used to provide the observational basis of this work. We compared the observations with synthetic observables derived from the Bifrost solar atmospheric model. Our analysis of the Bifrost simulations show that internetwork and enhanced-network regions exhibit significantly different wave-propagation properties, which are important for accurate wave flux estimates. The inferred wave energy fluxes based on our observations are not sufficient to maintain the solar chromosphere. We point out that the systematics of the modeling approaches in the literature lead to differences which could determine the conclusions of this type of study, based on the same observations.