Bias Correction Methods Research Articles

Assessment of Future Climate Change in the Huaihe River Basin Using Bias-Corrected CMIP5 GCMs with Consideration of Climate Non-Stationarity

The Huaihe River Basin is particularly vulnerable to climate change. This paper first evaluated interpolation methods for different meteorological elements, followed by an assessment of the simulation performance of various Coupled Model Intercomparison Project 5 (CMIP5) Global Climate Models (GCMs) for these elements. We then applied the Improved Quantile Mapping (IQM) method for bias correction of the GCMs. Finally, we analyzed the characteristics of future climate change in the Huaihe River Basin. The results show the following: (1) The radial basis function interpolation method is the most effective for rainfall, while Kriging performs best for air temperature. (2) The HadGEM2-AO model provides the most accurate rainfall simulations, MIROC-ESM best simulates maximum air temperature, and HadGEM2-ES is most effective for minimum air temperature. (3) The IQM method outperforms other approaches for bias correction of climate variables in the basin. (4) Future projections show an increase in both rainfall and air temperature, with more pronounced rises under the RCP8.5 scenario. Additionally, rainfall and maximum air temperature show considerable spatial variation across emission scenarios, while minimum air temperature consistently exhibits an upward trend.

A deep learning method for bias correction of wind field in the South China Sea

A deep learning method for bias correction of wind field in the South China Sea

Robust spatial changes in climate classes: insights from bias-corrected CMIP6 models across Chile

Abstract The climate in Continental Chile is marked by strong latitudinal and elevation gradients, exacerbated by diverse geographical features, such as the Andes. Despite previous studies projecting warmer and dryer conditions for most of the territory, there is concern about the robustness (i.e. level of agreement among models) of changes projected for its magnitude, not only for the impact on climate indices across this domain but also to identify changes in the spatial distribution of climate classes. Hence, we statistically downscaled and bias-corrected daily CMIP6 model outputs for continental Chile, using a multivariate bias correction method, to project climate changes under the SSP5-8.5 scenario. The results reveal that General Circulation Models (GCMs) project increased dryness across the study domain by the end of the 21st century, especially in Central Chile (−30% in precipitation), with notable sensitivities of precipitation projections to the implementation of bias correction methods in the northern and austral macrozones. Temperature projections show less dispersion, with higher increments in northern Chile and the Andes (4 ∘C–5 ∘C). Notable shifts in the extension of Köppen–Geiger climate classes are projected for the next decades, with the expansion of deserts in northern Chile and the prevalence of temperate climates with dry summers in central Chile. The Andes subdomain is expected to face the most dramatic changes in Köppen–Geiger classes (inter-model agreement > 70%). Surprisingly, despite the large spread in GCM projections, there is high agreement among models regarding spatial changes in climate classes. Additionally, our results project drastic reductions in snowfall across the Andes, with higher freezing level heights that may exacerbate flooding and landslide risk across the country.

Climate change impacts on the Chiffa basin (northern Algeria) using bias-corrected RCM data

IntroductionThis study aims to assess the efficacy of Quantile mapping (QM) and Delta change (DC) bias correction methods to improve hydrological simulations of the Chiffa basin in northern Algeria. The main issue addressed is the need for corrected climate data to provide reliable hydrological projections in semi-arid climates.MethodsHydrological simulations were conducted using the GR2M conceptual rainfall-runoff model, recognized for its robustness in Mediterranean climates. This model was coupled with precipitation simulations from the Rossby Centre regional atmospheric model RCA4 of the Coordinated Regional Climate Downscaling Experiment (Cordex-Africa) forced by two global circulation models (MPI-ESM-LR and CRNM-CM5). Hydrological projections were produced for the future period 20702099 under RCP 4.5 and RCP 8.5 scenarios, comparing raw and bias-corrected data.Results and discussionThe findings indicate that raw precipitation data are inadequate for reflecting future rainfall trends and simulating future flows. Bias correction methods significantly improved the models performance, with the coefficient of determination (R2) increasing from 0.440.53 to 0.830.97. Additionally, regional climate models project a 5 to 8% decrease in annual flows by the end of the 21st century under RCP 4.5 and RCP 8.5 scenarios. These results highlight the importance of bias correction methods for hydrological impact studies, and we recommend implementing specific adaptation measures, such as improved irrigation efficiency, development of water storage infrastructure, and adoption of drought-resistant agricultural practices. Future research should focus on employing multivariate bias correction methods, utilizing higher-resolution climate data (≤10 km), and implementing ensemble modeling approaches to better characterize uncertainties.

Analytical noise bias correction for precise weak lensing shear inference

Abstract Noise bias is a significant source of systematic error in weak gravitational lensing measurements that must be corrected to satisfy the stringent standards of modern imaging surveys in the era of precision cosmology. This paper reviews the analytical noise bias correction method and provides analytical derivations demonstrating that we can recover shear to its second order using the ‘renoising’ noise bias correction approach introduced by METACALIBRATION. We implement this analytical noise bias correction within the AnaCal shear estimation framework and propose several enhancements to the noise bias correction algorithm. We evaluate the improved AnaCal using simulations designed to replicate Rubin LSST imaging data. These simulations feature semi-realistic galaxies and stars, complete with representative distributions of magnitudes and Galactic spatial density. We conduct tests under various observational challenges, including cosmic rays, defective CCD columns, bright star saturation, bleed trails, and spatially variable point spread functions. Our results indicate a multiplicative bias in weak lensing shear recovery of less than a few tenths of a percent, meeting LSST DESC requirements without requiring calibration from external image simulations. Additionally, our algorithm achieves rapid processing, handling one galaxy in less than a millisecond.

Improving the Seasonal Forecast of Summer Precipitation in Southeastern China Using a CycleGAN-based Deep Learning Bias Correction Method

Improving the Seasonal Forecast of Summer Precipitation in Southeastern China Using a CycleGAN-based Deep Learning Bias Correction Method

Assessing the Effect of Bias Correction Methods on the Development of Intensity–Duration–Frequency Curves Based on Projections from the CORDEX Central America GCM-RCM Multimodel-Ensemble

This work aims to examine the effect of bias correction (BC) methods on the development of Intensity–Duration–Frequency (IDF) curves under climate change at multiple temporal scales. Daily outputs from a 9-member CORDEX-CA GCM-RCM multi-model ensemble (MME) under RCP 8.5 were used to represent future precipitation. Two stationary BC methods, empirical quantile mapping (EQM) and gamma-pareto quantile mapping (GPM), along with three non-stationary BC methods, detrended quantile mapping (DQM), quantile delta mapping (QDM), and robust quantile mapping (RQM), were selected to adjust daily biases between MME members and observations from the SJO weather station located in Costa Rica. The equidistant quantile-matching (EDQM) temporal disaggregation method was applied to obtain future sub-daily annual maximum precipitation series (AMPs) based on daily projections from the bias-corrected ensemble members. Both historical and future IDF curves were developed based on 5 min temporal resolution AMP series using the Generalized Extreme Value (GEV) distribution. The results indicate that projected future precipitation intensities (2020–2100) vary significantly from historical IDF curves (1970–2020), depending on individual GCM-RCMs, BC methods, durations, and return periods. Regardless of stationarity, the ensemble spread increases steadily with the return period, as uncertainties are further amplified with increasing return periods. Stationary BC methods show a wide variety of trends depending on individual GCM-RCM models, many of which are unrealistic and physically improbable. In contrast, non-stationary BC methods generally show a tendency towards higher precipitation intensities as the return period increases for individual GCM-RCMs, despite differences in the magnitude of changes. Precipitation intensities based on ensemble means are found to increase with the change factor (CF), ranging between 2 and 25% depending on the temporal scale, return period, and non-stationary BC method, with moderately smaller increases for short-durations and long-durations, and slightly higher for mid-durations. In summary, it can be concluded that stationary BC methods underperform compared to non-stationary BC methods. DQM and RQM are the most suitable BC methods for generating future IDF curves, recommending the use of ensemble means over ensemble medians or individual GCM-RCM outcomes.

Exploring the characteristics of Fengyun-4A Advanced Geostationary Radiation Imager (AGRI) visible reflectance using the China Meteorological Administration Mesoscale (CMA-MESO) forecasts and its implications for data assimilation

Abstract. The Advanced Geostationary Radiation Imager (AGRI) on board the Fengyun (FY)-4A geostationary satellite has provided high-spatiotemporal-resolution visible reflectance data since 12 March 2018. Data assimilation experiments under the framework of observing system simulation experiments have shown the great potential of these data to improve the forecasting skills of numerical weather prediction (NWP) models. To assimilate the AGRI visible reflectance in real-world cases, it is important to evaluate the quality and to quantify the observation errors in these data. In this study, the FY-4A AGRI channel 2 (0.55–0.75 µm) reflectance data (O) were compared with the equivalents (B) derived from the short-term forecasts of the China Meteorological Administration Mesoscale (CMA-MESO) model using the Radiative Transfer for the Television Infrared Observation Satellite Operational Vertical Sounder (RTTOV, v12.3). It is shown that the O–B biases could be used to reveal the abrupt change related to the measurement calibration processes. In general, the O–B departure was positively biased in most cases. Potential causes include the deficiencies of the NWP model, the forward-operator errors, and the unresolved aerosol processes. The relative biases of O–B computed from cloud-free and cloudy pixels were used to correct the systematic biases for the corresponding scenarios over land and sea surfaces separately. In general, the method effectively reduced the O–B biases. Moreover, the bias-correction method based on an ensemble forecast is more robust than a deterministic forecast due to the advantages of the former in dealing with uncertainties in cloud simulations. The findings demonstrate that analyzing the O–B biases has a potential to monitor the performance of the FY-4A AGRI visible instrument and to correct the systematic biases in the observations, which will facilitate the assimilation of these data in conventional data assimilation applications.

New Method to Correct Vegetation Bias in a Copernicus Digital Elevation Model to Improve Flow Path Delineation

Digital elevation models (DEM) are widely used in many hydrologic applications, providing key information about the topography, which is a major driver of water flow in a landscape. Several open access DEMs with near-global coverage are currently available, however, they represent the elevation of the earth’s surface including all its elements, such as vegetation cover and buildings. These features introduce a positive elevation bias that can skew the water flow paths, impacting the extraction of hydrological features and the accuracy of hydrodynamic models. Many attempts have been made to reduce the effects of this bias over the years, leading to the generation of improved datasets based on the original global DEMs, such as MERIT DEM and, more recently, FABDEM. However, even after these corrections, the remaining bias still affects flow path delineation in a significant way. Aiming to improve on this aspect, a new vegetation bias correction method is proposed in this work. The method consists of subtracting from the Copernicus DEM elevations their respective forest height but adjusted by correction factors to compensate for the partial penetration of the SAR pulses into the vegetation cover during the Copernicus DEM acquisition process. These factors were calculated by a new approach where the slope around the pixels at the borders of each vegetation patch were analyzed. The forest height was obtained from a global dataset developed for the year 2019. Moreover, to avoid temporal vegetation cover mismatch between the DEM and the forest height dataset, we introduced a process where the latter is automatically adjusted to best match the Copernicus acquisition year. The correction method was applied for regions with different forest cover percentages and topographic characteristics, and the result was compared to the original Copernicus DEM and FABDEM, which was used as a benchmark for vegetation bias correction. The comparison method was hydrology-based, using drainage networks obtained from topographic maps as reference. The new corrected DEM showed significant improvements over both the Copernicus DEM and FABDEM in all tested scenarios. Moreover, a qualitative comparison of these DEMs was also performed through exhaustive visual analysis, corroborating these findings. These results suggest that the use of this new vegetation bias correction method has the potential to improve DEM-based hydrological applications worldwide.

Bias in control selection associated with the use of rapid tests in influenza vaccine effectiveness studies.

In test-negative design studies that use rapid tests to estimate influenza vaccine effectiveness (VE) a common concern is case/control misclassification due to imperfect test sensitivity and specificity. However, an imperfect test can also fail to exclude from the control group people that do not represent the source population, including people infected with other influenza types or other vaccine-preventable respiratory viruses for which vaccination status is correlated. We investigated these biases by comparing the effectiveness of seasonal 2023/24 influenza vaccination against influenza A and B based on PCR versus rapid test results, excluding controls who tested positive for SARS-CoV-2 or the other type of influenza. By PCR, VE against influenza A was 49% (95%CI 26-65%) after exclusion of PCR-confirmed influenza B and SARS-CoV-2 controls. Corresponding VE against influenza B was 65% (95%CI 35-81%). VE estimated by adjusting for COVID-19 vaccination status yielded similar estimates to the scenario that excluded SARS-CoV-2-positive controls. When case/control status and exclusions from test-negative controls were determined by rapid test, VE was reduced by 5-15 percentage points. Bias correction methods were able to reduce these discrepancies. When estimating VE from a test-negative study using rapid test results, methods to correct misclassification bias are recommended.

Improving wind power modelling through granular spatial and temporal bias correction of reanalysis data

There is a need for efficient methods to simulate wind power output to assist the expected rapid uptake of new wind farms. Reanalysis products provide our best estimate for the previous state of the atmosphere and are popular due to their global coverage and convenience. However, these models are known to misestimate wind power output by up to ±50% due to significant spatial biases. Previous work applied bias correction methods to improve power simulations. However, there has been no assessment of the spatial and temporal resolution that these bias correction factors should be derived at for the best accuracy. In this paper, we investigate the impact of the spatial and temporal resolution by grouping turbines into a varying number of clusters and varying the frequency at which correction factors are calculated across a year. The correction factors are used to simulate the power output of 4,834 turbines across Denmark resulting in monthly capacity factors. The best correction scenario decreased the error of simulated outputs by 43%. Increasing the spatial resolution of bias correction reduced the error by up to 11%. Correction factors with a bimonthly (every two months) frequency decreased the error by 3% from the time-independent correction factors.

Integrating machine learning and zoning-based techniques for bias correction in gridded precipitation data to improve hydrological estimation in the data-scarce region

Gridded precipitation products are valuable for hydrological assessments due to their wide spatial coverage and improved spatiotemporal resolution compared to the use of rain gauges. They have been extensively used in hydrology studies over the past decade. However, it’s important to recognize that these products come with inherent uncertainties, which can impact hydrological simulations.To address this limitation, our study introduces a novel bias correction technique that combines machine learning and zoning-based approaches. We applied this technique in a case study to correct bias in the gauge-based gridded precipitation product in a data-scarce region, such as the Mekong Basin. To evaluate the effectiveness of this proposed method, we compared it against conventional bias correction methods, including mean-based and distribution-based approaches, using various statistical indices and hydrological simulations.Our findings consistently reveal a bias pattern within the gridded precipitation product across the study area, which affects streamflow estimations. All correction methods show promise in reducing precipitation biases and improving streamflow predictions. Among these methods, one particularly promising approach involves integrating machine learning techniques and taking into account climate zones. This integrated approach has emerged as a superior strategy, offering significant advantages in terms of both correcting precipitation data and improving broader hydrological assessments.This investigation underscores the crucial role of this integrated method in optimizing hydrological simulations across diverse geographical areas, especially in regions where data availability is limited.

A comprehensive comparison of bias correction methods in climate model simulations: Application on ERA5-Land across different temporal resolutions

Climate data plays a crucial role in water resources management, which is becoming an increasingly relevant asset in all types of hydrological analysis not only for climate change studies but for various horizon forecasting. Though the ever-improving accuracy of climate models' spatial and temporal resolution has surged the validity of their outputs, the products of global and regional climate models need to be corrected to be reliably used for local purposes. Here, we propose a comprehensive analysis of statistical univariate and multivariate, as well as machine learning methods for bias correction, which are compared on different temporal scales, ranging from hourly time steps to monthly aggregations, in an environment of complex Alpine orthography, using ERA5-Land reanalysis data. The results reveal different trends in the performance of the bias correction methods for precipitation and temperature across the various time resolutions.

Identification of thresholds and key drivers on water use efficiency in different maize ecoregions in Yellow River Basin of China

Identifying the constrains on water use efficiency (WUE) of crops along a wet-to-dry gradient is important due to irrigation water scarcity, as well as the increasing drought risk under climate change in China. This study coupled five high-resolution climate models from Coupled Model Intercomparison Project Phase 6 (CMIP6) with the Decision Support System for Agrotechnology Transfer (DSSAT)-CERES-Maize model to quantify drought risk and the drivers affecting WUE in five major maize ecoregions of the Yellow River Basin (YRB) under three future scenarios (SSP126, SSP370, and SSP585) for both the historical baseline (1985–2014) and three future periods: 2021–2040 (2030s), 2041–2070 (2050s), and 2071–2100 (2080s). And a bias correction method was implemented for the crop model to analyze optimal WUE thresholds for maize across varying dry-wet gradients. The results indicated that future drought risk will likely persist in the YRB under all scenarios, but with regional differences in drought severity and frequency. The southwestern region (V) experienced the highest frequency of drought (62.50%-SSP126), while the northwestern region (III) exhibited the lowest frequency (33.00%-SSP585) in 2030s, and 83.30% of areas in the southwestern (V) showed significant wetting in the 2080s under SSP126. The bias-corrected CERES-Maize model effectively simulated crop yield and evapotranspiration (ET), resulting in an average reduction of 4.00% and 9.73% in normalized root mean square error (nRMSE) respectively. Distinct WUE thresholds ranging from 1.96 to 8.41 kg ha−1 mm−1 were observed across various scenarios-periods in the maize regions, mostly under slight and moderate dry/wet conditions. Notably, all SSP585 scenarios demonstrated a decrease in WUE thresholds compared to the baseline. Across all scenarios and periods, WUE was mainly driven by yield in the eastern regions (I and II) but by ET in the western regions (III, IV, and V). These findings suggest that regions experiencing varying degrees of drought severity should undergo differentiated management and optimization of agricultural practices to improve WUE under future climate scenarios.

Projections of future tropical cyclone landfalling activity in the East Asia region

This study reveals the possible future changes in tropical cyclone (TC) landfalling activity along the East Asian coast under different climate change scenarios based on global circulation model (GCM) simulations. We first identify those GCMs that have the “best” performance in simulating the TC activity over the western North Pacific (WNP) during the current climate (1979–2014) by examining the simulated TCs in each of the GCMs and then compare these simulated TCs with the observed TC climatological features of annual frequency, track densities and genesis locations. Based on such comparisons, we have identified five (TaiESM1, EC-Earth3, ACCESS-CM2, ACCESS-ESM1-5 and HadGEM3-GC31-LL) models among all the available GCMs. A multi-model ensemble gives a further improvement when compared with observations.Future projections from some of these models are then used to identify the frequency of TC activity over the entire WNP as well as landfalling TCs in six East Asia coastal regions under two climate change scenarios (SSP2-4.5 and SSP5-8.5) for two periods, 2041-70 and 2071-2100. A bias-correction method is also applied to the projected intensity of these landfalling TCs to estimate the landfall intensity.In general, these GCMs project a possible decrease in TC genesis frequency over the entire WNP, consistent with the results of most of the other studies. At mid-century, decreases in TC genesis frequency are projected to be around 10% for both scenarios. Towards the end of the century, the decreases will be more significant, with the percentage changes of 14.9% (SSP2-4.5) and 22.4% (SSP5-8.5). For landfalling TCs, the northern part of the East Asian coast will likely have an increase in frequency, ranging from 17 to 60% but a decrease of 14–27% in the southern part. In general, the average intensity of landfalling TCs will likely increase although the percentages are not large, ranging from 2 to 14%.

Bias correction of CORDEX-Africa regional climate model simulations for climate change projections in northeastern Lake Chad: Comparative analysis of three bias correction methods

Bias correction of CORDEX-Africa regional climate model simulations for climate change projections in northeastern Lake Chad: Comparative analysis of three bias correction methods

Relationship between physical exercise and college students' social adaptation: the chain mediating role of self-esteem and peer attachment.

Physical exercise is an important way for college students to keep healthy, and social adaptation is an important part of college students' mental health. Therefore, this study explores strategies to enhance college students' social adaptation from the perspective of physical exercise, examining the correlation between physical exercise and college students' social adaptation, and delving into the roles of self-esteem and peer attachment in this relationship. A stratified cluster sampling method was used to collect data from 809 college students at Zhaoqing University (average age 19.88 ± 1.22, of whom 399 were male and 410 were female) using the physical exercise scale, college students' social adaptation scale, self-esteem scale, and peer attachment scale. For data analysis, Pearson correlation analysis, structural equation modeling, and bias-corrected percentile bootstrap methods were sequentially performed. (1) Physical exercise was positively correlated with college students' social adaptation (r = 0.58, p < 0.01), and the direct path between physical exercise and college students' social adaptation was significant (β = 0.28, p < 0.01, CI[0.22, 0.33]); (2) Physical exercise was positively correlated with self-esteem (β = 0.56, p < 0.01, CI[0.50, 0.62]) and peer attachment (β = 0.18, p < 0.01, CI[0.11, 0.26]); self-esteem was positively correlated with peer attachment (β = 0.36, p < 0.01, CI[0.28, 0.43]) and college students' social adaptation (β = 0.43, p < 0.01, CI[0.37, 0.49]); peer attachment was positively correlated with college students' social adaptation (β = 0.18, p < 0.01, CI[0.12, 0.23]); (3) The relationship between physical exercise and social adaptation was not only mediated independently by self-esteem and peer attachment, but also indirectly by the same two factors in a chain reaction. Physical exercise can not only directly predict college students' social adaptation, but also indirectly predict college students' social adaptation through the independent mediation and chain mediation of self-esteem and peer attachment. It reveals that we should combine more important physical exercise with mental health education for students.

HiCPC: A new 10-km CMIP6 downscaled daily climate projections over China

Accurate climate projections are critical for various applications and impact assessments in environmental science and management. This study presents HiCPC (High-resolution CMIP6 downscaled daily Climate Projections over China), a novel dataset tailored to China’s specific needs. HiCPC leverages outputs from 22 global climate models (GCMs) from the Coupled Model Intercomparison Project Phase 6 (CMIP6). To address inherent biases in daily GCM simulations, an advanced Bias Correction and Spatial Disaggregation (BCSD) method is employed, using the China Meteorological Forcing Dataset (CMFD) as a reference. HiCPC offers detailed daily precipitation and temperature data across China at an enhanced spatial resolution of 0.1° × 0.1°. It covers both the historical period (1979–2014) and future projections (2015–2100) based on four CMIP6 Shared Socioeconomic Pathways (SSPs) scenarios (SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5). Upon validation, HiCPC demonstrates good performance, surpassing CMIP6 GCMs across the historical period. This reinforces its significance for essential research in climate change evaluation and its associated implications within China.

Assessment of CMIP6 models and multi-model averaging for temperature and precipitation over Iran

In this study, the performances of 40 Coupled Model Intercomparison Project Phase 6 are evaluated against observational data at synoptic stations in Iran using various evaluation criteria. The results reveal diverse model accuracy across different climate conditions and criteria, emphasizing particularly notable disparities in the nonstationarity R criterion compared to others. Although according to the ranking of the raw and bias-corrected outputs of CMIP6 GCMs for Iran, the NorESM2-MM, AWI-ESM-1-1-LR, and MPI-ESM1-2-LR models are consistently among the top six ranked models for precipitation in both raw and corrected outputs. For temperature, MPI-ESM1-2-LR, TaiESM1, INM-CM4-8, and IITM-ESM are consistently among the top six models for both the raw and bias-corrected outputs of CMIP6 GCMs. The Bias correction methods, including quantile mapping and linear scaling, integrated with Bayesian model averaging, were applied. While quantile mapping demonstrates superior performance and less disparity than linear scaling, it proves ineffective for correcting biases at stations with bias nonstationarity over time. The RMSE for monthly precipitation ranges from almost 0 to 200 mm, with a large RMSE value related to the high precipitation stations, and the monthly temperature exhibits a range of 0 to 4 °C. The use of a multi-model ensemble improves accuracy compared to individual models, resulting in a reduction in the differences between the minimum and maximum RMSE values from 178.6 to 91.0. Additionally, the range for mean absolute error decreases from 126.9 to 93.3, and the difference in the correlation coefficient narrows from 0.9 to 0.42. Averaging models after bias correction prevents significant fluctuations while maintaining higher accuracy, in contrast to the second method, which involves bias-correcting models after averaging.

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.