Global Root Mean Research Articles

Downscaling sea surface height and currents in coastal regions using convolutional neural network

Downscaling is the process to obtain high-resolution data from low-resolution data. Recently statistical models using convolutional neural networks have gained popularity for fast downscaling of environmental fields, while their application to the coastal sea surface height and currents is lacking. This research aims to downscale sea surface height and depth-averaged current to a resolution of hundreds of meters in coastal regions with dynamic shorelines using convolutional neural networks. Hourly outputs over one year from a physical numerical model for a coastal region in the German Bight are used as the low-resolution input and high-resolution ground truth for the network. The results show that the network effectively reconstructs sea surface height and current in the region to a resolution of hundreds of meters with a scale factor of 16 or even 64, and accurately traces the moving sea surface and shorelines. The global mean absolute error and root mean square error for the sea surface height are found to be less than 0.03 m and 0.07 m, respectively, and for the current less than 0.03 m/s and 0.05 m/s, respectively. These values are around ten times smaller than those obtained from interpolation methods including nearest neighbor, bilinear and bicubic. The network also effectively replicates the distribution of high-resolution data. The errors in the reconstructed time average, 1st percentile and 99th percentile are significantly smaller than those from interpolation methods, especially for the current. These results highlight the ability of the network to downscale sea surface height and currents in regions with complex shorelines, and have implications for downscaling other coastal fields and shoreline tracking.

Research on reconstruction of the global sound speed profile combining partial underwater prior information

The sound speed profile (SSP) is an important factor affecting the acoustic propagation characteristics of the ocean, making the accurate acquisition of SSP a crucial step in the interdisciplinary research of oceanography and underwater acoustics. Limited by the cost of in-situ measurement and the performance of the instrument itself, direct measurement of SSP inevitably leads to insufficient depth or even missing information. In this paper, we propose using partial underwater prior information (UWPI) only including underwater sound speed to obtain preliminary reconstruction results of global SSP for the first time. The empirical orthogonal function (EOF) reconstruction algorithm is optimized by employing assimilated SSP as the background SSP to further reduce reconstruction errors. The maximum global average reconstruction error and root mean square error (RMSE) after optimization decrease by >51% and 71%, respectively, which indicates that the performance of the optimized algorithm combined with partial UWPI is further improved. Finally, the performance of the optimized algorithm is discussed from the perspective of acoustic propagation. This research provides a reliable technical approach for SSP reconstruction under incomplete depth conditions, which can be applied in underwater sound field prediction and acoustic detection in the future.

Estimating the mixed layer depth of the global ocean by combining multisource remote sensing and spatiotemporal deep learning

ABSTRACT Estimating the ocean mixed layer depth (MLD) is crucial for studying the atmosphere-ocean interaction and global climate change. Satellite observations can accurately estimate the MLD over large scales, effectively overcoming the limitation of sparse in situ observations and reducing uncertainty caused by estimation based on in situ and reanalysis data. However, combining multisource satellite observations to accurately estimate the global MLD is still extremely challenging. This study proposed a novel Residual Convolutional Gate Recurrent Unit (ResConvGRU) neural networks, to accurately estimate global MLD along with multisource remote sensing data and Argo gridded data. With the inherent spatiotemporal nonlinearity and dependence of the ocean dynamic process, the proposed method is effective in spatiotemporal feature learning by considering temporal dependence and capturing more spatial features of the ocean observation data. The performance metrics show that the proposed ResConvGRU outperforms other well-used machine learning models, with a global determination coefficient (R2) and a global root mean squared error (RMSE) of 0.886 and 17.83 m, respectively. Overall, the new deep learning approach proposed is more robust and advantageous in data-driven spatiotemporal modeling for retrieving ocean MLD at the global scale, and significantly improves the estimation accuracy of MLD from remote sensing observations.

Improving Stratocumulus Cloud Amounts in a 200‐m Resolution Multi‐Scale Modeling Framework Through Tuning of Its Interior Physics

AbstractHigh‐Resolution Multi‐scale Modeling Frameworks (HR)—global climate models that embed separate, convection‐resolving models with high enough resolution to resolve boundary layer eddies—have exciting potential for investigating low cloud feedback dynamics due to reduced parameterization and ability for multidecadal throughput on modern computing hardware. However low clouds in past HR have suffered a stubborn problem of over‐entrainment due to an uncontrolled source of mixing across the marine subtropical inversion manifesting as stratocumulus dim biases in present‐day climate, limiting their scientific utility. We report new results showing that this over‐entrainment can be partly offset by using hyperviscosity and cloud droplet sedimentation. Hyperviscosity damps small‐scale momentum fluctuations associated with the formulation of the momentum solver of the embedded large eddy simulation. By considering the sedimentation process adjacent to default one‐moment microphysics in HR, condensed phase particles can be removed from the entrainment zone, which further reduces entrainment efficiency. The result is an HR that can produce more low clouds with a higher liquid water path and a reduced stratocumulus dim bias. Associated improvements in the explicitly simulated sub‐cloud eddy spectrum are observed. We report these sensitivities in multi‐week tests and then explore their operational potential alongside microphysical retuning in decadal simulations at operational 1.5° exterior resolution. The result is a new HR having desired improvements in the baseline present‐day low cloud climatology, and a reduced global mean bias and root mean squared error of absorbed shortwave radiation. We suggest it should be promising for examining low cloud feedbacks with minimal approximation.

Synthesis‐Style Auto‐Correlation‐Based Transformer: A Learner on Ionospheric TEC Series Forecasting

AbstractAccurate 1‐day global total electron content (TEC) forecasting is essential for ionospheric monitoring and satellite communications. However, it faces challenges due to limited data and difficulty in modeling long‐term dependencies. This study develops a highly accurate model for 1‐day global TEC forecasting. We utilized generative TEC data augmentation based on the International Global Navigation Satellite Service (IGS) data set from 1998 to 2017 to enhance the model's prediction ability. Our model takes the TEC sequence of the previous 2 days as input and predicts the global TEC value for each hourly step of the next day. We compared the performance of our model with 1‐day predicted ionospheric products provided by both the Center for Orbit Determination in Europe (C1PG) and Beihang University (B1PG). We proposed a two‐step framework: (a) a time series generative model to produce realistic synthetic TEC data for training, and (b) an auto‐correlation‐based transformer model designed to capture long‐range dependencies in the TEC sequence. Experiments demonstrate that our model significantly improves 1‐day forecast accuracy over prior approaches. On the 2018 benchmark data set, the global root mean squared error (RMSE) of our model is reduced to 1.17 TEC units (TECU), while the RMSE of the C1PG model is 2.07 TECU. Reliability is higher in middle and high latitudes but lower in low latitudes (RMSE < 2.5 TECU), indicating room for improvement. This study highlights the potential of using data augmentation and auto‐correlation‐based transformer models trained on synthetic data to achieve high‐quality 1‐day global TEC forecasting.

Comparative Analysis of Global Terrestrial Water Storage Simulations: Assessing CABLE, Noah-MP, PCR-GLOBWB, and GLDAS Performances during the GRACE and GRACE-FO Era

Hydrology and land surface and models (HM and LSM) are essential tools for estimating global terrestrial water storage (TWS), an important component of the global water budget for assessing the accessibility and long-term variability of water supplies. With the expansion of open-source and open-data policies, the community can now perform model TWS simulation from source codes as well as directly exploit end-user hydrologic products for water resource applications. Regardless of the model effectiveness and usability, an accuracy assessment is necessary to quantify the model’s global and regional strengths, weaknesses, and reliability. This paper compares the most recent global TWS estimates from six models, namely the PCRaster Global Water Balance (PCR-GLOBWB), Noah, Noah-Multiparameterization (Noah-MP), Catchment LSM, and Variable Infiltration Capacity (VIC), and Community Atmosphere Biosphere Land Exchange (CABLE)—the latter of which is cross validated for the first time. TWS observations from the Gravity Recovery And Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) satellite missions between 2002 and 2021 are used to validate the model. The analyses show that Noah-MP outperforms other models in terms of global average correlations and root mean square errors. PCR-GLOBWB performance is superior in irrigated regions because of the inclusion of human intervention components in the model. CABLE, a core LSM of the Australian climate model, significantly outperforms all others in Australia. CLSM performs reasonably well, but the TWS long-term trend appears to be incorrect due to an overestimated groundwater component. Noah performs similarly (but inferiorly) to Noah-MP, most likely due to model physics sharing. VIC has the least agreement with GRACE and GRACE-FO. The evaluation also sheds some light on the role of forcing data in model performance, particularly for ready-to-use products such as GLDAS, where incorporating MERRA-2 or ERA5 data into GLDAS Noah simulations may potentially improve its TWS accuracy, which has previously been overlooked due to limited modeling capacity. Despite each model’s unique strength, the ensemble mean TWS, particularly when Noah-MP and PCR-GLOBWB are included, yields better TWS estimates than an individual model result. The findings of this study could serve as a benchmark for future model development and the data published in this paper could aid in the scientific advancement and discoveries of the hydrology community.

Exploring forearm muscle coordination and training applications of various grip positions during maximal isometric finger dead-hangs in rock climbers.

Maximal isometric finger dead-hangs are used in rock climbing to strengthen finger flexors. Although various grip positions are often used when performing finger dead-hangs, little is known regarding how these grip positions can affect forearm muscle activity. Understanding how forearm muscles are recruited during dead-hangs could help foreseeing the potential for training of different grip positions. The aim of the present study was to explore the training applications of the various grip positions by comparing the activity of forearm muscles during maximal dead-hangs in rock climbers. Twenty-five climbers performed maximal dead-hangs in three climbing-specific grip positions: CRIMP, SLOPE, and SLOPER. We recorded the maximal loads used and the sEMG of the flexor digitorum profundus (FDP), the flexor digitorum superficialis (FDS), the flexor carpi radialis (FCR), and the extensor digitorum communis (EDC). Individual and global (sum of all muscles) root mean square (RMS) and neuromuscular efficiency (NME) values were computed. Repeated measures analysis were performed to assess grip differences (p<0.05). SLOPER showed the largest maximal load values among the three grip positions (p<0.001, d≥2.772). Greater global (p≤0.044, d≥0.268), FDS (p≤0.005, d≥0.277), and FCR (p<0.001, d≥1.049) activity was observed for the SLOPER compared to CRIMP and SLOPE, while EDC (p≤0.005, d≥0.505) showed lower activity in the SLOPER compared to the other two grip positions. SLOPER presented the highest global (p<0.001, d≥0.629), FDP (p<0.001, d ≥ 0.777), FDS (only CRIMP vs SLOPER: p < 0.001, d = 0.140), and EDC NME (p < 0.001, d ≥ 1.194). The CRIMP showed greater FDS activity (p = 0.001, d = 0.386) and lower NME (p = 0.003, d = 0.125) compared to SLOPE. These results revealed that, under maximum intensity conditions, SLOPER could stimulate the FDS and FCR better than the other grip positions at the expense of using greater loads. Similarly, maximum CRIMP dead-hang could better stimulate the FDS than the SLOPE, even when using similar loads.

Performance Comparison of Deterministic and Stochastic Modifications in Stokes’s and Hotine’s Formulas: The Case of Jilin Province, China

The high-precision regional geoid model provides important fundamental geospatial information for developing and applying many disciplines. Deterministic and stochastic modifications are applied to Stokes’s and Hotine’s formulas of geoid modeling to reduce errors. Based on the Experimental Geopotential Model 2019 (XGM2019), this paper used Stokes’s and Hotine’s formulas to analyze the variation of global root mean square error (RMSE) with modification parameters for two deterministic (Wong and Gore; and Vaníček and Kleusberg) and three stochastic modifications (biased, unbiased, and optimum). Taking the quasigeoid refinement of Jilin Province as an example, the global RMSE, approximate geoid undulation, and additive corrections were calculated. The parameter analysis and the global RMSE calculation showed that the variation of the modification limits and the terrestrial gravity data error variance had a centimeter-level effect on the global RMSE. In contrast, the impact of the integration radius was relatively small. The stochastic modifications were better than the deterministic ones in calculating the global RMSE. The global RMSE of Hotine’s formula was smaller than that of Stokes’s, and its unbiased and optimum modifications reached the minimum value of 12.9 mm. The validation of XGM2019 and the refined quasigeoid based on the high accuracy GPS/leveling points showed that the standard deviation (STD) of XGM2019 was 5.8 cm in Jilin Province, and the refined optimal quasigeoid model was 2.9 cm. Stokes’s and Hotine’s formulas provided the same accuracy in the study area. In the western plain area, the accuracy of the deterministic modifications was 2.0 cm, which was about 0.4 cm higher than that of the stochastic modifications. In the eastern mountainous area, the stochastic modifications were better than the deterministic ones, and the accuracy was about 3.2 cm. Stokes’s and Hotine’s formulas based on deterministic and stochastic modifications significantly improve the accuracy of the XGM2019. The deterministic and stochastic modifications show millimeter-level differences in plain and mountainous areas.

Data Driven Models for the Design of Rocket Injector Elements

Improving the predictive capabilities of reduced-order models for the design of injector and chamber elements of rocket engines could greatly improve the quality of early rocket chamber designs. In the present work, we propose an innovative methodology that uses high-fidelity numerical simulations of turbulent reactive flows and artificial intelligence for the generation of surrogate models. The surrogate models that were generated and analyzed are deep learning networks trained on a dataset of 100 large eddy simulations of a single-shear coaxial injector chamber. The design of experiments was created considering three design parameters: chamber diameter, recess length, and oxidizer–fuel ratio. The paper presents the methodology developed for training and optimizing the data-driven models. Fully connected neural networks (FCNNs) and U-Nets were utilized as surrogate-modeling technology. Eventually, the surrogate models for the global quantity, average, and root mean square fields were used in order to analyze the impact of the length of the post’s recess on the performances obtained and the behavior of the flow.

Extended Superficial Musculoaponeurotic System Face-Lift With Vertical Vector for Asian Patients: A 3-Dimensional Analysis of Facial Contour.

In this study, the authors report the experience of extended superficial musculoaponeurotic system (SMAS) face-lift with the vertical vector in Asian ethnicity and investigate the 3-dimensional change of facial contour. A total of 32 patients with Korean ethnicity underwent extended SMAS face-lift with vertical vector from 2015 to 2018. Patients with aging face were included for the study subjects, whereas those who were diagnosed with any craniofacial deformity were excluded. Using 3-dimensional photogrammetry, surface contour analysis was performed in the cheek region to calculate the mean, maximal, and minimal difference of surface projection and global root mean square error between the preoperative and 1-year postoperative period. The change of horizontal facial widths and jawline angle was evaluated. In contour analysis, the mean difference of surface contour was highest in anterior, followed by lateral cheek and lower face, sequentially. The maximal difference of surface contour was highest in anterior cheek, followed by lateral cheek and lower face, whereas the minimal difference of surface contour was lowest in lower face, followed by anterior cheek and lateral cheek, sequentially. No significant differences in the midfacial and lower facial distances were observed between the preoperative and postoperative periods. There was significant increase of jawline angle, from 20.78 to 23.14 degree of mean value ( P =0.001). In conclusion, the extended SMAS face-lift with vertical vector can be an optimal option for Asian subjects in terms of the midfacial volumetric shift, sharpening of jawline and avoidance of midfacial widening.

Updated conceptual and numerical model of the Los Humeros Geothermal Field

The Los Humeros Geothermal Field is one of the five geothermal fields currently operating in Mexico. In this study, an updated conceptual model was developed considering studies of geology, hydrology, hydrogeology, structural geology, hydrogeochemistry, geophysics, temperature and pressure data from wells, as well as previous conceptual models. To explain the behavior of this geothermal field in greater detail, as many studies as possible were integrated into the conceptual model, which required building a 3D numerical model of fluid flow and heat transfer using the TOUGH3 simulator code. The numerical model has an area of 400 km2 and a thickness of 4 km, and it is composed of 64,000, each 500 m long × 500 m wide × 100 m high. In addition, ten rock types were included in the numerical model assigning different permeability values, from 4.00E-14 to 5.28E-17 m2. Model calibration was carried out considering downhole temperature profile data from 38 wells. The obtained modeling temperatures achieved a global Root Mean Square Error (RMSE) of 35.81 °C, while for specific wells from 16.14 to 60.39 °C. The numerical model was validated under transient-state conditions during production history, using bottom pressure data of wells H-1 and H-1D from 1982 to 2006, reaching an RMSE pressure of 4.43 bar, corresponding to 3.05% of the maximum pressure. The conceptual model update developed improves previous numerical models of Los Humeros because it allows considering registered variations of bottom pressure over the almost entire exploitation history. This updated conceptual model will help locate new exploration wells and define extraction policies.

Solar photovoltaic Maximum Power Point Tracking controller optimization using Grey Wolf Optimizer: A performance comparison between bio-inspired and traditional algorithms

Solar photovoltaic systems are widely used; however, their performance is bound to weather conditions, depending on irradiation, temperature, and the effect of shadows. Maximum Power Point Tracking techniques have been developed to solve this issue. Standard methods use mainly-two algorithms: Perturb and Observe and Incremental Conductance. However, such algorithms perform differently when the Solar photovoltaic system works under sudden solar irradiation changes, temperature, and load changes. This research proposes an optimized Maximum Power Point Tracking controller based on the Grey Wolf Optimization algorithm using the MATLAB/Simulink software as an alternative to the traditional techniques. Global efficiency and Root Mean Square Error evaluate the controller's performance. The response time is analyzed using the Grey Wolf Optimizer algorithm, Wolf Optimizer Algorithm, Simulated Annealing, and Particle Swarm Optimization. These four metaheuristic algorithms are compared to the Perturb and Observe, and Incremental Conductance algorithms. The models are analyzed for the transient state and full-day operation scenarios for constant and variable irradiations, temperatures, and loads. The comparative results show that the Maximum Power Point Tracking controller optimized by the Grey Wolf Optimizer algorithm has superior performance, giving an average 6% output power higher than the other controllers under the test scenarios evaluated. The efficiency of the proposed model was, on average, 3% higher than the Incremental Conductance and Perturb & Observe controllers. For the MPPT controller tunning stage, the Grey Wolf Optimizer Algorithm had the best performance with an RMSE of 255.3549 with a compute time of 27.3 min; the worst performing was the Particle Swarm Optimization with an RMSE of 332.4075 and 27.8 min computation time. The proposed GWO optimized MPPT controller had the faster settling time for each irradiation level compared, with an average of 0.175 s. Also, results showed an improvement of the system response throughout the Maximum Power Point Tracking controller optimized by the Grey Wolf Optimizer algorithm since a lower curling effect is obtained at power converter outputs.

Empirical Orthogonal Function Analysis and Modeling of Global Tropospheric Delay Spherical Harmonic Coefficients

Based on the ERA-5 meteorological data from 2015 to 2019, we establish the global tropospheric delay spherical harmonic (SH) coefficients set called the SH_set and develop the global tropospheric delay SH coefficients empirical model called EGtrop using the empirical orthogonal function (EOF) method and periodic functions. We apply tropospheric delay derived from IGS stations not involved in modeling as reference data for validating the dataset, and statistical results indicate that the global mean Bias of the SH_set is 0.08 cm, while the average global root mean square error (RMSE) is 2.61 cm, which meets the requirements of the tropospheric delay model applied in the wide-area augmentation system (WAAS), indicating the feasibility of the product strategy. The tropospheric delay calculated with global sounding station and tropospheric delay products of IGS stations in 2020 are employed to validate the new product model. It is verified that the EGtrop model has high accuracy with Bias and RMSE of −0.25 cm and 3.79 cm, respectively, with respect to the sounding station, and with Bias and RMSE of 0.42 cm and 3.65 cm, respectively, with respect to IGS products. The EGtrop model is applicable not only at the global scale but also at the regional scale and exhibits the advantage of local enhancement.

ERA5-Land: a state-of-the-art global reanalysis dataset for land applications

Abstract. Framed within the Copernicus Climate Change Service (C3S) of the European Commission, the European Centre for Medium-Range Weather Forecasts (ECMWF) is producing an enhanced global dataset for the land component of the fifth generation of European ReAnalysis (ERA5), hereafter referred to as ERA5-Land. Once completed, the period covered will span from 1950 to the present, with continuous updates to support land monitoring applications. ERA5-Land describes the evolution of the water and energy cycles over land in a consistent manner over the production period, which, among others, could be used to analyse trends and anomalies. This is achieved through global high-resolution numerical integrations of the ECMWF land surface model driven by the downscaled meteorological forcing from the ERA5 climate reanalysis, including an elevation correction for the thermodynamic near-surface state. ERA5-Land shares with ERA5 most of the parameterizations that guarantees the use of the state-of-the-art land surface modelling applied to numerical weather prediction (NWP) models. A main advantage of ERA5-Land compared to ERA5 and the older ERA-Interim is the horizontal resolution, which is enhanced globally to 9 km compared to 31 km (ERA5) or 80 km (ERA-Interim), whereas the temporal resolution is hourly as in ERA5. Evaluation against independent in situ observations and global model or satellite-based reference datasets shows the added value of ERA5-Land in the description of the hydrological cycle, in particular with enhanced soil moisture and lake description, and an overall better agreement of river discharge estimations with available observations. However, ERA5-Land snow depth fields present a mixed performance when compared to those of ERA5, depending on geographical location and altitude. The description of the energy cycle shows comparable results with ERA5. Nevertheless, ERA5-Land reduces the global averaged root mean square error of the skin temperature, taking as reference MODIS data, mainly due to the contribution of coastal points where spatial resolution is important. Since January 2020, the ERA5-Land period available has extended from January 1981 to the near present, with a 2- to 3-month delay with respect to real time. The segment prior to 1981 is in production, aiming for a release of the whole dataset in summer/autumn 2021. The high spatial and temporal resolution of ERA5-Land, its extended period, and the consistency of the fields produced makes it a valuable dataset to support hydrological studies, to initialize NWP and climate models, and to support diverse applications dealing with water resource, land, and environmental management. The full ERA5-Land hourly (Muñoz-Sabater, 2019a) and monthly (Muñoz-Sabater, 2019b) averaged datasets presented in this paper are available through the C3S Climate Data Store at https://doi.org/10.24381/cds.e2161bac and https://doi.org/10.24381/cds.68d2bb30, respectively.

An improved non-linear inter-calibration method on different radiometers for enhancing coverage of daily LST estimates in low latitudes

Most polar-orbit-satellite based passive microwave radiometers, e.g. AMSR-2 and the FY-3B Microwave Radiation Imager (FY3B-MWRI), have the revisit cycles of ~2 days in low latitudes. This indicates that requirement of complete global coverage on the daily basis has not been met. On the other hand, using synergistic observations from different radiometers seems promising to enhance the temporal resolution of observations in such areas, whereas cross-radiometer inter-calibration is essential prior to their synergism. For this purpose, conventional inter-calibration models are usually built based on linear relations of brightness temperature (TB) between different radiometers. However, the linear model has relatively poor performance in low latitudes primarily due to wet surface conditions. In this study, we propose an improved non-linear model for calibrating MWRI TB against AMSR-2 TB at 18.7 GHz and 23.8 GHz channels. Global land surface temperature (LST) is estimated using the post-calibration MWRI TB data and then validated against AMSR-2 based LST, MODIS based LST, and in situ near-surface air temperature datasets in low latitudes respectively. The validation results show that LST outcome based on the improved non-linear inter-calibration method has smaller global Root Mean Square Errors (RMSEs) below 3.5 K, compared with the RMSEs of ~6 K obtained from the conventional linear inter-calibration method and from the results without inter-calibration. Further analysis also shows that synergistic observations between AMSR-2 and MWRI are capable of shortening the maximum global revisit cycle of AMSR-2 LST from ~2 days to less than 1.2 days. These results indicate that the improved inter-calibration method is effective for obtaining daily LST datasets with quasi-complete global coverage and reliable accuracy.

Comparative study of Stochastic Taylor Methods and Derivative-Free Methods for Stochastic Differential Equations

Ordinary differential equations (ODEs) have been widely used to model the dynamical behaviour of biological and physical systems. However, modelling these systems using deterministic model such as ODEs is inadequate as the system is subjected to the uncontrolled factors of environmental noise. Stochastic differential equations (SDEs) which are originating from the irregular Brownian motion can be applied to model such systems that subjected to the uncontrolled factors of noisy behaviour. Numerical methods are required to approximate the solution of the model due to the complexity of the equation. Theoretically, methods with a higher order of convergence lead to a better approximation of the solutions. Though, the implementation of the methods might not reflect the theoretical finding as generating a lot of random numbers might contribute to the instability of the methods. This research is aimed to investigate the performance of stochastic Taylor methods of Euler-Maruyama, Milstein scheme, and derivative-free methods of second and fourth-order stochastic Runge-Kutta in approximating the solution of SDEs. Four types of mathematical models which include the Black-Scholes model, logistic model, stochastic Gompertz model, and prey-predator model are simulated using the aforementioned numerical methods. Numerical solutions of the Black-Scholes model are compared with the analytical solution meanwhile, the numerical solutions of the logistic model and stochastic Gompertz models are compared with the experimental data of the fermentation process and cancer cell growth, respectively. The simulated results of the prey-predator model are compared with the experimental data of the interaction between cancer cells (prey) and anticancer Chrondoitin Sulfate (predator). The prediction performance of the methods is measured using global error and root mean square errors (RMSE).

Trailer angle estimation using radar point clouds

Algorithms for trailer control and backup need to keep track of the trailer angle, therefore, the angle needs to be determined. This work shows that the angle can be estimated using 2D point clouds collected from two automotive radars installed in the taillight fixtures of a trailer-coupled truck. The detection threshold of each radar is reduced to allow more detections of the trailer. A tracking procedure is introduced to find the trailer detections as the trailer rotates; the tracked set of detections are then compared with one or more reference sets to estimate the angle. Estimated angles are further refined with a Kalman filter to obtain smooth estimates of the angle. The algorithm is tested on 15 datasets; each dataset is obtained in an experiment in which the trailer is rotated up to about 40∘ in both radar directions. The estimates from all the datasets result in a global root mean squared error of about 0.9∘ for up to 10∘ absolute trailer rotation; about 1.3∘ for up to 20∘ absolute rotation; about 1.5∘ for up to 30∘ absolute rotation; and about 1.9∘ for all trailer angles considered. The algorithm executes in about 3 ms on a typical personal computer.

A long term global daily soil moisture dataset derived from AMSR-E and AMSR2 (2002\u20132019)

Long term surface soil moisture (SSM) data with stable and consistent quality are critical for global environment and climate change monitoring. L band radiometers onboard the recently launched Soil Moisture Active Passive (SMAP) Mission can provide the state-of-the-art accuracy SSM, while Advanced Microwave Scanning Radiometer for EOS (AMSR-E) and AMSR2 series provide long term observational records of multi-frequency radiometers (C, X, and K bands). This study transfers the merits of SMAP to AMSR-E/2, and develops a global daily SSM dataset (named as NNsm) with stable and consistent quality at a 36 km resolution (2002–2019). The NNsm can reproduce the SMAP SSM accurately, with a global Root Mean Square Error (RMSE) of 0.029 m3/m3. NNsm also compares well with in situ SSM observations, and outperforms AMSR-E/2 standard SSM products from JAXA and LPRM. This global observation-driven dataset spans nearly two decades at present, and is extendable through the ongoing AMSR2 and upcoming AMSR3 missions for long-term studies of climate extremes, trends, and decadal variability.

Modelling of long-term Zn, Cu, Cd and Pb dynamics from soils fertilised with organic amendments

Abstract. Soil contamination by trace elements (TEs) is a major concern for sustainable land management. A potential source of excessive inputs of TEs into agricultural soils are organic amendments. Here, we used dynamic simulations carried out with the Intermediate Dynamic Model for Metals (IDMM) to describe the observed trends of topsoil Zn (zinc), Cu (copper), Pb (lead) and Cd (cadmium) concentrations in a long-term (&gt;60-year) crop trial in Switzerland, where soil plots have been treated with different organic amendments (farmyard manure, sewage sludge and compost). The observed ethylenediaminetetraacetic acid disodium salt (EDTA)-extractable concentrations ranged between 2.6 and 27.1 mg kg−1 for Zn, 4.9 and 29.0 mg kg−1 for Cu, 6.1–26.2 mg kg−1 for Pb, and 0.08 and 0.66 mg kg−1 for Cd. Metal input rates were initially estimated based on literature data. An additional, calibrated metal flux, tentatively attributed to mineral weathering, was necessary to fit the observed data. Dissolved organic carbon fluxes were estimated using a soil organic carbon model. The model adequately reproduced the EDTA-extractable (labile) concentrations when input rates were optimised and soil lateral mixing was invoked to account for the edge effect of mechanically ploughing the trial plots. The global average root mean square error (RMSE) was 2.7, and the average bias (overestimation) was −1.66, −2.18, −4.34 and −0.05 mg kg−1 for Zn, Cu, Pb and Cd, respectively. The calibrated model was used to project the long-term metal trends in field conditions (without soil lateral mixing), under stable climate and management practices, with soil organic carbon estimated by modelling and assumed trends in soil pH. Labile metal concentrations to 2100 were largely projected to remain near constant or to decline, except for some metals in plots receiving compost. Ecotoxicological thresholds (critical limits) were predicted to be exceeded presently under sewage sludge inputs and to remain so until 2100. Ecological risks were largely not indicated in the other plots, although some minor exceedances of critical limits were projected to occur for Zn before 2100. This study advances our understanding of TEs' long-term dynamics in agricultural fields, paving the way to quantitative applications of modelling at field scales.

OceanSODA-ETHZ: a global gridded data set of the surface ocean carbonate system for seasonal to decadal studies of ocean acidification

Abstract. Ocean acidification has profoundly altered the ocean's carbonate chemistry since preindustrial times, with potentially serious consequences for marine life. Yet, no long-term, global observation-based data set exists that allows us to study changes in ocean acidification for all carbonate system parameters over the last few decades. Here, we fill this gap and present a methodologically consistent global data set of all relevant surface ocean parameters, i.e., dissolved inorganic carbon (DIC), total alkalinity (TA), partial pressure of CO2 (pCO2), pH, and the saturation state with respect to mineral CaCO3 (Ω) at a monthly resolution over the period 1985 through 2018 at a spatial resolution of 1∘×1∘. This data set, named OceanSODA-ETHZ, was created by extrapolating in time and space the surface ocean observations of pCO2 (from the Surface Ocean CO2 Atlas, SOCAT) and total alkalinity (TA; from the Global Ocean Data Analysis Project, GLODAP) using the newly developed Geospatial Random Cluster Ensemble Regression (GRaCER) method (code available at https://doi.org/10.5281/zenodo.4455354, Gregor, 2021). This method is based on a two-step (cluster-regression) approach but extends it by considering an ensemble of such cluster regressions, leading to improved robustness. Surface ocean DIC, pH, and Ω were then computed from the globally mapped pCO2 and TA using the thermodynamic equations of the carbonate system. For the open ocean, the cluster-regression method estimates pCO2 and TA with global near-zero biases and root mean squared errors of 12 µatm and 13 µmol kg−1, respectively. Taking into account also the measurement and representation errors, the total uncertainty increases to 14 µatm and 21 µmol kg−1, respectively. We assess the fidelity of the computed parameters by comparing them to direct observations from GLODAP, finding surface ocean pH and DIC global biases of near zero, as well as root mean squared errors of 0.023 and 16 µmol kg−1, respectively. These uncertainties are very comparable to those expected by propagating the total uncertainty from pCO2 and TA through the thermodynamic computations, indicating a robust and conservative assessment of the uncertainties. We illustrate the potential of this new data set by analyzing the climatological mean seasonal cycles of the different parameters of the surface ocean carbonate system, highlighting their commonalities and differences. Further, this data set provides a novel constraint on the global- and basin-scale trends in ocean acidification for all parameters. Concretely, we find for the period 1990 through 2018 global mean trends of 8.6 ± 0.1 µmol kg−1 per decade for DIC, −0.016 ± 0.000 per decade for pH, 16.5 ± 0.1 µatm per decade for pCO2, and −0.07 ± 0.00 per decade for Ω. The OceanSODA-ETHZ data can be downloaded from https://doi.org/10.25921/m5wx-ja34 (Gregor and Gruber, 2020).