Grid Points Research Articles

Two different perspectives on heatwaves within the Lagrangian framework

Abstract. Although heatwaves are one of the most dangerous types of weather-related hazards, their underlying mechanisms are not yet sufficiently understood. In particular, there is still no scientific consensus about the relative importance of the three key processes: horizontal temperature transport, subsidence accompanied by adiabatic heating, and diabatic heating. The current study quantifies these processes using an Eulerian method based on tracer advection, which allows one to extract Lagrangian information. For each grid point at any time, the method yields a decomposition of temperature anomalies into the aforementioned processes, complemented by the contribution of a pre-existing anomaly. Two different approaches for this decomposition are employed. The first approach is based on the full fields of the respective terms and has been established in prior research. In contrast, the second approach is based on the anomaly fields of the respective terms, i.e. deviations from their corresponding climatologies, and is introduced in this study. The two approaches offer two distinct perspectives on the same subject matter. By analysing two recent heatwaves, it is shown that the two decompositions yield substantial differences regarding the relative importance of the processes. A statistical analysis indicates that these differences are not coincidental but are characteristic of the respective regions. We conclude that the Lagrangian characterization of heatwaves is a matter of perspective.

Forecasting contrail climate forcing for flight planning and air traffic management applications: the CocipGrid model in pycontrails 0.51.0

Abstract. The global annual mean contrail climate forcing may exceed that of aviation's cumulative CO2 emissions. As only 2 %–3 % of all flights are likely responsible for 80 % of the global annual contrail energy forcing (EFcontrail), re-routing these flights could reduce the occurrence of strongly warming contrails. Here, we develop a contrail forecasting tool that produces global maps of persistent contrail formation and their EFcontrail formatted to align with standard weather and turbulence forecasts for integration into existing flight planning and air traffic management workflows. This is achieved by extending the existing trajectory-based contrail cirrus prediction model (CoCiP), which simulates contrails formed along flight paths, to a grid-based approach that initializes an infinitesimal contrail segment at each point in a 4D spatiotemporal grid and tracks them until their end of life. Outputs are provided for N aircraft-engine groups, with groupings based on similarities in aircraft mass and engine particle number emissions: N=7 results in a 3 % mean error between the trajectory- and grid-based CoCiP, while N=3 facilitates operational simplicity but increases the mean error to 13 %. We use the grid-based CoCiP to simulate contrails globally using 2019 meteorology and compare its forecast patterns with those from previous studies. Two approaches are proposed to apply these forecasts for contrail mitigation: (i) monetizing EFcontrail and including it as an additional cost parameter within a flight trajectory optimizer or (ii) constructing polygons to avoid airspace volumes with strongly warming contrails. We also demonstrate a probabilistic formulation of the grid-based CoCiP by running it with ensemble meteorology and excluding grid cells with significant uncertainties in the simulated EFcontrail. This study establishes a working standard for incorporating contrail mitigation into flight management protocols and demonstrates how forecasting uncertainty can be incorporated to minimize unintended consequences associated with increased CO2 emissions from re-routes.

Coupling Fully Staggered Grids via Numerical Filtering for Wave Propagation Simulation

The fully staggered grid (FSG) combines multiple standard staggered grids (SSGs) to simulate seismic wave propagation in anisotropic elastic media. However, its accuracy is contingent upon the wavefield’s consistency and continuity across multiple sets of SSGs. In isotropic or weakly anisotropic media, decoupling or weak coupling between the SSGs can lead to wavefield discontinuities at adjacent grid points in the diagonal direction. Issues such as inconsistent source activation, medium parameter discontinuities, and different numerical treatments of boundary conditions over multiple sets of SSGs can exacerbate these problems. While previous methods, such as FD-consistent point source technique and equivalent medium parameterization methods, have partially addressed these issues, they do not completely solve the problem. This study, drawing inspiration from numerical damping techniques used in collocated-grid finite-difference schemes to eliminate odd-even oscillations, introduces an explicit filter operator along the diagonal direction of the FSG. This approach ensures wavefield consistency and continuity across multiple SSGs, improving the accuracy of the FSG scheme. Although this method increases computational costs, it is essential for reliable seismic modeling in anisotropic media.

Examining tropical cyclone thermodynamic structure with TROPICS observations

Abstract This study examines the three-dimensional thermodynamic structure of a rapidly intensifying tropical cyclone (TC) through the utilization of synthetic retrievals based off of the specifications of NASA’s Time-Resolved Observations of Precipitation structure and storm Intensity with a Constellation of Smallsats (TROPICS) mission. Proxy TROPICS vertical profiles of temperature and water vapor mixing ratio generated from the Hurricane Nature Run (HNR1; Nolan et al. 2013) are utilized to analyze the TC structure over a 10-day period that includes the HNR1 TC’s rapid intensification (RI) from a tropical storm to a major hurricane. Analyses are performed to assess how accurately TROPICS may be able to determine thermodynamic profiles both within the storm and in the environment by validating against the HNR1 model data. It is found that the TROPICS retrievals compare favorably with the HNR1 data at most heights and times with errors consistently less than the proposed mission requirements (2 K for temperature; 25% for humidity). In addition, the retrievals show the ability to qualitatively track extensive dry air that is present in the vicinity of the TC. Although a substantial dry bias is present within the storm region of the TC (between 0 – 200 km from the surface center) in the 350–550 mb layer in the TROPICS retrievals, this bias is reduced when the retrievals associated with precipitating grid points are removed from the analyses. However, despite this filtering, a significant bias remains, which suggests that the TROPICS retrievals will likely lose accuracy in regions of stronger scattering.

High-resolution gridded dataset of China’s offshore wind potential and costs under technical change

Assessing the dynamics of offshore wind potential and costs is essential for low-carbon energy policy decision-making and energy modeling, but no open-source, spatial explicit and technologically detailed dataset is available. This study addresses this gap by employing a consistent assessment framework that integrates GIS analysis, a wind reanalysis model, a component-based cost model and scenario analysis. It identifies suitable space for offshore wind deployment considering 12 technical and policy constraints, estimates hourly output curves, capacity factors, and technology cost dynamics by components across 5058 grid points with a 10 km resolution from 2020 to 2035 under three technical change scenarios. The dataset has been validated through comparisons with existing offshore wind projects and datasets, and is stored in two formats (GeoTIFF and NetCDF4). This dataset offers extensive potential for use as an input in climate policy and energy system research.

Finite Differences on Sparse Grids for Continuous-Time Heterogeneous Agent Models

We present a finite difference method working on sparse grids to solve higher dimensional heterogeneous agent models. If one wants to solve the arising Hamilton–Jacobi–Bellman equation on a standard full grid, one faces the problem that the number of grid points grows exponentially with the number of dimensions. Discretizations on sparse grids only involve O(N(logN)d−1) degrees of freedom in comparison to the O(Nd) degrees of freedom of conventional methods, where N denotes the number of grid points in one coordinate direction and d is the dimension of the problem. While one can show convergence for the used finite difference method on full grids by using the theory introduced by Barles and Souganidis, we explain why one cannot simply use their results for sparse grids. Our numerical studies show that our method converges to the full grid solution for a two-dimensional model. We analyze the convergence behavior for higher dimensional models and experiment with different sparse grid adaptivity types.

Spatial Signatures of Electron Correlation in Least-Squares Tensor Hypercontraction.

Least-squares tensor hypercontraction (LS-THC) has received some attention in recent years as an approach to reduce the significant computational costs of wave function-based methods in quantum chemistry. However, previous work has demonstrated that LS-THC factorization performs disproportionately worse in the description of wave function components (e.g., cluster amplitudes T̂2) than Hamiltonian components (e.g., electron repulsion integrals (pq|rs)). This work develops novel theoretical methods to study the source of these errors in the context of the real-space T̂2 kernel, and reports, for the first time, the existence of a "correlation feature" in the errors of the LS-THC representation of the "exchange-like" correlation energy EX and T̂2 that is remarkably consistent across ten molecular species, three correlated wave functions, and four basis sets. This correlation feature portends the existence of a "pair point kernel" missing in the usual LS-THC representation of the wave function, which critically depends upon pairs of grid points situated close to atoms and with interpair distances between one and two Bohr radii. These findings point the way for future LS-THC developments to address these shortcomings.

Cyclic Peak Extraction from a Spatial Likelihood Map for Multi-Array Multi-Target Bearing-Only Localization

In the context of multi-array multi-target bearing-only localization, due to the existence of direction-finding errors, the crossing results of bearing lines cannot accurately determine correspondence with targets. Under conditions that clutter interference and missing of detection in direction-finding, the traditional method will produce false alarm targets and miss some targets. To address this issue, this paper draws on the idea of a spatial likelihood map which calculates the likelihood of target presence at each grid point within the observation area by partitioning the observation area into grids and utilizing bearing data from each array, yielding the distribution of targets in the observation area. Then, a multi-target cyclic peak extraction algorithm based on a statistical dual-threshold is proposed, which eliminates false peaks by cyclic extraction of target positions, so as to reduce false targets. Simulation results demonstrate that the spatial likelihood mapping-based localization exhibits good performance. Furthermore, when the multi-target cyclic peak extraction algorithm based on statistical dual-thresholds is applied, it outperforms direct target extraction from the spatial likelihood map, showcasing enhanced multi-target localization capabilities. Moreover, compared to the position non-linear least squares multi-target localization method, the proposed method has lower optimal sub-pattern assignment distance and lower localization error under the condition of interference and missing detection.

Development of a Multidimensional Analysis and Integrated Visualization Method for Maritime Traffic Behaviors Using DBSCAN-Based Dynamic Clustering

Automatic Identification System (AIS) data offer essential insights into maritime traffic patterns; however, effective visualization tools for decision-making remain limited. This study presents an integrated visualization processing method to support ship operators by identifying maritime traffic behavior information, such as traffic density, direction, and flow in specific sea navigational areas. We analyzed AIS dynamic data from a specific sea area, calculated ship density distributions across a grid lattice, and obtained visualizations of traffic-dense areas as heat maps. Using the density-based spatial clustering of applications with a noise algorithm, we detected traffic direction at each grid point, which was visualized in the form of directional arrows, and clustered ship trajectories to identify representative traffic flows. The visualizations were integrated and overlaid onto an S-57-based electronic nautical map for Mokpo’s entry and exit routes, revealing primary shipping lanes and critical inflection points within the target area. This integrated visualization method simultaneously displays traffic density, flow, and customary routes. It is adapted for the electronic nautical chart (S-101) under the next-generation hydrographic information standard (S-100), which can be used as a tool to support decision-making for ship operators.

Efficient Sampling for Machine Learning Electron Density and Its Response in Real Space.

Electron density is a fundamental quantity that can in principle determine all ground state electronic properties of a given system. Although machine learning (ML) models for electron density based on either an atom-centered basis or a real-space grid have been proposed, the demand for a number of high-order basis functions or grid points is enormous. In this work, we propose an efficient grid-point sampling strategy that combines targeted sampling favoring a large density and a screening of grid points associated with linearly independent atomic features. This new sampling strategy is integrated with a field-induced recursively embedded atom neural network model to develop a real-space grid-based ML model for the electron density and its response to an electric field. This approach is applied to a QM9 molecular data set, a H2O/Pt(111) interfacial system, an Au(100) electrode, and an Au nanoparticle under an electric field. The number of training points is found to be much smaller than previous models, while yielding comparably accurate predictions for the electron density of the entire grid. The resultant machine-learned electron density model enables us to properly partition partial charge onto each atom and analyze the charge variation upon proton transfer in the H2O/Pt(111) system. The machine-learning electronic response model allows us to predict charge transfer and the electrostatic potential change induced by an electric field applied to an Au(100) electrode or an Au nanoparticle.

Control of Groundwater‐Lake Interaction Zone Structure on Spatial Variability of Lacustrine Groundwater Discharge in Oxbow Lake

AbstractLacustrine groundwater discharge (LGD) is an important water and nutrient source for lakes. Despite its importance, high‐resolution quantifying the spatial variability of LGD remains challenging. Particularly, little studies have explored the impact of the interaction zone structure between lakes and aquifers on this variability. Present study presents a high‐resolution quantitative estimation of LGD spatial patterns in an oxbow lake by combining thermal remote sensing with a 222Rn mass balance model. The vertical distribution characteristics of various parameters including lake water temperature, 222Rn concentration, electrical conductivity, and δ18O were examined to elucidate the influence of groundwater on the distribution pattern of lake surface temperature (LST). Regression equations were formulated to correlate LST with lake water 222Rn concentration across different water depth zones, enabling the inverse calculation of the 222Rn concentration in the water of the entire lake. Utilizing a 222Rn mass balance model across all grid points, the LGD rate was determined to vary from 0 to 330.96 mm/d, with an average of 55.02 ± 19.61 mm/d. In shallow water zones, the accumulation of lacustrine sediments has resulted in isolation from confined aquifers, causing LGD to primarily occur as springs in nearshore lake areas. Conversely, the direct connection between the deepwater zone of the lake and the water‐rich confined aquifer has resulted in a higher LGD rate in the lake interior. Present study not only offers a novel approach for quantifying the spatial patterns of LGD but also provides valuable insights for LGD studies conducted in lakes globally.

A pseudo-transient pressure gradient method for solving the incompressible Navier–Stokes equations

The fundamental problem behind the numerical solutions of incompressible viscous flow equations lies in the lack of an update equation for the pressure field. In essence, there is no explicit relation that can be utilized to update the pressure field from a given velocity field. Following the principle of the artificial compressibility method and considering that it is the pressure gradient that drives incompressible flows, this study introduces a new primitive variables method to solve the incompressible Navier–Stokes equations. This method ensures that the continuity condition is rigorously satisfied at every grid point within the flow domain. Its principle lies in modifying the continuity equation to include a pseudo-transient pressure gradient term that vanishes upon convergence, which allows the incompressibility constraint to be satisfied to machine zero. This method eliminates the numerical difficulties associated with pressure-based solvers and improves the convergence of all dependent variables. Numerical solutions for three steady-state validation problems, namely fully developed channel flow, lid-driven cavity flow (2D and 3D), and flow in a constricted channel, are obtained to validate the proposed method. The results show good agreement with solutions available in the literature and demonstrate substantially improved convergence.

Objective Lagrangian Vortex Cores and their Visual Representations.

The numerical extraction of vortex cores from time-dependent fluid flow attracted much attention over the past decades. A commonly agreed upon vortex definition remained elusive since a proper vortex core needs to satisfy two hard constraints: it must be objective and Lagrangian. Recent methods on objectivization met the first but not the second constraint, since there was no formal guarantee that the resulting vortex coreline is indeed a pathline of the fluid flow. In this paper, we propose the first vortex core definition that is both objective and Lagrangian. Our approach restricts observer motions to follow along pathlines, which reduces the degrees of freedoms: we only need to optimize for an observer rotation that makes the observed flow as steady as possible. This optimization succeeds along Lagrangian vortex corelines and will result in a non-zero time-partial everywhere else. By performing this optimization at each point of a spatial grid, we obtain a residual scalar field, which we call vortex deviation error. The local minima on the grid serve as seed points for a gradient descent optimization that delivers sub-voxel accurate corelines. The visualization of both 2D and 3D vortex cores is based on the separation of the movement of the vortex core and the swirling flow behavior around it. While the vortex core is represented by a pathline, the swirling motion around it is visualized by streamlines in the correct frame. We demonstrate the utility of the approach on several 2D and 3D time-dependent vector fields'.

Multi-AGV multitask collaborative scheduling based on an improved ant colony algorithm

Research on multitask scheduling systems in factory environments is a popular topic in the field of intelligent manufacturing. Existing research mainly focuses on the optimization of automated guided vehicle (AGV) path planning and scheduling, emphasizing on the minimization of conflicts and deadlocks, multi-objective task scheduling, and metaheuristic algorithm optimization, while ignoring path stability and real-time path planning in dynamic environments. Therefore, this paper aims to address these issues to better handle dynamic changes in actual operating environments. This paper establishes a mathematical model with the optimization objective of minimizing the overall running time of material distribution tasks and proposes an improved ant colony algorithm to optimize the model. First, the concept of prior time is introduced to improve the traditional ant colony algorithm. The path of the ongoing task is introduced with a time calculation, and the occupancy time window of each grid point on the path is calculated. Based on this, the initial pheromone distribution on subsequent paths is altered dynamically, which accelerates the convergence of the ants to a collision-free path. Second, in the pheromone update stage, the method of calculating the pheromone increment in the traditional ant colony algorithm is modified. The original distance influence factor is changed to a time influence factor, which ensures that all tasks still have the minimum running time when calculating a collision-free path. Finally, through 30 sets of simulation experiments on material distribution tasks, it is shown that the proposed algorithm shortens the total running time by 15.14%, 12.87%, and 10.59% compared to two ant colony algorithms and one strategic multi-AGV scheduling algorithm, respectively, thus verifying the effectiveness of the proposed method.

CFD Application Simulation & Research on the Influence of Maneuver Angle on Aerodynamic Forces Used on Cars

Nowadays, the automobile industry is increasingly developing, along with the requirements of reducing fuel consumption, the design of cars with good aerodynamic shape is of interest to many countries in the world. Therefore, reducing aerodynamic drag is one of the issues that car designers put first. The method of simulating fluid flow through the car uses the finite volume method for unstructured mesh, using Fluent software based on the Reynolds Navier - Stokes average equation and the standard k - ε turbulence model. The accuracy of the problem depends on the number of grid points and the computer resources. The problem is solved by the sequential solution method. The simulation results are shown in intuitive graphics, which are the pressure and velocity distribution fields.

Effective statistics of pairs of fractional powers of complex grid points

Effective statistics of pairs of fractional powers of complex grid points

A novel early‐warning standardized indicator for drought preparedness and management under multiple climate model projections

AbstractIncreasing global temperatures have triggered several environmental and ecological challenges. Recurring droughts across the globe are an adverse consequence of global warming. In this research, a new drought forecasting index—the Multimodal Forecastable Standardized Precipitation Evapotranspiration Index (MFSPEI)—has been suggested using projections from multiple climate models. The MFSPEI methodology is primarily based on the first component of the Forecastable Component Analysis (FCA) and the Standardized Precipitation Evapotranspiration Index (SPEI). For application purposes, the time series data of SPEI from 10 climatic models endorsed by the Coupled Model Intercomparison Project phase 6 (CMIP‐6) at 50 random locations over the region of the Tibetan Plateau (TP) have been considered. The outcomes show that the first component of FCA captures a sufficient amount of variation while maintaining high forecastability in all the selected grid points and the chosen prominent timescales of drought monitoring indices. To assess the predictive performance of the proposed index (MFSPEI), comparison matrices of artificial neural network (ANN) models were identified. During the training and testing phases, the forecast efficiency of the developed indicator (MFSPEI) proved superior to that of the individual SPEI. The numerical assessment indicates that the deviations and difficulties in interpreting SPEI data from individual climate models can be addressed more effectively with the proposed indicator. Therefore, MFSPEI effectively reinforces drought predictions for drought preparedness and management in the context of multiple climate model projections.

A new forcing approach for wall-modeled simulation of rough-wall turbulent flows

The effect of rough surface on turbulent flows is usually investigated using direct numerical simulation (DNS) with either body-fitted grids or immersed boundary method. Both methods, however, require a significant number of grids to resolve all rough scales, resulting in intolerable computational cost. In this paper, a new volume forcing approach is developed to simulate wall-bounded turbulent flows with surface roughness at the same computational cost as that with smooth walls. Specifically, two extra forcing terms are introduced in the Navier–Stokes equations to mimic roughness effects. One is the feedback force operating within the roughness cell and ensuring zero velocity at the grid points located therein. The other represents the vortex force around the roughness surface. A direct comparison with the model proposed in literature shows a significant improvement in the prediction of mean flow and Reynolds stresses. To further validate the new forcing model, simulation of channel flow with cubical roughnesses is implemented, which shows a good agreement with fully resolved DNS.

Air temperature prediction models for pavement design: a gradient boosting-based approach

ABSTRACT This article presents a machine learning-based approach for the prediction of 7-day maximum and 1-day minimum air temperatures in India. In this approach, a Gradient-boosting model is developed using latitude, longitude and altitude as model features. Raw data for this study consisted of hourly air temperature data collected over 30 years across 20,168 grid points within India. As part of the predictive methodology, cluster analysis was performed initially, which helped in obtaining homogeneous regions. Three different approaches empirical clustering, statewise clustering and k-mean clustering, were used. The model features pertaining to individual clusters were used with a gradient-boosting approach. Statistical analysis was conducted to check the accuracy of model predictions based on different clustering techniques. In all cases, predictions made at the global level resulted in poor predictions. In most cases, the results obtained with k-mean clustering showed that increasing the number of clusters improved the predictive accuracy. Furthermore, predictive accuracy with statewise or k-mean clustering was dependent on several features involved. The proposed predictive models have a very simple structure that requires the least input (i.e. geographical indicators). Hence the same can be used for faster and accurate computation of 7-day maximum and 1-day minimum air temperature.

Evaluating CMIP6 Global Climate Models Performances Over Nigeria: An Integrated Approach

ABSTRACTThe choice of global climate models (GCMs) for climate or hydrological studies remains a challenge due to their temporal and spatial variations and different performances in different parts of the globe. This study assesses the performances of 33 GCMs of the Coupled Model Intercomparison Project Phase 6 (CMIP6) for precipitation, maximum temperature and minimum temperature over Nigeria in order to select the best performing GCMs for aggregation into a multi model ensemble (MME). The study uses three statistical metrics (SM) and Random Forest (RF) machine learning method for the evaluation of the GCMs. In addition, the GCM performances were also estimated using spatial assessment, boxplots, scatter plots and mean monthly comparison at each grid point over the period 1985–2014. Finally, the average was used to generate variations of MMEs by increasing the number of models in the MME considering the inclusion of the better ranking ones first in order to determine the optimum MME for the variables. The highest ranking GCMs based on the average of the scores of the SM and RF were NESM3, CMCC‐ES, IPSL‐L‐R‐INCA and IPSL‐L‐R, MPI‐HAM and SAMO‐UNICON for precipitation; BCC‐C‐MR, MRI‐ESM, BCC‐ESM1, ACC‐ESM1‐5 and GISS‐E2‐CC for maximum temperature; and GFDL‐ESM, AWI‐C‐MR, IPSL‐L‐R, CAS‐ESM2 and AWI‐C‐LR for minimum temperature. The highest‐ranking model for all variables is ACC‐ESM1‐5, which ranked highest with a score of 0.6920 followed by BCC‐C‐MR with 0.6898, CAS‐ESM2 with 0.6597 and BCC‐ESM1 with 0.6545 score. The results of the spatial assessment, boxplots, scatter plots and the mean monthly comparison aligns with this. In the aggregation of MME for the three variables, the optimum number of models was obtained after averaging of the first four best ranking GCMs. This study presents a localised study, which is expected to reduce uncertainty in the projection of climate over Nigeria.