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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

New Approaches to Quantifying Transport Model Error in Atmospheric CO2 Simulations

In recent years, much progress has been made in observing CO2 distributions from space. However, the use of these observations to infer source/sink distributions in inversion studies continues to be complicated by difficulty in quantifying atmospheric transport model errors. We will present results from several different experiments designed to quantify different aspects of transport error using the Goddard Earth Observing System, Version 5 (GEOS-5) Atmospheric General Circulation Model (AGCM). In the first set of experiments, an ensemble of simulations is constructed using perturbations to parameters in the model s moist physics and turbulence parameterizations that control sub-grid scale transport of trace gases. Analysis of the ensemble spread and scales of temporal and spatial variability among the simulations allows insight into how parameterized, small-scale transport processes influence simulated CO2 distributions. In the second set of experiments, atmospheric tracers representing model error are constructed using observation minus analysis statistics from NASA's Modern-Era Retrospective Analysis for Research and Applications (MERRA). The goal of these simulations is to understand how errors in large scale dynamics are distributed, and how they propagate in space and time, affecting trace gas distributions. These simulations will also be compared to results from NASA's Carbon Monitoring System Flux Pilot Project that quantified the impact of uncertainty in satellite constrained CO2 flux estimates on atmospheric mixing ratios to assess the major factors governing uncertainty in global and regional trace gas distributions.

Ott, L.↗
NASA NTRS2012

A Robust Multi-Scale Modeling System for the Study of Cloud and Precipitation Processes

During the past decade, numerical weather and global non-hydrostatic models have started using more complex microphysical schemes originally developed for high resolution cloud resolving models (CRMs) with 1-2 km or less horizontal resolutions. These microphysical schemes affect the dynamic through the release of latent heat (buoyancy loading and pressure gradient) the radiation through the cloud coverage (vertical distribution of cloud species), and surface processes through rainfall (both amount and intensity). Recently, several major improvements of ice microphysical processes (or schemes) have been developed for cloud-resolving model (Goddard Cumulus Ensemble, GCE, model) and regional scale (Weather Research and Forecast, WRF) model. These improvements include an improved 3-ICE (cloud ice, snow and graupel) scheme (Lang et al. 2010); a 4-ICE (cloud ice, snow, graupel and hail) scheme and a spectral bin microphysics scheme and two different two-moment microphysics schemes. The performance of these schemes has been evaluated by using observational data from TRMM and other major field campaigns. In this talk, we will present the high-resolution (1 km) GeE and WRF model simulations and compared the simulated model results with observation from recent field campaigns [i.e., midlatitude continental spring season (MC3E; 2010), high latitude cold-season (C3VP, 2007; GCPEx, 2012), and tropical oceanic (TWP-ICE, 2006)].

Tao, Wei-Kuo↗
DOE OSTI2026

Atomic Evolution of Hydrogen Intercalation Wave Dynamics in Palladium Nanocrystals Revealed by Liquid-Phase Transmission Electron Microscopy

Solute-intercalation-induced phase separation creates spatial heterogeneities in host materials, a phenomenon ubiquitous in batteries, hydrogen storage, and other energy devices. Despite many efforts, probing intercalation processes at the atomic scale has been a significant challenge. By utilizing liquid-phase transmission electron microscopy (TEM), we study hydrogen (de)intercalation in palladium nanocrystals as a model system and have achieved unprecedented atomic-resolution imaging of hydrogen intercalation wave dynamics. Our observations reveal that intercalation wave mechanisms, instead of shrinking-core mechanisms, prevail at ambient temperature for palladium nanocubes ranging from ∼60 nm down to ∼10 nm. Systematic image analysis uncovers the atomic evolution of the hydrogen intercalation wave, transitioning from nonplanar and inclined boundaries to those closely aligned with {100} planes. Our kinetic Monte Carlo simulations demonstrate that the observed intercalation wave dynamics correspond to sorption pathways minimizing the lattice mismatch strain at the phase boundary. In conclusion, unveiling the atomic intercalation pathways holds profound implications for engineering intercalation-mediated devices and advancements in energy sciences.

Lee, Daewon [Lawrence Berkeley National Laboratory↗
NASA NTRS2001

A Self-Consistent Model of the Interacting Ring Current Ions and Electromagnetic ICWs. Initial Results: Waves and Precipitation Fluxes

Initial results from the new developed model of the interacting ring current ions and ion cyclotron waves are presented. The model described by the system of two bound kinetic equations: one equation describes the ring current ion dynamics, and another one gives wave evolution. Such system gives a self-consistent description of the ring current ions and ion cyclotron waves in a quasilinear approach. Calculating ion-wave relationships, on a global scale under non steady-state conditions during May 2-5, 1998 storm, we presented the data at three time cuts around initial, main, and late recovery phases of May 4, 1998 storm phase. The structure and dynamics of the ring current proton precipitating flux regions and the wave active ones are discussed in detail.

Khazanov, G. V.↗
NASA NTRS1977

A real-time subsynoptic, meso, and microscale severe storm forecast system

A system of differential equations is integrated numerically in space and time over several different matrices in an effort to simulate the atmospheric wave structures which organize severe local storms. Preliminary results with case studies indicate that dynamical fields produced by the numerical simulations can be translated into very fine scale space and time zones where severe storm forecast indices can be developed. These fine scale indices are now available in real-time when run on Langley's STAR 100 computer system.

Kaplan, M. L.↗
NASA NTRS2015

Integrated Modeling of Aerosol, Cloud, Precipitation and Land Processes at Satellite-Resolved Scales

With support from NASA's Modeling and Analysis Program, we have recently developed the NASA Unified-Weather Research and Forecasting model (NU-WRF). NU-WRF is an observation-driven integrated modeling system that represents aerosol, cloud, precipitation and land processes at satelliteresolved scales. "Satellite-resolved" scales (roughly 1e25 km), bridge the continuum between local (microscale), regional (mesoscale) and global (synoptic) processes. NU-WRF is a superset of the National Center for Atmospheric Research (NCAR) Advanced Research WRF (ARW) dynamical core model, achieved by fully integrating the GSFC Land Information System (LIS, already coupled to WRF), the WRF/ Chem enabled version of the Goddard Chemistry Aerosols Radiation Transport (GOCART) model, the Goddard Satellite Data Simulation Unit (G-SDSU), and custom boundary/initial condition preprocessors into a single software release, with source code available by agreement with NASA/GSFC. Full coupling between aerosol, cloud, precipitation and land processes is critical for predicting local and regional water and energy cycles.

Satellite-resolved↗
DOE OSTI2023

Graph-based quantum response theory and shadow Born–Oppenheimer molecular dynamics

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born–Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. Further, the proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS2006

Using Multi-scale Modeling System to Study the Interactions between Clouds, Precipitation, Aerosols, Radiation and Land Surface

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 kilometers, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-kilometer scales are resolved in horizontal domains as large as 10,000 kilometers in two-dimensions, and 1,000 x 1,000 square kilometers in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. A review of developments, improvements and applications of cloud models (GCE and WRF) at Goddard will be presented in this talk. In particular, a new approach to using multi-scale modeling system to study the interactions between clouds, precipitation, aerosols and land will be presented.

Tao, Wei-Kuo↗
NASA NTRS2006

Using Multi-scale Modeling System to Study the Interactions between Clouds, Precipitation, Aerosols, Radiation and Land Surface

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 kilometers, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial-lkm scales are resolved in horizontal domains as large as 10,000 kilometers in two-dimensions, and 1,000 x 1,000 square kilometers in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. A review of developments, improvements and applications of cloud models (GCE and WRF) at Goddard wlll be is presented in this talk. In particular, a new approach to using multi-scale modeling system to study the interactions between clouds, precipitation, aerosols and land will be presented.

Tao, Wei-Kuo↗
NASA NTRS2006

Using Multi-scale Modeling System to Study the Interactions between Clouds, Precipitation, Aerosols, Radiation and Land Surface

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 km, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-km scales are resolved in horizontal domains as large as 10,000 km in two-dimensions, and 1,000 x 1,000 sq km in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. A review of developments, improvements and applications of cloud models (GCE and WRF) at Goddard will be presented in this talk. In particular, a new approach to using multi-scale modeling system to study the interactions between clouds, precipitation, aerosols and land will be presented.

Tao, Wei-Kuo↗
NASA NTRSDate not supplied

Scale Resolving Simulations of Contra Rotating Open Rotor Noise Prediction

The development of breakthrough open-rotor propulsion systems that meet performance, fuel efficiency, and noise requirements for commercial viability relies heavily on the availability of reliable and computationally efficient aerodynamic performance and noise prediction tools.This investigation showcases the proficiency of the structured curvilinear overset grid Computational Fluid Dynamics solver implemented in the Launch, Ascent, and Vehicle Aerodynamics framework for predicting the aerodynamic and aeroacoustic characteristics of a Contra-RotatingOpen Rotor propulsion system. Additionally, the study includes comprehensive sensitivity analyses employing a Hybrid Reynolds-Averaged Navier-Stokes/Large Eddy Simulation - based scale-resolving turbulence closure treatment. The computed results are validated through comparison with existing experimental measurements.

ARMD↗
NASA NTRS1989

Preliminary assessment of rover power systems for the Mars Rover Sample Return Mission

Four isotope power system concepts were presented and compared on a common basis for application to on-board electrical prime power for an autonomous planetary rover vehicle. A representative design point corresponding to the Mars Rover Sample Return (MRSR) preliminary mission requirements (500 W) was selected for comparison purposes. All systems concepts utilize the General Purpose Heat Source (GPHS) isotope heat source developed by DOE. Two of the concepts employ thermoelectric (TE) conversion: one using the GPHS Radioisotope Thermoelectric Generator (RTG) used as a reference case, the other using an advanced RTG with improved thermoelectric materials. The other two concepts employed are dynamic isotope power systems (DIPS): one using a closed Brayton cycle (CBC) turboalternator, and the other using a free piston Stirling cycle engine/linear alternator (FPSE) with integrated heat source/heater head. Near term technology levels have been assumed for concept characterization using component technology figure-of-merit values taken from the published literature. For example, the CBC characterization draws from the historical test database accumulated from space Brayton cycle subsystems and components from the NASA B engine through the mini-Brayton rotating unit. TE system performance is estimated from Voyager/multihundred Watt (MHW)-RTG flight experience through Mod-RTG performance estimates considering recent advances in TE materials under the DOD/DOE/NASA SP-100 and NASA Committee on Scientific and Technological Information programs. The Stirling DIPS system is characterized from scaled-down Space Power Demonstrator Engine (SPDE) data using the GPHS directly incorporated into the heater head. The characterization/comparison results presented here differ from previous comparison of isotope power (made for Low Earth Orbit (LEO) applications) because of the elevated background temperature on the Martian surface compared to LEO, and the higher sensitivity of dynamic systems to elevated sink temperature. The mass advantage of dynamic systems is significantly reduced for this application due to Mars' elevated background temperature.

Bents, David J.↗
DOE OSTI2022

Development of scalable design optimization parameters for bi-component protective systems

Bi-component protection-systems need to withstand a variety of extreme loading conditions such as high-velocity projectile impact to shock and blast mitigation. The large number of parameters at each stage of bi-component protection system design process results in a near-infinite number of possible variables for optimization. The aim of this project is to identify the scaling laws linking material and geometric scales of the problem to the final impact performance, further including the effects of wave propagation/interaction and inter-component bonding. Specifically, the impact dynamics for different optimal projectile/target density ratios and relative component mass fractions are quantified for bonded ceramic/titanium alloy systems. The impact behavior such as wave mechanics and damage propagation within the target system is characterized and quantified via digital image correlation or via x-ray phase-contrast imaging.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Heat Integration Optimization and Dynamic Modeling Investigation for Advancing the Coal-Direct Chemical Looping Process

The purpose of the project is to address the optimization and startup operation of a modular coal direct chemical looping (CDCL) combustion system integrated with a steam cycle for power generation to reduce the risks involved in further scale-up of the technology. The modular reactor design of the CDCL process provides flexibility in the fabrication of the reactor and in its operating capacity (i.e. turndown ratio) at the cost of a more complex heat exchange network (HEN) design and integration. To address the technology gaps and advance the efficiency and economic feasibility of the CDCL technology, the project will perform a detailed and comprehensive analysis of the integration of a modular CDCL reactor system and a steam cycle system under both static and transient conditions via HEN process performance simulations and system dynamic modeling, respectively. The scope of work consists of 1) Experimental and computational studies of the CDCL combustor reactor 2) Comprehensive static (i.e. steady-state) system HEN design analysis in CDCL 550 MWe commercial unit for power generation and 3) Dynamic modeling of site specific design of 10MWe CDCL large pilot plant. The project team has successfully developed and validated a kinetic model for the oxidation of oxygen carriers in the combustor using the unreacted shrinking core model (UCSM). The model is capable of capturing the oxidation kinetics of fully or partially reduced oxygen carrier particles. A computational fluid dynamics (CFD) model is developed to simulate the hydrodynamics, heat transfer, and chemical reaction occurring in the CDCL combustor. The model is developed in MFIX and ANSYS Fluent. Key aspects of CDCL combustor operation, including heat transfer, oxygen carrier oxidation, and the transport of oxygen carrier particles, are simulated using this CFD model. The HEN for a commercial scale 550 MWe CDCL power plant is simulated and optimized using ASPEN Plus. Practical design considerations are incorporated based on industrial experiences. The performance and cost for the commercial CDCL plant is updated based on these analyses. A dynamic model for the 10 MWe CDCL pilot plant is developed in ProTRAX simulation software. The model is based on the pilot plant design developed in project DE-FE0027654 “10 MWe CDCL Large Pilot Plang – Pre-FEED Study” and the steam cycle data obtained from Dover Light & Power plant. The transient behaviors during pilot plant load variation are simulated using the dynamic model.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2025

Steric effects of central dogma processes on the compaction and segregation of bacterial nucleoids

The bacterial cytoplasm is characterized by a distinctive membrane-less organelle, the nucleoid, which harbors the chromosomal DNA. Here, we investigate the steric effects of dynamic processes associated with transcription and translation on the structure of this organelle using coarse-grained molecular dynamics simulations that incorporate out-of-equilibrium reactions. Our model captures the scale of the entire cell and incorporates a reaction-diffusion system for ribosomes and polyribosomes, coupling their nonequilibrium kinetics to DNA excluded volume interactions. Our findings demonstrate that out-of-equilibrium reactions increase the size of the nucleoid and the number of ribosomes in this subcellular region. In addition, we show that nucleoid size is proportional to transcriptional activity. Our model reproduces the time-dependent change in nucleoid size observed in rifampicin treatment experiments, where the pool of polyribosomes is depleted. Furthermore, we find that these active processes are essential for complete sister chromosome separation and correct nucleoid positioning within the cell. Overall, our study reveals the effects of the central dogma processes on the internal organization and localization of bacterial nucleoids.

Chang, Mu-Hung [Univ. of Tennessee, Knoxville, TN ↗
DOE OSTI2020

Collapse of the waiting time effect in a spin glass

Waiting time measurements are reported here for a bulk polycrystalline sample of the spin glass Cu 0.95 Mn 0.05 . We observe a suppression of aging as the glass temperature is approached from below. These results are interpreted in terms of a spin-glass correlation length approaching and reaching crystallite sizes. They provide a direct experimental connection between the correlation length scale and relaxation times in the spin-glass state. In particular, these measurements track the value of the dynamic critical exponent as the system transitions from the critical temperature regime to its low-temperature, quasistatic nonequilibrium phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Ice Multiplication by Fragmentation during Quasi-Spherical Freezing of Raindrops: A Theoretical Investigation

Ice multiplication by fragmentation during collision–freezing of supercooled rain or drizzle is investigated. A zero-dimensional dynamical system describes the time evolution of number densities of supercooled drops and ice crystals in a mixed-phase cloud. The characteristic time scale for this collision–freezing ice fragmentation is controlled by the collision efficiency, the number of ice fragments per freezing event, and the available number concentration of supercooled drops. The rate of the process is proportional to the number of supercooled drops available. Thus, ice may multiply extensively, even when the fragmentation number per freezing event is relatively small. The ratio of total numbers of ice particles to those from the first ice, namely, the “ice-enhancement factor,” is controlled both by the number of fragments per freezing event and by the available number concentration of supercooled drops in a similar manner. Especially, when ice fragmentation by freezing of supercooled drops is considered in isolation, the number of originally existing supercooled drops multiplied by the fragmentation number per freezing event yields the eventual number of ice crystals. When supercooled drops are continuously generated by coalescence, ice crystals from freezing fragmentation also continuously increase asymptotically at a rate equal to the generation rate of supercooled drops multiplied by the fragmentation number per freezing event. All these results are expressed by simple analytical forms, thanks to the simplicity of the theoretical model. These parameters can practically be used as a means for characterizing observed mixed-phase clouds.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Thermal Hydraulic Experimental Test Article - Fiscal Year 2023 (Final Report)

The Thermal Hydraulic Experimental Test Article (THETA) is a facility that is used to develop sodium components and instrumentation as well as acquire experimental data for validation of reactor thermal hydraulic and safety analysis codes. The facility simulates nominal conditions as well as protected/unprotected loss of flow accidents in a sodium-cooled fast reactor (SFR). High fidelity distributed temperature profiles of the developed flow field may be acquired with Rayleigh backscatter based optical fiber temperature sensors. The facility was designed in partnership with systems code experts to tailor the experiment to ensure the most relevant and highest quality data for code validation. THETA is comprised of a traditional primary coolant and secondary coolant system. The primary system is submerged in the pool of sodium and consists of a pump, electrically heated core, intermediate heat exchanger, and connected piping and thermal barriers (redan). The secondary system, located outside of the sodium pool, consists of a pump, sodium to air heat exchanger, and connected piping and valves. To date a test matrix has been completed utilizing the primary system of THETA. These tests, along with computational fluid dynamics and systems code models, determined the heat transfer across the core barrel and intermediate heat exchanger outlet was too great to effectively represent scaled thermal hydraulic phenomena of a liquid metal cooled reactor. Therefore, a significant effort was made to remove the primary system from the METL 28” test vessel #4 and clean the residual sodium from the primary system to facilitate upgrades. Thermal insulation was then incorporated in the core barrel and intermediate heat exchanger outlets. The primary system was then replaced, and a series of tests were performed to assess the performance of the thermal insulation. With primary system testing and upgrades complete, the secondary system could then be brought online. The tube side of the shell-and-tube intermediate heat exchanger was installed onto the primary system flange to begin installing the secondary system. The support structure for the secondary system was then erected on the METL mezzanine alongside the THETA primary system to facilitate installation of the secondary system components (sodium-to-air heat exchanger, flowmeter and pump). The piping and expansion tank were welded into the secondary system. Non-destructive examination of the secondary system welds was completed in order to satisfy ASME B31.3 pipe code for class M process fluids. The heating system and insulation were then added to prepare the system to be filled with sodium. The ancillary electrical equipment was installed which included the pump control box, blower VFD, pipe heater control system, etc. The secondary system will be filled, and a test matrix will be completed in early FY2024.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗