SEARCH · Search NASA

Results for “spatial and temporal scales”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20

All sources NASA NTRS DOE OSTI

NASA NTRS2020

Current and Future Remote Sensing of Harmful Algal Blooms in the Chesapeake Bay to Support the Shellfish Industry

Harmful algal bloom (HAB) species in the Chesapeake Bay can negatively impact fish, shellfish, and human health via the production of toxins and the degradation of water quality. Due to the deleterious effects of HAB species on economically and environmentally important resources, such as oyster reef systems, Bay area resource managers are seeking ways to monitor HABs and water quality at large spatial and fine temporal scales. The use of satellite ocean color imagery has proven to be a beneficial tool for resource management in other locations around the world where high-biomass, nearly monospecific HABs occur. However, remotely monitoring HABs in the Chesapeake Bay is complicated by the presence of multiple, often co-occurring, species and optically-complex waters. Here we present a summary of common marine and estuarine HAB species found in the Chesapeake Bay, Alexandrium monilatum, Karlodinium veneficum, Margalefidinium polykrikoides, and Prorocentrum minimum, that have been detected from space using multispectral data products from the Ocean and Land Color Imager (OLCI) sensor on the Sentinel-3 satellites and identified based on historic phytoplankton data, in situ sampling, and ecological associations. We review how future hyperspectral instruments will improve discrimination of potentially harmful species from other phytoplankton communities and present a framework in which satellite data products could aid Chesapeake Bay resource managers with monitoring water quality and protecting shellfish resources.

Chesapeake Bay, satellite remote sensing, harmful ↗

NASA NTRSDate not supplied

Atmospheric Variability and Measurement Uncertainty: Pitfalls in Averaging in situ Data

Satellite measurements and atmospheric models, two essential components of the integrated global observing system, provide crucial tools for monitoring and predicting regional and global foci, spanning numerous Earth Science fields. Unfortunately, models can lack the spatial and temporal resolution needed to resolve finer scale structure. Satellite measurements also have similar tempo-spatial restriction issues, but additionally can only measure certain species and can have biases that must be evaluated. Ground measurement networks are critical components of this system, by providing both independent inputs of species needed by models (including those that satellites do not provide) and assisting with investigation of biases in satellite products. Similarly, aircraft measurements play a vital role in closing the gaps between satellite measurements, model products, and ground monitoring networks by providing high accuracy, high-resolution data on local to regional spatial scales. Therefore, both ground-based and airborne observations are widely used to assess model predictions and satellite observations. One of the great challenges in using both ground and aircraft data in this fashion is matching the data temporally and spatially to the model/satellite data. A meaningful comparison with model or satellite requires a solid assessment of the variability of the in-situ measurements, which include both the instrument uncertainty and the statistical uncertainty due to atmospheric variability. While instrument uncertainty is generally more straightforwardly characterized, it can be challenging to accurately capture this variability uncertainty as it often presents in a non-Gaussian manner (e.g. emission plumes, frontal passages). We will present results examining spatial and temporal variability over a selection of scales relevant to satellite measurements and models of several in situ measurement species spanning both airborne and ground measurements. The extent of non-Gaussian variability will be quantified, and we will discuss additional statistical parameters that help assess the fitness of gaussian variability assumption when temporally or spatially averaging.

satellite validation↗

NASA NTRS2004

Diurnal, Seasonal, and Interannual Variations of Cloud Properties Derived for CERES From Imager Data

Simultaneous measurement of the radiation and cloud fields on a global basis is a key component in the effort to understand and model the interaction between clouds and radiation at the top of the atmosphere, at the surface, and within the atmosphere. The NASA Clouds and Earth s Radiant Energy System (CERES) Project, begun in 1998, is meeting this need. Broadband shortwave (SW) and longwave radiance measurements taken by the CERES scanners at resolutions between 10 and 20 km on the Tropical Rainfall Measuring Mission (TRMM), Terra, and Aqua satellites are matched to simultaneous retrievals of cloud height, phase, particle size, water path, and optical depth OD from the TRMM Visible Infrared Scanner (VIRS) and the Moderate Resolution Imaging Spectroradiometer (MODIS) on Terra and Aqua. Besides aiding the interpretation of the broadband radiances, the CERES cloud properties are valuable for understanding cloud variations at a variety of scales. In this paper, the resulting CERES cloud data taken to date are averaged at several temporal scales to examine the temporal and spatial variability of the cloud properties on a global scale at a 1 resolution.

Minnis, Patrick↗

NASA NTRS2010

Recent Spatial and Temporal Anomalies and Trends of OLR as Observed by CERES and Computed Based on AIRS Retrievals

We show that a recent CERES-observed negative trend in OLR of approx.-0.1 W/sq m/yr averaged over the globe, for the time period of September 2002 through February 2010 used in this study, is found in the AIRS OLR data as well. Most importantly, even minute details (down to 1 x 1 Degree GCM-scale resolution) of spatial and temporal anomalies and trends of OLR as observed by CERES and computed based on AIRS-retrieved surface and atmospheric geophysical parameters over this time period are essentially the same. We see this correspondence even in the very large spatial variations of these trends with local values ranging from -2.6 W/sq m/yr to +3.0 W/sq m/yr in the tropics. This essentially perfect agreement of OLR anomalies and even local trends derived from observations by two different instruments, in totally independent and different manners, implies that both sets of results must be highly accurate; and indirectly validates the anomalies and trends of other AIRS derived products as well. These products show that global and regional anomalies and trends of OLR, water vapor and cloud cover over the last 7+ years are strongly influenced by El-Nino-La Nina cycles . We use the anomalies and trends of AIRS derived products to explain why the global OLR has a large negative trend over this time period; Global and tropical OLR began to decrease significantly at the onset of a strong La Nina in mid-2007. AIRS products show that cloudiness and mid-tropospheric water vapor began to increase in the tropics at roughly the same time, especially in the region 5degN - 20degS latitude extending eastward from 150degW to 30degE longitude, with a corresponding very large drop in OLR in this region. Late 2009 is characterized by a strong El-Nino, with a corresponding change in sign of observed tropical water vapor, cloud cover, and OLR anomalies. If one excludes the area 5degN - 20degS, 150degW - 30degE from the statistics, area mean OLR trends over the rest of the globe are substantially reduced over the time period under study.

Molnar, Gyula↗

NASA NTRS2006

Exploring the Production of NOx by Lightning and Its Impact on Tropospheric Ozone

Our quantitative understanding of free tropospheric (FT) chemistry is quite poor. State-of-the-art regional air quality models (e.g., US EPA's CMAQ) perform very poorly in simulating FT chemistry, with Uniform ozone around 70 ppb throughout the FT in summer, while ozonesonde data show much higher levels of ozone and much spatial-temporal structure. Such models completely neglect lightning-NOx (LNOx) emissions (the most significant source of NOx in the FT), and also contain large uncertainties in the specifications of intercontinental transport, stratosphere-troposphere exchange (STE) and PBLFT exchange (PFTE). Global air chemistry models include LNOx, but in very crude fashion, with the frequency and distribution of lightning being based on modeled cloud parameters (hence large uncertainty), lightning energetics being assumed to be constant for all flashes (literature value, while in reality there is at least a two-orders of magnitude variability from flash-to-flash), and the production of NOx in the surrounding heated air, per Joule of heating, being assumed to be constant also (literature value, while in fact it is a non-linear function of the dissipated heat and local air density, p). This situation is commonly blamed on paucity of pertinent observational data, but for the USA, there is now a wealth of surface- and satellite-based data of lightning available to permit much improved observation-based estimation of LNOx emissions. In the FT, such NOx has a long residence time, and also the ozone production efficiency from NOx there is considerably higher than in the PBL. It is, therefore, of critical importance in FT chemistry. This paper will describe the approach and data products of an ongoing NSSTC project aimed at a much-improved quantification of not only LNOx production on the scale of continental USA based on local and regional lightning observations, but also of intercontinental transport, STE and PFTE, all in upgraded simulations of tropospheric transport and chemistry. In our approach for LNOx, (a) we utilize continuous observed lightning information from the NLDN ground network and from satellite imagers (OTD and LIS) to quantify lightning frequency and distribution at the spatial-temporal scales of models such as CMAQ; (b) we develop new methodologies to quantify flash-specific lightning energy dissipation as heat (epsilon) using data from the research-grade lightning measurement facility at NASA-KSC, and to parameterize epsilon based on regional lightning monitoring data (ground- and satellite-based); and, (c) we develop a new parameterization of NOx production as a function of epsilon and rho. Based on such observation-based information, we are working to develop a gridded, episodic LNOx emissions inventory for the USA for use in models like CMAQ. We are also developing approaches for global(MOZART)- regional(CMAQ) chemistry coupling to improve intercontinental transport and STE. Finally, we are developing new methodologies for assimilation of satellite-observed (GOES) clouds into meteorological modeling (MM5), to improve PFTE and to optimize co-location of cloud convection and observed lightning. We will incorporate these improvements in CMAQ simulations over the USA to better understand FT processes and chemistry, and its impact on ground-level ozone.

Gillani, Noor↗

NASA NTRS1989

Outputs of paired Gabor filters summed across the background frame of reference predict the direction of movement

A cortical neural network that computes the visibility of shifts in the direction of movement is proposed. The network computes: (1) the magnitude of the position difference between the test and background patterns, (2) localized contrast differences at different spatial scales analyzed by computing temporal gradients of the difference and sum of the outputs of paired even- and odd-symmetric bandpass filters convolved with the input pattern, and (3) using global processes that pool the output from paired even- and odd-symmetric simple and complex cells across the spatial extent of the background frame of reference the direction a test pattern moved relative to a textured background. Evidence that magnocellular pathways are used to discriminate the direction of movement is presented. Since magnocellular pathways are used to discriminate the direction of movement, this task is not affected by small pattern changes such as jitter, short presentations, blurring, and different background contrasts that result when the veiling illumination in a scene changes.

Lawton, Teri B.↗

NASA NTRS1992

Low-frequency variations of circulation and high cloudiness in the northern extratropics - Spatial and temporal relationships

The spatial and temporal relationships between fluctuations in geopotential height and high-cloud fractional area in low-pass (periods greater than 10 days) and intermediate-pass (10-30 days) time scales are investigated and compared with spatial and temporal relationships in the fast-pass (2.5-6 days) time scale, using NMC 500-hPa height and Nimbus-7 THIR-TOMS high-cloud data for October-March winter months of 1979-1985. It was found that, when moving from the low-pass and intermediate-pass time scales to the fast-pass regime, the temporal variance of the height field decreases, but the temporal variance of the high cloudiness increases. The spatial phase relationships between the height and the cloud fields in the low-pass and the fast-pass regimes were found to be different.

Charlock, Thomas P.↗

NASA NTRS1997

Theories of Simplification and Scaling of Spatially Distributed Processes

The problem of scaling is at the heart of ecological theory, the essence of understanding and of the development of a predictive capability. The description of any system depends on the spatial, temporal, and organizational perspective chosen; hence it is essential to understand not only how patterns and dynamics vary with scale, but also how patterns at one scale are manifestations of processes operating at other scales. Evolution has shaped the characteristics of species in ways that result in scale displacement: Each species experiences the environment at its own unique set of spatial and temporal scales and interfaces the biota through unique assemblages of phenotypes. In this way, coexistence becomes possible, and biodiversity is enhanced. By averaging over space, time, and biological interactions, a genotype filters variation at fine scales and selects the arena in which it will face the vicissitudes of nature. Variation at finer scales is then noise, of minor importance to the survival and dynamics of the species, and consequently of minor importance in any attempt at description. In attempting to model ecological interactions in space, contributors throughout this book have struggled with a trade-off between simplification and "realistic" complexity and detail. Although the challenge of simplification is widely recognized in ecology, less appreciated is the intertwining of scaling questions and scaling laws with the process of simplification. In the context of this chapter simplification will in general mean the use of spatial or ensemble means and low-order moments to capture more detailed interactions by integrating over given areas. In this way, one can derive descriptions of the system at different spatial scales, which provides the essentials for the extraction of scaling laws by examination of how system properties vary with scale.

Levin, Simon A.↗

NASA NTRS1992

Method and apparatus for predicting the direction of movement in machine vision

A computer-simulated cortical network is presented. The network is capable of computing the visibility of shifts in the direction of movement. Additionally, the network can compute the following: (1) the magnitude of the position difference between the test and background patterns; (2) localized contrast differences at different spatial scales analyzed by computing temporal gradients of the difference and sum of the outputs of paired even- and odd-symmetric bandpass filters convolved with the input pattern; and (3) the direction of a test pattern moved relative to a textured background. The direction of movement of an object in the field of view of a robotic vision system is detected in accordance with nonlinear Gabor function algorithms. The movement of objects relative to their background is used to infer the 3-dimensional structure and motion of object surfaces.

Lawton, Teri B.↗

NASA NTRS1998

Initial Response and Complex Polar Cap Structures of the Aurora in Response to the January 10, 1997 Magnetic Cloud

On January 10, 1997, a magnetic cloud originating at the Sun was incident on the Earth. The initial disturbance to the magnetosphere, as reflected in the activities of the aurora, was measured by the Ultraviolet Imager on the Polar Spacecraft. During this event we have observed the development of several unusual unique auroral forms that to our knowledge are unexplained in current models and theories. The observations were made on a global scale with unprecedented spatial and temporal resolution. The first activation of the aurora at local noon occurred within minutes of the arrival of the shock at 0107 UT. The substorm onset was observed at 0334 UT. During the intervening time significant polar cap precipitation occurred.

Spann, J. F.↗

NASA NTRS1999

An Intercomparison of Ground, Airborne, and Space Instrumentation Definitions of the Lightning Element

For the past century, scientists have made quantitative measurements of lightning discharges. In the process, they refined the definition of a lightning unit, or basic quantum of lightning, in order to base it on observable parameters. In this paper, we will use cluster analysis to derive a basic spatial and temporal definition or scale length for the unit of lightning. We will use data from three different systems that detected pulses from the same storm complex over Central Oklahoma during June, 1998. Since the different instruments detect lightning in different ways with different resolutions, there may not be a single definition of the unit of lightning that can be applied to all three systems. However, common components can be found since all instrumentation are detecting aspects of the same phenomenon.

Mach, Douglas↗

NASA NTRS2006

Detection of Ice Polar Stratospheric Clouds from Assimilation of Atmospheric Infrared Sounder Data

A novel technique is presented for detection of ice polar stratospheric clouds (PSCs) that form at extremely low temperatures in the lower polar stratosphere during winter. Temperature is a major factor in determining abundance of PSCs, which in turn provide surfaces for heterogeneous chemical reactions leading to ozone loss and radiative cooling. The technique infers the presence of ice PSCs using radiances from the Atmospheric Infrared Sounder (AIRS) in the Goddard Earth Observing System version 5 (GEOS-5) data assimilation system. Brightness temperatures are computed from short-term GEOS-5 forecasts for several hundred AIRS channels, using a radiation transfer module. The differences between collocated AIRS observations and these computed values are the observed-minus-forecast (O-F) residuals in the assimilation system. Because the radiation model assumes clear-sky conditions, we hypothesize that these O-F residuals contain quantitative information about PSCs. This is confirmed using sparse data from the Polar Ozone and Aerosol Measurement (POAM) III occultation instrument. The analysis focuses on 0-F residuals for the 6.79pm AIRS moisture channel. At coincident locations, when POAM III detects ice clouds, the AIRS O-F residuals for this channel are lower than -2K. When no ice PSCs are evident in POAM III data, the AIRS 0-F residuals are larger. Given this relationship, the high spatial density of AIRS data is used to construct maps of regions where 0-F residuals are lower than -2K, as a proxy for ice PSCs. The spatial scales and spatio-temporal variations of these PSCs in the Antarctic and Arctic are discussed on the basis of these maps.

Stajner, Ivanka↗

NASA NTRS2006

Development and Implementation of a Comprehensive Radiometric Validation Protocol for the CERES Earth Radiation Budget Climate Record Sensors

The CERES Flight Models 1 through 4 instruments were launched aboard NASA's Earth Observing System (EOS) Terra and Aqua Spacecraft into 705 Km sun-synchronous orbits with 10:30 a.m. and 1:30 p.m. equatorial crossing times. These instruments supplement measurements made by the CERES Proto Flight Model (PFM) instrument launched aboard NASA's Tropical Rainfall Measuring Mission (TRMM) into a 350 Km, 38-degree mid-inclined orbit. CERES Climate Data Records consist of geolocated and calibrated instantaneous filtered and unfiltered radiances through temporally and spatially averaged TOA, Surface and Atmospheric fluxes. CERES filtered radiance measurements cover three spectral bands including shortwave (0.3 to 5 microns), total (0.3 to 100 microns) and an atmospheric window channel (8 to 12 microns). The CERES Earth Radiation Budget measurements represent a new era in radiation climate data, realizing a factor of 2 to 4 improvement in calibration accuracy and stability over the previous ERBE climate records, while striving for the next goal of 0.3-percent per decade absolute stability. The current improvement is derived from two sources: the incorporation of lessons learned from the ERBE mission in the design of the CERES instruments and the development of a rigorous and comprehensive radiometric validation protocol consisting of individual studies covering different spatial, spectral and temporal time scales on data collected both pre and post launch. Once this ensemble of individual perspectives is collected and organized, a cohesive and highly rigorous picture of the overall end-to-end performance of the CERES instrument's and data processing algorithms may be clearly established. This approach has resulted in unprecedented levels of accuracy for radiation budget instruments and data products with calibration stability of better than 0.2-percent and calibration traceability from ground to flight of 0.25-percent. The current work summarizes the development, philosophy and implementation of the protocol designed to rigorously quantify the quality of the data products as well as the level of agreement between the CERES TRMM, Terra and Aqua climate data records.

Priestley, K. J.↗

NASA NTRS2011

Characterizing Land Surface Change and Levee Stability in the Sacramento-San Joaquin Delta Using UAVSAR Radar Imagery

The Sacramento-San Joaquin Delta is one of the primary water sources for the state of California and represents a complex geographical area comprised of tidal marshland, levee rimmed islands that are used primarily for agriculture, and urban encroachment. Land subsidence has dropped many of the Delta islands 3 to >7 meters below mean sea level and requires nearly 1700 km of levees to maintain the integrity of the islands and flow of water through the Delta. The current average subsidence rates for each island varies, with 1.23 cm/yr on Sherman Island and 2.2 cm/yr for Bacon Island, as determined by ground-based instruments located at isolated points in the Delta. The Delta's status as the most critical water resource for the state, an endangered ecosystem, and an area continuously threatened with levee breakage from hydrostatic pressure and the danger of earthquakes on several major faults in the San Francisco area make it a focus of monitoring efforts by both the state and national government. This activity is now almost entirely done by ground-based efforts, but the benefits of using remote sensing for wide scale spatial coverage and frequent temporal coverage is obvious. The UAVSAR airborne polarimetric and differential interferometric L-band synthetic aperture radar system has been used to collected monthly images of the Sacramento-San Joaquin Delta and much of the adjacent Suisun Marsh since July 2009 to characterize levee stability, image spatially varied subsidence, and assess how well the UAVSAR performs in an area with widespread agriculture production.

geographical area↗

NASA NTRS2017

Fluid Lensing and Applications to Remote Sensing of Aquatic Environments

The use of fluid lensing technology on UAVs is presented as a novel means for 3D imaging of aquatic ecosystems from above the water's surface at the centimeter scale. Preliminary results are presented from airborne fluid lensing campaigns conducted over the coral reefs of Ofu Island, American Samoa (2013) and the stromatolite reefs of Shark Bay, Western Australia (2014), covering a combined area of 15km2. These reef ecosystems were revealed with centimetre-scale 2D resolution, and an accompanying 3D bathymetry model was derived using fluid lensing, Structure from Motion and UAV position data. Data products were validated from in-situ survey methods including underwater calibration targets, depth measurements and millimetre-scale high-dynamic range gigapixel photogrammetry. Fluid lensing is an experimental technology that uses water transmitting wavelengths to passively image underwater objects at high-resolution by exploiting time-varying optical lensing events caused by surface waves. Fluid lensing data are captured from low-altitude, cost-effective electric UAVs to achieve multispectral imagery and bathymetry models at the centimetre scale over regional areas. As a passive system, fluid lensing is presently limited by signal-to-noise ratio and water column inherent optical properties to approximately 10 m depth over visible wavelengths in clear waters. The datasets derived from fluid lensing present the first centimetre-scale images of a reef acquired from above the ocean surface, without wave distortion. The 3D multispectral data distinguish coral, fish and invertebrates in American Samoa, and reveal previously undocumented, morphologically distinct, stromatolite structures in Shark Bay. These findings suggest fluid lensing and multirotor electric drones represent a promising advance in the remote sensing of aquatic environments at the centimetre scale, or 'reef scale' relevant to the conservation of reef ecosystems. Pending further development and validation of fluid lensing methods, these technologies present a solution for large-scale 3D surveys of shallow aquatic habitats with centimetre-scale spatial resolution and hourly temporal sampling.

Aquatic↗

NASA NTRS2021

Sub-city Scale Hourly Air Quality Forecasting by Combining Models, Satellite Observations, and Ground Measurements

While multiple information sources exist concerning surface-level air pollution, no individual source simultaneously provides large-scale spatial coverage, fine spatial and temporal resolution, and high accuracy. It is, therefore, necessary to integrate multiple data sources, using the strengths of each source to compensate for the weaknesses of others. In this study, we propose a method incorporating outputs of NASA’s GEOS Composition Forecasting model system with satellite information from the TROPOMI instrument and ground measurement data on surface concentrations. Although we use ground monitoring data from the Environmental Protection Agency network in the continental United States, the model and satellite data sources used have the potential to allow for global application. This method is demonstrated using surface measurements of nitrogen dioxide as a test case in regions surrounding five major US cities. The proposed method is assessed through cross-validation against withheld ground monitoring sites. In these assessments, the proposed method demonstrates major improvements over two baseline approaches which use ground-based measurements only. Results also indicate the potential for near-term updating of forecasts based on recent ground measurements.

C. Malings↗

NASA NTRS2020

Development of a Daily GRACE Mascon Solution for Terrestrial Water Storage

The Gravity Recovery and Climate Experiment (GRACE) and GRACE-Follow On missions have provided a global history of terrestrial water storage changes since 2002. Traditional GRACE products resolve monthly time-variable gravity at spatial resolutions of 300-500 km, with many recent efforts focusing on regularized mass concentration (mascon) solutions to better resolve signals spatially. However, monthly resolution inhibits the applicability of GRACE to investigations of sub-monthly signals. This study presents a new daily mass change solution estimated as deviations from the NASA Goddard Space Flight Center (GSFC) converged monthly mascon product and quantifies the fundamental trade-off between temporal and spatial resolution in GRACE-only solutions. As an iteration of the GSFC product, this daily solution represents a mixing of monthly information at higher relative spatial resolution with daily information at lower relative spatial resolution, resolving each temporal scale at the best resolution achievable without requiring hydrological model dependencies in the estimation. The resolution of the daily mascons is 300-400 km at high latitudes and 600-1,000 km lower, depending on each daily orbital track and the proximity of each mascon to constraint region boundaries (e.g., coastlines). Through simulations and model comparisons, we demonstrate that daily signals over areas larger than 400,000 km(2) are recoverable, with basins larger than 800,000 km(2) exhibiting strong signal recovery relative to leakage. This analysis establishes baselines for daily signal recovery from GRACE in the context of longer time scale solutions, characterizes leakage inherent in daily GRACE information, and creates new opportunities for applying GRACE to investigations of sub-monthly signals.

M. J. Croteau↗

NASA NTRS2021

A Living Catalog of Stream Interaction Regions in the Parker Solar Probe Era

Stream interaction regions (SIRs) and corotating interaction regions (CIRs) are important phenomena in heliospheric physics. These large-scale structures vary temporally and spatially, both in latitude and with radial distance. The additions of Parker Solar Probe(PSP) and Solar Orbiter have allowed for investigations into the radial evolution of these structures over a wide range of heliocentric distances for the first time since the Helios era. To better enable investigations of SIRs and CIRs within the inner heliosphere, we have developed a living catalog of SIR and CIR observations by Parker Solar Probe with corresponding observations by STEREO-A as well as ACE and Wind at 1 au. The methodology used for the identification of events and the generation of this catalog, the initial catalog of PSP observations spanning orbits one through five along with corresponding 1 au observations, and information on accessing the living catalog for future studies is described. This list of SIR and CIR events from PSP and corresponding observations from other heliophysics missions will enable case studies utilizing unique orbital arrangements, as well as aid in future statistical studies to further understand the properties and evolution of these structures.

Catalogs↗