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At least 145 records · Page 8

MODIS Aerosol Observations used to Constrain Dust Distributions and Lifecycle in the NASA GEOS-5 Model

Approximately 240 Tg of mineral dust aerosol are transported annually from Saharan Africa to the Atlantic Ocean. Dust affects the Earth radiation budget, and plays direct (through scattering and absorption of radiation) and indirect (through modification of cloud properties and environment) roles in climate. Deposition of dust to the surface provides an important nutrient source to terrestrial and oceanic ecosystems. Dust is additionally a contributor to adverse air quality. Among the tools toward understanding the lifecycle and impacts of mineral dust aerosols are numerical models. Important constraints on these models come from quantitative satellite observations, like those from the space-based Moderate Resolution Imaging Spectroradiometer (MODIS). In particular, Kauhan et al. [2005] used MODIS aerosol observations to infer transport and deposition fluxes of Saharan dust over the Atlantic, Caribbean, and Amazonian basins. Those observations are used here to constrain the transport of dust and its interannual variability simulated in the NASA GEOS-5 general circulation model and data assimilation system. Significant uncertainty exists in the MODIS-derived fluxes, however, due to uncertainty in the wind fields provided by meteorological analyses in this region. That same uncertainty in the wind fields is manifest in our GEOS-5 simulations of dust distributions. Here we use MODIS observations to investigate the seasonality and location of the Saharan dust plume and explore through sensitivity analysis of our model the meteorological controls on the dust distribution, including dust direct radiative effects and sub-gridscale source and sink processes.

Colarco, P.↗

CFD Validation Study of a Hypersonic Cone-Slice-Flap Variable Geometry Configuration

Model validation is the process of determining the degree of accuracy between physical reality and the model. The result of model validation can either be used to improve the model through calibration or quantify the model-form uncertainty. This work focuses on providing the model-form uncertainty through an area metric for a hypersonic cone-slice-flap variable geometry configuration given uncertainty in both the simulation and experimental data. The research here compares two different turbulence models for the simulations. For a variable geometry, performing uncertainty quantification to capture the model-form uncertainty on every configuration is computationally challenging. This work lays out a procedure that can give an accurate representation of the model-form uncertainty using a small number of high-fidelity runs and many low-fidelity runs on multiple configurations. Running this comparison provides a quantifiable measurement for the accuracy of each turbulence model for this type of design. The high-fidelity CFD solver used was VULCAN-CFD and the low-fidelity results came from Cart3D. The experimental data came from the 20-Inch Mach 6 Tunnel located at NASA Langley Research Center. The present work showed that the using both the Spalart and Allamaras and Menter Shear-Stress Transport turbulence models overpredicted the drag and lift coefficient, while underpredicting the pitching moment coefficient. The model-form uncertainty estimate resulted in up to a 13.6% change in the total uncertainty for the drag coefficient, up to a 57.4% change in total uncertainty for the lift coefficient, and up to a 100% change in total uncertainty for the pitching moment coefficient.

Laura M. White↗

Interpolating Fields of Carbon Monoxide Data Using a Hybrid Statistical-Physical Model

Atmospheric Carbon Monoxide (CO) is a pollutant gas of which the US congress has mandated regular monitoring, and satellite sensors can be used to retrieve regional concentrations of CO over several vertical layers. However, CO at cloudy locations cannot be observed and have to be estimated from the observed data set, resulting in an interpolation problem. The current state-of-the-art solution is to combine prior information, computed by a deterministic physical model, with observations. However, the deterministic model may introduce uncertainties that do not derive from the data. While sharing certain features with the physical model, this paper presents a Bayesian hierarchical model for interpolating CO on a 3-dimensional spatial grid, across time. To our knowledge such a model has not been considered before. The model is applied to a hypothetical air-quality monitoring scenario, and is compared to existing interpolation methods. The results provide motivation for the use of the statistical model for regional to local applications.

Arellano, A. A.↗

Proton-induced fragmentation of carbon at energies below 100 MeV

Radiation effects caused by single cosmic ray particles have been studied for many years in radiobiological experiments for different biological objects and biological end-points. Additionally, single event effects in microelectronic devices have gained large interest. There are two fundamental mechanisms by which a single particle can cause radiation effects. On the one hand, a cosmic ray ion with high linear energy transfer can deposit a high dose along its path. On the other hand, in a nuclear collision, a high dose can be deposited by short range particles emitted from the target nucleus. In low earth orbits a large contribution to target fragmentation events originates from trapped protons which are encountered in the South Atlantic Anomaly. These protons have energies up to a few hundred MeV. We study the fragmentation of C, O and Si nuclei - the target nuclei of biological material and microelectronic devices - in nuclear collisions. Our aim is to measure production cross sections, energy spectra, emission directions and charge correlations of the emitted fragments. The present knowledge concerning these data is rather poor. M. Alurralde et al. have calculated cross sections and average energies of fragments produced from Si using the cascade-evaporation model. D.M. Ngo et al. have used the semiempirical cross section formula of Silberberg and Tsao to calculate fragment yields and the statistical model of Goldhaber to describe the reaction kinematics. Cross sections used in these models have uncertainties within a factor of two. Our data will help to test and improve existing models especially for energies below 300 MeV/nucleon. Charge correlations of fragments emitted in the same interaction are of particular importance, since high doses can be deposited if more than one heavy fragment with a short range is produced.

Schmitz, M.↗

New Data Source for Studying and Modelling the Topside Ionosphere

The existing uncertainties about density profiles in the topside ionosphere, i.e., in the height regime from hmF2 to approx. 2000 km, requires the search for new data sources. Millions of ionograms had been recorded by the ISIS and Alouette satellites in the sixties and seventies, that never were analyzed in terms of electron density profiles. In recent years an effort started to digitize the analog recordings to prepare the ionograms for computerized analysis. This paper shows how the digital ionograms are processed and the electron density profiles (from satellite orbit altitude, 1400 km for ISIS-2, down to the F peak) are calculated. The most difficult part of the task is the automatic scaling of the echo traces in the ISIS ionograms. Unlike the ionograms from modern ionosondes, the ISIS ionograms do not identify the wave polarization of the different echo traces, so physical logic must be applied to identify the ordinary ()) and extraordinary (X) traces, and this is not always successful. Characteristic resonance features seen in the topside ionograms occur at the gyro and plasma frequencies. An elaborate scheme was developed to identify these resonance frequencies in order to determine the local plasma and gyrofrequencies. This information helps in the identification of the O and X traces, and it provides the starting density of the electron density profile. The inversion of the echo traces into electron density profiles uses the same modified Chebyshev polynomial fitting technique that is successfully applied in the ground-based Digisonde network. The automatic topside ionogram scaler with true height algorithm TOPIST is successfully scaling approx. 70% of the ionograms. An 'editing process' is available to manually scale the more difficult ionograms. The home page for the ISIS project is at http://nssdc.gsfc.nasa.gov/space/isis/isis-status.html. It provides access to as of January 2001, 3000,000 digitized ISIS ionogram data and to related software. A search page lets users select data location, time, and a host of other search criteria. The automated processing of the ISIS ionograms will begin later this year and the electron density profiles will be made available from the project home page. The ISIS data restoration efforts are supported through NASA's Applied Systems and Information Research Program.

Huang, Xue-Qin↗

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↗

From Exploration Flight Test-1 to Artemis II--A NASA Langley's Orion Aerosciences Overview

The Orion Aerosciences program at NASA Langley has played a central role in advancing the aerodynamic and aeroheating prediction capabilities required for the Orion crew vehicle’s return from deep space. This presentation provides a technical overview of aerosciences contributions spanning Exploration Flight Test-1 (EFT-1), Artemis I, and the ongoing post-flight analysis of Artemis II. EFT-1 provided the first high-energy entry dataset for Orion, enabling critical validation of aerodynamic force and moment predictions, static and dynamic stability characteristics, and aeroheating environments at relevant flight Mach and Reynolds numbers. Flight-derived pressure data were used to refine the Flush Air Data System (FADS) methodology for atmospheric density reconstruction and to improve Best Estimated Trajectory (BET) solutions. The EFT-1 data also offered key insights into heat shield performance, including char layer recession, in-depth thermal response, and material retention behavior under flight conditions, informing updates to both thermal response models and uncertainty quantification practices. Building on EFT-1, Artemis I extended the database to true lunar-return conditions. Observations of heat shield performance, including localized char loss, bondline response, and recession variability, provided an unprecedented opportunity to reassess Thermal Protection System (TPS) and aeroheating modeling assumptions. Aerodynamic reconstruction efforts incorporated improved FADS calibration, enhanced atmospheric modeling, and refined force and moment databases to reduce trajectory and load uncertainties. Aeroheating comparisons between pre-flight predictions and flight data enabled targeted model updates, particularly in transitional flow environments and wake heating regions. For Artemis II, these lessons were systematically incorporated into the pre-flight prediction process. Updates included refined aerodynamic databases anchored to flight-validated corrections, improved density estimation and BET methodologies using enhanced database interpolation algorithm and FADS modeling, and revised aeroheating design environments informed by Artemis I material response observations. By the time of the workshop, Artemis II post-flight analysis will be underway, and preliminary findings will be presented where available, including early comparisons of aerodynamic reconstruction, atmospheric density estimation, and thermal protection system performance relative to updated predictions. Collectively, this body of work is a testament to the dedicated and multidisciplinary team whose sustained efforts have contributed to the program’s success and to the progressive maturation of Orion aerosciences modeling through numerical modeling, ground and flight data assimilation. The integrated advancement of aerodynamics, trajectory reconstruction, FADS-based density estimation, and aeroheating analysis has reduced predictive uncertainty and strengthened confidence for future crewed lunar and deep-space missions.

Orion↗

Regression Analysis of Long-Term Profile Ozone Data Set from BUV Instruments

We have produced a profile merged ozone data set (MOD) based on the SBUV/SBUV2 series of nadir-viewing satellite backscatter instruments, covering the period from November 1978 - December 2003. In 2004, data from the Nimbus 7 SBUV and NOAA 9, ll, and 16 SBUV/2 instruments were reprocessed using the Version 8 (V8) algorithm and most recent calibrations. More recently, data from the Nimbus 4 BUT instrument, which was operational from 1970 - 1977, were also reprocessed using the V8 algorithm. As part of the V8 profile calibration, the Nimbus 7 and NOAA 9 (1993-1997 only) instrument calibrations have been adjusted to match the NOAA 11 calibration, which was established based on comparisons with SSBUV shuttle flight data. Differences between NOAA 11, Nimbus 7 and NOAA 9 profile zonal means are within plus or minus 5% at all levels when averaged over the respective periods of data overlap. NOAA 16 SBUV/2 data have insufficient overlap with NOAA 11, so its calibration is based on pre-flight information. Mean differences over 4 months of overlap are within plus or minus 7%. Given the level of agreement between the data sets, we simply average the ozone values during periods of instrument overlap to produce the MOD profile data set. Initial comparisons of coincident matches of N4 BUV and Arosa Umkehr data show mean differences of 0.5 (0.5)% at 30km; 7.5 (0.5)% at 35 km; and 11 (0.7)% at 40 km, where the number in parentheses is the standard error of the mean. In this study, we use the MOD profile data set (1978-2003) to estimate the change in profile ozone due to changing stratospheric chlorine levels. We use a standard linear regression model with proxies for the seasonal cycle, solar cycle, QBO, and ozone trend. To account for the non-linearity of stratospheric chlorine levels since the late 1990s, we use a time series of Effective Chlorine, defined as the global average of Chlorine + 50 * Bromine at 1 hPa, as the trend proxy. The Effective Chlorine data are taken from the 3-D Goddard CTM. We will show the latest trend results using this statistical model. In addition, the Nimbus 4 BUV data offer an opportunity to test the physical properties of our statistical model. From ground-based comparisons we will establish an uncertainty range for the Nimbus 4 data. We then extrapolate our statistical model fit backwards in time and compare to the Nimbus 4 data. We compare the characteristics of the residual, defined as the difference between the data and statistical regression fit, during the Nimbus 4 time period and the 1978-2003 period over which the statistical model coefficients were estimated, and present these results.

Stolarski, Richard S.↗

The application of sensitivity analysis to models of large scale physiological systems

A survey of the literature of sensitivity analysis as it applies to biological systems is reported as well as a brief development of sensitivity theory. A simple population model and a more complex thermoregulatory model illustrate the investigatory techniques and interpretation of parameter sensitivity analysis. The role of sensitivity analysis in validating and verifying models, and in identifying relative parameter influence in estimating errors in model behavior due to uncertainty in input data is presented. This analysis is valuable to the simulationist and the experimentalist in allocating resources for data collection. A method for reducing highly complex, nonlinear models to simple linear algebraic models that could be useful for making rapid, first order calculations of system behavior is presented.

Leonard, J. I.↗

Algorithm for Atmospheric Corrections of Aircraft and Satellite Imagery

A simple and fast atmospheric correction algorithm is described which is used to correct radiances of scattered sunlight measured by aircraft and/or satellite above a uniform surface. The atmospheric effect, the basic equations, a description of the computational procedure, and a sensitivity study are discussed. The program is designed to take the measured radiances, view and illumination directions, and the aerosol and gaseous absorption optical thickness to compute the radiance just above the surface, the irradiance on the surface, and surface reflectance. Alternatively, the program will compute the upward radiance at a specific altitude for a given surface reflectance, view and illumination directions, and aerosol and gaseous absorption optical thickness. The algorithm can be applied for any view and illumination directions and any wavelength in the range 0.48 micron to 2.2 micron. The relation between the measured radiance and surface reflectance, which is expressed as a function of atmospheric properties and measurement geometry, is computed using a radiative transfer routine. The results of the computations are presented in a table which forms the basis of the correction algorithm. The algorithm can be used for atmospheric corrections in the presence of a rural aerosol. The sensitivity of the derived surface reflectance to uncertainties in the model and input data is discussed.

Fraser, Robert S.↗

Towards a methodology for robust parameter identification

Consideration is given to the problem of estimating, from experimental data, real parameters for a model with uncertainty in the form of both additive noise and norm-bounded perturbations. Such models frequently arise in robust control theory, and a framework is introduced for the consideration of experimental data in robust control analysis problems. If the analysis tools applied include robust stability tests for real parameter variations (real mu), the framework can be used to address the problem of robust parameter identification. While the techniques discussed can quickly become computationally overwhelming when applied to physical systems and real data, the approach introduces a novel way of looking at the identification problem and may be helpful in arriving at a more tractable methodology.

Smith, Roy S.↗

Algorithm for atmospheric corrections of aircraft and satellite imagery

A simple and fast atmospheric correction algorithm is described which is used to correct radiances of scattered sunlight measured by aircraft and/or satellite above a uniform surface. The atmospheric effect, the basic equations, a description of the computational procedure, and a sensitivity study are discussed. The program is designed to take the measured radiances, view and illumination directions, and the aerosol and gaseous absorption optical thickness to compute the radiance just above the surface, the irradiance on the surface, and surface reflectance. Alternatively, the program will compute the upward radiance at a specific altitude for a given surface reflectance, view and illumination directions, and aerosol and gaseous absorption optical thickness. The algorithm can be applied for any view and illumination directions and any wavelength in the range 0.48 micron to 2.2 microns. The relation between the measured radiance and surface reflectance, which is expressed as a function of atmospheric properties and measurement geometry, is computed using a radiative transfer routine. The results of the computations are presented in a table which forms the basis of the correction algorithm. The algorithm can be used for atmospheric corrections in the presence of a rural aerosol. The sensitivity of the derived surface reflectance to uncertainties in the model and input data is discussed.

Fraser, R. S.↗

Requirements and Challenges for CFD Validation within the High-Lift Common Research Model Ecosystem

The High-Lift Common Research Model (CRM-HL) ecosystem is envisioned to become an industry standard set of test cases for high-lift aerodynamics prediction, with data generated providing a strong foundation for CFD validation. Since its original development, preliminary wind tunnel tests have been conducted to further understand and configure the geometry, and several more are in the planning phases. It is anticipated that the data generated in these tests will be used extensively by the CFD community for research, development, and validation of new techniques that yield more accurate results. To derive the maximum benefit from planned wind tunnel testing, data acquisition will be focused in several key areas to address specific shortcomings in CFD predictive capabilities. Significant challenges currently exist in areas including, but not limited to, characterizing high-lift flow phenomena, quantifying effects due to configuration changes, understanding wind tunnel and model installation effects, and establishing data uncertainty. This paper will discuss the current state-of-the-art in high-lift CFD prediction, key limitations of current CFD methods and tools, establishing a validation dialog between test and CFD practitioners, and the flow phenomena of highest interest, in an effort to begin to address these challenges. To this end, it is expected that the data generated from CRM-HL tests will form a strong foundation for future predictive capability.

Adam M Clark↗

Invited: uPSP Launch Vehicle Demonstration Test at NASA Ames Research Center

The Unsteady Pressure-Sensitive Paint (uPSP) Development Team outof NASA Ames Research Center (ARC) has spent the past five yearsimproving the systems and processes to advance the uPSP technology for production-level wind tunnel testing. Already considered turnkey for small-scale and research applications, development in acquisition, calibration, data transfer, and data processing were needed to be useful to customers testing at NASA wind tunnels. This development focused at ARC at the Unitary Plan Wind Tunnel (UPWT) 11-by 11-ft Transonic Wind Tunnel due to the large optical access of the test section and the NASA Advanced Supercomputer(NAS), also located at ARC. A Launch Vehicle Demonstration Test (LVDT) at the UPWT represents a milestone of this initial phase of development where several new improvements were demonstrated in a production wind tunnel environment for the first time. LVDT was conducted in April 2024 and used a 4% forebody Space Launch System (SLS) Block 1B model as the test article. Both a crew and cargo configuration were tested, with varying Mach numbers, pressures, model positions, and camera magnifications. This paper summarizes the details of the test and is part of a collection with four additional papers that provide greater detail on: high-speed lifetime methodology, spectral proper orthogonal decomposition analysis, quality of high-resolution data compared to Corcos model, and data quality, calibration, and uncertainty.

SLS↗

Application of Interval Predictor Models to Space Radiation Shielding

This paper develops techniques for predicting the uncertainty range of an output variable given input-output data. These models are called Interval Predictor Models (IPM) because they yield an interval valued function of the input. This paper develops IPMs having a radial basis structure. This structure enables the formal description of (i) the uncertainty in the models parameters, (ii) the predicted output interval, and (iii) the probability that a future observation would fall in such an interval. In contrast to other metamodeling techniques, this probabilistic certi cate of correctness does not require making any assumptions on the structure of the mechanism from which data are drawn. Optimization-based strategies for calculating IPMs having minimal spread while containing all the data are developed. Constraints for bounding the minimum interval spread over the continuum of inputs, regulating the IPMs variation/oscillation, and centering its spread about a target point, are used to prevent data over tting. Furthermore, we develop an approach for using expert opinion during extrapolation. This metamodeling technique is illustrated using a radiation shielding application for space exploration. In this application, we use IPMs to describe the error incurred in predicting the ux of particles resulting from the interaction between a high-energy incident beam and a target.

Crespo, Luis G.↗

Collisional cascading - The limits of population growth in low earth orbit

Random collisions between made-made objects in earth orbit will lead to a significant source of orbital debris, but there are a number of uncertainties in these models, and additional analysis and data are required to fully characterize the future environment. However, the nature of these uncertainties are such that while the future environment is uncertain, the fact that collisions will control the future environment is less uncertain. The data that already exist is sufficient to show that cascading collisions will control the future debris environment with no, or very minor increases in the current low-earth-orbit population. Two populations control this process: explosion fragments and expended rocket bodies and payloads. Practices are already changing to limit explosions in low earth orbit; it is necessary to begin limiting the number of expended rocket bodies and payloads in orbit.

Kessler, Donald J.↗

Daily Ambient Air Pollution Metrics for Five Cities: Evaluation of Data Fusion-Based Estimates and Uncertainties

Spatiotemporal characterization of ambient air pollutant concentrations is increasingly relying on the combination of observations and air quality models to provide well-constrained, spatially and temporally complete pollutant concentration fields. Air quality models, in particular, are attractive, as they characterize the emissions, meteorological, and physiochemical process linkages explicitly while providing continuous spatial structure. However, such modeling is computationally intensive and has biases. The limitations of spatially sparse and temporally incomplete observations can be overcome by blending the data with estimates from a physically and chemically coherent model, driven by emissions and meteorological inputs. We recently developed a data fusion method that blends ambient ground observations and chemical transport-modeled (CTM) data to estimate daily, spatially resolved pollutant concentrations and associatedcorrelations. In this study, we assess the ability of the data fusion method to produce daily metrics (i.e., 1-hr max, 8-hr max, and 24-hr average) of ambient air pollution that capture spatiotemporal air pollution trends for 12 pollutants (CO, NO2, NOx, O3, SO2, PM (sub10), PM (sub 2.5), and five PM (sub 2.5) components) across five metropolitan areas (Atlanta, Birmingham, Dallas, Pittsburgh, and St. Louis), from 2002 to 2008. Three sets of comparisons are performed: (1) the CTM concentrations are evaluated for each pollutant and metropolitan domain, (2) the data fusion concentrations are compared with the monitor data, (3) a comprehensive cross-validation analysis against observed data evaluates the quality of the data fusion model simulations across multiple metropolitan domains. The resulting daily spatial field estimates of air pollutant concentrations and uncertainties are not only consistent with observations, emissions, andmeteorology, but substantially improve CTM-derived results for nearly all pollutants and all cities, with the exception of NO2 for Birmingham. The greatest improvements occur for O3 and PM (sub 2.5). Squared spatiotemporal correlation coefficients range between simulations and observations determined using cross-validation across all cities for air pollutants of secondary and mixed origins are R-squared equal to 0.88-0.93 (O3), 0.81-0.89 (SO4), 0.67-0.83 (PM (sub 2.5)), 0.52-0.72 (NO3), 0.43-0.80 (NH4), 0.32-0.51 (OC), and 0.14-0.71 (PM (sub 10)). Results for relatively homogeneous pollutants of secondary origin, tend to be better than those for more spatially heterogeneous (larger spatial gradients) pollutants of primary origin (NOx, CO, SO2 and EC). Generally, background concentrations and spatial concentration gradients reflect interurban airshed complexity and the effects of regional transport, whereas daily spatial pattern variability shows intra urban consistency in the fused data. With sufficiently high CTM spatial resolution, traffic-related pollutants exhibit gradual concentration gradients that peak toward the urban centers. Ambient pollutant concentration uncertainty estimates for the fused data are both more accurate and smaller than those for either the observations or the model simulations alone.

spatiotemporal fusion↗

Atmospheric studies related to aerospace activities and remote sensing technology

Parallel investigations were conducted relating to: the sensitivity of 1-D photochemical model simulated column ozone perturbations due to a projected fleet of 1000 aircraft cruising 7 hours per day at altitudes of 15-16 and 18-19 km to uncertainties in kinetic rate constant data determining modeled OH concentrations and eddy diffusivity profile parameterization and a comparison of the inherent strengths and weaknesses of Eulerian and Langrangian averaging processes in the development of multidimensional models and investigation of approaches to applying the Generalized Lagrangian Mean (GLM) formalism to zonal-mean models. The role of multiple scattering and Earth curvature in the evaluation of diurnally dependent photodissociation rates and trace species variations was examined.

Sze, N. D.↗