Results for “spatial discretization” — Page 25

NASA NTRS1994

The Visibility of DCT Quantization Noise: Spatial Frequency Summation

Computational models of the ability to detect image compression artifacts facilitate the optimization of compression parameters, such as the JPEG quantization matrix. For simplicity, some models assume that the visibility of artifacts containing different spatial frequency components is determined by the most visible component, that is, no summation over components. Using the type of noise generated by quantization in the Discrete Cosine Transform (DCT) domain, we find a degree of summation between that of probability summation and contrast energy summation.

Peterson, H. A.↗

NASA NTRSDate not supplied

On Computationally Efficient Radiative Transfer Calculations for Three-dimensional Entry Problems

The current work presents an efficient simulation framework for rigorously modeling radiative fields emanating from non-equilibrium planetary entry flows in complex three-dimensional domains. Key to this endeavor is adoption of finite-volume discretization in lieu of brute-force ray tracing. This change in conjunction with mesh sweeping and Lebedev-type quadrature for angular integration allows spatial-angular resolution of radiative transfer to be performed in a computationally tractable manner. Additionally, a new methodology has been established to build standalone reduced-order spectral databases for non-equilibrium radiative properties that can be applied to a broad range of hypersonic planetary entry problems with minimal loss in accuracy. The efficacy of the new framework has been demonstrated on the atomic nitrogen radiative system. The resulting reduced-order model requires three orders-of-magnitude fewer spectral evaluations and results in a 95% decrease in memory footprint. A comparative study for representative forebody and afterbody lines-of-sight from Stardust, FIRE II, and meteor entries into the Earth atmosphere indicates that both total intensity variation and detailed spectra can be retrieved with as few as 625 reduced-order groups (contrasting with the 100,000 frequencies in the original full set model). Similarly, three-dimensional predictions of radiative heating experienced by the Orion forebody are in excellent agreement with legacy radiation solvers while requiring only a sliver (roughly 0.5%) of computing wall time.

3D radiation↗

NASA NTRSDate not supplied

On Computationally Efficient Radiative Transfer Calculations for Three-Dimensional Entry Problems

The current work presents an efficient simulation framework for rigorously modeling radiative fields emanating from non-equilibrium planetary entry flows in complex three-dimensional domains. Key to this endeavor is adoption of finite-volume discretization in lieu of brute-force ray tracing. This change in conjunction with mesh sweeping and Lebedev-type quadrature for angular integration allows spatial-angular resolution of radiative transfer to be performed in a computationally tractable manner. Additionally, a new methodology has been established to build standalone reduced-order spectral databases for non-equilibrium radiative properties that can be applied to a broad range of hypersonic planetary entry problems with minimal loss in accuracy. The efficacy of the new framework has been demonstrated on the atomic nitrogen radiative system. The resulting reduced-order model requires three orders-of-magnitude fewer spectral evaluations and results in a 95% decrease in memory footprint. A comparative study for representative forebody and afterbody lines-of-sight from Stardust, FIRE II, and meteor entries into the Earth atmosphere indicates that both total intensity variation and detailed spectra can be retrieved with as few as 625 reduced-order groups (contrasting with the 100,000 frequencies in the original full set model). Similarly, three-dimensional predictions of radiative heating experienced by the Orion forebody are in excellent agreement with legacy radiation solvers while requiring only a sliver (roughly 0.5%) of computing wall time.

3D radiation↗

NASA NTRSDate not supplied

An Automated Marching Scheme for Overset Structured Surface Mesh Generation

Starting with a Boundary Representation (BRep) of the geometry of an aerospace vehicle, an automated marching scheme is presented for generation of structured overset surface meshes. First, a pre-processing step automatically generates discrete representations of the BRep faces and BRep edges by tessellating in parameter space. Topological connectivity between the discretized BRep edges is then established, followed by automatic grid point distribution on these edges based on local turning angle, proximity to sharp geometric features, and prescribed maximum stretching ratio and grid spacing. A set of initial curves for algebraic or hyperbolic marching on a surface is then derived from the redistributed edge curves. A spatially-variable marching distance together with a grid point distribution in the marching direction are automatically determined for each initial curve. A set of overset surface meshes that covers the entire geometry is then obtained by combining the surface meshes around the BRep edges, and the structured meshes derived from the discretized BRep faces

Shishir A Pandya↗

NASA NTRS1993

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

Scott, James R.↗

NASA NTRS1989

Sensitivity of actively damped structures to imperfections and modeling errors

The sensitivity of actively damped response of structures with respect to errors in the structural modeling is studied. Two ways of representing errors are considered. The first approach assumes errors in the form of spatial variations (or imperfections) in the assumed mass and stiffness properties of the structures. The second approach assumes errors due to such factors as unknown joint stiffnesses, discretization errors, and nonlinearities. These errors are represented here as discrepancies between experimental and analytical mode shapes and frequencies. The actively damped system considered here is a direct-rate feedback regulator based on a number of colocated velocity sensors and force actuators. The response of the controlled structure is characterized by the eigenvalues of the closed-loop system. The effects of the modeling errors are thus presented as the sensitivity of the eigenvalues of the closed-loop system. Results are presented for two examples: (1) a three-span simply supported beam controlled by three sensors and actuators, and (2) a laboratory structure consisting of a cruciform beam supported by cables.

Haftka, Raphael T.↗

NASA NTRS2004

The Ultra-Luminous X-ray Source Population from the Chandra Archive of Galaxies

One hundred fifty-four discrete non-nuclear Ultra-Luminous X-ray (ULX) sources, with spectroscopically-determined intrinsic X-ray luminosities greater than 1 e39 ergs/s, are identified in 82 galaxies observed with Chandra's Advanced CCD Imaging Spectrometer. Source positions, X-ray luminosities, and spectral and timing characteristics are tabulated. Statistical comparisons between these X-ray properties and those of the weaker discrete sources in the same fields (mainly neutron star and stellar-mass black hole binaries) are made. Sources above approximately le38 ergs per second display similar spatial, spectral, color, and variability distributions. In particular, there is no compelling evidence in the sample for a new and distinct class of X-ray object such as the intermediate-mass black holes. 83% of ULX candidates have spectra that can be described as absorbed power laws with index = 1.74 and column density = 2.24e21 l per square centimeter, or approximately 5 times the average Galactic column. About 20% of the ULX's have much steeper indices indicative of a soft, and likely thermal, spectrum. The locations of ULXs in their host galaxies are strongly peaked towards their galaxy centers. The deprojected radial distribution of the ULX candidates is somewhat steeper than an exponential disk, indistinguishable from that of the weaker sources. About 5--15% of ULX candidates are variable during the Chandra observations (which average 39.5 ks). Comparison of the cumulative X-ray luminosity functions of the ULXs to Chandra Deep Field results suggests approximately 25% of the sources may be background objects including 14% of the ULX candidates in the sample of spiral galaxies and 44% of those in elliptical galaxies implying the elliptical galaxy ULX population is severely compromised by background active galactic nuclei. Correlations with host galaxy properties confirm the number and total X-ray luminosity of the ULXs are associated with recent star formation and with galaxy merging and interactions. The preponderance of ULXs in star-forming galaxies as well as their similarities to less-luminous sources suggest they originate in a young but short-lived population such as the high-mass X-ray binaries with a smaller contribution (based on spectral slope) from recent supernovae. The number of ULXs in elliptical galaxies scales with host galaxy mass and can be explained most simply as the high-luminosity end of the low-mass X-ray binary population.

Swartz, Douglas A.↗

NASA NTRS2011

Vertical Distribution of Aersols and Water Vapor Using CRISM Limb Observations

Near-infrared spectra taken in a limb-viewing geometry by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) on-board the Mars Reconnaissance Orbiter (MRO) provide a useful tool for probing atmospheric structure. Specifically, the observed radiance as a function of wavelength and height above the limb allows the vertical distribution of both dust and ice aerosols to be retrieved. These data serve as an important supplement to the aerosol profiling provided by the MRO/MCS instrument allowing independent validation and giving additional information on particle physical and scattering properties through multi-wavelength studies. A total of at least ten CRISM limb observations have been taken so far covering a full Martian year. Each set of limb observations nominally contains about four dozen scans across the limb giving pole-to-pole coverage for two orbits at roughly 100 and 290 W longitude over the Tharsis and Syrtis/Hellas regions, respectively. At each longitude, limb scans are spaced roughly 10 degrees apart in latitude, with a vertical spatial resolution on the limb of roughly 800 m. Radiative transfer modeling is used to model the observations. We compute synthetic CRISM limb spectra using a discrete-ordinates radiative transfer code that accounts for multiple scattering from aerosols and accounts for spherical geometry of the limb observations by integrating the source functions along curved paths in that coordinate system. Retrieved are 14-point vertical profiles for dust and water ice aerosols with resolution of 0.4 scale heights between one and six scale heights above the surface. After the aerosol retrieval is completed, the abundances of C02 (or surface pressure) and H20 gas are retrieved by matching the depth of absorption bands at 2000 nm for carbon dioxide and at 2600 run for water vapor. In addition to the column abundance of water vapor, limited information on its vertical structure can also be retrieved depending on the signal available from aerosol scattering.

Smith, Michael D.↗

NASA NTRSDate not supplied

Overview of NASA's Ocean Color Instrument Solar Calibration Architecture, Pre-Launch Tests and Preliminary On-Orbit Results

Launched in February 2024, the PACE mission represents NASA’s next investment in ocean biology, clouds, and aerosol data records. A key feature of PACE is the inclusion of an advanced satellite radiometer known as the Ocean Color Instrument (OCI), a global mapping radiometer that combines multispectral and hyperspectral remote sensing. Like its predecessors, OCI will provide two day global coverage of TOA radiances. Unlike its predecessors, OCI will cover a spectral range from 340nm to 2260nm. Below 900nm, OCI will include two spectrometers that continuously span the ultraviolet to 600nm and 600nm to near-infrared spectral regions to provide hyperspectral radiances sampled every 2.5 nm, with a bandwidth of 5 nm for each channel. Wavelengths above 900nm are measured in seven discrete multispectral bands of varying bandwidths, six of which are at similar wavelengths to those on heritage missions to support both atmospheric and ocean color applications. Nominal spatial resolution is similar to the SeaWiFS instrument with 1050 m at nadir. As for SeaWiFS, the pixel size increases due to a ~20 degree tilt and as a function of scan angle. Variations in the radiometric sensitivity of each OCI channel over time will be monitored by solar diffuser measurements for short term instrument gain adjustments and independent lunar measurements for trend adjustments of long time periods, similar to the approach employed for the VIIRS instrument [4]. The OCI flight-unit was built at NASA’s Goddard Space Flight Center. At the time of this writing, OCI has completed on-orbit commissioning activities and normal science operations have begun. A key aspect of the OCI architecture is the capability to trend absolute and relative calibration changes over the course of mission life with solar calibration. Every 24 hours, the PACE spacecraft performs an inertial hold as the ground track nears the North Pole which orients a Quasi-Volume Diffuser (QVD) mounted on OCI towards the sun. By knowing the irradiance of the sun and the reflectivity of the target, the absolute radiance at the input to the OCI aperture can be computed as OCI scans the target. The allowable absolute uncertainty budget for each solar calibration measurement is 1.6% 1-sigma below 900nm at beginning of life (BOL) and the allowable relative uncertainty budget is ~0.26% 1-sigma. The Solar Calibration Assembly (SCA) consists of three targets selectable via a single mechanism which also opens a door. The targets consist of a Daily Bright Target (DBT), Monthly Bright Target (MBT), and Daily Dim Target (DDT). The bright targets are quartz QVDs with the monthly target being used to track the degradation of the daily target. The dim target is used to track CCD linearity using Progressive Time-Delay Integration (PTDI). A composite baffle is attached to the SCA housing aperture to block Earth shine and stray light from the spacecraft. The SCA assembly is mounted to a view port ~90° from OCI nadir. This paper provides an overview of driving solar calibration requirements, error-budgets and early trade studies which drove the solar calibration assembly (SCA) architecture and on-orbit maneuver. Measurements of the diffuser Bidirectional Reflectance Distribution Function (BRDF) at TNO, Netherlands and GSFC are briefly described. Optical modelling and test results at the sub-system and instrument level are included. Finally, preliminary measurements on-orbit are compared to pre-launch predictions.

Joseph J Knuble↗

NASA NTRSDate not supplied

Overview of NASA's Ocean Color Instrument Solar Calibration Architecture, Pre-Launch Tests and Preliminary On-Orbit Results

Launched in February 2024, the PACE mission represents NASA’s next investment in ocean biology, clouds, and aerosol data records. A key feature of PACE is the inclusion of an advanced satellite radiometer known as the Ocean Color Instrument (OCI), a global mapping radiometer that combines multispectral and hyperspectral remote sensing. Like its predecessors, OCI will provide two day global coverage of TOA radiances. Unlike its predecessors, OCI will cover a spectral range from 340nm to 2260nm. Below 900nm, OCI will include two spectrometers that continuously span the ultraviolet to 600nm and 600nm to near-infrared spectral regions to provide hyperspectral radiances sampled every 2.5 nm, with a bandwidth of 5 nm for each channel. Wavelengths above 900nm are measured in seven discrete multispectral bands of varying bandwidths, six of which are at similar wavelengths to those on heritage missions to support both atmospheric and ocean color applications. Nominal spatial resolution is similar to the SeaWiFS instrument with 1050 m at nadir. As for SeaWiFS, the pixel size increases due to a ~20 degree tilt and as a function of scan angle. Variations in the radiometric sensitivity of each OCI channel over time will be monitored by solar diffuser measurements for short term instrument gain adjustments and independent lunar measurements for trend adjustments of long time periods, similar to the approach employed for the VIIRS instrument [4]. The OCI flight-unit was built at NASA’s Goddard Space Flight Center. At the time of this writing, OCI has completed on-orbit commissioning activities and normal science operations have begun. A key aspect of the OCI architecture is the capability to trend absolute and relative calibration changes over the course of mission life with solar calibration. Every 24 hours, the PACE spacecraft performs an inertial hold as the ground track nears the North Pole which orients a Quasi-Volume Diffuser (QVD) mounted on OCI towards the sun. By knowing the irradiance of the sun and the reflectivity of the target, the absolute radiance at the input to the OCI aperture can be computed as OCI scans the target. The allowable absolute uncertainty budget for each solar calibration measurement is 1.6% 1-sigma below 900nm at beginning of life (BOL) and the allowable relative uncertainty budget is ~0.26% 1-sigma. The Solar Calibration Assembly (SCA) consists of three targets selectable via a single mechanism which also opens a door. The targets consist of a Daily Bright Target (DBT), Monthly Bright Target (MBT), and Daily Dim Target (DDT). The bright targets are quartz QVDs with the monthly target being used to track the degradation of the daily target. The dim target is used to track CCD linearity using Progressive Time-Delay Integration (PTDI). A composite baffle is attached to the SCA housing aperture to block Earth shine and stray light from the spacecraft. The SCA assembly is mounted to a view port ~90° from OCI nadir. This paper provides an overview of driving solar calibration requirements, error-budgets and early trade studies which drove the solar calibration assembly (SCA) architecture and on-orbit maneuver. Measurements of the diffuser Bidirectional Reflectance Distribution Function (BRDF) at TNO, Netherlands and GSFC are briefly described. Optical modelling and test results at the sub-system and instrument level are included. Finally, preliminary measurements on-orbit are compared to pre-launch predictions.

ocean color↗

NASA NTRS1992

Boundary-layer receptivity due to distributed surface imperfections of a deterministic or random nature

Acoustic receptivity of a Blasius boundary layer in the presence of distributed surface irregularities is investigated analytically. It is shown that, out of the entire spatial spectrum of the surface irregularities, only a small band of Fourier components can lead to an efficient conversion of the acoustic input at any given frequency to an unstable eigenmode of the boundary layer flow. The location, and width, of this most receptive band of wavenumbers corresponds to a relative detuning of O(R sub l.b.(exp -3/8)) with respect to the lower-neutral instability wavenumber at the frequency under consideration, R sub l.b. being the Reynolds number based on a typical boundary-layer thickness at the lower branch of the neutral stability curve. Surface imperfections in the form of discrete mode waviness in this range of wavenumbers lead to initial instability amplitudes which are O(R sub l.b.(exp 3/8)) larger than those caused by a single, isolated roughness element. In contrast, irregularities with a continuous spatial spectrum produce much smaller instability amplitudes, even compared to the isolated case, since the increase due to the resonant nature of the response is more than that compensated for by the asymptotically small band-width of the receptivity process. Analytical expressions for the maximum possible instability amplitudes, as well as their expectation for an ensemble of statistically irregular surfaces with random phase distributions, are also presented.

Choudhari, Meelan↗

NASA NTRS1992

A low-altitude mechanism for mesoscale dynamics, structure, and current filamentation in the discrete aurora

The 2D nonlinear evolution of the ionization-driven adiabatic auroral arc instability is studied. We find: (1) the adiabatic auroral arc instability can fully develop on time scales of tens to hundreds of seconds and on spatial scales of tens to hundreds of kilometers; (2) the evolution of this instability leads to nonlinear 'hook-shaped' conductivity structures: (3) this instability can lead to parallel current filamentation over a wide range of scale sizes; and (4) the k-spectra of the density, electric field, and parallel current develop into inverse power laws in agreement with satellite observations. Comparison with mesoscale auroral phenomenology and current filamentation structures is made.

Keskinen, M. J.↗

NASA NTRS1994

Evolution of solitary density waves in stellar winds of early-type stars: A simple explanation of discrete absorption component behavior

We model the evolution of a density shell propagating through the stellar wind of an early-type star, in order to investigate the effects of such shells on UV P Cygni line profiles. Unlike previous treatments, we solve the mass, momentum, and energy conservation equations, using an explicit time-differencing scheme, and present a parametric study of the density, velocity, and temperature response. Under the assumed conditions, relatively large spatial scale, large-amplitude density shells propagate as stable waves through the supersonic portion of the wind. Their dynamical behavior appears to mimic propagating 'solitary waves,' and they are found to accelerate at the same rate as the underlying steady state stellar wind (i.e., the shell rides the wind). These hydrodynamically stable structures quantitatively reproduce the anomalous 'discrete absorption component' (DAC) behavior observed in the winds of luminous early-type stars, as illustrated by comparisons of model predictions to an extensive International Ultraviolet Explorer (IUE) time series of spectra of zeta Puppis (O4f). From these comparisons, we find no conclusive evidence indicative of DACs accelerating at a significantly slower rate than the underlying stellar wind, contrary to earlier reports. In addition, these density shells are found to be consistent within the constraints set by the IR observations. We conclude that the concept of propagating density shells should be seriously reconsidered as a possible explanation of the DAC phenomenon in early-type stars.

Waldron, Wayne L.↗

NASA NTRS1975

Development of a spectroscopic photoelectric imaging Fabry-Perot interferometer preliminary observational results

In order to observe extended astronomical objects at high spatial and spectral resolution, a spectroscopic photoelectric imaging Fabry-Perot interferometer was constructed. Among the properties chosen for the instrument are an air-spaced, piezoelectrically scanned design allowing an accurately settable free spectral range and employing a single etalon of high finesse. Careful design of the etalon mountings and optical train preserves high ligh throughput. Spectra of single spatial elements with a photomultiplier were obtained, and an SEC vidicon detector was used to record a series of images through the interferometer while scanning the wavelength in discrete steps. The latter procedure yields sufficient information to reconstruct spectral features over the entire object, and for the conditions assumed, either series of observations requires only a small fraction of a rotational period for Jupiter or Saturn. An electronic control system was also constructed which permits rapid and flexible variation of the operational mode of the Fabry-Perot and its ancilliary devices so as to minimize loss of observational time.

Smith, W. H.↗

NASA NTRS1986

International Halley Watch: Discipline specialists for near-nucleus studies

The purpose of the Near-Nucleus Studies Net is to study the processes taking place in the near-nucleus environment as they relate to the nature of nucleus. This is accomplisghed by measuring the spatial and temporal distribution of dust, gases and ions in the coma on high resolution images taken from many observatories around the world. By modeling the motions of discrete dust features in Comet Halley, it is often possible to determine the locations of the emission sources on the surface and learn about the nucleus structure. In addition to the general goals shared by all IHW nets, the scientific goals of the net has been to determine (1)the gross surface structure of the nucleus, (2)the nucleus spin vector, (3)the distribution and evolution of jet sources and (4)the interrelationships between the gas, dust and ion components of the coma. An additional Comet Giacobini-Zinner watch was carried out by the NNSN in support of the NASA International Cometary Explorer flyby.

Larson, S.↗

NASA NTRS1989

Comparison of Landsat Thematic Mapper and Geophysical and Environmental Research Imaging Spectrometer data for the Cuprite mining district, Esmeralda, and Nye counties, Nevada

Landsat TM images and Geophysical and Environmental Research Imaging Spectrometer (GERIS) data were analyzed for the Cuprite mining district and compared to available geologic and alteration maps of the area. The TM data, with 30 m resolution and 6 broadbands, allowed discrimination of general mineral groups. Clay minerals, playa deposits, and unaltered rocks were mapped as discrete spectral units using the TM data, but specific minerals were not determined, and definition of the individual alteration zones was not possible. The GERIS, with 15 m spatial resolution and 63 spectral bands, permitted construction of complete spectra and identification of specific minerals. Detailed spectra extracted from the images provided the ability to identify the minerals alunite, kaolinite, hematite, and buddingtonite by their spectral characteristics. The GERIS data show a roughly concentrically zoned hydrothermal system. The mineralogy mapped with the aircraft system conforms to previous field and multispectral image mapping. However, identification of individual minerals and spatial display of the dominant mineralogy add information that can be used to help determine the morphology and genetic origin of the hydrothermal system.

Kierein-Young, Kathryn S.↗

NASA NTRS1990

Numerical simulation of spatially-evolving instability

A computational study of the spatial stability of plane Poiseuille flow is presented. The numerical scheme employs a time-splitting method to integrate the full Navier-Stokes equations using spectral collocation/finite-difference discretization on a non-staggered mesh. The eigenvalue decomposition procedure is applied for the solution of the Poisson equations using the capacitance matrix technique. The buffer domain method is incorporated for the outflow boundary conditions. The input perturbation velocities are obtained by solving the Orr-Sommerfeld equation for the nonlinear eigenvalue problem employing the companion matrix method. Computational results are compared with the linear theory for two-dimensional disturbances.

Danabasoglu, G.↗

NASA NTRS2013

Downscaling Satellite Precipitation with Emphasis on Extremes: A Variational 1-Norm Regularization in the Derivative Domain

The increasing availability of precipitation observations from space, e.g., from the Tropical Rainfall Measuring Mission (TRMM) and the forthcoming Global Precipitation Measuring (GPM) Mission, has fueled renewed interest in developing frameworks for downscaling and multi-sensor data fusion that can handle large data sets in computationally efficient ways while optimally reproducing desired properties of the underlying rainfall fields. Of special interest is the reproduction of extreme precipitation intensities and gradients, as these are directly relevant to hazard prediction. In this paper, we present a new formalism for downscaling satellite precipitation observations, which explicitly allows for the preservation of some key geometrical and statistical properties of spatial precipitation. These include sharp intensity gradients (due to high-intensity regions embedded within lower-intensity areas), coherent spatial structures (due to regions of slowly varying rainfall),and thicker-than-Gaussian tails of precipitation gradients and intensities. Specifically, we pose the downscaling problem as a discrete inverse problem and solve it via a regularized variational approach (variational downscaling) where the regularization term is selected to impose the desired smoothness in the solution while allowing for some steep gradients(called 1-norm or total variation regularization). We demonstrate the duality between this geometrically inspired solution and its Bayesian statistical interpretation, which is equivalent to assuming a Laplace prior distribution for the precipitation intensities in the derivative (wavelet) space. When the observation operator is not known, we discuss the effect of its misspecification and explore a previously proposed dictionary-based sparse inverse downscaling methodology to indirectly learn the observation operator from a database of coincidental high- and low-resolution observations. The proposed method and ideas are illustrated in case studies featuring the downscaling of a hurricane precipitation field.

Hurricanes↗