Reconstruction of missing data in remote sensing images using conditional stochastic optimization with global geometric constraints

This paper addresses the issue of missing data reconstruction for partially sampled, two-dimensional, rectangular grid images of differentiable random fields. We introduce a stochastic gradient–curvature (GC) reconstruction method, which is based on the concept of a random field model defined by means of local interactions (constraints). The GC reconstruction method aims to match the gradient and curvature constraints for the entire grid with those of the sample using conditional Monte Carlo simulations that honor the sample values. The GC reconstruction method does not assume a parametric form for the underlying probability distribution of the data. It is also computationally efficient and requires minimal user input, properties that make it suitable for automated processing of large data sets (e.g. remotely sensed images). The GC reconstruction performance is compared with established classification and interpolation methods for both synthetic and real world data. The impact of various factors such as domain size, degree of thinning, discretization, initialization, correlation properties, and noise on GC reconstruction performance are investigated by means of simulated random field realizations. An assessment of GC reconstruction performance on real data is conducted by removing randomly selected and contiguous groups of points from satellite rainfall data and an image of the lunar surface.     

Secular Love numbers of the major planets

Secular Love numbers of the major planets have been determined by solving the first (Dirichlet's) boundary — value problem for the level ellipsoid as the boundary surface. It has been demonstrated that the rotational distortions are responsible for the actual figure of the bodies above. The 6th degree Stokes zonal parameter for Uranus and for Neptune have been predicted.     

Mean Earth'S Equipotential Surface From Topex/Poseidon Altimetry

The geopotential value of W ₀ = (62 636 855.611 ± 0.008) m ² s ^–2 which specifies the equipotential surface fitting the mean ocean surface best, was obtained from four years (1993 - 1996) of TOPEX/POSEIDON altimeter data (AVISO, 1995). The altimeter calibration error limits the actual accuracy of W ₀ to about (0.2 - 0.5) m ² s ^–2 (2 - 5) cm. The same accuracy limits also apply to the corresponding semimajor axis of the mean Earth's level ellipsoid a = 6 378 136.72 m (mean tide system), a = 6 378 136.62 m (zero tide system), a = 6 378 136.59 m (tide-free). The variations in the yearly mean values of the geopotential did not exceed ±0.025 m ² s ^–2 (±2.5 mm).     

Tidal potential due to general bodies

The exact definition of the tidal potential is given on the basis of the theory of the restricted three-body problem. There are no limitations as regards the perturbing terms in the gravitational fields of the tide forming bodies; andno a priori conditions are needed in the definition.     

Long-Term Stability Of Geoidal Geopotential FromTopex/Poseidon Satellite Altimetry 1993–1999

The TOPEX/POSEIDON (T/P) satellite altimeter data from January 1, 1993to October 24, 1999 (cycles 11–261) was used for investigating thelong-term variations in the geoidal geopotential W₀ and/orin the geopotential scale factor R₀ = GM/W₀ (GM is theadopted geocentric gravitational constant). The mean valuesdetermined for the whole period covered are: W₀ =(62 636 856.161 ± 0.002) m² s^-2, R₀ =(6 363 672.5448 ± 0.0002) m. The actual accuracy is limited bythe altimeter calibration error (2–3 cm) and it isestimated to be about ± 0.5 m² s^-2 (± 5 cm).The yearly variations of the above mean values are at the formalerror level. No long-term trend in W₀, representing the oceanvolume change, was found for the seven years period 1993–9 on thebasis of T/P altimeter (AVISO) data. No sea surface topography modelwas used in the solution. This revised version was published online in July 2006 with corrections to the Cover Date.     

Comparison of satellite and terrestrial gravity data

Summary The integral mean values of gravity on the surface W=W ₀ , obtained from satellite observations with the use of harmonic coefficients[3, 7] and from terrestrial gravity measurements[12], are compared. The squares and products of the harmonic coefficients were neglected, with the exception of [J ₂ ⁽⁰⁾ ] ² , which was taken into account. The Potsdam correction and the geocentric constant are being discussed. The paper ties up with[13–15] and the symbols used are the same. The given problem was treated, e.g., in[2, 4, 6, 8–10]; in the present paper the values of gravity are compared directly.     

A new hybrid framework of site selection for groundwater recharge

Since incorrect site selection has sometimes led to the failure of artificial recharge projects,it is necessary to increase the effectiveness of such projects and minimize their failure by employing new techniques.Therefore,the present research used a combination of decision-making models,numerical groundwater modeling and clustering technique to determine suitable sites for implementation of an artificial recharge project.This hybrid approach was employed for the Yasouj aquifer located in southwestern Iran.In the first stage,by employing an AHP decision-making model,hydraulic conductivity,specific yield,slope,land use,depth to groundwater,and aquifer thickness were selected from 21 criteria used in previous research.The selected criteria were then entered as input into the classical k-means clustering model.Using the output,aquifer was divided into seven different regions or clusters.These clusters were then matched with the land use map,and some of the abandoned land areas were selected as the final option for implementing the artificial recharge project.Finally,the MODFLOW code in the GMS software was used to simulate the groundwater level and cluster the sites selected,with regards to increase in groundwater level.Results indicated that the most significant increases in groundwater level(43 and 27 cm) were those of Clusters 2 and 6 in the northern and western parts of the aquifer,respectively.Therefore,this approach can be used in other similar aquifers in arid and semi-arid regions to select the best sites for artificial recharge and to prevent loss of floodwaters.     

The geopotential value <Emphasis Type="Italic">W</Emphasis><Subscript>0</Subscript> for specifying the relativistic atomic time scale and a global vertical reference system

The TOPEX/Poseidon (T/P) satellite alti- meter mission marked a new era in determining the geopotential constant W ₀. On the basis of T/P data during 1993–2003 (cycles 11–414), long-term variations in W ₀ have been investigated. The rounded value W ₀ = 62636856.0 ± 0.5) m ² s ⁻² has already been adopted by the International Astronomical Union for the definition of the constant L _G = W ₀/c ² = 6.969290134 × 10⁻¹⁰ (where c is the speed of light), which is required for the realization of the relativistic atomic time scale. The constant L _G , based on the above value of W ₀, is also included in the 2003 International Earth Rotation and Reference Frames Service conventions. It has also been suggested that W ₀ is used to specify a global vertical reference system (GVRS). W ₀ ensures the consistency with the International Terrestrial Reference System, i.e. after adopting W ₀, along with the geocentric gravitational constant (GM), the Earth’s rotational velocity (ω) and the second zonal geopotential coefficient (J ₂) as primary constants (parameters), then the ellipsoidal parameters (a,α) can be computed and adopted as derived parameters. The scale of the International Terrestrial Reference Frame 2000 (ITRF2000) has also been specified with the use of W ₀ to be consistent with the geocentric coordinate time. As an example of using W ₀ for a GVRS realization, the geopotential difference between the adopted W ₀ and the geopotential at the Rimouski tide-gauge point, specifying the North American Vertical Datum 1988 (NAVD88), has been estimated.