Good Approximation Research Articles

Comparison of time-domain and frequency-domain models for vibration prediction of a rail transit viaduct paved with floating slab track

Noise from rail transit viaducts often has a negative effect on surrounding buildings and nearby residents. To reduce the bridge vibration and radiated noise, floating slab tracks have been widely adopted in rail transit viaducts. To calculate the vibration of coupled track-bridge systems, both time-domain and frequency-domain methods can be applied although their relative performance is not very clear. This study aims to compare the two approaches and then provide some guidelines in choosing the appropriate method for predicting the vibration. The principle and methodology of the two calculation methods are firstly introduced, and the models for the train, floating slab track and bridge are developed using similar parameters. To further improve the efficiency and accuracy of the frequency-domain method, a half period method and a weighted average method are proposed to calculate the average responses of a certain point on the rail, floating slab and bridge to approximate the response during the pass-by. An indirect method is used to estimate the wheel–rail combined roughness from the measured rail acceleration when the train is running on the bridge, and compared with the direct measurement rail roughness. For the vibration of the bridge and floating slab, comparisons are made between results obtained from the time-domain and frequency-domain methods with different train speeds, and between results from experiment and simulation with different roughness. It is found that the wheel–rail contact forces and other structural responses from the two approaches show good consistency in the frequency region above 20 Hz. It is shown that a good approximation of the response during the pass-by can be obtained using the frequency-domain method by adopting the half period average or a simplified weighted average of two wheel position cases. When using the measured roughness and estimated roughness, the simulated vibration of the floating slab and bridge match well with the experimental results, and the indirect method can be used to modify direct measurement roughness in lower frequency regions. In the vibration prediction, the rail vibration or roughness, and other parameters in the vehicle–track–bridge system, should be measured accurately to ensure high reliability.

On a stabilization of the Ingard-Myers impedance boundary condition and its time domain implementation

It has been well-known that the Ingard-Myers impedance condition, while simple to apply, is subject to the hydrodynamic Kelvin-Helmholtz-type instability due to its use of a vortex sheet in modeling the flow at the liner boundary. Recently, in the development of a time domain boundary element method for acoustic scattering by treated surfaces, it was found that by neglecting a certain second-order spatial derivative term in the Ingard-Myers formulation, the hydrodynamic instability can be avoided. The present paper aims to provide further analysis of this modified condition, hereby referred to as the Truncated Ingard-Myers Impedance Boundary Condition (TIMIBC). It will be shown, based on the dispersion relations of linear waves, that the instability intrinsic to the Ingard-Myers condition is eliminated in the proposed new formulation. Quantitative assessments on the accuracy of the TIMIBC for scattering of acoustic waves by lined surfaces are carried out, and its effectiveness is demonstrated by a numerical example. It is found that the TIMIBC provides a good approximation to the original Ingard-Myers condition for flows of low to mid subsonic Mach numbers. As such, the proposed TIMIBC can offer a practical solution for overcoming the intrinsic instability associated with the Ingard-Myers condition. Moreover, time domain implementation of the TIMIBC is also discussed and illustrated with a numerical example using a finite difference scheme. In particular, a minimization procedure for finding the poles and coefficients of a broadband multipole expansion for the impedance function is formulated by which, unlike the commonly used vector-fitting method, passivity of the model is ensured.

On Aspects of Continuous Approximation of Diatomic Lattice

This paper is devoted to the continualization of a diatomic lattice, taking into account natural intervals of wavenumber changes. Continualization refers to the replacement of the original pseudo-differential equations by a system of PDEs that provides a good approximation of the dispersion relations. In this regard, the Padé approximants based on the conditions for matching the values of the dispersion relations of the discrete and continuous models at several characteristic points are utilized. As a result, a sixth-order unconditionally stable system with modified inertia is obtained. Appropriate boundary conditions are formulated. The obtained continuous approximation accurately describes the amplitude ratios of neighboring masses. It is also shown that the resulting continuous system provides a good approximation for the natural frequencies.

Analytic solutions to nonlinear ODEs via spectral power series

Solutions to most nonlinear ordinary differential equations (ODEs) rely on numerical solvers, but this gives little insight into the nature of the trajectories and is relatively expense to compute. In this paper, we derive analytic solutions to a class of nonlinear, homogeneous ODEs with linear and quadratic terms on the right-hand side. We formulate a power series expansion of each state variable, whose function depends on the eigenvalues of the linearized system, and solve for the coefficients using some linear algebra and combinatorics. Various experiments exhibit quickly decaying coefficients, such that a good approximation to the true solution consists of just a few terms.

Nonconforming virtual element methods for velocity-pressure Stokes eigenvalue problem

In this work, we investigate a divergence-free, nonconforming virtual element method for the numerical approximation of the Stokes eigenvalue problems using polygonal unstructured meshes on polygonal domain. By employing an elliptic projection operator, we “enhance” the definition of the virtual element space to make the L2-projection operator computable with optimal order. Furthermore, we prove the optimal order of convergence of the eigenfunction approximation and the double order of convergence of the eigenvalue approximation through compactness arguments for the solution operator (Babuška-Osborn Theory). Finally, we present a set of numerical experiments to assess the good approximation behavior of the method and show its computational performance.

The Temperature of the Deep Ocean Is a Robust Proxy for Global Mean Surface Temperature During the Cenozoic

AbstractReconstructing global mean surface temperature (GMST) is one of the key contributions that paleoclimate science can make in addressing societally relevant questions and is required to determine equilibrium climate sensitivity (ECS). GMST has been derived from the temperature of the deep ocean (Td), with previous work suggesting a simple Td‐GMST scaling factor of 1 prior to the Pliocene. However, this factor lacks a robust mechanistic basis, and indeed, is intuitively difficult to envisage given that polar amplification is a ubiquitous feature of past warm climate states and deep water overwhelmingly forms at high latitudes. Here, we interrogate whether and crucially, why, this relationship exists using a suite of curated data compilations and two sets of paleoclimate model simulations. We show that models and data are in full agreement that a 1:1 relationship is a good approximation. Taken together, the two sets of climate models suggest that (a) a lower sensitivity of SST in the season of deep water formation than high latitude mean annual SST in response to climate forcing, and moreover (b) a greater degree of land versus ocean surface warming are the two processes that act to counterbalance a possible polar amplification‐derived bias on Td‐derived GMST. Using this knowledge, we provide a new Cenozoic record of GMST. Our estimates are substantially warmer than similar previous efforts for much of the Paleogene and are thus consistent with a substantially higher‐than‐modern ECS during deep‐time high CO2 climate states.

Improvements in the Quantification of End-Member Vapor Compositions in Fluid Inclusion Boiling Assemblages and Implications for Metal Transport by Low-Density Fluids

Abstract Under conditions typically found in the Earth’s crust, there is a large pressure-temperature-composition range in the H2O-NaCl system where fluids may separate into a low-salinity vapor end member and a high-salinity liquid end member. However, heterogeneous trapping is common during the formation of fluid inclusions in an immiscible fluid system, violating the fundamental assumption of homogeneous entrapment for fluid inclusion microthermometry. This has profound consequences on the composition of these fluid phases and consequently on the formation of ore deposits from hydrothermal systems. At the same time, minor mixture of the high-salinity liquid phase with the low-salinity vapor phase cannot be distinguished from the end-member vapor-rich fluid inclusions by their bubble sizes. Precise determination of the salinities of vapor-rich fluid inclusions using microthermometry is deterred by the very small proportion of the liquid phase and the limitation of the analytical precision. All this will lead to erroneous compositional data from fluid inclusion analysis. We have quantitively calculated the variations of fluid inclusion properties caused by heterogeneous entrapment during phase separation in the H2O-NaCl system and showed that the salinity, and thereby the element contents and element/Na ratios of the vapor-rich fluid inclusions, is significantly changed in heterogeneously trapped fluid inclusions. The addition of 1 vol % of the high-salinity end member to the low-salinity end member results in a salinity change from 0.99 to 4.4 wt % NaCl equiv at the phase separation condition of 800 bar and 750°C. This will have a significant impact when it comes to determining the concentration of elements transported as chlorine complexes and typically leads to an overestimation of the mass transport capability by the vapor phase. Therefore, every effort should be taken during microthermometry to find and measure the least affected vapor-rich fluid inclusions. Our numerical calculations and synthetic fluid inclusions reveal that there is a linear relationship between the salinity and element contents for fluid inclusions at different extents of heterogeneous entrapment. Therefore, linear correction to the measured lowest vapor salinity can obtain a good approximation of the element contents in the end-member vapor phase.

Government consumption in the DINA framework: allocation methods and consequences for post-tax income inequality

About half of government expenditure in the United States takes the form of government consumption (e.g., education, defense, infrastructure). In many studies of post-tax inequality based on the Dina framework (including the influential study by Piketty et al. (Q J Econ 133(2):553–609, 2018), government consumption is allocated either proportionally to post-tax disposable income or on a per-capita basis, and the level of inequality is fairly sensitive to this choice. This paper provides direct evidence on how public education spending (a substantial part of government consumption) is actually distributed. An allocation proportional to post-tax disposable income is clearly rejected, while a lump-sum allocation is found to provide a good approximation.

On the non-local nature of turbulent fluxes of passive scalars

The parameterization of fluxes associated with representing unresolved dynamics in turbulent flows, especially in the atmosphere and ocean (which have a vast range of scales), remains a challenging task. This is especially true for Earth system models including complex biogeochemistry and requiring very long simulations. The problem of representing the dependence of the mean flux of a passive tracer in terms of the mean has a very long history; in this study, we take a somewhat different approach. We use a formalism showing that the mean flux will be a functional of the mean gradients, a formalism that can be used to calculate the structure of the functional which is non-local in both space and time. Two-dimensional turbulent simulations are used to explore the weight of nearby (in space or time) gradients. We also use stochastic velocities and iterated maps to show that the results are similar. The functional formalism provides an understanding of when non-locality needs to be considered and when a local eddy diffusivity can be a reasonably good approximation. Furthermore, the formalism provides guidance for the development of data-driven parameterizations.

Shear Strength and Durability of Expansive Soil Treated with Recycled Gypsum and Rice Husk Ash

Expansive soil underlying structures pose a significant risk to the integrity of superstructures. Chemical soil stabilization can be used to strengthen soils due to the cost and impracticality of mechanical approaches. Waste materials such as recycled gypsum and rice husk ash have been considered alternatives because of their sustainable and economic advantages. A combination of these additives was used to address the high absorption of gypsum and the lack of cohesion of the pozzolan. The study assessed the short-term and long-term performance of expansive soil treated with recycled gypsum and rice husk ash under normal and fluctuating moisture conditions. Direct shear tests indicated ductile and compressive soil behavior with improved shear strength. A good approximation of stress–strain response was made with a modified hyperbolic model for treated soils that exhibited strain hardening and compressive volumetric strain. Durability and water immersion tests were performed for samples after varying curing periods and cycles of capillary soaking to assess the behavior when exposed to varied environmental conditions. Samples under the modified durability test experienced significant strength loss, with decreasing compressive strength as curing durations increased. Specimens in the modified water immersion test experienced significant strength loss; however, it was determined that curing durations did not contribute to the change in the strength of the sample. Expansion index tests also determined that the treatment effectively mitigated expansivity and collapsibility in all samples. Despite improvement in shear strength and expansion potential, further investigation is needed to enhance the durability of soil treated with gypsum and rice husk ash.

Fatigue Crack Propagation of 51CrV4 Steels for Leaf Spring Suspensions of Railway Freight Wagons.

Leaf springs are critical components for the railway vehicle safety in which they are installed. Although these components are produced in high-strength alloyed steel and designed to operate under cyclic loading conditions in the high-cyclic fatigue region, their failure is still possible, which can lead to economic and human catastrophes. The aim of this document was to precisely characterise the mechanical crack growth behaviour of the chromium-vanadium alloyed steel representative of leaf springs under cyclic conditions, that is, the crack propagation in mode I. The common fatigue crack growth prediction models (Paris and Walker) considering the effect of stress ratio and parameters such as propagation threshold, critical stress intensity factor and crack closure ratio were also determined using statistical methods, which resulted in good approximations with respect to the experimental results. Lastly, the fracture surfaces under the different test conditions were analysed using SEM, with no significant differences to declare. As a result of this research work, it is expected that the developed properties and fatigue crack growth prediction models can assist design and maintenance engineers in understanding fatigue behaviour in the initiation and propagation phase of cracks in leaf springs for railway freight wagons.

Design of Quantum Gates Using Quantum Scattering Theory

Given two Hamiltonians \(H_0,H_1=H_0+V\) corresponding respectively to a free particle Hamiltonian and the free particle Hamiltonian plus its interaction energy with a scattering centre, we can compute the S-matrix, i.e., the matrix that determines the quantum mechanical amplitude of the process involving a particle coming from a free particle state at an infinite distance from the scattering centre at time \(t=-\infty\), entering into an initial scattered state, interacting with the scattering centre, entering into a final scattered state, and then escaping away to infinity at time \(t\rightarrow\infty\) to a final free particle state. Such amplitudes were first studied by Lippmann and Schwinger (Steven Weinberg, The Quantum Theory of Fields, Vol. 1, W.O. Amrein, Hilbert Space Methods in Quantum Mechanics) and then analyzed in a mathematically precise way by [T. Kato], [W. Amrein], and [K.B. Sinha]. In this paper, we first derive the Lippmann-Schwinger equation for the input and output scattered states in terms of the input and output free particle states using intuitive arguments originally due to Lippmann and Schwinger, and then, using rigorous operator theoretic arguments revolving around the spectral theorem for unbounded self-adjoint operators in a Hilbert space, we obtain an elegant formula for the scattering matrix elements in terms of the interaction potential and the free particle Hamiltonian between two free particle states corresponding to the same measure. We then discuss a computationally more efficient method based on the Dyson series expansion (Steven Weinberg, The Quantum Theory of Fields, Vol. 1), which works even in the case when the interaction Hamiltonian is time varying, in contrast to the Lippmann-Schwinger method, for calculating the S-matrix. We assume that the scattering potential, which can be time varying, can be controlled by incorporating control parameters and explain how the resulting unitary S-matrix can be made to approximate a given unitary gate in infinite-dimensional Hilbert space by optimizing the Hilbert-Schmidt/Frobenius norm distance between the given gate and the S-matrix gate, in which the latter is approximated by a truncated Dyson series. Of course, the S-matrix given by the Dyson series is a Taylor series functional expansion in the interaction potential and hence is a highly nonlinear function of the control parameters, and hence we propose numerical methods for such optimization. We then observe that if the control parameters are taken as random variables with joint moments, then the TPCP map involving statistical averaging of the adjoint action of the S-matrix acting on an initial mixed state w.r.t. the probability distribution of the control parameters will result in a final mixed state that is linear in the statistical moments of the control parameters, and hence optimization w.r.t. these moments can be easily carried out. Our method of TPCP map design is to optimize the sum of Frobenius distance squares between a sequence of desired output mixed states and the S-matrix based formula for the TPCP map acting on the corresponding input mixed states w.r.t. the statistical moments of the control parameters. We then generalize this method to include the case of TPCP maps obtained from the Hudson-Parthasarathy quantum noisy Schrödinger equation. In summary, we simulate the S-matrix gate for independent realizations of the control parameters having a probability distribution defined by their joint moments obtained by the above optimization procedure and apply the adjoint action of these independent S-matrices on a given input state, and take their ensemble average to obtain a good approximation to the action of the desired TPCP map on any given input state. This suggests that TPCP maps of arbitrarily large size can be realized using scattering experiments in the laboratory.

Effective Spatial Degrees of Freedom of Natural Temperature Variability as a Function of Frequency

Abstract A fundamental statistic of climate variability is its spatiotemporal correlation function. Its complex structure can be concisely summarized by a frequency-dependent measure of the effective spatial degrees of freedom (ESDOF). Here we present, for the first time, frequency-dependent ESDOF estimates of global natural surface temperature variability from purely instrumental measurements, using the HadCRUT4 dataset (1850–2014). The approach is based on a newly developed method for estimating the frequency-dependent spatial correlation function from gappy data fields. Results reveal a multicomponent structure of the spatial correlation function, including a large-amplitude short-distance component (with weak time scale dependence) and a small-amplitude long-distance component (with increasing relative amplitude toward the longer time scales). Two frequency-dependent ESDOF measures are applied, each responding mainly to either of the two components. Both measures exhibit a significant ESDOF reduction from monthly to multidecadal time scales, implying an increase of the effective spatial scale of natural surface temperature fluctuations. Moreover, it is found that a good approximation to the global number of equally spaced samples needed to estimate the variance of global mean temperature is given, at any frequency, by the greater one of the two ESDOF measures, decreasing from ∼130 at monthly to ∼30 at multidecadal time scales. Finally, the multicomponent structure of the correlation function together with the detected ESDOF scaling properties indicate that the ESDOF reduction toward the longer time scales cannot be explained simply by diffusion acting on stochastically driven anomalies, as it might be suggested from simple stochastic-diffusive energy balance models.

A Fast IAA–Based SR–STAP Method for Airborne Radar

Space–time adaptive processing (STAP) is an effective technology in clutter suppression and moving target detection for airborne radar. When working in the heterogeneous environment, the number of training samples that satisfy independent and identically distributed (IID) conditions is insufficient, making it difficult to ensure the estimation accuracy of the clutter plus noise covariance matrix for traditional STAP methods. Sparse recovery–based STAP (SR–STAP) methods have received widespread attention in the past few years. The accurate estimation of the clutter plus noise covariance matrix can be achieved using only a few training samples. The iterative adaptive approach (IAA) can quickly and accurately estimate the power spectrum, but applying this method directly to the STAP method cannot produce good performance. In this paper, a fast IAA–based SR–STAP method is proposed. Based on the weighted l1 problem, the IAA spectrum is used as a weighted term to obtain a good approximation. In order to obtain an analytical solution, we use the weighted l2 norm to approximate the weighted l1 norm without loss of performance. Compared with the IAA–STAP method, the proposed method is more robust to errors. Moreover, the proposed method has a fast computational speed. The effectiveness of the proposed method is demonstrated by simulations.

The Influence of Ink Chemistry on the Microstructure Evolution and GHz RF Response of Printed Ag Transmission Lines.

High-frequency transmission is limited to the skin depth in metals. Because poor conductivity cannot be compensated for by increasing the conductor thickness as with DC, optimal transport properties are prerequisites for radio frequency (RF) use. Structural and chemical analyses of transmission lines printed using a traditional ink consisting of Ag nanoflakes in a dispersing phase revealed that optimized thermal treatments yielded thorough burnout of the binder, significant grain growth, elimination of the pore volume, and electrical responses that were comparable to values obtained for thermally evaporated, fully dense Ag controls. Specifically, a low DC resistivity of 2.3 μΩ·cm (1.4× bulk Ag) and RF transmission coefficients of 0.87 and 0.75 at 5 GHz and 10 GHz, respectively, were measured in the nanoflake Ag prints. Conversely, in transmission lines printed from a metal-organic decomposition ink, residual chemical contamination impeded diffusion and densification, yielding greater porosity, small grains that are pinned, and a degraded RF response. Reasonably good porosity approximations were obtained from a model based on percolation theory. The results indicate that contaminants at interfaces and pore surfaces impede diffusion, pore elimination, and full densification, and further, alter carrier dynamics and degrade RF response.

Evaluating the performance of key ERA‐Interim, ERA5 and ERA5‐Land climate variables across Siberia

AbstractReanalysis datasets provide a continuous picture of the past climate for every point on Earth. They are especially useful in areas with few direct observations, such as Siberia. However, to ensure these datasets are sufficiently accurate they need to be validated against readings from meteorological stations. Here, we analyse how values of six climate variables—the minimum, mean and maximum 2‐metre air temperature, snow depth (SD), total precipitation and wind speed (WSP)—from three reanalysis datasets—ERA‐Interim, ERA5 and ERA5‐Land—compare against observations from 29 meteorological stations across Siberia and the Russian Far East on a daily timescale from 1979 to 2019. All three reanalyses produce values of the mean and maximum daily 2‐metre air temperature that are close to those observed, with the average absolute bias not exceeding 1.54°C. However, care should be taken for the minimum 2‐metre air temperature during the summer months—there are nine stations where correlation values are <0.60 due to inadequate night‐time cooling. The reanalysis values of SD are generally close to those observed after 1992, especially ERA5, when data from some of the meteorological stations began to be assimilated, but the reanalysis SD should be used with caution (if at all) before 1992 as the lack of assimilation leads to large overestimations. For low daily precipitation values the reanalyses provide good approximations, however they struggle to attain the extreme high values. Similarly, for the 10‐metre WSP; the reanalyses perform well with speeds up to 2.5 ms−1 but struggle with those above 5.0 ms−1. For these variables, we recommend using ERA5 over ERA‐Interim and ERA5‐Land in future research. ERA5 shows minor improvements over ERA‐Interim, and, despite an increased spatial resolution, there is no advantage to using ERA5‐Land.

A comparison of the accumulation-based, trip-based and time delay macroscopic fundamental diagram models

Macroscopic fundamental diagram (MFD) is widely applied in network modelling and management, such as route guidance and vehicle relocation, which are formulated as generalised dynamic traffic assignment (DTA) problems. MFD can effectively reduce the spatial dimension thus making the generalised DTA problems computationally efficient. In the literature, three MFD models, the accumulation-based model, the trip-based model, and the time delay model, were proposed to capture the traffic flow propagation under different traffic conditions and demand scenarios. However, no consensus has been reached on their computational efficiency and which model should be chosen under certain traffic conditions and demand scenarios. In this paper, we revisit these models regarding two important theoretical properties regarding flow propagation in the DTA, i.e. the first-in-first-out (FIFO) principle and causality. Corresponding dynamic network loading algorithms are designed to compare their numerical accuracy and computational efficiency. Numerical comparisons with Lighthill-Whitham-Richards (LWR) model and a micro simulator confirm that the accumulation-based model is valid in saturation, the trip-based model is valid in free-flow, while the time delay model provides a good approximation in both free-flow and saturation scenarios. On the other hand, violation of strict causality is observed in the accumulation-based and trip-based models, rendering it hard to pursue analytical DTA. This issue is not observed in the time delay model. Overall, the time delay model is a promising alternative for dynamic network loading in large-scale network applications.

Spatial modeling tool to assess and rank peri-urban land use in an agricultural region of the Midwestern United States

America is the continent with the largest area of genetically modified crops, the United States being the leading producer. Numerous studies show a panorama of potential exposure from agricultural pesticide use for this types of crops near to cities across a vast region of the United States. For the reasons mentioned above, we have chosen to investigate the following issues in this study: How does the implementation of an indexbased spatial modeling tool effectively rank the proximity of peri-urban crops, and what factors impact its effectiveness across diverse peri-urban agricultural landscapes? To address these questions, the research employs the Crop Proximity Index (CPI) model in various cities across the Midwest region of the United States. Six hundred and seventy cities in the state of Iowa were selected, and their peripheries were analysed using weighted perimeter rings, from 0 to 2000 m. The Crop Proximity Index was used to simulate a model of proximity to crops by considering the spatial quantification occupied by agriculture, forest cover, shrubs, pastures and buffer zones. This index varies from 0 to 1 and serves to rank the cities under study. It was estimated that a Crop Proximity Index equal to or >0.8 is a good approximation to a model with less proximity of crops and that only 62 cities (9%) meet this condition. Some 457 cities (68%) have CPIs equal to or <0.5 due to the large areas of crops and the low peripheral forest levels. The CPI is an index that makes it possible to obtain vital exploratory data in order to focus on future research that would determine how the proximity of agro-industrial crops has possible negative consequences for the environment and human health in greater detail.

R-VGAL: a sequential variational Bayes algorithm for generalised linear mixed models

Models with random effects, such as generalised linear mixed models (GLMMs), are often used for analysing clustered data. Parameter inference with these models is difficult because of the presence of cluster-specific random effects, which must be integrated out when evaluating the likelihood function. Here, we propose a sequential variational Bayes algorithm, called Recursive Variational Gaussian Approximation for Latent variable models (R-VGAL), for estimating parameters in GLMMs. The R-VGAL algorithm operates on the data sequentially, requires only a single pass through the data, and can provide parameter updates as new data are collected without the need of re-processing the previous data. At each update, the R-VGAL algorithm requires the gradient and Hessian of a “partial” log-likelihood function evaluated at the new observation, which are generally not available in closed form for GLMMs. To circumvent this issue, we propose using an importance-sampling-based approach for estimating the gradient and Hessian via Fisher’s and Louis’ identities. We find that R-VGAL can be unstable when traversing the first few data points, but that this issue can be mitigated by introducing a damping factor in the initial steps of the algorithm. Through illustrations on both simulated and real datasets, we show that R-VGAL provides good approximations to posterior distributions, that it can be made robust through damping, and that it is computationally efficient.

Application of generalised atomic wavelets in image processing problems

The problem of processing large data arrays is considered. Development of effective algorithms is the basis of successful application of new technologies. Complexity of the algorithm and accuracy of the results are the key quality indicators. The use of compact carrier functions leads to a decrease in processing time and complexity of the numerical algorithm. The accuracy of the data representation and the correctness of the results mainly depend on the approximation properties. It follows that a combination of the above characteristics is necessary to create efficient algorithms for processing large data sets. Aim of article – to develop and evaluate the possibilities of application of generalised wavelets based on Kravchenko-Rvachev functions for image processing with a given quality on the basis of the analysis of the quality loss control mechanism. Discrete image compression by Kravchenko-Rvachev functions possessing such fundamental qualities as good approximation properties, high order of smoothness and existence of a basis with a local carrier in spaces of atomic functions is considered. Since the generalised up-functions have the same properties, similar compression results can be obtained using the generalised discrete atomic transform, which is based on their application, which is a promising direction in digital image processing. The presented method of image processing can be used for various purposes, including reducing the size of data before their transmission through the communication channel from the sensor to the point of reception via a communication line with limited bandwidth, for storing the received images for their further use in the centres of information processing of remote sensing of the earth, as well as for data transmission to potential users.