Short-wave Model Research Articles

A DPD Algorithm of Maximum Likelihood Based on DOAs and Doppler

Direct position determination (DPD) is a single step method that estimates the position of target by received signals. Localization in 3D scene is a complicated problem, because the signal propagation channel is complex, and it has many kinds of interference and noise. This paper establishes the Over-the-horizon (OTH) shortwave signals and line-of-sight propagation of ultra short wave model, and proposes a joint localization algorithm. We compare the Cramér-Rao Bound(CRB) and the root mean square error (RMSE) between the proposed algorithm and DPD used single information like DOA and Doppler. The simulation results verify the superiority of the proposed algorithm, and prove it has higher accuracy.

Dynamics of general higher-order rogue waves in the two-component long wave–short wave model of Newell type

An integrable two component long-wave–short-wave (2-LS) model of Newell type governing the resonant interaction between two capillary waves with a common gravity wave is considered. The general higher order rogue wave (RW) solutions of this system are obtained by employing the bilinear KP hierarchy reduction method. Our study explores three different families of RWs depending upon the root structure of an algebraic equation characterizing them. Those are the Nth-order bounded rogue waves, mixed bounded (N1,N2)th-order rogue waves and degradable bounded (N¯1,N¯2)th-order rogue waves, respectively, where N,N1,N2 are arbitrary positive integer and N¯1,N¯2 are arbitrary non-negative integers. It is interesting to note that the fundamental rogue wave in one short wave (SW) component can attain a peak amplitude as high as more than six times the background amplitude while it is three times the background amplitude in the other SW component. We identify that the Nth-order bounded rogue waves are composed of N(N+1)2 fundamental rogue waves, the mixed bounded (N1,N2)th-order rogue waves comprise N1th-order bounded rogue waves mixing with another type N2th-order bounded rogue waves existing in different state, and the degradable bounded (N¯1,N¯2)th-order rogue waves consist of N¯12+N¯22−N¯1(N¯2−1) fundamental rogue waves. Non-trivial super rouge waves are reported.

Rogue wave patterns of Newell type long-wave–short-wave model

The general rogue wave solutions of long-wave–short-wave model are obtained by using the Kadomtsev–Petviashvili (KP) hierarchy reduction method. Unlike previous studies, we have refined the differential operators involved in the solutions by eliminating the recursiveness. Based on the simplified expression, the rogue wave patterns from the second to fifth order are displayed. Specifically, there are N−1 (N≥2) polygonal patterns of Nth-order rogue waves, which are found to be connected to the Yablonskii–Vorob’ev polynomial hierarchy.

A new 3-component Degasperis–Procesi hierarchy

We propose a new 3-component Degasperis–Procesi (3-DP) system. By investigating the bi-Hamiltonian structure of the corresponding hierarchy, we find that the Hamiltonian functionals of the 3-DP hierarchy are local in the negative direction and homogeneous in both directions. We show that the 3-DP system is related to the first negative flow in a modified Yajima–Oikawa hierarchy via a reciprocal transformation. With the help of this reciprocal transformation and a Darboux transformation of the associated 3-DP system, we construct a Bäcklund transformation for the 3-DP system. Furthermore, we present a short-wave model of the 3-DP system.

Degenerate and non-degenerate vector solitons and their interactions in the two-component long-wave–short-wave model of Newell type

The focus of this paper is on the dynamics of degenerate and non-degenerate vector solitons and their collision scenarios in the two-component long-wave–short-wave (2-LS) model of Newell type. The model equation that we study here governs the resonance interactions between two capillary waves (short waves) with a common gravity wave (long wave) for the surface wave of deep water. These degenerate and non-degenerate soliton solutions of the 2-LS model of Newell type are constructed via the bilinear KP-hierarchy reduction method and are expressed in forms of determinants. The degenerate solitons having only single-hump or single-valley profiles can undergo both elastic and inelastic collisions. Two particular types of degenerate solitons are also obtained, i.e., bound state solitons and V/Y-shaped solitons. The non-degenerate solitons and their collision scenarios have more interesting properties in contrast with the degenerate ones. The obvious one is that the non-degenerate one solitons possess symmetric or asymmetric double-hump and double-valley profiles if they propagate with identical velocities in all short-wave (SW) and long-wave (LW) components. Additionally, the soliton wavenumbers in the SW components and the LW component are unequal if the ones in the two SW components propagate with different velocities. The non-degenerate two solitons can undergo two different types of elastic collision scenarios in both SW and LW components: shape-preserving and shape-changing scenarios. We also study the collisions of non-degenerate solitons with degenerate ones, and find some intriguing properties. For instance, if the degenerate one soliton in one of the two SW components vanishes into background, then there is only one fundamental non-degenerate soliton in the corresponding SW component. However, this fundamental non-degenerate soliton still alters its profile from a symmetric double-hump waveform to an asymmetric double-hump one during its propagation process without interacting with other solitons. Furthermore, it is found a new class of soliton solutions referred to as (1,2,3) solitons. In these new types of soliton solutions, one SW component has only a single soliton, the other SW component has two solitons, whereas the LW component has three solitons.

Performance Improvement of NIR Spectral Pattern Recognition from Three Compensation Models' Voting and Multi-Modal Fusion.

Inspired by aquaphotomics, the optical path length of measurement was regarded as a perturbation factor. Near-infrared (NIR) spectroscopy with multi-measurement modals was applied to the discriminant analysis of three categories of drinking water. Moving window-k nearest neighbor (MW-kNN) and Norris derivative filter were used for modeling and optimization. Drawing on the idea of game theory, the strategy for two-category priority compensation and three-model voting with multi-modal fusion was proposed. Moving window correlation coefficient (MWCC), inter-category and intra-category MWCC spectra, and k-shortest distances plotting with MW-kNN were proposed to evaluate weak differences between two spectral populations. For three measurement modals (1 mm, 4 mm, and 10 mm), the optimal MW-kNN models, and two-category priority compensation models were determined. The joint models for three compensation models’ voting were established. Comprehensive discrimination effects of joint models were better than their sub-models; multi-modal fusion was better than single-modal fusion. The best joint model was the dual-modal fusion of compensation models of one- and two-category priority (1 mm), one- and three-category priority (10 mm), and two- and three-category priority (1 mm), validation’s total recognition accuracy rate reached 95.5%. It fused long-wave models (1 mm, containing 1450 nm) and short-wave models (10 mm, containing 974 nm). The results showed that compensation models’ voting and multi-modal fusion can effectively improve the performance of NIR spectral pattern recognition.

Validation of the CERES Edition-4A Surface-Only Flux Algorithms

AbstractSurface radiative fluxes have been derived with the objective of supplementing top-of-atmosphere (TOA) radiative fluxes being measured under NASA’s Clouds and the Earth’s Radiant Energy System (CERES) project. This has been accomplished by using combinations of CERES TOA measurements, parameterized radiative transfer algorithms, and high-quality meteorological datasets available from reanalysis projects. Current CERES footprint-level products include surface fluxes derived from two shortwave (SW) and three longwave (LW) algorithms designated as SW models A and B and LW models A, B, and C. The SW and LW models A work for clear conditions only; the other models work for both clear and cloudy conditions. The current CERES Edition-4A computed surface fluxes from all models are validated against ground-based flux measurements from high-quality surface networks like the Baseline Surface Radiation Network and NOAA’s Surface Radiation Budget Network (SURFRAD). Validation results as systematic and random errors are provided for all models, separately for five different surface types and combined for all surface types as tables and scatterplots. Validation of surface fluxes is now a part of CERES processing and is used to continually improve the above algorithms. Since both models B work for clear and cloudy conditions alike and meet the accuracy requirement, their results are considered to be the most reliable and most likely to be retained for future work. Both models A have limited use given that they work for clear skies only. Models B will continue to undergo further improvement as more validation results become available.

High-order rogue waves of a long-wave-short-wave model of Newell type.

The long-wave-short-wave (LWSW) model of Newell type is an integrable model describing the interaction between the gravity wave (long wave) and the capillary wave (short wave) for the surface wave of deep water under certain resonance conditions. In the present paper, we are concerned with rogue-wave solutions to the LWSW model of Newell type. By combining the Hirota's bilinear method and the KP hierarchy reduction, we construct its general rational solution expressed by the determinant. It is found that the fundamental rogue wave for the short wave can be classified into three different patterns: bright, intermediate, and dark states, whereas the one for the long wave is always a bright state. The higher-order rogue wave corresponds to the superposition of fundamental ones. The modulation instability analysis shows that the condition of the baseband modulation instability where an unstable continuous-wave background corresponds to perturbations with infinitesimally small frequencies, coincides with the condition for the existence of rogue-wave solutions.

Breaking wave solutions of a short wave model

In this paper, the breaking wave solutions of a short wave model is investigated by employing the bifurcation method of dynamical systems. All possible explicit breaking kink wave solutions and compacton solutions are obtained. Dynamical analysis reveals that the loop solutions actually contain two or more branches of breaking wave solutions. Some previous results are improved.

Toward operational shortwave radiation modeling and retrieval over rugged terrain

Shortwave radiation (0.3–3.0μm) is a dominant component of land surface all-wave radiation budget. Reliable estimation of shortwave radiation throughout the globe is particularly important for an in-depth understanding of global changes. Unfortunately, a large number of existing space-based algorithms ignore the effects of topography by simply assuming that the surface is ideally flat. As pointed out by many studies, such neglect toward topographic effects leads to significant errors in derived radiation. This study proposes a shortwave topographic radiation model (SWTRM) by quantifying solar direct radiation shielding, occlusion of sky radiation, reflected radiation from nearby terrain, and invisibility of certain targets. To drive the SWTRM, an artificial neural network (ANN) approach was employed to generate multiple components of the shortwave radiation budget. The new model was run over the Tibetan Plateau region and used MODIS products coupled with digital elevation data (DEM). Topographically corrected shortwave fluxes were derived by coupling SWTRM and ANN outputs. The results show that: (1) the proposed SWTRM works well over mountainous regions; (2) the ANN-based shortwave model provides reasonable retrieval accuracy (RMSE <60W/m2, bias<13W/m2 for all shortwave radiation components). More importantly, the ANN model can simultaneously provide all radiation components that are indispensable for driving the SWTRM; (3) over mountainous areas, the induced error can exceed 600W/m2 for shortwave net flux. Hence, topographic effects cannot be neglected; and (4) topography and solar illumination angle are key modulators in deriving shortwave radiation from space, which control the magnitude and spatial distribution of shortwave radiation over mountainous regions.

The Initial-boundary Value Problem for the Ostrovsky-Vakhnenko Equation on the Half-line

We analyze an initial-boundary value problem for the Ostrovsky-Vakhnenko equation on the half-line. This equation can be viewed as the short wave model for the Degasperis-Procesi (DP) equation. We show that the solution u(x,t) can be recovered from its initial and boundary values via the solution of a vector Riemann-Hilbert problem formulated in the plane of a complex spectral parameter z.

GPU Compute Unified Device Architecture (CUDA)-based Parallelization of the RRTMG Shortwave Rapid Radiative Transfer Model

Radiative transfer of electromagnetic radiation through a planetary atmosphere is computed using an atmospheric radiative transfer model (RTM). One RTM is the rapid RTM (RRTM), which calculates both longwave and shortwave atmospheric radiative fluxes and heating rates. Broadband radiative transfer code for general circulation model (GCM) applications, rapid RTM for global (RRTMG), is based on the single-column reference code, RRTM. The focus of this paper is on the RRTMG shortwave (RRTMG_SW) model. Due to its accuracy, RRTMG_SW has been implemented operationally in many weather forecast and climate models. In this paper, we examine the feasibility of using graphics processing units (GPUs) to accelerate the RRTMG_SW for a massive amount of atmospheric profiles. In recent years, GPUs have emerged as a low-cost, low-power, and a very high-performance alternative to conventional central processing units (CPUs). GPUs can provide a substantial improvement in RRTMG speed by supporting the parallel computation of large numbers of independent radiative calculations in separate atmospheric profiles. A GPU-compatible version of RRTMG was implemented and thorough testing was performed to ensure that the original level of accuracy is retained. Our results show that GPUs can provide significant speedup over conventional CPUs. In particular, Nvidia’s Tesla K40 GPU card can provide a speedup of ${{202}} \times $ compared to its single-threaded Fortran counterpart running on Intel Xeon E5-2603 CPU, whereas the speedup for four CPU cores, on one CPU socket, with respect to 1 CPU core is ${{5}}.{{6}} \times $ .

Estimating Roof Solar Energy Potential in the Downtown Area Using a GPU-Accelerated Solar Radiation Model and Airborne LiDAR Data

Solar energy, as a clean and renewable resource is becoming increasingly important in the global context of climate change and energy crisis. Utilization of solar energy in urban areas is of great importance in urban energy planning, environmental conservation, and sustainable development. However, available spaces for solar panel installation in cities are quite limited except for building roofs. Furthermore, complex urban 3D morphology greatly affects sunlit patterns on building roofs, especially in downtown areas, which makes the determination of roof solar energy potential a challenging task. The object of this study is to estimate the solar radiation on building roofs in an urban area in Shanghai, China, and select suitable spaces for installing solar panels that can effectively utilize solar energy. A Graphic Processing Unit (GPU)-based solar radiation model named SHORTWAVE-C simulating direct and non-direct solar radiation intensity was developed by adding the capability of considering cloud influence into the previous SHORTWAVE model. Airborne Light Detection and Ranging (LiDAR) data was used as the input of the SHORTWAVE-C model and to investigate the morphological characteristics of the study area. The results show that the SHORTWAVE-C model can accurately estimate the solar radiation intensity in a complex urban environment under cloudy conditions, and the GPU acceleration method can reduce the computation time by up to 46%. Two sites with different building densities and rooftop structures were selected to illustrate the influence of urban morphology on the solar radiation and solar illumination duration. Based on the findings, an object-based method was implemented to identify suitable places for rooftop solar panel installation that can fully utilize the solar energy potential. Our study provides useful strategic guidelines for the selection and assessment of roof solar energy potential for urban energy planning.

The Ostrovsky–Vakhnenko equation by a Riemann–Hilbert approach*

We present an inverse scattering transform (IST) approach for the (differentiated) Ostrovsky–Vakhnenko equation u txx − 3 u x + 3 u x u xx + uu xxx = 0 . ?>This equation can also be viewed as the short wave model for the Degasperis–Procesi (sDP) equation. Our IST approach is based on an associated Riemann–Hilbert problem, which allows us to give a representation for the classical (smooth) solution, to get the principal term of its long time asymptotics, and also to describe loop soliton solutions.

Algebro-geometric Solutions for the Derivative Burgers Hierarchy

Though completely integrable Camassa-Holm (CH) equation and Degasperis-Procesi(DP)equationarecastinthesamepeakonfamily,theypossessthe second- and third-order Lax operators, respectively. From the viewpoint of algebro- geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyperelliptic curves lead to great difficulty in the construction of algebro- geometric solutions of the DP equation. In this paper, we study algebro-geometric solutions for the derivative Burgers (DB) equation, which is derived by Qiao and Li (2004) as a short wave model of the DP equation with the help of functional gradient and a pair of Lenard operators. Based on the characteristic polynomial of a Lax matrix for the DB equation, we introduce a third order algebraic curve Kr −1 with genus r − 1, from which the associated Baker-Akhiezer functions, meromorphic function, and Dubrovin-type equations are constructed. Furthermore, the theory of algebraic curve is applied to derive explicit representations of the theta function for the Baker- Akhiezerfunctionsandthemeromorphicfunction.Inparticular,thealgebro-geometric solutions are obtained for all equations in the whole DB hierarchy.

Evaluation of broadband surface solar irradiance derived from the Ozone Monitoring Instrument

Surface solar irradiance (SSI) data are important for planning and estimating the production of solar power plants. Long-term high quality surface solar radiation data are needed for monitoring climate change. This paper presents a new surface solar irradiance dataset, the broadband (0.2–4μm) surface solar irradiance product derived from the Ozone Monitoring Instrument (OMI). The OMI SSI algorithm is based on the Heliosat method and uses the OMI O2–O2 cloud product as main input. The OMI SSI data are validated against the globally distributed Baseline Surface Radiation Network (BSRN) measurements at 19 stations for the year 2008. Furthermore, the monthly mean OMI SSI data are compared to independent surface solar irradiance products from International Satellite Cloud Climatology Project Flux Data (ISCCP-FD) and Clouds and the Earth's Radiant Energy System (CERES) data for the year 2005. The mean difference between OMI SSI and BSRN global (direct+diffuse) irradiances is −1.2Wm−2 (−0.2%), the root mean square error is 100.1Wm−2 (18.1%), and the mean absolute error is 67.8Wm−2 (12.2%). The differences between OMI SSI and BSRN global irradiances are smaller over continental and coastal sites and larger over deserts and islands. OMI SSI has a good agreement with the CERES shortwave (SW) model B surface downward flux (SDF) product. The correlation coefficient and index of agreement between monthly mean 1-degree gridded OMI SSI and CERES SW SDF are >0.99. OMI SSI is lower than CERES SW SDF which is partly due to the solar zenith angle. On average, OMI SSI is 13.5Wm−2 (2.5%) lower than the ISCCP-FD SW surface downward flux and the correlation coefficient and index of agreement are >0.98 for every month.

The Ostrovsky–Vakhnenko equation: A Riemann–Hilbert approach

We present an inverse scattering transform approach for the (differentiated) Ostrovsky–Vakhnenko equation:utxx−3ux+3uxuxx+uuxxx=0. This equation can also be viewed as the short-wave model for the Degasperis–Procesi equation. The approach is based on an associated Riemann–Hilbert problem, which allows us to give a representation for the classical (smooth) solution of the Cauchy problem, to get the principal term of its long-time asymptotics, and also to find, in a natural way, loop soliton solutions.

Lie symmetries and exact solutions for a short-wave model

In this paper, the Lie symmetry analysis and generalized symmetry method are performed for a short-wave model. The symmetries for this equation are given, and the phase portraits of the traveling wave systems are analyzed using the bifurcation theory of dynamical systems. The exact parametric representations of four types of traveling wave solutions are obtained.

The short-wave model for the Camassa–Holm equation: a Riemann–Hilbert approach

We present the inverse scattering transform approach to the Cauchy problem on the line for the short-wave model for the Camassa–Holm equation in the form of an associated Riemann–Hilbert problem. This approach allows us to give a representation of the classical (smooth) solutions, describe their asymptotics as t → ∞ and describe cuspons—non-smooth soliton solutions with a cusp.

Loop soliton solutions of a short wave model for a degasperis-procesi equation

An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explicit analytic solutions of loop soliton governing the propagation of short waves were obtained. By means of the transformation of independent variables, an analysis one-loop soliton solution expressed by a series of exponential functions was obtained, which agreed well with the exact solution. The results reveal the validity and great potential of the homotopy analysis method in solving complicated solitary water wave problems.