remote sensing Article Multiscale Decomposition Prediction of Propagation Loss in Oceanic Tropospheric Ducts Mingxia Dang 1, Jiaji Wu 1,*, Shengcheng Cui 2, Xing Guo 1, Yunhua Cao 3, Heli Wei 2 and Zhensen Wu 3 1 School of Electronic Engineering, Xidian University, Xi’an 710071, China; [email protected] (M.D.); [email protected] (X.G.) 2 Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China; [email protected] (S.C.); [email protected] (H.W.) 3 School of Physical and Optoelectronic Engineering, Xidian University, Xi’an 710071, China; [email protected] (Y.C.); [email protected] (Z.W.) * Correspondence: [email protected] Abstract: The oceanic tropospheric duct is a structure with an abnormal atmospheric refractive index. This structure severely affects the remote sensing detection capability of electromagnetic systems designed for an environment with normal atmospheric refraction. The propagation loss of electromagnetic waves in the oceanic duct is an important concept in oceanic duct research. Owing to the long-term stability and short-term irregular changes in marine environmental parameters, the propagation loss in oceanic ducts has nonstationary and multiscale time characteristics. In this paper, we propose a multiscale decomposition prediction method for predicting the propagation loss in oceanic tropospheric ducts. The prediction performance was verified by simulating propagation loss data with noise. Using different evaluation criteria, the experimental results indicated that the proposed method outperforms six other comparison methods. Under noisy conditions, ensemble empirical mode decomposition effectively disassembles the original propagation loss into a limited Citation: Dang, M.; Wu, J.; Cui, S.; Guo, X.; Cao, Y.; Wei, H.; Wu, Z. number of stable sequences with different scale characteristics. Accordingly, predictive modeling was Multiscale Decomposition Prediction conducted based on multiscale propagation loss characteristic sequences. Finally, we reconstructed of Propagation Loss in Oceanic the predicted result to obtain the predicted value of the propagation loss in the oceanic duct. Addi- Tropospheric Ducts. Remote Sens. tionally, a genetic algorithm was used to improve the generalization ability of the proposed method 2021, 13, 1173. https://doi.org/ while avoiding the nonlinear predictor from falling into a local optimum. 10.3390/rs13061173 Keywords: propagation loss in oceanic tropospheric duct prediction; nonlinear prediction; division- Academic Editor: Edoardo Pasolli and-conquest strategy; artificial neural network optimization Received: 31 January 2021 Accepted: 15 March 2021 Published: 19 March 2021 1. Introduction The oceanic tropospheric duct often occurs in sea areas with large negative refraction Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in gradients. [1]. The propagation process of electromagnetic (EM) waves in an oceanic duct is published maps and institutional affil- shown in Figure1. The duct traps EM waves at a particular frequency and elevation range iations. and changes their propagation direction. EM waves propagate periodically in the duct layer with a weak propagation loss as they propagate in a metal conduit [2]. In oceanic ducts, the propagation loss of radar radio waves is frequently weaker than in environments with normal refractive indices; hence, the coverage and range of remote sensing-based detection capability will be expanded [3,4]. Correspondingly, oceanic ducts will also produce adverse Copyright: © 2021 by the authors. effects, such as communication blind spots and electromagnetic holes. The propagation Licensee MDPI, Basel, Switzerland. This article is an open access article loss of EM waves in the oceanic tropospheric duct is an important concept in oceanic distributed under the terms and duct research and has important applications in the performance evaluation of remote conditions of the Creative Commons sensing radar, the design and evaluation of maritime communication systems, and the Attribution (CC BY) license (https:// monitoring theory of oceanic atmospheric ducts. Therefore, the study of the propagation creativecommons.org/licenses/by/ loss of EM waves in an oceanic duct environment can aid in improving the performance of 4.0/). Remote Sens. 2021, 13, 1173. https://doi.org/10.3390/rs13061173 https://www.mdpi.com/journal/remotesensing Remote Sens. 2021, 13, x FOR PEER REVIEW 2 of 23 Remote Sens. 2021, 13, 1173 2 of 23 the performance of remote sensing radar or communication systems, as well as fully uti- remotelizing the sensing information radar or conveyed communication by the systems, propagation as well loss as to fully study utilizing the joint the informationinversion of conveyedatmospheric by theducts propagation [5–8]. loss to study the joint inversion of atmospheric ducts [5–8]. Normal Refraction Upper boundary Oceanic Duct Layer Trap Lower Rough Sea Level Refraction boundary FigureFigure 1.1.Propagation Propagation ofof electromagneticelectromagnetic waveswaves in in an an oceanic oceanic duct duct layer. layer. TheThe randomrandom weatherweather processprocess andand interactioninteraction ofof meteorologicalmeteorological factorsfactors inin an an oceanic oceanic ductduct environmentenvironment willwill causecause complexcomplex fluctuationsfluctuations inin propagationpropagation lossloss inin timetime andand space.space. ForFor aa longlong time,time, thethe predictionprediction ofof EMEM wavewave propagationpropagation lossloss inin thethe oceanicoceanic ductduct environ-environ- mentment hashas been been primarily primarily based based on on the the following following three three methods: methods: ray ray tracing tracing (RT) (RT) theory theory [9]; mode[9]; mode theory theory [10]; [10]; and parabolicand parabolic equation equation (PE) (PE) theory theory [11]. [11]. By introducing By introducing the split-step the split- Fourierstep Fourier transform transform (SSFT) (SSFT) and its and variant, its variant, the PE the method PE method has been has widely been usedwidely considering used con- thesidering effects the of effects the atmospheric of the atmospheric refractive refractive index [12 ,index13]. However, [12,13]. However, quantifying quantifying the patterns the ofpatterns oceanic of ducts oceanic is difficult. ducts is difficult. As the main As the factor main causing factor propagationcausing propagation loss in the loss oceanic in the duct,oceanic sea duct, breezes sea arebreezes uncertain are uncertain and seasonal and seasonal [14,15]. An[14,15]. actual An sea actual breeze sea isbreeze frequently is fre- gustyquently and gusty varies and in intensity;varies in hence,intensity; the hence, roughness the ofroughness the sea surface of the causedsea surface by sea caused breezes by changes.sea breezes The changes. PE method The PE has method difficulty has in difficulty describing in describing the effects the of effects this dynamic of this dynamic change on the propagation loss by introducing a roughness attenuation factor and estimating the change on the propagation loss by introducing a roughness attenuation factor and esti- grazing angle [16–18]. In addition, the actual structure of an oceanic duct has horizontal mating the grazing angle [16–18]. In addition, the actual structure of an oceanic duct has inhomogeneity. The horizontal inhomogeneity of an oceanic duct is primarily divided into horizontal inhomogeneity. The horizontal inhomogeneity of an oceanic duct is primarily partial horizontal inhomogeneity caused by obstacles (such as islands and passing ships) divided into partial horizontal inhomogeneity caused by obstacles (such as islands and and large-scale horizontal inhomogeneity of the duct caused by the difference between passing ships) and large-scale horizontal inhomogeneity of the duct caused by the differ- large-scale meteorological conditions and sea conditions. The horizontal inhomogeneity ence between large-scale meteorological conditions and sea conditions. The horizontal in- of the oceanic duct has a significant effect on the propagation loss [19,20]. The vertical homogeneity of the oceanic duct has a significant effect on the propagation loss [19,20]. refractive index distribution of the atmosphere at each step is required when using the The vertical refractive index distribution of the atmosphere at each step is required when PE method to calculate the propagation loss in an uneven horizontal duct. The refractive using the PE method to calculate the propagation loss in an uneven horizontal duct. The index profile of the oceanic duct can be estimated using wave refraction technology (RFC) orrefractive global positioning index profile system of the signals oceanic [21 duct–23]. can However, be estimated because using of the wave short refraction iteration steptech- ofnology the PE (RFC) (depending or global on positi the frequency,oning system the step signals range [21–23]. is between However, 200–900 because m), the of refractive the short indexiteration profile step must of the still PE be (depending adjusted through on the frequency, interpolation. the Meteorologicalstep range is between noise (such 200–900 as wind,m), the rain, refractive and hail index noise) profile is an must important still be noiseadjusted source through in various interpolation. sea areas Meteorologi- [24,25]. Its effectscal noise on the(such propagation as wind, rain, loss and should hail not noise) be ignored. is an important noise source