ABSTRACT. The discrete dynamics generated by a continuous map can be represented combinatorially by an appropriate multivalued map on a discretization of the phase space such as a cubical grid or triangulation. In this paper we provide explicit algorithms and computational complexity bounds for computing dynamical structures for the resulting combinatorial multivalued maps. Specifically we focus on the computation attractor-repeller pairs and Lyapunov functions for Morse decompositions. These discrete Lyapunov functions are weak Lyapunov functions and well-approximate a continuous Lyapunov function for the underlying map.

Abstract:Satellite remote sensing provides significant information for the monitoring of natural disasters. Recently, on a global scale, floods have been increasing both in frequency and in magnitude. In order to map the inundation area, flooding events are investigated using unique RGB composite imagery based on the MODIS surface reflectance (MOD09GA) data obtained from the Terra satellite, which is used to visualize and analyze these events. This study proposes using an RGB combination of MODIS band 6 (1.64 µm), band 5 (1.24 µm), and band 2 (0.86 µm) data from the visible and the near-infrared spectral ranges to map flood events. The flooding events that were investigated in this study occurred on 25 October 2015 along the Pampanga River in the Philippines, and on 28 July 2016 along the Poyang and Dongting Lakes in China. In the case of the Pampanga River, the inundated areas were estimated with surface reflectance (R) thresholds of 0.0 ≤ R 6 ≤ 0.102, 0.0 ≤ R 5 ≤ 0.138, and 0.03 ≤ R 2 ≤ 0.148 for MODIS bands 6, 5, and 2, respectively, which were determined using Otsu's method. The total inundated area was estimated to be 487.75 km 2 . This estimate was indirectly compared with the results obtained from SENTINEL-1A Synthetic Aperture Radar (SAR) data. The total inundated area on 26 October 2015 for the case of the Pampanga River was estimated to be 486.37 km 2 using histogram analysis based on Otsu's method. For the flooding case in China, the total estimated inundated area using MODIS RGB imagery on 28 July 2016 and SAR on 3 August 2016 was 1148.25 km 2 and 1110.096 km 2 , respectively. In addition, RGB imagery results using MODIS 6-5-2 bands were supported by the refractive index retrieval along the inundation area. A threshold of 1.6 for the real part of the complex refractive index allows for the discrimination between the flooded and non-flooded areas using the Hong and ASH approximations. This study shows that the RGB composite techniques using advanced sensors with more bands and higher spatio-temporal resolutions, and supported by the refractive index retrieval method, are useful for estimating flood events.

The visible band of satellite sensors is of limited use during the night due to a lack of solar reflection. This study presents an improved conditional generative adversarial networks (CGAN) model to generate virtual nighttime visible imagery using infrared multiband satellite observations and the brightness temperature difference between the two infrared bands in the Communication, Ocean and Meteorological Satellite. For summer daytime case study with visible band imagery, our multiband CGAN model showed better statistical results (correlation coefficient = 0.952, bias =-1.752 (in a digital number (DN) unit from 0 to 255, converted from reflectance from 0 to 1), and rootmean-square-error (RMSE) = 26.851 DN) than the single-band CGAN model using a pair of visible and infrared bands (correlation coefficient = 0.916, bias =-4.073 DN, and RMSE = 35.349 DN). The proposed multiband CGAN model performed better than the single-band CGAN model, particularly, in convective clouds and typhoons, because of the sounding effects from the water vapor band. In addition, our multiband CGAN model provided detailed patterns for clouds and typhoons at twilight. Therefore, our results could be used for visible-based nighttime weather analysis of convective clouds and typhoons, using data from next-generation geostationary meteorological satellites.

Accurate cloud-masking procedures to distinguish cloud-free pixels from cloudy pixels are essential for optical satellite remote sensing. Many studies on satellite-based cloud-detection have been performed using the spectral characteristics of clouds in terms of reflectance and temperature. This study proposes a cloud-detection method using reflectance in four bands: 0.56 μm, 0.86 μm, 1.38 μm, and 1.61 μm. Methodologically, we present a conversion relationship between the normalized difference water index (NDWI) and the green band in the visible spectrum for thick cloud detection using moderate-resolution imaging spectroradiometer (MODIS) observations. NDWI consists of reflectance at the 0.56 and 0.86 μm bands. For thin cloud detection, the 1.38 and 1.61 μm bands were applied with empirically determined threshold values. Case study analyses for the four seasons from 2000 to 2019 were performed for the sea surface area of the Yellow Sea and Bohai Sea. In the case studies, the comparison of the proposed cloud-detection method with the MODIS cloud mask (CM) and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation data indicated a probability of detection of 0.933, a false-alarm ratio of 0.086, and a Heidke Skill Score of 0.753. Our method demonstrated an additional important benefit in distinguishing clouds from sea ice or yellow dust, compared to the MODIS CM products, which usually misidentify the latter as clouds. Consequently, our cloud-detection method could be applied to a variety of low-orbit and geostationary satellites with 0.56, 0.86, 1.38, and 1.61 μm bands.

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