The variable-step L1 scheme preserving a compatible energy law for time-fractional Allen-Cahn equation

In this work, we revisit the adaptive L1 time-stepping scheme for solving the time-fractional Allen-Cahn equation in the Caputo's form. The L1 implicit scheme is shown to preserve a variational energy dissipation law on arbitrary nonuniform time meshes by using the recent discrete analysis tools, i.e., the discrete orthogonal convolution kernels and discrete complementary convolution kernels. Then the discrete embedding techniques and the fractional Gr\"onwall inequality were applied to establish an $L^2$ norm error estimate on nonuniform time meshes. An adaptive time-stepping strategy according to the dynamical feature of the system is presented to capture the multi-scale behaviors and to improve the computational performance.Comment: 17 pages, 20 figures, 2 table

Model Debiasing via Gradient-based Explanation on Representation

Machine learning systems produce biased results towards certain demographic groups, known as the fairness problem. Recent approaches to tackle this problem learn a latent code (i.e., representation) through disentangled representation learning and then discard the latent code dimensions correlated with sensitive attributes (e.g., gender). Nevertheless, these approaches may suffer from incomplete disentanglement and overlook proxy attributes (proxies for sensitive attributes) when processing real-world data, especially for unstructured data, causing performance degradation in fairness and loss of useful information for downstream tasks. In this paper, we propose a novel fairness framework that performs debiasing with regard to both sensitive attributes and proxy attributes, which boosts the prediction performance of downstream task models without complete disentanglement. The main idea is to, first, leverage gradient-based explanation to find two model focuses, 1) one focus for predicting sensitive attributes and 2) the other focus for predicting downstream task labels, and second, use them to perturb the latent code that guides the training of downstream task models towards fairness and utility goals. We show empirically that our framework works with both disentangled and non-disentangled representation learning methods and achieves better fairness-accuracy trade-off on unstructured and structured datasets than previous state-of-the-art approaches

Daily MODIS 500 m Reflectance Anisotropy Direct Broadcast (DB) Products for Monitoring Vegetation Phenology Dynamics

Land surface vegetation phenology is an efficient bio-indicator for monitoring ecosystem variation in response to changes in climatic factors. The primary objective of the current article is to examine the utility of the daily MODIS 500 m reflectance anisotropy direct broadcast (DB) product for monitoring the evolution of vegetation phenological trends over selected crop, orchard, and forest regions. Although numerous model-fitted satellite data have been widely used to assess the spatio-temporal distribution of land surface phenological patterns to understand phenological process and phenomena, current efforts to investigate the details of phenological trends, especially for natural phenological variations that occur on short time scales, are less well served by remote sensing challenges and lack of anisotropy correction in satellite data sources. The daily MODIS 500 m reflectance anisotropy product is employed to retrieve daily vegetation indices (VI) of a 1 year period for an almond orchard in California and for a winter wheat field in northeast China, as well as a 2 year period for a deciduous forest region in New Hampshire, USA. Compared with the ground records from these regions, the VI trajectories derived from the cloud-free and atmospherically corrected MODIS Nadir BRDF (bidirectional reflectance distribution function) adjusted reflectance (NBAR) capture not only the detailed footprint and principal attributes of the phenological events (such as flowering and blooming) but also the substantial inter-annual variability. This study demonstrates the utility of the daily 500 m MODIS reflectance anisotropy DB product to provide daily VI for monitoring and detecting changes of the natural vegetation phenology as exemplified by study regions comprising winter wheat, almond trees, and deciduous forest

Daily MODIS 500 m Reflectance Anisotropy Direct Broadcast (DB) Products for Monitoring Vegetation Phenology Dynamics

Land surface vegetation phenology is an efficient bio-indicator for monitoring ecosystem variation in response to changes in climatic factors. The primary objective of the current article is to examine the utility of the daily MODIS 500 m reflectance anisotropy direct broadcast (DB) product for monitoring the evolution of vegetation phenological trends over selected crop, orchard, and forest regions. Although numerous model-fitted satellite data have been widely used to assess the spatio-temporal distribution of land surface phenological patterns to understand phenological process and phenomena, current efforts to investigate the details of phenological trends, especially for natural phenological variations that occur on short time scales, are less well served by remote sensing challenges and lack of anisotropy correction in satellite data sources. The daily MODIS 500 m reflectance anisotropy product is employed to retrieve daily vegetation indices (VI) of a 1 year period for an almond orchard in California and for a winter wheat field in northeast China, as well as a 2 year period for a deciduous forest region in New Hampshire, USA. Compared with the ground records from these regions, the VI trajectories derived from the cloud-free and atmospherically corrected MODIS Nadir BRDF (bidirectional reflectance distribution function) adjusted reflectance (NBAR) capture not only the detailed footprint and principal attributes of the phenological events (such as flowering and blooming) but also the substantial inter-annual variability. This study demonstrates the utility of the daily 500 m MODIS reflectance anisotropy DB product to provide daily VI for monitoring and detecting changes of the natural vegetation phenology as exemplified by study regions comprising winter wheat, almond trees, and deciduous forest

Polarographic Analysis of Reductive Fading Reactions of 4-Aza-2\u27-ethyl-4\u27-Diethylaminophenyl-Quinones

This paper concerns the effect of substituent groups of phenolic couplers on dark stability of cyan quinonimine dyes deduced from the polarographic analysis of the solutions of two structure types of this class of dyes. These dyes were prepared by oxidative coupling of CD-2 developing agent (2-amino-5-diethylaminotoluene) with m-cresol or a 2-, 5-diacylamino-Pheno1. Polarographic measurements of these dyes were carried out in a mixture of ethanol and Britton-Robinson (borate-acetate-phosphate) buffer solution (volume ratio, 1.5 : 1) as a supporting electrolyte at 20±O.2℃,bubbled with nitrogen gas. Plots of E versus log {i/(i_d-i)} reveal that the leuco dye formations of these dyes are two-electron processes. In the case of the m-cresol dye, the proton number calculated from a plot of pH versus E_ was 2.8 in the range of pH 6.1～6.9,and 2.0, pH 7.1～7.8. Consequently, the fading reaction of the dye can be written as follows : Dye+2e+3H^+ → Leuco Dye・H^+ (Protonated Leuco Dye), in the lower pH region, and Dye+2e+2H^+ → Leuco Dye, in the higher pH region. The half-wave potential of the acylaminophenol dye was much more negative than that of the m-cresol dye. Thus, the fading reaction of the dye does not proceed easily in the presence of a reducing agent. The proton number that the dye required was approximately 2.0 in the pH range 5.9～7.6. The chemical equation for the redox reaction of the dye can be expressed as follows : Dye+2e+2H^+ → Leuco Dye. The m-cresol dye could be easily reduced and thus fade in the presence of thiosulfate or EDTA-Fe (II), because there was a big difference between the half-wave potential of the dye and these reducing agents. For example, in the faded solution with thiosulfate polarographic waves of the leuco dye and tetrathionate ions were observed separately. Therefore, the leuco dye formation of m-cresol dye in the fading reaction with reducing agent can be written as follows : Dye+2Red.+3H^+ → Leuco Dye・H^++2O_x. in the lower pH region, Dye+2Red.+2H^+ → Leuco Dye+2Ox. in the higher pH region. On the other hand, the half-wave potential of the acylamino-Phenol dye is close to those of the reducing agents. As 21 result, the polarographic waves of the leuco dye and the oxides of the reeucing agents were not observed separately. It is suggested that the cyan dye image formed with an acylaminophenol dye would be much more stable than a m-cresol dye under the reductive conditions. Consequently, some basic information to predict dad stability of cyan quinonimine dye images under reductive conditions can be obtained by measurement of the half-wave potential of dye solutions

Estimation of surface albedo and directional reflectance from Moderate Resolution Imaging Spectroradiometer (MODIS) observations

Land surface albedo is one of the key geophysical variables controlling the surface radiation budget. In recent years, land surface albedo products have been generated using data from various satellites. However, some problems exist in those products due to either the failure of the current retrieving procedures resulting from persistent clouds and/or abrupt surface changes, or the reduced temporal or spatial coverage, which may limit their applications. Rapidly generated albedo products that help reduce the impacts of cloud contamination and improve the capture of events such as ephemeral snow and vegetation growth are in demand. In this study, we propose a method for estimating the land surface albedo from Moderate Resolution Imaging Spectroradiometer (MODIS) data using a short temporal window. Instead of executing the atmospheric correction first and then fitting the surface reflectance in the current MODIS albedo procedure, the atmospheric properties (e.g., aerosol optical depth) and surface properties (e.g., surface bidirectional reflectance) were estimated simultaneously. Validations were carried out using various data sources including ground measurements (e.g., from the Surface Radiation (SURFRAD) Network and Greenland Climate Network (GC-Net)) and MODIS AERONET-based Surface Reflectance Validation Network (MODASRVN) data. The results showed comparable albedo estimates with both MODIS data and ground measurements, and the MODASRVN instantaneous surface reflectance was in good agreement with the reflectance estimation from our method. Aerosol optical depth (AOD) retrievals over SURFRAD and MODASRVN sites were also compared with ground measurements. Validation results showed estimation accuracies similar to those of MODIS aerosol products

Modifying Geometric-Optical Bidirectional Reflectance Model for Direct Inversion of Forest Canopy Leaf Area Index

Forest canopy leaf area index (LAI) inversion based on remote sensing data is an important method to obtain LAI. Currently, the most widely-used model to achieve forest canopy structure parameters is the Li-Strahler geometric-optical bidirectional reflectance model, by considering the effect of crown shape and mutual shadowing, which is referred to as the GOMS model. However, it is difficult to retrieve LAI through the GOMS model directly because LAI is not a fundamental parameter of the model. In this study, a gap probability model was used to obtain the relationship between the canopy structure parameter nR2 and LAI. Thus, LAI was introduced into the GOMS model as an independent variable by replacing nR2 The modified GOMS (MGOMS) model was validated by application to Dayekou in the Heihe River Basin of China. The LAI retrieved using the MGOMS model with optical multi-angle remote sensing data, high spatial resolution images and field-measured data was in good agreement with the field-measured LAI, with an R-square (R2) of 0.64, and an RMSE of 0.67. The results demonstrate that the MGOMS model obtained by replacing the canopy structure parameter nR2 of the GOMS model with LAI can be used to invert LAI directly and precisely

A Prior Knowledge-Based Method to Derivate High-Resolution Leaf Area Index Maps with Limited Field Measurements

High-resolution leaf area index (LAI) maps from remote sensing data largely depend on empirical models, which link field LAI measurements to the vegetation index. The existing empirical methods often require the field measurements to be sufficient for constructing a reliable model. However, in many regions of the world, there are limited field measurements available. This paper presents a prior knowledge-based (PKB) method to derivate LAI with limited field measurements, in an effort to improve the accuracy of empirical model. Based on the assumption that the experimental sites with the same vegetation type can be represented by similar models, a priori knowledge for crops was extracted from the published models in various cropland sites. The knowledge, composed of an initial guess of each model parameter with the associated uncertainty, was then combined with the local field measurements to determine a semi-empirical model using the Bayesian inversion method. The proposed method was evaluated at a cropland site in the Huailai region of Hebei Province, China. Compared with the regression method, the proposed PKB method can effectively improve the accuracy of empirical model and LAI estimation, when the field measurements were limited. The results demonstrate that a priori knowledge extracted from the universal sites can provide important auxiliary information to improve the representativeness of the empirical model in a given study area

Detecting Forest Disturbance in Northeast China from GLASS LAI Time Series Data Using a Dynamic Model

Large-scale forest disturbance often leads to changes in forest cover and structure, which imposes a great uncertainty in the estimation of the forest carbon cycle and biomass and affects other applications. In northeastern China, the Daxinganling region has abundant forest resources, where the forest coverage is about 30%. The Global LAnd Surface Satellite (GLASS) leaf area index (LAI) time series data provide important information to monitor the possible change of forests. In this study, we developed a new method to detect forest disturbances using GLASS LAI data over the Daxinganling region of Northeast China. As a dynamic model, the season-trend model has a higher sensitivity toward a seasonal change in LAI. Based on the accumulation of multi-year GLASS LAI products from 1997 to 2002, the dynamic model of LAI time series for each pixel is established first. The time-stepping modeling (TSM) process was designed by using the season-trend method, and sequential tests for detecting disturbances from a time series of pixels. Significant changes in the model parameters were captured as disturbance signals. Then, the near-infrared and shortwave-infrared bands of Moderate Resolution Imaging Spectroradiometer (MODIS) surface reflectance are used as auxiliary information to distinguish the types of forest disturbances. Here, the algorithm led to the detection of two different types of disturbances: fire and other (e.g., insect, drought, deforestation). In this study, we took the forest region as the study area, used the 8-day composite GLASS LAI data at 1000-m spatial resolution to identify each pixel as a fire disturbance, other disturbance, or non-disturbance. Validation was performed using reference burned area data derived from Landsat 30 m imagery. Results were also compared with the MCD64 product. The validation results were based on confusion matrices showing the overall accuracy (OA) exceeded 92% for our method and the MCD64 product. Statistical tests identified that TSM’s product accuracy is higher than that of MCD64. This study demonstrated that the TSM algorithm using a season-trend model provides a simple and automated approach to identify and map forest disturbance