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The normalized difference vegetation index (NDVI) is one of the key input variables for developing drought indices. However, the NDVI quickly saturates in high vegetation surfaces, and thus, the generalization of a drought index over different ecosystems becomes a challenge. This paper presents a novel, dynamic stretching algorithm to overcome the saturation effect in NDVI. A scaling transformation function to eliminate saturation effects when the vegetation fraction (VF) is large is proposed. Dynamic range adjustment is conducted using three coefficients, namely, the normalization factor ( a), the stretching range controlling factor ( m), and the stretching size controlling factor ( e). The results show that the stretched NDVI (S-NDVI) is more sensitive to vegetation fraction than NDVI when the VF is large, ranging from 0.75 to 1.00. Moreover, the saturation effect in NDVI is effectively removed by using the S-NDVI. Further analysis suggests that there is a good linear correlation between the S-NDVI and the leaf area index (LAI). At the same time, the proposed S-NDVI significantly reduces or even eliminates the saturation effect over high biomass. A comparative analysis is performed between drought indices derived from NDVI and S-NDVI, respectively. In the experiment, reflectance data from the moderate resolution imaging spectroradiometer (MODIS) products and in-situ observation data from the meteorological sites at a regional scale are used. In this study, the coefficient of determination ( R) of the stretched drought index (S-DI) is above 0.5, indicating the reliability of the proposed algorithm with surface soil moisture content. Thus, the S-DI is suggested to be used as a drought index in extended regions, thus regional heterogeneity should be taken into account when applying stretching method. [ABSTRACT FROM AUTHOR]

Terrestrial ecosystem and climate system are closely related to each other. Faced with the unavoidable global climate change, it is important to investigate terrestrial ecosystem responding to climate change. In inland river basin of arid and semi-arid regions in China, sensitivity difference of vegetation responding to climate change from 1998 to 2007 was analyzed in this paper. (1) Differences in the global spatio-temporal distribution of vegetation and climate are obvious. The vegetation change shows a slight degradation in this whole region. Degradation is more obvious in densely vegetated areas. Temperature shows a general downward trend with a linear trend coefficient of −1.1467. Conversely, precipitation shows an increasing trend with a linear trend coefficient of 0.3896. (2) About the central tendency response, there are similar features in spatial distribution of both NDVI responding to precipitation (NDVI-P) and NDVI responding to AI (NDVI-AI), which are contrary to that of NDVI responding to air temperature (NDVI-T). Typical sensitivity region of NDVI-P and NDVI-AI mainly covers the northern temperate arid steppe and the northern temperate desert steppe. NDVI-T typical sensitivity region mainly covers the northern temperate desert steppe. (3) Regarding the fluctuation amplitude response, NDVI-T is dominated by the lower sensitivity, typical regions of the warm temperate shrubby, selui-shrubby, bare extreme dry desert, and northern temperate meadow steppe in the east and temperate semi-shrubby, dwarf arboreous desert in the north are high response. (4) Fluctuation amplitude responses between NDVI-P and NDVI-AI present a similar spatial distribution. The typical sensitivity region mainly covers the northern temperate desert steppe. There are various linear change trend responses of NDVI-T, NDVI-P and NDVI-AI. As to the NDVI-T and NDVI-AI, which are influenced by the boundary effect of semi-arid and semi-humid climate zones, there is less correlation of their linear change tendency along the border. There is stronger correlation in other regions, especially in the NDVI-T in the northern temperate desert steppe and NDVI-AI in the warm temperate shrubby, selui-shrubby, bare, extreme and dry desert. [ABSTRACT FROM AUTHOR]

In this paper, a simple, effective drought monitoring method is developed using two dimensional spectral space obtained from reflectance of near-infrared (NIR) and Red wavelengths. First, NIR–Red reflectance space is established using atmospheric and geometric corrected ETM+ data, which is manifested by a triangle shape and in which different surface targets possess certain spatial distribution rules. Second, perpendicular drought index (PDI) is developed on the basis of spatial characteristics of moisture distribution in NIR–Red space, as well as the relationships between PDI and soil moisture is examined. Validation work includes: comparison of PDI with in-situ drought index obtained from field measured data in the study area which includes bulk soil moisture content at different soil depths, field moisture capacity and wilting coefficient, etc.; and comparison of PDI with other recognized drought monitoring methods such as LST/NDVI and vegetation temperature condition index (VTCI). It is evident from the results that graph of PDI of field measured plots demonstrates very similar trends with ground truth drought data, LST/NDVI and VTCI. PDI is highly correlated with in-situ drought values calculated from 0 to 20 cm mean soil moisture with correlation coefficients of R 2 = 0.49 ( r = 0.75). This paper concludes that PDI has a potential in remote estimation of drought phenomenon as a simple, effective drought monitoring index. [ABSTRACT FROM AUTHOR]

Drought is a complex natural disaster that occurs frequently. Soil moisture has been the main issue in remote monitoring of drought events as the most direct and important variable describing the drought. Spatio-temporal distribution and variation of soil moisture evidently affect surface evapotranspiration, agricultural water demand, etc. In this paper, a new simple method for soil moisture monitoring is developed using near-infrared versus red (NIR-red) spectral reflectance space. First, NIR-red spectral reflectance space is established using atmospheric and geometric corrected ETM+ data, which is manifested by a triangle shape, in which different surface covers have similar spatial distribution rules. Next, the model of soil moisture monitoring by remote sensing (SMMRS) is developed on the basis of the distribution characteristics of soil moisture in the NIR-red spectral reflectance space. Then, the SMMRS model is validated by comparison with field measured soil moisture data at different depths. The results showed that satellite estimated soil moisture by SMMRS is highly accordant with field measured data at 5 cm soil depth and average soil moisture at 0–20 cm soil depths, correlation coefficients are 0.80 and 0.87, respectively. This paper concludes that, being simple and effective, the SMMRS model has great potential to estimate surface moisture conditions. [ABSTRACT FROM AUTHOR]

We present the analytical expressions of eigenstates and eigenenergies by using a parameter λ without the assumption of Bethe anzatz for three kinds of seven-bosonic-mode mixing models. The parameter is shown to be, determined by the roots of a simple polynomial. We also demonstrate the exact analytical expressions of eigenstates and energies without any unknown parameter. [ABSTRACT FROM AUTHOR]