## 1 Introduction  
The occurrence and intensity of extreme climate events have significantly increased due to the large-scale climate warming observed since the mid-20 th century [1, 2]. It is anticipated that this trend will only grow stronger in the future [3, 4]. Due to the unpredictable and destructive nature of an extreme climate, it has a negative impact on ecosystems and the social economy [5]. It has become evident that vegetation growth in terrestrial ecosystemsis significantly impacted by climate change [6]. Extreme climates have a greater and more pronounced impact on vegetation compared to a typical climate. This is due to the abrupt onset of extreme climate, which leaves vegetation communities with insufficient time to adapt, causing the population of crucial species in the ecosystem to decline, and causing terrestrial ecosystems to face significant challenges [7; 8; 9; 10; 11]. Vegetation change caused by extreme climate represents the most urgent and significant consequences of climate change for both the economy and the environment. As a result, extensive research has been implemented for the sake of the impacts of extreme climate upon vegetation [12; 13; 14; 15]; monitoring vegetation change and its response to climate extremes is essential to inform ecosystem mitigation responses [16]. Data obtained through remote sensing can be employed to observe the varying changes in vegetation [17]. Commonly used vegetation ecological indices include the Normalized Difference Vegetation Index (NDVI) [18], Fraction of Vegetation Cover (FVC) [19], Enhanced Vegetation Index (EVI) [20], Gross Primary Productivity (GPP) [21], and Net Primary Productivity (NPP) [22]. However, these vegetation ecological indices reflect only one of the vegetation indicators of vegetation coverage or productivity. The growth status of vegetation is not solely indicated by a single characteristic measure of vegetation productivity or coverage, and the outcomes are not exhaustive [23]. Therefore, some scholars have improved the vegetation index and constructed a comprehensive index through multiple vegetation ecological indices to reflect the comprehensive growth of vegetation. At present, the study on vegetation NPP and FVC is still in the research and application phase of individual estimation methods [14; 19], and few models and methods based on the two have been observed to estimate the overall ecological quality of vegetation [23]. In 2019, the China Meteorological Administration released the Land Vegetation Meteorological and Ecological Quality Monitoring and Evaluation Level, which introduced the Vegetation Ecological Quality Index (EQI) composed of the FVC and NPP as two key characteristic quantities to comprehensively reflect the overall condition of vegetation and ecosystems; by adjusting the weight coefficients of FVC and NPP, the EQI can be applied to different regions [24]. Currently, research on the EQI mainly focuses on monitoring dynamic changes in vegetation and reflecting the impact of climate change, human activities, and other factors on vegetation [25; 26; 27; 28]. There are also studies using the EQI to reflect the response of vegetation in the Yellow River Basin [29], the Chengdu-Chongqing Economic Zone in China [30], and the Aksu region of Xinjiang [31] to extreme climates. These studies have demonstrated the feasibility of using the EQI to study the dynamic changes in vegetation and its response to extreme climates. However, research on the EQI is still limited, especially in relation to the Tarim Basin EQI, which is currently restricted to the Aksu region on the northern edge of the Tarim Basin, and the weights of FVC and NPP in the EQI calculation of the Tarim Basin refer to the EQI calculation of the Aksu area [31]. The temporal and spatial characteristics of EQI changes are affected by the research period, region, and vegetation type, leading to some differences [29]. Therefore, it is necessary to conduct further research on the Tarim Basin EQI.