## 1 Introduction
The rain use efficiency (RUE) as proposed by [19]--the ratio of NPP to rainfall--has been used as an indicator of degradation [7; 17; 20; 26; 27] and ecosystem functioning [18; 28]. The residual trend analysis (RESTEND) method as proposed by [11] was used frequently to estimate changes in productivity by relating annual maximum NDVI and precipitation [11; 13; 25; 29]. In the second category, the breaks for additive and seasonal and trend (BFAST) developed by [30; 31], have been employed to assess change in vegetation phenology with time (e.g., [32]). Both RESTEND and BFAST, however, have limitations in accurately detecting land degradation when the relationship between vegetation and climate breaks and due to oversensitiveness in areas where natural climate variabilities are prevalent, respectively [5; 8; 22]. Over sensitiveness is represented by the detection of false breakpoints using BFAST when dryland vegetation skips phonological cycles in response to drought while the ecosystem is healthy. The time series segmented residual trend analysis (TSS-RESTEND) method was developed by [8; 22; 23] to address this limitation by combining BFAST and RESTREND to detect the breakpoints where the relationship between vegetation and precipitation or temperature changes [8; 23]. The TSS-RESTREND leverages the ability of BFAST in detecting breakpoints in NDVI long timeseries [5; 8]. The TSS-RESTREND was applied to detect land degradation in Australia and its results were qualitatively evaluated using wildfire data [8]. However, the TSS-RESTREND lacked in providing a quantitative assessment of detected breakpoints [8]. About 40% of the United States of America (USA) land is classified as drylands [33]. The largest portion of these drylands is rangelands--comprising 31% of the USA land [34]--which are mostly situated in the Western USA [35]. Rangelands support livestock production particularly beef cattle and major local economies in the Great Plains, the Intermountain West, and the Southwest rely heavily on this industry [36]. Since the pre-settlement era, about 34% of the USA rangelands have been permanently modified by human activities [37]. Woody plants encroachment, invasive species, prolonged drought, low resilience and management of rangelands could be the most critical factors that can affect current and future rangeland productivity [37; 38]. Further, urban development, energy extraction (i.e., oil and gas), and expansion in agricultural lands are expected to contribute to rangelands fragmentation [39]. The degree to which climate variables (e.g., interannual variability of precipitation) can cause structural changes and affect forage productivity in New Mexico's (NM) rangeland ecosystems has not been adequately studied. Structural change in an ecosystems can be described as the significant change in the pattern of organization of the ecosystem necessary for functioning [35]. A structural change of rangeland was considered as when a pixel has a significant break in its vegetation- precipitation relationships (VPR) that leads to irreversible degradation or significant increase in productivity. Moreover, quantitative assessment of rangeland degradation and its impacts on NM's food-water-energy systems is critical for the sustainable use of its resources. The goal of this study was to identify long-term structural and productivity changes in rangeland ecosystems due to interannual climate variability based on precipitation in New Mexico during the 1982-2015 period. Taking advantage of the consistent NDVI timeseries of Global Inventory Modeling and Mapping Studies (GIMMS), the study tested the hypothesis that there is no significant change in rangeland productivity in NM between 1982-2015 by evaluating the prevalence of significant difference in NM's rangelands mean productivity before and after the years where the VPR breaks were occurred.