Background With the growth of trajectory data, the large amount of data causes a lot of problems with storage, analysis, mining, etc. Most of the traditional trajectory data compression methods are focused on preserving spatial characteristic information and pay little attention to other temporal information on trajectory data, such as speed change points or stop points. Methods A data compression algorithm based on the spatio-temporal characteristics (CASC) of the trajectory data is proposed to solve this problem. This algorithm compresses trajectory data by taking the azimuth difference, velocity difference and time interval as parameters in order to preserve spatial-temporal characteristics. Microsoft’s Geolife1.3 data set was used for a compression test to verify the validity of the algorithm. The compression results were compared with the traditional Douglas-Peucker (DP), Top-Down Time Ratio (TD-TR) and Opening Window (OPW) algorithms. Compression rate, the direction information of trajectory points, vertical synchronization distance, and algorithm type (online/offline) were used to evaluate the above algorithms. Results The experimental results show that with the same compression rate, the ability of the CASC to retain the forward direction trajectory is optimal, followed by TD-TR, DP, and then OPW. The velocity characteristics of the trajectories are also stably retained when the speed threshold value is not more than 100%. Unlike the DP and TD-TR algorithms, CASC is an online algorithm. Compared with OPW, which is also an online algorithm, CASC has better compression quality. The error distributions of the four algorithms have been compared, and CASC is the most stable algorithm. Taken together, CASC outperforms DP, TD-TR and OPW in trajectory compression.

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Based on energy balance theory, using Theil–Sen median trend analysis and the Mann–Kendall test, this research studied the applicability of the complementary theory of evapotranspiration (ET) over Ningxia in the Upper Reaches of the Yellow River with MOD16 ET product and the measured data of meteorological stations, based on which ET drought index (EDI) was proposed for the first time. Moreover, the usability of EDI was also verified and its influencing factors were analyzed. The results revealed that there was a complementary relationship between AET and PET in 91.1% of the area in Ningxia, including strictly complementary and asymmetrically complementary relationships in 69.2% and 21.9% of the total area, respectively. EDI ranged from 0 to 1 and was useful to accurately reflect the degree of drought of the study area on the annual and monthly scales. From 2001 to 2020, the average annual EDI was 0.66, and the smallest monthly EDI was in January and the largest was in May. EDI of different time scales had different influencing factors. Precipitation was the most influencing factor of annual EDI, but the influencing factors of monthly EDI was different over time. However, surface non-precipitation water replenishment, such as irrigation, had great impact both on annual EDI and monthly EDI. The application scope of the theory of ET complementarity was extended to the study area for the first time, and EDI was proposed and applied, which will provide a theoretical basis and empirical reference for drought research based on ET data in arid and semi-arid areas.

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