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Trend testing is essential for time sequence analysis. However, the existing trend testing methods mainly study the trends of the sequence as a whole, while there is a lack of feasible research tools for the internal trends of the sequence. Therefore, a non-parametric method was proposed to study the overall and internal trends of the sequence using the ideas of set pair, Cox-Stuart, Innovative Trend Analysis Methodology, and Mann-Kendall and applied to temperature and precipitation sequences. The applied study indicated that the overall and internal trends for global temperature were significantly increasing at the confidence level of α = 0.05. For precipitation, the trends (both overall and internal) of Laifeng and Leibo were increasing and decreasing, respectively, and some of the internal trends were significant (α = 0.05); however, the overall and internal trends of Pingbian and Sangzhi were not exactly the same, i.e., the trend of high (low) values in Pingbian (Sangzhi) was different from the other trends of the rest. In general, the method successfully tested not only the overall trends in temperature and precipitation, but also their internal (divided into low, middle, and high values) trends. These results agreed with the linear slope, Sen's slope, Mann-Kendall, and its improved. Therefore, the method can be used for trend analysis of the sequences.

The representation of spatial discrete data is crucial for the data analysis of meteorology, agriculture, geological exploration, and other fields. Among various methods for scattered data interpolation, the multiquadric (MQ) method is the most favorable in the field of surface construction. However, the classical MQ method has accuracy concern on the boundary and is time consuming for large dataset. This study proposes an algorithm by integrating the MQ method with trend surface analysis. In which, the low-order polynomial trend surface equation is first used to model the overall trend. Then, the MQ equation is applied to fit the residual surface after removal the trend from the data. Our implementation can eliminate the distortion in data missing areas by the classical MQ method, and the modeling efficiency can be improved significantly since the local MQ method divide the residual surface into a group of subsurfaces. The accuracy and efficiency of the proposed algorithm are validated on a synthetic model. The performance of the developed algorithm is further examined on the elevation data collected in Tibet and the seabed of a strait in Norway. The results show that with an equivalent resolution, the developed algorithm can be much more efficient than the classical MQ method and well-developed Kriging method.

• A nonparametric trend testing method was proposed. • The statistical values of this method have asymptotic normality. • It tests not only overall but also internal trends in precipitation and temperature. Trend testing is essential for time sequence analysis. However, the existing trend testing methods mainly study the trends of the sequence as a whole, while there is a lack of feasible research tools for the internal trends of the sequence. Therefore, a non-parametric method was proposed to study the overall and internal trends of the sequence using the ideas of set pair, Cox-Stuart, Innovative Trend Analysis Methodology, and Mann-Kendall and applied to temperature and precipitation sequences. The applied study indicated that the overall and internal trends for global temperature were significantly increasing at the confidence level of α = 0.05. For precipitation, the trends (both overall and internal) of Laifeng and Leibo were increasing and decreasing, respectively, and some of the internal trends were significant (α = 0.05); however, the overall and internal trends of Pingbian and Sangzhi were not exactly the same, i.e., the trend of high (low) values in Pingbian (Sangzhi) was different from the other trends of the rest. In general, the method successfully tested not only the overall trends in temperature and precipitation, but also their internal (divided into low, middle, and high values) trends. These results agreed with the linear slope, Sen's slope, Mann-Kendall, and its improved. Therefore, the method can be used for trend analysis of the sequences. [ABSTRACT FROM AUTHOR]