Figure 1

Adaptive algorithm used to capture the trend signals for the global annual sea surface temperature (SST): (a) original data and trends determined by global linear trend and AFA with two window sizes; (b) the residuals related to the three trends. The residuals designated as the blue and the red curves had been shifted upward and downward by 0.5, respectively."

Figure 2

Adaptive algorithm used to capture the trend signals for Atlantic Multidecadal Oscillation (AMO): the detrended North Atlantic sea surface temperature anomalies data (grey) and the blue multideccadal signal are obtained from the NOAA°s website, http://www.cdc.noaa.gov/data/climateindices/List, the red and green signals are obtained by the adaptive algorithm. Clearly, the red curve is better than the blue one in tracing out the variations in the original signal, while the green curve is the best in only capturing the multidecadal oscillation."

Figure 3

Adaptive algorithm used to capture the trend signals of the soil moisture at 4 cm of A’rou station in the Heihe River Basin in different seasons"

Figure 4

Adaptive algorithm used to capture the detrended data of the raw soil moisture at 4 cm of A’rou station in the Heihe River Basin in different seasons"

Figure 5

Power spectral density (PSD) curves for the detrended soil moisture at 4 cm of A’rou station in the Heihe River Basin in different seasons (corresponding to Figure 4)"

Figure 6

A schematic of the three super stations at the Heihe River Basin: A’rou station, Daman station, and Sidaoqiao station"

Figure 7

AFA of wind speed data at the A’rou station (a1-c1), the Daman station (a2-c2), and the Sidaoqiao station (a3-c3) at 5 m, 10 m and 15 m from January 2015 to July 2015, respectively. The slopes denoted by H1 and H2 are the Hurst parameters."

Figure 8

Variation of the Hurst parameter for wind speed with heights for the three stations: (a) short time scale H1 and (b) long time scale H2."

Figure 9

Detecting chaos in the Colorado River flow data: (a): error growth curves; (b): SDLE curves. The blue (solid) and red (dashed) curves are for the original and denoised data, respectively. Here, embedding parameters are m=6, L=3, and different curves are based on a few different shells described by Eq. (16). Except at the initial stage in the error growth curves, they collapse on each other."