There are three trend line options for fitting a trend to the variable values along a dimension: linear, harmonic, and polynomial. The three trend fitting options are described below. In addition to the line options, there are two options to determine whether the pixels in the multidimensional imagery layer have a statistically significant trend: Mann-Kendall and Seasonal Mann-Kendall.

• Linear—The linear trend line is a best-fit straight line that is used to estimate simple linear relationships. A linear trend highlights a rate of change that is increasing or decreasing at a steady rate. The formula for the linear trend line is as follows:

  

  • y=The pixel's variable value
  • x=The dimension value
  • ß₀=The y-intercept

  • ß₁=The linear slope or rate of change

    ß₁>0 indicates an increasing trend

    ß₁<0 indicates a decreasing trend
• Harmonic—The harmonic trend line is a periodically repeating curved line that is best used to describe data that follows a cyclical pattern, such as seasonal temperature changes. The formula for the harmonic trend line is as follows:

  

  • y=The pixel's variable value
  • t=The Julian date
  • ß₀=The y-intercept
  • ß₁=The rate of change
  • α, γ=Coefficients of inter-annual or intra-annual changes
  • ω=i
  • f=The harmonic frequency
• Polynomial—The polynomial trend line is a curved line that is useful for data that fluctuates. In this case, a polynomial order value is used to indicate the maximum number of fluctuations that occur. The formula for the polynomial trend line is as follows:

  

  • y=The pixel's variable value
  • x=The dimension value
  • ß₀, ß₁, ß₂, ß₃, ..., ß_n=Constant coefficients

• Mann-Kendall—Pixels will be evaluated using the Mann-Kendall trend test.

  The Mann-Kendall and Seasonal Mann-Kendall tests are used to determine whether there is a monotonic trend in the data. They are nonparametric, meaning they do not assume a specific distribution of data. The Mann-Kendall test does not consider serial correlation or seasonal effects. If the data is seasonal, the Seasonal Mann-Kendall test is more appropriate.
• Seasonal-Kendall—Pixel values will be evaluated using the Seasonal Mann-Kendall trend test.

• RMSE—Specifies whether the root mean square error (RMSE) of the trend fit line will be calculated. If selected, RMSE will be calculated and included as one of the bands of the trend imagery layer.
• R-squared—Specifies whether the R-squared goodness-of-fit statistic for the trend fit line will be calculated. If selected, the R-squared value will be calculated and included as one of the bands of the trend imagery layer.
• P-value of slope coefficient—Specifies whether the p-value statistic for the slope coefficient of the trend line will be calculated. If selected, the p-value will be calculated and included as one of the bands of the trend imagery layer.