NISTnls (version 0.9-13)

ENSO: Atmospheric pressure differences

Description

The ENSO data frame has 168 rows and 2 columns giving atmospheric pressure differences over time.

Format

This data frame contains the following columns:

y

A numeric vector of monthly averaged atmospheric pressure differences between Easter Island and Darwin, Australia.

x

A numeric vector of time values.

Source

Kahaner, D., C. Moler, and S. Nash, (1989). Numerical Methods and Software. Englewood Cliffs, NJ: Prentice Hall, pp. 441-445.

Details

The data are monthly averaged atmospheric pressure differences between Easter Island and Darwin, Australia. This difference drives the trade winds in the southern hemisphere. Fourier analysis of the data reveals 3 significant cycles. The annual cycle is the strongest, but cycles with periods of approximately 44 and 26 months are also present. These cycles correspond to the El Nino and the Southern Oscillation. Arguments to the SIN and COS functions are in radians.

Examples

Try <- function(expr) if (!inherits(val <- try(expr), "try-error")) val
plot(y ~ x, data = ENSO)
plot(y ~ x, data = ENSO, type = "l")  # to see the pattern more clearly
Try(fm1 <- nls(y ~ b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 ) 
                   + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 )
                   + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ),
            data = ENSO, trace = TRUE,
            start = c(b1 = 11.0, b2 = 3.0, b3 = 0.5, b4 = 40.0, b5 = -0.7,
                      b6 = -1.3, b7 = 25.0, b8 = -0.3, b9 = 1.4)))
Try(fm1a <- nls(y ~ b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 ) 
                    + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 )
                    + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ),
             data = ENSO, trace = TRUE, alg = "port",
             start = c(b1 = 11.0, b2 = 3.0, b3 = 0.5, b4 = 40.0, b5 = -0.7,
                       b6 = -1.3, b7 = 25.0, b8 = -0.3, b9 = 1.4)))
Try(fm2 <- nls(y ~ b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 ) 
                   + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 )
                   + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ),
            data = ENSO, trace = TRUE,
            start = c(b1 = 10.0, b2 =  3.0, b3 =  0.5, b4 = 44.0, b5 = -1.5,
                     b6 =  0.5, b7 = 26.0, b8 = -0.1, b9 =  1.5)))
Try(fm2a <- nls(y ~ b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 ) 
                    + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 )
                    + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ),
             data = ENSO, trace = TRUE, alg = "port",
             start = c(b1 = 10.0, b2 =  3.0, b3 =  0.5, b4 = 44.0, b5 = -1.5,
                     b6 =  0.5, b7 = 26.0, b8 = -0.1, b9 =  1.5)))
Try(fm3 <- nls(y ~ cbind(1, cos( 2*pi*x/12 ), sin( 2*pi*x/12 ), cos( 2*pi*x/b4 ),
                      sin( 2*pi*x/b4 ), cos( 2*pi*x/b7 ), sin( 2*pi*x/b7 )),
            data = ENSO, trace = TRUE,
            start = c(b4 = 40.0, b7 = 25.0), algorithm = "plinear"))
Try(fm4 <- nls(y ~ cbind(1, cos( 2*pi*x/12 ), sin( 2*pi*x/12 ), cos( 2*pi*x/b4 ),
                    sin( 2*pi*x/b4 ), cos( 2*pi*x/b7 ), sin( 2*pi*x/b7 )),
            data = ENSO, trace = TRUE,
            start = c(b4 = 44.0, b7 = 26.0), algorithm = "plinear"))