Finds various measures of the phase of the annual cycle, or of some specified month range.

## Arguments

x A seasonal time series, or a class zoo object. A vector of two numbers specifying the season range to be considered. The form of the output. Additional arguments to be passed for changing integration defaults.

## Value

A data frame with columns year, time of the maximum, fulcrum, weighted mean time and -- in the case of zoo objects -- number of observations. In the case of seasonal time series, the results are all given as decimal seasons of the year. In the case of dated observations, the results can be dates, day of the year, or julian day with an origin of 1970-01-01, depending on the option out.

## Details

phenoPhase gives three measures of the phasing of a seasonal cycle: the time of the maximum (Cloern and Jassby 2008), the fulcrum or center of gravity, and the weighted mean season (Colebrook 1979). The latter has sometimes been referred to in the literature as “centre of gravity”, but it is not actually the same. These measures differ in their sensitivity to changes in the seasonal pattern, and therefore also in their susceptibility to sampling variability. The time of maximum is the most sensitive, the weighted mean the least.

These measures can be restricted to a subset of the year by giving the desired range of seasons. This can be useful for isolating measures of, say, the spring and autumn phytoplankton blooms in temperate waters. In the case of a seasonal time series, a non-missing value is required for every season or the result will be NA, so using a period shorter than one year can also help avoid any seasons that are typically not covered by the sampling program. Similarly, in the case of dated observations, a shorter period can help avoid times of sparse data. The method for time series allows for other than monthly frequencies, but season.range is always interpreted as months for zoo objects. The method for time series requires data for all seasons in season.range. The method for zoo objects will provide a result regardless of number of sampling days, so make sure that data are sufficient for a meaningful result.

The measures are annum-centric, i.e., they reflect the use of calendar year as the annum, which may not be appropriate for cases in which important features occur in winter and span two calendar years. Such cases can be handled by lagging the time series by an appropriate number of months, or by subtracting an appropriate number of days from the individual dates.

tsMake can be used to produce ts and zoo objects suitable as arguments to this function.

The default parameters used for the integrate function in phenoPhase may fail for certain datasets. Try increasing the number of subdivisions above its default of 100 by adding, for example, subdivisions = 1000 to the arguments of phenoPhase.

## References

Cloern, J.E. and Jassby, A.D. (2008) Complex seasonal patterns of primary producers at the land-sea interface. Ecology Letters 11, 1294--1303.

Colebrook, J.M. (1979) Continuous plankton records - seasonal cycles of phytoplankton and copepods in the North Atlantic ocean and the North Sea. Marine Biology 51, 23--32.

phenoAmp, tsMake

## Examples


# ts example
y <- sfbayChla[, 's27']
p1 <- phenoPhase(y)
p1
#>    year max.time fulcrum mean.wt
#> 1  1978       NA      NA      NA
#> 2  1979       NA      NA      NA
#> 3  1980        4    4.52    5.54
#> 4  1981       NA      NA      NA
#> 5  1982       NA      NA      NA
#> 6  1983       NA      NA      NA
#> 7  1984       NA      NA      NA
#> 8  1985       NA      NA      NA
#> 9  1986       NA      NA      NA
#> 10 1987        4    4.87    5.54
#> 11 1988       NA      NA      NA
#> 12 1989       NA      NA      NA
#> 13 1990       NA      NA      NA
#> 14 1991       NA      NA      NA
#> 15 1992       NA      NA      NA
#> 16 1993       NA      NA      NA
#> 17 1994       NA      NA      NA
#> 18 1995       NA      NA      NA
#> 19 1996        4    4.24    5.43
#> 20 1997       NA      NA      NA
#> 21 1998       NA      NA      NA
#> 22 1999       NA      NA      NA
#> 23 2000       11   10.51    8.66
#> 24 2001       NA      NA      NA
#> 25 2002       NA      NA      NA
#> 26 2003        2    3.15    4.29
#> 27 2004        3    5.03    6.06
#> 28 2005       NA      NA      NA
#> 29 2006       NA      NA      NA
#> 30 2007       NA      NA      NA
#> 31 2008        4    4.55    5.39
#> 32 2009       NA      NA      NAapply(p1, 2, sd, na.rm=TRUE)  # max.time > fulcrum > mean.wt
#>     year max.time  fulcrum  mean.wt
#> 9.380832 2.935821 2.391350 1.351158 phenoPhase(y, c(3, 10))
#>    year max.time fulcrum mean.wt
#> 1  1978       NA      NA      NA
#> 2  1979        6    6.11    6.17
#> 3  1980        4    4.56    5.33
#> 4  1981       NA      NA      NA
#> 5  1982       NA      NA      NA
#> 6  1983        5    4.74    4.97
#> 7  1984        4    4.71    5.55
#> 8  1985       NA      NA      NA
#> 9  1986       NA      NA      NA
#> 10 1987        4    5.11    5.52
#> 11 1988        4    5.48    5.80
#> 12 1989        4    4.48    5.10
#> 13 1990       NA      NA      NA
#> 14 1991       NA      NA      NA
#> 15 1992       NA      NA      NA
#> 16 1993       NA      NA      NA
#> 17 1994        3    5.28    5.15
#> 18 1995        3    4.12    4.79
#> 19 1996        4    4.28    4.96
#> 20 1997        4    4.46    5.37
#> 21 1998       NA      NA      NA
#> 22 1999       NA      NA      NA
#> 23 2000        4    4.40    5.16
#> 24 2001       NA      NA      NA
#> 25 2002       NA      NA      NA
#> 26 2003        3    4.86    5.09
#> 27 2004        3    5.78    5.77
#> 28 2005       NA      NA      NA
#> 29 2006       NA      NA      NA
#> 30 2007       NA      NA      NA
#> 31 2008        4    4.73    5.29
#> 32 2009       NA      NA      NA
# zoo example
sfb <- wqData(sfbay, c(1,3,4), 5:12, site.order = TRUE, type = "wide",
time.format = "%m/%d/%Y")
y <- tsMake(sfb, focus = 'chl', layer = c(0, 5), type = 'zoo')
phenoPhase(y[, 's27'])
#>    year   max.time    fulcrum    mean.wt  n
#> 1  1985 1985-03-29 1985-03-31 1985-04-19 17
#> 2  1986 1986-04-29 1986-04-25 1986-04-27 21
#> 3  1987 1987-04-16 1987-05-13 1987-05-18 20
#> 4  1988 1988-04-14 1988-04-27 1988-06-09 16
#> 5  1989 1989-03-01 1989-04-12 1989-04-12 25
#> 6  1990 1990-04-12 1990-04-30 1990-04-21 13
#> 7  1991 1991-04-11 1991-05-14 1991-04-22 18
#> 8  1992 1992-04-14 1992-04-26 1992-04-25 21
#> 9  1993 1993-03-25 1993-04-02 1993-04-04 17
#> 10 1994 1994-03-04 1994-05-06 1994-04-20 20
#> 11 1995 1995-03-30 1995-04-16 1995-04-11 22
#> 12 1996 1996-04-03 1996-04-09 1996-04-21 21
#> 13 1997 1997-02-19 1997-04-20 1997-04-06 20
#> 14 1998 1998-04-09 1998-04-14 1998-04-10 23
#> 15 1999 1999-03-24 1999-06-05 1999-06-04 13
#> 16 2000 2000-11-09 2000-11-06 2000-07-26 16
#> 17 2001 2001-04-16 2001-04-15 2001-04-27 16
#> 18 2002 2002-03-12 2002-03-17 2002-05-21 13
#> 19 2003 2003-02-24 2003-03-21 2003-04-03 21
#> 20 2004 2004-03-24 2004-05-16 2004-05-22 18