seas.norm: Calculate annual and seasonal 'normal' statistics, including...

In seas: Seasonal Analysis and Graphics, Especially for Climatology

Calculate annual and seasonal ‘normal’ statistics, including precipitation normals

Description

Calculates annual and seasonal ‘normal’ statistics on a seas.sum object, including precipitation normals for rain, snow and total precipitation.

Usage

seas.norm(x, var, fun = "median", norm = "days", year.filter,
          ann.only = FALSE, precip.norm = FALSE)

precip.norm(x, fun = "median", norm = "days", year.filter)

Arguments

x	seas.sum object
var	variable name for the ‘normal’; if omitted will use x$prime (the prime variable of the seas.sum object), or if precip.norm=TRUE will be "precip"
norm	variable for normalization of the sum, usually the number of "days" in each bin, but it can also be "active" to estimate the precipitation normal for days of active precipitation
year.filter	filter specific years for analysis
fun	character of an existing function object, or a function to operate across the number of years of observations, usually "mean" or "median" (default); details described below
ann.only	only annual statistics returned (saves time from other calculations)
precip.norm	logical; computes precipitation normal statistics, which is done slightly differently since it involves rain, snow and total precipitation; if TRUE, x$var must include "rain", "snow" and "precip" summed variables

Details

This function calculates the statistics of precipitation data on an annual and seasonal scope from a seas.sum object.

The seasonal input data are normalized by the number of days in each bin, to produce a precipitation rate in ‘mm/day’. This is because the number of days in each bin is not equal. The function fun is then applied to the normalized precipitation, and operates along each bin, across multiple years of data. The supplied function is usually "median" or "mean", but it can also be a built in R function, such as "var" for variance, or a composite such as:

function(i, na.rm)(quantile(i, 0.2, na.rm=na.rm, names=F))	the 20% quantile
function(i, na.rm)(mean(i, na.rm=na.rm)/(sd(i, na.rm=na.rm)^3))	skewness

If fun = "mean", then the statistics are straightforward (using apply), however if fun = "median" and there are more than 2 years of data, a different approach is taken. The median is a special case of the quantile function, where the probability is 50% of the population. The median and quantile functions are more resistant to outliers than mean, and can have advantages on precipitation data. Precipitation occurring at a given time of year does not have a normal distribution since it is a value that is not always occurring. It often has a left-skewed distribution, consisting of many zero measurements, and few extreme precipitation events.

In this function, if fun = "median" (default) the median function is only used to calculate the median annual precipitation. The quantile function is used to calculate the seasonal statistics, since the sum of medians applied in each bin are less than the median annual precipitation. This is because there are usually many measurements of no rain, which skew the distribution to the left. The percentile for the quantile function is found using a secant method (Cheny and Kincaid, 1999) such that the sum of the quantiles from each bin are equal to the median of the annual precipitation.

Snow and rain (which are the two components of precipitation) are calculated similarly (if fun = "median"). The annual total rain and snow amounts are determined by finding the percentile of a quantile function where the sum is equal to the median of the annual precipitation. The seasonal snow and rain amounts are independently found using the same method to find the seasonal precipitation. The fraction of the snow in each bin, snow.frac.b=snow.b/(snow.b+rain.b) is multiplied by the seasonal precipitation to determine the seasonal rain and snow amounts. This is because the sum of rain and snow in each bin does not equal the seasonal precipitation. This way, a figure with precip.only = TRUE and = FALSE will have identical daily precipitation rates in each bin.

The pitfalls of calculating precipitation ‘normals’ is that it assumes that precipitation occurs every day at a constant rate within each bin. This is not realistic, as the precipitation rates are much higher when it is actually occurring.

Value

Returns a precip.norm object, which is a list with the following elements:

seas	An array of seasonal precipitation statistics: precip, rain and snow (if precip.only = FALSE) are in ‘mm/day’; freq and na are the fraction of a day in which precipitation is occurring and that data is missing.
ann	Annual precipitation statistics. precip, rain and snow (if precip.only = FALSE) are in ‘mm/year’; active and na are the number of days per year which are active (for example, days with precipitation) and that data are missing.
width	from x
bins	from x
bin.lengths	maximum number of days in each bin
year.range	from x
start.day	from x
var	same as input parameter
units	units for var, usnig attr
long.name	long name for var, using attr
ann.only	ann.only same as input parameter
precip.only	from same as input parameter
a.cut	from x
fun	function used in analysis
id	from x
name	from x

Note

Seasonal data are explicitly normalized to a rate per day (i.e., mm/day), and not per month (i.e., mm/month). This is because a time-derivative per month has unequal intervals of time, ranging between 28 to 31 days. This directly creates up to 10% error in the analysis between months.

Units for annual normals, however, remain per year, since a year is a suitable time derivative.

Author(s)

Mike Toews

References

Cheny, E. W. and Kincaid, D. 1999, Numerical Mathematics and Computing, Pacific Grove: Brooks/Cole Pub., 671 p.

Guttman, N.B. 1989, ‘Statistical descriptors of climate’, American Meteorological Society, 70, 602–607.

See Also

plot.seas.norm, seas.var.plot, precip.dep

Examples

data(mscdata)

# calculate precipitation normal
dat <- mksub(mscdata, id=1108447)
dat.ss <- seas.sum(dat)
dat.nm <- precip.norm(dat.ss, fun="mean")

# plot precipitation normal
plot(dat.nm) # this is the same as plot.precip.norm(dat.nm)

# use precipitation normal
dat.dep <- precip.dep(dat, dat.nm)
plot(dep ~ date, dat.dep, type="l",
     main="CPD from mean normals")

seas documentation built on May 2, 2022, 5:08 p.m.