SPEI (version 1.0)

Kernel functions: Time kernel for computing the SPEI at different time scales.

Description

Function kern is used internally by spei and spifor computing drought indices at different time scales.

Usage

kern(scale, type = 'rectangular', shift = 0)
kern.plot(scale = 12, shift = 0)

Arguments

scale

numeric, time scale or length of the kernel.

type

character, shape of the kernel function.

shift

numeric, shifting of the kernel peak.

Value

• A vector of lenght equal to scale with weights used for computing the drought index.

Details

Drought indices, such as the SPEI or the SPI, are usually computed at different time scales to adapt to the different response times of systems affected by drought. This is acomplished by applying a kernel function to the data prior to computation of the SPEI. Aplication of a kernel has the effect of smoothing the temporal variability of the resulting SPEI, allowing for the major patterns to emerge from the noise. Other way of considering it is that the kernel allows incorporating information of previous time steps into the calculation of the current time step, so the resulting values of the SPEI adapt to the memory of the system under study.

The most common kernel function is rectangular, i.e. all the data of the previous n time steps are given equal weight. This was the way the Standardized Precipitation Index (SPI) was defined, and it is also the way the SPEI is computed. This would be the default option for the kern function. However, data from the past can be thought of as having a decreasing influence in the current state of the system as the temporal lag between them increases. The function kern allows weighting the past data as a function of the time lapse, according to a series of pre-defined shapes. Available options are 'rectangular' (default), 'triangular', 'circular' and 'gaussian'.

By default the highest weight will be given to the observation of the current month. However, it is possible to modify this by setting the shift parameter to a value higher than zero. This will cause the highest weight be given to the n antecedent observation.

kern.plot produces plots of the weighting factor against the time lag for the four different kernel shapes so they can be compared.

References

S.M. Vicente-Serrano, S. Beguería, J.I. López-Moreno. 2010. A Multi-scalar drought index sensitive to global warming: The Standardized Precipitation Evapotranspiration Index – SPEI. Journal of Climate 23: 1696, DOI: 10.1175/2009JCLI2909.1.

Examples

# A rectangular kernel with a time scale of 12 and no shift
kern(12)

# A gaussian kernel with a time scale of 12 and no shift
kern(12,'gaussian')

# Comparison of the four kernels, with and without shift
kern.plot(12)
kern.plot(12,2)