Drought-indices: Calculation of the Standardized...

Description Usage Arguments Details Value Input data Time scales Probability distributions Fitting methods User-provided parameters Reference period Processing large datasets Author(s) References See Also Examples

Description

Given a time series of the climatic water balance (precipitation minus potential evapotranspiration), gives a time series of the Standardized Precipitation-Evapotranspiration Index (SPEI).

Usage

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spei(data, scale, kernel = list(type = 'rectangular', shift = 0),
distribution = 'log-Logistic', fit = 'ub-pwm', na.rm = FALSE,
ref.start=NULL, ref.end=NULL, x=FALSE, params=NULL, ...)

spi(data, scale, kernel = list(type = "rectangular", shift = 0),
  distribution = "Gamma", fit = "ub-pwm", na.rm = FALSE,
  ref.start = NULL, ref.end = NULL, x = FALSE, params = NULL, ...)

Arguments

data

a vector, matrix or data frame with time ordered values of precipitation (for the SPI) or of the climatic balance precipitation minus potential evapotranspiration (for the SPEI).

scale

an integer, representing the time scale at which the SPEI / SPI will be computed.

kernel

optional, a list defining the type of kernel used for computing the SPEI / SPI at scales higher than one. Defaults to unshifted rectangular kernel.

distribution

optional, name of the distribution function to be used for computing the SPEI / SPI (one of 'log-Logistic', 'Gamma' and 'PearsonIII'). Defaults to 'log-Logistic' for spei, and to 'Gamma' for spi.

fit

optional, name of the method used for computing the distribution function parameters (one of 'ub-pwm', 'pp-pwm' and 'max-lik'). Defaults to 'ub-pwm'.

na.rm

optional, a logical value indicating whether NA values should be stripped from the computations. Defaults to FALSE, i.e. no NA are allowed in the data.

ref.start

optional, starting point of the reference period used for computing the index. Defaults to NULL, indicating that the first value in data will be used as starting point.

ref.end

optional, ending point of the reference period used for computing the index. Defaults to NULL, indicating that the last value in data will be used as ending point.

x

optional, a logical value indicating wether the data used for fitting the model should be kept. Defaults to FALSE.

params

optional, an array of parameters for computing the spei. This option overrides computation of fitting parameters.

...

other possible parameters.

Details

The spei and spi functions allow computing the SPEI and the SPI indices. These are climatic proxies widely used for drought quantification and monitoring. Both functions are identical (in fact, spi is just a wrapper for spei), but they are kept separated for clarity. Basically, the functions standardize a variable following a log-Logistic (or Gamma, or PearsonIII) distribution function (i.e., they transform it to a standard Gaussian variate with zero mean and standard deviation of one).

Value

Functions spei and spi return an object of class spei. The generic functions print and summary can be used to obtain summaries of the results. The generic accessor functions coefficients and fitted extract useful features of the object.

An object of class spei is a list containing at least the following components:

Input data

The input variable is a time ordered series of precipitation values for spi, or a series of the climatic water balance (precipitation minus potential evapotranspiration) for spei. When used with the default options, it would yield values of both indices exactly as defined in the references given below.

The SPEI and the SPI were defined for monthly data. Since the PDFs of the data are not homogenous from month to month, the data is split into twelve series (one for each month) and independent PDFs are fit to each series. If data is a vector or a matrix it will be treated as a sequence of monthly values starting in January. If it is a (univariate or multivariate) time series then the function cycle will be used to determine the position of each observation within the year (month), allowing the data to start in a month other than January.

Time series with a frequency other than 12 can also be used.

Time scales

An important advantage of the SPEI and the SPI is that they can be computed at different time scales. This way it is possible to incorporate the influence of the past values of the variable in the computation enabling the index to adapt to the memory of the system under study. The magnitude of this memory is controlled by parameter scale. For example, a value of six would imply that data from the current month and of the past five months will be used for computing the SPEI or SPI value for a given month. By default all past data will have the same weight in computing the index, as it was originally proposed in the references below. Other kernels, however, are available through parameter kernel. The parameter kernel is a list defining the shape of the kernel and a time shift. These parameters are then passed to the function kern.

Probability distributions

Following the original definitions spei uses a log-Logistic distribution by default, and spi uses a Gamma distribution. This behaviour can be modified, however, through parameter distribution.

Fitting methods

The default method for parameter fitting is based on unbiased Probability Weighted Moments ('ub-pwm'), but other methods can be used through parameter fit. A valid alternative is the plotting-position PWM ('pp-pwm') method. For the log-Logistic distribution, also the maximum likelihood method ('max-lik') is available.

User-provided parameters

An option exists to override parameter fitting and provide user default parameters. This is activated with the parameter params. The exact values provided to this parameter depend on the distribution function being used. For log-Logistic and PearsonIII it should be a three-dimensional array with dimensions (3,number of series in data,12), containing twelve parameter triads (xi, alpha, kappa) for each data series, one for each month. For Gamma, a three-dimensional array with dimensions (2,number of series in data,12), containing twelve parameter pairs (alpha, beta). It is a good idea to look at the coefficients slot of a previously fit spei spei object in order to understand the structure of the parameter array. The parameter distribution is still used under this option in order to know what distribution function should be used.

Reference period

The default behaviour of the functions is using all the values provided in data for parameter fitting. However, this can be modified with help of parameters ref.start and ref.end. These parameters allow defining a subset of values that will be used for parameter fitting, i.e. a reference period. The functions, however, will compute the values of the indices for the whole data set. For these options to work it is necessary that data will be a time series object. The starting and ending points of the reference period will then be defined as pairs of year and month values, e.g. c(1900,1).

Processing large datasets

It is possible to use the spei and spi functions for processing multivariate datasets at once. If a matrix or data frame is supplied as data, with time series of precipitation or precipitation minus potential evapotranspiration arranged in columns, the result would be a matrix (data frame) of spi or spei series. This makes processing large datasets extremely easy, since no loops need to be used.

Author(s)

Santiago Beguería and Sergio M. Vicente-Serrano. Maintainer: Santiago Beguería.

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.

Beguería S, Vicente-Serrano SM, Reig F, Latorre B. 2014. Standardized precipitation evapotranspiration index (SPEI) revisited: parameter fitting, evapotranspiration models, tools, datasets and drought monitoring. International Journal of Climatology 34(10): 3001-3023.

http://spei.csic.es

See Also

kern for different kernel functions available. thornthwaite, hargreaves and penman for ways of calculating potential evapotranspiration. summary.spei and print.spei for summaries of spei objects. plot.spei for plotting spei objects.

Examples

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# Load data
data(wichita)

# One and tvelwe-months SPEI
wichita$PET <- thornthwaite(wichita$TMED,37.6475)
spei1 <- spei(wichita$PRCP-wichita$PET,1)
spei12 <- spei(wichita$PRCP-wichita$PET,12)

# Extract information from spei object
summary(spei1)
names(spei1)
spei1$call
spei1$fitted
spei1$coefficients

# Plot spei object
par(mfrow=c(2,1))
plot(spei1)
plot(spei12,'Wichita')

# One and tvelwe-months SPI
spi_1 <- spi(wichita$PRCP,1)
spi_12 <- spi(wichita$PRCP,12)
par(mfrow=c(2,1))
plot(spi_1)
plot(spi_12)

# Define the properties of the time series with ts()
plot(spei(ts(wichita$PRCP-wichita$PET,freq=12,start=c(1980,1)),12))

# Time series not starting in January
plot(spei(ts(wichita$PRCP-wichita$PET,freq=12,start=c(1980,6)),12))

# Using a particular reference period
plot(spei(ts(wichita$PRCP-wichita$PET,freq=12,start=c(1980,1)),12,
	ref.start=c(1980,1), ref.end=c(2000,1)))

# Using different kernels
spei24 <- spei(wichita$PRCP-wichita$PET,24)
spei24_gau <- spei(wichita$PRCP-wichita$PET,24,kernel=list(type='gaussian',shift=0))
par(mfrow=c(2,1))
plot(spei24,'Rectangular kernel')
plot(spei24_gau,'Gaussian kernel')

# Computing several time series at a time
data(balance)
names(balance)
bal_spei12 <- spei(balance,12)
plot(bal_spei12)

# User provided parameters
coe <- spei1$coefficients
dim(coe)
spei(wichita$PRCP-wichita$PET,1,params=coe)

sbegueria/SPEI documentation built on March 22, 2018, 3:42 p.m.