generateMTSFast: Faster simulation of multiple time series with approximately...

In TycheLab/CoSMoS: Complete Stochastic Modelling Solution

Description

For more details see section 6 in Serinaldi and Kilsby (2018), and section 2.4 in Papalexiou and Serinaldi (2020).

Usage

generateMTSFast(
  n,
  spacepoints,
  margdist,
  margarg,
  p0,
  distbounds = c(-Inf, Inf),
  stcsid,
  stcsarg,
  scalefactor = 1,
  anisotropyid = "affine",
  anisotropyarg = list(phi1 = 1, phi2 = 1, phi12 = 0, theta = 0)
)

Arguments

n	number of fields (time steps) to simulate
spacepoints	matrix (d x 2) of coordinates (e.g. longitude and latitude) of d spatial locations (e.g. d gauge stations)
margdist	target marginal distribution
margarg	list of marginal distribution arguments. Please consult the documentation of the selected marginal distribution indicated in the argument margdist for the list of required parameters
p0	probability zero
distbounds	distribution bounds (default set to c(-Inf, Inf))
stcsid	spatiotemporal correlation structure ID
stcsarg	list of spatiotemporal correlation structure arguments. Please consult the documentation of the selected spatiotemporal correlation structure indicated in the argument stcsid for the list of required parameters
scalefactor	factor specifying the distance between the centers of two pixels (default set to 1)
anisotropyid	spatial anisotropy ID (affine by default, swirl or wave)
anisotropyarg	list of arguments characterizing the spatial anisotropy according to the syntax of the function anisotropyT. Isotropic fields by default

Details

generateMTSFast provides a faster approach to multivariate simulation compared to generateMTS by exploiting circulant embedding fast Fourier transformation. However, this approach is feasible only for approximately separable target spatiotemporal correlation functions. generateMTSFast comprises fitting and simulation in a single function. Here, we give indicative CPU times for some settings, referring to a Windows 10 Pro x64 laptop with Intel(R) Core(TM) i7-6700HQ CPU @ 2.60GHz, 4-core, 8 logical processors, and 32GB RAM.
CPU time:
d = 2500, n = 1000: ~58s
d = 2500, n = 10000: ~160s
d = 10000, n = 1000: ~2955s (~50min)

References

Serinaldi, F., Kilsby, C.G. (2018). Unsurprising Surprises: The Frequency of Record-breaking and Overthreshold Hydrological Extremes Under Spatial and Temporal Dependence. Water Resources Research, 54(9), 6460-6487, doi: 10.1029/2018WR023055

Papalexiou, S.M., Serinaldi, F. (2020). Random Fields Simplified: Preserving Marginal Distributions, Correlations, and Intermittency, With Applications From Rainfall to Humidity. Water Resources Research, 56(2), e2019WR026331, doi: 10.1029/2019WR026331

Examples

coord <- cbind(runif(4)*30, runif(4)*30)

sim <- generateMTSFast(
    n = 50,
    spacepoints = coord,
    p0 = 0.7,
    margdist ='paretoII',
    margarg = list(scale = 1,
                   shape = .3),
    stcsarg = list(scfid = "weibull",
                   tcfid = "weibull",
                   scfarg = list(scale = 20,
                                 shape = 0.7),
                   tcfarg = list(scale = 1.1,
                                 shape = 0.8))
)

TycheLab/CoSMoS documentation built on June 6, 2021, 2:35 a.m.