generateMTSFast function

Faster simulation of multiple time series with approximately separable spatiotemporal correlation structure

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

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)

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))
)

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, tools:::Rd_expr_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, tools:::Rd_expr_doi("10.1029/2019WR026331")