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Title: Half-spectral space–time covariance models

Publication Date:
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
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Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Spatial Statistics
Additional Journal Information:
Journal Volume: 19; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-12-12 16:00:03; Journal ID: ISSN 2211-6753
Country of Publication:
Country unknown/Code not available

Citation Formats

Horrell, Michael T., and Stein, Michael L. Half-spectral space–time covariance models. Country unknown/Code not available: N. p., 2017. Web. doi:10.1016/j.spasta.2016.12.002.
Horrell, Michael T., & Stein, Michael L. Half-spectral space–time covariance models. Country unknown/Code not available. doi:10.1016/j.spasta.2016.12.002.
Horrell, Michael T., and Stein, Michael L. Wed . "Half-spectral space–time covariance models". Country unknown/Code not available. doi:10.1016/j.spasta.2016.12.002.
title = {Half-spectral space–time covariance models},
author = {Horrell, Michael T. and Stein, Michael L.},
abstractNote = {},
doi = {10.1016/j.spasta.2016.12.002},
journal = {Spatial Statistics},
number = C,
volume = 19,
place = {Country unknown/Code not available},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.spasta.2016.12.002

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  • It is proposed that the space-time used by any observer has a cellular structure which is determined by the observer himself within the limits of the energy available for the refinement of his apparatus. The exact natures of the cells of each structure and the transformations between the cellular structures of different observers are discussed. It is found that these transformations depend on the information exchanged by the observers concerning their placements within their own cellular structures of a common finite set of events, and it is found that the transformations become more exact as more information is exchanged. Itmore » is shown how the readings resulting from the application of a set of observables may be grouped in a way which corresponds to the grouping of tensor components in theories involving continuous space-time, and rules are given for the transformations of these groups between observers. It is found that the requirement of the covariance of physical laws within the framework of cellular space-time theory necessitates the use of double-argument transformation operators acting on these groups. (auth)« less
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  • Over the range of time scales from about 10 days to 30–100 years, in addition to the familiar weather and climate regimes, there is an intermediate “macroweather” regime characterized by negative temporal fluctuation exponents: implying that fluctuations tend to cancel each other out so that averages tend to converge. We show theoretically and numerically that macroweather precipitation can be modeled by a stochastic weather-climate model (the Climate Extended Fractionally Integrated Flux, model, CEFIF) first proposed for macroweather temperatures and we show numerically that a four parameter space-time CEFIF model can approximately reproduce eight or so empirical space-time exponents. In spitemore » of this success, CEFIF is theoretically and numerically difficult to manage. We therefore propose a simplified stochastic model in which the temporal behavior is modeled as a fractional Gaussian noise but the spatial behaviour as a multifractal (climate) cascade: a spatial extension of the recently introduced ScaLIng Macroweather Model, SLIMM. Both the CEFIF and this spatial SLIMM model have a property often implicitly assumed by climatologists that climate statistics can be “homogenized” by normalizing them with the standard deviation of the anomalies. Physically, it means that the spatial macroweather variability corresponds to different climate zones that multiplicatively modulate the local, temporal statistics. This simplified macroweather model provides a framework for macroweather forecasting that exploits the system's long range memory and spatial correlations; for it, the forecasting problem has been solved. We test this factorization property and the model with the help of three centennial, global scale precipitation products that we analyze jointly in space and in time.« less
  • By virtue of the images used in the dislocation solution, the deformation at the free surface produced throughout the earthquake cycle by slippage on a long strike-slip fault in an Earth model consisting of an elastic plate (lithosphere) overlying a visoelastic half-space (asthenosphere) can be duplicated by prescribed slip on a vertical fault embedded in an elastic half-space. For the case in which each earthquake ruptures the entire lithosphere (thickness H), the half-space equivalent slip rate is as follows: Depth interval 0-H, slip identical to that in lithosphere-asthenosphere model (i.e., abrupt coseismic slip and no subsequent slip); depth interval (2nmore » {minus} 1) H to (2n + 1) H (n = 1,2,...), slip rate uniform in space and dependent upon time as F{sub n}(t) exp ({minus}t/{tau}) where F{sub n} is a (n {minus} 1) degree polynomial in t, {tau} is twice the asthenosphere relaxation time, and t is measured from the instant after the preceding earthquake. The slip rate averaged over the seismic cycle in each depth interval equals the secular rate of relative plate motion. The surface deformation due to the earthquake cycle in the lithosphere-asthenosphere model can be calculated very simply from the half-space model with time-dependent slip in the two depth intervals H-3H and 3H-5H, and uniform slip at a rate equal to the secular relative plate velocity below depth 5H. Inversion of 1973-1988 geodetic measurements of deformation across the segment of the San Andrea fault in the Transverse Ranges north of Los Angeles for the half-space equivalent slip distribution suggests no significant slip on the fault above 30 km and a uniform slip rate of 36 mm/yr below 30 km.« less
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