Abstract
Surface ocean currents are often of interest in environmental monitoring. These vectorial data can be reasonably treated as a finite realization of a complex-valued random field, where the decomposition in modulus (current speed) and direction (current direction) of the current field is natural. Moreover, when observations are also available for different time points (other than at several locations), it is useful to evaluate the evolution of their complex correlation over time (rather than in space) and the corresponding modeling which is required for estimation purposes. This paper illustrates a first approach where the temporal profile of surface ocean currents is considered. After introducing the fundamental aspects of the complex formalism of a random field indexed in time, a new class of models suitable for including the temporal component is proposed and applied to describe the time-varying complex covariance function of current data. The analysis concerns ocean current observations, taken hourly on 30 April 2016 through high frequency radar systems at some stations located in the Northeastern Caribbean Sea. The selected complex covariance model indexed in time is used for estimation purposes and its reliability is confirmed by a numerical analysis.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bochner S (1933) Monotone Funktionen, Stieltjessche Integrale und Harmonische Analyse. Math Ann 108(1):378–410
Box GEP, Jenkins GM, Reinsel GC, Ljung GM (2015) Time series analysis: forecasting and control. Wiley, Hoboken
Brown BG, Katz RW, Murphy AH (1984) Time series models to simulate and forecast wind speed and wind power. J Clim Appl Meteorol 23(8):1184–1195
Christakos G (2017) Spatio-temporal random fields: theory and applications. Elsevier, New York
Cressie N (1993) Statistics for spatial data. Wiley, New York
Cressie N, Huang H (1999) Classes of nonseparable, spatio-temporal stationary covariance functions. J Am Stat Assoc 94(448):1330–1340
Cressie N, Wikle CK (2011) Statistics for spatio-temporal data. Wiley, Hoboken
De Iaco S (2017) The cgeostat software for analyzing complex-valued random fields. J Stat Softw 79(5):1–32
De Iaco S, Posa D (2016) Wind velocity prediction through complex kriging: formalism and computational aspects. Environ Ecol Stat 23(1):115–139
De Iaco S, Palma M, Posa D (2003) Covariance functions and models for complex-valued random fields. Stoch Environ Res Risk A 17(3):145–156
De Iaco S, Posa D, Palma M (2013) Complex-valued random fields for vectorial data: estimating and modeling aspects. Math Geosci 45(5):557–573
Erdem E, Shi J (2011) ARMA based approaches for forecasting the tuple of wind speed and direction. Appl Energy 88:1405–1414
Gneiting T (2002) Nonseparable, stationary covariance functions for space-time data. J Am Stat Assoc 97(458):590–600
Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York
Grzebyk M (1993) Ajustement d’une coregionalisation stationnaire. PhD thesis, Ecoles des Mines, Paris
Gumiaux C, Gapais D, Brun JP (2003) Geostatistics applied to best-fit interpolation of orientation data. Tectonophysics 376:241–259
Haslett J, Raftery AE (1989) Space–time modelling with long-memory dependence: assessing Ireland’s wind power resource. J R Stat Soc C Appl 38(1):1–50
Horel JD (1984) Complex principal component analysis: theory and examples. J Clim Appl Meteorol 23(12):1660–1673
Kaihatu JM, Handler RA, Marmorino GO, Shay LK (1998) Empirical orthogonal function analysis of ocean surface currents using complex and real-vector methods. J Atmos Ocean Technol 15(4):927–941
Lajaunie C, Béjaoui R (1991) Sur le krigeage des fonctions complexes. Note N-23/91/G, Centre de Geostatistique, Ecole des Mines de Paris, Fontainebleau
Monestiez P, Petrenko A, Leredde Y, Ongari B (2004) Geostatistical analysis of three dimensional current patterns in coastal oceanography: application to the gulf of lions (NW Mediterranean Sea). In: Sanchez-Vila X, Ramírez J, Gomez-Hernandez J (eds) GeoENV IV - Proceedings of the fourth European conference on geostatistics for environmental applications, Barcelona, Spain, 27–29 November 2002, pp 367–378
Posa D (1993) A simple description of spatial–temporal processes. Comput Stat Data Anal 15(4):425–437
Rouhani S, Hall TJ (1989) Space–time kriging of groundwater data. In: Armstrong M (ed) Quantitative geology and geostatistics, vol 4. Springer, Dordrecht, pp 639–651
Shoji T (2006) Statistical and geostatistical analysis of wind: a case study of direction statistics. Comput Geosci 32(8):1025–1039
Stein ML (1986) A simple model for spatial–temporal processes. Water Resour Res 22(13):2107–2110
Wackernagel H (2003) Multivariate geostatistics: an introduction with applications. Springer series in statistics. Springer, Berlin
Wikle CK, Zammit-Mangion A, Cressie N (2019) Spatio-temporal statistics with R. Chapman & Hall/CRC, Boca Raton
Yaglom AM (1987) Correlation theory of stationary and related random functions. Springer series in statistics, vol I, II. Springer, Berlin
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cappello, C., De Iaco, S., Maggio, S. et al. Modeling Ocean Currents Through Complex Random Fields Indexed in Time. Math Geosci 53, 999–1025 (2021). https://doi.org/10.1007/s11004-020-09880-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11004-020-09880-3