A Matérn model of the spatial covariance structure of point rain rates

Stochastic Environmental Research and Risk Assessment

Volumn 29, Issue 2, 2015, Pages 411-416

  Sun, Ying ^a   Bowman, Kenneth P ^b   Genton, Marc G ^c   Tokay, Ali ^d,e  

^a OHIO STATE UNIVERSITY   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

^c KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Saudi Arabia)

^d UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

^e NASA GODDARD SPACE FLIGHT CENTER   (United States)

Author keywords

Covariance model; Exponential covariance; Mat rn covariance; Point rain rates; Spectral model; Time scales

Indexed keywords

RAIN; RAIN GAGES; STOCHASTIC SYSTEMS; TIME MEASUREMENT;

COVARIANCE MODELING; EXPONENTIAL COVARIANCE; RAIN RATES; SPECTRAL MODELING; TIME-SCALES;

STOCHASTIC MODELS;

AERIAL SURVEY; COVARIANCE ANALYSIS; PRECIPITATION ASSESSMENT; PRECIPITATION INTENSITY; RAINFALL; RAINGAUGE; SPECTRAL ANALYSIS; TIMESCALE;

EID: 84920617151     PISSN: 14363240     EISSN: 14363259     Source Type: Journal    
DOI: 10.1007/s00477-014-0923-2     Document Type: Article

References (25)

1. Abramowitz M, Stegun IA (1964) Handbook of mathematical functions with formulas, graphs, and mathematical tables. No. 55 in National Bureau of Standards Applied Mathematics Series. Superintendent of Documents, U.S. Government Printing Office, Washington, DC
2. Apanasovich TV, Genton MG, Sun Y (2012) A valid Matérn class of cross-covariance functions for multivariate random fields with any number of components. J Am Stat Assoc 107:180–193
3. Bell TL (1987) A space–time stochastic model of rainfall for satellite remote-sensing studies. J Geophys Res 92:9631–9643. doi:10.1029/JD092iD08p09631
4. Bell TL, Kundu PK (1996) A study of the sampling error in satellite rainfall estimates using optimal averaging of data and a stochastic model. J Clim 9:1251–1268
5. Bell TL, Kundu PK (2003) Comparing satellite rainfall estimates with rain gauge data: optimal strategies suggested by a spectral model. J Geophys Res 108:4121. doi:10.1029/2002JD002641
6. Bruno F, Cocchi D, Greco F, Scardovi E (2014) Spatial reconstruction of rainfall fields from rain gauge and radar data. Stoch Environ Res Risk Assess 28:1235–1245
7. Chakraborty A, De S, Bowman K, Sang H, Genton MG, Mallick B (2014) An adaptive spatial model for precipitation data from multiple satellites over large regions. Stat Comput (in press)
8. Essenwanger OM (1985) General climatology: elements of statistical analysis, vol 1B., World survey of climatology, Elsevier, Amsterdam
9. Genton MG, Kleiber W (2014) Cross-covariance functions for multivariate geostatistics. Stat Sci (in press)
10. Gneiting T (2004) Stochastic models that separate fractal dimension and the hurst effect. SIAM Rev 46:269–282
11. Gneiting T, Kleiber W, Schlather M (2010) Matérn cross-covariance functions for multivariate random fields. J Am Stat Assoc 105:1167–1177
12. Guttorp P, Gneiting T (2006) Studies in the history of probability and statistics XLIX: on the Matérn correlation family. Biometrika 93:989–995. doi:10.1093/biomet/93.4.989
13. Habib E, Krajewski WF, Ciach GJ (2001) Estimation of rainfall interstation correlation. J Hydrometeorol 2:621–629
14. Handcock MS, Stein ML (1993) A Bayesian analysis of kriging. Technometrics 35:403–410
15. Krajewski WF, Ciach GJ, McCollum JR, Bacotiu C (2000) Initial validation of the Global Precipitation Climatology Project monthly rainfall over the United States. J Appl Meteorol 39:1071–1086
16. Kundu PK, Siddani RK (2011) Scale dependence of spatiotemporal intermittence of rain. Water Resour Res 47:318–340. doi:10.1029/2010WR010070
17. Laughlin CR (1981) On the effect of temporal sampling on the observation of mean rainfall. In: Atlas D, Thiele OW (eds) Precipitation measurement from space. National Aeronautics and Space Administration, Greenbelt, pp D59–66
18. Li B, Murthi A, Bowman K, North G, Genton MG, Sherman M (2009) Statistical tests of Taylor’s hypothesis: an application to precipitation fields. J Hydrometeorol 10:254–265
19. Marchenko YV, Genton MG (2010) Multivariate log-skew-elliptical distributions with applications to precipitation data. Environmetrics 21:318–340
20. Matérn B (1986) Spatial variation. In: Lecture notes in statistics, vol. 36, 2nd edn. Springer, Berlin
21. North GR, Nakamoto S (1989) Formalism for comparing rain estimation designs. J Atmos Oceanic Technol 6:985–992
22. North GR, Wang J, Genton MG (2011) Correlation models for temperature fields. J Clim 24:5850–5862. doi:10.1175/2011JCLI4199.1
23. Oliveira VD (2004) A simple model for spatial rainfall fields. Stoch Environ Res Risk Assess 18:131–140
24. Onof C, Chandler RE, Kakou A, Northrop P, Wheater HS, Isham V (2000) Rainfall modelling using Poisson-cluster processes: a review of developments. Stoch Environ Res Risk Assess 14:384–411
25. Tokay A, Bashor PG, McDowell VL (2010) Comparison of rain gauge measurements in the mid-Atlantic region. J Hydrometeorol 11:553–565. doi:10.1175/2009JHM1137.1