A theoretical framework for the sampling error variance for three-dimensional climate averages of ICOADS monthly ship data
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Meteorological and oceanographic data from ships of opportunity are the largest contributor to the world’s ocean surface database and thus are extensively used to estimate the change in climatic properties over the world’s oceans during the previous 150 years. The importance of these data for climate change studies underscores the need to fully understand the error associated with averages of these data. The sampling error problem is especially acute for ship data due to the fact that ships are moving platforms and, thus, report observations from constantly varying locations with time. This paper develops a theoretical framework for assessing the averaged sampling error associated with monthly, 1°×1° latitude-longitude box averaged ship data. It should be noted that the time-space distribution of ships within the averaging domain strongly affects the sampling error. This is shown in our derivation. The framework developed here can be used to improve upon existing methods for estimating the sampling error associated with three-dimensional box averages of meteorological and oceanographic data obtained from ship records. The framework is complimentary to existing methods of assessing biases and random error due to instrumentation, recording, etc. It is demonstrated mathematically that the uncertainty due to incomplete sampling is primarily a trade off between of the number of observations and their relative locations within the box as well as the inherent time-space correlation structure of the variable of interest. This work differs from other studies in that the three-dimensional interdependence of data is taken into account in deriving an expression for the sampling error.
KeywordsCorrelation Function Probability Density Function Sampling Error Average Domain Incomplete Sampling
The authors would like to thank those who attended the Brussels CLIMAR-II Conference held in 2003 for their encouragement to pursue this work. We also would like to acknowledge the generous help from NOAA’s Climate and Global Change Program’s Climate Observations Element contract number NA17RJ1227. Thanks also go out to M. Klatt for his help in organizing the data.
- Briffa KR, Jones PD (1990) Basic chronology statistics and assessment. In: Cook E, Kairiukstis L (eds) Methods of dendrochronology: applications in the environmental sciences. Kluwer, Dordrecht, The Netherlands, pp 137–152Google Scholar
- Brohan P, Kennedy JJ, Harris I, Tett SFB, Jones PD (2006) Uncertainty estimates in regional and global observed temperature changes: a new data set from 1850. J Geophys Res 111:12,106–12,127Google Scholar
- Cayan D (1992) Variability of latent and sensible heat fluxes estimated using bulk formulae. Atmos Ocean Techn 301–42Google Scholar
- De Luna X, Genton MG (2005) Predictive spatio-temporal models for spatially sparse environmental data. Stat Sin 15:547–568Google Scholar
- Gneiting T, Genton MG, Guttorp P (2007) Geostatistical space-time models, stationarity, separability and full symmetry. In: Finkenstadt B, Held L, Isham V (eds) Statistical methods for spatio-temporal systems, CRC, Boca Raton, FL, USA, pp 151–175Google Scholar
- Journel AG, Huijbregts ChJ (1989) Mining geostatistics. Academic, San Diego, CA, USA, 600 ppGoogle Scholar
- Kagan RL (1997) Averaging of meteorological fields. Kluwer, Dordrecht, The Netherlands, 279 ppGoogle Scholar
- Morrissey ML, Greene JS (1998) Uncertainty of satellite rainfall algorithms over the tropical Pacific. J Geophys Res 103:19,569–19,576Google Scholar
- Woodruff SD (2001) COADS updates including newly digitized data and the blend with the UK meteorological office marine data bank and quality control in recent COADS updates. Proceedings of Workshop on Preparation, Processing and Use of Historical Marine Meteorological Data, Tokyo, Japan, 28–29 November 2000, Japan Meteorological Agency and the Ship and Ocean Foundation, Tokyo, pp 9–53Google Scholar