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Gappy POD-based reconstruction of the temperature field in Tibet

  • Basang Tsering-xiao
  • Qinwu XuEmail author
Original Paper
  • 15 Downloads

Abstract

Meteorological observations in Tibet are poor in quality with a severe amount of missing data; this is mostly caused by extreme climatological conditions and higher maintenance costs. This paper focuses on the imputation of missing data and the reconstruction of the regional temperature field. Due to insufficient observation stations and complicated topography, we employ the weather research and forecasting (WRF) model to produce the proper orthogonal decomposition (POD) basis for the study region. We then develop the gappy POD method for the imputation of missing data. Both methods are compared and tested for various missing data cases, and the results show that the gappy POD method dramatically outperforms the regularized EM algorithm when the amount of missing spatial data is not severe. Furthermore, between the two methods, only the gappy POD method is capable of reconstructing the temperature field at locations where the data are absent. The gappy POD method can also be generalized for data assimilation with the assumption that the data across all model grids have missing values.

Keywords

Reconstruction Gappy POD Tibet Missing value 

Notes

Acknowledgments

We are immensely grateful to Prof. Pingwen Zhang at School of Mathematical Sciences of PKU and Prof. Yun Chen at National Meteorological Center of CMA for their helpful discussion and valuable suggestions. We would also like to extent our gratitude to the anonymous reviewer for their comments that greatly improved the manuscript.

References

  1. Bui-Thanh T, Damodaran M, Willcox KE (2004) Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition. AIAA J 42(8):1505–1516CrossRefGoogle Scholar
  2. Carrega P (1995) A method for the reconstruction of mountain air temperatures with automatic cartographic applications. Theor Appl Climatol 52:69–84CrossRefGoogle Scholar
  3. Everson R, Sirovich L (1995) The Karhunen-Loeve procedure for gappy data. J Opt Soc Am 12:1657–1664CrossRefGoogle Scholar
  4. Haginoya S, Fujii H, Kuwagata T, Xu J, Ishigooka Y, Kang S, Zhang Y (2009) Air-Lake Interaction Features Found in Heat and Water Exchanges over Nam Co on the Tibetan Plateau. Sola 5:172– 175CrossRefGoogle Scholar
  5. Lee K, Mavris DN (2010) Unifying perspective for gappy proper orthogonal decomposition and probabilistic principal components analysis. AIAA J 48(6):1117–1129Google Scholar
  6. Murray NE, Ukeiley LS (2006) Flow field dynamics in open cavity flows. AIAA Paper 2428:1–16Google Scholar
  7. Murray NE, Ukeiley LS (2007) An application of Gappy POD. Exper Fluids 42(1):79–91CrossRefGoogle Scholar
  8. Murray N, Seiner J (2008) The effects of gappy POD on higher-order turbulence quantities. AIAA Paper, 241Google Scholar
  9. Maussion F, Scherer D, Finkelnburg R, Richters J, Yang W, Yao T (2010) WRF simulation of a precipitation event over the Tibetan Plateau, China – an assessment using remote sensing and ground observations, vol 7.  https://doi.org/10.5194/hessd-7-3551-2010
  10. Roger Barry G. (1992) Mountain weather and climate. Cambridge University Press, Cambridge, pp 251–363Google Scholar
  11. Robinson TD, Eldred MS, Willcox KE et al (2006) Strategies for multifidelity optimization with variable dimensional hierarchical models. In: Proceedings of the 2nd AIAA Multidisciplinary Design Optimization Specialist Conference, Newport, RI 2006(1819)Google Scholar
  12. Schneider T (2001) Analysis of incomplete climate data: Estimation of mean values and covariance matrices and imputation of missing values. J Clim 14:853–871CrossRefGoogle Scholar
  13. Skamarock WC, Klemp JB, Dudhia J et al (2005) A description of the advanced research WRF version 2. National Center For Atmospheric Research Boulder Co Mesoscale and Microscale Meteorology Div.Google Scholar
  14. Tveito O, Wegehenkel M, Van der Wel F, Dobesch H (2006) The Use of Geographic Information Systems in Climatology and Meteorology - Final Report COST Action 719Google Scholar
  15. Tveito O et al (2007) The developments in spatialization of meteorological and climatological elements. In: Dobesch H (ed) Spatial interpolation for climate data: the use of GIS in climatology and meteorology. ISTE Ltd, London, pp 73–86Google Scholar
  16. Tan BT (2003) Proper orthogonal decomposition extensions and their applications in steady aerodynamics. Singapore-MIT Alliance. (Thesis)Google Scholar
  17. Vendl A, Fabbender H (2010) Proper orthogonal decomposition for steady aerodynamic applications. PAMM 10(1):635–636CrossRefGoogle Scholar
  18. Venturi D, Karniadakis GE (2004) Gappy data and reconstruction procedures for flow past a cylinder. J Fluid Mech 519:315–336CrossRefGoogle Scholar
  19. Willcox K (2006) Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition. Comput Fluids 35(2):208–226CrossRefGoogle Scholar
  20. Yang J, Duan K, Wu J et al (2015) Effect of data assimilation using WRF-3DVAR for heavy rain prediction on the northeastern edge of the Tibetan Plateau. Advances in Meteorology 2015(1):1–14Google Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mathematical Department of Tibet UniversityLhasaPeople’s Republic of China
  2. 2.Department of MathematicsNanjing UniversityNanjingPeople’s Republic of China

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