Meteorology and Atmospheric Physics

, Volume 131, Issue 5, pp 1387–1399 | Cite as

Unobserved component modeling for seasonal rainfall patterns in Rayalaseema region, India 1951–2015

  • K. V. Narasimha MurthyEmail author
  • R. Saravana
  • P. Rajendra
Original Paper


Rainfall is the significant parameter for climate change, meteorological and hydrological process. The present paper describes the seasonal rainfall patterns in the Rayalaseema region of Andhra Pradesh state, India using the unobserved component model (UCM) with the hidden components like trend, seasonal, cyclical and irregular. The seasonal rainfall data were provided by India Meteorological Department (IMD), using daily gridded rainfall data with 10 automatic weather stations spread over the Rayalaseema region and the study deals with four seasons of rainfall as classified by IMD, namely winter, pre-monsoon, southwest monsoon and northeast monsoon. Basic Structural Model (BSM) with the components of constant trend, deterministic trigonometric seasonal, deterministic cycle and irregular is selected from the parsimonious models of UCM based on Akaike’s information criteria (AIC), Bayesian information criteria (BIC), significant tests and statistical fit. The model parameters are obtained using maximum likelihood method; the adequacy of the selected model is determined through correlation and normal diagnostics. The forecast of the seasonal rainfall patterns during the years 2016–2018 has been noticed with the help of selected UCM. From the model forecast, it is observed that the pre-monsoon season receives rainfall of 96.7 mm in the years 2016 and 2018, whereas 71.3 mm in the year 2017; the southwest monsoon season receives the rainfall of 396.0 mm in the year 2016, 424.2 mm in 2017 and 419.2 mm in 2018; the northeast monsoon season receives the rainfall of 286.8 mm in 2016, 261.3 mm in 2017 and 286.8 mm in 2018.



This research was supported by the SERO/UGC (F MRP-6727/16).


  1. Box GEP, Jenkins GM, Reinsel GC (1994) Time series analysis: forecasting and control, 3rd edn. Prentice Hall, New JerseyGoogle Scholar
  2. Cryer JD, Chan KS (2008) Time series analysis with application in R, 2nd edn. Springer, New YorkGoogle Scholar
  3. Enakshi S, Arnab H, Pabitra B (2016) SARIMA modeling of the monthly average maximum and minimum temperatures in the eastern plateau region of India. Mausam, 67(4):841–848Google Scholar
  4. Harvey AC (2001a) Testing in unobserved components models. J Forecast 20:1–19CrossRefGoogle Scholar
  5. Harvey AC (2001b) Forecasting, structural time series models and the Kalman filter. Cambridge University Press, CambridgeGoogle Scholar
  6. Kaipa Viswanath NM, Ramachandran S (2018) Unobservable component modelling of monthly average maximum and minimum temperature patterns in India 1981–2015. Pure Appl Geophys. Google Scholar
  7. Mikkonen S, Laine M, Makela HM, Gregow H, Tuomenvirta H, Lahtinen M, Laaksonen A (2015) Trends in the average temperature in Finland, 1847–2013. Stoch Environ Res Risk Assess 29:1521–1529. CrossRefGoogle Scholar
  8. Narasimha Murthy KV, Saravana R, Rajendra P (2018a) Critical comparison of north east monsoon rainfall for different regions through analysis of means technique. MAUSAM 69(3):413–420Google Scholar
  9. Narasimha Murthy KV, Saravana R, Vijaya Kumar K (2018b) Modeling and forecasting rainfall patterns of southwest monsoons in North-East India as a SARIMA process. Meteorol Atmos Phys 130(1):99–106. CrossRefGoogle Scholar
  10. Narasimha Murthy KV, Saravana R, Vijaya Kumar K (2018c) Stochastic modelling of the monthly average maximum and minimum temperature patterns in India 1981–2015. Meteorol Atmos Phys. Google Scholar
  11. SAS Institute Inc. (2014) SAS/ETS® 13.2 User’s Guide, The UCM procedure. SAS Institute Inc., Cary, NCGoogle Scholar
  12. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464CrossRefGoogle Scholar
  13. Seetharam K (2013) Rainfall analysis over Rayalaseema meteorological sub-division. MAUSAM 64(3):558–565Google Scholar
  14. Srivastava AK, Rajeevan M, Kshirsagar SR (2009) Development of a high resolution daily gridded temperature data set (1969–2005) for the Indian region. Atmos Sci Lett 10(4):249–254Google Scholar
  15. Stoffer DS, Shumway RH (2010) Time series analysis and its application. 3rd edn. Springer, New York, vol 10, pp 1441978658Google Scholar
  16. Tom Fomby (2008) The unobserved component model. Accessed Oct 2008
  17. West M, Harrision J (1999) Bayesian forecasting and dynamic models, 2nd edn. Springer, New YorkGoogle Scholar
  18. Young, PC (2011) Unobserved component models. Recursive estimation and time-series analysis. Springer, Berlin, Heidelberg.

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • K. V. Narasimha Murthy
    • 1
    Email author
  • R. Saravana
    • 1
  • P. Rajendra
    • 1
  1. 1.Department of MathematicsMadanapalle Institute of Technology and ScienceMadanapalleIndia

Personalised recommendations