Pros and cons of using wavelets in conjunction with genetic programming and generalised linear models in statistical downscaling of precipitation

  • D. A. SachindraEmail author
  • K. Ahmed
  • Md. Mamunur Rashid
  • V. Sehgal
  • S. Shahid
  • B. J. C. Perera
Original Paper


Among the regression techniques used in building statistical downscaling models, genetic programming (GP) which mimics Darwin’s theory of biological evolution possesses several pros such as it evolves explicit linear or non-linear relationships while identifying optimum predictors, and it discards irrelevant and redundant information in predictors. However, GP is known to simulate unphysically large outliers of predictands. In statistical downscaling, decomposition of predictand and predictor data into number of different time-frequency components with wavelet transform and modelling each component separately should better simulate the time-frequency properties of the predictand, in theory. Therefore, it is important to investigate pros and cons of using GP with wavelet transform in building downscaling models. In this study, wavelet and non-wavelet-based precipitation downscaling models were developed employing GP and generalised liner models (GLM) for 50 stations located in wet and dry climate, with 20CR and NCEP/NCAR reanalysis data, for the investigation of the above matter. It was found that regardless of the mother wavelet, vanishing moment and climate regime, with the increase in decomposition level, the wavelet-based downscaling models developed with GLM tended to show a distinct deterioration in performance in both calibration and validation unlike the wavelet-based downscaling models developed with GP. This was because GP is able to discard unnecessary/redundant information flowing into the model with the increase in the decomposition level through evolution. Furthermore, it was found that when GP is coupled with wavelet transform, the simulation of unphysically large values of the predictand increases significantly.


Supplementary material

704_2019_2848_MOESM1_ESM.pdf (2.9 mb)
Figure S1 (PDF 2975 kb)
704_2019_2848_MOESM2_ESM.pdf (3.1 mb)
Figure S2 (PDF 3204 kb)
704_2019_2848_MOESM3_ESM.pdf (3.2 mb)
Figure S3 (PDF 3227 kb)
704_2019_2848_MOESM4_ESM.pdf (3.8 mb)
Figure S4 (PDF 3856 kb)
704_2019_2848_MOESM5_ESM.pdf (3.7 mb)
Figure S5 (PDF 3803 kb)
704_2019_2848_MOESM6_ESM.pdf (3.8 mb)
Figure S6 (PDF 3884 kb)


  1. Ahmed K, Shahid S, Nawaz N, Khan N (2018) Modeling climate change impacts on precipitation in arid regions of Pakistan: a non-local model output statistics downscaling approach. Theor Appl Climatol (article in press).
  2. Ahrens B (2003) Rainfall downscaling in an alpine watershed applying a multiresolution approach. J Geophys Res Atmos 108:D8. CrossRefGoogle Scholar
  3. Anandhi A, Srinivas VV, Kumar DN, Nanjundiah RS (2009) Role of predictors in downscaling surface temperature to river basin in India for IPCC SRES scenarios using support vector machine. Int J Climatol 29:583–603. CrossRefGoogle Scholar
  4. Baghanam AH, Nourani V, Keynejad MA, Taghipour H, Alami MT (2018) Conjunction of wavelet-entropy and SOM clustering for multi-GCM statistical downscaling. Hydrol Res Article in press 50:1–23. CrossRefGoogle Scholar
  5. Beecham S, Rashid M, Chowdhury RK (2014) Statistical downscaling of multi-site daily rainfall in a South Australian catchment using a generalized linear model. Int J Climatol 34:3654–3670. CrossRefGoogle Scholar
  6. Benestad R, Hanssen-Bauer I, Chen D (2008) Empirical-statistical downscaling. World Scientific Publishing Company, Singapore 228 ppCrossRefGoogle Scholar
  7. Cai Y (2009) Statistical analysis in downscaling climate models: wavelet and Bayesian methods in multimodel ensembles. Masters Thesis. Accessed on 05/06/2018
  8. Chandrasekhar E, Dimri VP, Gadre VM (2013) Wavelets and fractals in earth system sciences. CRC Press, Boca Raton 306 ppCrossRefGoogle Scholar
  9. Compo GP, Whitaker JS, Sardeshmukh PD, Matsui N, Allan RJ, Yin X, Gleason BE, Vose RS, Rutledge G, Bessemoulin P, Brönnimann S, Brunet M, Crouthamel RI, Grant AN, Groisman PY, Jones PD, Kruk M, Kruger AC, Marshall GJ, Maugeri M, Mok HY, Nordli Ø, Ross TF, Trigo RM, Wang XL, Woodruff SD, Worley SJ (2011) The twentieth century reanalysis project. Quarterly J Roy Meteorol Soc 137:1–28. CrossRefGoogle Scholar
  10. Coulibaly P (2004) Downscaling daily extreme temperatures with genetic programming. Geophys Res Lett 31:L16203. CrossRefGoogle Scholar
  11. Dadu KS, Deka PC (2016) Applications of wavelet transform technique in hydrology—a brief review. In: Sarma AK et al (eds) Urban hydrology, watershed management and socio-economic aspects, Water Science and Technology Library 73. Google Scholar
  12. Danandeh Mehr A, Kahya E, Olyaie E (2013) Streamflow prediction using linear genetic programming in comparison with a neuro-wavelet technique. J Hydrol 505:240–249. CrossRefGoogle Scholar
  13. Danandeh Mehr A, Nourani V, Kahya E, Hrnjica B, Sattar AMA, Yaseen ZM (2018) Genetic programming in water resources engineering: a state-of-the-art review. J Hydrol 566:643–667. CrossRefGoogle Scholar
  14. Daubechies I (1992) Ten lectures on wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics. 369 ppGoogle Scholar
  15. Dixit P, Londhe S, Deo M (2016) Review of applications of neuro-wavelet techniques in water flows. INAE Letters 1:99–104. CrossRefGoogle Scholar
  16. Eden JM, Widmann M, Grawe D, Rast S (2012) Skill, correction, and downscaling of GCM-simulated precipitation. J Clim 25:3970–3984. CrossRefGoogle Scholar
  17. Fowler HJ, Wilby RL (2010) Detecting changes in seasonal precipitation extremes using regional climate model projections: implications for managing fluvial flood risk. Water Resour Res 46:W03525. CrossRefGoogle Scholar
  18. Guven A, Kisi O (2013) Monthly pan evaporation modelling using linear genetic programming. J Hydrol 503:178–185. CrossRefGoogle Scholar
  19. Kalnay E, Kanamitsu M, Kistler R, Collins W, Deaven D, Gandin L, Iredell M, Saha S, White G, Woollen J, Zhu Y, Chelliah M, Ebisuzaki W, Higgins W, Janowiak J, Mo KC, Ropelewski C, Wang J, Leetmaa A, Reynolds R, Jenne R, Joseph D (1996) The NCEP/NCAR 40-year reanalysis project. Bull Amer Meteor Soc 77:437–472.<0437:TNYRP>2.0.CO;2 CrossRefGoogle Scholar
  20. Kisi O, Dailr AH, Cimen M, Shiri J (2012) Suspended sediment modeling using genetic programming and soft computing techniques. J Hydrol 450:48–58. CrossRefGoogle Scholar
  21. Koukidis EN, Berg AA (2009) Sensitivity of the statistical downscaling model (SDSM) to reanalysis products. Atmosphere-Ocean 47:1–18 CrossRefGoogle Scholar
  22. Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. MIT Press, CambridgeGoogle Scholar
  23. Krause P, Boyle DP, Bäse F (2005) Comparison of different efficiency criteria for hydrological model assessment. Adv Geosci 5:89–97. CrossRefGoogle Scholar
  24. Labat D, Ronchail J, Guyot JL (2005) Recent advances in wavelet analyses: part 2—Amazon, Parana, Orinoco and Congo discharges time scale variability. J Hydrol 314:289–311. CrossRefGoogle Scholar
  25. Lakhanpal A, Sehgal V, Maheswaran R, Khosa R, Sridhar V (2017) A non-linear and non-stationary perspective for downscaling mean monthly temperature: a wavelet coupled second order Volterra model. Stoch Env Res Risk A 31:2159–2181. CrossRefGoogle Scholar
  26. Liu J, Han D (2013) On selection of the optimal data time interval for real-time hydrological forecasting. Hydrol Earth Syst Sci 17:3639–3659. CrossRefGoogle Scholar
  27. Maheswaran R, Khosa R (2012) Comparative study of different wavelets for hydrologic forecasting. Comput Geosci 46:284–295. CrossRefGoogle Scholar
  28. Maurer E, Hidalgo H (2008) Utility of daily vs monthly large-scale climate data: an intercomparison of two statistical downscaling methods. Hydrol Earth Syst Sci 12:551–563. CrossRefGoogle Scholar
  29. Maurer EP, Hidalgo HG, Das T, Dettinger M, Cayan D (2010) The utility of daily large-scale climate data in the assessment of climate change impacts on daily streamflow in California. Hydrol Earth Syst Sci 14:1125–1138. CrossRefGoogle Scholar
  30. Nahar J, Johnson F, Sharma A (2017) A rank-based approach for correcting systematic biases in spatial disaggregation of coarse-scale climate simulations. J Hydrol 550:716–725. CrossRefGoogle Scholar
  31. Nelder JA, Wedderburn RWM (1972) Generalized linear models. J R Stat Soc Ser A (General) 135:370–384. CrossRefGoogle Scholar
  32. Nourani V, Komasi M, Alami MT (2012) Hybrid wavelet-genetic programming approach to optimize ANN modeling of rainfall-runoff process. J Hydrol Eng 17:724–741. CrossRefGoogle Scholar
  33. Nourani V, Baghanam AH, Adamowski J, Kisi O (2014) Applications of hybrid wavelet–artificial intelligence models in hydrology: a review. J Hydrol 514:358–377. CrossRefGoogle Scholar
  34. Okkan U, Inan G (2015a) Statistical downscaling of monthly reservoir inflows for Kemer watershed in Turkey: use of machine learning methods, multiple GCMs and emission scenarios. Int J Climatol 35:3274–3295. CrossRefGoogle Scholar
  35. Okkan U, Inan G (2015b) Bayesian learning and relevance vector machines approach for downscaling of monthly precipitation. J Hydrol Eng 20:04014051-1-04014051–13. CrossRefGoogle Scholar
  36. Parasuraman K, Elshorbagy A, Carey SK (2007) Modelling the dynamics of the evapotranspiration process using genetic programming. Hydrolog Sci J 52:563–578. CrossRefGoogle Scholar
  37. Pour SH, Shahid S, Chung ES, Wang XJ (2018) Model output statistics downscaling using support vector machine for the projection of spatial and temporal changes in rainfall of Bangladesh. Atmos Res 213:149–162. CrossRefGoogle Scholar
  38. Rashid MM, Beecham S, Chowdhury RK (2016) Statistical downscaling of rainfall: a non-stationary and multi-resolution approach. Theor Appl Climatol 124:919–933. CrossRefGoogle Scholar
  39. Sa'adi Z, Shahid S, Chung ES, Ismail TB (2017) Projection of spatial and temporal changes of rainfall in Sarawak of Borneo Island using statistical downscaling of CMIP5 models. Atmos Res 197:446–460. CrossRefGoogle Scholar
  40. Sachindra DA, Huang F, Barton A, Perera BJC (2013) Least square support vector and multi-linear regression for statistically downscaling general circulation model outputs to catchment streamflows. Int J Climatol 33:1087–1106. CrossRefGoogle Scholar
  41. Sachindra DA, Ahmed K, Rashid MM, Shahid S, Perera BJC (2018a) Statistical downscaling of precipitation using machine learning techniques. Atmos Res 212:240–258. CrossRefGoogle Scholar
  42. Sachindra DA, Ahmed K, Shahid S, Perera BJC (2018b) Cautionary note on the use of genetic programming in statistical downscaling. Int J Climatol 38:3449–3465. CrossRefGoogle Scholar
  43. Sang YF (2013) A review on the applications of wavelet transform in hydrology time series analysis. Atmos Res 122:8–15. CrossRefGoogle Scholar
  44. Sang YF, Wang D, Wu JC (2010) Entropy-based method of choosing the decomposition level in wavelet threshold de-noising. Entropy 12:1499–1513. CrossRefGoogle Scholar
  45. Sang YF, Singh VP, Sun F, Chen Y, Liu Y, Yang M (2016) Wavelet-based hydrological time series forecasting. J Hydrol Eng 21:06016001. CrossRefGoogle Scholar
  46. Sehgal V, Tiwari MK, Chatterjee C (2014) Wavelet bootstrap multiple linear regression-based hybrid modelling for daily river discharge forecasting. Water Resour Manag 28:2793–2811. CrossRefGoogle Scholar
  47. Sehgal V, Lakhanpal A, Maheswaran R, Khosa R, Sridhar V (2018) Application of multi-scale wavelet entropy and multi-resolution Volterra models for climatic downscaling. J Hydrol 556:1078–1095. CrossRefGoogle Scholar
  48. Sehgal V, Sridhar V, Rathinasamy M (2019) Comparative analysis of the performance of wavelet-based and stand-alone models in capturing non-stationarity in climate downscaling. In: Rathinasamy M, Chandramouli S, Phanindra KBVN, Mahesh U (eds) Water resources and environmental engineering II: climate and environment. Springer, Singapore, pp 195–203. CrossRefGoogle Scholar
  49. Torrence C, Compo GP (1998) A practical guide to wavelet analysis. B Am Meteorol Soc 79:61–78.<0061:APGTWA>2.0.CO;2 CrossRefGoogle Scholar
  50. Widmann M, Bretherton CS, Salathé EP Jr (2003) Statistical precipitation downscaling over the northwestern United States using numerically simulated precipitation as a predictor. J Clim 16:799–816.<0799:SPDOTN>2.0.CO;2 CrossRefGoogle Scholar
  51. Wilby RL, Wigley TML (1997) Downscaling general circulation model output: a review of methods and limitations. Prog Phys Geogr 21:530–548. CrossRefGoogle Scholar
  52. Zhang X, Peng Y, Zhang C, Wang B (2015) Are hybrid models integrated with data preprocessing techniques suitable for monthly streamflow forecasting? Some experiment evidences. J Hydrol 530:137–152. CrossRefGoogle Scholar
  53. Zubler EM, Fischer AM, Frob F, Liniger MA (2016) Climate change signals of CMIP5 general circulation models over the Alps—impact of model selection. Int J Climatol 36:3088–3104. CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Institute for Sustainability and Innovation, College of Engineering and Science, Footscray Park CampusVictoria UniversityMelbourneAustralia
  2. 2.Faculty of Water Resources ManagementLasbela University of Agriculture, Water and Marine SciencesUthalPakistan
  3. 3.Faculty of Civil EngineeringUniversiti Teknologi MalaysiaJohor BahruMalaysia
  4. 4.Civil, Environmental, and Construction Engineering DepartmentUniversity of Central FloridaOrlandoUSA
  5. 5.Water Management and Hydrological ScienceTexas A&M UniversityCollege StationUSA

Personalised recommendations