Analysis of Precipitation Time Series of Urban Centers of Northeastern Brazil using Wavelet Transform
The urban centers within northeastern Brazil are
mainly influenced by the intense rainfalls, which can occur after long
periods of drought, when flood events can be observed during such
events. Thus, this paper aims to study the rainfall frequencies in such
region through the wavelet transform. An application of wavelet
analysis is done with long time series of the total monthly rainfall
amount at the capital cities of northeastern Brazil. The main
frequency components in the time series are studied by the global
wavelet spectrum and the modulation in separated periodicity bands
were done in order to extract additional information, e.g., the 8 and
16 months band was examined by an average of all scales, giving a
measure of the average annual variance versus time, where the
periods with low or high variance could be identified. The important
increases were identified in the average variance for some periods,
e.g. 1947 to 1952 at Teresina city, which can be considered as high
wet periods. Although, the precipitation in those sites showed similar
global wavelet spectra, the wavelet spectra revealed particular
features. This study can be considered an important tool for time
series analysis, which can help the studies concerning flood control,
mainly when they are applied together with rainfall-runoff
simulations.
[1] A. Grossman, and J. Morlet, "Decomposition of Hardy functions into
square integrable wavelets of constant shape," SIAM J. Math. Anal., vol.
15, pp. 723-736, 1984.
[2] A. Graps, "An introduction to wavelets," IEEE Computational Science
and Engineering, vol. 2, No. 2, pp. 50-61, 1995.
[3] C. Torrence, and G. P. Compo, "A practical guide to wavelet analysis,"
Bull. Amer. Meteor. Soc., vol. 79, No. 1, pp. 61-78, 1998.
[4] M. Farge, "Wavelet transforms and their applications to turbulence,"
Ann. Rev. Fluid Mech., vol. 24, pp. 395-457, 1992.
[5] L. C. Smith, D. L. Turcitte and B. L. Isacks, "Stream flow
characterization and feature detection using a discrete wavelet
transform," Hydrological Processes, vol. 12, pp. 233-249, 1998.
[6] I. Y. L. G. Braga, and C. A. G. Santos. "Viability of rainwater use in
condominiums based on the precipitation frequency for reservoir sizing
analysis," J. Urban and Environ. Engng, vol. 4, No. 1, pp. 23-28, 2010.
[7] C. A. G. Santos, B. S. Morais, and G. B. L. Silva. "Drought forecast
using Artificial Neural Network for three hydrological zones in San
Francisco river basin," IAHS Publication, vol. 333, pp. 302-312, 2009.
[8] C. A. G. Santos, V. S. Srinivasan, K. Suzuki, and M. Watanabe,
"Application of an optimization technique to a physically based erosion
model," Hydrological Processes, v. 17, No. 5, pp. 989-1003, 2003.
[1] A. Grossman, and J. Morlet, "Decomposition of Hardy functions into
square integrable wavelets of constant shape," SIAM J. Math. Anal., vol.
15, pp. 723-736, 1984.
[2] A. Graps, "An introduction to wavelets," IEEE Computational Science
and Engineering, vol. 2, No. 2, pp. 50-61, 1995.
[3] C. Torrence, and G. P. Compo, "A practical guide to wavelet analysis,"
Bull. Amer. Meteor. Soc., vol. 79, No. 1, pp. 61-78, 1998.
[4] M. Farge, "Wavelet transforms and their applications to turbulence,"
Ann. Rev. Fluid Mech., vol. 24, pp. 395-457, 1992.
[5] L. C. Smith, D. L. Turcitte and B. L. Isacks, "Stream flow
characterization and feature detection using a discrete wavelet
transform," Hydrological Processes, vol. 12, pp. 233-249, 1998.
[6] I. Y. L. G. Braga, and C. A. G. Santos. "Viability of rainwater use in
condominiums based on the precipitation frequency for reservoir sizing
analysis," J. Urban and Environ. Engng, vol. 4, No. 1, pp. 23-28, 2010.
[7] C. A. G. Santos, B. S. Morais, and G. B. L. Silva. "Drought forecast
using Artificial Neural Network for three hydrological zones in San
Francisco river basin," IAHS Publication, vol. 333, pp. 302-312, 2009.
[8] C. A. G. Santos, V. S. Srinivasan, K. Suzuki, and M. Watanabe,
"Application of an optimization technique to a physically based erosion
model," Hydrological Processes, v. 17, No. 5, pp. 989-1003, 2003.
@article{"International Journal of Earth, Energy and Environmental Sciences:58752", author = "Celso A. G. Santos and Paula K. M. M. Freire", title = "Analysis of Precipitation Time Series of Urban Centers of Northeastern Brazil using Wavelet Transform", abstract = "The urban centers within northeastern Brazil are
mainly influenced by the intense rainfalls, which can occur after long
periods of drought, when flood events can be observed during such
events. Thus, this paper aims to study the rainfall frequencies in such
region through the wavelet transform. An application of wavelet
analysis is done with long time series of the total monthly rainfall
amount at the capital cities of northeastern Brazil. The main
frequency components in the time series are studied by the global
wavelet spectrum and the modulation in separated periodicity bands
were done in order to extract additional information, e.g., the 8 and
16 months band was examined by an average of all scales, giving a
measure of the average annual variance versus time, where the
periods with low or high variance could be identified. The important
increases were identified in the average variance for some periods,
e.g. 1947 to 1952 at Teresina city, which can be considered as high
wet periods. Although, the precipitation in those sites showed similar
global wavelet spectra, the wavelet spectra revealed particular
features. This study can be considered an important tool for time
series analysis, which can help the studies concerning flood control,
mainly when they are applied together with rainfall-runoff
simulations.", keywords = "rainfall data, urban center, wavelet transform.", volume = "6", number = "7", pages = "426-6", }