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Ability Assessment of the Stationary and Cyclostationary Time Series Models to Predict Drought Indices

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Abstract

Drought forecasting and monitoring play a significant role in reducing the negative effects of global meteorological droughts caused by different intensities at different temporal and spatial scales in different regions, especially in regions with high dependency on rainwater. The present study tries to compare the accuracy of stationary time series (ST) models including autoregressive moving average (ARMA), moving average (MA) and autoregressive (AR) and cyclostationary time series (CT) models including periodic autoregressive moving average (PARMA), periodic moving average (PMA) and periodic autoregressive (PAR) to predict drought index (i.e. monthly reconnaissance drought index (RDI)) in periodic data series considering that CT models are more powerful and efficient than ST models by using data series of 8 synoptic stations with different climate conditions in Iran from 1967 to 2017. According to the results the monthly RDI was significantly periodic in all selected stations. The PAR (25) model was the best fitted CT model in data series at all stations and on the other hand, the following models were the best-fitted ST models in data series: the AR models at Babolsar and Rasht AR (25) and at Gorgan AR (24) and ARMA models at Tehran ARMA (2, 3), at Zahedan and Shiraz ARMA (2, 4) and at Esfahan and Shahre Kord ARMA (2, 5). Based on the best fitted CT and ST models, the results showed that the correlation coefficients (R) between observed and simulated RDI vary from 0.882 to 0.946 and from 0.693 to 0.874, respectively from January 1967 to December 2017. According to the best fitted CT and ST models, the validation test of the best fitted models indicated that the R between observed and simulated RDI vary from 0.634 to 0.883 and 0.585 to 0.847, respectively from January 2012 to December 2017. In total, it can be concluded that that the accuracy and capability of CT models in predicting the RDI were more than those of the ST models at all stations and the hypothesis of the study was confirmed.

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Data Availability

The was used data in this research will be available (by the corresponding author), upon reasonable request.

Abbreviations

ST:

Stationary time series models.

ARMA:

Autoregressive Moving Average.

MA:

Moving Average.

AR:

Autoregressive.

CT:

Cyclostationary time series models.

PARMA:

Periodic Autoregressive Moving Average.

PMA:

Periodic Moving Average.

PAR:

Periodic Autoregressive.

RDI:

Reconnaissance Drought Index.

SPI:

Standardized Precipitation Index.

IMO:

Iran Meteorological Organization.

PET:

Potential Evapotranspiration.

ACF:

Autocorrelation Function.

PACF:

Partial autocorrelation function

PEACF:

Periodic Autocorrelation Function.

PEPACF:

Periodic Partial autocorrelation function

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Acknowledgments

The authors of the article would like to thank the meteorological organization of Iran for supplying the necessary meteorological information.

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Authors and Affiliations

  1. Department of Range and Watershed Management (Nature Engineering), College of Agricultural Science, Fasa University, Fasa, Iran

    Abdol Rassoul Zarei

  2. Department of Statistics, Faculty of Science, Fasa University, Fasa, Iran

    Mohammad Reza Mahmoudi

  3. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Mohammad Reza Mahmoudi

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  1. Abdol Rassoul Zarei
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Contributions

The participation of Abdol Rassoul Zarei in the article includes data collection, data evaluation, assistance in analyzing the results and writing the article, and the participation of Mohammad Reza Mahmoudi includes Programming and implementation of statistical models and assistance in analyzing the results.

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Correspondence to Abdol Rassoul Zarei.

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Zarei, A.R., Mahmoudi, M.R. Ability Assessment of the Stationary and Cyclostationary Time Series Models to Predict Drought Indices. Water Resour Manage 34, 5009–5029 (2020). https://doi.org/10.1007/s11269-020-02710-5

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