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Trend analysis and forecasting of the Gökırmak River streamflow (Turkey)

Gökhan Arslan
Gökhan Arslan
, 
Semih Kale
Semih Kale
 y 
Adem Yavuz Sönmez
Adem Yavuz Sönmez
   | 25 sept 2020
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Article Category: Research Article
Publicado en línea: 25 sept 2020
Páginas: 230 - 246
Recibido: 25 feb 2020
Aceptado: 20 abr 2020
DOI: https://doi.org/10.1515/ohs-2020-0021
© 2020 Faculty of Oceanography and Geography, University of Gdańsk, Poland
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1

The Gökırmak River and the location of the streamflow gauging station
The Gökırmak River and the location of the streamflow gauging station

Figure 2

The autocorrelation functions (ACF) and partial autocorrelation functions (PACF) of the natural logarithm of annual and mean seasonal streamflow data. The lines represent the 95% confidence interval.
The autocorrelation functions (ACF) and partial autocorrelation functions (PACF) of the natural logarithm of annual and mean seasonal streamflow data. The lines represent the 95% confidence interval.

Figure 3

The autocorrelation functions (ACF) of the natural logarithm of mean monthly streamflow data. The lines represent the 95% confidence interval.
The autocorrelation functions (ACF) of the natural logarithm of mean monthly streamflow data. The lines represent the 95% confidence interval.

Figure 4

The partial autocorrelation functions (PACF) of the natural logarithm of the mean monthly streamflow data. The lines represent the 95% confidence interval.
The partial autocorrelation functions (PACF) of the natural logarithm of the mean monthly streamflow data. The lines represent the 95% confidence interval.

Figure 5

Trend analysis results for mean annual streamflow. In variable box; actual is the observed value; forecasts are the predicted values; fits are calculated values that best fitting to forecast. The accuracy of models was assessed by using commonly used performance measures which are mean absolute deviation (MAD), mean squared deviation (MSD), mean absolute percentage error (MAPE).
Trend analysis results for mean annual streamflow. In variable box; actual is the observed value; forecasts are the predicted values; fits are calculated values that best fitting to forecast. The accuracy of models was assessed by using commonly used performance measures which are mean absolute deviation (MAD), mean squared deviation (MSD), mean absolute percentage error (MAPE).

Figure 6

Trend analysis results for mean seasonal streamflow. In variable box; actual is the observed value; forecasts are the predicted values; fits are calculated values that best fitting to forecast. The accuracy of models was assessed by using commonly used performance measures which are mean absolute deviation (MAD), mean squared deviation (MSD), mean absolute percentage error (MAPE).
Trend analysis results for mean seasonal streamflow. In variable box; actual is the observed value; forecasts are the predicted values; fits are calculated values that best fitting to forecast. The accuracy of models was assessed by using commonly used performance measures which are mean absolute deviation (MAD), mean squared deviation (MSD), mean absolute percentage error (MAPE).

Figure 7

Trend analysis results for mean monthly streamflow. In variable box; actual is the observed value; forecasts are the predicted values; fits are calculated values that best fitting to forecast. The accuracy of models was assessed by using commonly used performance measures which are mean absolute deviation (MAD), mean squared deviation (MSD), mean absolute percentage error (MAPE).
Trend analysis results for mean monthly streamflow. In variable box; actual is the observed value; forecasts are the predicted values; fits are calculated values that best fitting to forecast. The accuracy of models was assessed by using commonly used performance measures which are mean absolute deviation (MAD), mean squared deviation (MSD), mean absolute percentage error (MAPE).

Descriptive statistics of the streamflow data

Streamflow Mean SD CV CS Maximum value Minimum value Range
Annual 28.48 3.43 0.45 202.46 49.90 10.46 39.44
Spring 64.89 8.16 0.47 415.31 111.77 25.37 86.40
Summer 21.27 4.17 0.73 78.39 50.71 3.64 47.06
Autumn 8.70 0.89 0.38 69.84 13.90 1.38 12.52
Winter 19.07 2.53 0.50 105.58 34.73 5.00 29.73

Results of skewness, kurtosis and normality tests

Streamflow Skewness SEskewness Zskewness Kurtosis SEkurtosis Zkurtosis Kolmogorov–Smirnov* Shapiro–Wilk
Statistics p-value Statistics p-value
Annual 0.04 0.597 0.067 −1.35 1.154 −0.001 0.175 0.200* 0.935 0.200*
Spring 0.18 0.597 0.302 −1.53 1.154 −0.001 0.139 0.200* 0.921 0.200*
Summer 0.42 0.597 0.704 −1.01 1.154 −0.001 0.182 0.200* 0.924 0.200*
Autumn −0.58 0.597 −0.972 0.55 1.154 0.000 0.129 0.200* 0.853 0.042
Winter 0.21 0.597 0.352 −1.12 1.154 −0.001 0.137 0.200* 0.956 0.200*

Parameters of ARIMA models for annual streamflow data

Parameters Models
ARIMA (1, 1, 0) ARIMA (0, 1, 1) ARIMA (1, 1, 1)
AR MA AR MA
  Coefficient −0.637 0.890 −0.126 0.894
  SE 0.255 0.314 0.377 344
  p-value 0.029 0.016 0.746 0.027
  Normalized BIC 15.616 15.409 15.863
  R2 −0.565 −0.272 −0.479
  Ljung–Box Statistics 25.31 19.11 18.12
  Ljung–Box p-value 0.005 0.039 0.034

Values of non-parametric tests and trend status

Period Streamflow Kendall’s tau p Trend Spearman’s rho p Trend
Annual Annual −0.055 0.784 ▼ −0.055 0.852 ▼
Seasonal Spring −0.209 0.298 ▼ −0.297 0.303 ▼
Summer 0.143 0.477 ▲ 0.240 0.409 ▲
Autumn −0.297 0.169 ▼ −0.437 0.118 ▼
Winter −0.099 0.622 ▼ −0.108 0.714 ▼
Monthly January −0.209 0.298 ▼ −0.262 0.366 ▼
February −0.165 0.412 ▼ −0.204 0.483 ▼
March −0.055 0.784 ▼ −0.099 0.737 ▼
April −0.209 0.298 ▼ −0.288 0.318 ▼
May −0.143 0.477 ▼ −0.143 0.626 ▼
June 0.209 0.298 ▲ 0.244 0.401 ▲
July 0.011 0.956 ▲ 0.156 0.594 ▲
August −0.231 0.250 ▼ −0.288 0.318 ▼
September −0.209 0.298 ▼ −0.341 0.233 ▼
October −0.231 0.250 ▼ −0.349 0.221 ▼
November −0.209 0.298 ▼ −0.226 0.436 ▼
December 0.033 0.870 ▲ −0.011 0.970 ▼
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