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

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

Table 2

Results of skewness, kurtosis and normality tests

Streamflow	Skewness	SE_skewness	Z_skewness	Kurtosis	SE_kurtosis	Z_kurtosis	Kolmogorov–Smirnov^*		Shapiro–Wilk
Streamflow	Skewness	SE_skewness	Z_skewness	Kurtosis	SE_kurtosis	Z_kurtosis	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^*

[i] Note: ^*indicates the lower limit of the true significance.

^a indicates the Lilliefors Significance Correction

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) of the natural logarithm of 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.

Table 3

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

[i] Note: ARIMA means autoregressive integrated moving average; AR – autoregressive; MA– moving average; SE – standard error; BIC – Bayesian Information Criterion.

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 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 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).

Table 4

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	▼

[i] Note: ▼ indicates decreasing trends; ▲ indicates increasing trends

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DOI: https://doi.org/10.1515/ohs-2020-0021 | Journal eISSN: 1897-3191 | Journal ISSN: 1730-413X

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Language: English

Page range: 230 - 246

Submitted on: Feb 25, 2020

Accepted on: Apr 20, 2020

Published on: Sep 25, 2020

Published by: University of Gdańsk

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

river,

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© 2020 Gökhan Arslan, Semih Kale, Adem Yavuz Sönmez, published by University of Gdańsk
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 49 (2020): Issue 3 (September 2020)

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

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