# Combined Use of Graphical and Statistical Approaches for Analyzing Historical Precipitation Changes in the Black Sea Region of Turkey

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data

#### 2.2. Methods

#### 2.2.1. Refined Graphical–statistical CSD Trend Test and Diagnosis

_{1}) with the mean (variance) of zero (one) using

_{1}becomes zero, meaning that e

_{i}= 0 for 1 ≤ i ≤ n. A step-wise summation can be applied to d and e to obtain c and q, respectively, using

_{CSD}can be given by

_{CSD}is approximately normal with the mean of zero and the variance given by

_{CSD}with the mean of zero and variance equal to one can be computed using

_{α/2}denote the standard normal variate at a selected α. The null hypothesis H

_{0}(no trend) is rejected if |Z| > Z

_{α/2}at α; otherwise, the H

_{0}is not rejected.

_{k}versus k or time of observations. Positive and negative trends are shown by the right tail of the scatter plot above and below the reference (q

_{k}= 0 line), respectively. At a selected α, (100–α)% Confidences Interval (CI) limits are constructed and included in the plot of q

_{k}versus k. The (100–α)% CI limits Q based on the V* and Z

_{α/2}given by

_{0}(no trend) is rejected, otherwise, the H

_{0}is not rejected [27].

#### 2.2.2. Mann–Kendall (MK) Test

_{j}and x

_{i}are the sequential data values, n is the length of the data set and $\mathrm{sgn}(\theta )$ is equal to 1, 0, −1 if θ is greater than, equal to, or less than zero, respectively. The variance of S is obtained through:

_{i}is the number of data points in the ith group. Finally, the Mann–Kendall statistic, Z

_{MK}, is given by:

_{MK}values are approximately normally distributed, the null hypothesis, H

_{0}, of no trend is rejected if $\left|{Z}_{MK}\right|>\left|{Z}_{\alpha /2}\right|$, where Z

_{MK}is taken from the standard normal distribution table and α is the significance level. The positive and negative values of Z

_{MK}denote increasing and decreasing trends, respectively.

#### 2.2.3. ITA and Change Boxes

#### 2.2.4. Trend Magnitude

## 3. Results and Discussion

_{0}(no trend) was not rejected (p > 0.05) in the Winter, Spring and Autumn rainfall at all the selected stations. However, the H

_{0}(no trend) was rejected (p < 0.05) in the Summer rainfall from Amasya station. The annual rainfall was mainly characterized by positive trends for which H

_{0}(no trend) was rejected (p < 0.05) in the rainfall from 4 stations including Sinop, Giresun, Trabzon and Artvin. Considering the trends in the first and second halve of the time series, the highest number of significant trends is observed in the Autumn rainfall of the second half sub-series with significant trends at 56% of the selected stations.

_{0}(no trend) was rejected in terms of rainfall at Sinop, Giresun, Trabzon, and Artvin (Figure 4c,f–g,i).

_{MK}denote that the H

_{0}(no trend) was rejected at the 5% significance level. As observed from the table, there are significant increasing trends for the annual rainfall of Sinop, Ordu, Giresun, Trabzon, Artvin and Tokat, while seasons do not have significant trend when full rainfall time series is considered. Only summer season of Samsun has an increasing trend with respect to 5% significance level. Considering the first and second half of the time series, it is observed that most of the annual trends disappeared; there is only one station, Ordu, with increasing trend in the first half while two stations, Trabzon and Amasya have significantly increasing trends in the second half of the annual rainfall series. In this case, however, seasonal trends increased; Winter rainfall of Sinop and Samsun, Spring rainfall of Bartin and Rize and Autumn rainfall of Samsun have decreasing trends in the first halve while in the second sub series, Winter rainfall of Zonguldak and Artvin, Spring rainfall of Trabzon, and Autumn rainfall of Bartin, Zonguldak, Artvin, Kastamonu, Corum and Gumushane have increasing/decreasing trends. Summer rainfall does not show significant trend in subseries (first and second halves).

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**CSD-based graphical diagnoses of the trend significance for annual rainfall at stations (

**a**–

**p**) selected across the study area.

**Table 1.**Statistical information of monthly rainfall data and the record length at the observation stations (X

_{min}, X

_{max}and X

_{mean}: minimum, maximum and mean monthly precipitation; SD: standard deviation; C

_{v}: coefficient of variation; C

_{sx}: coefficient of skewness).

Station | Full Period | First Half | Second Half | X_{min} | X_{max} | X_{mean} | SD | C_{v} | C_{sx} |
---|---|---|---|---|---|---|---|---|---|

Bartın | 1965–2015 | 1964–1989 | 1990–2015 | 0 | 349.1 | 86.7 | 61.65 | 0.71 | 1.15 |

Zonguldak | 1960–2015 | 1960–1987 | 1988–2015 | 0 | 359.8 | 101.3 | 68.6 | 0.68 | 0.86 |

Sinop | 1960–2015 | 1960–1987 | 1988–2015 | 0 | 324.0 | 57.2 | 42.9 | 0.75 | 1.44 |

Samsun | 1960–2015 | 1960–1987 | 1988–2015 | 0 | 350.3 | 58.8 | 40.4 | 0.69 | 1.68 |

Ordu | 1963–2015 | 1963–1989 | 1990–2015 | 0.3 | 267.6 | 85.8 | 50.7 | 0.59 | 1.00 |

Giresun | 1960–2015 | 1960–1987 | 1988–2015 | 0.2 | 521.6 | 104.97 | 61.89 | 0.59 | 1.41 |

Trabzon | 1960–2015 | 1960–1983 | 1984–2005 | 2.8 | 293.0 | 68.1 | 43.8 | 0.64 | 1.28 |

Rize | 1960–2015 | 1960–1987 | 1988–2015 | 8.2 | 516.6 | 186.4 | 102.1 | 0.55 | 0.84 |

Artvin | 1960–2015 | 1960–1987 | 1988–2015 | 0.9 | 342.2 | 59.2 | 43.2 | 0.73 | 1.99 |

Bolu | 1960–2015 | 1960–1987 | 1988–2015 | 0 | 174.4 | 46.4 | 29.1 | 0.63 | 0.94 |

Duzce | 1960–2015 | 1961–1987 | 1988–2015 | 0 | 227.2 | 68.5 | 43.1 | 0.63 | 0.75 |

Kastamonu | 1960–2015 | 1960–1987 | 1988–2015 | 0 | 278.7 | 41.6 | 31.7 | 0.76 | 1.80 |

Corum | 1960–2015 | 1960–1987 | 1988–2015 | 0 | 220.1 | 36.8 | 28.4 | 0.77 | 1.37 |

Amasya | 1960–2015 | 1960–1987 | 1988–2015 | 0 | 144.6 | 38.3 | 28.4 | 0.74 | 0.87 |

Tokat | 1961–2015 | 1960–1987 | 1988–2015 | 0 | 141.1 | 36.1 | 27.3 | 0.76 | 0.87 |

Gumushane | 1965–2015 | 1965–1989 | 1990–2015 | 0 | 141.9 | 38.5 | 26.8 | 0.70 | 0.78 |

**Table 2.**Statistical results of trend analysis for seasonal and annual rainfall using the CSD method.

Rainfall Station | Full Time Series | First Half Sub−series | Second Half Sub−series | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Win | Spr | Sum | Aut | Ann | Win | Spr | Sum | Aut | Ann | Win | Spr | Sum | Aut | Ann | |

Bartin | −0.63 | −0.48 | 0.20 | 0.26 | 0.57 | −1.69 | −2.44 | 0.68 | 0.21 | −0.83 | 1.58 | 1.64 | −0.84 | 2.88 | 0.03 |

Zonguldak | −0.61 | −1.14 | −1.31 | −0.43 | −1.22 | −1.65 | −1.66 | −0.01 | −0.11 | −1.89 | 2.58 | 1.41 | −1.64 | 2.77 | −1.99 |

Sinop | 0.62 | 0.51 | 0.98 | 0.14 | 2.11 | −2.32 | −1.38 | 0.65 | −2.16 | −1.52 | 1.48 | 0.67 | 0.40 | −0.38 | 0.36 |

Samsun | −0.06 | −0.19 | 1.22 | 0.04 | 0.97 | −1.92 | −0.42 | 1.01 | −2.28 | −1.00 | 1.59 | 0.84 | 0.79 | 1.71 | 0.86 |

Ordu | 0.63 | 1.92 | −0.74 | 1.25 | 1.88 | 0.45 | 1.76 | 0.08 | 1.40 | 1.93 | −0.75 | −0.31 | 1.37 | 0.20 | 0.92 |

Giresun | −0.26 | 0.73 | 0.53 | 0.19 | 3.08 | 0.00 | 0.23 | 1.21 | −0.31 | 1.68 | 1.35 | 0.01 | −0.36 | 0.66 | 1.36 |

Trabzon | 1.93 | 1.53 | 1.64 | 1.58 | 3.35 | 0.15 | −0.99 | 0.64 | −0.36 | −0.09 | 1.53 | 2.01 | 0.33 | 0.32 | 1.99 |

Rize | −0.29 | −1.16 | 1.35 | −0.70 | 1.75 | −0.04 | −2.24 | −0.43 | −0.37 | −0.64 | −0.81 | 0.41 | 1.37 | −0.92 | 0.47 |

Artvin | 0.30 | 1.51 | 1.47 | 0.70 | 2.64 | 1.15 | 0.07 | −1.31 | 1.17 | 0.21 | −2.16 | 1.21 | 0.86 | −2.39 | −0.76 |

Bolu | −0.98 | 0.72 | 0.39 | 0.07 | 0.32 | 0.24 | −1.58 | −0.16 | 1.22 | −0.69 | 1.52 | 1.94 | 0.12 | 1.99 | 1.31 |

Duzce | −1.15 | −1.33 | −0.71 | −0.87 | −1.61 | −0.87 | −0.93 | 0.60 | 0.20 | −0.31 | −0.48 | 0.18 | −0.71 | 0.75 | −0.83 |

Kastamonu | 0.01 | 1.36 | 0.94 | −0.47 | 1.40 | 0.33 | 1.19 | 0.16 | 0.37 | 0.96 | 1.31 | 0.91 | 1.39 | 2.19 | 1.82 |

Corum | −1.32 | 0.29 | 1.13 | −0.38 | 0.79 | −0.20 | 1.12 | −0.28 | 0.56 | 1.00 | 0.86 | −1.05 | −0.21 | 2.49 | −0.19 |

Amasya | −0.99 | 1.10 | 2.11 | −0.73 | 1.22 | −2.02 | −0.43 | 1.59 | −0.46 | 0.35 | 1.86 | 0.37 | 1.60 | 3.11 | 1.94 |

Tokat | −1.21 | 1.33 | 0.89 | −0.06 | 1.80 | −0.81 | 1.15 | 0.51 | 1.23 | 1.60 | 0.42 | −1.13 | 0.44 | 2.48 | −0.62 |

Gumushane | −0.91 | 0.41 | −0.25 | 1.36 | 0.99 | 0.09 | −0.41 | 0.11 | 1.15 | 1.03 | 1.01 | 0.36 | −0.62 | 2.90 | 0.90 |

_{0}(no trend) was rejected (p < 0.05) are presented in bold.

Rainfall Station | Full Time Series | First Half Sub−series | Second Half Sub−series | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Win | Spr | Sum | Aut | Ann | Win | Spr | Sum | Aut | Ann | Win | Spr | Sum | Aut | Ann | |

Bartin | −0.71 | −0.35 | 0.19 | 0.29 | 0.95 | −4.6 | −3.54 | 1.28 | 0.82 | −4.95 | 3.19 | 2.14 | −1.84 | 6.47 | −0.72 |

Zonguldak | −0.51 | −0.63 | −0.97 | −0.43 | −1.45 | −2.3 | −3.46 | −0.05 | −0.01 | −6.77 | 6.06 | 1.31 | −3.26 | 6.62 | −6.78 |

Sinop | 0.40 | 0.24 | 0.51 | 0.09 | 2.46 | −3 | −1.52 | 0.97 | −2.20 | −6.22 | 1.55 | 0.79 | 0.67 | −0.42 | 0.78 |

Samsun | 0.04 | −0.05 | 1.21 | 0.01 | 1.20 | −2.8 | −0.55 | 1.24 | −3.39 | −3.65 | 2.46 | 0.79 | 1.43 | 1.92 | 2.61 |

Ordu | 0.33 | 0.88 | −0.54 | 1.16 | 2.22 | 0.6 | 1.52 | −0.10 | 2.44 | 9.24 | −0.9 | −0.51 | 2.68 | 0.49 | 1.33 |

Giresun | −0.18 | 0.41 | 0.36 | 0.15 | 3.44 | −0 | 0.59 | 1.34 | −0.42 | 3.94 | 1.76 | 0.26 | −1.59 | 1.31 | 5.86 |

Trabzon | 1.33 | 0.60 | 0.68 | 1.34 | 4.32 | 0.63 | −0.93 | 0.89 | −0.58 | −0.09 | 2.7 | 2.77 | 0.24 | 1.24 | 6.61 |

Rize | −0.53 | −0.81 | 1.07 | −0.92 | 3.94 | −0.5 | −3.07 | −1.24 | −0.64 | −4.15 | −2.1 | 0.37 | 5.12 | −1.82 | 3.21 |

Artvin | 0.13 | 0.35 | 0.64 | 0.49 | 2.23 | 2.35 | 0.01 | −0.71 | 1.80 | 0.58 | −5.8 | 1.00 | 0.95 | −8.19 | −2.55 |

Bolu | −0.14 | 0.21 | 0.38 | 0.06 | 0.39 | 0.03 | −1.54 | −0.13 | 1.68 | −0.92 | 1.85 | 2.19 | 0.16 | 2.83 | 2.36 |

Duzce | −1.28 | −0.37 | −0.39 | −0.71 | −1.85 | −1.4 | −1.58 | 0.83 | 0.50 | −1.32 | −1.3 | 0.47 | −2.26 | 1.17 | −1.84 |

Kastamonu | −0.04 | 0.49 | 0.56 | −0.17 | 1.39 | 0.41 | 1.36 | 0.01 | 0.43 | 2.16 | 1.21 | 1.39 | 2.92 | 1.88 | 5.40 |

Corum | −0.59 | 0.06 | 0.30 | −0.13 | 0.30 | −0.2 | 0.94 | −0.52 | 0.99 | 1.88 | 1.33 | −0.91 | −0.59 | 2.77 | −0.71 |

Amasya | −0.80 | 0.33 | 0.37 | −0.53 | 0.83 | −2.6 | −0.51 | 1.27 | −0.59 | 0.71 | 2.96 | 0.73 | 1.12 | 3.90 | 4.26 |

Tokat | −0.53 | 0.43 | 0.28 | 0.02 | 1.27 | −0.9 | 0.82 | 0.24 | 1.88 | 3.34 | 0.24 | −0.96 | 0.28 | 1.89 | −1.25 |

Gumushane | −0.29 | 0.20 | −0.03 | 0.50 | 0.87 | 0.07 | −0.52 | 0.15 | 1.13 | 2.62 | 1.12 | 0.71 | −0.32 | 2.26 | 1.94 |

Rainfall Station | Full Time Series | First Half Sub−series | Second Half Sub−series | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Win | Spr | Sum | Aut | Ann | Win | Spr | Sum | Aut | Ann | Win | Spr | Sum | Aut | Ann | |

Bartin | −0.26 | −0.49 | 0.26 | 0.32 | 0.50 | −0.63 | −2.31 | 0.63 | 0.30 | −1.17 | 1.76 | 1.45 | −0.66 | 2.71 | −0.49 |

Zonguldak | −0.73 | −0.94 | −1.38 | −0.76 | −1.16 | −1.63 | −1.72 | −0.02 | 0.02 | −1.92 | 2.70 | 1.52 | −1.52 | 2.53 | −1.70 |

Sinop | 0.78 | 0.62 | 1.11 | −0.11 | 2.18 | −2.75 | −1.32 | 0.77 | −1.80 | −1.88 | 1.18 | 0.85 | 0.49 | −0.86 | 0.38 |

Samsun | 0.09 | −0.11 | 2.36 | −0.17 | 1.32 | −2.23 | −0.49 | 1.01 | −2.43 | −1.01 | 1.32 | 0.85 | 1.02 | 1.22 | 1.05 |

Ordu | 0.96 | 1.84 | −0.77 | 1.10 | 2.11 | 1.04 | 0.88 | −0.04 | 1.28 | 1.97 | −0.66 | −0.93 | 1.42 | 0.29 | 0.48 |

Giresun | −0.31 | 0.70 | 0.48 | 0.19 | 3.28 | −0.54 | 0.24 | 0.97 | −0.10 | 1.68 | 0.29 | 0.04 | −0.45 | 0.53 | 1.48 |

Trabzon | 1.35 | 1.40 | 1.58 | 1.18 | 3.39 | 0.21 | −1.00 | 0.58 | −0.32 | −0.05 | 0.74 | 2.17 | 0.24 | −0.03 | 2.01 |

Rize | −0.46 | −1.34 | 1.19 | −1.02 | 1.77 | −0.36 | −2.23 | −0.53 | −0.26 | −0.57 | −1.44 | 0.22 | 1.26 | −1.18 | 0.55 |

Artvin | 0.12 | 1.35 | 1.93 | 0.97 | 2.25 | 0.79 | 0.02 | −1.13 | 1.28 | 0.30 | −2.31 | 1.09 | 0.85 | −2.23 | −0.69 |

Bolu | −0.48 | 0.63 | 0.72 | −0.12 | 0.56 | 0.19 | −1.42 | −0.10 | 1.40 | −0.61 | 1.52 | 1.76 | 0.13 | 1.50 | 1.05 |

Duzce | −1.66 | −0.78 | −0.66 | −1.08 | −1.54 | −0.13 | −0.79 | 0.64 | 0.52 | −0.33 | −0.17 | 0.25 | −0.79 | 0.51 | −0.83 |

Kastamonu | −0.12 | 0.98 | 0.85 | −0.75 | 1.58 | 0.42 | 1.17 | 0.02 | 0.40 | 1.01 | 1.05 | 0.77 | 1.40 | 1.96 | 1.92 |

Corum | −1.32 | 0.19 | 0.58 | −0.69 | 0.41 | −0.34 | 1.21 | −0.28 | 0.69 | 1.03 | 0.38 | −1.15 | −0.26 | 2.13 | −0.38 |

Amasya | −1.26 | 0.86 | 1.61 | −1.39 | 1.36 | −1.42 | −0.38 | 1.06 | −0.46 | 0.30 | 1.80 | 0.71 | 1.03 | 1.93 | 2.04 |

Tokat | −0.88 | 1.13 | 0.99 | −0.33 | 2.03 | −0.21 | 0.96 | 0.13 | 1.04 | 1.63 | 0.22 | −0.87 | 0.18 | 1.37 | −0.54 |

Gumushane | −0.43 | 0.39 | −0.13 | 1.60 | 1.19 | 0.53 | −0.44 | 0.12 | 1.23 | 1.48 | 1.05 | 0.48 | −0.49 | 2.27 | 1.19 |

_{MK}denote that the H

_{0}(no trend) was rejected at the 5% significance level.

**Table 5.**Trends and change rates of annual rainfall at all stations using the ITA-CB (Minimum, mean and maximum percentage changes for each group are presented).

Station | Low Group | High Group | All Group | ||||||
---|---|---|---|---|---|---|---|---|---|

Min | Mean | Max | Min | Mean | Max | Min | Mean | Max | |

Bartin | 4.25 | 6.09 | 7.50 | −0.88 | 6.75 | 11.90 | −0.88 | 6.65 | 11.90 |

Zonguldak | −8.04 | 4.29 | 13.39 | 5.12 | 15.27 | 3.27 | 13.39 | 3.27 | 20.00 |

Sinop | 35.17 | 46.70 | 59.29 | −3.49 | 4.15 | 10.24 | 59.29 | 19.25 | 59.29 |

Samsun | 14.42 | 17.70 | 21.54 | −6.33 | −4.05 | −1.29 | −6.33 | 6.52 | 21.54 |

Ordu | 16.69 | 18.00 | 20.69 | −3.90 | −1.04 | 3.22 | −3.90 | 6.06 | 20.69 |

Giresun | −8.18 | 1.61 | 5.08 | 3.48 | 13.01 | 22.42 | −8.18 | 7.58 | 22.42 |

Trabzon | 9.72 | 16.69 | 19.46 | 10.52 | 12.27 | 13.60 | 6.43 | 13.70 | 19.46 |

Rize | −35.57 | 13.40 | 4.82 | 3.65 | 3.93 | 21.12 | −35.57 | 7.23 | 21.12 |

Artvin | 18.81 | 21.29 | 27.23 | 3.86 | 8.96 | 15.09 | 3.86 | 15.09 | 27.23 |

Bolu | −6.57 | −3.43 | 1.35 | −4.80 | 1.54 | 5.26 | −6.57 | 0.98 | 6.15 |

Duzce | −11.81 | −1.54 | 3.68 | −9.72 | −5.38 | 3.06 | −11.81 | −5.20 | 3.68 |

Kastamonu | −6.83 | −2.22 | 8.91 | 2.80 | 20.10 | 5.95 | −6.83 | 5.95 | 40.51 |

Corum | −21.80 | 4.81 | 17.53 | 4.47 | 6.69 | 8.29 | −21.80 | 1.75 | 17.53 |

Amasya | −1.60 | 1.68 | 7.73 | −4.00 | 4.56 | 2.29 | −4.00 | 2.29 | 11.15 |

Tokat | 6.64 | 9.61 | 13.08 | 5.33 | 6.64 | 8.18 | 13.09 | 8.18 | 13.09 |

Gumushane | −11.02 | −0.82 | 3.04 | −5.58 | 1.86 | 8.70 | −11.02 | 1.02 | 8.70 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Cengiz, T.M.; Tabari, H.; Onyutha, C.; Kisi, O. Combined Use of Graphical and Statistical Approaches for Analyzing Historical Precipitation Changes in the Black Sea Region of Turkey. *Water* **2020**, *12*, 705.
https://doi.org/10.3390/w12030705

**AMA Style**

Cengiz TM, Tabari H, Onyutha C, Kisi O. Combined Use of Graphical and Statistical Approaches for Analyzing Historical Precipitation Changes in the Black Sea Region of Turkey. *Water*. 2020; 12(3):705.
https://doi.org/10.3390/w12030705

**Chicago/Turabian Style**

Cengiz, Taner Mustafa, Hossein Tabari, Charles Onyutha, and Ozgur Kisi. 2020. "Combined Use of Graphical and Statistical Approaches for Analyzing Historical Precipitation Changes in the Black Sea Region of Turkey" *Water* 12, no. 3: 705.
https://doi.org/10.3390/w12030705