# Investigation of Annual Lake Water Levels and Water Volumes with Şen Innovation and Mann-Kendall Rank Correlation Trend Tests: Example of Lake Eğirdir, Turkey

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## Abstract

**:**

^{3}in approximately 32 years. The actions to be taken based on the values determined in this study will help protect the water resources of lakes. As a result of the tests used in our study, it was determined that there were decreases in both the water level and the volume of the lake. The climatic changes in the lake basin and the decrease in the water resources feeding the lake are shown as the biggest factor in these reductions.

## 1. Introduction

^{3}, is mostly found in oceans and seas, as saltwater that people cannot use in a healthy and economical way [3,4]. Regardless of its severity, the concept of drought, which is one of the most serious problems for societies and ecosystems, has become more important in recent years in parallel with climate changes [5]. Turkey is a country that is faced with many different effects of climate change. Heavy rains, floods, drought, and extreme heat are just some of these threats to the climate and environment. It was stated that to postpone the devastating effects of climate change and to be able to combat climate change, all aspects of the current situation should be handled and understood [6,7,8,9].

## 2. Materials and Methods

#### 2.1. Materials

^{3}) measured between the years 1988 and 2019 by DSI (General Directorates of the State Hydraulic Works) for Lake Eğirdir were used. This study aimed to determine the trend values of the changes in the used lake water level and volume.

^{2}and the lake surface area is 480 km

^{2}on average. Although it varies according to years, its average elevation is 915.0 m and the maximum water elevation is 919.2 m [16,17]. The Lake Eğirdir lake level measurement station and meteorological measurement station features are given in Table 1 [18,19,20,21].

#### 2.2. Methods

#### 2.2.1. Dependency Test (DT)

#### 2.2.2. Autocorrelation Coefficient Significance Test

_{0}: ${\rho}_{1}$ = 0), and if it is outside the interval, it is decided that there is autocorrelation (H

_{1}: ${\rho}_{1}$ ≠ 0). In the absence of autocorrelation (${\rho}_{1}$), the data are used in studies to be carried out without making any changes in the time series. However, in the case of autocorrelation (${\rho}_{1}$), the pre-whitening process is applied to the observation series. The data obtained from the time series are used in studies to be carried out (such as regression analysis) [24,28,32,33,34].

#### 2.2.3. Linear Regression Analysis (LRA)

- Hypothesis tests are used to test whether the ${\beta}_{i}$ coefficients are significant in the developed regression equation. The hypotheses established are: H
_{0}= no relationship between the dependent and independent variables (${\beta}_{i}$ = 0), and H_{1}= there is a relationship between the dependent and independent variables (${\beta}_{i}$ ≠ 0), and it is checked whether the parameters are equal to zero.

_{1}hypothesis), and it is said that the b coefficient is significant. If ${t}_{H}$ < ${t}_{Table}$, the slope is insignificant (H

_{0}hypothesis) and rejected and it is decided that the coefficient b is statistically insignificant [25,26,38,39].

#### 2.2.4. t-Test (Student’s t)

_{0}: (${\overline{x}}_{1}-{\overline{x}}_{2})=0$ or H

_{1}: (${\overline{x}}_{1}-{\overline{x}}_{2})\ne 0$ hypotheses check), the ${t}_{H}$ statistic is used. The following Equation (1) is used for the calculations:

- ${t}_{H}$ = calculated test statistic;
- ${\overline{x}}_{1}$, ${\overline{x}}_{2}$ = series start and end average;
- n = number of observations;
- $s$ = standard deviation.

_{0}: ${\overline{x}}_{1}={\overline{x}}_{2}$, H

_{1}: ${\overline{x}}_{1}\ne {\overline{x}}_{2}$ hypothesis, when the series is divided into two non-overlapping subgroups, the t-test is performed according to the conditions that the number of observations of the subgroups is equal or not. While testing the difference between two averages, the following classification is made in terms of test statistics [25,26,32,38,39,40]. If the series subgroups have equal numbers of data (${n}_{1}$ = ${n}_{2}$), the ${t}_{H}$ statistic is calculated using the combined variance according to the Equation (2):

- ${t}_{H}$ = calculated test statistic;
- ${\overline{x}}_{1}$, ${\overline{x}}_{2}$ = average of each sub-series;
- ${s}_{1}^{2},$ ${s}_{2}^{2}$ = standard deviation of each sub-series;
- n = total number of data in the series;
- ${n}_{1}$, ${n}_{2}$ = number of data for each sub-series.

- ${t}_{H}$ = calculated test statistic;
- ${\overline{x}}_{1}$, ${\overline{x}}_{2}$ = average of each sub-series;
- ${s}_{1}^{2},$ ${s}_{2}^{2}$ = variance of each subseries;
- n = total number of data in the series;
- ${n}_{1}$, ${n}_{2}$ = number of data for each sub-series.

#### 2.2.5. Rate of Change (CR)

- CR = rate of change (%);
- $S{D}_{1}$ = first series average;
- $S{D}_{2}$ = second series average.

#### 2.2.6. Pre-Whitening Analysis (PA)

#### 2.2.7. Trend Free Pre-Whitening

- ${y}_{t}$ = de-trend series;
- ${x}_{t}$ = chronologically ordered (t) observation series value;
- ${\beta}_{1}$ = calculated slope value of the LRA;

- ${y}_{t}^{\prime}$ = value of the de-trended series at time t;
- ${y}_{t}$ = de-trend series;
- ${\rho}_{1}$ = lagged-1 autocorrelation coefficient of the old (with dependency) series;
- ${y}_{t-1}$ = de-trended series at time t − 1, the recalculated lag–1 autocorrelation coefficient for the de-trended series is (${\rho}_{1}$).

- ${X}_{t}^{\ast}$ = re-trendless pre-adjusted series;
- ${y}_{t}^{\prime}$ = value of the de-trended series at time t;
- ${\beta}_{1}$ = calculated slope value of the LRA;
- t = chronologically ordered time.

#### 2.2.8. Trend Test

_{0}). Different methods have been developed to control the null hypothesis, which is expressed as H

_{0}: no trend and H

_{1}: trend [53,54].

#### 2.2.9. Mann-Kendall Rank Correlation Trend Test (MKRCTT)

- ${m}_{i}$ = smaller or bigger value after its ordinal number within the ordinal numbers of the serial values;
- ${t}_{i}$ = ${m}_{i}$ total number;
- n = number of the observations;
- i = serial chronological ordinal number;
- N = total number of data in the series;
- $E\left({t}_{i}\right)$ = series average;
- var(t
_{i}) = series variance; - ${n}_{i}$ = ordinal number of each data in the series;

#### 2.2.10. Şen Innovation Trend Test (SITT)

- The slope of the trend test is calculated using Equation (13):$$s=\frac{2\times \left({\overline{y}}_{2}-{\overline{y}}_{1}\right)}{n},$$
- $s$ = standard deviation;
- ${\overline{y}}_{1},{\overline{y}}_{2}$ = the arithmetic means of each sub-series (first sub-series (${\overline{y}}_{1}$) and second sub-series (${\overline{y}}_{2}$)) formed by dividing the dependent variable series into two;
- n = serial total number of data.

- The relative error of the trend slope is calculated using Equation (14):$${r}_{e}=100\times \left(\frac{{\beta}_{0r}-{\beta}_{0g}}{{\beta}_{0r}}\right),$$
- ${r}_{e}$ = relative error of the trend slope;
- ${\beta}_{0r}$ = trend equation ${\beta}_{0}$ coefficient created by LRA of the new de-trended series;
- ${\beta}_{0g}$ = ${\beta}_{0}$ coefficient of the LRA equation created by graphing the two lower series.

- 3.
- The cross-correlation coefficient (${\rho}_{{\overline{y}}_{2}{\overline{y}}_{1}}$) is calculated using Equation (15):$${\rho}_{{\overline{y}}_{2}{\overline{y}}_{1}}=\frac{\left[E\left({\overline{y}}_{2}{\overline{y}}_{1}\right)-E\left({\overline{y}}_{2}\right)\times E\left({\overline{y}}_{1}\right)\right]}{{\sigma}_{{\overline{y}}_{2}}\times {\sigma}_{{\overline{y}}_{1}}},$$
- ${\overline{y}}_{1},{\overline{y}}_{2}$ = the arithmetic means of each sub-series (first sub-series (${\overline{y}}_{1}$) and second sub-series (${\overline{y}}_{2}$)) formed by dividing the dependent variable series into two;
- E(${\overline{y}}_{1}),$E(${\overline{y}}_{2})$ = each subseries slope (first-order moment);
- ${\sigma}_{{\overline{y}}_{1}}$, ${\sigma}_{{\overline{y}}_{2}}$ = variance of each subseries slope;
- ${\rho}_{{\overline{y}}_{2}{\overline{y}}_{1}}$ = the cross-correlation coefficient between two parts.

- 4.
- The standard deviation of the trend slope is calculated using Equation (16):$${\sigma}_{s}=\frac{2\ast \sigma}{n}\times \sqrt{\frac{2\times \left(1-{\rho}_{{\overline{y}}_{2}{\overline{y}}_{1}}\right)}{n}},$$
- ${\sigma}_{s}$ = standard deviation of the trend slope;
- $\sigma $ = series variance;
- n = serial total number of data;
- ${\overline{y}}_{1},{\overline{y}}_{2}$ = the arithmetic means of each sub-series (first sub-series (${\overline{y}}_{1}$) and second sub-series (${\overline{y}}_{2}$)) formed by dividing the dependent variable series into two.

- 5.
- The confidence limits of the trend slope ($CLU$ = upper confidence limit, $CLL$ = lower confidence limit) are calculated using Equation (17):$$CL=0\pm {t}_{t}\times {\sigma}_{s},$$
- $CL$ = confidence limit;
- ${\sigma}_{s}$ = standard deviation of the trend slope;

## 3. Results and Discussion

#### 3.1. Dependency Test Results

#### 3.2. t-Test Results

#### 3.3. Rate of Change Results

#### 3.4. Pre-Whitening Method Results

#### 3.5. Mann-Kendall Rank Correlation Trend Test Results

#### 3.6. Şen Innovation Trend Test Results

^{−1}(maximum), −0.076 m year

^{−1}(average), and −0.109 m year

^{−1}(minimum) in the LWL series, and −2.280 hm

^{3}year

^{−1}(maximum), −11.082 hm

^{3}year

^{−1}(average), and −33.816 hm

^{3}year

^{−1}(minimum) in the LWV series), moderately decreasing trends were determined. It was determined that the maximum decrease in the LWL series was −0.109 m year

^{−1}in the minimum LWL series and the maximum decrease in the LWV series was in the minimum LWV series with −33.816 hm

^{3}year

^{−1}. The SITT test results were determined to support the MKRCTT results.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Linear regression analysis for different periods of Lake Eğirdir annual LWL and LWV series.

**Figure 6.**Lagged-1 autocorrelation coefficients of the de-trended LWL and LWV series. CLU = upper confidence limit; CLL = lower confidence limit.

**Figure 7.**MKRCTT results for the LWL and LWV series. $u\left({t}_{i}\right)$ = calculated Mann-Kendall rank correlation trend test statistic; CLU = upper confidence limit; CLL = lower confidence limit.

**Figure 8.**Şen innovation trend test for the annual LWL and LWV series. Dashed lines were used to show the trend levels (low, medium, and high) in each LWL and LWV series. Green dots were used to show a low trend in the minimum LWV series.

Station | Coordinate | Height (m, a.s.l.) | Registration Years | |
---|---|---|---|---|

Latitude | Longitude | |||

Lake Level Measurement Statom (09–09) | 37°53′00″ | 30°50′00″ | 916 | 1988–2019 |

Lake Meteorology Measurement Station (17,882) | 37°83′77″ | 30°87′20″ | 920 | 1988–2019 |

Lake Eğirdir Features | ||||

Height of the lake (m, a.s.l.) | 915 | |||

Maximum depth of the lake (m) | 13.5–15.00 | |||

Average depth of the lake (m) | 8–9 |

Variable | $\mathbf{Average}\left(\overline{\mathit{x}}\right)$ | Standard Deviation (σ) | Maximum (x_{max}) | Minimum (x_{min}) | Coefficient of Change (%) | |||||
---|---|---|---|---|---|---|---|---|---|---|

LWL (m) | LWV (hm^{3}) | LWL (m) | LWV (hm^{3}) | LWL (m) | LWV (hm^{3}) | LWL (m) | LWV (hm^{3}) | LWL (m) | LWV (hm^{3}) | |

Maximum | 917.5 | 3566.3 | 0.57 | 269.1 | 918.5 | 3984.3 | 916.5 | 3039.3 | 0.063 | 7.55 |

Average | 917.1 | 3361.7 | 0.54 | 244.5 | 918.1 | 3774.4 | 916.0 | 2872.0 | 0.059 | 7.27 |

Minimum | 916.6 | 3159.2 | 0.52 | 233.4 | 917.5 | 3613.3 | 915.6 | 2683.8 | 0.056 | 7.38 |

**Table 3.**Linear regression analysis equations for the different periods of the annual LWL and LWV series.

Variable | Period | Equation | Total Number of Data in the Series of Observations (N) | $\mathbf{Mean}\text{}\mathbf{of}\text{}\mathbf{the}\text{}\mathbf{Observation}\text{}\mathbf{Series}\left(\overline{\mathit{x}}\right)$ | Standard Deviation (s) |
---|---|---|---|---|---|

Lake Water Level | |||||

Maximum | 1988–2004 | LWL1 = +0.06413 × T + 916.84 | 18 | 917.45 | 0.59 |

2005–2019 | LWL2 = −0.01659 × T + 917.98 | 14 | 917.55 | 0.45 | |

Average | 1988–2004 | LWL1 = +0.05427 × T + 916.46 | 17 | 916.55 | 0.56 |

2005–2019 | LWL2 = −0.02815 × T + 917.91 | 15 | 917.21 | 0.44 | |

Minimum | 1988–2004 | LWL1 = +0.05088 × T + 916.10 | 17 | 916.55 | 0.53 |

2005–2019 | LWL2 = −0.02946 × T + 917.50 | 15 | 916.77 | 0.47 | |

Lake Water Volume | |||||

Maximum | 1988–2005 | LWV1 = +21.065 × T + 3458.10 | 18 | 3658.18 | 242.43 |

2006–2019 | LWV2= −17.381 × T + 3891.50 | 14 | 3448.259 | 237.01 | |

Average | 1988–2000 | LWV1 = +5.915 × T + 3552.90 | 13 | 3394.29 | 273.06 |

2001–2019 | LWV2 = −24.889 × T+3911.80 | 19 | 3339.38 | 195.55 | |

Minimum | 1988–1999 | LWV1 = −8.1228 × T + 3239.40 | 12 | 3186.61 | 240.26 |

2000–2019 | LWV2 = −25.244 × T + 3710.80 | 20 | 3142.78 | 192.02 |

Variable | $\mathbf{Slope}\text{}\mathbf{Coefficient}\left({\mathit{\beta}}_{1}\right)$ | Standard Error of Slope Coefficient (s_{b}) | Calculated Test Statistic (t_{H}) | Table Value of the t Distribution (t_{Table}) | Probability p < 0.05 | ||||
---|---|---|---|---|---|---|---|---|---|

LWL (m) | LWV (hm^{3}) | LWL | LWV | LWL | LWV | LWL | LWV | ||

Maximum | −0.0566 | −5.6686 | 0.0268 | 6.450 | −2.110 | −0.879 | +2.0399 | 0.043 | 0.345 |

Average | −0.0623 | −10.4240 | 0.0260 | 5.830 | −5.180 | −1.787 | 0.000 | 0.084 | |

Minimum | −0.0849 | −9.0038 | 0.0226 | 8.080 | −3.750 | −1.114 | 0.001 | 0.274 |

**Table 5.**The t-test results obtained by dividing the annual lake water level and lake water volume series in two.

Variable | Period | Total Number of Data in the Series (n) | $\mathbf{Average}(\overline{\mathit{x}})$ | Standard Deviation (s) | Calculated Test Statistic (T_{Calculation}) | Table Value of the t Distribution (t_{Table}) | Significance |
---|---|---|---|---|---|---|---|

$t-\mathrm{Test}\text{}\mathrm{Between}\text{}\mathrm{Sub}-\mathrm{Series}\text{}({n}_{1}={n}_{2}$) Formed by Splitting the Series into Two | |||||||

Lake Water Level | |||||||

Maximum | 1988–2003 | 16 | 918.332 | 0.956 | −2.723 | ±2.0399 | Significant |

2004–2019 | 917.370 | 1.755 | |||||

Average | 1988–2003 | 917.004 | 0.538 | −7.135 | |||

2004–2019 | 915.869 | 0.721 | |||||

Minimum | 1988–2003 | 917.297 | 0.827 | −5.457 | |||

2004–2019 | 915.700 | 1.434 | |||||

Lake Water Volume | |||||||

Maximum | 1988–2003 | 16 | 3579.502 | 325.243 | +0.0634 | ±2.0399 | Insignificant |

2004–2019 | 3585.331 | 406.322 | |||||

Average | 1988–2003 | 3448.929 | 322.527 | −2.558 | Significant | ||

2004–2019 | 3254.446 | 284.644 | |||||

Minimum | 1988–2003 | 3308.079 | 525.182 | −1.717 | Insignificant | ||

2004–2019 | 3127.627 | 228.506 | |||||

$t-\mathrm{Test}\text{}\mathrm{between}\text{}\mathrm{Sub}-\mathrm{Series}\text{}({n}_{1}\ne {n}_{2}$) before and after the Time When the Change in the Series Started | |||||||

Lake Water Level | |||||||

Maximum | 1988–2004 | 18 | 918.687 | 1.410 | −26.755 | ±2.0399 | Significant |

2005–2019 | 14 | 916.776 | 0.606 | ||||

Average | 1988–2005 | 13 | 916.907 | 0.544 | −16.270 | ||

2006–2019 | 19 | 916.115 | 0.883 | ||||

Minimum | 1988–2004 | 17 | 917.483 | 1.110 | −35.810 | ||

2005–2019 | 15 | 915.382 | 0.688 | ||||

Lake Water Volume | |||||||

Maximum | 1988–2000 | 18 | 3641.296 | 369.866 | −5.910 | ±2.0399 | Significant |

2001–2019 | 14 | 3506.714 | 350.300 | ||||

Average | 1988–2005 | 13 | 3407.163 | 329.695 | −4.635 | ||

2006–2019 | 19 | 3313.731 | 307.906 | ||||

Minimum | 1988–1999 | 13 | 3309.342 | 578.477 | −5.719 | ||

2000–2019 | 19 | 3155.255 | 275.193 | ||||

t-Test Inter Sub-Series before and after the Time When Trend Initiation in the Series | |||||||

Lake Water Level | |||||||

Maximum | 1988–2001 | 14 | 918.179 | 0.917 | −6.311 | ±2.0399 | Significant |

2002–2019 | 18 | 917.596 | 1.777 | ||||

Average | 1988–2000 | 13 | 916.907 | 0.544 | −16.270 | ||

2001–2019 | 19 | 916.115 | 0.883 | ||||

Minimum | 1988–2002 | 15 | 917.225 | 0.803 | −17.524 | ||

2003–2019 | 17 | 915.857 | 1.533 | ||||

Lake Water Volume | |||||||

Maximum | 1988–1990 | 3 | 3896.705 | 204.211 | −9.166 | ±2.0399 | Significant |

1991–2019 | 29 | 3549.904 | 361.202 | ||||

Average | 1988–1993 | 6 | 3510.745 | 231.944 | −7.876 | ||

1994–2019 | 26 | 3314.982 | 323.880 | ||||

Minimum | 1988–1989 | 2 | 3577.423 | 202.632 | −7.077 | ||

1990–2019 | 30 | 3193.882 | 425.203 | ||||

t-Test of All Series (n) | |||||||

Lake Water Level | |||||||

Maximum | 1988–2019 | 32 | 917.851 | 1.473 | −4277.326 | ±2.0399 | Significant |

Average | 1988–2019 | 916.437 | 0.850 | −5621.346 | |||

Minimum | 1988–2019 | 916.498 | 1.409 | −4367.685 | |||

Lake Water Volume | |||||||

Maximum | 1988–2019 | 32 | 3582.417 | 362.049 | −1065.043 | ±2.0399 | Significant |

Average | 1988–2019 | 3351.688 | 315.118 | −1068.076 | |||

Minimum | 1988–2019 | 3217.853 | 423.581 | −884.449 |

Variable | Period | Total Number of Data in the Series (n) | Sub-Series Change Rate (%) | Series Change Rate (%) |
---|---|---|---|---|

$\mathrm{The}\text{}\mathrm{CR}\text{}\mathrm{between}\text{}\mathrm{Sub}-\mathrm{Series}\text{}({n}_{1}={n}_{2}$) Formed by Splitting the Series into Two | ||||

Lake Water Level | ||||

Maximum | 1988–2003 | 16 | +0.158 | −0.294 |

2004–2019 | –0.547 | |||

Average | 1988–2003 | +0.019 | −0.321 | |

2004–2019 | −0.364 | |||

Minimum | 1988–2003 | +0.087 | −0.396 | |

2004–2019 | −0.712 | |||

Lake Water Volume | ||||

Maximum | 1988–2003 | 16 | +0.333 | −36.364 |

2004–2019 | −28.723 | |||

Average | 1988–2003 | +5.414 | −40.637 | |

2004–2019 | −27.827 | |||

Minimum | 1988–2003 | +8.754 | −43.632 | |

2004–2019 | −34.502 | |||

The CR between Sub-Series before and after the Start of Change in the Series | ||||

Lake Water Level | ||||

Maximum | 1988–2005 | 18 | +0.463 | −0.294 |

2006–2019 | 14 | −0.215 | ||

Average | 1988–2000 | 13 | +0.097 | −0.321 |

2001–2019 | 19 | −0.201 | ||

Minimum | 1988–2004 | 17 | +0.314 | −0.396 |

2005–2019 | 15 | −0.290 | ||

Lake Water Volume | ||||

Maximum | 1988–2005 | 18 | +8.723 | −36.364 |

2006–2019 | 14 | −44.673 | ||

Average | 1988–2000 | 13 | +8.680 | −40.637 |

2001–2019 | 19 | −27.068 | ||

Minimum | 1988–2004 | 13 | +25.931 | −43.632 |

2005–2019 | 19 | −16.574 | ||

The CR between Sub-Series before and after the Trend in the Series Started | ||||

Lake Water Level | ||||

Maximum | 1988–2001 | 14 | +0.121 | −0.294 |

2002–2019 | 18 | −0.390 | ||

Average | 1988–2000 | 13 | +0.003 | −0.321 |

2001–2019 | 19 | −0.281 | ||

Minimum | 1988–2000 | 13 | +0.066 | −0.396 |

2001–2019 | 19 | −0.483 | ||

Lake Water Volume | ||||

Maximum | 1988–1990 | 3 | +9.596 | −36.364 |

1991–2019 | 29 | −12.909 | ||

Average | 1988–1993 | 6 | +8.465 | −40.637 |

1994–2019 | 26 | −21.372 | ||

Minimum | 1988–1989 | 2 | +7.884 | −43.632 |

1990–2019 | 30 | −26.579 |

Variables | $\mathbf{Calculated}\text{}\mathbf{MKRCTT}\text{}\mathbf{Test}\text{}\mathbf{Statistics}\text{}(\mathit{u}\left(\mathit{t}\right))$ | Statistical Confidence Limits | Trend Beginning (Year) | Trend Result | ||||
---|---|---|---|---|---|---|---|---|

LWL | LWV | CLU * | CLL ** | LWL | LWV | LWL | LWV | |

Maximum | −2.368 | −1.135 | +2.0399 | −2.0399 | mid-2001 | mid-1990 | Yes | No |

Average | −4.216 | −0.616 | mid-2000 | mid-1993 | ||||

Minimum | −3.665 | −1.058 | mid-2002 | mid-1989 |

Variable | n * | Trend Slope (s) | Trend Standard Deviation (σ_{s}) | Trend Correlation Coefficient $\left({\mathit{\rho}}_{\mathit{L}\mathit{W}\mathit{L}\mathit{x},\mathit{L}\mathit{W}\mathit{L}\mathit{y}}\right)$ | Standard Deviation (σ) | Relative Error (%) | Confidence Limits at 5% Significance | Trend Result | |
---|---|---|---|---|---|---|---|---|---|

CLU ** | CLL *** | ||||||||

Lake Water Level | |||||||||

Maximum | 32 | –0.03975 | 0.00975 | 0.821 | 1.473 | –0.050 | +0.001989 | –0.001989 | Yes |

Average | 32 | –0.07646 | 0.00428 | 0.896 | 0.850 | +0.248 | +0.008721 | –0.008721 | |

Minimum | 32 | –0.10982 | 0.00853 | 0.850 | 1.409 | –0.119 | +0.017392 | –0.017392 | |

Lake Water Volume | |||||||||

Maximum | 32 | –2.28063 | 1.08967 | 0.957 | 336.402 | +3.817 | +2.22281 | –2.22281 | Yes |

Average | 32 | –11.08250 | 1.25678 | 0.935 | 315.118 | +0.020 | +2.56370 | –2.56370 | |

Minimum | 32 | –33.81688 | 3.39780 | 0.736 | 423.581 | –6.067 | +6.93117 | –6.93117 |

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## Share and Cite

**MDPI and ACS Style**

Yücel, A.; Markovic, M.; Atilgan, A.; Rolbiecki, R.; Ertop, H.; Jagosz, B.; Ptach, W.; Łangowski, A.; Jakubowski, T. Investigation of Annual Lake Water Levels and Water Volumes with Şen Innovation and Mann-Kendall Rank Correlation Trend Tests: Example of Lake Eğirdir, Turkey. *Water* **2022**, *14*, 2374.
https://doi.org/10.3390/w14152374

**AMA Style**

Yücel A, Markovic M, Atilgan A, Rolbiecki R, Ertop H, Jagosz B, Ptach W, Łangowski A, Jakubowski T. Investigation of Annual Lake Water Levels and Water Volumes with Şen Innovation and Mann-Kendall Rank Correlation Trend Tests: Example of Lake Eğirdir, Turkey. *Water*. 2022; 14(15):2374.
https://doi.org/10.3390/w14152374

**Chicago/Turabian Style**

Yücel, Ali, Monika Markovic, Atilgan Atilgan, Roman Rolbiecki, Hasan Ertop, Barbara Jagosz, Wiesław Ptach, Ariel Łangowski, and Tomasz Jakubowski. 2022. "Investigation of Annual Lake Water Levels and Water Volumes with Şen Innovation and Mann-Kendall Rank Correlation Trend Tests: Example of Lake Eğirdir, Turkey" *Water* 14, no. 15: 2374.
https://doi.org/10.3390/w14152374