# Lake Level Evolution of the Largest Freshwater Lake on the Mediterranean Islands through Drought Analysis and Machine Learning

^{*}

## Abstract

**:**

^{3}of fresh drinking water, represents a specific karst phenomenon. To better understand the impact of water level change drivers, the occurrence of meteorological and hydrological droughts was analysed. Basic machine learning methods (ML) such as the multiple linear regression (MLR), multiple nonlinear regression (MNLR), and artificial neural network (ANN) were used to simulate water levels. Modelling was carried out considering annual inputs of precipitation, air temperature, and abstraction rate as well as their influential lags which were determined by auto-correlation and cross-correlation techniques. Hydrological droughts have been recorded since 1986, and after 2006 a series of mostly mild hot to moderate hot years was recorded. All three ML models have been trained to recognize extreme conditions in the form of less precipitation, high abstraction rate, and, consequently, low water levels in the testing (predicting) period. The best statistical indicators were achieved with the MNLR model. The methodologies applied in the study were found to be useful tools for the analysis of changes in water levels. Extended monitoring of water balance elements should precede any future increase in the abstraction rate.

## 1. Introduction

^{2}, making it the largest island in the Adriatic Sea. The lake is 5 km long with a maximum width of 1.45 km. The lake area is approximately 5.7 km

^{2}, and it is at an average altitude of 12.78 m above sea level (a.s.l.) [41]. It contains 220 million m

^{3}of fresh water. Because of its good water quality, the lake is used to supply water to the islands of Cres and Lošinj, and is the only source of drinking water for these islands with highly developed tourism. The water consumption rate is approximately 45–55 L/s during winter months, while over summer, it reaches approximately 150 L/s. The total abstraction rate from Lake Vrana in 2019 reached 2365.07 × 10

^{3}m

^{3}, which is approximately 75 L/s. In many countries it is not always possible to satisfy increased water demands; pressure on karst aquifers will rise, and regulatory measures will be need to prevent or mitigate over-exploitation [42]. Fortunately, this still does not apply to the island of Cres, but it points the need for further research into this natural phenomenon with the application of new scientific methods, which is one of the main goals of this paper. The results of the work should contribute to the development of a better and more comprehensive monitoring system and the future sustainable management of this extremely valuable water supply resource in changed climatic conditions.

## 2. Geological and Hydrogeological Settings

_{1,2}), the influence of strike-slip tectonics (pull-apart structure), and the last sea level rise.

## 3. Data and Methods

#### 3.1. Data Source

#### 3.2. Calculation of the Standardised Drought Indices

_{i}, P

_{mean}, and S

_{P}are the monthly precipitation, mean, and standard deviation, respectively.

#### 3.3. Trend Analysis Method

_{i}is from i = 1, 2, …, n − 1, and x

_{j}is from j = i + 1, …, n. If n is greater than 8, then S approximates to normal distribution.

#### 3.4. Auto- and Cross-Correlation Method

_{i}= (x

_{1}, … x

_{n}) is a time series of n data for which m auto-correlation coefficients, i.e., r(k) = (r

_{0}, … r

_{m}) are calculated.

_{x}and σ

_{y}are the standard deviations of the input and output series, respectively.

#### 3.5. Multiple Linear and Nonlinear Regressions

_{MLR}= c + β

_{1}X

_{1}+ β

_{2}X

_{2}+ … + β

_{n}X

_{n}

_{MNLR}= c + β

_{1}X

_{1}

^{β}

_{2}+ β

_{3}X

_{2}

^{β}

_{4}+ … + β

_{m}X

_{n}

^{β}

_{m+1}

#### 3.6. Artificial Neural Networks

_{i}, which are real numbers. Each input value x

_{i}is multiplied by the weight value w

_{ji}, which describes the connection between input i and hidden neuron j, and then summed as per the following equation:

_{j}is processed using the activation function of the hidden layer f (h

_{j}) and the output from the neural network is equal to y

_{j}.

_{k}) can be expressed as follows:

_{kj}is the connection weight between output neuron k and hidden neuron j, h

_{j}is the output from neuron j in the hidden layer, m is the number of neurons in the hidden layer, and f is the activation function of the output layer.

^{2}), mean absolute error (MAE), and root mean squared residual (RMSE), scatter index (SI), and bias:

_{o}is the observed water level, H

_{p}is the predicted (simulated) water level, and $\overline{{H}_{o}}$ is the mean value of the observed water levels.

## 4. Results

#### 4.1. Changes in the Standardised Drought Indices

#### 4.2. Time Series of Investigated Variables

#### 4.3. Auto-Correlation and Cross-Correlation of Variables

_{(t−1)}, Q(

_{t−2)}, Q

_{(t−3)}, and Q

_{(t−4)}are very similar because of the gradual increase in abstraction rates. For precipitation and water level, the best matching was achieved with a lag of 1 year. There was no lag between the time series for air temperature and water level.

#### 4.4. Developed Machine Learning Models

_{(t−1)}and Q

_{(t−2)}were used as input data for the MLR, MNLR, and ANN methods. The effect of evaporation was partially annulled by the introduction of air temperature because a pronounced increase in T causes water loss by evaporation from the lake surface. Owing to the typically strong auto-correlation of the water level time series, the simulated water level has been significantly influenced by past water levels. Therefore, the water level from the previous year, H

_{(t−1)}, was added as an explanatory variable.

#### 4.4.1. Multiple Linear Regression Model

_{(t−1)}, Q

_{(t−2)}, and H

_{(t−1)}), the best MLR model in the training phase (1954–2004) was achieved using the four independent variables P, P

_{(t−1)}, Q

_{(t−2)}, and H

_{(t−1)}. The R value between observed and simulated water levels was 0.95, MSE was 0.17 m, MAE was 0.34, and RMSE was 0.41 m (Table 3). The equation for the MLR model obtained to simulate the water levels in the lake is as follows:

_{(t−1)}, which means that the weight of this variable is more important. This is followed by variables P

_{(t−1)}and Q

_{(t−2)}. These variables, as well as the P variable, were statistically significant (p < 0.05). The other two variables, T and Q, are not significant and therefore not included in this model. The R

^{2}value of 0.90 means that 90% of the variability of H is explained by the four variables P, P

_{(t−1)}, Q

_{(t−2)}, and H

_{(t−1)}.

_{(t−2)}(β = −0.753), suggesting that the weight of this variable is more important. This is followed by the variables H

_{(t−1)}(β = 0.546) and P

_{(t−1)}(β = 0.316). These variables, as well as the P variable, were statistically significant (p < 0.05). The beta coefficient of Q was 0.448, with a significance of p = 0.05. Furthermore, air temperature has slightly higher beta coefficient values (β = −0.063) in this period than in the period 1954–2004; however, it is still statistically insignificant (p = 0.244). It can be assumed that in the coming years, owing to climate change, the impact of air temperature will strengthen. Figure 4b clearly highlights the mostly mild to moderate increase in average air temperature since 2006 compared to the previous period. Investigating monthly climatic (precipitation, air temperature and evaporation), and management (abstraction rate) drivers of water level changes in Lake Bracciano near Rome, Italy, Guyennon et al. [30] also found a marginal role for temperature, an increasing role of abstraction during the past two decades, and a key role for increased precipitation variability. Negative values of the beta coefficients for the abstraction rate and air temperature indicate that an increase in pumping causes a decrease in the water level, and an increasing air temperature drives higher evaporation rates, also causing a decrease in the water level.

^{3}T

^{−1}) on the water level of the lake. However, the unstandardized coefficient should not be used to rank the independent variables to the outcome of the dependent variable because it does not eliminate dimensions.

#### 4.4.2. Multiple Nonlinear Regression Model

#### 4.4.3. Artificial Neural Networks Model

## 5. Discussion

#### 5.1. Comparison of Models

^{2}and R, a lower value of the regression model accuracy (MAE, RMSE and SI) implies a higher accuracy of the regression model. In both training periods (1954–2004 and 1954–2019), the MNLR model produced the lowest MAE (0.29 and 0.21), RMSE (0.36 and 0.28) and SI (0.029 and 0.023), and highest R

^{2}(0.93 and 0.96) and R (0.96 and 0.98) indicating that this method has a better fitting ability compared to the other two methods. Bias value for all models in the both training period is 0.00.

^{2}(0.5) and R (0.71) were significantly reduced, while the values of MAE (0.52), RMSE (0.7) and SI (0.062) were increased. Bias value for MNLR model in the testing period is very close to 0 (−0.02). For the MLR model, the bias is −0.13, and for the ANN model −0.28, which indicates a slight underestimation compared to observations. For instance, Figure 9b clearly shows that the simulated water levels in the MNLR model during the period 2013–2015 differ significantly from the observed water levels. The other two models also clearly show deviations of the simulated water levels from the observed values (Figure 9a,c). Based on the visual inspection of the observed and predicted water levels (Figure 9), as well as the indicators of the best match (Table 3), it is not possible to conclude with certainty which model gives the best results for the water level simulation in the testing period. Nevertheless, during the training period, all three models trained the impact of intensive water abstraction and less rainfall, which caused very low water levels in the early 1990s. As a result, in the testing period they recognised small amount of precipitation and high abstraction rate (Figure 2, Figure 4a and Figure 7), and correctly predicted a significant drop in water levels in 2008 and 2012 (Figure 9).

^{2}values in the training period 1954–2004 of 0.9 for the MLR model, of 0.93 for the MNLR model and of 0.82 for the ANN model mean that 90% of the variability of H is explained by the four variables P, P

_{(t−1)}, Q

_{(t−2)}and H

_{(t−1)}in the MLR model, i.e., 93% in the MNLR model and 82% in the ANN model. For the training period 1954–2019, these four variables explain 89% of the variability in H in the MLR model, i.e., 96% in the MNLR model and 81% in the ANN model. Bonacci [37,61] found that the values of R of the MLR models in the periods 1967–2013 and 1948–2015 are 0.733 and 0.734, from which it follows that the value of R

^{2}is 0.54, i.e., that only 54% of the variability of the water level in the lake is explained by the analysed independent variables P, T and Q. The predictive ability in these articles was not tested, but considering that a relatively low percentage of the variability of H is explained by the analyzed variables P, T and Q, it can be assumed that during the testing period this model would show a very weak prediction ability the water level in the lake.

^{2}= 0.97) than those obtained with the NWN model (R

^{2}= 0.95). Annual input data being used for time series analysis is not only a rarity in the research of lake water level variations, but also in the research of time series of other hydrological variables. Shiri and Kisi [72] investigated the use of daily, monthly, and annual streamflow data using single neuro-fuzzy (NF) and wavelet-neuro-fuzzy (WNF) models. For the test period in both models, the best results were achieved using daily and monthly input data, but they are somewhat worse for the NF model compared to the WNF model. However, for annual input data, the results of the NF model were significantly worse than the results of the WNF model; Pearson’s correlation coefficient was −0.338 in the NF model, and 0.994 in the WNF model. The authors concluded that a model architecture that works well on one case does not necessarily work on another. The results obtained in our study, as well as the results of other described studies, point to the need for further research. Other modern forecasting methods should certainly be applied in order to find the best method for water level forecasting with applied input data.

#### 5.2. Impact on the Water Level of Vrana Lake

^{6}m

^{3}, the average evaporation from the lake surface 6.7 × 10

^{6}m

^{3}, and the average annual underground runoff (losses) from the lake was approximately 11.7 × 10

^{6}m

^{3}. The average annual water level in the lake was 13.10 m a.s.l. Owing to the large area of the lake in relation to the catchment area, 33% of the total inflow into the lake is from precipitation that falls directly on the surface of the lake, and the remainder is underground recharge from the catchment area. According to the results of the modelling, the authors determined that the surface of the catchment area that optimally satisfied the water balance conditions was approximately 24 km

^{2}.

^{6}m

^{3}/year to 2.2 × 10

^{6}m

^{3}/year (by approximately 40%), and the water level decreased from 13.8 m a.s.l. at 9.5 m a.s.l. (by approximately 30%). Precipitation and air temperature did not show any significant trend. Precipitation in this entire period mainly reflected drought (Figure 4a) with no noticeable trend. The air temperature did not show drought, also without a clearly expressed trend (Figure 4b). Prior to 1982, no significant trends in the changes in the water level of the lake were found (Table 1), although the trend of increasing abstraction rates (p > 0.0001) was significant. Mean annual abstraction rates in that period increased from 0.14 × 10

^{6}m

^{3}in 1967 to 1.6 × 10

^{6}m

^{3}in 1982.

^{6}m

^{3}in 1991 to approximately 2.5 × 10

^{6}m

^{3}in 2018. However, the average annual abstraction rate in that period was very similar to that in the period 1982–1990, when there was a sharp drawdown in the water level of the lake (Table 5). In the same period (1991–2019), the average annual rainfall was almost 16% higher than that in the period 1982–1990. Based on these observations, it can be assumed that new water balance conditions have been established which, with an increase in precipitation, enable the same abstraction rate at a lower water level. Lower water levels and the associated reduction of the hydraulic gradient towards the sea have reduced underground runoff (losses) from the lake. A gradient of change underground runoff per each meter of water level was estimated at approximately 0.028 m

^{3}/s (0.88 × 10

^{6}m

^{3}/year) [47]. The average water level in the period 1991–2019 was 0.9 m lower compared to the average water level in the period 1982–1990, which means that these losses are reduced by approximately 0.8 × 10

^{6}m

^{3}. Furthermore, Bonacci [44] found that an increase in annual air temperature of 1 °C increases evaporation by approximately 0.5 × 10

^{6}m

^{3}of water. The average air temperature in the period 1991–2019 was 0.7 higher than the average air temperature in the period 1982–1990 (Table 5). Assuming linear relationships, this would mean that evaporation in the period 1991–2019 increased by 0.35 × 10

^{6}m

^{3}. Based on these relationships, it can be assumed that the losses related to underground runoff from the lake and evaporation reduced by 0.45 × 10

^{6}m

^{3}in the period 1991–2019 in relation to the period 1982–1990. At the same time, it is possible that the underground recharge from the surrounding aquifer increased as a result of the increase in the catchment area, i.e., the increase in the cone of depression due to the lower level of the lake. During the period 1982–1990, the average rainfall was 13.5% less, and the average abstraction rate was approximately 4% less than that in the period 1991–2019. Still, such an abstraction rate, with the occurrence of unfavourable hydrological conditions (Figure 4a and Figure 6b), caused the appearance of very low water levels, as recorded in 2008 and 2012 (Figure 7 and Figure 9).

#### 5.3. Limitations

#### 5.4. Practical Implications

## 6. Conclusions

- The dominant no-drought conditions (SWI > 0) recorded in the previous intervals (1929–1958 and 1959–1989) were not recorded in the period 1989–2019.
- After 2006, sharp increase in temperature was noticeable, where an almost continuous series from mild hot to moderate hot years were seen.
- The MLR, MNLR, and ANN models have been trained to recognize extreme conditions in the form of less precipitation, high abstraction rate and, consequently, low water levels in the testing (predicting) period.
- The best result was achieved with the MNLR model for the entire trained period of 1954–2019.
- The use of a time series (long period) of historical annual data can be very interesting from the point of view of analysing the impact of current climate change on water resources, particularly when studying multiparametric systems that react very sluggishly to change.
- New water balance conditions have been established, probably by reducing underground runoff (losses) and widening the catchment area, which, with a slight increase in precipitation, has enabled the same abstraction rate and stabilization of water levels.
- The establishment of monitoring of all elements affecting the lake water level is of crucial importance for all further research including the development of a new, more reliable physical model, development of new models using machine learning, and comparisons with the results of this study.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Hydrogeological map of Vrana Lake area—Geology after Magaš [45].

**Figure 2.**Change in standardised annual precipitation index (SPI) and standardised annual water level index (SWI) from 1929 to 2019.

**Figure 3.**Percentage of class occurrences of the standardized annual precipitation index (SPI) (

**a**) and standardized annual water level index (SWI) (

**b**) for the periods 1929–1958, 1959–1988, 1989–2019, and 1929–2019.

**Figure 4.**Change in (

**a**) standardised monthly precipitation index (SPI) and standardised monthly water level index (SWI) and (

**b**) standardised monthly temperature index (STI) in the hydrological years from 1981 to 2019.

**Figure 5.**Percentage of class occurrence of the standardised monthly precipitation index (SPI), standardised monthly water level index (SWI), and standardised monthly temperature index (STI) in the hydrological years from 1981 to 2019.

**Figure 6.**Change in (

**a**) standardised precipitation index (SPI) and (

**b**) standardised water level index (SWI) at 6-month periods (October–March and April–September) in the hydrological years 1981–2019.

**Figure 7.**Time series of the mean annual precipitation (P), mean annual air temperature (T), mean annual abstraction rate (Q), and mean annual lake water level (H) in the period 1929–2019.

**Figure 9.**Time series of the observed and predicted water levels using (

**a**) MLR, (

**b**) MNLR, and (

**c**) ANN model.

**Figure 10.**Box plots of residuals (observed minus simulated) during the training (1954–2004) (1-MLR, 2-MNLR, 3-ANN) and testing (2005–2019) periods (4-MLR, 5-MNLR, 6-ANN) as well as the entire period 1954–2019 (7-MLR, 8-MNLR, 9-ANN)). The boxes show the mean (red plus), median (black line), minimum and maximum values (red dots), and the 25th and 75th percentiles (limits of the box).

**Table 1.**Mann–Kendall test results for time series of the mean annual precipitation (P), mean annual air temperature (T), mean annual abstraction rate (Q), and mean annual lake water level (H) in the different periods.

Precipitation (P) | Air Temperature (T) | Water Level (H) | Abstraction Rate (Q) | |
---|---|---|---|---|

Observation period | 1929–2019 | |||

No. of data | 91 | 39 * | 91 | 66 ** |

p-value | 0.472 | <0.0001 | <0.0001 | <0.0001 |

Kendall’s τ | 0.052 | 0.553 | −0.529 | 0.844 |

Type of trend | n.s.s. | increasing | decreasing | increasing |

Observation period | 1929–1953 | |||

No. of data | 25 | 25 | ||

p-value | 0.455 | 0.726 | ||

Kendall’s τ | −0.110 | −0.053 | ||

Type of trend | n.s.s. | n.s.s. | ||

Observation period | 1954–2019 | |||

No. of data | 66 | 39 * | 66 | 66 |

p-value | 0.486 | <0.0001 | <0.0001 | <0.0001 |

Kendall’s τ | 0.059 | 0.553 | −0.493 | 0.844 |

Type of trend | n.s.s. | increasing | decreasing | increasing |

Observation period | 1954–1990 | |||

No. of data | 37 | 10 * | 37 | 37 |

p-value | 0.724 | 0.210 | 0.013 | <0.0001 |

Kendall’s τ | −0.042 | 0.333 | −0.287 | 0.964 |

Type of trend | n.s.s. | n.s.s. | decreasing | increasing |

Observation period | 1991–2019 | |||

No. of data | 29 | 29 | 29 | 29 |

p-value | 0.358 | 0.0005 | 0.293 | <0.0001 |

Kendall’s τ | 0.123 | 0.463 | 0.141 | 0.749 |

Type of trend | n.s.s. | increasing | n.s.s. | increasing |

Observation period | 1954–1981 | |||

No. of data | 28 | 28 | 28 | |

p-value | 0.038 | 0.607 | <0.0001 | |

Kendall’s τ | 0.280 | −0.072 | 0.974 | |

Type of trend | increasing | n.s.s. | increasing | |

Observation period | 1982–1990 | |||

No. of data | 9 | 9 | 9 | 9 |

p-value | 0.466 | 0.466 | 0.001 | 0.029 |

Kendall’s τ | −0.222 | 0.222 | −0.889 | 0.611 |

Type of trend | n.s.s. | n.s.s. | decreasing | increasing |

**Table 2.**Cross-correlation between lake water levels and three independent variables: precipitation (P), air temperature (T), and abstraction rate (Q).

Period | Correlation Coefficient (R) | Lag (Year) | ||||
---|---|---|---|---|---|---|

P | T | Q | P | T | Q | |

1929–2019 | 0.30 | - | - | 1 | - | - |

1954–2019 | 0.37 | −0.35 | −0.7 (±0.04) | 1 | 0 | <4 |

**Table 3.**Goodness of fit between the observed and predicted water levels for the multiple linear regression (MLR), multiple nonlinear regression (MNLR), and artificial neural networks (ANN) models.

Training Period (1954–2004) | Testing Period (2005–2019) | Training of Entire Period (1954–2019) | |||||||
---|---|---|---|---|---|---|---|---|---|

MLR | MNLR | ANN | MLR | MNLR | ANN | MLR | MNLR | ANN | |

R^{2} | 0.90 | 0.93 | 0.82 | 0.42 | 0.50 | 0.43 | 0.89 | 0.96 | 0.81 |

R | 0.95 | 0.96 | 0.90 | 0.65 | 0.71 | 0.66 | 0.94 | 0.98 | 0.90 |

MAE (m) | 0.34 | 0.29 | 0.39 | 0.54 | 0.52 | 0.45 | 0.36 | 0.21 | 0.43 |

RMSE (m) | 0.41 | 0.36 | 0.55 | 0.64 | 0.70 | 0.67 | 0.44 | 0.28 | 0.57 |

SI | 0.033 | 0.029 | 0.045 | 0.057 | 0.062 | 0.060 | 0.036 | 0.023 | 0.047 |

Bias (m) | 0.00 | 0.00 | 0.00 | −0.13 | −0.02 | −0.28 | 0.00 | 0.00 | 0.00 |

Variable | Beta | p-Value |
---|---|---|

P | 0.187 | 0.0004 |

P_{(t−1)} | 0.323 | <0.0001 |

Q_{(t−2)} | −0.207 | 0.0004 |

H_{(t−1)} | 0.681 | <0.0001 |

Period | H_{av} (m a.s.l) | P_{av} (mm) | T_{av} (°C) | Q_{av} (×10^{6}) (m^{3}) |
---|---|---|---|---|

1954–1981 | 13.3 | 1115.9 | 13.9 | 0.55 |

1954–1990 | 13.0 | 1076.5 | 14.3 | 0.91 |

1982–1990 | 12.1 | 954.0 | 14.4 | 2.01 |

1991–2019 | 11.2 | 1104.3 | 15.1 | 2.09 |

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## Share and Cite

**MDPI and ACS Style**

Brkić, Ž.; Kuhta, M.
Lake Level Evolution of the Largest Freshwater Lake on the Mediterranean Islands through Drought Analysis and Machine Learning. *Sustainability* **2022**, *14*, 10447.
https://doi.org/10.3390/su141610447

**AMA Style**

Brkić Ž, Kuhta M.
Lake Level Evolution of the Largest Freshwater Lake on the Mediterranean Islands through Drought Analysis and Machine Learning. *Sustainability*. 2022; 14(16):10447.
https://doi.org/10.3390/su141610447

**Chicago/Turabian Style**

Brkić, Željka, and Mladen Kuhta.
2022. "Lake Level Evolution of the Largest Freshwater Lake on the Mediterranean Islands through Drought Analysis and Machine Learning" *Sustainability* 14, no. 16: 10447.
https://doi.org/10.3390/su141610447