## ABSTRACT

This study has been investigated using the new criterion measuring complexity Hilbert-Huang entropy (HHE), changes, and fluctuations in groundwater levels under the influence of climate change factors and humans. In this regard, the 120-month time series of groundwater level, precipitation, temperature, and runoff parameters (period 2009–2018) are first divided into five 24-month periods, then by applying the Hilbert-Huang transform. Each period is decomposed down into smaller periods, and finally, the HHE criterion measures the complexity of the time series. The examination of changes in the HHE complexity criterion shows a decrease of 2.02, 2.93, and 29.58% in the groundwater level in the second, third, and fourth periods. Also, according to the results of changes in the complexity of precipitation and temperature time series as climate change factors, these two parameters have decreased in the third and fourth periods, with the rate of decrease for the temperature time series being 18.8 and 8.3%, respectively, and for the precipitation time series is obtained by 30.6 and 4.4%, respectively. Hence, according to the results, the discharge parameter, as a human factor in the second and fourth periods, shows a decrease of 8.6 and 39.1%, respectively.

## HIGHLIGHTS

Temperature and precipitation parameters are considered climatic factors.

Runoff parameters are considered human factors.

## INTRODUCTION

Sustainable management and the use of water resources are very important for all-around human development, and without water, sustainable development is not possible. Groundwater resources, as one of the most sensitive water resources, are directly related to human life and the sustainable development of a community. In recent decades, many changes in the groundwater level have occurred due to climate change and human activity. Any anomaly or change in the oscillating pattern of atmospheric and meteorological indicators, including precipitation and temperature, which, due to climate change, will disrupt natural ecosystems such as the groundwater cycle because, in the hydrological cycle, surface water resources are directly related to atmospheric indicators and groundwater resources are interdependent (Loaiciga *et al.* 1996; Mohammadi 2011). Climatic factors are reflected in the amount of rainfall and evaporation through increasing temperature (Chen *et al.* 2004) and human activities that are manifested by increasing demand and harvesting through exploitation wells, such as the growth and development of urban life, population growth, construction of factories and industrial complexes, and changing the pattern of the cultivation and development of the agricultural industry. Each of them can play a special and decisive role in the changes and fluctuations of the groundwater level of that area, depending on the conditions of the study area. Therefore, the analysis of groundwater level fluctuations in order to identify the effective factors of these resources and also a comprehensive understanding of the relationship between these reserves with climate change and human activities and their actions and reactions can provide a good basis for preventing the continuous and increasing decrease of groundwater level, scientific management of water resources, and sustainable development and effective use of these resources. Anomalies and changes in groundwater resources affected by climatic and human factors can be inferred in a variety of ways, including the concept of complexity. In this regard, entropy is one of the methods that can be used in this field. The theory of entropy, coined quantitatively and mathematically by Shannon in 1948, is defined as a measure of irregularity and uncertainty in a system (Shannon 1948). The entropy criterion can provide a suitable indicator in predicting future conditions for the better use of water resources using proper water resources management. The concept of entropy due to its capacity and ability to solve problems in various fields as an interdisciplinary science has been used by many researchers (Yogesan *et al.* 1996; Steinborn & Svirezhev 2000; Pharwaha & Singh 2009). Much research has been done to identify groundwater levels. Singh & Cui (2015) examined the potential of the theory of relative entropy, configured entropy, and Borg entropy in hydrology and groundwater modeling. They used the groundwater depth characteristic observed from the earth's surface to evaluate the mentioned theories. The results showed that the hourly time series of groundwater levels shows a significant daily alternation, which shows the relative entropy of this alternation with the highest resolution. Komasi *et al.* (2016) used entropy to identify the factors that reduce the groundwater level of the Silakhor Plain. The results showed that 71% reduction in the complexity of the discharge of the rivers leaving this region has had a greater impact on the reduction of the underground water level in this region than the factors of precipitation and temperature. Nath *et al.* (2021) studied the impact of urbanization on land-use and land cover change in Guwahati city, India and its implication on declining groundwater levels. The increase in impervious surface coverage, due to urbanization, has extensively reduced the areas of high-potential groundwater recharge zones, thereby dropping the level of groundwater in the wells. Ghimire *et al.* (2021) investigated climate and land-use change impacts on spatiotemporal variations in groundwater recharge in a case study of the Bangkok area, Thailand. Groundwater recharge is expected to decrease in high and medium urbanization areas, ranging from 5.84 to 20.91 mm/yr for the RCP4.5 scenario and 4.07 to 18.72 mm/yr for RCP8.5. In contrast, for the low urbanization scenario, the model projects an increase in groundwater recharge ranging from 7.9 to 16.66 mm/yr for the RCP4.5 scenario and 5.54 to 20.04 mm/yr for RCP8.5. Nourani *et al.* (2015) used the wavelet-entropy criterion to study changes in hydrological processes in Lake Urmia, Iran. In this method, the time series of hydrological processes are divided into smaller intervals; in the next step, each interval is decomposed under wavelet transformation, and finally, the criterion of the wavelet-entropy complexity is calculated for each of the time intervals. Decreasing the complexity of the runoff is the main factor in reducing the complexity and water level of the lake. Razzaq *et al.* (2018) used a wavelet-entropy criterion to identify the factors affecting the fluctuations of groundwater resources in the Tasuj Plain, Iran. The results showed a greater contribution of pumping than changes in temperature and precipitation in the decrease of groundwater level. Hassanzadeh *et al.* (2022) investigated the effects of climate change on the decrease of groundwater levels in the Khorramabad city of Lorestan province, Iran, using an entropy wavelet. Precipitation changes had the greatest effect on reducing the groundwater level. Declining groundwater levels will have social and economic consequences, including the disruption of farmers' activities, the region's animal husbandry, the lack of drinking water, the disruption of public health, and rising unemployment. Zafari & Rouhani (2017) studied the consequences of the crisis of declining groundwater levels in Tehran. Uncontrolled abstraction of groundwater has led to the destruction of the region's ecosystem, damage to buildings, reduced economic power of the people, and reduced agricultural production. Seifipour *et al.* (2020) investigated the application of entropy theory in assessing the groundwater quality monitoring network of Sefiddasht city Chaharmahal and Bakhtiari province, Iran. The optimum station for groundwater quality in this plain is the Safarpour well, and the Tahmasebi well and Shadikhar Qanat, gaining low rank in the network, have a critical situation and their continuation requires a general revision. In the Kuhdasht plain, because the groundwater level has decreased, finding the reasons for this and providing a solution for managing these water resources will make us not see a shortage of groundwater resources in the future. The detection of period changes can be done by various tools such as Fourier transform, short-time Fourier transform, wavelet transformation, and so on. In other words, the purpose of applying a mathematical transform on a signal is to obtain information that is not accessible in the original signal. Each mentioned method in the field of signal processing has limitations and problems. The Hilbert-Huang transformation criterion was proposed by Huang *et al.* (1999) to cover the weaknesses of other signal processing methods. The ability of this method to process all types of signals has made this method widely used by researchers in various fields. This method has been used in the fields of structural health monitoring and damage identification (Gao & Yan 2006; Pines & Salvino 2006; Roveri & Carcaterra 2012, Ghodrati Amiri et al*.* 2016).

However, this processor has not been used in water resources engineering so far. In this study, relying on the concept of complexity and disorder, using 10-year time-series data of precipitation, temperature, and runoff and the new Hilbert-Huang entropy (HHE) approach, the impact rate of climate change and human factors impact on decreased fluctuations and groundwater levels decrease has been reviewed in the Kuhdasht plain.

### Case study

^{2}and that of the aquifer is 182.1 km

^{2}. This plain has 310 explatory wells, four observation wells and Piezometric wells. Therefore, the groundwater level time series is the result of the average groundwater level in these wells. Also, this plain has rivers, such as Seymareh, Kashkan, Madian River, Siab, Khaleh River, Diyaly, and Solabeh. The Kuhdasht plain has a relatively warm climate. Table 1 shows the average statistical characteristics of the study area from 2009 to 2018. Figures 2–4 also show the changes in the parameters of groundwater level, precipitation, temperature, and runoff during the study period.

Parameter . | Minimum . | Maximum . | Average . | Standard deviation . | Skewness . |
---|---|---|---|---|---|

Average groundwater level (m) | 1,210.5 | 1,213.7 | 1,212.9 | 2.5 | 0.8 |

Precipitation (mm) | 0 | 176.3 | 45.1 | 60.1 | 1.5 |

Air temperature (°C) | −1 | 38.3 | 21.3 | 8.8 | 0.1 |

Runoff (m^{3}/s) | 127.3 | 502.4 | 231.9 | 151.7 | 1.9 |

Parameter . | Minimum . | Maximum . | Average . | Standard deviation . | Skewness . |
---|---|---|---|---|---|

Average groundwater level (m) | 1,210.5 | 1,213.7 | 1,212.9 | 2.5 | 0.8 |

Precipitation (mm) | 0 | 176.3 | 45.1 | 60.1 | 1.5 |

Air temperature (°C) | −1 | 38.3 | 21.3 | 8.8 | 0.1 |

Runoff (m^{3}/s) | 127.3 | 502.4 | 231.9 | 151.7 | 1.9 |

## MATERIAL AND METHODS

### The Hilbert-Huang transform (HHT) methods

This method consists of two parts: empirical mode decomposition (EMD) and Hilbert transform. Compared to other known methods in the field of signal processing, such as wavelet transform and Fourier transform, it can process a variety of signals, such as linear and nonlinear signals, and static and non-static signals (Huang *et al.* 1999).

#### Empirical mode decomposition

The application of the EMD method is such that a complex signal is decomposed into several intrinsic mode functions or intrinsic mode functions (IMF) functions over some time, in such a way that each intrinsic mode function has a length equal to the primitive signal and the sum of these functions reproduces the original data. Intrinsic mode functions must meet the following two conditions (Huang *et al.* 1999):

(1) The number of points at which the horizontal axis intersects, with the equal number of extremum points or the maximum difference between them.

(2) At any moment, the average push up and push down signal is defined by maximum and minimum local, which is zero. Intrinsic mode functions are determined by an algorithm called screening processing, which was first introduced by Huang

*et al.*(1999). The steps of this algorithm for the time series or the initial signal*x*(*t*) are as follows (Huang*et al.*1999):1. Determining the extremum (maximum and minimum points) of the initial signal.

2. Connecting the maximum points and the minimum points by applying an interpolation function such as the function spline third to create a push up and down signal.

- The above step is done to estimate the first intrinsic mode function, but
*h*_{1}(*t*) is not always the first intrinsic mode function. In this case, the previous steps are repeated*k*times in order to reach the appropriate stop criterion, and finally, the first intrinsic mode function*c*_{1}(*t*) is determined according to Equation (2): - 4. In this step, in order to determine the first remaining [
*r*(_{1}*t*)], the difference between the first intrinsic mode function obtained and the initial signal according to Equation (3) is obtained.

*r*

_{1}) is considered the initial signal, and all the mentioned steps are implemented on it in order to determine other intrinsic mode functions. This process continues until the last residue has no extremum. Finally, after the screening process is completed, considering the existence of

*n*intrinsic mode function, the initial signal is reproduced using Equation (4):

*c*(

_{j}*t*) is the intrinsic mode function of the rank

*j*,

*n*is the number of intrinsic mode functions, and

*r*(

_{n}*t*) is the remainder of the signal decomposition process. Steps (A) to (E) of the screening process for a hypothetical signal are illustrated in Figure 5. This step is performed to estimate the first intrinsic mode function.

#### Hilbert transformation (HT)

*et al.*1999). The HT for time data

*x*(

*t*) is according to Equation (5):

*y*(

*t*) is the HT of the signal

*x*(

*t*), in which

*x*(

*t*) temporal and variable data

*τ*, the variable is part of the time

*t*that is smaller than that. Each intrinsic mode function under the HT produces analytical signal

*Y*(

*t*), which is calculated according to Equation (6):

### Entropy

*x*is a discrete random variable with the values

*x*

_{1},

*x*

_{2}, … ,

*x*and the corresponding probabilities

_{n}*p*

_{1},

*p*

_{2}, … ,

*p*, the Shannon entropy can be measured according to Equation (10) (Singh 2011):where

_{n}*H*(

*x*) the entropy is

*x*, which is also called the Shannon entropy function, and

*P*is the probability distribution which is defined as

*P*= {

*p*,

_{i}*i*= 1,2 … ,

*N*}. As can be deduced from the above relationship, the amount of entropy is related to the probability of occurrence and uncertainty of a phenomenon and this relationship is inverse (Shannon 1948).

### HHE criterion

*et al.*2001):where

*m*is the main signal separation scale,

*Y*[

_{m}*m*= 1,2,3, … ,

*M*], and

*n*is the number of intrinsic mode functions available on the

*m*scale. In the next step, the signal total energy and the normalized energy of the analytical signals are calculated according to Equations (12) and (13) (Rosso

*et al.*2001), respectively, and finally, the HHE criterion is obtained using Equation (14). The procedure for calculating the HHE index is shown schematically in Figure 6.

## RESULTS AND DISCUSSION

In recent decades, increasing population, industry, agriculture, uncontrolled and unprofessional harvesting of groundwater, as well as changes in cultivation patterns that are not compatible with the state of water resources in the region, have caused a great need for water in the study area. As a result, the exploitation of groundwater resources by digging multiple wells and the exploitation of surface water have directly and indirectly affected the reduction of the groundwater level. Also, rising air temperatures and consequent climate changes are some of the biggest challenges facing the world and changing climate patterns. In this study, to investigate the impact of climatic and human factors on reducing the groundwater level, three parameters have been used: precipitation, runoff (runoff refers to the water flow in the study area), and air temperature. Precipitation and air temperature are representative of climatic factors, and the runoff parameter, due to increased human harvesting from surface water resources to meet the needs of drinking, agriculture, and industry reducing water flow, is considered a human factor. Changes in the runoff parameter cannot be a clear and precise criterion for the effect rate of human actions on groundwater resources because the runoff of surface currents is somehow affected by atmospheric and climatic factors, because there is no accurate criterion to assess the impact of humans, runoff water is considered a human factor. The withdrawal from this groundwater for various uses has played an important role in reducing the level of these waters. Figure 2 shows the fluctuations in the groundwater level of Kuhdasht from 2009–2018. As can be seen in Figure 2, from the beginning of 2009 to the end of 2018, the average groundwater level has decreased by about 5 m. In order to evaluate and measure the changes in groundwater level fluctuations in the Kuhdasht plain, use the new HHE criterion. To achieve this goal, initially, the 120 months of groundwater level in the Kuhdasht plain are divided into five 24-month periods. Then each period was then decomposed in the second order under the Hilbert-Huang transformation. Due to the complex nature of the time series of hydrological processes, HHT to decompose periods into subsets facilitates access to more information from the time series of the data and more accurate results. In the next step, the energy of the subsets obtained from the HHT is calculated and normalized, and finally, the HHE criterion is obtained. Table 2 shows the results of the foregoing steps for the groundwater level time series.

Normalized energy of subsets . | 24-month subsets . | ||||
---|---|---|---|---|---|

First period . | Second period . | Third period . | Fourth period . | Fifth period . | |

ρ_{1} | 0.1717 | 0.1566 | 0.2718 | 0.0181 | 0.2296 |

ρ_{2} | 0.4347 | 0.3633 | 0.3657 | 0.2946 | 0.4285 |

ρ_{3} | 0.3909 | 0.4801 | 0.3625 | 0.6872 | 0.3420 |

HHE criterion | 1.0314 | 1.0105 | 0.9808 | 0.6906 | 1.0679 |

Changes (%) | n/a | −2.02 | −2.93 | −29.58 | 54.63 |

Normalized energy of subsets . | 24-month subsets . | ||||
---|---|---|---|---|---|

First period . | Second period . | Third period . | Fourth period . | Fifth period . | |

ρ_{1} | 0.1717 | 0.1566 | 0.2718 | 0.0181 | 0.2296 |

ρ_{2} | 0.4347 | 0.3633 | 0.3657 | 0.2946 | 0.4285 |

ρ_{3} | 0.3909 | 0.4801 | 0.3625 | 0.6872 | 0.3420 |

HHE criterion | 1.0314 | 1.0105 | 0.9808 | 0.6906 | 1.0679 |

Changes (%) | n/a | −2.02 | −2.93 | −29.58 | 54.63 |

*et al.*2015). Therefore, the groundwater level of the Kuhdasht plain has become an anomaly in the second, third, and fourth periods. The HHE criterion changes for the groundwater level time series, as shown in Figure 7.

### Investigating the relationship between complexity changes of groundwater level with climate change and human factors

In order to investigate the effect of climate change and human factors on groundwater fluctuations, three parameters of precipitation, temperature, and runoff have been used as representative of climate change and human factors. The 120-month time series of each parameter was divided into five 24-month periods and then was under HHT with the second rank. Then, the energy of the subsets obtained from the HHT is calculated and normalized, and finally, the HHE complexity criterion is obtained for each period, the results of which can be seen in Tables 3–5.

Normalized energy of subsets . | 24-month subsets . | ||||
---|---|---|---|---|---|

First period . | Second period . | Third period . | Fourth period . | Fifth period . | |

ρ_{1} | 0.3330 | 0.3336 | 0.0095 | 0.0226 | 0.0336 |

ρ_{2} | 0.3340 | 0.3336 | 0.3916 | 0.7326 | 0.4760 |

ρ_{3} | 0.3330 | 0.3328 | 0.5989 | 0.2448 | 0.4904 |

HHE criterion | 1.0968 | 1.0968 | 0.8984 | 0.6582 | 0.8169 |

Changes (%) | n/a | 0 | −18.08 | −8.3 | 24.1 |

Normalized energy of subsets . | 24-month subsets . | ||||
---|---|---|---|---|---|

First period . | Second period . | Third period . | Fourth period . | Fifth period . | |

ρ_{1} | 0.3330 | 0.3336 | 0.0095 | 0.0226 | 0.0336 |

ρ_{2} | 0.3340 | 0.3336 | 0.3916 | 0.7326 | 0.4760 |

ρ_{3} | 0.3330 | 0.3328 | 0.5989 | 0.2448 | 0.4904 |

HHE criterion | 1.0968 | 1.0968 | 0.8984 | 0.6582 | 0.8169 |

Changes (%) | n/a | 0 | −18.08 | −8.3 | 24.1 |

Normalized energy of subsets . | 24-month subsets . | ||||
---|---|---|---|---|---|

First period . | Second period . | Third period . | Fourth period . | Fifth period . | |

ρ_{1} | 0.1373 | 0.2082 | 0.0393 | 0.1235 | 0.3771 |

ρ_{2} | 0.4491 | 0.4455 | 0.4927 | 0.4721 | 0.3362 |

ρ_{3} | 0.4135 | 0.3463 | 0.4680 | 0.4044 | 0.2867 |

HHE criterion | 0.9973 | 1.0542 | 0.7312 | 0.6988 | 1.0924 |

Changes (%) | n/a | 5.7 | −30.6 | −4.4 | 56.3 |

Normalized energy of subsets . | 24-month subsets . | ||||
---|---|---|---|---|---|

First period . | Second period . | Third period . | Fourth period . | Fifth period . | |

ρ_{1} | 0.1373 | 0.2082 | 0.0393 | 0.1235 | 0.3771 |

ρ_{2} | 0.4491 | 0.4455 | 0.4927 | 0.4721 | 0.3362 |

ρ_{3} | 0.4135 | 0.3463 | 0.4680 | 0.4044 | 0.2867 |

HHE criterion | 0.9973 | 1.0542 | 0.7312 | 0.6988 | 1.0924 |

Changes (%) | n/a | 5.7 | −30.6 | −4.4 | 56.3 |

Normalized energy of subsets . | 24-month subsets . | ||||
---|---|---|---|---|---|

First period . | Second period . | Third period . | Fourth period . | Fifth period . | |

ρ_{1} | 0.2020 | 0.0250 | 0.0015 | 0.0759 | 0.0059 |

ρ_{2} | 0.4362 | 0.7343 | 0.4769 | 0.3991 | 0.5035 |

ρ_{3} | 0.3619 | 0.2407 | 0.5216 | 0.5250 | 0.4905 |

HHE criterion | 1.0528 | 0.9620 | 0.9871 | 0.6002 | 0.7252 |

Changes (%) | n/a | −8.6 | 2.6 | −39.1 | 20.8 |

Normalized energy of subsets . | 24-month subsets . | ||||
---|---|---|---|---|---|

First period . | Second period . | Third period . | Fourth period . | Fifth period . | |

ρ_{1} | 0.2020 | 0.0250 | 0.0015 | 0.0759 | 0.0059 |

ρ_{2} | 0.4362 | 0.7343 | 0.4769 | 0.3991 | 0.5035 |

ρ_{3} | 0.3619 | 0.2407 | 0.5216 | 0.5250 | 0.4905 |

HHE criterion | 1.0528 | 0.9620 | 0.9871 | 0.6002 | 0.7252 |

Changes (%) | n/a | −8.6 | 2.6 | −39.1 | 20.8 |

## CONCLUSION

The high dependence of human societies on groundwater resources has made these resources have special importance and status; therefore, understanding the groundwater system and the dual effects of climate change and human activities on these resources to protect them quantitatively and qualitatively seems necessary. In this study, in order to evaluate the effects of climate change and humans on groundwater, time series fluctuations in the Kuhdasht plain aquifer have been used in the HHE complexity assay criterion. For this purpose, first, the 120-month groundwater level time series, precipitation, temperature, and runoff were each divided into five 24-month periods, and finally, the HHE criterion for each time series was calculated. The results showed that the complexity of the groundwater level time series in the second, third, and fourth periods had a decreasing trend of 2.02, 2.93, and 29.58%, respectively. This decreasing trend indicates the reduction of water level fluctuations and also the occurrence of some kind of anomaly in the groundwater cycle in the study area. In order to evaluate the effect rate of climatic and human variables in the occurrence of this anomaly, the changes in the HHE criterion for temperature, precipitation, and runoff parameters were matched with changes in groundwater level. According to the results, in the third period, precipitation and temperature parameters are climatic factors with a decrease of 30.6 and 18.08%, respectively; also in the fourth period, temperature and precipitation parameters have decreased by 4.4 and 8.3%, respectively. Hence, the parameters of runoff as a human factor in the second and fourth periods with a decrease of 8.6 and 39.1%, respectively, have been effective in decreasing the complexity and fluctuations of groundwater level, and as can be seen, the share of runoff time series in the period the fourth has been more than the share of temperature and precipitation. Also, the highest correlation between time series belongs to the level-runoff time series with a correlation coefficient of 0.1173. Therefore, the results obtained for the study period are witness to the significant effect of human factors in creating an anomaly and decreasing the groundwater level in the study area. In the effect of human factors in reducing the underground water level of the Kuhdasht plain, it is recommended that if the underground water level decreases in the future, it should be done with appropriate management measures and increasing the efficiency of drip irrigation. Also, avoid planting crops that use a lot of water to prevent future groundwater depletion. With this trend, it will not be long before the Kuhdasht plain faces a crisis of water shortage, economic and social problems caused by water shortage, and other precipitation cannot be effective in improving this crisis. The use of other criteria and methods of time-series analyses such as the entropy wavelet criterion and the Mann–Kendall test and also the use of multiple time series such as evaporation and humidity in different time scales can be a good suggestion to investigate factors effective on the decrease of groundwater levels in the region for future research.

## ACKNOWLEDGEMENTS

The authors would like to thank the Lorestan Province Regional Water Company for (consultation).

Conflict of interest on behalf of all authors, the corresponding author states that there is no conflict of interest. Open Access: This article is licensed under a Creative Commons Attribution4.0 International License, which permits use, sharing, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third-party material in this article is included in the article's Creative Commons license unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Common license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## DATA AVAILABILITY STATEMENT

Data cannot be made publicly available; readers should contact the corresponding author for details.

## CONFLICT OF INTEREST

The authors declare there is no conflict.

## REFERENCES

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