ABSTRACT
This study investigates the dynamics of daily Urmia Lake level (ULL) changes using spectral analysis tools to discover fluctuating patterns in the ULL series. Therefore, in the present research, the empirical mode decomposition (EMD), variational mode decomposition (VMD), empirical wavelet transform (EWT), and empirical Fourier decomposition (EFD) were used to analyze the ULL signal. ULL series were decomposed into subseries, and the optimized outcome was used. All methods concluded that the ULL series has a steep downward trend. Signal reconstruction was performed, and it was inferred that EFD could not estimate the ULL series appropriately and had root-mean-square error (RMSE) = 12.26. Different from EFD, other methods performed better signal construction according to RMSE and error analysis. The mode-mixing issue was the last step in verifying the capabilities of signal-analyzing methods. Based on the power spectral density (PSD), it was seen that EMDs had mode-mixing problems and limitations in signal decomposition, whereas VMD and EWT did not have these issues. Results demonstrated that the present study has some limitations. Overall, it was concluded that VMD performed better in terms of RMSE, error analysis, reconstruction, mode-mixing problems, and PSD analysis while decomposing and extracting features from the ULL signal.
HIGHLIGHTS
Urmia Lake level (ULL) time series presented a steep downward trend, making it hard for signal processing methods to analyze accurately.
Variational mode decomposition (VMD) performed better than other methods in analyzing the ULL signal.
Empirical Fourier decomposition did not perform appropriately and was the weakest among other methods.
VMD had no mode-mixing issues contrary to empirical mode decompositions.
INTRODUCTION
As one of the frequent environmental issues, endorheic saline lakes have declined or are almost extinct in dry areas of the world due to rising water demand, anthropogenic influences, and occasionally climate change (Alivernini et al. 2018). Salt lakes worldwide, with a volume of about 8,300 km3 representing about 40% of all lakes, are found in arid zones (Wurtsbaugh et al. 2017). Because lakes play critical roles in natural systems, it is critical to investigate the core causes of this problem (Ye et al. 2020). Large salinity lakes rapidly decline worldwide, endangering habitats, human health, and economic activity. Similarly, saline lakes have declined in Iran. The most important example is the one currently occurring in the northwest of Iran, the Urmia Lake.
In the present research, we have studied the Urmia Lake level (ULL), Iran's most prominent and the second-largest saltwater lake on Earth, which has declined significantly in the past two decades. It would be informative to use a methodology to capture the nonlinear alteration in the lake level. Also, such an outcome could be useful in examining the drought in the basin (e.g., Amirataee et al. 2018; Lashkari et al. 2021). According to several studies, human activity on water and land is the basis of the problem (e.g., Khazaei et al. 2019; Foroumandi et al. 2021). However, a report that discovered a similar pattern in headwater areas disproved the claim made in earlier studies that dam construction was the primary reason for the reduction (Fathian et al. 2014). Drought, climate change, and anthropogenic activity are the leading causes of the issues affecting salty lakes. The Great Salt Lake, Mono Lake, Walker Lake (the United States), the Dead Sea (the Jordan region), and the Aral Sea (Kazakhstan in the north and Uzbekistan) all have similar occurrences. When a lake's level dropped, it harmed human health, culture, economy, and more. Lake restoration necessitates integrating many fields of science, technology, engineering, management, and governance to avoid the fragmentation of research on these interdependent human–natural systems (Hart 1996; White et al. 2015; Elmore et al. 2016; Micklin 2016; Edwards & Null 2019; HDR 2020). Lake Urmia has shrunk 7 m and lost almost 90% of its volume since 2000 due to agricultural water development. Because of this reduction, the salinity has increased, and the density of the salts was changed, causing environmental effects such as decreasing the population of brine shrimp, namely, Artemia SPP. which is believed to be the birds' (especially flamingos) primary source of feeding (Abbaspour & Nazaridoust 2007). The lake level's decrease distanced resorts from water deep enough for leisure (Sima et al. 2021), resulting in the closure of tourist resorts. A further risk to the neighboring population's health occurred when the subsequent lake-level dropped, revealing that the lakebed caused the release of a complicated mixture of aerosols. It is crucial to highlight the stakeholders affected by Urmia Lake's water level drop and elaborate on the potential impact on agriculture, industry, and the local population.
The pattern of Urmia Lake's water level drop creates a significant problem for its stakeholders, particularly the agricultural (e.g., farmers) and industrial sectors (e.g., Ministry of Energy) and local population (e.g., Urmia City). A major contribution to the identification of the stakeholders and their different roles is very important (Cong et al. 2017; Shahid et al. 2018). To this end, a workshop in the city of Urmia was held to address the Ecosystem Approach to the Management of Urmia Lake. About 200 representatives of different stakeholder groups were identified as follows: provincial offices (East and West Azerbaijan provinces) (50%); ministries and governmental organizations (20%); universities, education, and research centers (20%); and NGOs (farmers and local population included) (10%). Based on these facts, it is important to propose approaches considering various concepts of lake-level decline (e.g., time series, spectral analysis, and so on).
Taking advantage of the trend in the water level's decline is one strategy to deal with the aforementioned issue. Therefore, by examining the dynamics of the water level changes around Urmia Lake, the current study looks into potential causes for the issue. In this study, the proper methodologies are used to identify trends and fluctuations in the ULL series. Applying spectral methods can produce good results when examining the intricacy and variations of the ULL time series, taking into account the seasonality of the hydrological processes. Any survival strategy and Urmia Lake restoration project must start by using effective mathematical methods to assess the ULL series components (e.g., Khazaei et al. 2019; Foroumandi et al. 2022).
Due to the nature of random variation, stochastic dynamics can account for the apparent irregularity and unpredictability of lake-level behavior (de Domenico et al. 2013). To determine the degree to which each component affects the lake level, time series decomposition is a valuable tool. Long-term fluctuations have drawn attention and can be examined independently if necessary or excluded from calculations (Soomere et al. 2015). By separating the time series, we could identify the nonlinear trend in a particular phenomenon. A recently popular approach to decomposing nonstationary series is called empirical mode decomposition (EMD). An intrinsic mode function (IMF) is captured when EMD processes a signal. As an illustration, 60 years of Chinese sea level were modeled using EMD to eliminate long-term fluctuation from gauge records to reduce the uncertainty surrounding long-term sea-level variation in the calculation of sea-level acceleration (Jevrejeva et al. 2008; Sallenger et al. 2012; Calafat & Chambers 2013; Haigh et al. 2014; Cheng et al. 2016; Dehghan et al. 2022). Due to mode mixing issues in EMD, Wu & Huang (2009) proposed a noise-aided technique, namely, ensemble EMD (EEMD), to solve this problem. The EEMD approach was used by Devlin et al. (2020) to examine multiresolution variation in the tides of the Indian Ocean. Results indicated that, similarly, the EEMD results show the mode-mixing issue when decomposing nonlinear time series. To overcome this issue, Torres et al. (2011) suggested complete ensemble empirical mode decomposition adaptive noise (CEEMDAN). The processing of signals with nonlinear and nonstationary properties can be effectively and adaptively done using CEEMDAN (Cao et al. 2019). The decomposition of a complicated wideband time series into IMFs, resulting in a relatively modest subcomponent with various temporal features, is generally done using a binary filter. CEEMDAN delivers temporal data considering the original signal properties and captures adaptive IMFs. These IMFs have different properties of temporal scales and frequencies ranging from high to low and residual components, which extract the trend component associated with signal oscillation. Strong regularity in the decomposed IMFs component sequence is advantageous for model learning and raises prediction accuracy. The EMD family (EMDs), consisting of the EMD, EEMD, and CEEMDAN, will be utilized to extract signal features together in the present research.
As a data-driven approach, EMD captures IMFs from a signal of interest independent of its characteristics. After synthesizing each component's instantaneous information, the original signal's entire time and frequency information can be retrieved (Huang et al. 1998). Liu et al. (2020) mentioned that mode mixing and over-envelope, under-envelope, and end-point impact issues are some drawbacks in EMD. To prevail over these problems, the variational mode decomposition (VMD) method was devised by Dragomiretskiy & Zosso (2013), in which a signal with nonlinear and nonstationary features could be decomposed into numerous subseries having a specific bandwidth and center frequency by imposing variational restrictions. VMD is widely utilized in the processing of vibrations and diagnosis of faults (Li et al. 2019). However, the VMD parameters must be adjusted beforehand. Several academics have offered techniques for enhancing the VMD parameters, and significant progress has been made in the related field (Miao et al. 2019).
Gilles (2013) presented the empirical wavelet transform (EWT), similar to the wavelet transform, a unique decomposition method that may isolate a complicated signal into numerous subseries. In the EWT method, the segmentation of the frequency spectrum is performed based on the method of frequency band division derived from data, and each segmented interval is then reconstructed by creating orthogonal wavelet filter banks by applying the functions of scaling and wavelet (Shi et al. 2021; Zheng et al. 2022). EWT separates signals into components called empirical wavelet functions (EWFs). It must be noted that the decomposition of EWT relies on the spectrum segmentation border. Zheng et al. (2021) have recently presented the empirical Fourier decomposition (EFD) for nonstationary signal analysis based on fast Fourier transform (FFT) and adaptive spectrum segmentation technology. However, the spectrum division boundary of EFD must be determined in advance based on users' experience (Zheng et al. 2022).
The world's large saltwater lakes, including Lake Urmia, are confronting numerous issues. As there is an immediate demand for water resources administration, the present research used signal feature extraction analysis to analyze Urmia Lake's environmental and hydrological problems. To the authors' knowledge, crucial information extraction of daily ULL signal is provided for the first time utilizing both spectrum and frequency analysis based on our methodology. Using EMDs, VMD, EWT, and EFD, the primary purpose of this study is the spectral and temporal analysis of the daily ULL series from 1990 to 2021. The decomposition and trend analysis results are further reviewed and contrasted to determine their ability to process signals in the time–frequency domain, their progress in mode-mixing circumstances, and their benefits and drawbacks. In addition, the reconstruction of the signal will be investigated. The document arrangement is as follows: the Materials and Methods section describes the materials and methods used, study area, and data used in this investigation. In the Results and Discussion section, the spectrum and frequency analysis findings are displayed and discussed. Finally, this study is concluded in the Conclusion section.
MATERIALS AND METHODS
Study area and data
(a) Geographic location of Urmia Lake and (b) daily time series of ULL.
Empirical mode decomposition, ensemble EMD, and complete EEMD with adaptive noise
The decomposition of a time series into a finite number of specific oscillatory mode functions known as IMFs is done using the entirely adaptive EMD approach. Through the sifting process, these IMFs reveal the oscillation modes in the data. IMFs are generated using an iterative method and meet the following two criteria: (1) the total number of extrema and zero-crossings must either be equal or differ by no more than one, and (2) the local average of the upper and lower envelopes must always be zero. The following describes how the EMD algorithm functions:
Identify the series' local maxima and minima (or extrema).
Create emax(t) and emin(t) using the cubic spline interpolation approach (upper and lower envelopes, respectively).
The mean value m1(t) = (emax(t) +emin(t))/2 is defined.
Determine the emax(t) +emin(t)/2 as the mean value (m1(t)).
To get the first nominee for the IMF, h1(t), the mean value m1(t) is subtracted from the signal y(t), so h1(t) =y(t) − m1(t).
If h1(t) meets the requirements for an IMF property, it is verified. If so, it counts as the first IMF, c1(t) =h1(t). It is then removed from the original signal, and in step 1, the first residual, r1(t) =y(t) − c1(t), is regarded as the new series. If not, the sifting procedure is repeated as often as necessary to produce an IMF.
The key steps of the EEMD approach are as follows:
Create a white noise sequence and apply it to the target signal. Decompose the signal with additional noise into the specified number of IMFs using the EMD technique.
Repeat step 1 several times. Note that each of the added white noise series is distinct.
Calculate the final EEMD values by averaging the respective IMFs.
As a result of the EEMD decomposition, the added time series of white noise cancel each other out when combined (Alizadeh et al. 2019). The mean IMFs of EEMD maintain the beneficial characteristics of the EMD technique; however, the strength of the mode mixing in EEMD reduces relative to the EMD model (Wu & Huang 2009).
Variational mode decomposition
VMD is a powerful nonrecursive signal decomposition method (Dragomiretskiy & Zosso 2013). VMD can decompose a complex signal into a series of subsignals (i.e., modes) with specific bandwidth in the frequency domain to mine characteristics of complex nonlinear signals (Upadhyay & Pachori 2015). Recently, VMD has been employed to solve many engineering problems, including the diagnosis of faults in mechanical engineering (Wang et al. 2015), the processing of economic data signals (Lahmiri 2016), value estimation in metals (Liu et al. 2020), sea-level signal analysis (Dehghan et al. 2022), and processing signals in biomedicine (Lahmiri 2014).
In this problem, the Lagrange multiplier (λ(t)) is utilized as a constraint constrictor, α is the parameter of balancing the data constancy constraint, and is the term of quadratic penalty to perform the convergence rate acceleration. The mentioned optimization in Equation (2) is settled by locating the saddle point of the augmented Lagrange equation using the alternating direction method of multipliers (Hestenes 1969).
Empirical wavelet transforms
A novel method for creating adaptive wavelets is presented by Gilles' EWT method (Gilles 2013). The fundamental concept is to create a wavelet filter bank that is suitable for the process and is capable of extracting the various signal modes. EWT has been utilized in signal processing and time series modeling extensively since its inception (Amezquita-Sanchez & Adeli 2015; Xin et al. 2019). In contrast to discrete wavelet transform and EMD, EWT performs an FFT on the time series and then directly analyzes it in the Fourier domain before using band-pass filtering to execute a spectral separation (Flandrin et al. 2004).
The first stage in the EWT is to divide the Fourier spectrum of the signal to be decomposed using an adaptive segmentation technique, and the second is to build a wavelet filter bank (Daubechies 1992). Assume that the spectrum is specified on the range [−π, π] of normalized frequencies. The following are descriptions of the segmentation method and wavelet filter bank for the frequency range [0, π], whereas those for the frequency range [−π, 0] can be inferred from the Hermitian symmetry of the Fourier spectrum in the normalized frequency range [−π, π].
Following is a stepwise explanation of the EWT for a signal y(t).
Apply the FT to determine the Fourier spectrum of y(t).
Use a segmentation approach, such as the lowest minima or local maxima techniques, to divide the spectrum in step 1.
Create a wavelet filter bank using the frequency segments from step 1 as a foundation for decomposing.
Based on the wavelet filter bank from step 3, express approximation and detail coefficient functions.
Breakdown y(t) and reconstruct it. The EWT can produce reliable decomposition results when y(t) has widely separated modes. However, a mode-mixing issue may arise because of the transition period when y(t) modes are tightly spaced.
Empirical Fourier decomposition
Similar to the EWT, the EFD consists of two critical steps: an improved segmentation technique and the construction of a zero-phase filter bank. In the EFD, the Fourier spectrum of a signal to be decomposed is defined on a normalized frequency range [−π, π], and the improved segmentation technique and construction of a zero-phase filter bank for the spectrum in the frequency range [0, π] are described in this section (Zhou et al. 2022).



Step 2. Determine boundaries of segment ωn using the improved segmentation technique based on the Fourier spectrum obtained in step 1.
Step 3. Construct a zero-phase filter bank based on ωn obtained in step 2.
Step 4. Obtain filtered signals in the frequency domain using
obtained in step 3.
Step 5. Obtain decomposed components yn(t) in the time domain using inverse Fourier transforms of obtained in step 4.
Proposed ULL signal analysis
RESULTS AND DISCUSSION
This section reports the results of the decomposing of the ULL time series, and the analysis of the results of the six models is reported. First, preprocessing and data analysis are presented. Next, the ULL time series analysis based on the EMD family will be discussed. VMD, EWT, and EFD are used to analyze the ULL signal. Finally, an evaluation of the results and comparative performance of these tools will be presented.
Decomposition of daily ULL series using (a) EMD, (b) EEMD, and (c) CEEMDAN.
The settings K were found to produce the optimal decomposition for the VMD process in terms of least reconstruction error and best performance. As a result, Figure 5 might not have any hydrologic meaning. As seen, all modes separated from the ULL series are grouped in Figure 5 according to their frequencies, from lowest to highest. In the deconstructed results, VMD's imf1 is comparatively steady, but imf2 and imf3 exhibit subcomponents more often fluctuating. Compared with the first three IMFs, imf4 and imf5 are more complex and exhibit high volatility. In the ULL, the residual component exhibits a declination.
Each IMF component has a unique hydrological meaning as the ULL's structural component. The Res subseries, the main component of the ULL trend, fluctuates slowly around the ULL's long-term average values. It may be deduced by contrasting the original signal and Res in the corresponding decomposition outcomes shown in Figure 5. Each increase or decrease in the lower frequency components (such as imf2 and imf3) typically corresponds to significant occasions with an impact on the hydrological events. Small amplitudes and high frequencies characterize the higher frequency components (imf4 and imf5), primarily representations of the ULL's daily or short-term variations.
VMD is an appropriate instrument for signal analysis because the lake series primarily exhibits a nonstationary characteristic. Some modes are produced following the original ULL series' VMD decomposition, as depicted in Figure 5. The decomposed modes by VMD in Figure 5 exhibit more steady fluctuation, distinct regularity, and a simple structure when compared with the original series. All of the modes, except the Res component, are almost stationary, according to the results of the ULL time series' VMD decomposition. All these aspects of the VMD decomposition findings make the model design easier.
(a) Spectrum segmentation by EWT method, (b) EWFs decomposed by EWT, and (c) filter on top of the magnitude spectrum of the input signal based on decompositions.
(a) Spectrum segmentation by EWT method, (b) EWFs decomposed by EWT, and (c) filter on top of the magnitude spectrum of the input signal based on decompositions.
Figure 6(b) shows the waveform of each EWT subseries after decomposition. Each component's x-axis in the figure indicates times, which is a unit equal to a day. The ordinate of ULL oscillations is amplitude, measured in metres. It demonstrates that the low-frequency interference and trend components – essentially devoid of periodicity – make up ewt1 in its entirety. The periodicity of each original signal can be accurately reflected by the excellent periodicity that ewt2 exhibits. The other component (ewt3) consists primarily of high-frequency portions that can effectively express the variation in ULL signals between states. Figure 6(c) plots each filter on top of the magnitude spectrum of the input signal based on decompositions. The plots are on the frequency interval [−π, π]; the magnitude spectrum is normalized.
(a) Spectrum segmentation by EFD method and (b) IMFs decomposed by EWT.
In contrast to EWT, the EFD approach can successfully separate each component by spectral envelope processing. Both EFD and EWT have adequate and comparable spectrum segmentation boundaries. Each of EFD and EWT's two ideal frequency bands contains the least amount of noise interference. As depicted in Figure 7(a), when the decomposition time is five, the spectrum with a frequency between 0 and 2.7 Hz and higher will constitute a single entity. Figure 7(b) depicts the decomposition results of EFD for the simulated ULL signal.
Signal reconstruction
Based on the methodology used herein, it was seen how the aforementioned methods can be used to analyze, or decompose, signals and time series. This process is called decomposition or signal breakdown (Alizadeh et al. 2019). The second half of the proposed methodology is how those broken-down parts may be put back together into the original signal without information being lost. This method is known as reconstruction or synthesis. Inverse analysis refers to the type of mathematical operation that impacts synthesis. Three separate meters were utilized for this purpose. First, all decomposed subseries for each approach were stacked and individually examined to reconstruct the signal. Second, the original and estimated ULL series' root-mean-square errors (RMSE) were compared (Roushangar et al. 2018a, 2018b). In the final step, the estimating error series was depicted, and the outcomes were examined and contrasted.
RMSE of original and reconstructed signals
. | Method . | |||||
---|---|---|---|---|---|---|
EMD . | CEEMDAN . | EEMD . | VMD . | EWT . | EFD . | |
RMSE | 0.000864 | 0.00081 | 0.009553 | 0.000805 | 0.00081 | 12.26 |
. | Method . | |||||
---|---|---|---|---|---|---|
EMD . | CEEMDAN . | EEMD . | VMD . | EWT . | EFD . | |
RMSE | 0.000864 | 0.00081 | 0.009553 | 0.000805 | 0.00081 | 12.26 |
(a) Reconstructed time series from EMDs, VMD, EWT, and EFD versus ULL series; (b) zooming into a specific period of time.
(a) Reconstructed time series from EMDs, VMD, EWT, and EFD versus ULL series; (b) zooming into a specific period of time.
Error time series created during the reconstruction process by EMDs, VMD, EWT, and EFD.
Error time series created during the reconstruction process by EMDs, VMD, EWT, and EFD.
Mode-mixing analysis
Mode mixing occurs when a single IMF/EWF comprises numerous intrinsic timescales or when similar intrinsic timescales are dispersed over many IMFs/EWFs. The aliasings of two nearby IMF/EWF waveforms influence each other, making them harder to distinguish. In other words, mode mixing can be characterized as a single IMF/EWF consisting of vastly different scales or similar scales living in various IMF/EWF components, and the physical meaning of each IMF/EWF in the mode-mixing area is uncertain (Wu & Huang 2009; Xu et al. 2016). In other words, the energy of the same lake-level species – a collection of lake-level elements with comparable frequencies – exists in more than one subseries, which is a reflection of the mode mixing in terms of lake levels. The mode-mixing situation is unavoidable, but it must be appropriately managed. This section addresses the presence of mode mixing and discovers which method handles the situation better.
Power spectral density analysis of IMFs captured by (a) EMD, (b) EEMD, (c) CEEMDAN, (d) VMD, and (e) EWT for mode-mixing analysis.
Power spectral density analysis of IMFs captured by (a) EMD, (b) EEMD, (c) CEEMDAN, (d) VMD, and (e) EWT for mode-mixing analysis.
According to Dragomiretskiy & Zosso (2013), their development of VMD was able to solve the mode-mixing scenario of EMD. According to Figure 10(d) and 10(e), the PSD of VMD provides an almost perfect power/frequency versus frequency figure with distinct peaks and no mode-mixing issue. In the case of EWT, similarly, no mode mixing was found; however, it should be noted that just two EWFs were retrieved. Overall, it is possible to infer that VMD performs better in terms of RMSE, error series, reconstruction, mode-mixing problems, and PSD analysis while decomposing and extracting features from the ULL signal.
CONCLUSION
Determining lake-level variations is critical for the authenticity of management practices in rural areas, particularly those next to cities. Because of its unique natural and hydrological conditions, Urmia Lake's location, and proximity to the rural area, ULL has always attracted considerable attention in terms of the economy, tourism, and investment, among other things. On the other hand, the recent reduction in the water level of Urmia Lake is a severe threat to this region. This study advocated looking into the dynamics of daily ULL variations using appropriate methodologies for detecting patterns and oscillations in the ULL series. This work investigated the capacity of specific data-adaptive multiresolution approaches, notably EMD, EEMD, CEEMDAN (EMDs), VMD, EWT, and EFD, to break down a signal into physically relevant components to assess the structure of daily ULL data. As a result, data were fragmented into various band-limited IMFs. The use of such a technique for ULL data yielded encouraging results. To examine diverse signal-processing methods, the VMD, EWT, and EFD approaches have been used simultaneously. However, to the best of our knowledge, no such multiresolution analysis has been applied to the lake-level series. Based on these methodologies, data-adaptive analysis splits the ULL series into different modes. The signal reconstruction approach was used to test the capabilities of the data analysis method. Except for the EFD, all approaches were found to have an acceptable range of errors based on RMSE and the error analysis method. Mode mixing was also examined since capturing subseries with unique frequencies, periods, and physically relevant features is critical. All EMD approaches suffered from mode mixing, whereas VMD and EWT could capture the ideal time–frequency characteristics. The investigation findings determined that VMD performed the best in signal decomposition, accurate reconstruction, and feature extraction. As the first attempt to use data-adaptive methods to distinguish the lake level, this study discovered that VMD performed better when dealing with nonstationary ULL time series. Results demonstrated that the present study has some limitations. According to the analysis, it was deduced that the EMD family has limitations in the decomposition of the signal. As an illustration, mode-mixing issues and inaccurate temporal estimations, number of iterations, physically meaningless components, etc. are some of the EMD issues that might be faced when using this tool. On the other hand, EWT has some parameters to be tuned, and it is very sensitive, which can lead to unfavorable results. Reconstruction results approved that EFD is not capable of analyzing ULL signals. However, further studies are required to support EFD's capability. Despite VMD's best outcome, it also has some limitations. Parameter tuning and decomposition-level determination need careful settings.
This study considered the spectral analysis of lake-level time series and changes via various methods. For future work, it is suggested to use the outcome of the present study on ULL alterations considering climate conditions in different periods and the outcome could be compared to demonstrate the effect of climate change on lake systems.
ACKNOWLEDGEMENTS
This research was supported by the research grant of the University of Tabriz (number 212).
AUTHORSHIP CONTRIBUTION STATEMENT
Farhad Alizadeh: methodology, software, and investigation. Validation. Kiyoumars Roushangar: supervision.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.