## Abstract

In this paper, wavelet transform coherence is implemented to examine the impacts of hydroclimatological variables on water level fluctuations in two large saline lakes in the Middle East with a similar geographical location, namely, Urmia Lake in north-west Iran, which has an extremely simple ecological pyramid where water level decrease produces a very sensitive ecosystem, and Van Lake in north-east Turkey. The present study investigates trends in higher order moments of hydrological time series. The aim of this paper is to investigate the complexity of Urmia Lake water level time series which could lead to decrease fluctuations of time series. To this end, the strength and relationships between five hydroclimatological variables, including rainfall, runoff, temperature, relative humidity, as well as evaporation and water level fluctuations in the lakes were determined and discussed in terms of high common power region, phase relationships, and local multi-scale correlations. The results showed that among the hydroclimatological variables, runoff has the most coherencies (0.9–1) with water level fluctuations in the lakes. Although both lakes are located in a similar climatic region, for the recent 15 years, adverse trend in water level fluctuations of Urmia Lake indicates a critical condition for this lake.

## INTRODUCTION

Finding an appropriate measure to evaluate potential variations of hydroclimatological processes/variables is one of the most important topics in recent hydroclimatological studies. The hydrological process is so complex that simple data-driven models are not able to describe its behavior (Chen *et al.* 2015). Hydroclimatological time series are often nonstationary and show trends affected by various factors, such as climatic variation, human activities, and others. Investigation of the potential trend in such series, particularly rainfall and runoff, and their driving variables are important topics that have attracted the attention of water resource specialists. To this end, either parametric, for example, regression analysis, or nonparametric methods, such as Spearman correlation coefficient test, Mann–Kendall (MK) test, singular spectrum analysis (SSA), or wavelet transform have been used (Mann 1945; Kendall 1975; Kahya & Kalayc 2004; Wu *et al.* 2010). Owing to the high ability of wavelet transform to evaluate nonstationary signals, it has been used frequently in hydrological signals processing (e.g., Partal & Kisi 2007; Nourani *et al.* 2009; Holman *et al.* 2011; Singh 2011; Danandeh Mehr *et al.* 2013; Nourani & Zanardo 2014). The main purpose of wavelet analysis is separating a given signal as a function of time into its components at different frequencies (Danandeh Mehr *et al.* 2014). Using wavelet transform, different studies have been conducted to decompose hydroclimatological series and characterize their nonstationary features. For instance, Grinsted *et al.* (2004) considered wavelet transform analyses to gain physical relationships between geophysical time series. Andreo *et al.* (2006) analyzed hydrological and outflow signals in the south of the Iberian Peninsula by means of correlation and continuous wavelet transform (CWT), and no long-term trends in precipitation and temperature time series were detected. Adamowski (2008) developed a short-term river flood forecasting method for snowmelt-driven floods using cross wavelet analysis to decompose meteorological time series. Holman *et al.* (2011) used wavelet methods to identify nonstationary time–frequency relation between North Atlantic Oscillation (NAO) atmosphere tele-connection patterns and groundwater levels. In contrast to CWT, which assesses data set periodicities and phase lag, it was concluded that cross wavelet transform (XWT) can be used to identify the cross wavelet power of time series (Holman *et al.* 2011). Yu & Lin (2015) proposed an integration of XWT and empirical orthogonal function (EOF) to analyze time–space nonlinear relationships between precipitation and groundwater variations. More recently, Nourani *et al.* (2015) analyzed precipitation and stream flow time series of Tampa Bay using non-parametric MK and discrete wavelet transform (DWT) methods.

Although XWT is a useful tool to distinguish the phase spectrum, it may produce misleading results if it is calculated by non-normalized wavelet power spectrums (WPS) (Maraun & Kurths 2004). Thus without normalizing WPS, wavelet cross spectrum could not completely reflect the possible links between time series and, therefore, not be useful to identify the governing relationship (Ng & Chan 2012). For example, Maraun & Kurths (2004) demonstrated that wavelet cross spectrum appears to be unsuitable to explain interrelation between El Niño–Southern Oscillation (ENSO) and NAO series. The authors recommended use of wavelet transform coherence (WTC) analysis, which normalizes the WPS at first and then measures the cross correlation of the series. In a similar study, Jevrejeva *et al.* (2003) used WTC to investigate the effect of Arctic Oscillation (AO) and NAO on ice conditions in the Baltic Sea. In addition to such applications, Henderson *et al.* (2009) used CWT and XWT to detect fluctuations of sub-daily to daily pumping of submarine groundwater. More recently, Fu *et al.* (2012) examined long-term records of solar activity and El Niño for their combined influence on streamflow time series across southern Canada using Fourier spectrum analysis (FSA), CWT, and WTC. The results identified that solar activity can be transferred by El Niño to streamflow influence. Also, Zhufeng *et al.* (2015) demonstrated the usefulness of the wavelet coherence method for a more in-depth validation of spatially highly resolved 3D hydrological models.

Among lakes, saline and hypersaline lakes need particular attention due to their highly vulnerable ecosystems and the irreversible socio-environmental impacts of their desiccation (Karbassi *et al.* 2010; Shadkam *et al.* 2016). Urmia Lake, the second largest permanent hypersaline lake on Earth, is one of the vital hydrological natural quarters of Iran which lately has met reduction in the lake water level. The decreasing trend of Urmia Lake water level poses a drastic problem for its stakeholders, particularly agricultural and industrial sectors. Salinity of the lake is increasing as a result of natural processes and anthropological effects. These changes in the ecosystem of the lake have resulted in water scarcity and socio-economic stresses in the lake basin. The growing stress and challenges in the water resources in the basin could easily become a crisis and this socio-ecological system could lose its resilience. To cope with this problem, one way is to intercept the decreasing trend in the water level if it is derived by human activities. Therefore, the present study investigates potential reasons behind the problem via analyzing dynamics of different hydroclimatological variables in the region and their impacts on the water level fluctuations across Urmia Lake. To this end, WTC is applied to detect trends in the representative hydroclimatological variables in the region and also to figure out potential relations between the variables and water level fluctuation over Urmia Lake. To the best of our knowledge, this is the first study that applies wavelet coherence measure to investigate water level fluctuations across Urmia Lake. It should be noted that there is a fundamental difference between climate fluctuations and trend in climate change. The climate fluctuations are periodic and give information about climate-deviation components such as rainfall, relative humidity, and temperature from their average and can occur in different time periods, but trend in climate change is the change in wide-scale fluctuations of the region's climate. Most of the earlier studies of Urmia Lake considered only the first moment of hydroclimatological time series (i.e., mean) (e.g., Fathian *et al.* 2014; Malekian & Kazemzadeh 2015), but the present study investigates trends in higher order moments as well. The aim of this paper is to investigate the complexity of the Urmia Lake water level which has reduced over time. Reduction of the complexity leads to water level fluctuations decreasing and causing the system to behave in a more regular form. All of these factors can be affected on the first, second, and higher order moments of Urmia Lake water level time series. Due to the seasonality of hydrological processes, applying wavelet coherence measure can lead to good results in investigating the complexity and fluctuations of hydroclimatological time series. Use of such an efficient mathematical tool for evaluating the interaction between water level fluctuations and the relevant hydroclimatological components is a required step in any survival plan and restoration projects for Urmia Lake which is dramatically receding and is going to vanish entirely. The analysis is also carried out for the hydroclimatological variables at Van Lake basin, a neighboring basin in Turkey, which direct the results to regional-scale conclusions. In this research, the comparison of water level in Lake Urmia with Lake Van in Turkey was performed, the lakes being relatively similar regarding geographic and climate conditions. There has been a downward trend in Lake Urmia water level for the past recent years, while in Lake Van there is not, and hence this difference can be attributed to non-climatic factors which were investigated in this research more precisely.

## MATERIALS AND METHODS

### Study areas and used data

Urmia Lake is one of the endorheic salt lakes located in north-western Iran; approximately between 37°03′N–38°17′N and 44°59′E–45°56′E (Figure 1). With a length of 145 km, maximum width of 55 km and surface area 5,700 km², it used to be the biggest salt water lake in the Middle East and the second largest hypersaline lake on Earth. Urmia Lake is fed by 13 permanent rivers, smaller perennial, seasonal streams, and direct precipitation. The main tributaries include Ajichai, Zarine, Zola, Simine, Nazloo, and Baranduz rivers. A large proportion of the lake's water content is carried by the Ajichai, Zarine, and Simine rivers. It has a closed basin, therefore, the only outflow from the lake is evaporation.

This study, for comparison, also presents results of a similar analysis for Van Lake basin because of its close geographical coordinates, i.e., located in the same latitude with approximately 157 km longitudinal distance to Urmia Lake (see Figure 1). Van Lake is a saline lake, lies in the far east of the Turkey between the coordinates 38°38′N and 42°49′E. It is the largest lake in the country, receiving water from numerous streams descending from surrounding mountains. The surface and drainage areas of the lake are 3,502 km^{2} and 12,956 km^{2}, respectively. The lake is fed by direct precipitation, snowmelt, and river flows mainly from Karasu, Hoşap, Güzelsu, Bendimahi, Zilan, and Yeniköprü rivers. Akin to Urmia Lake, it is an endorheic lake (having no outlet); in other words, Lake Van does not have any natural outlet except evaporation as is the case of Urmia Lake.

The variations of regional climatological conditions and their impact on water level fluctuations over the two lakes are investigated in this study. Figure 2 shows water level fluctuations in the lakes for the period 1960–2014. Both the lakes have a similar trend in water level fluctuations for the period 1961–2000, but for the last 15 years, the adverse trend in water level fluctuations of the lakes can be seen in the figure. While the water level of Lake Van shows positive trend, a significant decrease in water level of Urmia Lake is clearly observed. Inasmuch as both the lakes are located in a similar climatic region, such a negative trend in Urmia Lake cannot be related only to the impact of climatic variations in the region. Thus, anthropogenic impacts on the environment and water resources of the basin might be more effective in the basin.

In order to investigate the effect of hydroclimatological variables on water level fluctuation in the lakes, five hydroclimatological variables, including total monthly rainfall (hereafter rainfall), mean monthly streamflow (hereafter runoff), mean monthly temperature (hereafter temperature), mean monthly relative humidity (hereafter relative humidity), and total monthly evaporation (hereafter evaporation), recorded at selected stations in the study area (see Figure 1) were considered in this study. Since the available data set for the investigated time range includes large record gaps and a complete data set was not available, and estimating data with any software such as SPSS also included some errors, this study was conducted based on the time period of available data without any record gaps. (It should be noted that the location of Vanyar station in AJI basin has also been displaced and long-term records are not available in its new location, so the research was carried out on the previous station.) The geographical location of each station and descriptive statistics of the observational records available at each station are tabulated in Table 1. The rainfall and runoff time series of the stations are depicted in Figure 3.

River . | . | Average std. deviation range . |
---|---|---|

Saeed Abad | Longitude 46.35° | Rainfall (mm) 32.31 37.12 294 |

Latitude 37.59° | Runoff (m^{3}/s) 0.31 0.38 3.08 | |

Height (m) 1,850 | ||

Ajichai | Longitude 46.26° | Runoff (m^{3}/s) 12.43 19.93 168.8 |

Latitude 38.07° | ||

Height (m) 1,460 | ||

Lighvan | Longitude 46.26° | Temperature (°C) 7.91 7.96 35.10 |

Latitude 38.50° | Relative humidity (%) 66.06 11.10 57.00 | |

Height (m) 2,200 | Evaporation (mm/month) 92.78 76.00 250.30 | |

Simine | Longitude 46.02° | Rainfall (mm) 32.31 5.18 38 |

Runoff (m^{3}/s) 14.47 24.86 205.35 | ||

Latitude 36.59° | Temperature (°C) 11.52 8.31 34.80 | |

Height (m) 1,300 | Relative humidity (%) 66.06 10.88 46.00 | |

Evaporation (mm/month) 135.95 85.03 344.90 | ||

Zarine | Longitude 46.29° | Rainfall (mm) 4.58 5.72 39.00 |

Latitude 36.59° | ||

Height (m) 1,380 | Runoff (m^{3}) 47.09 58.74 440.47 | |

Nazloo | Longitude 45.08° | Rainfall (mm) 23.29 29.67 290.40 |

Latitude 37.43° | Runoff (m^{3}/s) 7.19 13.59 89.19 | |

Height (m) 1,290 | ||

Van | Longitude 43°22′48″ | Rainfall (mm) 11.54 4.05 60.20 |

Latitude 38°29′39″ | ||

Height (m) 1,725 | ||

Van | Longitude 38°28′42″ | Runoff (m^{3}/s) 1.71 2.79 20.24 |

Latitude 42°22′1″ | ||

Height (m) 1,775 |

River . | . | Average std. deviation range . |
---|---|---|

Saeed Abad | Longitude 46.35° | Rainfall (mm) 32.31 37.12 294 |

Latitude 37.59° | Runoff (m^{3}/s) 0.31 0.38 3.08 | |

Height (m) 1,850 | ||

Ajichai | Longitude 46.26° | Runoff (m^{3}/s) 12.43 19.93 168.8 |

Latitude 38.07° | ||

Height (m) 1,460 | ||

Lighvan | Longitude 46.26° | Temperature (°C) 7.91 7.96 35.10 |

Latitude 38.50° | Relative humidity (%) 66.06 11.10 57.00 | |

Height (m) 2,200 | Evaporation (mm/month) 92.78 76.00 250.30 | |

Simine | Longitude 46.02° | Rainfall (mm) 32.31 5.18 38 |

Runoff (m^{3}/s) 14.47 24.86 205.35 | ||

Latitude 36.59° | Temperature (°C) 11.52 8.31 34.80 | |

Height (m) 1,300 | Relative humidity (%) 66.06 10.88 46.00 | |

Evaporation (mm/month) 135.95 85.03 344.90 | ||

Zarine | Longitude 46.29° | Rainfall (mm) 4.58 5.72 39.00 |

Latitude 36.59° | ||

Height (m) 1,380 | Runoff (m^{3}) 47.09 58.74 440.47 | |

Nazloo | Longitude 45.08° | Rainfall (mm) 23.29 29.67 290.40 |

Latitude 37.43° | Runoff (m^{3}/s) 7.19 13.59 89.19 | |

Height (m) 1,290 | ||

Van | Longitude 43°22′48″ | Rainfall (mm) 11.54 4.05 60.20 |

Latitude 38°29′39″ | ||

Height (m) 1,725 | ||

Van | Longitude 38°28′42″ | Runoff (m^{3}/s) 1.71 2.79 20.24 |

Latitude 42°22′1″ | ||

Height (m) 1,775 |

Figure 3 implies that rainfall time series, more or less, have an increasing trend in all the stations. By contrast, runoff time series belonging to the stations in Urmia Lake basin show decreasing trend consistent and compatible with decreasing trend in Urmia Lake water level fluctuation.

### Wavelet analysis

Different time series analysis methods, such as Fourier transform and wavelet analysis, can be used to study the frequency of hydrological parameter time series and its effect on Urmia Lake water level fluctuation. Wavelet analysis was originally introduced in order to improve seismic signal analysis by switching from Fourier analysis to new, better algorithms to detect and analyze abrupt changes in signals, and for its multi-frequency ability. In time–frequency analysis of a signal, the classical Fourier transform analysis is inadequate because Fourier transform of a signal does not contain any local information (Strang 1993). This is the major drawback of the Fourier transform and to overcome this drawback, wavelet analysis was used in this research.

*et al.*2014). In addition, some important features of signals including downward/upward trends, abrupt changes, breakdown points, and discontinuities in the data set can be revealed by CWT analysis which other signal processing techniques might miss (Nourani

*et al.*2015). The CWT is a powerful tool for analyzing nonstationary time series in the time–frequency domains. It is used to divide a continuous-time function into wavelets. Unlike Fourier transform, the CWT possesses the ability to construct a time–frequency representation of a signal that offers very good time and frequency localization. CWT is an integral transform as (Mallat 1989):

where ψ is defined as the mother wavelet and (*) denotes the complex conjugate of the mother wavelet. The main purpose of the mother wavelet is to provide a source function to generate the other wavelets which are simply the translated and scaled versions of the mother wavelet. In this paper, Morlet mother wavelet was considered which includes both real and imaginary parts. Complex or analytic wavelets have Fourier transforms which are zero for negative frequencies (Addison 2002). The parameter ‘*a*’ can be interpreted as a dilation factor or contraction factor of the mother wavelet corresponding to different scales of observation (Danandeh Mehr *et al.* 2014). The parameter ‘*b*’ is a temporal translation value (or shift) of the mother wavelet, which allows the study of the signal locally around the specified time. In order to normalize different scales, the coefficient is applied.

*X*(

*t*) is determined (Torrence & Compo 1998):where

*C*(

^{X}*a*,

*b*) and , are continuous wavelet coefficients of the time series

*X*(

*t*) and its complex conjugate, respectively. Then, XWT is used to obtain high common power and phase relationships between the time series. If one takes the average of wavelet spectrum over the entire time, it is known as global wavelet power spectrum (Torrence & Compo 1998). In general, the CWT helps to detect the periods of the given signal

*X*(

*t*), but XWT is applied to distinguish cross wavelet power of two signals such as

*X*(

*t*) and

*Y*(

*t*). Moreover, XWT determines the scale characteristics and oscillation periods. Similar to the definition of wavelet spectrum (see Equation (2)), the cross wavelet spectrum, i.e., , can be defined between two different signals as (Liu 1995; Labat 2010):where

*C*(

^{X}*a*,

*b*) is the continuous wavelet coefficients of the signal

*X*(

*t*) and is the complex wavelet coefficients of the signal

*Y*(

*t*). This spectrum is suitable for phases estimating but is not useful for the detection of relations between two time series (Maraun & Kurths 2004; Nourani

*et al.*2016). Complex cross wavelet spectrum is similar to Fourier cross spectrum and can decompose into cross wavelet power and phase, and may be written as (Ng & Chan 2012):

The phase *φ _{is}* indicates the phase difference between two signals at the time t

_{i}on scale s. The cross wavelet power reveals regions with high common power. Wavelet cross spectrum describes the common power of two processes without normalization to the single wavelet power spectrum. This can produce misleading results, because one essentially multiplies the CWTs of two time series (Maraun & Kurths 2004; Nourani

*et al.*2016). Another effective measure is how coherent the cross wavelet transform is in time–frequency space and how to interact two processes to each other (Grinsted

*et al.*2004). In other words, coherence is a measure of the intensity of the covariance between hydrological signals in time–frequency space, unlike the cross wavelet power which is a tool for measuring common power (Jevrejeva

*et al.*2003) and enhance linear correlation analysis that helps to reveal intermittent correlation between two phenomena and their significant linear correlation relationship in time–frequency space (Kareem & Gurley 1999).

*SW*(

_{XX}*a*,

*b*) is smooth estimate of x time series wavelet spectrum,

*SW*(

_{YY}*a*,

*b*) is smooth estimate of y time series and

*SW*(

_{XY}*a*,

*b*) is smooth estimate of cross wavelet spectrum for

*X*and

*Y*time series which are defined as follows (Torrence & Webster 1999):where it ranges from 0 to 1 given by smoothing operators. Monte Carlo methods are used to determine the statistical significance level of WTC. It uses random sampling and statistical modeling to estimate mathematical functions and mimic the operations of complex systems in which the probability distributions within the model can be easily and flexibly used, without the need to approximate them; and also correlations and other relations and dependencies can be modeled without difficulty in this simulation (Harrison 2010). A value of 1 means a linear relationship between

*x*(

*t*) and

_{i}*y*(

*t*) around time t

_{i}_{i}on scale s. A value of zero is obtained for vanishing correlation (Luterbacher

*et al.*2002). Because of normalization, artificial peaks for regions with low wavelet power may occur, therefore it should be noted that phrases included in the above equation are calculated separately; otherwise, the numerator and denominator equal to each other and wavelet coherence will be equal to 1 that does not show the actual value of wavelet coherence. Thus, for measuring wavelet coherence of observation data, numerator and denominator should be smoothed separately (Maraun & Kurths 2004).

*et al.*2008):The phase information is plotted on WTC graphs and indicated by the direction of an arrow in terms of the radians. An arrow pointing up and to the right indicates a positive correlation (in-phase) between two cycles with x leading. Arrows indicate the phase difference between parameters: a horizontal arrow pointing left to right signifies in-phase, an arrow with the opposite direction implies anti-phase, and an arrow pointing vertically upward means the second series lags the first by 90°. Overall, XWT and WTC are powerful methods to evaluate the relationship between two time series. Where cross wavelet transform has high common power, wavelet coherence transform shows localized phase behavior and gives a powerful output, which is a measure to detect the possible relationship between the two time series of hydroclimatological data. Generally, there are three main sections in the WTC graph:

- 1.
Wavelet coherence period at 5% significant level, which is shown with thick black lines.

- 2.
Phase relation between time series, which is described by the direction of the arrows.

- 3.
Cone of influence (COI), which indicates regions of the wavelet spectrum that impact edges, is ignored due to the limited length of hydrological time series.

## RESULTS AND DISCUSSION

As mentioned earlier, the coherency and relationship between hydroclimatological variables and water level time series and also to check the seasonality trend of time series in the lakes were measured using XWT and WTC in this study. It is worth mentioning that the original time series were standardized before applying wavelet transformation to have zero mean and unit variance. The results are presented and discussed in the following subsections.

### Rainfall and runoff vs. water level fluctuations of Urmia Lake

Figures 4 and 5 illustrate the results of WTC analysis between rainfall/runoff time series and water level fluctuations of Urmia Lake, respectively.

Regarding the coherence results given for the stations Saeed Abad, Tazekand (Miandoab), Abajaloosofla, and Sarighamish, Figure 4(a), 4(c), and 4(d)) show that the common periodicities between rainfall and water level signals have a 8–16 month frequency band, which indicates the most coherency with Urmia Lake water level fluctuations. An anti-phase correlation between rainfall and water level signals was observed and one time series leads to another by a quarter period length in the 8–16 month frequency band which means rainfall time series variations effect water level fluctuation with a 2–4 month time lag. As shown in Figure 4(a), rainfall effect has been stretched on the lake water level from the beginning of the study period (excluding 1971) on the 8–16 month frequency band. This indicates the absence of small fluctuations and effect of rainfall in larger periods during this period; while the impact of rainfall data has been changed to a smaller period from 1984 which indicates the existence of small fluctuations and, consequently, increasing the effect of rainfall parameter. Considering the coherence graph between Sarighamish station rainfall and the lake water level (Figure 4(c)), this parameter has almost constant behavior and high coherency from the beginning to the end of the investigated period. Also, it is clear that wavelet coherence between rainfall and water level fluctuations in Abajaloosofla station (Figure 4(d)) has almost a constant trend and there is no considerable change in terms of frequency band, arrows' direction, and overall coherence graph. Therefore, it can be said that the impact of rainfall is almost constant even though it gradually increased during the studied time period while the fluctuations of lake water level decreased. Thus, it can be proved that the role of this factor on Urmia Lake water level decreasing is not so important.

Figure 5 also illustrates that runoff signals effect the water level fluctuations in the 8–16 month frequency band with high coherency in all the stations. The correlations between runoff and water level fluctuations time series in the 8–16 month frequency band are mainly anti-phase, so that runoff leads to water level fluctuations time series by a quarter period length and effects on water level fluctuations time series by a 2–4 month time lag. Figure 5(b) illustrates that the coherence between runoff and water level fluctuations has increased from 8–14 month frequency band in 1974 to 8–17 month frequency band in 1981; also from 1984, runoff effect on the lake water level period was stretched to 88–132 month frequency band which shows the period increasing and phase lag impact on water level fluctuations. As shown in Figure 5(e), the runoff is effective on water level fluctuations from the beginning up to 2001; however, since 1981, its impact has larger frequency bands and long-term periods. This represents the relevance of runoff effect on decreasing water level and so the fluctuations which increase the phase lag are confirmatory on this output.

According to wavelet coherence graphs of rainfall and lake water level time series for Zarine basin (Figure 4(c)), it can be seen that rainfall parameter has a high coherency value from the beginning to the end of the investigated time intervals. In addition to rainfall data, as can be seen in WTC graphs between runoff and water level time series in Zarine river (Figure 5(d)), the effect of this variable from the beginning of the investigated time in 8–16 month period is gradually reduced and even has become negligible since 1981, whereas the impact of runoff has been changed to a period of 46–84 months since 1977 to 1997. In other words, in this time interval, the runoff has affected the water level fluctuations in larger periods, which causes decrease in fluctuations and, consequently, decreasing water level in the lake. Also, phase lag in this period increases compared to the previous periods. Therefore, since the Zarine River originates from the Chelcheshme mountains in Sagez, it can be concluded that runoff parameter and human factors have less impact than natural factors in the Kurdistan region on the lake water level fluctuations.

### Temperature and evaporation vs. water level fluctuations of Urmia Lake

Wavelet coherence analysis between temperature/evaporation time series and water level fluctuations are shown in Figure 6. Due to the lack of long-term temperature data, the given scale is shorter than the others. Figure 6(a) and 6(c) show that in the 8–16 month frequency band with 0.9–1 coherency value, temperature has an effect on water level fluctuations. Mean temperature at Urmia Lake basin in the periods 1971–1985, 1985–1999, and 1999–2013 is 11.8 °C, 12.4 °C, and 13.4 °C, respectively. Also, as can be seen in Figure 6(a) and 6(c), temperature effect on water level has not changed much before the reduction of Urmia Lake water level and after it. Therefore, considering these slight changes in the temperature and wavelet coherence graphs (Figure 6(a) and 6(c)), it can be concluded that this parameter has a stable behavior during the investigated time intervals and does not play an important role in decreasing Urmia Lake water level.

Regarding the evaporation results, the 8–16 month frequency band reflects the impact of evaporation fluctuations on the Urmia Lake water level (Figure 6(b) and 6(d)). The XWT graph also approves such a coherency. As shown in Figure 6(d), from the beginning of 1980, the frequency band of evaporation has increased from a 8–16 month to 4–16 month period. Such small fluctuations in the evaporation can be the result of decrease in the water depth and, consequently, evaporation increase in the lake basin. The same direction of the arrows in maximum wavelet coherency regions (approximately 0° angle) indicates an in-phase impact of temperature and evaporation fluctuations on Urmia Lake water level.

### Relative humidity vs. water level fluctuations of Urmia Lake

Wavelet coherence analysis between relative humidity and water level fluctuations is illustrated in Figure 7. The 8–16 month frequency band with the 0.8–0.9 wavelet coherency during 2002–2008 and 1999–2010 in Figure 7(a), indicates an influence of relative humidity of the basin on Urmia Lake water level fluctuations in recent years. An anti-phase direction of the arrows in both stations (approximate 180° angle) illustrates that with increasing relative humidity in the lake basin, water level fluctuations were decreased without time lag and vice versa. As a result of wavelet coherence between temperature and water level fluctuations, relative humidity and evaporation parameters have shown the same behavior. although not as the main cause, but are effective in water level fluctuations.

### Investigation of Van Lake

Similar to the above-mentioned results, the wavelet coherence graphs between rainfall/runoff time series and water level fluctuations of Van Lake are shown in Figure 8.

Rainfall time series in the 8–16 month frequency band during 1946–1955, 1988–1992 and 4–16 month frequency band during 1958–1969, 1973–1986 and 4–8 month frequency band during 1976–1980, 1988–1993 with 0.8–0.9 coherency value showed the most effects on the lake water level fluctuations (Figure 8(a)). Also, coherency values between 0.8 and 0.9 have been obtained for the periods 1969–1958 and 1986–1973 at 4–16 month frequency band. Arrows in Figure 8(a) with approximately 180° angle represent an anti-phase relationship between rainfall hydrological parameters and Van Lake water level fluctuations. Considering the coherence graph between runoff and Van Lake water level (Figure 8(b)), the 8–17 month frequency band during 1971–2002 with 0.9–1 coherency value reflects the impact of the fluctuations in most recent years. Also, in the 4–8 month frequency band between the periods 1970–1976, 1992–1995, 1998–2000, 2001–2002, runoff and water level fluctuations have shown 0.8–0.9 wavelet coherency value. In the 24–40 month frequency band during 1985–1993, 40–60 months during 1974–1976 with 0.8–0.9 wavelet coherency and 7–14 months during 1969–1970 with 0.7–0.8 wavelet coherency, runoff is effective on Van Lake water level fluctuations and out of these bands, there is no common power between the runoff and the water level (Figure 8(b)). The phase lag between runoff and water level fluctuations is shown by the direction arrows within 5% significance level. As can be seen in Figure 8(b), the same direction of the arrows between the two time series reflects that runoff time series impact on Van Lake water level fluctuations without a significant time lag (delay).

The obtained results for Van Lake demonstrate that rainfall influence on water level fluctuation has the same behavior as Urmia Lake. The effective periods of rainfall on Van Lake fluctuations gradually become smaller; also according to phase arrows, the phase lag in these periods is gradually decreasing (Figure 8(a)). Regarding the coherence between runoff and Van Lake water level fluctuations, runoff is almost constant during the study period. The results indicate that the 8–16 month period is extended throughout the entire interval. Even in 1989, the frequency band has become smaller. The direction of phase arrows confirms the absence of phase lag in runoff change and its impact on Van Lake water levels, while Urmia Lake in early 1981 has experienced larger frequency band. In addition, the direction of phase arrows at significant levels indicates the impact of runoff phase lag on Urmia Lake water level fluctuations. General comparison between the water level time series of Urmia and Van lakes shows stable behavior in the same period. As a representative of climatic factors, rainfall results show that this variable has the same behavior on both the lakes' level. Therefore, it can be concluded that rainfall has less impact on the water level fluctuations of Urmia Lake. On the other hand, runoff, as a representative factor of human influence on the lake level, has almost constant trend until the end of the study period.

According to WTC graphs between the water level of Lake Van and runoff (Figure 8(b)), the fluctuations have gradually become smaller since 1989 and the Van Lake water level has risen, thus lack of phase lag in the runoff parameter changes confirms consistency with Van Lake water level fluctuations. The runoff parameter in stations located around Urmia Lake has experienced greater periods in the same interval since early 1981 leading to decreasing water level. Overall, it is clear that the impact of rainfall data on the two lakes' fluctuations shows the same behavior but runoff parameter has almost the dominant role in decreasing of water level fluctuations.

Region . | Station . | River . | 1971–1981 . | 1981–1991 . | 1991–2001 . | After 2001 . | . |
---|---|---|---|---|---|---|---|

East Azerbaijan | Saeed Abad | Saeed Abad | 8–16 months | 4–16 months | 4–16 months | 8–16 months | Rainfall (mm) 22.0% |

8–16 months | 8–16 months | 8–16 months | 40–70 months | Runoff (m^{3}/s) 22.3% | |||

24–38 months | 40–70 months | ||||||

40–70 month | |||||||

Vanyar | Ajichai | 8–14 months | 8–17 months | 8–14 months | 8–14 months | Runoff (m^{3}/s) 27.0% | |

Lighvan | Lighvan | – | 8–16 months | 8–16 months | 8–16 months | Temperature (°C) 21.5% | |

– | – | – | 8–16 months | Relative humidity (%) 2.3% | |||

– | – | 8–16 months | 8–16 months | Evaporation (mm/month) 5.1% | |||

West Azerbaijan | Tazekand | Simine | – | 18–38 months | 9–18 months | – | Rainfall (mm) 3.4% |

4–16 months | 4–18 months | 4–18 months | 4–18 months | Runoff (m^{3} s) 15.6% | |||

48–64 months | 48–64 months | ||||||

100–140 months | |||||||

8–16 months | 8–16 months | 8–16 months | 8–16 months | Temperature (°C) 9.4% | |||

8–16 months | 4–16 months | 8–16 months | 8–16 months | Evaporation (mm/month) 13.1% | |||

– | – | 8–16 months | 8–16 months | Relative humidity (%) 2.7% | |||

Sarighamish | Zarine | 8–16 montha | 8–16 months | 8–16 months | – | Rainfall (mm) 12.2% | |

8–16 montha | 8–16 months | 8–16 months | – | Runoff (m^{3}/s) 9.6% | |||

48–64 montha | 48–64 months | 48–64 months | – | ||||

Abajaloosofla | Nazloo | – | 3–21 months | 3–21 months | 3–21 months | Rainfall (mm) 12.6% | |

7–20 montha | 7–20 months | 7–20 months | 7–20 months | Runoff (m^{3}/s) 19.5% | |||

39–133 months | 39–133 months | 39–133 months | – |

Region . | Station . | River . | 1971–1981 . | 1981–1991 . | 1991–2001 . | After 2001 . | . |
---|---|---|---|---|---|---|---|

East Azerbaijan | Saeed Abad | Saeed Abad | 8–16 months | 4–16 months | 4–16 months | 8–16 months | Rainfall (mm) 22.0% |

8–16 months | 8–16 months | 8–16 months | 40–70 months | Runoff (m^{3}/s) 22.3% | |||

24–38 months | 40–70 months | ||||||

40–70 month | |||||||

Vanyar | Ajichai | 8–14 months | 8–17 months | 8–14 months | 8–14 months | Runoff (m^{3}/s) 27.0% | |

Lighvan | Lighvan | – | 8–16 months | 8–16 months | 8–16 months | Temperature (°C) 21.5% | |

– | – | – | 8–16 months | Relative humidity (%) 2.3% | |||

– | – | 8–16 months | 8–16 months | Evaporation (mm/month) 5.1% | |||

West Azerbaijan | Tazekand | Simine | – | 18–38 months | 9–18 months | – | Rainfall (mm) 3.4% |

4–16 months | 4–18 months | 4–18 months | 4–18 months | Runoff (m^{3} s) 15.6% | |||

48–64 months | 48–64 months | ||||||

100–140 months | |||||||

8–16 months | 8–16 months | 8–16 months | 8–16 months | Temperature (°C) 9.4% | |||

8–16 months | 4–16 months | 8–16 months | 8–16 months | Evaporation (mm/month) 13.1% | |||

– | – | 8–16 months | 8–16 months | Relative humidity (%) 2.7% | |||

Sarighamish | Zarine | 8–16 montha | 8–16 months | 8–16 months | – | Rainfall (mm) 12.2% | |

8–16 montha | 8–16 months | 8–16 months | – | Runoff (m^{3}/s) 9.6% | |||

48–64 montha | 48–64 months | 48–64 months | – | ||||

Abajaloosofla | Nazloo | – | 3–21 months | 3–21 months | 3–21 months | Rainfall (mm) 12.6% | |

7–20 montha | 7–20 months | 7–20 months | 7–20 months | Runoff (m^{3}/s) 19.5% | |||

39–133 months | 39–133 months | 39–133 months | – |

In short, coherency results indicate that among all the hydroclimatological variables, runoff has the strongest wavelet coherency with water level fluctuations. Overall, in 1971, runoff parameter has the same trend with almost constant time periods, but since early 1981 the effect of runoff parameter has stretched to larger periods, so downscaled fluctuations are gradually becoming larger and causing that trend in seasonality to decrease over the time periods. This becomes a considerable reason for Urmia Lake shrinking. Obtained results presented in Table 2 show the contribution of hydroclimatological parameters (in the west and east of Urmia Lake) on the lake's water level. Overall, with regard to Figure 9, it can be concluded that the maximum energy of global wavelet power spectrum is obtained from normalization and integration of the maximum period area under the curves (about 8–16 month frequency band in all of the investigated rivers) in wavelet power spectrum graphs. The results of the wavelet coherence between hydroclimatological parameters and Urmia Lake water level fluctuations and with regard to wavelet spectrum graphs (Figure 9), indicate that among the considered hydroclimatological parameters, observed runoff in Saeed Abad, Ajichai, Simine, Zarine, and Nazloo basins have respectively a 22.3%, 27.0%, 15.6%, 9.6%, and 19.5% contribution on Urmia Lake water level fluctuations. This is obtained from wavelet power spectrum (Figure 9) through integration on the efficient period and frequency band weighted by wavelet coherency values. In general, according to comparison with the Van Lake basin in similar climate condition and investigating wavelet coherence graphs and phase lags at significant levels, it becomes clear that runoff time series change has a direct impact on Urmia Lake water level fluctuations caused by different factors. Due to these impacts, coherence graphs and phase lags at significant levels, it becomes clear that runoff effect is greater than other parameters, thus it is the reason for the priority of human factors rather than climatic factors in reducing fluctuations of Urmia Lake water level.

## CONCLUSIONS

WTC analysis was implemented to identify high common power region, phase relationships, and local multi-scale correlations between different hydroclimatological variables and water level fluctuations in Urmia and Van lakes. Decreasing in Urmia Lake water level could be affected by the region's decreasing hydroclimatological parameter fluctuations which caused frequency periods to become larger over time periods. It can be concluded that the fluctuation and complexity of Urmia Lake water level time series has decreased, thus showing a high compliance with decreasing in fluctuations of runoff coming from the upstream basin. Due to the placement of the lake in a closed drainage basin, only the direct precipitation, and inflow from streams and rivers count as sources of input waters to the lake, and evaporation from the lake as the only output. Thus, continuous reduction of water volume and lack of adequate input water sources to compensate for the lack and maintain water balance is regarded as the main cause of lake shrinkage. On completion of the present research, some suggestions for future studies are proposed, for example, examining other possible factors involved in reducing the water level of Urmia Lake, such as human factors and climate change during recent centuries and separating each of these contributions on water level fluctuations. The effects of ground water, drainage rate, harvesting rate, etc., on Urmia Lake water level fluctuations can also be examined (Gholami *et al.* 2015). However, since they do not have an important role in water level fluctuation and the five investigated parameters are the main factors having an effect on the other climatic variables (directly or indirectly), these other parameters are not included in the modelling. For more precise analysis, for future research, they may also be considered in the modeling. Also to confirm the results of this paper, it is suggested that this measure is examined on the adjacent stations in neighboring provinces.