Low-frequency sea level changes in the Caspian Sea: long-term and seasonal trends

The analysis of seasonal and long-term changes of the Caspian Sea level examined from historical long time tide gauge data in order to consider the influence of climate factors on sea level changes in this lake system using spectral analysis method. The major peak at spectra corresponds to the annual cycle and semiannual oscillations peak is located at next vigorous. Effects of different global and regional factors on lake level changes are investigated by signal processing methods. Results show that annual cycle of Siberian High and Volga River discharge have the considerable effects on the Caspian Sea level changes in global and regional scales, respectively. Analyzing of seasonal cycle revealed that Volga river discharge is significant on sea level fluctuations by 1-month lag in northern and central sub-basins and 2 months delay for southern sub-basin. The results of long-term cycle show ascending trend of evaporation in Caspian central sub-basin, which it is the main driver of decreasing trend of the Caspian Sea level since 1990s.


Introduction
The Caspian Sea (CS) is largest inland water body on the earth located in Eurasia. According to its geomorphological conditions, the CS is traditionally divided into three southern, central and northern sub-basins (Fig. 1). The Absheron sill with a maximum depth of 170 m separates southern and central sub-basins with the maximum depth of about 1025 and 788 m, respectively. The northern subbasin is the shallow extension of the sea with a maximum depth of about 20 m and is separated from the central subbasin by Mangyshlak Ridge. At present, mean CS level is ~ 27.5 m below world ocean level (Ataei et al. 2019;Chen et al. 2017;Ghaffari et al. 2010;Kosarev 2005;Peeters et al. 2000;Zonn and Kostianoy 2016).
Without a connection to the ocean, the CS level is mainly controlled by rivers inflow, precipitation, evaporation, and water inflow into Kara-Bogaz Bay (Terziev et al. 1992).
Among the 130 rivers that flow into the CS, the main contribution of freshwater is from Volga, with more than 80% of the total rivers runoff (Kosarev 2005;Roshan et al. 2012). Due to the extensive watershed area of the CS (~ 2.5 million km 2 ), and the low ration of the sea surface to catchment (1:10),the CS level particularly is sensitive to climatic conditions and their inter-decadal fluctuations in the catchment (Kosarev 2005;Zonn and Kostianoy 2016).
Over the past few decades, the CS level has been characterized by significant fluctuations and several meters variations, which had a considerable affect the sea ecosystem and socioeconomic activities in the region (Zonn 2005). For example, a drop in the sea level suffers the maritime transport and fishery industry. On the other hand, rising sea level harms the coastal regions and infrastructures (Frolov 2000;Rodionov 1994). Two sever abrupt changes in the sea level were observed in the 20th century. A fast drop in the CS level occurred between the 1930 and 1970 s with ~ 3 m which has been ascribed to the decrease of the Volga River discharge owing to reduction in precipitation and water withdrawal from the catchment area for land-use (Arpe et al. 2000;Beni et al. 2013;Chen et al. 2017). Another fastunexpected change happened between 1978 and 1995 that sea level elevated about 2.5 m (Chen et al. 2017). Those abrupt variations in the sea level indicate that changes in the 1 3 CS level can be explained by the water budget, particularly inflow from Volga (Syrlybekkyzy et al. 2014). Hence, most of the hydrological hypotheses are built upon the effects of the regional climate variation over the surface area of the CS and the surrounding areas, as well as global climate change (Arpe and Leroy 2007; Molavi-Arabshahi and Arpe 2022). Climate variation causes water budget alteration and consequently leads to CS level changes. In fact, Climate change negatively impacts the global lake ecosystems, including the CS. Lake surface conditions, such as ice cover, surface temperature, evaporation, and water level, respond dramatically to the climatic alterations (Woolway et al. 2020).
For analyzing global and regional signals in geophysical data sets, managing of time and frequency domain have vital importance. Spectral density analysis and wavelet transform are common signal processing tools in geoscience for correlative analyzing of localized variations within a time series (Azizpour and Ghaffari 2021). Spectral methods decompose and transport a time series from the time domain into the frequency domain, where it is possible to determine both dominant modes of variability and how those modes vary in time (Grinsted et al. 2004). It is possible to capture localized energies using wavelet technics, which indicate the exact signal-occurrence time by translating signals into the time domain and identifying dominant regional and global processes in the sea level fluctuations.
In global and regional scales, most of the teleconnection indices (usually defined as anomalies of a climatic variable) can serve as prognostic tools based on their ability to explain the climatic variability of a region, particularly when they influence sea hydrodynamics (Criado-Aldeanueva and Soto-Navarro 2013b; Lopez-Bustins et al. 2008;Molavi-Arabshahi et al. 2016).
Among the numerous problems of the CS, one of the most important is its water level fluctuations owing to affect almost all of the region economy. Drop in water level suffers maritime transport, fishery industry, especially in the northern sub-basin. On the other hand, rising level of the CS cause erosion of shores, beaches, and recreational areas, flooding of building and manmade structures (Rodionov 1994). Some problems about the CS level fluctuations and climate changes are still unsolved and remain a challenge to scientists.
In this paper, we investigated the effects of local and global signals on the CS level changes using signal processing methods. We attempted to study the correlation between the CS level oscillations and the teleconnection indices.

Materials and methods
The CS extends from 36 • to 47 • and 47 • to 54 • in the North and East directions (Fig. 1), respectively, located within an endorheic basin between Europe and Asia. Due to the meridional extension of the basin, the sub-basins are in different climatic zones. While the northern parts experience a continental climate, the western coasts have a moderately warm climate, the southern sub-basin characterized by a semi-tropical climate, and the eastern costs refer to a desert climate (Kosarev 2005). In the northern and central parts of CS, weather is controlled by continental polar air in wintertime, while southern cyclones are presented in southern sub-basin. In summertime, stable and dry weather is dominant over the CS. The air temperature ranges from −10 °C in the north to 12 °C in the south. Air temperature differences between northern and southern parts are 2-3 10 °C at the summer time. The main regimes of wind over the CS are northerly and southeasterly during the main part of the year. About 40% of winds are notherly, which is dominant in summer and almost half of the winds are northwesterly (Kosarev 2005;Serykh and Kostianoy 2020). The rate of evaporation and precipitation in distinct subbasins of the CS are completely different and so we study basins separately. The Caspian Sea with three distinct sub-basins and main rivers, solid circles and stars denote to stations and rivers, respectively 1 3

Regional scale factors
The processing of the regional factors was carried out based on a synthetic database that comprises monthly historical data of sea level observations (tide gauge), air and water temperatures, and in-situ river discharge from several stations along the coastline of the CS (see Fig. 1).
The details of the stations and data availability is provided in Table 1. Additionally, ECMWF ERA5 reanalysis dataset (https:// cds. clima te. coper nicus. eu) was used for evaporation (calculated based on the Penman-Monteith approach (Cleugh et al. 2007;Monteith 1965)) and precipitation. The longest overlap between the CS level data and regional meteorological dataset (from 1950 to 2017) is considered for further analysis in this work. Terek ( The NAO index (Fig. 2a) is a standardized index based on the surface sea-level pressure difference between the Azores High and the Subpolar Low. The positive phase of the NAO reflects below-normal heights and pressure across the high latitudes of the North Atlantic and above-normal heights and pressure over the central North Atlantic. The negative phase reflects an opposite pattern of height and pressure anomalies around the North Atlantic region (Hurrell et al. 2003;Rousi et al. 2020).
The AO index (Fig. 2b) is a climate pattern considered by winds circulating counterclockwise around the Arctic at around 55°N latitude. In positive phase of the AO, strong winds act around the North Pole that confine colder air across Polar Regions. This belt of winds becomes weaker and more distorted in the negative phase of the AO, which allows an easier southward penetration of colder, arctic air masses and increased storminess into the mid-latitudes (Thompson and Wallace 1998).
The SO index ( Fig. 2c) is based on the observed sea level pressure differences between Tahiti and Darwin, Australia. The SO index is one measure of the large-scale fluctuations in air pressure occurring between the western and eastern tropical Pacific during El Niño and La Niña episodes.
The WMO index (Fig. 2d) is defined within the synoptic framework of the western Mediterranean basin and its vicinities. The suggested areas are the Po plain, in the north of the Italian peninsula, an area with a relatively high barometric variability due to the different influence of the central European anticyclone and the Liguria low; and the Gulf of Cádiz, in the southwest of the Iberian peninsula, often subject to the influence of the Azores anticyclone and, episodically, to the cut off of circumpolar lows or to its own cyclogenesis (Criado-Aldeanueva and Soto-Navarro 2013a; Martin-Vide and Lopez-Bustins 2006; Palutikof 2003).
The SH index (Fig. 2e) is a semi-permanent anticyclone centered over Eurasia and it is associated with some of the coldest, densest air masses in the Northern Hemisphere. The SH is of greater intensity than the pressure systems of the North Atlantic and North Pacific regions (Sahsamanoglou et al. 1991). Radiative cooling over snow-covered Eurasia maintains the large-scale descending motion of SH and makes it stronger in wintertime (Ding and Krishnamurti 1987).

Data processing
Atmospheric parameters synthetic dataset passed through a twofold quality control processes by (1) visual inspection and removing spikes and (2) flagging out and double-checking data point that falls beyond 2-fold standard deviation. Small gaps in the records (< 3 months) are replaced by linear interpolation of the adjacent values. Longer gaps are closed by an iterative process based on discrete cosine transform method (Garcia 2010;Wang et al. 2012).
To study the periodical component of the data sets, spectral density analysis is performed based on the fast Fourier transform. Stochastic spectral analyses used to estimate the distribution of a parameter variance, i.e. energy, over the frequency domain. Depending on the nature of the oscillations, the spectrum can have a continuous character of the energy distribution or the form of sharp delta-like peaks (Azizpour and Ghaffari 2021).
The spectrum of energy distribution often contains essential information about the nature of physical processes and events in a time series. However, it does not give any information on the temporal variation of the events. To capture and investigate temporal variations of low frequency the CS level oscillations, we applied the wavelet signal processing method.
A wavelet (t) is a function, oscillates with zero-mean around t-axis, which contains both frequency and time and loses strength as it moves away from the mean. A wavelet can be described based on its localization in time ( t) and frequency ( f , or the bandwidth). One common wavelet is the mother, defined by: The mother wavelet is expanded to form a basis for Hilbert space. In relation (1), is mother wavelet, b is a position parameter, and a is a scaling parameter. |a| − 1 2 is a normalizing constant. Consequently, continuous wavelet transform is given by where, w (a, b) are called wavelet coefficients (Hariharan 2019). It decomposes the time series into time-frequency space and reveals all dominant modes of the variability and the way these modes change in time.
In this study, we utilized the wavelet coherence method (Grinsted et al. 2004;Jevrejeva et al. 2005;Torrence and Compo 1998) to investigate possible direct links between the CS level and global such as AO, NAO, SO, SH and WMO indexes and regional signals such as Volga River

Spectral analysis
Historical sea level data (Fig. 3a), reveals around 30.5 m difference between 1900 and 2017, which took place in several phases. From 1900 to 1970 s sea level decreased in three consequent phases with the rate of 6.53, 19.86 and 5.45 cm/yr. From late 1978 to late 1996, a sharp increase happened with a rate of 16.08 cm/yr, followed by a steep dropwith a rate of 14.02 cm/yr. The spectral density analysis of the CS level oscillation (Fig. 3b) reveals the accumulation of energy on multiple time scales, with the main pick on the annual cycle, which can be considered as an indication of the influence of both regional and global factors. Semiannual (6 months) oscillations are located at the next vigorous. For long-term oscillations, there are a number of distinguishable peaks e.g., at around 14 and 30 years periods. However, the spectral density indicates the necessity of a longer time series to resolve low-frequency signals. The amplitudes of higher seasonal harmonics (except for 4 months period) are small, and it is difficult to detect them in the background noise at the spectra. The CS tidal is negligible ) and its energy in spectra is not detectible from background noise. Figure 3c shows wavelet power spectrum for monthly CS level changes from 1900 to 2017, where the strong nonstationary behavior of the spectra is evident. This result confirms the accumulation of energy on the annual scale, along with some discrete semi-annual events. Additionally, high energetic signals are appeared in low frequency signals (periods larger than 128 months). In some years, annual signal is absent e.g., 1969-1970, 1981-1985 and 1996-1998 (vertical line in Fig. 3c). For two first periods, semi-annual signal of evaporation is dominant (Fig. 5a) while for the last period , the effects of NAO Fig. 3 (a) Monthly Caspian Sea level changes recorded by tide gauges and related trends (peak to peak) from 1900 to 2017 behind yearly lowpassed data (gray line), (b) the Caspian Sea level spectra generated by sea level data, and (c) Morlet wavelet power spectrum of the sea level data annual period effects on CS level increases (Fig. 4b). Comparing of global ocean-atmospheric oscillation patterns phases in extreme CS level (since 1950) time series show that in lower CS level (year 1977) AO, NAO, SO indexes experienced negative phase while WMO index was in positive phase and higher level (year 1995) AO, NAO and WMO indexes were in positive phase, but SO index experienced negative phase.

Wavelet analysis
Wavelet coherency between Synchronous monthly the CS level and global teleconnection indices are shown in Fig. 4 for the period of 1950 to end 2017. All teleconnection indices, more or less, have direct annual, semiannual, and seasonal effects on the CS level fluctuations. The strong annual AO index happened in different episodes including 1960-1965, ~ 1980, 1989-1995 and 2003. The first episode of AO strengthening is in-phase with CS level while the episode of 1989-1995 is anti-phase with sea level. In the anti-phase lag, water level increased, while during in-phase episodes the sea level decreased. In semi-annual and seasonal frequencies bands, there is at least one decadal peak in which the strongest peak belongs to ~ 1970. For more than one-year period, an influential is occurred from 1964 to 1971. During this period, the CS level dropped (in-phase). Comparing positive and negative phases of AO ( Fig. 2b) with wavelet coherency between AO and CS level reveals that, AO effect on CS level is considerable when AO is in its negative phase. Strongest negative phase of AO occurred in years 1977 and 2010. Figure 3B illustrates wavelet coherency between the CS level and NAO index. Effects of NAO index on the CS level are considerable for annual and less than four years period from late 1980s to late 2015. Another high coherency happens in 6-10 years period, from 1950 to 1975. Since 2010, strongest NAO experienced in positive and negative phases alternately.
Pattern of the SO index coherency is rather similar to NAO index (Fig. 4c), however effects of low frequency band in the SO index are stronger. Strong effects occurs in annual frequency band, particularly, between the CS level and the SH (Fig. 4d). In this frequency band, phase of coherency primarily is negative (anti-phase). Effects of the SH in seasonal and semi-annual frequencies bands is weak and could be ignored. In addition, for 3-7 years period, effects of the SH from late 1960s to early 2000 is remarkable. The SH index alternately changes every ~ 6 months period (Fig. 2e) and generally positive phase happens in cold seasons and vice versa.
Wavelet coherency and phase difference between CS level and the WMO index are shown in Fig. 4e. In annual period band, some strong coherencies with different phase happen.  Fig. 4f. For > 10 yrs. period band, effects of NAO and SO in negative phase on the CS level are remarkable, though contributions of SO is higher in contrast with NAO. From 1960to 1975 yrs. period band has strong coherency in positive phase, which all indexes except SH have contributed. In annual period band, SH has main contribution in coherence between global indexes and CS level in the last two decades . Figure 4f shows that, SH effects on CS level have been neutralized by WMO index at ~ 1955, by AO from 1960to 1965and with other non-global indexes from 1975to 1982 Effects of regional factors (evaporation, total precipitation Volga River discharge and air temperature) on the CS level are investigated from 1950 to 2017 by monthly synchronous time series based on wavelet coherence analysis (Fig. 5). Annual cycle band has the dominant coherency between CS level and all regional factors. The CS level leading evaporation by 90 • . Rather decussate, 5 years period, semiannual cycle between CS level and evaporation has also strong coherency (Fig. 5a). Another strong coherency occurs from 1990s to late 2000s for 2 to ~ 8 year's periods by in-phase mode. It seems that the contribution of evaporation on the CS level changes is increased since 1990s. Figure 5b shows wavelet coherence and the phase difference between the CS level and total precipitation. Effects of total precipitation in annual cycle are similar to evaporation and a strong coherency happens in semiannual cycle from 1978 to 1983. The seasonal component is not significant and only strong coherency observes around 1985. For cycle of 5 to about 10 years period (except 1970s), an intense coherency situate at all times. Strong coherency occurs between the CS level and Volga River discharge in several frequencies bands. Generally, seasonal period band is not important, while semiannual period has stronger coherency, especially for 1950s, and around yearscenered in 1970for 1950s, and around yearscenered in , 1981for 1950s, and around yearscenered in , 1992for 1950s, and around yearscenered in , 2002for 1950s, and around yearscenered in and 2011). Pattern of wavelet coherency between CS and air temperature (Fig. 5d) are very similar to evaporation pattern for annual and longer periods bands. Strongest coherency occurs in annual band in all times. Other strong coherencies take place in 3 and 4 years periods during 1992 to 1998 and 2001 to 2010, respectively. Annual phase and two recent coherencies are in positive phase with CS level.

Mean seasonal cycle
The mean seasonal cycle is computed for each monthly evaporation, total precipitation, sea level tide gauge record for three distinct basins and Volga River discharge by averaging the values for each calendar month. Figure 6 shows the mean seasonal cycle over the complete period 1950 to end 2017. Rate of evaporation varies in different sub-basins of the CS (Fig. 6a, d and g). The pattern of the evaporation rate for the central and southern sub-basins is similar, although the rate of evaporation in the southern subbasin is larger than central sub-basin. Maximum quantity of evaporation takes place in the northern sub-basin in the July, while for the central and southern sub-basins occur in September. Similar to evaporation, total precipitation are illustrated in Fig. 5b, e, and h. The maximum amount of total precipitation happens in the winter and fall. The mean seasonal pattern for total precipitation exhibits a clear latitudinal dependence where precipitation increases southward.
The mean seasonal cycle for sea level fluctuations has a different behavior comparing to evaporation and total precipitations. As a matter of fact, maximum quantities of sea level are recorded when amount of evaporation is in highest level and total precipitation amount is in lowest level (Fig. 6c, f and i). Considering a month delay, the pattern of CS level and Volga River discharge are the same. Maximum discharge of the Volga river is in May (Fig. 6j) while the northern and central sub-basins touch the highest values in June and the southern sub-basin reaches to highest level in July. As a result, seasonal variability of CS level is strongly governed by Volga River discharge.

Climate cycle
The impacts of climate changes on different parameters in three distinct sub-basins of the CS, long-term time series of evaporation, total precipitation, air temperature, water temperature and also river discharges are analyzed (Fig. 7). Although evaporation in the CS has increased since 1950 to end 2017, the slope of evaporation trend for central sub-basin is steeper than two other sub-basins. Moreover, the data show that the evaporation rate has accelerated in central sub-basin since 1990s. Generally, the trends show that the entire basin has received less precipitation through the time but the least decrease has experienced in central sub-basin, where maximum evaporation rate is observed, as well. Increasing in total precipitation is considerable in northern sub-basin (slope = 0.004) that it is at least 1.5 times greater than other sub-basins. Centered around 1980, evaporation in the whole the CS decreased while the amount of total precipitation increased and it could be the reason behind the CS level rise in that time. Third row of Fig. 7 shows air temperature time series in Peshnoy (northern sub-basin), Makhachkala (central sub-basin) and Anzali port (southern sub-basin) by different periods. The slopes of linear trend are ascending similar to evaporation and total precipitation. Increasing the air temperature in the northern sub-basin is more evident. The same pattern is observed for water temperature in entire CS. The water temperature in the selected stations has increased in three sub-basins. Similar to air temperature, the slope of water temperature in the northern subbasin (Tyuleniy station) is greater than other sub-basins, although measurements time is not synchronized. As the northern sub-basin is shallow water body, it is immediately affected by meteorological variations. Except Kura River, the discharge of Volga and Terek rivers has increased. Comparing to other rivers the Volga River, as the main water supplier of the CS has steepest slope of increasing trends (slope = 0.0018). Though the time, the maximum values of Volga River discharge has decreased but simultaneously minimum values of discharge has increased and over all the discharge of the Volga River has increased from 1938 to 2017.

Conclusion
The monthly mean long-term CS level changes are discussed by signal analysis processing method. The cross wavelet analysis is revealed that maximum coherency between the CS level and regional and global factors occurs in annual period. Moreover, maximum coherency between the CS and regional and global factors are Volga River discharge and Siberian High, respectively.
The mean seasonal cycle of sea level variability in the CS shows that the sea level reaches its minimum values in winter and maximum values in late spring for the northern and central sub-basins and with delay in early summer for the southern sub-basin. The Volga River discharge has key effect on CS level in seasonal cycle by 1-2 month delay.
Effects of global climate change are reflected in increasing in evaporation, total precipitation, air temperature, water temperature, and discharge of inflowing rivers in to the CS (except for Kura River). Despite the increase in flowing discharge, the CS level has decreased in last two decades. One of main reasons behinds the sea level fall could be linked to increasing the evaporation rate in the whole Caspian basin, especially in central sub-basin since mid-1990s. Serykh and Kostianoy (2020) showed that negative anomalies of zonal wind (changes wind speed and direction) cause evaporation growth in the central sub-basins since 1995 that has led to sea level drop. The role of global change in Caspian sea-level fall since 1995 is attributed to the higher frequency of winds crossing dry Central Asia and the CS that is reinforced by higher sea surface evaporation (Serykh and Kostianoy 2020).