Response of Extreme Precipitation to Solar Activity and El Nino Events in Typical Regions of the Loess Plateau

1 Institute of Soil and Water Conservation, Chinese Academy of Sciences and Ministry of Water Resources, Yangling, Shaanxi Province 712100, China 2Northwest A&F University, Yangling, Shaanxi Province 712100, China 3University of Chinese Academy of Sciences, Beijing 100049, China 4Hunan Provincial Water Resources Department, Changsha, Hunan Province 410007, China 5Ansai County Meteorological Bureau, Ansai, Shaanxi Province 717400, China


Introduction
According to the IPCC AR4, atmospheric temperature has increased globally, a trend that is closely related to greenhouse gas emissions and land-cover and land-use changes.Global climate change is characterized by climate warming, and concomitant changes in extreme climates have seriously affected many aspects of the environment and economic development, as well as social stability, at global and regional scales.A warmer climate may also lead to increases in extreme precipitation in many world regions.
The Loess Plateau of China has historically suffered from considerable soil erosion, resulting in severe environmental and economic problems, such as desertification, rangeland degradation, and channel deposition [1].In the Loess Plateau, severe soil erosion is often caused by infrequent heavy rain and storms and extreme precipitation [2].Exploring the variation and occurrence of regional extreme precipitation under climate change is crucial to help evaluate potential risks to soil erosion and to take adaptive measures in advance.
Many studies have been undertaken to access the changing trends of extreme precipitation in different world regions, such as Europe, North America, Africa, India, and China.The occurrence of most extreme precipitation is influenced by many factors, such as solar activity, El Nino South Oscillation, global warming, or human activities.
Solar activity, such as solar winds, flares, and solar radiation bursts, can lead to plasma movement and radiation enhancement [3,4].Many scholars have researched the periodic variation of solar activity [5,6] and shown that the solar cycle has important impacts on climate change in a wide variety of ways.In addition, the solar cycle significantly influences regional hydrometeorological phenomenon [7].Previously, a number of studies have investigated the relationships between solar activity and runoff, precipitation, and intense loess erosion using statistical methods [3].These studies revealed close relationships between solar activity and hydrometeorological processes.El Nino is a well-known global scale ocean-atmospheric coupled phenomenon over the tropical Pacific.The El Nino Southern Oscillation (ENSO) has a strong influence on interannual precipitation variability in many parts of the world [8].The same ENSO events may be linked with droughts or floods in different regions.

Advances in Meteorology
There have been many studies on the relationships between extreme precipitation and solar activity and El Nino worldwide.However, adequate study of the Loess Plateau is still required.Under the background of global climate change, extreme precipitation occurs frequently.Analyzing the variation and mechanism of extreme precipitation in the Loess Plateau and predicting the future trends are urgently needed.In this paper, we take Yan'an as a case study to analyze the long-term precipitation series in Yan'an from 1951 to 2015 based on the Morlet wavelet method and then evaluate the relationship between extreme precipitation, sunspots, and El Nino events.First, a Morlet wavelet method was introduced to analyze the correlation between extreme precipitation and sunspots.Then, a statistical method was used to analyze the connection between extreme precipitation and El Nino events.Finally, the relationship among extreme precipitation, sunspots, and El Nino events was explored based on wavelet coefficients and statistical results, and the possible effects of the sunspots and El Nino events on extreme precipitation of the Loess Plateau are discussed.

Study Area.
The Yan'an area is an area of serious soil erosion in the loess hilly gully region, covering approximately 37,000 km 2 within Shaanxi Province.Its geographical position (35 ∘ 21  ∼37 ∘ 31  N, 107 ∘ 41  ∼110 ∘ 31  E) is in the middle of the Loess Plateau (Figure 1).The area is located in a typical warm temperate continental monsoonal climatic region with a mean annual precipitation of approximately 500 mm, and more than 70% of the precipitation is distributed from June to September.The mean temperature varies from 7.7 to 10.6 ∘ C. The Yan River is the primary river in the study area and is a first-order branch of the Yellow River.Due to poor corrosion resistance and loose soil particles, soil is prone to erosion.In 2013, the annual Yan'an precipitation was the highest in 100 years and caused serious soil erosion.
Large-scale climatic conditions have been successfully evaluated using the Southern Oscillation Index (SOI) [9].The SOI is an inverse correlation of the atmospheric pressure between the tropical Pacific and the tropical Indian Ocean and is computed using the standardized anomaly of the mean sea level pressure (MLSP) difference between Tahiti and Darwin.When the SOI is negative, there is an El Nino phenomenon.The Sea Level Press standardized data from 1951 to 2015 were obtained from the National Oceanic and Atmospheric Administration (NOAA) (http://www.cpc.ncep.noaa.gov/data/indices/).The formula used is as follows: where  diff is (average Tahiti MSLP for the month) − (average Darwin MSLP for the month),  diffav is long-term average of  diff for the month of study, and SD( diff ) is long-term standard deviation of  diff for the month of study.The multiplication by 10 is a convention that results in whole number SOI ranges from about −35 to +35.
All data used in this study have been checked for quality control by corresponding agencies and are of good quality.

Wavelet Analysis.
The wavelet transform (WT) has been a major development in the field of data analysis since the 1980s.WT is an effective means to process time series data, especially those with nonstationary characteristics [10].It is frequently applied in hydroclimatic time series [11,12].In this paper, the complex Morlet wavelet is mainly used to analyze the variation tendency and periodicity in precipitation and sunspot numbers, their interrelationships, and interannual variability.
The wavelet function in this paper is the complex Morlet wavelet, which was defined as where () is the complex conjugate of the wavelet function () (the mother wavelet),   is a bandwidth parameter, and   is a wavelet center frequency.In this study,   :   = 1.5 : 1, and  denotes the imaginary part.The real-value Morlet is the real part of the complex version of the Morlet wavelet.
The real part and imaginary part exist with a phase difference of /2 to eliminate oscillations so that the results are more accurate.
A complex Morlet wavelet provides important pieces of information including (a) the modulus for energy density; (b) the phase that detects singularities and measures instantaneous frequencies; (c) the real part of the wavelet coefficient that depicts both the intensity and phase of the signal variation, at particular, scales and locations in wave domain (the time-frequency domain); and (d) the second power of modulus that represents the energy spectrum and shows the energy variability at particular scales.In general, a greater modulus results in a clearer periodic change at a corresponding scale and time.The real part of the wavelet coefficients has a similar ability, which is applied to the structures of one time series on different scales.The main period of the time series is obtained by wavelet variance, which can be expressed as where Var() is the wavelet variance, (  )(, ) is the wavelet coefficient,  is the frequency/scale variable, and  is the time variable.The largest peak value has the strongest oscillation, which is used to analyze the oscillation variation and average period for precipitation and sunspot numbers.The second and third largest peak values correspond to the second and third main periods.

Statistical Analysis and Trend Detection.
The mean, the maximum, and the minimum were used to calculate precipitation.The mean and the standard deviation were used for SOI.The correlation between sunspot and precipitation was analyzed by regression analysis.When the difference between the annual precipitation and its annual mean value is more than the double meansquare deviation, it is defined as extreme precipitation (definition from the World Meteorological Organization).

Wavelet Analyses of Precipitation and Sunspot Number.
The annual precipitation at Yan'an station from 1951 to 2015 was highly nonstationary and nonlinear, which had no clear periodic fluctuation (Figure 2).In the research, the sunspot number was used for solar activity analyses.Unlike precipitation, the sunspot number showed a clear period (Figure 2).Compared with the statistics of precipitation and sunspot number, the precipitation trend in the Yan'an area and sunspot number were consistent (Figure 2).With an increase in sunspot number, the precipitation in the Yan'an area increased.The maximum precipitation occurred mainly at the peak of sunspot number or 2a near it.From Figure 2, there were five peak values for sunspot number from 1951 to 2015.They were 1958, 1969, 1980, 1990, and 2002; in comparison, the maximum precipitation occurred in 1958 (716.53 mm), 1969 (589.29 mm), 1981 (775 mm), 1988 (739.29 mm), and 2003 (660.7 mm).The results were similar to those of Li and Yang [13], who also reported that the annual precipitation at the Yellow River showed hysteresis for sunspot number.Zhang et al. [14] reported that, at the peak of sunspot activity or 2a near it, the summer precipitation in Xi'an increased sharply.When the sunspot number was in decline, the precipitation showed a downward trend.However, the minimum precipitation and valley value for sunspot number were not significantly correlated relationships.There were six valley values for sunspot numbers from 1951 to 2015, which were 1955, 1964, 1975, 1987, 1998, and  To decompose the original data and analyze the period of sunspot number and precipitation, the wavelet analyses method was introduced in this research.The 64-year scale was chosen, and the wavelet coefficient contour map of the precipitation time series was plotted based on the Morlet wavelet method.The wavelet map represents the correlation of the wavelet with the signal.The wavelet transform can be analyzed through the real part, the modulus, and the second power of modulus of the wavelet.The intensity at each - point represents the magnitude of the wavelet coefficients.The real part of the complex Morlet wavelet coefficient includes both the phase and intensity of the signal transformation, at particular locations and scales in the timefrequency domain.In the precipitation wavelet coefficient, a positive real part coefficient denotes that the precipitation was higher and vice versa.From the real part periodic variability, the precipitation structures with higher flow and lower flow phases were clearly shown on different scales.The lower scales were more complex and nested into higher scales.
The real part of the precipitation at Yan'an station in the Loess Plateau during 1951-2015 is plotted in Figure 3(a).In the figure, the red zone represents higher precipitation, the blue zone indicates lower precipitation, and other colors show middle precipitation.As shown in Figure 3(a), the precipitation varied from scales of 28-48 years, with 10-year periodical characteristics within a 64-year scale.On a 28-48year scale, there were more than two-cycle oscillations.The periods of 1956-1967, 1979-1994, and 2008-2015 were the high-precipitation periods, while 1951-1955, 1967-1979, and 1994-2008 were the low-precipitation periods.The precipitation remained a high-precipitation period after 2015.From the wavelet variance (Figure 4(a)), the 41-year period was the most significant on a 64-year scale.Its real part wave coefficients changes on a 41-year scale are shown in Figure 4(b).On a 10-year scale, there were more cycle oscillations.The oscillation frequency was complicated and high.
The modulus of the wavelet coefficient represents the power density, which showed the periodic variability over different time scales (Figure 3(b)).For the modulus and second power, higher values indicated a more obvious periodic variability in scale and time.In Figure 3(a), there was obvious periodic variability with 28-45 years, 51-64 years, and less than 10 years.The second modulus power represents the energy spectrum, which shows energy variability over different time scales.From Figure 3(c), there was one center of energy.
As with the wavelet analyses of precipitation, the sunspot number from 1951 to 2015 was also decomposed on a 64year scale using the Morlet wavelet.The real part, modulus, and second modulus power of the wavelet coefficient of the sunspot number are shown in Figures 5(a)-5(c).The sunspot number showed dramatic periodic variability, especially on a 16-year scale, and there were two energy centers on about the 16-year scale in the modulus and the second power of the wave coefficient.From the wavelet variance (Figure 6(a)), the 16-year period was the most significant on a 64-year scale.Its real part wave coefficients changed on a 41-year scale, as shown in Figure 6(b).
As shown in Figures 4(a) and 6(a), the precipitation and sunspot numbers had 41-and 16-year periods, respectively.Therefore, the possible impacts of solar activity on precipitation at Yan'an station showed 16-and 41-year features.In the study, their real part wavelet coefficient series for 16-year and 41-year scales were applied to analyze their correlations.The correlation coefficients were 0.784 and 0.893, respectively (Table 1), showing high correlations from 1951 to 2015.These results showed that the relationships between sunspot number and precipitation were close and that solar activity had significant impacts on precipitation at Yan'an station.
From Figure 5(a), the new solar activity week (the twentyfourth) began since 2009 and reached a maximum value in 2013-2014.Based on Figure 2, the annual Yan'an precipitation in 2013 was 959.1 mm, the highest in 100 years.In addition to the maximum month, the maximum and the annual precipitation all reached historic, extreme values.This phenomenon again verified the results above.

Correlations between Precipitation and El Nino.
Prestes et al. [15] showed that regional precipitation anomalies, floods, and other disasters all have good response relationships to solar activity, global climate anomalies, atmospheric circulation, and El Nino events.Figure 7 shows that precipitation in the Yan'an area continuously fluctuates.The maximum and minimum precipitation differed greatly, and precipitation anomalies exist.For years with anomalies, the precipitation time series data were examined to identify changes associated with the large-scale circulation modes of the Southern Oscillation Index (SOI).El Nino referred to positive anomalies in sea surface temperature (SST) for eastern and    The monthly standardized anomaly of the sea level pressure difference between Tahiti and Darwin, Australia, is defined as the Southern Oscillation Index (SOI), which is a frequently used index of ENSO events [22].Nino-3.4 is the mean SST in the eastern equatorial Pacific Ocean, which spans 5 ∘ N∼5 ∘ S and 170 ∘ ∼120 ∘ W. This area best represented the El Nino variability that was used in this study.
As was shown in Table 2, there were 25 El Nino years from 1951 to 2015, among which 10 strong El Nino events occurred.In addition to 1958 and 1983, precipitation significantly declined in strong El Nino years (Figure 7).The other eight strong El Nino events occurred in 1957, 1972, 1982, 1986, 1987, 1991, 1992, and 1997, and   was in 1958 (317.8 mm), 1973 (217.8 mm), 1983 (217.8 mm), 1992 (107.1 mm), and 1998 (189.3 mm).The increments were all more than 100 mm and in some years more than 300 mm.In the weak and moderate El Nino years, the precipitation in years following the El Nino year also showed an increasing trend but weaker than the strong El Nino year.Of the strong

Figure 1 :
Figure 1: Spatial distribution of the nine weather stations in the Yan'an area.

Figure 2 :
Figure 2: Variation in precipitation in the Yan'an area and sunspot number.

Figure 3 :
Figure 3: The real part, modulus, and the second power of the modulus of the wavelet coefficient contour of precipitation: (a) real part wavelet coefficient contour map of precipitation; (b) modulus of wavelet coefficient contour map of precipitation; (c) the second power of the modulus of the wavelet coefficient contour map of precipitation.

Figure 4 :Figure 5 :Figure 6 :
Figure 4: Wavelet variance and real part coefficient change in precipitation: (a) wavelet variance of precipitation; (b) real part coefficients change in precipitation on a 41-year scale.
the corresponding precipitation was in 1957 (397.5 mm), 1972 (310.7 mm), 1982 (460.7 mm), 1986 (446.4 mm), 1987 (489.3 mm), 1991 (453.6 mm), 1992 (460.7 mm), and 1997 (375 mm), respectively.But after dry years, the years following a strong El Nino year showed sharply increased precipitation and an increment of annual precipitation in the Yan'an area.Following the strong El Nino years, the corresponding increments of annual precipitation year moving average data SOI: 5-year moving average data

Figure 7 :
Figure 7: Variation in precipitation at Yan'an station and the SOI index from 1951 to 2015.Note.When the SOI was negative, El Nino occurred in the corresponding year.

Table 1 :
Correlation coefficients of the WT real part coefficient series of 16-and 41-year scales between sunspot number and precipitation at Yan'an station from 1951 to 2015.

Table 2 :
El Nino events from 1951 to 2015.