Prospects of Precipitation Based on Reconstruction over the Last 2000 Years in the Qilian Mountains

Abstract

The prospect of precipitation is of great significance to the distribution of industry and agriculture in Northwest China. The cycle characteristics of temperature and precipitation in the Qilian Mountains were identified by complex Morlet wavelet analysis and were simulated with sine functions. The results indicate that the main cycle of 200 years modulates the variations of temperature and precipitation over the past 2000 years and that cycle simulations fluctuate around the long-term trend. The temperature in the Qilian Mountains exhibits an obvious upward trend during the period 1570–1990 AD, while the precipitation trend shows a slight increase. The “wet-island” moisture pattern of the Qilian Mountains may be responsible for this. The moisture of the Qilian Mountains is principally sourced from the evapotranspiration of adjacent arid and semi-arid areas and is controlled by regional climate. The precipitation is close to the relative maximum and is at the positive phase of main cycle. It may not be beyond 400 mm in the next 200-year cycle, and the increment of precipitation might result from regional climate change.

1. Introduction

The precipitation is a vital factor for the economic and social development of Northwest China. The Qilian Mountains are the representative arid and semi-arid areas controlled by the continental climate and influenced by the local climate of Tibetan Plateau [1]. The river runoff in the alpine regions is mainly derived from the local precipitation and the glacier and snow melting during the warm season [2,3]. The occurrence of precipitation events and flood events in the desert in recent decades is one of great concern in Northwest China. The climate in the last half-century appears to be the wettest in 3500 years [4]. It is urgent to further evaluate the situation of regional precipitation to provide a scientific basis for the distribution and relative policy of industry and agriculture.

Shi et al. [5] proposed the reversion of climate type from warm–dry to warm–wet in Northwest China according to the datasets over the last 50 years, which was supported by many studies [6,7,8,9,10,11]. However, some scholars [12,13] believe the water shortage situation and climate pattern have no substantial change, and the annual precipitation still varies from 200 to 400 mm in Northwestern China [14].

The study of periodic characteristics is helpful for understanding climate variability [15,16], including the relative maximum, amplitude, and evolution route of the warming and moistening climate. The interannual and interdecadal cycles of precipitation have been identified according to the instrumental records [1,17,18]. The paleoclimate records present the long-term history of climate for understanding the current and future climate. The stable oxygen isotopic ratio (δ¹⁸O) [19] and annual net accumulation [20] in ice cores are interpreted as the paleoclimatic proxies for temperature and precipitation reconstructions, respectively. Tree-ring records also present regional precipitation and temperature information in annual resolution [21,22]. There are some distinguishable cycles of temperature in China over the last 2000 years, such as 50~70 years, 100~120 years, and 200~250 years [23]. Moreover, the precipitation cycles from interannual and multidecadal to centennial scales have been found for the Qilian Mountains [24,25]. In addition, solar activity is perhaps associated with the centennial cycles of temperature and precipitation [24,26,27]. These research studies, over long-term proxy records, focus on the identification of cycles. Nevertheless, the components of cycles, such as the amplitude, phase, and prospects of precipitation still require further analysis.

This study focuses on the components of cycles (e.g., frequency, main cycle, amplitude, and phase) in temperature and precipitation over the last 2000 years in Qilian Mountains and qualitatively recognizes the current phase of climate through cycle simulations. Then, we make a semi-quantitative prediction for the next cycle of precipitation via the Seasonal Autoregressive Integrated Moving Average (SARIMA) model. This is able to assess the evolution route and prospects of precipitation by comparing the results of the cycle simulation and the SARIMA model, which is of significance for precipitation environment assessment and ecological economic sustainable development in Qilian Mountains and its surrounding areas.

2. Materials and Methods

2.1. Study Area

The Qilian Mountains (93.5°–103.9° E, 35.8°–40.0° N) are located at the northern margin of the Tibetan Plateau and are the representative arid and semi-arid regions of Northwest China. This region consists of parallel mountains and valleys in the northwest–southeast direction, which spans across the Gansu and Qinghai provinces (Figure 1). The rivers (the Shule River, Heihe River, and Datong River) in the arid and semi-arid areas originate from the alpine regions. Precipitation in the alpine regions is generally larger than that in plain regions [28], and regional precipitation always affects local water resources, ecology, and economic development.

2.2. Data Sources

2.2.1. Temperature

Three China-wide temperature series over 0–1990 AD with decadal resolution are reconstructed by combining multiple paleoclimate proxies [29]. Our study adopts the “Weighted” temperature series, which is the clearest one, to express the general features of temperature in China. The reconstructed temperature series indicates the warm and cool conditions, such as the Medieval Warm Period and the cool Little Ice Age Period. The area weights of Eastern China, Dunde ice core, Guliya ice core, southern TP tree-rings, Jinchuan peat, and Great Ghost Lake and Jiaming Lake in Taiwan are 0.329, 0.198, 0.149, 0.182, 0.131, and 0.011, respectively [29].

2.2.2. Precipitation

Yang et al. [4] reconstruct an annual resolved precipitation series of Qilian Mountains spanning 3500 years. The samples are collected from 17 sites in the Qilian Mountains, where tree growth is sensitive to humidity changes and is mainly limited by precipitation [15]. The correlation between the reconstruction and adjacent observation is 0.84 (p < 0.01) over the calibration period (AD 1957–2011), which is considered to be sufficiently reliable. The reconstruction has been taken into account, using uncertainty estimates from the residuals and used in many studies of climate evolution [30,31]. We select the dataset with a decadal resolution for about 2000 years to analyze the centennial cycles of precipitation.

2.3. Methods

2.3.1. Morlet Wavelet Analysis

Wavelet analysis inherits and develops an idea of the short-time Fourier transform. It shows a sliding window changed with frequency to the perform time–frequency localization of cycles [32], which is an excellent tool for cycle analysis [33,34,35,36]. The Morlet wavelet analysis provides a good balance between the temporal domain and frequency domain as a particular wavelet and accurately identifies the cycles of time series [37]. The Morlet wavelet functional form is as follows [38]:

$${\Psi }_0\left(t\right)={\pi }^{-1/4}{e}^{i{\omega }_{0}t}{e}^{-t^2/2}$$

(1)

where ${\omega }_0$ is the nondimensional frequency, and t is a nondimensional “time” parameter.

2.3.2. Cycle Simulation

1.

Detrended method of moving average;

Detrended method of moving average (DMA) is used to reduce the interference of the trend on cycle analysis and to convert the non-stationary series into a stationary series [39,40,41]. The detrending procedure: first, this study applies the main cycle as a moving average parameter for smoothing the series to present the long-term trend. Then, the actual value minus the moving average to obtain the difference value (DV) series, which removes the interference of a long-term trend while retaining cycle information.

2.

Sine function fitting.

Periodicity is an important order of time series, and periodic characteristics can be expressed by sine or cosine functions with 3 main parameters, including amplitude, frequency, and initial phase [42,43,44], which are applied in the studies of temperature and precipitation [45,46]. The process of cycle simulation in this study is as follows (Figure 2): firstly, the amplitude of main cycle is defined as the 2 SD of DV series. Secondly, with known amplitude and frequency (main cycle), the initial phase is obtained by the curve fitting of the MATLAB platform. The optimal sine function fitting of the DV series shows the cycle evolution route and provides a premise for cycle simulation. Finally, the simulated series is made available by adding the optimal fitting results to the smoothing series [47].

The cycle simulation fluctuates around the long-term trend and is divided into positive and negative phases through the smoothing series. It is carried out to distinguish the stages from the rising and falling of series under the modulation of the main cycle as well. Indeed, the fundamental of the moving average is the conservation of the expected average [43]. Therefore, an extrapolation, based on the extensibility of the sine function and trend, makes it possible to simulate the evolution route of the cycle and to make a qualitative analysis of climate change under the control of the trend and main cycle.

2.3.3. SARIMA Model

The Autoregressive Integrated Moving Average (ARIMA) model combines the autoregressive (AR) model with the moving average (MA) model and extends it to the non-stationary series by differencing [48]. It is a regression model to interpret the data and make future predictions, in which the independent variables are all lags of the dependent variable and errors. The SARIMA model, adding a seasonal or periodic component on ARIMA (p, d, q) [49], is applied to analyze periodic characteristics of time series. It is widely used to predict precipitation with high flexibility and accuracy, and many research studies indicate a high degree of model fitness to the observed data [50,51,52,53]. The model is usually represented as SARIMA (p, d, q) × (P, D, Q)_S. This study concentrates on the decadal precipitation time series, and the periodic parameter S represents the main cycle of precipitation. The formula is defined as followed [54]:

$${\Phi }_P\left(B^S\right){\varphi }_p\left(B\right){\nabla }_S^D{\nabla }^d{x}_t=\mu +{\Theta }_Q\left(B^S\right){\theta }_q\left(B\right)a_t$$

(2)

where $a_t$ is non-stationary time series, S is the period, and B is the backshift operator. The p, d, and q correspond to the order of the autoregressive, integrated, and moving average processes, respectively. P, D, and Q are the relevant seasonal parameters. ${\varphi }_p\left(B\right)$ and ${\theta }_q\left(B\right)$ are the regular AR and MA operator of order p and q. ${\Phi }_P\left(B^S\right)$ and ${\Theta }_Q\left(B^S\right)$ are the SAR and SMA operator of order P and Q, respectively.

3. Results

3.1. Main Cycle

The periodic features in the paleoclimate series can be analyzed by complex Morlet wavelet, and it is conducive to recognizing the current phase of the climate. The “boundary effect” is eliminated before wavelet analysis, and the wavelet function is determined as complex Morlet (1–1.5) and the 1/3 of data length is regarded as the maximum period. The cycles of temperature (Figure 3a,b) and precipitation (Figure 3c,d) during the last 2000 years are identified through complex Morlet wavelet. The real-part of the wavelet coefficient from top to bottom corresponds to cycles from low to high frequency, and the wavelet variance diagram reflects the strength of cycles and main cycle [55].

The temperature and precipitation show the quasi-periodicities of 250~350 and 400~640 years according to the distributions of the wavelet coefficient. The periodic signals of temperature are most obvious in the 280-year and 480-year scales, as shown in Figure 3b, and the wavelet variance of precipitation shows two significant peaks of 320 and 590 years, as shown in Figure 3d. The wavelet coefficients at different time scales indicate the periodic oscillation and the cycle length of temperature and precipitation (Figure 4). The 200-year and 306-year cycles of temperature are noticeable, and the 200-year and 380-year cycles are obvious in precipitation series. The main cycles of temperature and precipitation are both 200 years, indicating that the centennial-scale cycle modulates the variations of temperature and precipitation.

3.2. Simulation

3.2.1. Simulated Temperature

The temperature simulation is carried out to understand the background and future of precipitation in Qilian Mountains. The moving average parameter is set as 200, corresponding to the main cycle of temperature and precipitation, and the DV series is averaged by 20 years to improve the curve fitting effect. The amplitude of temperature is about 0.63 °C under the limits of 2 SD. The optimal fitting function and the formula of simulated temperature in the main cycle are as follows:

$$T_F=0.63sin\left(2\pi t/200+1.72\right)$$

(3)

$$T_S=T_F+T_M$$

(4)

where T_F is the fitting temperature of the DV series with the 200-year cycle (°C), t is the time (year), T_M is the moving average value of temperature, and T_S is the simulated temperature.

As shown in Figure 5a, the DV series of temperature disregards long-term effects and displays an obvious feature of main cycle. The peaks and troughs of sine function fitting correspond to the periodic variation of the DV series. The fitting curve contains nine whole cycles and fits well with the detrended temperature. This has shifted to the positive phase of main cycle since 1950 AD. The simulated temperature fluctuates around the long-term trend and reflects the route of cold–warm transition over the past 2000 years (Figure 5b). The correlation coefficient between simulated and original series is 0.66 during the overlapping period (90–1990 AD). When the long-term trend is in the declining zone (90–500 AD, 1300–1570 AD), the simulation shows downward fluctuations; otherwise, it shows upward ones (500–780 AD, 1570–1990 AD). The current temperature is in a warm phase and is close to the end of the rising stage of the main cycle.

3.2.2. Simulated Precipitation

The precipitation in the Qilian Mountains shows an obvious change between decadal years. As shown in Figure 6a, the boxplots for every two centuries are performed to compare the distribution of precipitation in each main cycle. The distribution of precipitation is relatively concentrated between samples despite the influence of extreme data, especially during 800–1400 AD. In addition, the median and mean are generally around 200 mm, and the shapes of the precipitation boxplots for the main cycle are near symmetric. The last box of precipitation (1800–2010 AD) shows a higher mean and more scattered distribution.

The precipitation simulation is also focused on main cycle, and the amplitude of the 200-year cycle is about 51.82 mm under the limits of 2 SD. The optimal fitting function, simulated precipitation, and the extended series established on the linear trends are defined as follows:

$$P_F=51.82sin\left(2\pi t/200+1.54\right)$$

(5)

$$P_S=P_F+P_M$$

(6)

$$P_E=\{\begin{array}{c}{P}_F+0.15t-43.33, \left(Rising linear trend, 1540\le t\le 2210\right)\hfill \\ P_F+0.009t+201.86, \left(Linear trend, 0\le t\le 2210\right)\hfill \end{array}$$

(7)

where P_F represents the fitting precipitation of the DV series with 200-year cycle (mm), t is the time (year), P_M is the moving average value of precipitation, P_S is the simulated precipitation, and P_E indicates the extended series established on the linear trends of the rising zone or whole series.

The fitted curve displays nine whole cycles and a rising stage in the tenth cycle (1900–2010 AD), and the amplitude indicates the fluctuation range of precipitation under the modulation of the main cycle. Figure 6b shows the cyclic route of detrended precipitation in the next 200 years, which eliminates the influence of the long-term precipitation trend. The simulated precipitation fluctuates around the long-term trend in a periodic form (Figure 6c), and the correlation between simulation and precipitation is 0.40 (90–2010 AD). The average precipitation is about 210 mm during the last 2000 years. In addition, the long-term trend of precipitation is relatively stable, and this is also shown in the mean values’ change in boxplots. The current precipitation is in the rising zone of the long-term trend that begins at 1540 AD; however, the rate of the rising linear trend is only 1.5 mm/10 a. The simulated series integrates the trend and cycle, which is extended to the next 200-year cycle based on the (rising) linear trend to probe the variation scope (Figure 6d). Results indicate that precipitation will increase in a limited scope in the next cycle.

3.3. Model Prediction

The parameter S of the SARIMA model is set to be 20 to represent the 200-year main cycle of the precipitation series. The SARIMA (0,1,1) × (0,1,1)₂₀ is determined by the minimum values of the Akaike Information Criterion (AIC = 1643.20) and Bayesian Information Criterion (BIC = 1652.41), and they passed the residual normality test (Figure 7). The histogram of standardized residuals is in agreement with the normal curve, and the Quantile–Quantile (QQ) plot follows the normal reference line, demonstrating that the residuals are normally distributed. Simultaneously, the result of the Durbin Watson test is 1.96, suggesting that the residual information is not an autocorrelation and that the model is statistically valid.

To avoid the unclear changes caused by influences such as the industrial revolution or other human activities, it is beneficial to use a half-and-half method of split-sampling, which is the classical approach for validation in hydrology [56,57]. Thus, the precipitation series is divided into the train part (0–1000 AD) and a test one (1010–2010 AD) to assess the validity of the SARIMA model (Figure 8a). In the validation period, the actual values are included in the 95% confidence limits of prediction, albeit below the general in-sample prediction, which results from the capture of a near-term rising trend in the model prediction. This suggests a limitation that the model assumes that the time series continues to rise as before and cannot predict the change of trend, such as the rising and falling. The accuracy is tested by statistical evaluation, where the Mean Absolute Percentage Error (MAPE) is 0.26, the Mean Absolute Error (MAE) is 47.12, and the Root Mean Square Error (RMSE) is 58.21. These results indicate that the selected model and parameters are appropriate and reliable.

As shown in Figure 8b, the model fitting agrees with both the actual values and cycle simulation during the overlapping period. The evolution route of the main cycle, controlled by the rising trend since 1540 AD, is performed for the qualitative analysis of precipitation. The model projection is consistent with the cyclic evolution and reveals more detailed changes of the time series. The precipitation shows an increasing trend with a fluctuation in the main cycle, while the forecasts, under 95% confidence limits, do not exceed 400 mm in the next 200 years.

4. Discussion

4.1. Cycle and Trend

The temperature and precipitation over the past 2000 years appear to be consistent in the main cycle of 200 years, which is possibly affected by the same factor. The changes may be affected by the solar de Vries cycle (~205 years) [58], showing that solar activity or total solar irradiance dominates the climate changes [59]. In addition, the present climate is at the positive phase of the principal cycle and close to the relative extreme values. The initial phases of the simulated temperature and precipitation are 1.72 and 1.54, implying that the temperature influences precipitation under the modulation of the main cycle.

The long-term trends of temperature and precipitation imply the millennial-scale cycles. Ice-core records indicate that temperature and precipitation in the Qinghai–Tibet Plateau are positively correlated in general trends and in low-frequency changes [60]. Several other studies reflect the millennial-scale cycles in climate change [61,62] and have demonstrated that it can be reconstructed by the superposition of two cycles (87 and 210 years) [63]. The millennial-scale cycle regulates the century-scale cycles and reflects the long-term trend of the series [64], which may be further studied and simulated with longer series of temperature and precipitation.

Meanwhile, centennial-scale cycle simulation fluctuates around the long-term trend that represents the millennial-scale cycle. For example, the simulated temperature shows downward fluctuations of the 200-year cycle during the declining stage of the millennial-scale cycle (90–500 AD, 1300–1570 AD), and it shows upward fluctuations during 500–780 AD and 1570–1990 AD (Figure 5b). The simulated precipitation fluctuates similarly (Figure 6b). Cycle simulation incorporates the cycle and long-term trend of time series, and it is performed to qualitatively recognize the evolution route of main cycle. The current temperature and precipitation, fluctuating around the rising stage of millennial-scale cycle, are at the positive phase of the principal cycle, which may explain the warm–wet features that have emerged in the past half-century.

4.2. “Wet-Island” Pattern

The moisture recycling intensifies under global warming, mainly contributed by both local evapotranspiration and advection moisture [65]. Nevertheless, the Qilian Mountains are the northern limit of the Asian summer monsoon (from the Northern Indian and Western Pacific oceans) [4,22], and the transported water vapor has no close contact with the westerlies [66]. The annual precipitation in the valleys and adjacent plains only vary in a limited range under the semi-arid climate.

The moisture recycling in the Qilian Mountains is more like a “wet-island” pattern, and local evapotranspiration is the major moisture source (Figure 9), which may interpret the phenomena of a steady long-term trend in precipitation with the background of a noticeable trend in temperature. The precipitation recycling is strong and cannot be ignored, especially in arid and semi-arid conditions [65]. The evapotranspiration is sourced from the basin, and alluvial fans lying on the southern and northern slopes of the Qilian Mountains and mountain ranges “capture” the moisture from the atmosphere to form precipitation [67]. Mountainous runoff provides water resources for the basin, and recycled moisture generated from evapotranspiration over the basin is transported to the mountains [68]. The glaciers, precipitation, and evapotranspiration are sensitive to climate change, and the water-internal recycle process is closely connected with regional temperature [69]. The precipitation in the Qilian Mountains is mainly influenced by evapotranspiration. Regional warming may result in rising precipitation; however, it suggests a limited increment under the “wet-island” pattern.

5. Conclusions

The main cycle of 200 years is identified in the temperature and precipitation series, and temperature influences precipitation under the modulation of the main cycle. The temperature and precipitation are currently close to the maximum of the 200-year cycle for being at the relative extreme value of the positive phase. Cycle simulations fluctuate around the long-term trend.

The temperature exhibits an obvious upward trend during the 1570–1990 AD period, while the precipitation trend displays a limited increase. The “wet-island” moisture pattern of the Qilian Mountains may be responsible for this. The moisture of the Qilian Mountains is principally sourced from the evapotranspiration of adjacent arid and semi-arid areas and is controlled by regional temperature. The average precipitation is about 210 mm during the past 2000 years and may not exceed 400 mm in the next 200-year cycle. The increment of precipitation might be due to the change in regional climate.

This study focuses on the main cycle and qualitative analysis, and the detailed changes of the time series may be simulated by periodic superposition in the future. Additionally, further studies on the water consumption of basins are needed to prove the “wet-island” effect, which will be an essential basis for the scientific distribution of water-consuming industry and agriculture.