Analysis and projection of runoff variation in three Chinese rivers

Temporal variability in river runoff has an important impact on water use. An insight into this variability could help in counteracting negative effects of water deficit and provide valuable information for hydrological and ecological strategies (Krasovskaia 1995; Hannah et al. 2005; Chaves et al. 2010). Monthly runoff variation patterns have been discussed in many studies within a non-stationarity context (e.g., Gottschalk & Krasovskaia 1997; Bower et al. 2004; Dibike & Coulibaly 2005; Naik & Jay 2011).

Runoff variability caused by natural variation in climatic system as well as by human impact has long been a focus of hydrological research. Advances in the field of climatology have shown that ocean–atmosphere interactions are not necessarily chaotic or random and that patterns of low-frequency variability can be present (López & Francés 2013). These patterns are commonly characterized by different indices which can be used to investigate the influence of climate patterns on river flow (Barlow & Tippett 2008). The impact of climate on river flow in China has attracted significant interest due to water shortages experienced in many north-western provinces. Many Chinese investigations have focused on the influence of El Niño-Southern Oscillation (ENSO) characterized by sea surface temperature in the Niño 3.4 region (SST Niño 3.4) (e.g., Wu et al. 2010; Feng et al. 2011; Zhang et al. 2011; Zhu et al. 2011; Li et al. 2013). These studies have reported a strong connection between the flow variation and anomalies in low-frequency atmospheric circulation patterns. The impact of ENSO appears to be evolving over time and varies between different regions. In general, the large-scale climate forcing was identified as a potential modulator of the irregularities of flow regime patterns in China. The influence of other atmospheric circulation patterns has attracted less attention. In particular, the influence of the Polar-Eurasian Oscillation (PEO) has been indicated as relevant for northern China by the NOAA Climate Prediction Center (http://www.cpc.ncep.noaa.gov). However, to our knowledge, there are few studies in this regard in China. In addition to low-frequency climate variability, the increasing pressure from human interferences (e.g., land use change, urbanization, river regulation by dams and reservoirs) in most Chinese river basins also calls for the elucidation of the resulting impacts on river flow (e.g., Li et al. 2007; Zhang et al. 2008; Xiong et al. 2014; Jiang et al. 2015).

Qualitative and quantitative analyses of both climatic and human impact factors have attracted significant attention in the hydrological community. For example, Hundecha & Bárdossy (2004) used the HBV model to evaluate the effect of land use on the runoff in the Rhine basin. López & Francés (2013) examined the links between climate and floods by statistical regression models. Chen et al. (2014) investigated the impact of climate and human activity on the annual runoff of the Yangtze River via multiple regression analysis. Jiang et al. (2015) applied Budyko-type equations to separate the impact of climatic and human on the runoff variation in the Wei River. Dong et al. (2015) concluded that agricultural land use was one of the most important factors behind the observed changes of direct runoff in the Wei River.

Currently, projection of hydrological characteristics based on future climate scenarios is in the focus of hydrological research. In general, there are two main approaches: applying statistical methods to predicted climate variables (e.g., Du et al. 2015) and extrapolating runoff by means of hydrological models with simulated precipitation and temperature (e.g., Chen et al. 2012). Running a hydrological model on various climatic scenarios may help address the uncertainties induced by the scenarios, but not the uncertainty that originates from insufficient knowledge regarding the interactions of integral processes. We conjecture that projecting possible future changes in runoff characteristics based on precipitation scenarios and variation patterns discerned from long-term runoff observations can complement the results derived from hydrological models. Assessment of impacts on human and natural systems that have already occurred as a result of recent climate change is an important complement to model projections of future impacts (IPCC 2013).

Flow duration curve (FDC) is another important characteristic of runoff variation for environmental flow assessment and water management. In China, the FDCs have not been previously examined in the light of possible variation in patterns. In spite of widespread doubts and rejection of the concept of flow stationarity, the FDC is still assumed to follow the long-term stationary pattern. Innovative thinking and methods that consider possible non-stationarity in FDC patterns are obviously required given the changing environment (Li et al. 2007; Zhang et al. 2008). Possible changes in FDCs induced by climate change and future projection of these changes have not yet received due attention.

The aim of the paper is to study runoff temporal variability patterns, analyze possible mechanisms behind this variability, and apply the findings for projecting runoff variability patterns for future. To achieve these goals, we utilize the characteristics of the identified runoff variation patterns and future precipitation scenarios produced by a number of General Circulation Models (GCMs). We perform the analyses individually on the data for three Chinese rivers, i.e. the Wei (Weihe), the Bei (Beijiang), and the Qing (Qingjiang), without comparisons as the records do not cover exactly the same observation period though there is much overlap. First, we focus on temporal flow variability by examining the differences in average monthly runoff variation patterns and FDCs for the years when the mean annual runoff is at least equal (‘non-deficit’ years) or lower (‘deficit’ years) than the long-term average. We then study possible mechanisms behind this variability of flow by analyzing the effects of the PEO, SST (Niño 3.4), and human activities. We conclude the study by constructing FDCs and average monthly runoff variation patterns for future precipitation scenarios using the discerned patterns for deficit and non-deficit years.

The Weihe, the biggest tributary of the Yellow River, is known as the ‘Mother River’ of the Guanzhong Plain in the southern part of the Loess Plateau. The Weihe basin has a semi-arid continental climate with dry winters and warm summers (Du et al. 2015). The Beijiang is the second biggest tributary of the Pearl River, and it flows across Guangdong Province, one of the well developed coastal provinces of southern China. The basin is mostly located in the mountains and has a subtropical climate with high temperatures and abundant precipitation (Luo et al. 2008). The Qingjiang, a tributary of the middle reaches of the Yangtze River, is subject to a subtropical monsoon type climate with abundant precipitation (Chen et al. 2012; Yu et al. 2014).

The chosen basin sizes represent an appropriate regional scale at which the effect of local factors on data analyses is minor (Woods 2005). The data used are all officially supplied and were previously successfully used in both research and practical fields (e.g., Xiong et al. 2014; Yu et al. 2014; Du et al. 2015; Jiang et al. 2015). For the Weihe runoff data were provided by the Hydrology Bureau of the Yellow River Conservancy Commission; for the Beijiang – by the Administration of Feilaixia Water Conservancy Project of Guangdong Province; and for the Qingjiang – by the hydrological bulletins of the Yangtze River Water Resources Commission. Daily precipitation and temperature series originated from the National Climate Center of the China Meteorological Administration. Areal average series of precipitation and temperature were used instead of point-scale precipitation (e.g., Szolgayova et al. 2014). Table 1 shows basic information of discharge, precipitation, and temperature records for the three study areas.

We focus on two teleconnections that are relevant for the study area: the PEO and SST (Niño 3.4). The PEO pattern represents a dipole of pressure anomalies with the positive phase associated with above-average geopotential height anomalies over northern China and Mongolia as well as low heights over the polar region (Wilby et al. 2004). Monthly data for the PEO and SST (Niño 3.4) originated from the NOAA Climate Prediction Center (http://www.cpc.ncep.noaa.gov/data).

A set of human activity factors were considered: population level (million); cultivated land (million ha); irrigated area (million ha); water supply (million t); grain yield (million t); gross domestic product (GDP; yuan); afforested area (ha); hydroelectricity (billion kWh); reservoir storage (billon m³); and area of soil-water conservation (ha), which have been frequently used by other researchers (e.g., Wang & Hejazi 2011). The first eight factors that could influence runoff variation in the Weihe, the Beijiang, and the Qingjiang were extracted for the same period as runoff records from statistical yearbooks for the Shaanxi (Yang 2009), Guangdong (Chen & Bu 1999), and Hubei (Li & Xu 2014) provinces, respectively. The records for the Beijiang and the Qingjiang basins have a small gap before 1956. The last two factors originating from yearbook of China water resources (Wu 2010) for all three basins were much shorter (15 years). The runoff data were adjusted accordingly for correlation analysis. Population level, water supply, and GDP are indirect characteristics of urbanization. Cultivated land, irrigated area, grain yield, afforested area, and area of soil-water conservation (e.g., terraces, grasses) are relevant indices for the alterations of land use and land cover of a catchment that might affect water balance and evaporation losses in particular. Grain yield may also serve as an indirect indicator of ‘green water,’ (Falkenmark 1995) herein water consumed by agricultural crops. River regulation may exert an important effect on regional hydro-cycles, especially in the Weihe, where numerous dams have been built to meet high demands on water, electricity-generation, etc.

GCMs remain one of the main tools for climate projections to future (Chen et al. 2012). Precipitation scenarios were obtained from both GCMs (http://cmip-pcmdi.llnl.gov/cmip5) and NOAA NCEP reanalysis (http://www.esrl.noaa.gov) datasets. We utilized the latest generation of GCMs developed by the research institutions of the countries participating in the Coupled Model Intercomparison Project Phase 5 (CMIP5) due to its improvement of predictive ability. Seven GCMs under a high greenhouse gas scenario (RCP8.5) were considered, i.e., CanESM2, CCSM4, CNRM-CM5, GFDL-ESM2M, MIROC-ESM, MIROC-ESM-CHEM, and NorESM1-M (Du et al. 2015). However, it is beyond the scope of this study to analyze the relative advantages and disadvantages of these GCMs.

The basic statistical methods of empirical orthogonal functions (EOF) (Lorenz 1956) and contingency analysis were the main tools for investigating hydrological data series.

When studying high-dimensional data in search for variation patterns, it is advantageous to first reduce the dimension in order to eliminate redundant information and noise. Decomposition into EOF is a convenient tool to accomplish this goal. According to the EOF-method, the original time series are represented by a set of orthogonal (amplitude) functions (AF) with weights equal to the eigenvectors of the covariance function of the original data. While AFs do not change, the weights are different for different observation years. The series decomposition can be truncated to eliminate noise when a sufficiently high level of the explained variance (commonly 90%) is reached. EOF decomposition has been successfully used in hydrology studies for dimensionality reduction and pattern recognition with regard to river flow (Krasovskaia et al. 1999; Sauquet et al. 2000, 2008; Gottschalk et al. 2015). For example, Li et al. (2013) utilized EOF when studying the relationship between SST indices and precipitation in China.

We perform EOF decomposition of the monthly runoff series for several purposes. First, we study grouping of the weights during deficit and non-deficit years to discern differences in the runoff variation patterns. Second, we attempt to identify the human impact signal in monthly runoff variation via investigation of the correlation between the weights and the human activity factors.

Contingency tables displaying the frequency distribution of variables are a widely used tool in engineering and scientific research (e.g., Cassou 2008; Stoll et al. 2013). They indicate the degree of interrelation between two variables. Li et al. (2015) used contingency tables to compare actual land use maps and simulated land use according to different scenarios of water use. We apply contingency tables to study the impact of low-frequency atmospheric oscillations on the occurrence of deficit and non-deficit years. The significance of the interrelationship is assessed via Chi-square test, while the degree of association is estimated using Cramér's V statistic (Cramér 1971). These are both standard methods for the analysis of contingencies.

Downscaling of GCM data to represent the local-scale climate for the three basins is performed by means of the statistical downscaling model (SDSM) for projection of runoff variation. The SDSM operation includes several steps: analyzing the correlation between the NCEP reanalysis predictors and historical precipitation record by a multiple linear regression; running weather generator in the SDSM to simulate precipitation based on the constructed multiple linear regressions; calibrating the SDSM by assessing the predictive performance; and projecting precipitation scenarios from the GCMs data in the calibrated SDSM. More technical details on the structure and application of the SDSM can be found in Wilby et al. (2002) and Wilby & Dawson (2007).

In the Weihe basin, Ps has a maximum in July–August in 66% of the years. Ps maxima occur a month later in 20% of the years, and they occur earlier in 12% of the years. Qs are significantly correlated with Ps (R = 0.92), with a one month lag. Maximum Qs typically occur in late summer-autumn (68% of the years), less frequently in July (20% of the years), and rarely during April–June (12% of the years).

In the Beijiang basin, maximum Ps typically occurs during May and July, representing 39% and 31% of the years, respectively. Correlation between Qs and Ps is high (R = 0.98), with a lag of approximately one month. Maximum Qs are usually observed in June (47% of the years), May (31% of the years), and April (18% of the years).

In the Qingjiang basin, Ps frequently exhibits maxima in July (31% of the years) and during the period of May–June (22% of the years). Qs are highly correlated with Ps (R = 0.98). Maximum Qs are typically observed in July (41% of years) or June (20% of years).

The frequency of deficit precipitation and runoff years is very similar: 60% and 56%, respectively, for the Weihe basin; 57% and 64% for the Beijiang basin; and 49% and 53%, for the Qingjiang basin.

In the Beijiang, slight changes in Q_ann, T_ann, and P_ann can be noted between different decades (Figure 3(c) and 3(d)). The magnitudes of deficit in P_ann and Q_ann are in agreement. Although P_ann, Q_ann, and T_ann were 13%, 8%, and 3%, respectively, higher in the last decade than their long-term means, they showed no significant uptrends for the entire period (MK test).

In the Qingjiang, the deficit in Q_ann often appears to be greater than that of P_ann (Figure 3(e)). A tendency for decreasing P_ann and Q_ann during the last two decades can be noticed (Figure 3(f)). During the first and the last decades, T_ann was approximately 0.5 °C and 1 °C, respectively, higher than the average, which might have contributed to the runoff deficit. However, no significant trends in Q_ann, P_ann, and T_ann over the studied period were detected (MK test).

Mean annual runoff proved to be significantly different for deficit and non-deficit years (t-test, at the 5% significance level). We continued to investigate whether the flow variation patterns differ between these years. Grouping the weights of the AFs for different years as obtained by EOF decomposition can be used for discriminating the flow variation patterns in the observation series (Krasovskaia et al. 1999, 2003). Table 2 presents the values of the relative explained variance after a truncation level of approximately 90% and the number of AFs necessary to reach this level. It can be observed that for all three series the first AF represents 60–70% of the variation in monthly runoff. In general, the first AF reflects the average monthly variation pattern, while the second and higher AFs might indicate shifts from this pattern (Krasovskaia et al. 1999).

In the Beijiang basin, the monthly runoff peaks occur earlier during the deficit years than on the average. A majority (63%) of runoff maxima are observed during April–May, while less than half occur that early on the average. During non-deficit years the percent of years with early maxima decreases to 38%, and 57% of the years have maxima in June. These results indicate that early monthly runoff maxima are often associated with deficit years.

In the Qingjiang basin, there is an obvious connection between the timing of runoff maxima and annual runoff deficit. During runoff deficit years, 50% of runoff maxima occur earlier than July, while the corresponding rate for the average pattern is only 36%. In contrast, during non-deficit years early peaks occur only in 24% of the years, and maxima occur in July or later in the majority of years.

On the basis of these results, we conclude that monthly runoff variation patterns differ between years with annual runoff deficit and those without a deficit. This difference is reflected in the variations in the timing of monthly flow peaks and FDCs.

We use contingency tables to investigate the impact of the positive and negative phases of the PEO and SST (Niño 3.4) on the occurrence of the deficit and non-deficit runoff years, respectively. Table 3 shows the six contingency tables (for three rivers and two indices), where the contingency values are shown in percent from the lengths of the phase of the respective index. All the contingencies proved to be significant at the 95% confidence level (Chi-square test), except for the contingency between the occurrence of deficit/non-deficit years and the SST (Niño 3.4) phase in the Beijiang. It can be seen that deficit runoff years are contingent with the negative PEO phase and vice versa. In contrast, deficit runoff years are contingent with the positive phase of SST (Niño 3.4) and vice versa.

The next step was to estimate the degree of association between positive/negative phases of the utilized indices and the occurrence of deficit/non-deficit years, respectively, using Cramér's V statistic (Table 3). We note moderate to high association with PEO (V = 1 is obtained only if the series are similar) and lower association with SST (Niño 3.4).

The results in general confirm a significant interrelationship between the phases of PEO and SST (Niño 3.4) and the occurrence of deficit and non-deficit runoff years for the river basins studied, with the exception of the Beijiang. Taking into consideration the changing relationship between precipitation patterns in China and the ENSO (Gao & Wang 2007), the predictive value of the ENSO phase is decreasing.

We attempt to estimate the human impact on the long-term runoff variability using the correlation between the human activity factors and the weights obtained by decomposing the original runoff series into EOFs. A significant (though low) correlation between the studied factors and the weights are detected (Table 4).

In the Weihe basin, the 1st weight has significant correlations with the population level and water supply. As the first AF represents 65% of the relative explained variance (Table 2), we can estimate the impact of the population level and water supply on the long-term runoff variability via multiplying the contribution of the first AF by the respective correlations to these human activity factors (Table 4). This yield 22% and 25%, respectively. The 2nd weight showed a significant correlation with the reservoir storage and area of soil water conservation (due to a limited record length, the result should be taken with caution), and the 4th weight – with other six factors. The contributions of the 2nd and 4th AFs to the total explained variance are low (11% and 7%, respectively), which yields the negligible impact of 3–6%.

In the Beijiang basin, the afforested area significantly correlates with the 1st weight, which yields an impact of 28% as the 1st AF contributes with 70% to the explained variance. The 2nd and 4th weights significantly correlate with most studied factors. The contributions of the 2nd and 4th AFs to the explained variance are 12% and 4%, respectively, leading to the negligible impact of 1–7%.

For the Qingjiang basin, only the 3rd weight and the irrigated area exhibited a significant correlation. However, the relative contribution of the 3rd AF to the total runoff variation is only 9%, which yields the negligible impact of 3%.

To summarize, we estimate that the human impact on the long-term variation of monthly runoff is 22–25% in the Weihe, 28% in the Beijiang, and negligible in the Qingjiang. Dong et al. (2015) estimated the impact of land use changes on the direct runoff of the Weihe basin at 1.2%. They focused on changes in the different land use types for a much shorter period in contrast to the present study, which may explain differences in the results. Examining the relative contribution of climatic and human impact factors to the 45% decrease of annual runoff in the Weihe basin during 1988–2008 (the end of our study period), Du & Shi (2012) estimated the contribution of the latter at 51%, which yields a 23% contribution to the total runoff variation. This agrees well with the results found in this study. The uncertainties involved in the estimations of the role of human activities in temporal runoff variation highlights the necessity of verification using different methods.

The proportions of deficit/non-deficit precipitation years differ considerably between the models for any of the three basins (Figure 7). For example, all the models indicate more deficit precipitation years for the Weihe but while the NorESM1-M prediction yields proportions of deficit years that are very close to the present values, the other models indicate a much higher percent of years with deficits in P_ann. The discrepancy between different models is very large for Beijiang (e.g., CCSM4 and CNRM-CM5). For Qingjiang, five out of seven models have predictions of more deficit years. The large differences in the results originate from the differences in the precipitation simulated by the GCMs and their different predictive performance, as noted by Chen & Frauenfeld (2014).

The differences in the variation patterns between deficit and non-deficit runoff years with respect to monthly flow and FDC as well as the influence of low-frequency atmospheric circulation patterns and human impact on this variability were investigated separately for three Chinese river basins. The characteristics of the discerned patterns of variation were used for projecting future runoff variability patterns based on a set of precipitation scenarios. The following conclusions have been made on the basis of the analyses.

Analyses of the frequency and changes in the occurrence of the deficit and non-deficit runoff years indicate the following. (1) In the Weihe basin, significant trends of decrease in runoff and increase in temperature were noted, but there was no similar trend in the precipitation. (2) In the Beijiang basin, very slight increases in the precipitation, runoff, and temperature were found. The variability of deficit/non-deficit precipitation and runoff years exhibited a higher level of agreement. (3) In the Qingjiang basin, there was a non-significant tendency for decreasing precipitation and runoff.

Monthly runoff variation patterns and FDCs differ between deficit and non-deficit years. The deficit years generally demonstrate earlier and more dispersed flow maxima, while the runoff pattern during non-deficit years resembles the average pattern.

The significant contingency between the phase of PEO and the occurrence of deficit and non-deficit runoff years was noted for all three river basins. The association with SST (Niño 3.4) was lower but still significant, except for the Beijiang. Deficit runoff years were associated with the negative phase of PEO and vice versa, while they were contingent with the positive phase of SST (Niño 3.4) and vice versa. The noted contingency may be developed towards probabilistic forecasts of the occurrence of deficit and non-deficit runoff years based on the phases of the studied indices.

The human impact on long-term monthly runoff variation was detectable: 22–25% in the Weihe, 28% in the Beijiang, and negligible in the Qingjiang.

There are considerable differences in the predicted FDCs and monthly runoff variation patterns based on the precipitation scenarios by different GCMs. Earlier and more dispersed monthly flow maxima could be expected if the frequency of deficit precipitation years increases in the future.

We utilized a ‘top-down’ approach that ‘begins with the identification of important regularities at the less fundamental level and defers until later understanding of the underlying, more fundamental mechanisms’ (Gell-Mann 1995) and attempted to study runoff variation by letting the data ‘speak for themselves.’ The suggested approach complements the more common use of hydrological models and avoids more uncertainties incurred by hydrological models for future projection of runoff variation. It shares the dominant part in the uncertainty, i.e., from precipitation scenarios, with the ‘modeling approach’. We showed the differences in the future projections of runoff variation to stress the importance of considering the range of uncertainties instead of averaging the results by seven GCMs. A minor source of uncertainty in the suggested approach originates from the statistical errors due to the limited length of the records and the fact that we used only two classes (deficit/non-deficit). The former type of uncertainty is also present in the ‘modeling approach’ but the model uncertainty is enlarged due to different choices of hydrological models, parameter estimation technique, etc. Using the proportion of the deficit/non-deficit precipitation years based on the scenarios as a proxy for deficit/non-deficit runoff years may also be a source of uncertainty. A comparative study of the uncertainties in both approaches applied to the same precipitation scenarios would be a topic for further investigation. Given a constant increase in the human impact on runoff variation, a further challenge would be introducing ‘corrections’ stemming from this impact in the future projections of runoff variation.

The financially support by the National Natural Science Foundation of China (Grants 51525902, 51479139, 51190094) is gratefully acknowledged.