Streamflow data used in this study are obtained from the Water Resources Agency in Taiwan, the primary authority in charge of installing and monitoring most of the river gauges over the country, and from the Taiwan Power Company, measuring streamflow for the sake of hydroelectricity. We select a total of 28 upstream and 13 downstream gauges of satisfactory quality and extended record. The collective contributing area associated with those downstream gauges located at the outlets of 13 major watersheds is approximately 16 731 km2, ∼ 46 % of Taiwan's territory. Because streamflow data observed at the downstream gauges are subject to human intervention (e.g. water regulation and withdrawal for various consumption), a distinction has been made to separate those upstream gauges with pristine flows from the downstream gauges, as shown in Fig. 1. From here onward, two batches of the same analysis will be performed for the upstream and downstream data. To minimize the effect of human intervention on streamflow data, this study emphasizes data during the high-flow season instead of low-flow seasons when more frequent regulations occur. Without loss of generality, July to September (JAS) is identified as the target high-flow season, from which seasonal streamflow data are aggregated for our follow-up analysis. It is noted that JAS is also known as the major typhoon season in Taiwan.

The periods of record and the missing data percentages for all 41 catchments are listed in Table 1. One sufficient condition for correlation analysis is a long period of data record. Thus, we decide to use all available data even though some of their periods of record differ: 30 out of 41 gauges present less than 3 % missing data (e.g. 1 out of 40 years is missing), indicating the reasonable quality of JAS flow data. For those missing-data years, we simply skip the flow and teleconnection index data pair for the calculation of correlation values to avoid the creation of any artificial, subjective flow quantities from data filling.

JAS streamflow data prepared thus far for the upstream and downstream gauges represent our target variable to be correlated with the major teleconnection indices. This correlation analysis is purposeful since the major teleconnection patterns can emulate a miniature of the full-scale climate system for considerable climate variability explained, thereby providing some clues regarding the causations of the interannual variations of Taiwan's streamflow. A list of the major teleconnection indices has been compiled. The desired list should cover as many teleconnection patterns as possible, but those selected should show certain signs of connections to East Asian climate based on previous entries in the literature. The ENSO is characterized as an air–sea coupled phenomenon: a zonal sea level pressure (SLP) anomaly in the tropical Pacific (i.e. the Southern Oscillation) and a quasi-periodic sea surface temperature (SST) warming/cooling in the tropical eastern Pacific (i.e. El Niño/La Niña). As the impact of ENSO on East Asian climate is well known, the list begins with three ENSO indices, namely NINO 1 + 2, NINO  3.4, and NINO 4, which represent the sources of influence from the east, eastern-central, and central tropical Pacific, respectively. In the immediate vicinity of the Pacific, the Indian Ocean has the IOD as the leading mode with evidence of steering East Asian monsoons and other weather systems , so the IOD index is selected. Over the farther side and higher latitude of the Pacific, the EP–NP and PNA patterns, found to be associated with the intensity and location of the Pacific jet stream e.g., are included in the list. Although sprung from the polar regions, more and more studies have indicated that the AO and AAO can affect climate variability in remote, subtropical regions e.g.; it would be reasonable to have these two indices in the list. To account for possible transoceanic interactions addressed by some studies , the NAO index, referred to as the meridional seesaw of the SLP field with the northern and southern centres near Iceland and the Azores, respectively, is also included. Furthermore, as the predictand of interest is highly related to summertime tropical cyclone (TC) activity, the list contains the QBO Quasi-Biennial Oscillation,, WP, and PJ indices . The QBO depicts a quasi-periodic oscillation between easterlies (positive) and westerlies (negative phase) over the lower tropical stratosphere, and the period is approximately 20–36 months. The WP pattern is one of the leading modes of low-frequency variability over the North Pacific, consisting of three anomaly centres: a meridional dipole with one centre near the Kamchatka Peninsula and another over the subtropical western North Pacific (WNP), and a third centre over the eastern North Pacific. The PJ pattern is a meridional teleconnection characterized by cyclonic and anticyclonic anomalies over the mid-latitude WNP. Beyond the above teleconnection indices, the PDO and AMO indices, as representatives of the interdecadal oscillations, are also included for the examination of any low-frequency connections. The PDO is characterized by a long-lived ENSO-like pattern that shifts phases with a period of at least 15–25 years, and the AMO is signified with long-term SST variations over the North Atlantic Ocean with a period of 50–70 years. Table 2 displays the list of the teleconnection indices and depicts their sources as well as some key references.

To reveal large-scale patterns pertaining to certain teleconnection indices (or even unprecedented signals) that dominate Taiwan's streamflow variability, this study uses various other data sets, including the Extended Reconstructed Sea Surface Temperature ERSST Version 4,, NCEP/NCAR Reanalysis SLP, geopotential height, and zonal wind , and Global Precipitation Climatology Project GPCP Version 2,.

In this study, correlation analysis is designed as follows. First, Pearson correlation coefficients between the JAS flow data at each gauge and different teleconnection indices in the same season (e.g. the JAS ENSO index) are calculated, representing the “concurrent” correlations. Second, to explore any forecasting utility, lagged correlations are computed as well. Lagged correlations are calculated between the JAS flow data and the teleconnection indices averaged over the preceding 3-, 6-, and 9-month seasons, namely, AMJ, JFMAMJ, and ONDJFMAMJ, respectively. This average scheme, commonly adopted by plentiful forecasting studies e.g., can eliminate high-frequency or artificial data disturbances. To examine prediction skills for longer lead times, we also calculate lagged correlations between the JAS flow data and the teleconnection indices averaged over two preceding periods, ONDJFM and the previous OND.

The PJ index supplied by the source is derived from the JJA data only, so we have used the following steps to develop the new PJ index (with Hisayuki Kubota's guidance) to pursue consistent analysis with the remaining indices: we (1) first obtained atmospheric pressure data at Yokohama and Hengchun in Japan and Taiwan, respectively; (2) calculated the JAS (and all other tri-monthly periods, e.g. AMJ, JFM, and the previous OND) average of the atmospheric pressure anomaly and then normalized the values by the standard deviation at each station; and (3) derived the JAS (and all other tri-monthly periods) PJ index from the difference of the two normalized pressure anomalies, and then normalized the index again by its 1979–2009 standard deviation. Using the above steps, we have reproduced the JJA PJ index and produced the new JAS PJ index.

It should be noted that the concurrent analysis does not produce immediate forecasting utility. However, we believe that it is still important to examine concurrent correlations between teleconnection indices and streamflow since many climate patterns have been proven to drive regional climates in the current season. The idea of calculating contemporaneous correlations was best demonstrated by , who described several dominant teleconnection patterns at the Northern Hemisphere extratropics during winter (e.g. NAO). Besides, one of the most important concurrent relationships witnessed by several operating agencies and research organizations (e.g. CPC and IRI) is the impact of ENSO on world regions. Various maps of the concurrent relationships (e.g. composite and historical probability) have been produced and archived. Over the Indian Ocean basin, the different phases of the IOD are also known to have pronounced concurrent impacts on the formation of the trade wind and the short rains over eastern Africa from October to November . In contrast, significant lagged correlations can indeed generate some forecasting utility, but to assess the dynamical mechanisms of the lagged relationships found by statistical approaches is never a trivial task. To use concurrent relationships for forecasting, one can adopt a hierarchical or hybrid approach that applies another empirical or dynamical model to forecast the teleconnection indices in the first instance e.g.. However, the development of a forecasting model is beyond the scope of this study.

One of the most fundamental assumptions of correlation analysis is that the result of such analysis indicates no causality. The result can be two-way; that is, there is no physical implication for a predictor–predictand relationship. However, the assumption held by us is that significant correlations should suggest some large-scale dominance over the local-scale hydroclimate since the opposite route of dominance (i.e. the impact of an island-scale disturbance on large-scale circulations) is less intuitive.

As stated in the study objective, the following correlation analysis is the examination of the temporal disruption of found significant correlations. The temporal disruption or abrupt changes in a univariate time series can be commonly identified by using classic, nonparametric techniques, such as the Mann–Whitney–Pettitt MWP, and Kruskal–Wallis KW, tests. However, these techniques are not directly applicable to quantities such as temporal correlations derived from a bivariate time series. Another statistically sound approach to this problem, proposed by , is used in this study. Rodionov's method in detecting abrupt changes in the correlation coefficient is based on the fundamental property of variance. If there are two variables of interest, x and y (e.g. the streamflow and teleconnection index), the variance of the sum of x and y can be written as Sx+y2=Sx2+Sy2+2rSxSy, where S2, S, and r denote the sample variance, standard deviation, and correlation coefficient, respectively. Further, if the two variables have zero mean and unit variance, the above equation can be reduced to Sx+y2=2(1+r). Note that, because the sample correlation coefficient ranges from -1 to 1, the above variance is bounded between 0 and 4. Equation (2) also indicates that the identification of shifts in r is equivalent to that in Sx+y2. In his previous work, introduced a method for detecting the abrupt shifts in the variance (of a single variable) based on a “sequential F-test.” Therefore, the same method for the variance of x or y can be applied to the variance of x+y, thereby achieving the identification of shifts in the correlation coefficient. In essence, the above method can also be applied to the variance of x-y, Sx-y2=2(1-r), which should theoretically yield similar change points if the p-value computed from Fisher's r-to-z transformation, is less than 0.05. As per Rodionov's suggestion, the test is performed for both the sum and difference series to ensure that the minimum p-value is attained.

If the variables have not been normalized, stated that some pre-processing work on the time series is required: using the shift detection in the mean based on a “sequential t-test,” and variance to obtain the stepwise means/trends and variances, respectively. The variables can then be normalized for the shift detection in the correlation coefficient. In addition to the pre-processing work and the desired significance level, a cut-off length l should be determined for the method to detect change points and to calculate associated statistics. For more discussion regarding the caveats of using the CRS detection method and its detailed documentation, please refer to the supplementary material and Rodionov's previous studies.

We selectively illustrate the correlation values from the many combinations of the different gauges, teleconnection indices, and lagged periods. In Figs. 2 and 3, concurrent and lagged correlations between the JAS runoff at the upstream gauges and selected teleconnection indices are colour-coded over the maps of the catchments. The criterion for selecting teleconnection indices is that they must exhibit correlation values at the 95 % confidence level with at least one of the catchments under either the concurrent or lagged scenario. In other words, those teleconnection indices excluded from the plots do not show significant concurrent or lagged correlations with any of the upstream catchments. Additionally, please note that the lagged correlations shown in Fig. 3 are based on the average period over ONDJFMAMJ only (lagged correlations based on other average periods show quite similar patterns and are available upon request). In the two figures, the highest absolute correlation value among all the upstream catchments for a specific teleconnection index is also denoted in each plot.

Under the concurrent scenario (Fig. 2), (1) many upstream catchments show significant positive correlations with the teleconnection indices, and among these indices, the WP and PJ indices stand out as having the strongest, universally in-phase relationship with the JAS runoff; (2) the only teleconnection index showing all negative correlations with the upstream catchments is the PDO; and (3) surprisingly, the NAO, as the farthest teleconnection mode, shows quite strong correlations (∼ 99 % confidence level) with some upstream catchments. Alternatively, under the lagged scenario (Fig. 3), (1) in comparison with the concurrent correlation patterns, some of them experience a clear phase reversal over certain regions of Taiwan (e.g. north-north-east for IOD and WP and central-south-west for PNA); and (2) the most pronounced out-of-phase relationship, even stronger than any of the concurrent correlations, is observed from the QBO index. We will show some evidence of the strong correlations in the discussion section.

To further interpret the range of correlation values, Fig. 4 encapsulates the correlations of the JAS runoff at every gauge against every teleconnection index using box-and-whisker plots. Each box plot constituted by 28 (13) values represents the range of correlations observed from the upstream (downstream) gauges. The results for upstream and downstream gauges are illustrated in the left and right panels, respectively. Concurrent and lagged correlations with JAS, ONDJFMAMJ, ONDJFM, and OND teleconnection indices are shown from the top to bottom of Fig. 4 in sequence. Moreover, the abscissa of Fig. 4a and b is ranked by the mean correlation in each box plot for a clearer illustration of the performance between teleconnection indices. To observe whether a phase transition occurs, the same ranking is then inherited by Fig. 4c–h. In addition, the corresponding correlation values for all the downstream gauges are also enumerated in Tables 3 and 4 (values for the upstream gauges are available upon request).

Compare Fig. 4a with 4b: the ranking of the teleconnection index is nearly the same (except PNA), and the interquartile range (IQR) of each box plot is also similar, implying the catchment-wide consistency in response to large-scale circulations. The total ranges of correlation values are wider for the upstream, which possibly reflects the higher randomness of catchments at a smaller scale. Under the concurrent scenario, out of the 14 teleconnection indices, 10 (9) tend to positively correlate with the JAS runoff for the upstream (downstream). Under the lagged scenario (Fig. 4c and d), only four teleconnection indices remain to positively correlate with the JAS runoff for both the upstream and downstream, suggesting the aforementioned phase reversal. The PNA, IOD, NINO 4, NINO 3.4, and WP are the teleconnection indices showing the phase reversal for both the upstream and downstream. Among all the indices, the QBO again indicates the strongest negative correlations with Taiwan's streamflow as the lead time increases.

Although some of the correlation results for certain catchments against teleconnection indices disclosed above are at a moderate significance level, it is found that these correlations are subject to peculiar interannual variations. For instance, 20-year moving-window correlations with four teleconnection indices, namely the PDO, EPNP, AO, and PJ, are examined (Fig. S1, Supplement). From those plots in Fig. S1, several types of interannual variations as potential signs of CRS can be identified: (1) divergence of the total ranges over time (e.g. panels a, b, and c), (2) a gradual decreasing trend (e.g. panel b), (3) an abrupt increase or decrease (e.g. panels c and d), and (4) a change in sign in the mean correlation near the suspicious CRS year (e.g. panels b and c). We thus hypothesize that the relationship between Taiwan's streamflow and large-scale circulations have undergone several climate regime shifts. To validate this hypothesis and identify possible years of CRS, the CRS test is applied to the streamflow data and teleconnection indices. As a demonstration, the aggregated JAS runoff for eastern (western) Taiwan is computed from the average of HLI and SGL (WU, JS, and BG) data for the CRS test. Figure 5 presents the result of the CRS test for identifying any shifts in the correlation between the eastern and western Taiwan runoff versus the PJ index. The result indicates two highly significant change points in 1979 and 1999 (significant at p=0.0001 and 0.0003, respectively) for the eastern Taiwan runoff. Between 1979 and 1999, the correlation value is higher than 0.8, suggesting the dominant effect of the PJ pattern. The correlation is remarkable, but it deteriorates drastically after 1999, becoming slightly negative and close to zero. Likewise, two significant change points in 1988 and 2000 (significant at p=0.006 and 0.0003, respectively) can be identified for the western Taiwan runoff. While the first change point is identified in the late 1980s, the marked in-phase relationship between 1979 and 1999 is still notable. The same CRS test has been applied to Taiwan's runoff versus all the other teleconnection indices, but only less significant results can be found.

In the Supplement, we have put the above correlation and CRS analyses in the context of prediction through a hindcasting experiment using linear regression. Overall, using large-scale circulation indices can produce fair to good prediction skills in summer streamflow prediction for selected upstream and downstream catchments. Regarding the frequent predictors selected as the PDO and PJ indices, the result is consistent with our general correlation assessments (e.g. Table 3) and indicates the general dominance of summer teleconnection in Taiwan. Nevertheless, the regression models illustrate the dramatic variations in prediction skill from the pre- to post-regime shift epoch (Fig. S2). For instance, the cross-validated correlation value decreases from 0.84 to -0.16 for the SGL watershed (Fig. S2i). To summarize, the linear regression experiment indicates that the assumption of a stable predictor–predictand relationship could be problematic for hydro-climatic forecasting due to the observation of CRS. Please refer to the Supplement for more details about the experiment.

Since the WP and PJ indices are associated with cyclonic activity in the WNP, the strong concurrent correlations with the JAS runoff indicate the direct influence of typhoons on Taiwan in summer. It is worth noting that some recent studies e.g. have projected more strong typhoons hitting this region, so the JAS runoff is expected to increase. The PDO, on the other hand, also shows the strong (but negative) concurrent correlations; this out-of-phase relationship is supported by some existing findings e.g. regarding the PDO's influence on East Asian climates in general.

To confirm the best outstanding lagged correlation between Taiwan's streamflow and the QBO, additional literature reviews and field significance tests still need to be conducted. The strongest lagged correlation is very likely attributed to the TC activity in the WNP modulated by the QBO. has performed a cross-spectral analysis between the QBO and the number of TCs in the WNP and indicated that the leading westerly phase of the QBO can result in an increase in TC activity. He explained that the westerly phase of the QBO creates an environment of relatively low vertical wind shear in favour of TC formation. later found that, during the westerly (easterly) phase of the QBO, more TCs approach the East China Sea (the eastern shore of Japan). Therefore, the negative correlation between the QBO index and TC activity in the vicinity of Taiwan is carried over into the negative correlation with streamflow. In fact, such strong correlations found in 22 out of the 41 catchments also reach field significance. The number of catchments with significant temporal correlations has exceeded the critical value of field significance (p=0.05) from the empirical null distribution (Fig. S3) developed by using a Monte Carlo technique similar to those suggested by and ; 2000 Monte Carlo trials are used, and each trial depicts a significant local test for correlations between the “randomly ordered” QBO index and streamflow data at the 41 catchments, resulting in a count of the number of catchments with significant temporal correlations constituting the null distribution.

In this study, we find that the two change points for the response of Taiwan's streamflow to large-scale circulations are not a coincidence. Whereas the first change point in the late 1970s (for the eastern Taiwan runoff in particular) is likely in relation to the widely known CRS identified over the entire Pacific basin SST , the second change point in the late 1990s coincides with the CRS induced by a warming over the equatorial western Pacific and/or more frequent occurrences of the central Pacific El Niño . These change points are associated with the shifts in the mean of the teleconnection indices individually. To supplement our explanation here, the CRS analysis of shifts in the mean is also applied to all the teleconnection indices examined in this study, and the identified change points are listed in Table 5. From the table, the shifts in the mean identified for the PDO are consistent with previous studies, and only such shifts (rather than the PJ) are in perfect agreement with the identified shifts in the correlation for Taiwan's streamflow. Therefore, we draw our hypothesis regarding the identified CRS as follows: the CRS first emanates from the change in the basin-scale climatology over the Pacific (e.g. shift in the PDO), and then the reorganized large-scale patterns can reset the relationship between the island-scale streamflow with established regional circulations (e.g. the PJ pattern).

The above hypothesis can be supported by some existing findings. Because the PDO is strongly tied to ENSO, the shift in the PDO can induce changes in the ENSO-related SST anomalies as well as ENSO-related teleconnections . Such SST anomalies have been found to be robust in the WNP during summer , and numerical model experiments have verified the ENSO-forced PJ pattern . further noted that the ENSO–PJ relationship was strengthened after 1980 and then weakened after 2000, likely due to the phase shift in the PDO. When the ENSO–PJ relationship is more pronounced, the systematic impacts of the PJ pattern on TC activity, rainfall, and, subsequently, streamflow in Taiwan are clear. By contrast, if the PJ pattern is less forced by ENSO, the associated impacts can be ambiguous. Consequently, Taiwan's streamflow became less predictable after the post-regime shift epoch.

The observation of the CRS can profoundly influence predictor screening for empirical forecasting methods. Conventional predictor screening usually relies on pattern correlation , that is, identifying specific areas over a predictor field (e.g. SST) showing significant correlation with the predictand of interest (e.g. local precipitation or streamflow) over a sufficiently long period of time. This concept holds true if the predictor–predictand relationship remains quasi-stationary. In contrast, if the predictor–predictand relationship is no longer stationary (e.g. identification of a prominent CRS in the correlation), this concept of predictor screening would become questionable. To further illustrate the impact of the CRS on seasonal forecasting, we develop some large-scale diagnostics next.

First, two sets of pattern correlation of the PJ index with the SLP, SST, or GPCP (precipitation) data are generated using 1999 as a demarcation of the time window (Fig. 6). Before 1999, the PJ–SLP correlation indicates a marked dipole pattern with its two poles centred in southern Japan and near Taiwan. Along with the significant negative correlation (at p=0.05) extended to the Indian Ocean (regarding SST) and the positive correlation over Taiwan (regarding GPCP), all these patterns reasonably reproduce the canonical PJ pattern defined by previous studies e.g.. In contrast, from 1999 onward, the entire set of pattern correlation is altered dramatically: the dipole pattern for the PJ–SLP correlation becomes less significant, and the extensive negative correlation over the Indian Ocean for the PJ–SST correlation reverses sign. In addition, the positive correlation originally occupying the Taiwan area migrates north-east to the East China Sea. The above analysis implies that, owing to a possible CRS, a specific teleconnection index (e.g. PJ) can respond quite differently to large-scale circulations from one time window to another. More importantly, if such a teleconnection index is adopted as a predictor, its relationship with the predictand (e.g. precipitation over Taiwan) could largely weaken or even be terminated given the existence of a CRS.

If pattern correlation is calculated directly between the eastern Taiwan runoff (as the predictand) and the SLP, SST, or GPCP data (as the predictor fields), the bulk of significant areas in the predictor fields usually specify the spatial extent of potential predictors. This is in accordance with the common procedure of predictor screening appearing in many articles . Figure 7 demonstrates this procedure twice, once before and once after the identified CRS. The left column of Fig. 7 resembles that of Fig. 6 to a very high degree, indicating that the PJ pattern is indeed an ideal predictor candidate before 1999. Nevertheless, from 1999 onward, the right column of Fig. 7 resembles neither the left column of the same figure nor the right column of Fig. 6, implying that the PJ predictor should be replaced by some other predictor candidates.

To achieve some forecasting utility, lead time information can be incorporated into the procedure of predictor screening. For instance, Fig. 8 presents the evolution of the SST anomaly (SSTA) composites based on wet-minus-dry years (i.e. SSTA averaged over the wet years minus that over the dry years) according to the JAS runoff for eastern Taiwan. The composites can reveal significant predictor areas at varied lead times . The identified CRS is used to divide the generation of the SSTA composites. Before the CRS, (1982, 1984, 1985, and 1994) and (1980, 1983, 1993, and 1998) are identified as the wet and dry years, respectively. After the CRS, (2001, 2005, and 2007) and (1999, 2002, and 2010) are identified as the wet and dry years, respectively. Wet and dry years are identified as those years for which the JAS runoff is higher and lower than the 67th and 33rd percentiles of the entire data series, respectively. During the concurrent season, notwithstanding that Fig. 8a and b show the SSTA patterns as extensions of the patterns observed in Fig. 7c and d, it can be found that the change in the patterns before and after the CRS is significant up to the global scale. With increases in lead times, the two sets of SSTA composites display distinct evolutionary pathways. Eventually, in previous OND, the SSTA composite expresses a La Niña pattern for the before-CRS scenario, completely the opposite of the El Niño pattern for the after-CRS scenario. No significant SST difference relevant to wet or dry can be identified after the CRS, indicating the weakened source of predictability from the SST.

We also examine the evolution of composites for other variables, especially for those used to define such potential predictors as the WP, PJ, and QBO patterns. According to Table 2, these variables represent 500 mb geopotential height, sea level pressure, and 30 mb zonal wind. Therefore, the wet and dry contrasts of these variables, before and after the CRS, are presented in Figs. 9 and 10 using the same format as Fig. 8 (geopotential height plots are not shown for their high resemblance to the sea level pressure plots). From the sea level pressure composites, before the CRS, significant cyclonic anomalies over the WNP can be found from the concurrent typhoon season to even earlier periods of the same year (Fig. 9a, c, and e). After the CRS, while the WNP area is inactive with no significant cyclonic anomalies, some patterns with signs opposite of those before the CRS can be found in the mid-to-high latitude regions at varied lead times. From the zonal wind composites shown in Fig. 10, the phase reversal is marked along the Equator: whereas the zonal wind pattern evolves into (backward in time) easterly anomalies under the before-CRS scenario, strong easterly anomalies change into westerly anomalies in previous OND under the after-CRS scenario. Nevertheless, no statistically significant patterns for the wind anomalies are identified along the Equator, suggesting that further analysis should be conducted to validate the predictor–predictand relationship between the QBO and Taiwan's streamflow. Overall, the SSTA, sea level pressure, and zonal wind composites all indicate that the large-scale patterns reverse phases. Our discussion herein illustrates the importance of a predictor screening scheme to account for a forthcoming CRS.