Factors affecting interannual variation in late summer rainfall in the Red River Delta of Vietnam

Based on station monthly observational statistics, the major rainfall in the Red River Delta (RRD) of Vietnam occurs in late summer (July–September) with conspicuous year‑to‑year variation. Using the ± 0.8 of the seasonal total rainfall standard deviation as criteria, seven wet and six dry years are identified over the period 1983–2015. In addition to the 70.5% of the seasonal total rainfall contributed by the heavy rainfall days, the distinct heavy rainfall accumu‑ lation difference between wet and dry years seems to fundamentally establish these two separated extreme wet and dry groups. As revealed from further analyses, the large variability in rainfall is attributed to the influence of tropi‑ cal cyclones (TCs) and 7–24‑ and 30–60‑day intraseasonal oscillations (ISOs); in particular, the number of TCs affect‑ ing the RRD and rainfall produced by TCs are more (less) during the wet (dry) years, and the amplitudes of ISOs are also enhanced (reduced). In many cases, heavy rainfall days are induced by the combined effect of both ISOs and TCs, while some heavy rainfall events are mainly triggered by ISOs. It is found from the water vapor budget analyses that an anomalous cyclone (anticyclone) dominates over the Indochina Peninsula in wet (dry) years, resulting in more (less) water vapor being transported to the RRD, whereas the anomalous convergence (divergence) of water vapor flux leads to the maintenance of excessive (insufficient) rainfall over the RRD. However, the El Niño–Southern Oscilla‑ tion (ENSO) forcing shows minor effects on the interannual variation in rainfall in the RRD.


Introduction
Interannual variation in rainfall has a profound impact on rice production (Nhan et al. 2011;Chung et al., 2015; Abbas and Mayo 2021) as well as many aspects of human life. Therefore, many previous studies were conducted to examine the year-to-year variation in rainfall and its possible mechanism over the Asian monsoon region. For example, Chen and Yoon (2000) suggested that the interannual variation in summer monsoon rainfall over Indochina is primarily induced by two factors. The first is the occurrence frequency of weather disturbances (e.g., tropical cyclones [TCs] and monsoon lows) that propagate westward from the East Sea-western tropical Pacific to the Indochina Peninsula (ICP). Here, the East Sea, the sea east of Vietnam covering the latitudes between 8° and 17°N (International Hydrographic Organization 2002), is the Vietnamese name for the sea (as displayed in Fig. 1a), while it is called the West Philippine Sea in the Philippines since the sea is located between the Philippines and Vietnam. According to the International Hydrographic Page 2 of 14 Dinh et al. Terrestrial, Atmospheric and Oceanic Sciences (2023) 34:12 Organization (1953), it is named the South China Sea. The second factor is the variation in the global divergent water vapor flux induced by the El Niño-Southern Oscillation (ENSO) forcing. Yen et al. (2011) showed that the interannual variation in October-November rainfall along the coast of central Vietnam is negatively correlated with the sea surface temperature (SST) (Niño3.4) index, indicating that central Vietnam is wetter (drier) when the SSTs over the Niño3.4 region are colder (warmer).
In a further study, Chen et al. (2012a) investigated the interannual variation in October-November rainfall in central Vietnam from the perspective of the interannual variation in extreme weather systems, including heavy rainfall flood events, cold surge vortices, and TCs. They found that heavy rainfall flood events contribute 62% of the total rainfall and are the most important factor modulating the interannual rainfall variation in central Vietnam. However, Nguyen et al. (2007) reported that Page 3 of 14 Dinh et al. Terrestrial, Atmospheric and Oceanic Sciences (2023) 34:12 the July-September rainfall in a small area of the central highlands of Vietnam shows an in-phase relationship with the equatorial central to eastern Pacific SST. Bui-Manh et al. (2021) claimed that the July rainfall in the central highlands of Vietnam significantly increases in the El Niño developing phases. In contrast, Takahashi et al. (2015) noted that the interannual relationship between Thailand summer rainfall and SST over the Niño3.4 region is unclear, and the interannual variation in Thailand summer rainfall is mainly induced by westward-moving TCs. Similarly, Fujinami et al. (2011) demonstrated that total summer monsoon rainfall in Bangladesh is regulated by 7-25-day intraseasonal oscillations (ISOs) rather than by ENSO forcing. Ultimately, the main factors modulating the year-to-year rainfall variability differ significantly from region to region and by seasonality. Located in the coastal region of northern Vietnam, the Red River Delta (RRD), with its northeast and southwest sides bounded by mountains (Fig. 1a), is characterized by flat topography with dense rivers and streams, which creates a suitable environment for the development of transportation and infrastructure systems in this region. Moreover, Hanoi, the capital of Vietnam as well as the political, economic, and cultural center, also resides in the RRD in addition to one of the world's most densely populated deltas. Vietnam was among the top five rice exporting countries in 2022 (Shahbandeh 2022), and the RRD is the second largest rice producer after the Mekong River Delta in Vietnam. Based on 33-year (1983-2015) rain gauge observation statistics, it appears that the rainy season in the RRD is basically from May to September, with a peak in August (Fig. 1b). According to Takahashi and Yasunari (2006), the summer rainy season in the ICP can be divided into two subseasons based on the climatological monsoon break in late June: early summer (May-Jun) and late summer (July-September), with higher rainfall in the latter period than in the former period. The rainfall in the early summer is mainly induced by the southwesterly monsoon, while the rainfall in the late summer is primarily caused by tropical depression disturbances (TDs) moving westward from the East Sea-western North Pacific. In the RRD, the rainfall in the late summer months.
(July-September) is also higher than that in the early summer months (May-Jun), and more TCs occurred in the late summer (Fig. 1b). Furthermore, Nguyen-Thi et al. (2012) demonstrated that the RRD has maximum TC rainfall from July to September. Based on these climatological analysis results, it is legitimate to investigate longterm rainfall variability, such as the interannual variation in rainfall, by using late summer rainfall in the RRD. To evaluate the role/contribution of September rainfall in late summer, comparisons of the interannual variation in rainfall between late summer and other periods, including middle summer (July, August), entire summer (June, July, and August), and early summer (May, June) rainfall, are illustrated in Fig. 2. The high correlation coefficient (γ) between middle and late summer rainfall is 0.85 (Fig. 2a), so the middle summer rainfall explains 72% of the variation among observed late summer rainfall since the coefficient of determination (γ 2 ) is 0.72. Therefore, another 28% variation contributed from September rainfall should be included in this study to properly represent the major rainfall period in the RRD. In contrast, there is no relationship between late summer and early summer Fig. 2 Comparisons of the year-to-year variation in rainfall in the RRD between late summer (July-September) and other periods: a middle summer (July, August), b entire summer (June, July, and August), and c early summer (May, June) during the period 1983-2015. The blue histogram represents the late summer rainfall, while the red time series denotes each corresponding period in a-c. The correlation coefficient (γ) between late summer rainfall and each corresponding period rainfall is shown on the top right of each panel Page 4 of 14 Dinh et al. Terrestrial, Atmospheric and Oceanic Sciences (2023) 34:12 rainfall (with low γ = 0.04 in Fig. 2c), which is simply attributed to two apparently different rainfall systems between them previously pointed out by Takahashi and Yasunari (2006). Thus, the entire summer rainfall mixed with two types of rainfall systems obviously leads to a moderate correlation coefficient (γ = 0.80) between late summer and entire summer rainfall (Fig. 2b). The influence of ENSO on the rainfall variability in the RRD has been investigated in some previous studies. Nguyen et al. (2014) applied spatial correlation maps to explore the relationship between ENSO and rainfall variability over subregions in Vietnam during the 1971-2010 period. Their results showed that ENSO signals can hardly be found over the RRD during the entire summer. Using a statistic called Bayesian model averaging to study the effect of ENSO on the rainfall in Vietnam during the 1975-2006 period, Duc et al. (2018) demonstrated that the entire summer rainfall in the RRD is also less affected by ENSO. However, Gobin et al. (2016) compared the impact of La Niña and El Niño on the heavy rainfall patterns in Vietnam during the 1960-2009 period and found that the May-August rainfall and number of heavy rainfall months in the RRD during La Niña were significantly higher than those during El Niño.
Although the rainfall in this region is mainly induced by TCs, ISOs, the intertropical convergence zone (ITCZ), the monsoon trough, cold surges, and the interaction between them (Wu et al. 2011;Nguyen-Thi et al. 2012;Chen et al. 2012b;Truong and Tuan 2019;Tuan 2019), to the best of our knowledge, no efforts have been made to explore the interannual variation in late summer rainfall in the RRD. Most previous studies focused on the interannual relationship between middle or entire summer rainfall in the RRD and ENSO (Nguyen et al. 2014;Gobin et al. 2016;Duc et al. 2018). To fill this gap, the interannual variation in late summer rainfall in the RRD and the possible factors inducing rainfall variability are investigated in this study. The remainder of this paper is organized as follows. Section 2 introduces the datasets used in this study. The interannual variation in rainfall is described in Sect. 3. Section 4 presents the possible factors that are responsible for the year-to-year variation in rainfall. In this section, the roles of TCs, ISOs, the water vapor budget, and ENSO forcing are discussed. Finally, conclusions are given in Sect. 5.

Data
Daily rainfall data measured at 12 rain-gauge stations during the period 1983-2015 are collected to investigate the rainfall variation over the RRD. These data are provided by the National Central for Hydro-Meteorological Forecasting, Vietnam Meteorological and Hydrological Administration. The locations and information of the 12 stations are shown in Fig. 1a and Table 1. To investigate the relationship between rainfall variability in the RRD and the surrounding activity embedded in the large-scale environment, we used daily Precipitation.
Estimation from Remotely Sensed Information using Artificial Neural Networks for Climate Data Record (PERSIANN-CDR) at a resolution of 0.25° × 0.25°. These data were estimated from long-term multisatellite high-resolution observations covering the period 1983-present. (Ashouri et al. 2015). In fact, another PERSIANN-Cloud Classification System-Climate Data Record (PERSIANN-CCS-CDR) with a higher resolution of 0.04° × 0.04° spanning 1983-present (Sadeghi et al. 2021) is also currently available. However, comparisons of the interannual variation in late summer rainfall between station observations and PERSIANNCDR and PERSIANN-CCS-CDR rainfalls over the RRD show that PERSIANN-CDR, having a higher correlation coefficient (0.81) and smaller root mean square error (RMSE) of 1.71 mm•day −1 , outperformed PERSIANN-CCS-CDR, with respective values of 0.70 and 3.47 mm•day −1 . In general, these two datasets tend to overestimate precipitation over the RRD, which is quite different from the underestimated results over most of Taiwan in Huang et al. 's (2021) study. Although both correlation coefficients pass the 99% significance test, the PERSIANN-CDR data are more suitable for the current study. To depict the large-scale atmospheric circulation associated with interannual variation in rainfall over the RRD, daily ERA-Interim reanalysis on a 0.75° latitude-longitude grid of the European Centre for MediumRange Weather Forecasts (ECMWF) (Dee et al. 2011) is utilized. The TC best-track data obtained from the Joint Typhoon Warning Center (JTWC) (https:// www. metoc. navy. mil/ jtwc/ 3 Interannual variation in late summer rainfall Figure 3a shows the year-to-year variation in total rainfall in the RRD in the late summer during the 1983-2015 period. The mean rainfall over a period of 33 years is 801 mm, and the rainfall in the wettest year (1400 mm in 1994) is almost triple that in the driest year (476 mm in 1988). It appears that the late summer rainfall in the RRD shows distinct interannual variation. To investigate the interannual variation in late summer rainfall, seven wet years (1985, 1994, 1996, 1997, 2003, 2005, and 2013) and six dry years (1983, 1988, 1991, 1998, 1999, and 2002) are determined if the seasonal total rainfall exceeds the 0.8 or -0.8 standard deviation of the seasonal total rainfall mean over 33 years, respectively. The mean rainfall in the wet years (1084 mm) is almost double that in the dry years (557 mm).
In addition to the seasonal total rainfall amount, heavy rainfall events and the frequency of heavy rainfall days are two other important quantities contributing to rainfall variation. Therefore, the number of heavy rainfall days and rainfall accumulation during the heavy rainfall days (hereafter P HRDs ) are evaluated and displayed in Fig. 3b and c, respectively. In this study, heavy rainfall days are defined as days in which one or more rain gauges record a daily rainfall amount that is greater than 50 mm•day −1 . In fact, 50 mm•day −1 is the heavy rainfall threshold currently used by the forecasters of the National Center for Hydro-Meteorological Forecasting of Vietnam (Nguyen-Thi et al. 2012). For cautious verification, it turns out that the result from the 95th percentile rainfall (47.1 mm•day −1 ) is close to the operational threshold after several percentile criteria (e.g., 99th, 95th and 90th percentiles) are compared. The average number of heavy rainfall days for 33 years is 19.6 days, which is 21.3% of the total number of days in late summer. With these few heavy rainfall days generating such a huge amount of precipitation, the average P HRDs is 565 mm, which accounts for 70.5% of the seasonal total rainfall. Interestingly, the distinct P HRDs difference between wet and dry years in Fig. 3c seems to fundamentally establish these two separated extreme wet and dry groups.
Although some years (e.g., 1994, 2001, 2006 and 2012) have both high heavy rainfall days (Fig. 3b) and accumulations (Fig. 3c), they obviously contribute less to the remaining 29.5% of the seasonal total rainfall in addition to the P HRDs , which might lead them to not qualify as wet years. Furthermore, the average P HRDs in the wet years (824 mm) are nearly 2.5 times greater than those in the dry years (337 mm), suggesting that the atmospheric environment in wet years might provide favorable conditions for the appearance and evolution of heavy rainfall events. The possible factors will be explored in the following section.

Tropical cyclones and intraseasonal oscillations
Tropical cyclones are one of the major factors that contribute to seasonal total rainfall in the RRD during the late summer (Nguyen-Thi et al. 2012;Pham-Thanh et al. 2020 Fig. 4c), the  rainfall is designated typhoon rainfall (hereafter P TCs ). Figure 4a displays the interannual variation in the number of TCs affecting the RRD during the 1983-2015 period. The number of TCs affecting the RRD (4 TCs) in wet years is significantly higher than that (1.67 TCs) in dry years in addition to the overall average of 2.88 TCs per year. In general, the TCs have a common northwestward propagation track from the East Sea-western tropical Pacific to southern China-northern ICP for both wet and dry years ( Fig. 4c and d), except for a higher TC occurrence frequency during wet years. The average P TCs is 171 mm for the 33-year period (Fig. 4b), explaining 21.3% of the seasonal total rainfall. The correlation coefficient between P TCs and the number of TCs affecting the RRD is 0.7, which is statistically significant at the 99% confidence level, indicating that the greater the number of TCs affected the RRD, the more P TCs produced. Moreover, in dry years, one TC in 1988 (TC-1988) produced only 2 mm of rainfall, and two TCs in 2002 (TC1-2002 and TC22002) generated 10.7 mm of light rainfall over the RRD, excluding no TC affecting this region in 1999. Due to the northeasterly dry air blowing from southern China to the RRD during the evolution of TC-1988 ( Fig. 5a-e) and during 18-19 August of TC1-2002 ( Fig. 5g-h), these two TCs contribute much less precipitation to the seasonal total rainfall. Note that a similar situation also applies to the lower rainfall production for the two TCs in the 1985 wet year. Although the RRD is relatively close to the TC2-2002 center, the moist southwesterly helps with a light rainfall contribution during 12-13 September (Fig. 5m, n). As a result, the P TCs in the wet years (330 mm) contribute more sizeable precipitation than those of dry years (75 mm) to the seasonal total rainfall amount. In addition to TCs, ISOs are also important factors inducing rainfall in the RRD. The 7-24-day and 30-60day variations are two dominant ISOs over the RRD during the rainy season (Truong and Tuan 2019; Tuan 2019). Tuan (2019) noted that the 7-24-day mode plays an important role in producing heavy rainfall over the RRD. However, Chen et al. (2012b) suggested that the heavy rainfall in the RRD is caused by the interplay between three monsoon modes: 30-60 days, 10-20 days, and 5 days. Applying a fast Fourier transform (FFT) bandpass filter, 7-24-day and 30-60-day modes are extracted from daily rainfall. Figure 6 shows the daily variation in total rainfall, 30-60-day and 7-24-day ISO modes during the wet and dry years-in particular, the amplitudes of both ISO modes in dry years are, in general, much smaller than those in wet years. As seen in many cases, heavy rainfall days are induced by the combined effect of both ISOs and TCs. For example, three heavy rainfall events occurred during late August-middle September 1994 (Fig. 6b), a heavy rainfall event occurred during 23-24 August 1997 (Fig. 6d), and a heavy rainfall event occurred on 14 September 1998 (Fig. 6n). In some other cases, heavy rainfall events are mainly triggered by ISOs. For instance, a heavy rainfall event appeared during 09-13 September 1985 (Fig. 6a), a heavy rainfall event appeared during 9-10 September 2003 (Fig. 6e), and a heavy rainfall event appeared on 01 August 1983 (Fig. 6h). All these heavy rainfall events occurred during the active phase of both the 7-24-day and 30-60-day modes.
To explore the role played by these two intraseasonal modes on the heavy rainfall events, the synoptic charts constructed with the 850-hPa total winds (V) associated with streamfunction (ψ), along with 7-24-and 30-60day modes superimposed with the rainfall (P) of the corresponding frequency bands, (V,ψ, P), (V, ψ, P), and (V, ψ, P), are displayed in Fig. 7.
The 7-24-day mode is denoted with ( ) and the 30-60day mode with ( ). Interestingly, two ISO-induced heavy rainfall events occurred on 12 September 1985 (Fig. 7a) and 9 September 2003 (Fig. 7b), apparently with different horizontal structures between them. On 12 September 1985, a 7-24-day mode anticyclonic anomalous center located over the southern China coastal line (Fig. 7f ) coupled with the 30-60-day mode anticyclonic anomalous center to the east of Taiwan over the northwestern Pacific (Fig. 7k) brought the moist air from the ocean toward the RRD to generate heavy rainfall there. In contrast, a 7-24day mode cyclonic anomaly over the RRD (Fig. 7g) and the newly developing 30-60-day mode cyclonic anomaly just moving into the ICP and East Sea area (Fig. 7l) jointly contributed to the RRD heavy rainfall event on 9 September 2003 (Fig. 7b). Note that the 7-24-day mode obviously contributes more rainfall than the 30-60-day mode for these two events.
Regarding the combined effect of both ISOs and TCs on heavy rainfall events, two TC cases (13 September 1996 and 24 August 1997) during wet years and one TD case (14 September 1998) during dry years could provide us with more insight into their different contributions to heavy rainfall events. In addition to a TC just reaching the southern tip of the RRD, two other TCs appeared over the Philippine Sea on 13 September 1996 (Fig. 7c). These three TCs were clearly depicted on the 7-24-day mode (Fig. 7h), whereas the welldeveloped 30-60-day mode cyclonic anomalous circulation also provides a favorable environment for these three TCs to maintain (Fig. 7m). After a TC landfall on ICP with a residual low center over northern Thailand and Myanmar, another TC appeared on the Philippine Sea on 24 August 1997 (Fig. 7d). Fascinatingly, the TC (Amber later landfall Taiwan on 28 August 1997) sandwiched by two anomalous anticyclonic circulations Page 8 of 14 Dinh et al. Terrestrial, Atmospheric and Oceanic Sciences (2023) 34:12 from the Philippine Sea approaching Taiwan is distinctively identified in the 7-24-day mode in addition to the TC landfall ICP (Fig. 7i). On the other hand, the newly formed 30-60-day mode cyclonic circulation mildly contributes rainfall to these two TCs but not to the RRD (Fig. 7n). A TD reaching the RRD (Fig. 7e) together with a TC over the northwestern Pacific south of Japan were both detected in the 7-24-day mode (Fig. 7j), while the 30-60-day mode cyclonic anomalous circulation propagated further east without any rainfall contribution to the TD over the RRD (Fig. 7o). Except for a minor rainfall contribution on 13 September 1996, the 30-60-day mode does not contribute any rainfall to the other two heavy rainfall events over the RRD.
Again, it appears that the 7-24-day mode plays a major role in these TC and TD cases.

Water vapor budget analyses
The water vapor budget with the vertically integrated water balance equation is ∂W The daily variation in total rainfall (left axis, mm•day −1 ), 30-60-day mode (mm•day −1 ), and 7-24-day mode (right axis, mm•day −1 ) in the wet (a-g) and dry (h-p) years. The rainfall induced by TCs is colored blue Page 10 of 14 Dinh et al. Terrestrial, Atmospheric and Oceanic Sciences (2023) 34:12 where W = 1 g Ps 0 qdp is the precipitable water of the atmosphere, Q = 1 g Ps 0 qVdp is the horizontal flux of water vapor, and E, P, g, p s , q, p, and V are evaporation, precipitation, gravity, surface pressure, specific humidity, pressure, and velocity vector, respectively. Following Chen (1985), the water vapor flux Q can be decomposed into rotational (Q R ) and divergent (Q D ) components, which can be measured in terms of horizontal gradients of streamfunction (ψ Q ) and potential function (χ Q ), respectively, (2) Q = Q R + Q D = k × ∇ψ Q + ∇χ Q Fig. 7 The 850-hPa total wind vector (V) synoptic charts associated with streamfunction (ψ) and superimposed with precipitation (P) in three temporal regimes: a-e total field, f-j 7-24 days ( ), and k-o 30-60 days( ). Two ISO-induced heavy rainfall events in the RRD: a 12 September 1985 and b 9 September 2003. Three combined effects of both ISOs and TCs on heavy rainfall events in the RRD: c 13 September 1996, d 24 August 1997, and e 14 September 1998. f-j Same as a-e except for the 7-24-day mode. k-o Same as a-e except for the 30-60-day mode. The contour interval of ψ is 4 × 10 6 m 2 s −1 , and ψ̂ and ψ̃ are 3 × 10 6 m 2 s −1 The primary water vapor flux is depicted by ψ Q and illustrated by (ψ Q , Q R , W), whereas precipitation is mainly maintained by the convergence of water vapor flux (−∇•Q), which can be exemplified by (χ Q , Q D , P) (Yen et al. 2011;Chen et al. 2012a).
Regarding the pronounced interannual variation in rainfall over the RRD, we should focus on considering the critical role of the water vapor budget in differentiating late summer rainfall between wet and dry years. The late summer composite charts of (ψ Q , Q R , W) and (χ Q , Q D , P) for climate, wet, and dry years are displayed in Fig. 8. Compared to the climate environment in Fig. 8a, the Southeast Asian monsoon trough is deepened and extends from the RRD toward the Philippine Sea at approximately 135°E in wet years (Fig. 8b), resulting in abundant water vapor being transported from the East Sea toward the RRD. Moreover, the effective increase in precipitation over the RRD is accompanied and maintained by the enhancement of convergent water vapor flux, as illustrated in Fig. 8e. Conversely, the monsoon trough is filled and retreats farther westward in dry years (Fig. 8c), leading to a decrease in water vapor transported to the RRD. Additionally, the convergence of water vapor flux over the RRD is noticeably weakened, which results in considerable rainfall reduction over this region (Fig. 8f ). These arguments are illustrated further in Fig. 9. An anomalous cyclonic cell of water vapor flux over the ICP and East Sea associated with the enhanced water vapor is transported toward the upstream side east of the RRD (Fig. 9a), whereas the anomalous divergent water vapor flux ∆(χ Q , Q D , P) converges water vapor toward this region, including the RRD, to maintain excessive rainfall in wet years (Fig. 9c). In contrast, an anomalous anticyclonic circulation dominates the ICP, East Sea, and Same as a-c except for χ Q (contour) , Q D (vector), and P (shaded). The contour interval of ψ Q is 1 × 10 8 kgs −1 , and χ Q is 4 × 10 7 kgs −1 Page 12 of 14 Dinh et al. Terrestrial, Atmospheric and Oceanic Sciences (2023) 34:12 Philippine Sea in dry years (Fig. 9b), which suppresses the water vapor transport toward these regions, including the RRD. The anomalous divergent water vapor flux ∆(χ Q , Q D , P) diverges out water vapor over these regions, resulting in the significant rainfall deficit over the RRD (Fig. 9d). Evidently, the interannual rainfall variation in the RRD is ascertained by the composite rainfall differences ( Fig. 9c and d), confirming the decisive role of the water vapor budget in differentiating the late summer rainfall between wet and dry years. Note that the Southeast Asian monsoon trough is a region with a large moisture flux convergence, which favors the genesis and development of TCs, TDs, and 7-24-day ISO (Chen and Yoon 2000;Fudeyasu et al. 2006;Wu et al. 2015). Because the monsoon trough deepens (fills) in the wet (dry) years, the number of TCs affecting the RRD, the P TCs , and the amplitudes of 7-24 days are enhanced (reduced), as illustrated in Sect. 4.1.

ENSO forcing
To assess whether the possible factor underlying the notable interannual variation in the RRD rainfall is associated with ENSO events, the correlation between the SST(Niño3.4) index and the late summer rainfall in the RRD is evaluated. Their correlation coefficient is 0.2 and not statistically significant at the 90% confidence level, suggesting that the late summer rainfall variability in the RRD has no significant correlation with the ENSO signal. To further substantiate this argument, the composite charts of SST anomalies in the wet and dry years are displayed in Fig. 10. The horizontal distribution of SST anomalies in the wet (dry) years resembles the El Niño (La Niña) pattern. However, the anomalous SST over the tropical western Pacific is not statistically significant in the wet years, while a small area of the anomalous SST over the tropical western Pacific is statistically significant at the 90% confidence level in the dry years. These results imply that ENSO has a minor effect on the interannual variation in late summer rainfall in the RRD, which is in good agreement with previous studies (Nguyen et al. 2014;Duc et al. 2018).
The ENSO stages associated with the wet and dry years are shown in Table 2. Although wet years are more likely associated with El Niño developing/La Niña decaying phases and dry years tend to occur during La Niña developing phases, the ENSO stages are considerably diversified in both wet and dry years. The wet years are associated with two normal (1996 and 2013), three El Niño developing (1994, 1997, and 2003), one La Niña decaying (1985), and one La Niña developing phases (2005). The dry years are accompanied by three La Niña developing (1983, 1988, andFig. 9 Late summer composite charts of Δ(ψ Q , Q R ,W) for a wet and b dry years. c, d Same as a, b except for Δ(χ Q, Q D , P); shaded areas and black vectors in a-d indicate significant differences above the 90% confidence level. The contour interval of Δψ Q is 2 × 10 7 kgs −1 , and Δχ Q is 2 × 10 6 kgs −1 Page 13 of 14 Dinh et al. Terrestrial, Atmospheric and Oceanic Sciences (2023) 34:12 1998), one La Niña (1999), and two El Niño developing phases (1991 and 2002). The findings of this study are not consistent with those of Gobin et al. (2016), who pointed out that the seasonal rainfall and number of heavy rainfall months in the RRD in La Niña are larger than those in El Niño. This contrast may be simply due to the differences in season and station selected for the studies. In their research, using only one rainfall station (Nho Quan station) to compare the difference in May-August rainfall between El Niño and La Niña (their Fig. 4) might not be suitable enough to represent the entire rainfall feature over the RRD.

Conclusion
The RRD is not only an important economic zone but also a political and cultural center in Vietnam. Thus, the interannual variation in rainfall has a significant effect on many aspects of the social economic system and human life in the region. The major rainfall in the RRD is observed in the late summer (July-September) with a remarkable interannual variation. Therefore, this study was prompted to investigate the possible factors responsible for the interannual variation in late summer rainfall in the RRD during the 1983-2015 period. The main findings of this study are highlighted as follows.
Seven wet and six dry late summers are selected during the 1983-2015 period based on ± 0.8 of the seasonal total rainfall standard deviation. Heavy rainfall days contribute 70.5% of the seasonal total rainfall amount, and the apparent heavy rainfall accumulation difference between wet and dry years essentially builds up these two distinct extreme wet and dry clusters. The TCs and 7-24-and 30-60-day ISOs are the main factors leading to modulation of the variability of rainfall in the RRD. The number of TCs affecting the RRD and the TC-induced rainfall are more (less) in the wet (dry) years, and the amplitudes of ISOs are also enhanced (reduced). Many heavy rainfall days are induced by the combined effect of both TCs and ISOs, whereas some heavy rainfall events are simply triggered by ISOs. Due to the deepening (filling) of the Southeast Asian monsoon trough, cyclonic (anticyclonic) anomalous circulation dominates over the Indochina Peninsula, resulting in abundant (depleted) water vapor being transported toward the RRD in wet (dry) years. Based on the water vapor budget analyses, the anomalous divergent water vapor flux converges (diverges) water vapor toward (out of ) the RRD to maintain excessive (insufficient) rainfall in wet (dry) years. However, the ENSO forcing has a minor influence on the interannual variation in rainfall in the RRD.   et al. Terrestrial, Atmospheric and Oceanic Sciences (2023) 34:12 Although heavy rainfall events over a large area in the RRD are mainly induced by synoptic/large-scale weather systems such as TCs and ISOs, local heavy rainfall events are often caused by afternoon/evening thunderstorms, which are mesoscale weather systems. Therefore, the characteristics of thunderstorms and how thunderstorms contribute to late summer rainfall in the RRD also deserve further analysis.