The DO exhibits non-conservative behaviour during mixing in the estuary because of the oxygen source and sink processes described in Sect. 2.1.1 (Fig. 3a). As shown in Fig. 3b, the DO concentrations are controlled by both the conservative (represented by the theory mixing curve) and the non-conservative effects (represented by the shading areas). The conservative effects are associated with physical advection and diffusion, while the non-conservative effects are due to the oxygen source and sink processes (i.e. re-aeration, the water column production, and the SOD). Quantifying the relative contributions of the respective effect is important for understanding the DO dynamics during the mixing in the estuary. In a 0-D system, the non-conservative effects can be easily estimated as the products of time intervals and rates of corresponding source and sink processes. However, in a river- and tide-dominated estuary such as the PRE, this estimation is not straightforward because of the spatial connections of each source and sink process occurring in different locations. To address this problem, the DO species-tracing method (referred to as the physical modulation method in Wang et al., 2017) was introduced and implemented in our previous study to investigate the mechanisms of hypoxia in the PRE. By dividing the DO into different DO species, the tracing method can track the DO contributed by different source and sink processes. For example, Wang et al. (2017) found that about 28 % of surface DO supplied by the re-aeration penetrated to the bottom waters and hence modulated hypoxia in the PRE. In this study, the DO species-tracing method is used to track contributions of each source and sink process to the DO dynamics and hypoxia under the different riverine input scenarios. Interactions between the oxygen source and sink processes will be investigated as well.

The DO species-tracing method is incorporated into the biogeochemical model by explicitly including four numerical oxygen species as model tracers to track the DO contributed by the lateral boundary conditions (DOBC (mgO2L-1)), air–sea re-aeration (DOREA (mgO2L-1)), water column production (DOWCP (mgO2L-1)), and SOD (DOSOD (mgO2L-1)) (Table A1). Equations of the four numerical oxygen species are given below: ∂DOBC∂t+tranDOBC=0∂DOREA∂t+tranDOREA=REA∂DOWCP∂t+tranDOWCP=WCP∂DOSOD∂t+tranDOSOD=SOD, and DO=DOBC+DOREA+DOWCP-DOSODtran(DO)=tran(DOBC)+tran(DOREA)+tran(DOWCP)-tran(DOSOD), where “tran” represents the physical transport processes, i.e. advection (u∂∂x+v∂∂y+w∂∂z) and diffusion (-∂∂xEx∂∂x-∂∂yEy∂∂y-∂∂zEz∂∂z). REA (mgO2L-1day-1), WCP (mgO2L-1day-1), and SOD (mgO2L-1day-1) are the re-aeration, water column production, and SOD, which represent the net effects of the air–sea interface, the water column, and the water–sediment interface on the oxygen, respectively. Values of these terms are obtained from the biogeochemical model at each time step.

According to Eq. (4), the DOBC concentrations are only controlled by advection and diffusion. By assigning the initial conditions and lateral boundary conditions of DOBC the same as those for DO, the mixing curve of DOBC will overlap the theory mixing curve shown in Fig. 3b. It follows that the DOBC represents the conservative effects, while the DOREA, DOWCP, and DOSOD that include the oxygen source or sink term represent the non-conservative effects.

Eqs. (8) and (9) suggest that the DO concentration and its transport flux equal the sum of the concentrations and transport fluxes of the four DO species, the validity of which has been tested and confirmed in Wang et al. (2017). They show that there is little discrepancy between the DO concentrations calculated by Eqs. (9) and (1), with 97 % of the differences within the range -2 % to 6 % of the averaged DO concentrations. The hourly time series of domain-averaged DO calculated by the DO species-tracing method also agree well with that calculated by the biogeochemical model with the R-square coefficient >0.99 and the regression slope close to 1:1. In addition, the horizontal advective fluxes, vertical advective fluxes, and vertical diffusive fluxes calculated by the tracing method are found to agree well with the respective fluxes calculated by the biogeochemical model, indicating that the tracing method is able to satisfactorily reproduce the physical transport processes of DO.

We conducted three groups of sensitivity experiments to study the response of hypoxia and oxygen dynamics to different scenarios of riverine inputs. Each group has two simulations, where the concentration of one type of the riverine inputs at eight river outlets is decreased or increased by 50 %. These simulations are named Base, RivDO-50%, RivDO+50%, RivNtr-50%, RivNtr+50%, RivPOC-50% and RivPOC+50%, with the basic information of each simulation presented in Table 1.

The Base simulation uses the realistic riverine inputs as mentioned in Sect. 2.1.1. In the Base simulation, the DO concentration in the Humen outlet, the largest river outlet in the PRE, is set to 4 mgL-1 based on observations nearby. The RivDO-50% simulation in which DO concentration from the eight outlets is decreased by 50 % represents the scenario in which hypoxia has developed in the Humen outlet, which has been reported in previous studies (e.g. He et al., 2014). In contrast, the RivDO+50% simulation, in which the DO concentration from the eight outlets is increased by 50 % to be close to that from the open boundaries, represents the scenario in which the riverine input of DO is free from the anthropogenic impact. As for nutrient simulations, the RivNtr+50% and RivNtr-50% simulations increase and decrease nutrient concentrations from all eight outlets by 50 %, respectively. The resulting riverine inputs in the two simulations will be close to the scenarios in 2050 and 1970 as reported by Strokal et al. (2015). Note that, in the nutrient simulations, the concentrations of all nutrients (including dissolved silica, dissolved inorganic phosphorus, ammonia nitrogen, and nitrite and nitrate nitrogen) are set to vary at the same percentage at which the effects of different combinations of changes in nutrients are not considered. The hydrodynamic conditions are identical in all experiments.

The hypoxic extent in different simulations is quantified by the expected hypoxic area and hypoxic volume: Hypoxic area=∑p⋅ΔsHypoxic volume=∑p⋅Δv, where Δs, Δv, and p are the area, the volume, and the hypoxic frequency of each grid cell. The hypoxic frequency p is calculated by the following: p=NhNs⋅100%, where Nh is the number of hours in which hypoxia occurs, and Ns is the total number of hours. In this study, the threshold of hypoxia is defined as 3 mgL-1 (Luo et al., 2008; Rabalais et al., 2010).

As shown in Fig. 4, hypoxia in the PRE starts to develop in April, peaks in August, and disappears in October, which is highly correlated (R2=0.91) with the annual cycle of total river discharges with a time lag of 1 month. Figure 5 shows the model-simulated DO distributions and hypoxic frequency in the bottom layer during the May–October. In May, the hypoxia is confined to the upstream of the Modaomen sub-estuary. In June, the bottom DO declines along the west coast of the PRE and the hypoxia starts to develop near Gaolan Island (see Fig. 1 for its location). The hypoxia extends eastward to near Hengqin Island in July and August. After August, the hypoxia retreats westward and almost disappears in October. Unlike the large spatial extent of hypoxia observed in the Changjiang Estuary (Wang, 2009; Wang et al., 2012) and the NGOM (Rabouille et al., 2008), hypoxia in the PRE is confined to a small area as a result of the SOD and the re-aeration (Wang et al., 2017).

In 2006, oxygen observations are only available in July and August, which have demonstrated the occurrence of hypoxia. No observations are available for validating the model-simulated hypoxia in other months. We have collected and analysed the oxygen observations from 1993 to 2009. However, the available observations are insufficient to resolve the annual cycle of hypoxia in the PRE. To our knowledge, there are currently few studies on the annual cycle of hypoxia in the PRE due to the scarcity of observations. Discussions in this study therefore focus on hypoxia in July–August when the distinct hypoxia was both observed and simulated by the model. Another motivation of focusing on July and August is that these 2 months are among the typical wet seasons in the PRE (Fig. 4b), which is in line with our study on the effects of riverine inputs.

Figure 6 shows the comparisons of bottom DO concentrations and hypoxic frequency during July–August for different DO simulations. In the RivDO-50% simulation, the spatial distribution of bottom DO is similar to that in the Base simulation except that hypoxia additionally occurs near the river outlets due to the inputs of low-oxygen waters from the upstream river network (Fig. 6b, e). We have also examined the impact of reducing riverine DO in regions farther away from the river outlets by excluding the hypoxic region near the river outlets. In this case the expected hypoxic area in RivDO-50% is only 2 % higher than that in the Base simulation, while the hypoxic volume is 26 % higher (Fig. 7a), indicating that the thickness of hypoxic water is greatly increased in RivDO-50%. In contrast, the RivDO+50% simulation yields higher bottom DO concentrations, leading to reductions in hypoxic area and volume by 23 % and 30 % (Fig. 7a).

Figure 7b, c, d further show the changes in each DO species averaged over the bottom layer of the high-frequency zone for different simulations relative to the Base simulation. The high-frequency zone here is defined as the area encompassed by the 10 % isoline of July–August averaged hypoxic frequency and is denoted by the white contour in Fig. 8. To provide more insights into the response of different oxygen species to riverine inputs, the spatial distributions of DOBC and DOREA in the bottom water are shown in Fig. 8. Differences in DOWCP and DOSOD concentrations between simulations are much smaller and hence omitted here.

Halving the riverine DO inputs in the RivDO-50% simulation yields lower DOBC concentrations but higher DOREA in the bottom water (Figs. 7b and 8). The decrease in DOBC concentrations is largely balanced by the increase in DOREA concentration in RivDO-50% simulation, which ultimately reduces the magnitude of changes in hypoxic extent responding to the reduced riverine DO input. On the contrary, the RivDO+50% simulation leads to higher DOBC concentrations (Figs. 7b and 8c) but lower DOREA in the bottom water (Figs. 7b and 8f), which together reduces the net increase in bottom DO (Fig. 7b).

The re-aeration buffering effects can be explained by the surface apparent oxygen utilization (AOU, the difference between the actual DO concentration and its saturation at a known temperature and salinity). As shown in Eq. (2), the re-aeration is a function of surface AOU. Halving the riverine DO inputs decreases the DO concentrations in entire water column and therefore increases the surface AOU, which ultimately results in an increase in re-aeration rate. In our model simulations, the surface domain-averaged saturated DO concentration is ∼7.42 mgL-1, while the surface domain-averaged DO concentration in the Base and RivDO-50% simulations are 6.81 and 6.57 mgL-1. The surface AOU for the RivDO-50% simulation is 39 % higher than that for the Base simulation, which is consistent with the 38 % increase in re-aeration rate for the RivDO-50% simulation.

As shown in Fig. 7a, perturbing riverine nutrient inputs by 50 % has a relatively weak impact on hypoxic extent (changes are within 10 %). Among all the oxygen sink and source processes, the water column production and re-aeration are the two that are most sensitive to variations in nutrient inputs. Halving the nutrient inputs by 50 % in the RivNtr-50% simulation remarkably reduces the primary productivity and water column production rates, which in turn increases the surface AOU that facilitates the re-aeration. The increase in DOREA in the bottom water via vertical diffusion offsets ∼60 % of the total DO loss associated with the reduced nutrient inputs in the high-hypoxic-frequency zone (Fig. 7c). As a result, the hypoxic area and hypoxia volume only increase by about 10 % in the RivNtr-50% simulation relative to the Base simulation. In contrast, the RivNtr+50% simulation yields higher water column production and a lower re-aeration rate, while the changes in the two balance each other out, and hence the simulation only leads to 4 % and 6 % decreases in hypoxic area and hypoxic volume relative to the Base simulation.

As shown in Fig. 7, perturbing the riverine inputs of POC by 50 % leads to significant changes in DO concentrations and hypoxic extent. In the RivPOC-50% simulation, the DO concentration increases by 0.56 mgL-1 in the high-hypoxic-frequency zone and the hypoxic area and hypoxic volume decrease by 50 % and 64 %. On the contrary, RivPOC+50% simulation leads to a significant decrease in the DO concentration, causing an extension of hypoxic area by 64 % and a doubling of hypoxic volume (Fig. 7a).

As to oxygen dynamics, the RivPOC-50% simulation leads to a significant decline in the SOD rate (Fig. 7d) and increase in the water column production rate (Fig. 7d) as a result of the lower inputs of POC weakening the light attenuation in PRE. The combination of lower SOD and higher water column production rates increases oxygen concentration by 0.81 mgL-1 in the bottom waters of the high-hypoxic-frequency zone (Fig. 7d). However, decreasing the riverine inputs of POC in the RivPOC-50% simulation simultaneously weakens the re-aeration due to the decreased surface AOU. As a result, nearly 27 % of the increased DO concentrations is offset by the decreased re-aeration in the high-hypoxic-frequency zone. In contrast, increasing the riverine inputs of POC in the RivPOC+50% simulation increases the SOD rates but weakens the water column production rates, which consequently reduces bottom water oxygen; nevertheless, 26 % of the oxygen loss is offset by the enhanced re-aeration in this simulation.

To understand the impact of changing the riverine inputs of POC on the water column production rates, we further examine how phytoplankton growth responds to varying riverine inputs of POC. The equation for the phytoplankton growth rate GP (day-1) can be written as follows: GP=GPmax⋅G(T)⋅G(I)⋅G(N), where GPmax represents the maximum growth rate at the optimum conditions (day-1); G(T), G(I), and G(N) represent the limitations by temperature, light, and nutrients. These limitation coefficients are non-dimensional scale values ranging from 0 to 1, with 0 representing no growth and 1 no limitation. The two POC simulations and the Base simulation have identical physical processes and hence the same temperature limitation. Table 2 shows that changing the riverine inputs of POC has little impact on nutrient limitation but leads to large variations in light limitation, suggesting that the riverine inputs of POC can significantly affect the phytoplankton growth through light shading effects.

Considering the important role of re-aeration in POC simulations, we further quantify how re-aeration responds to the SOD by conducting a diagnostic analysis of DOSOD in July and August (Fig. 9). Three vertical layers are defined: the upper layer (top 20 % of the water column), middle layer (middle 60 % of the water column), and bottom layer (20 % of the water column above the sediment). Note that horizontal diffusion is omitted in the diagnostic analysis because its magnitude is much smaller than other terms. Diagnostic analysis of other DO species can be seen in Figs. 11 and 12 of Wang et al. (2017). As shown in Fig. 8, the SOD can affect the DO concentrations in the upper layer indirectly through the interactions with the vertical advection, the vertical diffusion, and the horizontal advection as explained below. First, the SOD consumes bottom DO by 0.53 mgL-1day-1 and decreases the upward advective DO fluxes, reaching the upper layer by 0.34 mgL-1day-1. Second, the deoxygenation induced by SOD can increase the vertical DO gradient and facilitate the downward vertical diffusion of oxygen by 0.02 mgL-1day-1 from the upper layer. Finally, the decreased upper DO concentrations affect the horizontal outfluxes of DO and ultimately result in a higher net horizontal advective flux of 0.21 mgL-1day-1. Consequently, the net effect of the SOD on the upper DO is 0.15 mgL-1day-1, which causes a decline of 2.22 mgL-1 in DO concentrations in the surface layer. Figure 9 shows contributions of the SOD and the water column production rates to the changes in surface DO. The positive values of Δ(-DOSOD) and Δ(DOWCP) represent the increased DO concentrations due to the decrease in the SOD and increase in the water column production. In the RivPOC-50% simulation, decreasing the POC input decreases the SOD rate but increases the water column production rate, which in combination increase the DO concentrations in the surface layer. As a result, the re-aeration in the RivPOC-50% simulation is weakened, especially in the west of the lower estuary (Fig. 10a).

In this study, we performed a series of numerical experiments together with the application of the DO species-tracing method to study the effects of different anthropogenic inputs on hypoxia and oxygen dynamics in the PRE. This study is the first attempt to quantitatively estimate the interactions between each DO source and sink processes (e.g. DO buffering effects) under the anthropogenic perturbations in the PRE. The year 2006 was selected because distinct hypoxia was observed, and the available observations are relatively more abundant than in other years. In addition, it is a wet year with the annual averaged total river discharge over 10 000 m3s-1 (interannual variations of total discharges during 1999–2010 in the PRE can be seen in Fig. S1 in the Supplement). Discussions only focus on hypoxia in July and August 2006 when oxygen observations are available. However, conclusions drawn here should be applicable to other years because previous studies have reported similar locations and spatial extents of hypoxia in other years (Lin et al., 2001; Zhang and Li, 2010). The mechanisms underlying hypoxia in summer 2006 found here are also consistent with previous studies on hypoxia in this region, such as the strong re-aeration (Zhang and Li, 2010), the dominance of the SOD (Yin et al., 2004; Zhang and Li, 2010), and the important contributions of the allochthonous POC (Hu et al., 2006; Yu et al., 2010).

Numerical experiments show that hypoxia in the PRE is more sensitive to the riverine inputs of POC rather than the nutrient loading (Fig. 6a). This is distinct from other hypoxic systems such as the Chesapeake Bay (Hagy et al., 2004) and the NGOM (Justić et al., 2003) that have observed close relation between nutrient loading and hypoxia. We attribute this to the different characteristics of hypoxia in these systems (Table 3). In the Chesapeake Bay, the dominant oxygen sink leading to hypoxia is the water column respiration, which is associated with high primary productivity stimulated by the excessive nutrient loading (Hong and Shen, 2013). In contrast, the bottom water DO depletions are dominated by the SOD in the NGOM (Murrell and Lehrter, 2011; Yu et al., 2015b) and the PRE (Yin et al., 2004; Zhang and Li, 2010). Hypoxia in the NGOM can be well simulated with appropriate parameterization of SOD while neglecting the water column processes (Yu et al., 2015a).

However, the relative contributions of autochthonous POC (i.e. the POC generated by settling of phytoplankton after death) versus allochthonous POC to the SOD are different in the NGOM and the PRE. In the NGOM, the autochthonous POC serves as the major source of POC (Green et al., 2006), which means that increasing the nutrient loading can facilitate the SOD by increasing the depositional fluxes of dead phytoplankton and ultimately promote the formation of hypoxia. In the PRE, the relative contributions of autochthonous versus allochthonous POC inputs to the SOD and hypoxia have long been a topic of debate. Some studies suggest that allochthonous POC dominates in wet seasons due to the high river discharges (Ye et al., 2017; Yu et al., 2010), while others argue that autochthonous inputs can also play an important role (Guo et al., 2015; Su et al., 2017). Previous studies (Guo et al., 2015; Hu et al., 2006; Ye et al., 2017) show that the ratios of allochthonous POC to autochthonous POC have distinct spatial and seasonal variabilities in the PRE. Generally, the allochthonous contributions dominate inside the estuary and gradually decrease seaward as the impact of the river discharges weakens (Hu et al., 2006; Jia and Peng, 2003). In our study, the high-hypoxic-frequency zone is near the Modaomen sub-estuary, which receives high depositional fluxes of allochthonous POC. Therefore, the allochthonous inputs have dominant contributions to the SOD and summer hypoxia in the high-hypoxic-frequency zone.

The different POC sources in the NGOM and the PRE might be explained by their distinct physical and biogeochemical processes (Table 4). Firstly, the relative magnitudes of autochthonous versus allochthonous POC are different in the two hypoxic systems. The allochthonous inputs of POC in the NGOM and PRE are at the same magnitude: 3.8×106 tyr-1 (Wang et al., 2004) and 2.5×106 tyr-1 (Zhang et al., 2013). However, the autochthonous inputs in the two systems are different. According to our model results, the primary productivity in the PRE is 310.8±427.5 mgCm-2day-1, which is within the range of 183.9–1213 mgCm-2day-1 reported by Ye et al. (2014). However, the observed primary productivity in the NGOM ranges from 330 to 7010 mgCm-2day-1 (Quigg et al., 2011), the upper range of which is much higher than that in the PRE. The relatively lower primary productivity in the PRE is a result of the stronger phosphorus limitation (DIN:DIP ratio of 126 in the PRE versus 33 in the NGOM) and the light shading effects of high suspended sediment concentrations. The dominant role of the allochthonous POC in highly turbid estuaries has been reported in previous studies (Fontugne and Jouanneau, 1987; Middelburg and Herman, 2007). Secondly, the fates of the allochthonous POC in the two systems are different due to the difference in the residence time between the systems. In the PRE, the residence time is 3–5 days during the wet season, which is much shorter than in the NGOM (∼95 days). It follows that the allochthonous POC cannot be degraded completely and hence can significantly fuel the SOD in the PRE. The difference in surface salinity distribution can also be used to explain the different relative roles of allochthonous POC in the two hypoxic systems. Previous studies have suggested a good correlation between the relative contributions of allochthonous POC and the salinity, namely that the contributions of allochthonous POC generally decrease as salinity increases seaward (Fontugne and Jouanneau, 1987; Middelburg and Herman, 2007). Similar correlations have also been reported in the PRE (Yu et al., 2010) and NGOM (Wang et al., 2004). The surface salinity in the high-hypoxia-frequency zone varies between 0 and 10 psu during the wet season based on our model results, while the surface salinity in the hypoxic zone of the NGOM is saltier than 24 psu, even in the wet season, according to the results from a well-validated physical model in Yu et al. (2015a). This implies a more important role of allochthonous POC in the PRE than in the NGOM. Finally, compositions of the allochthonous POC are different in the two hypoxic systems. Zhang and Li (2010) mentioned that contributions of labile POC to the allochthonous POC are higher in the PRE than in the NGOM.

Model results also highlight the importance of re-aeration in regulating DO dynamics and hypoxia migration in the PRE. On the one hand, based on our previous study by applying the same physical–biogeochemical model and tracing method as here (Wang et al., 2017), the re-aeration together with the SOD are the most important process controlling DO dynamics. Nearly 28 % of the surface DOREA can reach the bottom layer, exerting a strong constraint on the spatial extent and duration of hypoxia in the PRE. When turning off the re-aeration, the high SOD will lead to persistent hypoxia covering an area of over 3000 km2 in the PRE. On the other hand, the re-aeration responds rapidly to the perturbations of riverine inputs, which moderates the DO changes impacted by the perturbations. A conceptual diagram of these processes is illustrated in Fig. 11. Compared with other hypoxic systems, the re-aeration in the PRE is of great importance because of the shallow topography and the strong re-aeration, which enable the surface oxygen supplied by re-aeration to penetrate to the bottom water. Re-aeration can thus greatly influence spatial migration of hypoxia under the perturbations of riverine inputs in the PRE. Furthermore, the shallow topography in the PRE allows the bottom SOD to indirectly affect the surface DO by decreasing the upward DO advective fluxes, which also facilitates strong re-aeration in the PRE. As we have described in Sect. 3.3, the bottom SOD can lead to a decrease in surface DO concentrations by 2.22 mgL-1. If turning off the SOD, the surface AOU would change from 0.61 to -1.61 mgL-1, causing a change of re-aeration from 0.55 to -1.45 mgL-1day-1. This indicates that the SOD could shift the role of re-aeration from a strong oxygen sink to a strong source.

One counter-example to the shallow PRE is the NGOM, in which the hypoxic zone is deeper such that the surface water and bottom hypoxic water are detached. Also, the observed SOD varies from 0.06 to 0.70 gm-2day-1 in the summer season in the NGOM (Murrell and Lehrter, 2011), which is much lower than those in the PRE (0.72–3.89 gm-2day-1; Chung et al., 2004). These characteristics together with the supersaturated DO concentrations in the surface water due to the high primary productivity make the re-aeration primarily an outgassing process in the NGOM (Yu et al., 2015b).

In the other hypoxic system, the Chesapeake Bay as described earlier, extended the discussion on the importance of re-aeration is limited by a lack of observations and relevant studies of re-aeration. Nevertheless, according to our results, we can speculate that the re-aeration might be quite important in the Chesapeake Bay because the strong water column respiration can draw down the surface DO concentrations and enhance the re-aeration. However, the penetration of the oxygen supplied by re-aeration to the bottom layer is hard to estimate without applying the DO species-tracing method like in our study or method, similarly to the Chesapeake Bay. In general, more relevant studies are required to examine the role of the re-aeration on hypoxia in the Chesapeake Bay.