A numerical analysis of biogeochemical controls with physical 1 modulation on hypoxia during summer in the Pearl River Estuary 2

11 As an important biogeochemical indicator of aquatic ecosystem, dissolved oxygen (DO) is affected by the 12 boundary conditions and biogeochemical processes. Biogeochemical processes can affect DO concentrations by 13 directly consuming or generating oxygen locally, or through changing the DO fluxes from the ambient water bodies. 14 However, the latter mechanism is still unclear. In this study, a novel method named physical modulation of 15 biogeochemical terms is therefore proposed and coupled to a physical-biogeochemical model to investigate their 16 contributions to the hypoxia during the summer of the Pearl River Estuary (PRE). 17 According to the result of modulation method, re-aeration and sediment oxygen demand are the most important 18 biogeochemical processes, and determine the distribution, the spatial extent, and the duration of hypoxia in the PRE. A 19 DO balance analysis is conducted and reveals that although the re-aeration occurs on the air-sea interface, the 20 reoxygenation leads to a strong DO gradient form between the surface and lower layers. As a result, the majority (89 %) 21 of oxygen entering the surface layer from the atmosphere will be transported to the lower layer through the vertical 22 diffusion, and 28 % eventually reach the bottom layer. Similarly, after consuming the bottom DO, sediment oxygen 23 demand facilitates the downward DO flux of vertical diffusion and decreases the upward DO flux of vertical advection. 24 Under the modulation of physical processes, sediment oxygen demand causes a most significant decrease in DO 25 concentration by 4.31 mg L in the bottom of the HFZ (a high frequency zone of hypoxia located off the Modaomen 26 sub-estuary) and the west of lower estuary. However, the re-aeration supplements an average of 4.84 mg L DO on the 27 west of lower estuary, which leads to hypoxia only occur in HFZ. Numerical experiments show that turning off the 28 re-aeration leads to an expansion of hypoxic area from 237 km to 2203 km and results in a shift of hypoxic center to 29 the west of lower estuary. Moreover, a persistent hypoxia (hypoxic frequency>80 %) is observed in the west of lower 30 estuary. When compared with re-aeration and sediment oxygen demand, photosynthesis and water column respiration 31 have fewer effects on DO conditions. In the bottom of the HFZ, photosynthesis exceeds the water column respiration 32 and eventually supplements DO concentration by 0.98 mg L, causing an increase of hypoxic area to 591 km. 33 34 Biogeosciences Discuss., doi:10.5194/bg-2016-454, 2016 Manuscript under review for journal Biogeosciences Published: 21 November 2016 c © Author(s) 2016. CC-BY 3.0 License.


Abstract. 11
As an important biogeochemical indicator of aquatic ecosystem, dissolved oxygen (DO) is affected by the 12 boundary conditions and biogeochemical processes. Biogeochemical processes can affect DO concentrations by 13 directly consuming or generating oxygen locally, or through changing the DO fluxes from the ambient water bodies. 14 However, the latter mechanism is still unclear. In this study, a novel method named physical modulation of 15 biogeochemical terms is therefore proposed and coupled to a physical-biogeochemical model to investigate their 16 contributions to the hypoxia during the summer of the Pearl River Estuary (PRE). 17 According to the result of modulation method, re-aeration and sediment oxygen demand are the most important 18 biogeochemical processes, and determine the distribution, the spatial extent, and the duration of hypoxia in the PRE. A 19 DO balance analysis is conducted and reveals that although the re-aeration occurs on the air-sea interface, the 20 reoxygenation leads to a strong DO gradient form between the surface and lower layers. As a result, the majority (89 %) 21 of oxygen entering the surface layer from the atmosphere will be transported to the lower layer through the vertical 22 diffusion, and 28 % eventually reach the bottom layer. Similarly, after consuming the bottom DO, sediment oxygen 23 demand facilitates the downward DO flux of vertical diffusion and decreases the upward DO flux of vertical advection. 24 Under the modulation of physical processes, sediment oxygen demand causes a most significant decrease in DO 25 concentration by 4.31 mg L -1 in the bottom of the HFZ (a high frequency zone of hypoxia located off the Modaomen 26 sub-estuary) and the west of lower estuary. However, the re-aeration supplements an average of 4.84 mg L -1 DO on the 27 west of lower estuary, which leads to hypoxia only occur in HFZ. Numerical experiments show that turning off the 28 re-aeration leads to an expansion of hypoxic area from 237 km 2 to 2203 km 2 and results in a shift of hypoxic center to 29 the west of lower estuary. Moreover, a persistent hypoxia (hypoxic frequency>80 %) is observed in the west of lower 30 estuary. When compared with re-aeration and sediment oxygen demand, photosynthesis and water column respiration 31 have fewer effects on DO conditions. In the bottom of the HFZ, photosynthesis exceeds the water column respiration 32 and eventually supplements DO concentration by 0.98 mg L -1 , causing an increase of hypoxic area to 591 km 2 . 33 34

Introduction 1
Since dissolved oxygen (DO) is essential for the survival of aerobic aquatic organisms, hypoxia, a condition 2 where the water body is deprived of adequate oxygen is detrimental to the aquatic ecosystems in terms of the 3 behavioral, physiological, and productive impacts, such as reduced growth, mortality, and loss of reproductive capacity 4 (Rabalais et al., 2010). In recent decades, hypoxia has been dramatically exacerbated by human activities. As a result, 5 there have been over 400 coastal hypoxic zones covering more than 245,000 km 2 in the world (Diaz and Rosenberg,6 2008). 7 The formation and maintenance of hypoxia is related to the interactions of physical and biogeochemical processes. 8 Therefore, human activities that change biogeochemical processes affect DO conditions. For example, the excessive 9 nutrient loads will stimulate the growth of phytoplankton and hence promote photosynthesis to produce more oxygen. 10 However, phytoplankton will also use more oxygen for respiration to meet its growth. Moreover, the debris generated 11 after the death of phytoplankton will deposit to the sediment along with terrestrial particulate organic matter and form 12 the sediment oxygen demand. The statistical linkage between nutrient loads and the spatial extent of hypoxia is well 13 documented in the Chesapeake Bay (Hagy et al., 2004) and the northern Gulf of Mexico . In the 14 Pearl River estuary, a study conducted by Zhang and Li (2010) illustrates the input of terrestrial particulate organic 15 matter will affect sediment oxygen demand, and hence affect DO concentration. Physical processes affect DO 16 conditions by changing the horizontal and vertical DO transport. For example, the hypoxia in the Changjiang estuary is 17 related to the inflow of Taiwan Warm Current with low-oxygen level (Wang, 2009;Wang et al., 2012). In the 18 Chesapeake Bay, the summer hypoxia is caused by the stratification which inhibits the downward DO transport 19 through the vertical diffusion (Du and Shen, 2015). In addition, physical processes can regulate DO concentration by 20 changing the nutrient distributions. In some coastal areas, the upwelling will bring the bottom nutrients to the surface 21 layer and promote the primary productivity, followed by the occurrence of hypoxia (Rabalais et al., 2010). 22 Since physical and biogeochemical processes are highly interacted, it is essential to distinguish their contributions 23 to the DO conditions. In the Chesapeake Bay, Shen et al. (2013) use two timescales to quantify the physical and 24 biogeochemical processes concerning the DO conditions. Accordingly, they suggest that the physical processes 25 accounts for 88 % of variations in DO distribution in the hypoxic zone (Du and Shen, 2015). In addition, the DO 26 budget analysis is commonly used to investigate the contributions of physical and biogeochemical processes to 27 changes of DO ( . Biogeochemical processes exert 28 effects on DO conditions by two mechanisms, one is by directly consuming or producing oxygen locally, and the other 29 is by changing the DO fluxes from the ambient water bodies. The latter mechanism is understood as the contributions 30 of ambient biogeochemical processes on DO concentrations. Take the re-aeration as an example, in spite of its 31 occurrence on the air-sea interface, the oxygen entering the surface layer through the re-aeration will be transported to 32 lower layers and change DO concentration. Given this mechanism remains unclear, it is necessary to be investigated 33 since it may play an important role in DO conditions and provide a further insight into the DO dynamics. 34 The Pearl River is the second largest river in terms of the river discharge with an annual averaged discharge of 35 10,524 m 3 s -1 , among which 80 % is delivered during the wet season (Ou et al., 2009;Zhang and Li, 2010). The river 36 network includes Beijiang (North River), Xijiang (West River), Dongjiang (East River), Liuxi River, and Tan River,  1 covering a drainage of 4.5*10 5 km 2 . Fresh water from the river network is emptied into the Northern South China Sea 2 (NSCS) through the eight outlets, namely Humen, Jiaomen, Hongqili, Hengmen, Modaomen, Jitimen, Hutiaomen, and 3 Yamen. The Pearl River Estuary (PRE) is located on the Northern South China Sea and adjacent to the Pearl River 4 network. The PRE consists of four sub-estuaries, including the Lingdingyang, Modaomen, Jitimen, and Huangmaohai 5 sub-estuary, among which the Lingdingyang is the most principal and largest estuary with an area of almost 2,000 km 2 . 6 The PRE is a complex estuarine system characterized by the shallow bank in the west of the estuary with the depth of 7 less than 5 m and two deep channels with the depth more than 10 m and the width of 1km. In the summer, the physical 8 processes is influenced by the huge river discharge and southeasterly wind. Thus, the nutrient and DO distributions are 9 influenced by the combination of complicated dynamical and topographic characteristics to a large extend. although the hypoxia in the PRE has been observed for many years, the mechanisms remains unclear. 17 Motivated by these previous studies, the purpose of this study is introducing the physical modulation of 18 biogeochemical terms to investigate the characteristics of hypoxia in the PRE, including the distribution of hypoxia, 19 the major processes controlling DO balance, and the reasons for why the hypoxia in the PRE occurs in the specific area 20 and is not severe. The manuscript is organized as follows. In section 2, we describe the physical and water quality 21 model used in this study, as well as the theory and methodology of modulation method. In section 3, we validate the 22 coupled model and the modulation method. Section 4 provides the results and discussions. Summaries and conclusions 23 are given in section 5. 24

Physical model 26
In order to accurately simulate the dynamic processes forced by a multichannel river network, we use a 1-D and 27 3-D coupled physical model (Hu and Li, 2009;Hu et al., 2011) which integrates the Pearl River network, the Pearl 28 River Estuary (PRE), and its adjacent coastal waters in an overall modeling system. Specifically, a 1-D river network 29 model is dynamically coupled with a 3-D coastal model for the PRE using an explicit coupling approach. The eights 30 river outlets (see Fig. 1a) serve as the coupling interface between the 1-D and the 3-D model domains. These two 31 models run in parallel, and their model quantities are exchanged across the coupling interface during runtime. At each 32 time-step, the 3-D model utilizes the simulated discharge obtained from the 1-D model as the river boundary forcing 33 and the 3-D model sends simulated water levels to the 1-D model as the downstream boundary forcing for the next 34 time-step. A detailed description on the methodology and implementation of the coupled model can be found in Hu and 35 The 1-D model uses a Preissmann implicit scheme and an iterative approach to solve the Saint Venant equations 2 of mass and momentum conservation. A salinity transport module is also incorporated in the model. For details on the 3 1-D model and its governing equations, see Hu and Li (2009). The 1-D model simulates 299 major branches of the 4 river network with 1726 cross-sections and 189 nodes (see Fig. 1b). For the upstream boundaries, the real-time river 5 discharge or water levels with zero salinity are specified at Shizui, Gaoyao, Shijiao, Laoyagang, and Boluo (see Fig. 1a  6 for their locations). The initial conditions of water level and salinity are set to be zero homogeneously. The time step is 7 5 s for the 1-D hydrodynamic. 8 The 3-D model utilized is the Estuaries and Coastal Ocean Model with Sediment Module (ECOMSED) 9 (HydroQual, 2002), which has been extensively used in estuaries. In this study, the water quality model used is the Row-Column Aesop (RCA). RCA is developed by HydroQual 27 (HydroQual, 2004) and is able to directly interface with ECOM and ECOMSED. In the water column, RCA can 28 simulate five interacting systems including the carbon cycle (C), the nitrogen cycle (N), the phosphorus cycle (P), the 29 silicon cycle (Si), and dissolved oxygen (DO) (see Fig. 2a). In addition, a sediment flux module is incorporated to 30 RCA, which simulates the depositional flux of particulate organic matter (POM, including PON, POP, and POC), 31 diagenesis process in the sediment converting POM to dissolved matters, and transportation of dissolved matter from 32 sediment to overlying water (see Fig. 2b). Interactions between water column and sediment can be simulated internally In the wet seasons of the PRE, the high concentration of sediment will limit the growth of phytoplankton by 1 reducing the light penetration in the water column. In this case, the RCA is modified to simulate the shading effects of 2 sediment (Toro, 1978): Where Ke represents the light extinction coefficient (1 m -1 ), N represents the sediment concentration (mg L -1 ), D 5 represents the concentration of POM (mg L -1 ), and P represents the concentration of Chlorophyll-α (μg L -1 ). The 6 concentration of sediment is simulated by a sediment transport module which is incorporated to our physical model 7 (HydroQual, 2002;Hu and Li, 2009). 8 The equation for each water quality variable is given by: 9 Where represents concentrations of each water quality variables. , , and represent the two horizontal 11 coordinates and single vertical coordinate. , , and represent velocity components in the , , and 12 coordinates, respectively. , , and represent dispersion coefficients. The S parameter represents sources and 13 sinks. W represents external inputs of nutrients and oxygen-demanding materials which come from municipal and 14 industrial discharges, river discharges, and atmospheric deposition. 15 For the dissolved oxygen, the sources are re-aeration (Rea) for the air-sea interface and photosynthesis (Phot), the 16 sinks are nitrification (Nitri) of ammonia, oxidation (Oxid) of dissolved organic matter and dissolved sulfide, 17 respiration (Resp) by phytoplankton, and sediment oxygen demand (SOD) for the water-sediment interface. In this 18 study, we combine nitrification, oxidation, and respiration into water column respiration (WCR) to represent the total 19 DO depletion in the water column. The equation describing these kinetic processes is given as: 20 DO  Where a represents the surface mass transfer coefficient (m day -1 ) for re-aeration; a , 14,15 , 20,0 , 21,0 , 22,0 , 28 23,0 , O 2 * represent temperature coefficient; sat represents saturation concentration of dissolved oxygen (mg O 29 L -1 ); OC represents oxygen to carbon ratio; NH 4 represents preference for ammonium uptake by phytoplankton; 30 P represents specific phytoplankton growth rate (day -1 ); c represents phytoplankton biomass (mg C L -1 ); NO 23  represents oxygen to carbon ratio for nitrate uptake; ON represents oxygen to nitrogen ratio; 14,15 represents 1 nitrification rate at 20 O C (day -1 ); nitri , DO , DO O 2 * represents half saturation constant for oxygen limitation (mg O 2 L -1 ); 20,0 , 21,0 , 22,0 , 23,0 represents oxidation rate for RDOC, LDOC, ReDOC, and ExDOC at 20 O C (day -1 ), 3 whereby RDOC, LDOC, ReDOC, and ExDOC represent labile dissolved organic carbon, refractory dissolved organic 4 carbon, reactive dissolved organic carbon, and algal exudate dissolved organic carbon; LDOC represents Michaelis 5 constant for LDOC (mg C L -1 ); Pc represents half saturation constant for phytoplankton limitation (mg C 6 L -1 ); PR ( ) represents temperature corrected algal respiration rate (day -1 ); represents transfer coefficient between 7 the sediment and overlying water; sed represents concentration of dissolved oxygen in the sediment (mg O L -1 ); 8 and O 2 * represents oxidation rate of dissolved sulfide. 9 The simulation periods of water quality model are the same as the physical model with a time-step of 30 s. Initial

Physical modulation of biogeochemical terms 21
Since DO concentration is affected by boundary conditions and biogeochemical processes, the DO flux 22 transported by dynamical processes actually contains two kinds of effects originating from these two processes. 23 However, since traditional DO balance analysis does not distinguish between these two factors, we propose a method 24 named the physical modulatation of biogeochemical terms to simulate these two processes and investigate the 25 contributions of these two processes to DO conditions. The method assumes that DO can be divided into two separated 26 parts, including the simulated DO concentration forced by either boundary conditions ( BC ) or biogeochemical 27 processes ( Bio , the increase or decrease in DO concentration due to the effects of biogeochemical processes). 28 Equations of DO, BC , and Bio can be given as: 30 Where ADV represents the process of advection ( + + ); DIFF represents the process of diffusion 2 ( ( ) + ( ) + ( ) ); and represents biogeochemical sources and sinks which are calculated with 3 reference to Eq. (3), including re-aeration, photosynthesis, water column respiration, and sediment oxygen demand. 4 Therefore the can be estimated by: 5 Where Rea , Phot , WCR , and SOD represent the increase or decrease in DO concentration due to the 7 effects of re-aeration, photosynthesis, water column respiration, and sediment oxygen demand, respectively. These four 8 variables are simulated according to Eq. (7) except that ± represents each corresponding biogeochemical terms, 9 respectively. The negative values of WCR , and SOD indicate that water column respiration and sediment oxygen 10 demand are oxygen-consuming processes. The detailed derivations of Eq. (4) are given as follows. 11 According to the mathematical induction, we assume the Eq. (4) is satisfied in the time step i: 12 Then the DO concentration, BC , and Bio in the time step i+1 can be calculated by discretizing the Eq. (5)- (7): 14 Substituting Eq. (9) into Eq. (10), the DO concentration can be represented as: 18 Thus it can be concluded that in each time step, DO concentration satisfies the Eq. (4). Furthermore, the DO 24 increments can be divided into three parts as Eq. (14) shows: Where ∆ × [− ( Bio ) + ( Bio ) ] represents the contributions of ambient biogeochemical processes. 30 This term indicates the mechanism that biogeochemical processes can indirectly affect the DO concentration by processes for DO transport. 1 In this paper, we add five additional variables to the water quality model (RCA), namely BC , Rea , Phot , 2 WCR , and SOD . The same initial and boundary conditions are used for computing BC as used for DO 3 simulations. Rea , Phot , WCR , and SOD are set to be zero for initial and boundary conditions. The ± 4 represents each biogeochemical process associated with DO and is calculated at each time step by Eq. (3). In addition, 5 further validations of this modulation method against model results will be given out in the following section. Data sets used for model validation include hourly water level data from 8 tidal gauge stations and cruise 9 observations conducted in July and August 2006 (see Fig. 3a). These tidal gauge stations are located in Jiaomen, 10 Hengmen, Modaomen, Jitimen, Hutiaomen, Yamen, Zhuhai, and Wanshan Island. The cruise data set includes profiles 11 of salinity (black circles), temperature (black circles), and dissolved oxygen (DO) (red crosses). 12 As shown in Fig. 3b, the Taylor diagram shows a statistical evaluation of our physical and water quality coupled 13 model in terms of dynamical variables (e.g. water level, salinity, and temperature) and DO. Grey isolines provide a 14 measure of skill, which is represented by centered root-mean-square difference (RMSD) normalized by the observed 15 values. The distance between the observed point (red pentagram) and each simulated point is proportional to the 16 RMSD. The angular coordinate gives the magnitude of correlation with observations, and the radial coordinate 17 represents standard deviation of both observed and simulated values. The observation represents the perfect model 18 skills to reproduce observations with correlation 1, normalized RMSD 0, and normalized standard deviation 1. 19 The validation indicates that our coupled model is robust to simulate both dynamical and biogeochemical 20 processes regardless of their complexity. Specifically, the model simulates water levels at eight tidal gauge stations 21 (red triangles) and salinity (orange diamonds) distribution well, since the normalized RMSD is considerably small reproduces the observed spatial distribution in DO concentrations and captures the observed hypoxia (see Fig. 4c) on 1 the shelf off the Modaomen sub-estuary. The DO concentration is high in the upper reaches of the estuary and 2 increases gradually along the estuary to a value of 5mg L -1 in the lower estuary. This low DO concentration in the 3 upper reaches of the estuary is due to the low DO concentration discharged from the river outlets. 4 With quality control, a comparison between the simulated and historical estimated summer re-aeration, sediment 5 oxygen demand, and respiration by phytoplankton in the Lingdingyang Bay is shown in Table 2. The simulated values 6 are in reasonable agreement with the estimations and furthermore are comparable to the historical estimated 7 distributions. The re-aeration DO replenishment rates show strong spatial variability, with the maximum values near 8 the river outlets, and decreases sharply to negative in the mouth of the estuary. The values of the sediment oxygen 9 demand reach their maximum values in the middle of the estuary. 10

validations of physical modulation 11
In order to evaluate the accuracy of physical modulation to simulate the DO concentration, comparisons of the 12 two-month averaged DO concentration simulated by the water quality model and modulation method in the surface, 13 middle, and bottom layer are shown in Fig. 5. Overall, the DO distributions simulated by the modulation method are in 14 good agreement with those simulated by the water quality model. In the surface, the modulation method generally 15 overestimates RCA simulations in the estuary and its adjacent areas while underestimates RCA simulations on the shelf 16 (see Fig. 5a). This is the same true for the middle layer (see Fig. 6b). is shown in Fig. 6b with the regression coefficient R 2 >0.99 and the regression slope lying close to 1:1 ratio line. 26 Despite the overall good agreement between the modulation and RCA simulation, we now focus on the diagnostic 27 comparisons between the modulation and RCA simulations in terms of the magnitude and contribution of each 28 individual processes, including horizontal advection, vertical advection, and vertical diffusion (see Fig. 6 c-e). The 29 horizontal diffusion is much smaller than the above terms and hence neglected. The agreement indicates that the 30 modulation method is also reasonable for use in the diagnostic analysis. in Fig. 7a, b. Compared with the bottom layer, DO concentration in the surface is higher in most of areas except in the 1 upper estuary (see Fig. 7a) which receives a large number of low oxygen water (DO=4mg L -1 ) discharged from the 2 river outlets. In the bottom, the lowest DO concentration is about 2mg L -1 , and it appears between the Jitimen and 3 Modaomen sub-estuary, near the Gaolan Island (see Fig. 7b). There is a slender zone with relatively lower DO 4 concentration located on the shelf off the Modaomen sub-estuary linking the Gaolan Island and Hengqin Island. 5 However, the simulated mean DO concentration remains above 3 mg L -1 , which has long been used as the threshold of 6 hypoxia in the PRE (Luo et al., 2008). In terms of this, we estimate the hypoxic frequency in each model grids as 7 follows in order to identify whether the hypoxia has occurred in this zone during the two months. 8 = s * 100 % (15) 9 Where is the number of hours when hypoxia occurs, and s is the total number of hours for two months (i.e., 10 1488). When the hypoxia is defined as DO below 2 mg L -1 , which is widely used in the study of hypoxia (Rabalais et  11 al observed in both sections during the July and August. In the section A, the surface DO is between 6 and 7 mg L -1 and 20 the lowest bottom DO is as low as 4 mg L -1 , which occurs in the middle of the section (see Fig. 7e). In addition, the 21 relatively lower DO is confined to a thin layer above the sediment. In the south end of the section, where the depth is 22 as deep as 25 m, the surface DO with a concentration of 7 mg L -1 can penetrate to deeper than 15 m. The same is true 23 for section B (see Fig. 7f), where the surface DO is above 6 mg L -1 and the bottom DO is 4 mg L -1 . 24 When it is compared with the Chesapeake Bay (Hagy et al., 2004) Where is the hypoxic frequency calculated by Eq. (15) and ∆ is the area of each model grid cell. According to the 30 statistics, S is an expectation of the hypoxic area which takes temporal variability of hypoxic area into consideration. 31 When we define the threshold of hypoxia as 2 or 3 mg L -1 , the expected hypoxic area is 67 and 237 km 2 respectively, 32 and is much smaller than that in the Chesapeake Bay  In order to investigate which processes control the DO conditions, a diagnostic analysis of DO balance was 4 conducted for the PRE (see Fig. 8a) and HFZ (see Fig. 9a). Figure 7d shows that the HFZ is located on the shelf off the 5 Modaomen sub-estuary. It is encompassed by the isoline of 10 % when we define hypoxia as DO<3 mg L -1 , and covers 6 an area of 500 km 2 . In the diagnostic analysis, abbreviation PAR represents localized partial derivatives of DO; SOD 7 and SOD the sediment oxygen demand and the decrease in DO concentration due to the effects of sediment oxygen 8 demand; WCR and WCR the water column respiration and the decrease in DO concentration due to the effects of 9 water column respiration; Phot and Phot the photosynthesis and the increase in DO concentration due to 10 photosynthesis; Rea and Rea the re-aeration and the increase in DO concentration due to re-aeration; as well as the boundary conditions to vertical advection (see Fig. 8b and Fig. 9b), vertical diffusion (see Fig. 8c and Fig.  17 9c), and horizontal advection (see Fig. 8d and Fig. 9d) as Eq. (13). Horizontal diffusion is much smaller than the above 18 terms and hence is omitted. Fig. 8e and Fig. 9e show the gross contributions of boundary conditions, ambient 19 biogeochemical processes, and local biogeochemical processes to DO balance for the PRE and HFZ, respectively. 20 All of these terms are integrated at each desired grid cell and given for the surface layer, middle layer, and bottom 21 layer. According to the survey data of the PREPP project (Pearl River Estuary Pollution Project) , the 22 pycnocline in the PRE is located in the depth ranging from 1.5 to 3 m. We therefore define the surface layer as the top 23 20 % of depth for simplicity in view of the 10 m averaged depth in the PRE. The bottom layer is limited to 20 % of 24 depth above the sediment where the DO concentration is relatively lower (as demonstrated in Fig.7e, f) and hypoxia 25 most occurs. 26

PRE 27
In the surface layer, there is a re-aeration flux across the air-sea interface due to the presence of oxygen gradient 28 between the water and atmosphere. In the summer of the PRE, there is a DO supplement weighing about 9051 t 29 occurring in the surface layer every day, causing an increase of averaged DO concentration by 0.55 mg L -1 in the upper 30 20 % thickness of the PRE (see Fig. 8a). Although the re-aeration only occurs in the surface layer, the reoxygenation 31 will make the DO vertical gradient form and be a supplement of DO in the middle and bottom layers through the 32 vertical diffusion. According to Fig. 8c, the vast majority (89 %) of oxygen which enters the surface layer from the 33 atmosphere will be transported to the lower layers through the vertical diffusion, and eventually 28 % reach the bottom 34 (Fig. 8c). That is why the vertical diffusion is a sink of DO concentration in the surface layer. In addition, there also 35 exists a significant number of the oxygen replenished by the re-aeration involved in the circulation processes, such as 1 the horizontal and vertical advections. Figure 8c also reveals that re-aeration is a major contributor to the vertical 2 diffusion which contributes to 99 % of the vertical diffusion flux. Another important source is photosynthesis. Unlike 3 the re-aeration, photosynthesis occurs in the water body so that the vertical DO gradient is not so large. As a result, the 4 oxygen generated by photosynthesis rarely reaches the lower layers through vertical diffusion, but will be transported 5 by circulations including the horizontal and vertical advection (see Fig. 8b, c, d). surface layer, respectively. In addition to photosynthesis, the boundary condition is also a major contributor to the 10 horizontal and vertical advections, and its contribution to the DO flux reaches 0.54 mg L -1 (accounting for 77 % of 11 horizontal advection) and 0.77 mg L -1 (accounting for 94 % of vertical advection), respectively (see Fig. 8b, d). Water 12 column respiration is the only biogeochemical sink in the surface layer and it is similar to photosynthesis for its 13 occurrence in the water body and participation in circulations (see Fig. 8b, d). For sediment oxygen demand, the 14 traditional views believe that it occurs in the bottom layer and hence its impact on the surface layer will not be 15 considered. However, sediment oxygen demand will make a decline of the bottom DO concentration, thereby reduce 16 the upward DO flux reaching the surface layer, and eventually exert a negative effect on DO concentration in the 17 surface layer (see Fig. 8b). In general, the ambient and local biogeochemical processes are the most important factors 18 controlling the DO balance. Boundary conditions including river boundaries and open boundaries can affect the DO 19 concentration in the surface layer through circulations. However, since the horizontal and vertical advections 20 compensate each other, the net effects of boundary conditions appear limited (see Fig. 8e). 21 The middle layer is not influenced by re-aeration and sediment oxygen demand directly, therefore, photosynthesis 22 and water column respiration become the only two biogeochemical processes affecting the DO balance. However, 23 since the effects of photosynthesis and water column respiration are relatively small, the middle layer is mainly 24 controlled by the dynamical processes, in which horizontal and vertical advections are major sinks (see Fig. 8a). In the 25 middle layer, the oxygen is transported off the PRE by the horizontal advection and upward by the vertical advection. 26 As the DO content delivered from the middle layer to the surface layer exceeds that transported to the middle layer 27 from the bottom layer, the overall performance of the vertical advection makes DO concentration decreased. In general, 28 the DO balance in the middle layer is mainly controlled by boundary conditions. 29 In the bottom, the magnitude of horizontal and vertical advection decreases sharply since the velocities decrease 30 (see Fig. 8a). Therefore, unlike the surface layer, the vertical diffusion becomes the major physical source of DO in the 31 bottom layer. From the perspective of biogeochemical processes, since light weakens in the bottom, the growth of 32 phytoplankton is limited along the narrow coastal areas. As a result, the photosynthesis and water column respiration 33 play the trival roles in DO balance and sediment oxygen demand therefore becomes the major biogeochemical sink of 34 DO in the bottom layer. This is in contrast to the situations in the Chesapeake Bay . The discrepancies 35 in the dominant role of sediment oxygen demand responsible for the total oxygen depletion in the bottom results from 36 the differences in geometry. The Chesapeake Bay has a relatively deep channel where the sediment oxygen demand 37 ranges from 0.86 to 3.2 g m -2 day -1 , and the sediment oxygen demand only accounts for 16 % of total DO depletion in 1 the bottom layer (Boynton and Kemp, 1985). However, the PRE is characterized by the shallow banks less than 5m 2 where the sediment oxygen demand ranges from 0.49 to 3.5 g m -2 day -1 and causes a decline of 0.53 mg L -1 day -1 of 3 DO in the bottom 20 % thickness. Although the sediment oxygen demand only occurs in the bottom layer. However, 4 this deoxygenation will result in the vertical DO gradient between the middle and bottom layers and facilitate the 5 oxygen in the middle layer supplement the bottom layer through the vertical diffusion. This process can be viewed as 6 the effects of sediment oxygen demand is released from the bottom layer, then passes to the middle layer through the 7 vertical diffusion, and consequently leads to a decrease of oxygen consumptions in the bottom layer and an increase in 8 the middle layer. Figure 8c shows the sediment oxygen demand is a major cause of vertical diffusion followed by 9 re-aeration, both of which contribute 79 % and 25 % of vertical diffusion flux, respectively. It should be noted that the 10 vertical advection can also bring the effects of sediment oxygen demand to the middle and surface layer. In fact, the 11 vertical advection is the major mechanism of the effects of sediment oxygen demand to reach upper layers, while the 12 vertical diffusion can only bring the effects to a thin layer above the sediment (see Fig. 8b, c). Besides the vertical 13 diffusion and sediment oxygen demand, circulations including horizontal and vertical advections control the DO 14 balance to some extend as well (see Fig. 8a). In the PRE, the light freshwater spreads seaward in the surface layer 15 accompanied by an upward mixing of the heavy saline water, and consequently a landward compensation flow occurs 16 in the bottom layer (Dong et al., 2004). This circulation is characterized as a two-layer model and therefore explains 17 the seaward DO transport in the surface while the landward DO transport in the bottom, as well as the upward DO 18 transport in the vertical directions. In general, since the horizontal and vertical advections balance each other, the DO 19 balance in the bottom layer is mainly controlled by the ambient and local biogeochemical processes (see Fig. 8e). 20

HFZ 21
When compared with the surface layer in the PRE, the DO flux of vertical advection in the HFZ is almost 5.5 22 folds larger since its shallower depth and larger vertical velocities. As a result, the vertical advection becomes the most 23 important process controlling the DO balance in the surface (see Fig. 9a). Besides vertical advection, re-aeration is 24 another important source of DO. In the HFZ, re-aeration brings about 1.24mg L -1 oxygen to the surface layer everyday 25 (see Fig. 9a). However, as well as in the PRE, most (64 %) of the oxygen replenished by re-aeration reaches lower 26 layers through the vertical diffusion (see Fig. 9c)., and also participates in circulations (see Fig. 9b, d). In addition, the 27 magnitude of vertical advection even exceeds the vertical diffusion because of the large vertical velocities (see Fig. 9b,  28 c). 29 In the middle layer, the DO budget is mainly balanced by horizontal and vertical advections (see Fig. 9a), both of 30 which are mainly contributed by boundary conditions (see Fig. 9b, d). 31 As well as in the PRE, the sediment oxygen demand consumes DO in the bottom layer of HFZ and causes a 32 vertical diffusion flux. the oxygen upward. Since these two processes compensate each other, the DO balance in the bottom layer is mainly 1 controlled by the ambient and local biogeochemical processes. Generally, the physical and biogeochemical processes 2 concerning the DO conditions in the bottom layer of the HFZ and PRE are basically similar in terms of DO balance. 3 However, taking the hypoxia in the HFZ into consideration, it can be referred that only DO balance is not sufficient to 4 explain the formation of hypoxia and further discussions are still needed. 5

Why the hypoxia occurs in the HFZ 6
A study conducted by Zhang and Li (2010) shows hypoxia in the PRE is associated with the distribution of 7 sediment oxygen demand. Because of its dominant roles in bottom depletion, hypoxia occurs where the high rate of 8 sediment oxygen demand is. These spatial distributions of sediment oxygen demand are caused by the front, which 9 accelerates the deposition of particulate organic matter in the estuary and Modaomen sub-estuary, and hence forms two 10 distinct areas characterized by the high level of sediment oxygen demand (see Fig. 10a). However, as shown in Fig.  11 10a, the HFZ is not located in where the maximum of sediment oxygen demand is. Taking this in to consideration, one 12 possible reason is that other biogeochemical processes such as water column respiration and photosynthesis are not 13 considered. 14 In fact, it is hard to estimate the DO consumption rate in the bottom layer since we cannot determine the thickness 15 affected by sediment oxygen demand. In the Chesapeake Bay (Hong and Shen, 2013;Shen et al., 2013) and northern 16 Gulf of Mexico (Yu et al., 2015), sediment oxygen demand is divided by thickness of the lower layer in order to gain 17 its contributions to the DO consumption rate, assuming that the lower oxygen water could mix evenly below the 18 pycnocline. In this study, since we have argued earlier that the shallow depth and large vertical velocities enable the 19 effects of sediment oxygen demand reach the surface layer (see Fig. 8b and Fig.9b), we therefore add sediment oxygen 20 demand which is divided by the depth to water column respiration and photosynthesis to represent the gross depletion 21 rate, even though the estimations will be underestimated. The negative values represent DO consuming while the 22 positive values represent DO replenishing. Figure 10b shows the highest gross depletion rate exceeds 1.0 mg L -1 day -1 23 and occurs along the coast of PRE. In the estuary, the gross depletion rate ranges from 0.6 to more than 1.0 mg L -1 24 day -1 , sharply decreased near the mouth of the estuary. However, there is no hypoxia observed in the estuary. In the 25 bottom of HFZ, gross depletion decreased dramatically from the 1.0 mg L -1 day -1 near the Modaomen sub-estuary to 26 less than 0.2 mg L -1 day -1 . This indicates that only the biogeochemical processes are not sufficient to explain the 27 hypoxia in the HFZ since the effects of physical processes are also important. However, it remains difficult to quantify 28 the effects of physical processes on the distribution of hypoxia. 29 The proceeding DO balance analysis suggests that bottom DO is mainly controlled by ambient and local 30 biogeochemical processes. Although the boundary conditions can exert an impact on DO concentration through 31 circulations, the horizontal and vertical advections balanced each other, making the whole effects ignorable. Therefore, 32 we will focus on how ambient and local biogeochemical processes affect DO distributions. First, the Bio 33 distribution in the bottom is examined since it is determined only by these two processes. Figure 10c shows the 34 simulated Bio distribution in the bottom is in reasonable agreement with DO distribution, and the lowest Next, in order to further investigate why the biogeochemical processes have the largest negative effects in the HFZ, 2 the spatial distributions of SOD , WCR , Rea , and Phot are studied (see Fig. 11). In the bottom, the lowest 3 SOD is observed mainly in the coastal areas extending from the west of lower estuary to the HFZ, with a value 4 ranging from 4 to 5 mg L -1 (see Fig. 11a). Since sediment oxygen demand is the most important biogeochemical sink 5 of oxygen in the bottom, these coastal areas are most conductive to the formation of hypoxia. Reasons that no hypoxia 6 occurs in the west of lower estuary is related to re-aeration. According to the model results, there are high oxygen 7 influxes from the atmosphere in the upper estuary (not displayed). Because of the physical modulation, in the bottom 8 layer, re-aeration has the strongest positive effects on the west of lower estuary (see Fig. 11c). In general, in the west of 9 lower estuary, the high sediment oxygen demand rate is compensated by the high re-aeration replenishing rate, while in 10 the HFZ, sediment oxygen demand dominates the DO changes and exerts a strong negative effect on the DO 11 concentration. As a result, the HFZ is most conductive to hypoxia. Figure 11 also illustrates the reasons for that there is 12 no hypoxia in the upper estuary in spite of its high rate of DO consumption rate. This is because the upper estuary is 13 adjacent to the river network and hence is influenced by river discharges largely. As a result, the quick water exchange 14 brings low DO water parcels out of the bottom layer of upper estuary quickly, making the hypoxia not easy to happen. 15 This can be demonstrated by low concentrations of SOD and WCR in Fig. 11a, b. 16 Finally, in order to investigate why re-aeration has strongest positive effects on the west of lower estuary, the 17 budget of Rea in this area is conducted (see Fig. 11 e-g). The area is encompassed by the isoline of 4mg L -1 (black 18 lines in Fig. 11c). Fig. 11e shows a re-aeration flux across the air-sea interface, among which the vast majorities (76 %) 19 are transported to the lower layers (see Fig. 11e) and eventually 21 % reach the bottom (see Fig. 11g). In addition, 20 thanks to the high re-aeration rate in the surface of upper estuary, oxygen in the bottom is also fueled by the horizontal 21 advection, which brings about 0.31mg L -1 oxygen every day from the upstream (see Fig. 11g). Since the supplement 22 brought by vertical diffusion and horizontal advection exceed the loss caused by vertical advection, there remains a 23 considerable amount of oxygen replenish by re-aeration in the surface. In the HFZ, the re-aeration flux is 0.39 times 24 lower and hence the amount of oxygen reaching the bottom layer through vertical diffusion is only one fourth of that in 25 the west of lower estuary. When compared with turning off the photosynthesis and water column respiration (see 26 Fig.9921a), turning off the re-aeration (see Fig.9921b) leads to a more significant expansion of hypoxic area and 27 results in a shift of hypoxic center to the west of lower estuary. 28

Why the hypoxia in the PRE is not severe 29
Unlike extensive hypoxia which exists in the Chesapeake Bay (Hagy et al., 2004) and northern Gulf of Mexico 30 (Rabouille et al., 2008), hypoxia in the PRE is more like confined to small areas. According to the results of previous 31 studies, it is related to the dynamical conditions in the PRE. When compared with the long residence time in 32 Mississippi river (more than 95 days, Rabouille et al. (2008)), the short residence time (3-5 days) in the PRE prevents 33 the organic matter from completing their biogeochemical cycling (Yin et al., 2004). Moreover, the phosphorus 34 limitation and high turbidity also inhibit the complete utilization of nutrients and growth of phytoplankton in the PRE 35 (Yin et al., 2004). However, these explanations are not convincing enough. According to a study conducted by Zhang 36 is more related to terrestrial input of particulate organic matter. Therefore nutrients and the growth of phytoplankton 2 should have few effects on hypoxia in the PRE. 3 Nevertheless, in this study, we compare the gross depletion rate in the PRE with that in the northern Gulf of 4 Mexico and Chesapeake Bay (see Table 3). The gross depletion rate is computed as the sum of sediment oxygen 5 demand and net water column respiration. As shown in Table 3, in the northern Gulf of Mexico, sediment oxygen 6 demand ranges from 0.06 to 0.70 g m -2 day -1 during the summer of 2003-2006. Below pycnocline, the net water 7 column respiration which includes water column respiration and photosynthesis ranges from 0.57 to 3.60 g m -2 day -1 . 8 Therefore, the gross depletion rate ranges from 0.11 to 0.55 mg L -1 day -1 , with the areal extent of hypoxia averaged 9 13,500 km 2 . In the summer of the Chesapeake Bay, the gross depletion rate ranges from 0.16 to 0.96 mg L -1 day -1 in 10 the mainstem of the bay, where the persistent hypoxia extends for 8 km 3 . While in the PRE, the model results (see Fig.  11 10b) show the gross depletion ranges from less than 0.2 to more than 1.0 mg L -1 day -1 with the spatial average of 0.47 12 mg L -1 day -1 in the estuary and 0.40 mg L -1 day -1 in the HFZ. Therefore, in terms of the relatively high gross depletion 13 rate and confined hypoxic area (237 km 2 ), neither the high concentration of sediment, nor phosphorus limitation can be 14 convincing enough to explain why the hypoxia in the PRE is not severe. 15 Hypoxia in the PRE is not severe in terms of two aspects, including the limited hypoxic extent and relatively high 16 DO concentration. In this study, we conduct the correlation analysis of bottom DO against Bio and BC 17 concentration (not displayed). The strong (R 2 >0.9) and significant (Sig. <0.01) relations between DO and Bio 18 concentration confirms that bottom DO concentration is more associated with Bio than BC concentration, 19 which indicates the Bio concentration can be used to interpret hypoxia in the PRE. Figure 10c shows the simulated 20 Bio distribution reproduces the spatial distributions of hypoxia and DO concentration in the bottom. We have 21 argued earlier that the HFZ forms due to the physical modulation of biogeochemical processes, especially sediment 22 oxygen demand and re-aeration, making the largest negative effects occurs in the HFZ. According to Fig. 10c, the 23 Bio concentration ranges from -2 to -3 mg L -1 in the bottom of HFZ, and DO concentration hence ranges from 3 to 24 4 mg L -1 considering the BC concentration is more or less 6 mg L -1 . Therefore, the high DO concentration can be 25 attributed to the relatively low effects of biogeochemical processes. 26 It is related to re-aeration that Bio concentration is generally low. When compared with the Chesapeake Bay 27 the northern Gulf of Mexico, the PRE is characterized with relatively high sediment oxygen demand and shallow depth. 28 Therefore, the impact of sediment oxygen demand on the bottom DO is comparable more important. Figure 13 reveals 29 SOD ranges from -4 to -5 mg L -1 in the bottom of HFZ, with the spatial averaged value of -4.31 mg L -1 . This 30 indicates the averaged DO concentration in the bottom of the HFZ will be as low as 1.76 mg L -1 and the expected 31 hypoxic area will reach 3345 km 2 , presuming that other biogeochemical processes are neglected. Figure 13 also reveals 32 that photosynthesis offsets the water column respiration and eventually supplements the DO concentration by 0.98 mg 33 L -1 in the bottom. Re-aeration is another important source which averages 0.88 mg L -1 in the bottom. According to Fig.  34 12, taking either re-aeration or photosynthesis and water column respiration into consideration leads to the hypoxic 35 area decrease to 591 km 2 and 2203 km 2 , respectively. Moreover, Fig. 12 also reveals that without re-aeration, the west 36 of lower estuary is occupied with a persistent hypoxia (frequency>80 %), noting the fact that hypoxia is intermittent in 37

Summary and conclusions 2
In this study, we use a physical and biogeochemical coupled model to investigate the DO dynamics and hypoxia 3 during summer in the PRE. Comparisons with observations demonstrate that our model reasonably reproduces the 4 observed spatial and temporal characteristics of water level, salinity, temperature, and DO. The good agreement 5 between the model simulated and historical estimated rates of re-aeration, sediment oxygen demand, and water column 6 respiration further indicates our model can accurately simulate the biogeochemical processes concerning the DO 7 dynamics. In addition, we introduce a novel method named physical modulation of biogeochemical terms to 8 investigate the contributions of boundary conditions, ambient biogeochemical processes, and local biogeochemical 9 processes to DO conditions. The formula derivation and comparisons against model outputs reveal the modulation 10 method is reasonable for use in DO analysis. 11 Model results demonstrate there is a high frequency zone (HFZ) of hypoxia located on the shelf off the 12 Modaomen sub-estuary. However, when compared with other areas, hypoxia in the PRE is not severe in terms of its 13 intermittency and limited extent. Based on the modulation method, a diagnostic analysis of DO balance is conducted 14 for the PRE and HFZ to bring us a further insight into DO dynamics. The analysis results show that the bottom DO 15 conditions are mainly controlled by the ambient and local biogeochemical processes, both in the HFZ and PRE. 16 Although the circulation process can bring the DO originating from the boundaries to the bottom of the PRE and HFZ, 17 the influx of horizontal advection and outflux of vertical advection compensate each other, and hence the total impacts 18 of boundary conditions are limited. 19 Since Bio concentration is determined only by ambient and local biogeochemical processes, we compare 20 Bio and DO in terms of their spatial and temporal distributions. A good agreement further indicates that Bio can 21 be used to interpret formations of hypoxia. Re-aeration and sediment oxygen demand are two main biogeochemical 22 processes which control the distribution, the spatial extent, and the duration of hypoxia in the PRE. Though the high 23 rate gross depletion in the upper of the estuary, the hypoxic water in the bottom is soon diluted because of quick water 24 exchange. In the HFZ and the west of lower estuary, sediment oxygen demand decrease bottom DO concentration 25 distinctly, making these two areas potentially hypoxic. However, oxygen entering the surface layer through the 26 re-aeration will be transported to the bottom in the west of lower estuary, offseting the consumed oxygen by sediment 27 oxygen demand and therefore eliminating the hypoxia. Since this mechanism is not distinct in the HFZ, HFZ becomes 28 the most likely to form hypoxia in the PRE. Numerical simulations reveals that turning the re-aeration leads to a 29 northward expansion of hypoxic extent to the west of lower estuary with the persistent hypoxia observed. 30   Fig. 7 The spatial distribution of DO averaged over July and August in the PRE in surface (a) and bottom (b); the 2 spatial distribution of hypoxic frequency during July and August in the PRE when hypoxia is defined as DO<2 mg L -1 3

Acknowledgements
(c) and DO<3 mg L -1 (d); the distribution of DO averaged over July and August along the two transects. Positions of 4 the two transects are shown in Fig. 7(a-d).