Modeling spatial variability of harmful algal bloom in ...

Journal of Hydro-environment Research 20 (2018) 63–76

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Research papers

Modeling spatial variability of harmful algal bloom in regulated rivers using a depth-averaged 2D numerical model

T

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Jun Song Kim, Il Won Seo , Donghae Baek Dept. of Civil & Environmental Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744, South Korea

A R T I C LE I N FO

A B S T R A C T

Keywords: HAB Depth-averaged 2D model Geographically weighted regression Remote sensing Water residence time Blooming area

The depth-averaged two-dimensional (2D) model was applied to investigate the spatial variability of harmful algal bloom (HAB) in regulated rivers. This study adopted geographically weighted regression (GWR) to retrieve the spatial distribution of cyanobacterial concentration from satellite imagery data for the calibration of the 2D numerical model in the Nakdong River, South Korea. The GWR model proposed in this study yielded more accurate results compared to a conventional multiple linear regression (MLR) model. The 2D numerical model calibrated with the GWR results well reproduced a high accumulation of cyanobacteria along the shoreline where the cyanobacterial growth was preferred due to longer water residence time (WRT) associated with lower flow velocity. Simulations of HAB reduction scenarios using the calibrated 2D numerical model revealed that the blooming area and maximum concentration of the cyanobacteria in the study reach decreased drastically with an increase in inflow discharge from Gangjeong weir located upstream of the study reach. When the inflow discharge increased up to about 6 times the original level, the blooming area of cyanobacteria was almost eliminated as WRT decreased to about 37% of its original value. Furthermore, the shear velocity enhanced by the fast flow adequately suppressed the localized proliferation of the cyanobacteria along the shallow and slow flow zones in the study reach as it stimulated the lateral dispersion of water quality.

1. Introduction Harmful algal bloom (HAB) has been considered as a serious threat to public health and aquatic systems with deterioration of water quality in rivers and lakes (Huisman et al., 2005; Paerl et al., 2011; Brooks et al., 2016). High accumulation of toxic cyanobacteria has discolored water bodies and created undesirable taste and odor (Hoeger et al., 2005). Prevalence of HAB can be explained by several environmental and hydraulic factors such as light intensity, water temperature, concentration of phosphate and nitrate, and water flow (Paerl et al., 2001). In general, the reduction of phosphate inputs has been regarded as one of the most effective countermeasures for eliminating HAB in freshwater systems (Smith and Schindler, 2009) because the cyanobacterial biomass increases with high availability of phosphate and declines abruptly with its decreased availability (Kuo et al., 2006; Zhang et al., 2008; Liu et al., 2009; Wu and Xu, 2011). However, in eutrophic water bodies, the phosphate is not a limiting factor for cyanobacterial growth because it usually exceeds the assimilative capacity of the cyanobacterial growth (Reynolds, 1999; Paerl et al., 2001; Waylett et al., 2013). Thus, in the condition of nutrient enrichment, the factors controlling HAB are regarded as water temperature, light intensity and

⁎

water flow. Numerous studies have identified a hydraulic variable such as inflow discharge of the river systems as the most critical factor to control the abundance of cyanobacteria (Hilton et al., 2006; Salmaso and Braioni, 2008; Fornarelli and Antenucci, 2011). High biomass of cyanobacteria was usually observed in slower flow velocity conditions that lead to a longer water residence time (WRT) while the cyanobacterial proliferation was barely recorded during periods of high river discharge resulting in a shorter WRT (Kawara et al., 1998; Romo et al., 2013). Long et al. (2011) suggested that the critical flow velocity which accelerates the development of HAB in Jialing River, China was 0.04 m/s based on results of numerical simulation using a depth-averaged twodimensional (2D) model. They explained that, when the flow velocity exceeded this critical value, cyanobacteria were flushed out at a rate faster than the rate at which their concentrations reached a blooming level. It has been observed that, at the confluence of tributaries and a main river, poor mixing conditions are favorable for the cyanobacterial blooms. The incomplete mixing may lead to the localized deterioration of water quality downstream of the tributary confluence (Paerl et al., 2001; Carey et al., 2012). Mitrovic et al. (2003) suggested that the critical value of flow velocity to control HAB in Australian rivers was

Corresponding author. E-mail address: [email protected] (I.W. Seo).

https://doi.org/10.1016/j.jher.2018.04.008

Available online 01 May 2018 1570-6443/ © 2018 International Association for Hydro-environment Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.

Journal of Hydro-environment Research 20 (2018) 63–76

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Fig. 1. Study reach of the Nakdong River and its bathymetry with finite element mesh.

0.05 m/s with a shear velocity of 3 × 10−3 m/s which stimulated the dispersion of water quality to prevent the localized development of the cyanobacterial blooms. In line with these findings, it can be suggested that the cyanobacterial growth can be restrained by not only decreasing WRT but also enhancing the physical mixing by the high inflow discharge of the rivers (Forbes et al., 2008; Deus et al., 2013). As a result of the latest climate change, several multi-purpose weirs were built across the Nakdong River which is one of eutrophic rivers in South Korea with the aim of flood protection and combating drought in 2012, as shown in Fig. 1. After the construction of weirs, the Nakdong River has suffered from the proliferation of toxic cyanobacteria such as Anabaena, Aphaniozomenon and Microcystis during summer as the weirs have retarded the natural river flow (Yu et al., 2014; Srivastave et al., 2015). The phenomena can be explained by the artificial flow control regulated by the weirs because this causes change of flow patterns of rivers by extending WRT, which leads to the rapid increase in the cyanobacterial population (Hart et al., 2002; Mitrovic et al., 2006; Li et al., 2011; Yajima and Choi, 2013). In addition, Cha et al. (2017) reported that water temperature and water flow were important predictors of the cyanobacteria rather than phosphate in the Nakdong River. Their study showed that the water temperature was not a sitedependent factor but a temporal-dependent factor whereas the importance of the water flow in terms of WRT varied significantly over the space. Fragoso et al. (2008) also reported that flow patterns of shallow water bodies led to the spatial heterogeneity of cyanobacteria, and emphasized the importance of the hydrodynamic processes in identifying the zones with a higher potential for HAB based on numerical simulation results using the depth-averaged 2D model. Therefore, it is indispensable to investigate the spatial variability of cyanobacteria in the regulated rivers in purpose of preparing the countermeasures against HAB considering the variation of the water flow condition. This study is aimed at carrying out the 2D numerical simulation for predicting the spatial distribution of the cyanobacteria in the Nakdong River. In this study, the field survey for collection of cyanobacterial concentration data and hydraulic data including flow velocity and water depth was conducted to calibrate the numerical model. Moreover, as shown in Fig. 2, the spatial distribution of cyanobacterial

concentration was generated from the satellite imagery data adopting the geographically weighted regression (GWR) for the model calibration. Then, the calibrated numerical model was applied to scenarios for investigating the effect of inflow discharge from the weir on the spatial variability of HAB. 2. Numerical model In large rivers, where the channel width is much larger than the water depth, the vertical mixing of water quality is rapidly completed while the mixing in both lateral and longitudinal directions continue to occur far from a source of contaminants, thereby assuming that lateral dispersion dominates over vertical dispersion for the water quality mixing in natural streams (Yotsukura and Sayre, 1976; Rutherford, 1994; Jeon et al., 2007; Seo et al., 2016). As shown in Fig. 1, the study reach includes the confluence of both tributary inflow and meandering that considerably affect the lateral dispersion of the contaminants with a high reach-average aspect ratio of the channel width to the water depth equivalent to 52.2 corresponding to that of the shallow water (Prooijen and Uijttewaal, 2005; Franca and Lemmin, 2006). The depthaveraged 2D model could therefore be effective in investigating the spatial variability of cyanobacteria in the study reach of the Nakdong River. 2.1. Hydrodynamic model To simulate the 2D fields of velocity and water depth for a free surface flow, this study used the shallow-water equations such as the depth-averaged continuity and momentum equations as follows (Song et al., 2012):

∂h + h∇ · q+ q·∇h = 0 ∂t

(1)

gn2 ∂q 1 + q·∇u = −g ·∇ (z + h) + ·∇hν ·∇q− 4/3 q‖q‖ h h ∂t

(2)

where t is the time; h is the water depth; q= (u,v ) is the velocity vector 64

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Fig. 2. Outline and objectives of this study.

in x and y -directions of Cartesian coordinates, respectively; g is the acceleration of gravity; z is the bottom elevation; ν is the kinematic eddy viscosity; n is the Manning’s roughness coefficient; and ‖q‖ is the Euclidean norm of velocity. Using the Smagorinsky turbulent model, ν can be calculated as:

ν = (Cs Δg )2 2Sij Sij = (Cs Δg )2|S |

GT =

⎜

(3)

GI =

tensor of strain rate; and |S | = 2Sij Sij . To construct a numerical model, the shallow water equations were discretized by the SU/PG (Streamline Upwind Petrov-Galerkin) finite element scheme.

In this study, the 2D advection-dispersion equation was used to simulate water quality variables such as water temperature, nitrate, phosphate, and cyanobacterial concentration. The governing equation can be expressed as follows (Lee and Seo, 2007):

⎜

⎟

KH (Te−T ) h ρcp h

(4)

where Cφ is the concentration of the water quality variable φ ; D is the dispersion tensor; and R (C ,t ) is the reaction term to mathematically describe particular kinetics of each water quality variable. The equation above was also discretized with SU/PG finite element scheme. The dispersion tensor in the Cartesian coordinate, D was modeled in terms of DL and DT following Alavian’s equation (1986), in which DL and DT are the longitudinal coefficient and lateral dispersion coefficient in the natural coordinate, respectively. The cyanobacterial growth usually depends on water temperature, dissolved nutrient (nitrate and phosphate) concentrations and light intensity. Thus, the growth term was composed of three limitation functions dealing with the above factors while the decay terms include the process of respiration, death and excretion. Substituting Cφ with Cc in Eq. (4), the reaction term of the cyanobacterial dynamics can be therefore expressed as (Kim et al., 2018):

ω R (Cc,t ) = ⎛μmax GT GN GI −(kresp + kdeath + kexcr ) θT − 20− c ⎞ hCc h⎠ ⎝

(7)

I exp(−ke h) I exp(−ke h) ⎞ ·exp ⎛1− Is Is ⎝ ⎠

R (T , t ) = + ∇ ·hqCφ = ∇ (hD·∇Cφ) + R (Cφ,t )

⎟

(8)

where Topt is the optimal water temperature on growth; K1 and K2 are the curve parameter below and above Topt , respectively; CN is the nitrate concentration; KN is the half-saturation constant of nitrate; CP is the phosphate concentration; and KP is the half-saturation constant of phosphate; I is the light intensity; ke is the attenuation coefficient; and Is is the saturating light constant. In Eqs. (6)–(8), T , CN and CP were calculated by substituting Cφ with T , CN and CP in Eq. (4), and also replacing R (Cφ,t ) with the reaction terms as follows (Kim et al., 2018):

2.2. Water quality model

∂t

(6)

CN CP ⎞ , GN = min ⎛ ⎝ CN + KN CP + KP ⎠

where Cs is the Smagorinsky coefficient; Δg is the grid size; Sij is the

∂ (hCφ)

2 ⎧ exp[−K1 (Topt −T ) ], ifT ⩽ Topt ⎨ exp[−K2 (T −Topt )2], otherwise ⎩

(9)

R (CN ,t ) = [(kresp θT − 20−μmax GT GN GI ) αN Cc−kN θT − 20CN ] h

(10)

R (CP ,t ) = [(kexcr θT − 20−μmax GT GN GI ) αP Cc ] h

(11)

where KH is the heat exchange coefficient; Te is the heat equilibrium temperature; ρ is the density of water; cp is the specific heat of water; kN is the denitrification rate; and αN and αP are stoichiometric ratio of nitrate and phosphate to cyanobacterial concentration, respectively. 3. Data acquisition 3.1. Field survey The reach of about 10 km downstream from Gangjeong weir including the confluence with the Kumho River which is one of the largest tributaries in the Nakdong River, was selected as the study reach, as shown in Fig. 1. Serious water quality deterioration caused by HAB has often been reported at this confluence zone (Park and Lee, 2002; Kim et al., 2018) due to high concentration of phosphate introduced from the Kumho River, as shown in Fig. 3 a). Fig. 3 b) shows that cyanobacterial concentration observed at Gangjeong weir occasionally exceeded 10,000 cells/ml, which is a warning level of the HAB alert system operated by Korea Ministry of Environment (MOE). This was particularly observed during which can be attributed to favorable hydraulic and environmental conditions such as low river discharge with optimal light intensity and water temperature for cyanobacterial

(5)

where Cc is the cyanobacterial concentration; μmax is the maximum growth rate of cyanobacteria; GT is the water temperature limitation function; GN is the nutrient limitation function; GI is the light intensity limitation function; kresp , kdeath and kexcr are the respiration rate, death rate and excretion of cyanobacteria, respectively; θ is the temperature coefficient; T is the water temperature; and ωc is the settling velocity of cyanobacteria. The limitation function of Eq. (5) can be described as: 65

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(a) Total phosphorus and water temperature at Gangjeong weir and Kumho River 0.40

TP (mg/l)

0.30

50 40 30

0.20 20 0.10 0.00 Dec-14

10

Water temperature ( C)

TP (Gangjeong) TP (Kumho) WT (Gangjeong) WT (Kumho)

0 Apr-15

Aug-15

Dec-15

Apr-16

Aug-16

Dec-16

(b) Cyanobacterial concentration and discharge at Gangjeong weir Inflow discharge Cyanobacterial conc.

800

40,000 30,000

600 Warning level

400

20,000 10,000

200 0 Dec-14

50,000 Cyanobacteria (cells/ml)

Discharge (m3/s)

1,000

0 Apr-15 Aug-15

Dec-15

Apr-16 Aug-16

Dec-16

Fig. 3. Seasonal variation of water quality variables (total phosphorus, water temperature and cyanobacterial concentration) and inflow discharge from Gangjeong weir observed at the monitoring stations during January 2015-December 2016.

information corresponding to the hydraulic properties. In this study, the hydraulic data were collected at cross sections after the confluence of the Kumho River where the cyanobacteria concentration data were available. As a result of the measurements, the average discharges of the Nakdong River before the confluence and the Kumho River were 141.5 m3/s and 59.8 m3/s, respectively that were used for upstream boundaries of the hydrodynamic model. The average velocity and water depth of the study area after the confluence were 0.102 m/s and 6.02 m, respectively. The measured hydraulic data and observed cyanobacterial concentration data of the study reach are as summarized in Table 1.

growth (Cha et al., 2017). High concentration of cyanobacteria around the warning level was frequently observed in 2015 whereas the occurrence of HAB significantly decreased with an increase in inflow discharge from Gangjeong weir in 2016. The field survey was conducted to collect the spatial distribution of cyanobacterial concentration data and hydraulic data in the study reach on September 08, 2016. To observe cyanobacterial concentration, a fluorescence probe, AlgaeTorch 10 (bbe Moldaenke, Germany) was used. The AlageTorch 10 can measure cell counts of cyanobacteria and chlorophyll-a (Chl-a) of total phytoplankton separately adopting multiple LEDs (470 nm, 525 nm, 610 nm) to differentiate between spectral groups of cyanobacteria based on the relative fluorescence excitation spectrum of a chlorophyll-a pigment in cyanobacteria cells at 680 nm (Rolland et al., 2010). This multi-spectral device has been used frequently to approximate cyanobacterial contents and estimate their spatial distribution in water bodies (Pobel et al., 2011; Kudela et al., 2015; Kalaji et al., 2016; Cyr, 2017). In this study, AlgaeTorch 10 mounted on the boat was immersed to the center of water depth and observed cyanobacterial cell counts as an indicator of the concentration at 117 points of several cross sections, as shown in Fig. 4. During the observation periods, the predominant cyanobacteria in the study reach were found to be Microcystis (Kim et al., 2017). According to the observation results in Fig. 4, the high concentration of cyanobacteria was observed downstream of the study reach. Hilton et al. (2006) explained that the large biomass of the cyanobacteria can develop in the middle and lower reaches of large and impounded rivers because WRT is much longer than doubling times of the cyanobacterial population. Hydraulic data including flow velocity and water depth were measured to calibrate the hydrodynamic model using a moving-vessel mounted ADCP (Acoustic Doppler Current Profiler), RiverSurveyor M9 (Sontek, USA). This current meter equipped with the Real Time Kinematics-Global Positioning System (RTK-GPS) also provides position

3.2. Satellite remote sensing Remote sensing technique with satellite imagery has increasingly been applied in detection of HAB in coastal and inland water in which the reflectance information from the satellite imagery was utilized, based on spectral characteristics of cyanobacteria (Kuster et al., 2004; Shen et al., 2012). The satellite remote sensing can generate a high resolution map of target substances by prediction in ungaged regions corresponding to the numerical mesh resolution for the calibration of the water quality model. On the other hand, the conventional field survey methods such as in-situ ship observation or laboratory analysis only represent the coarse spatial resolution of cyanobacterial concentration because these methods are not usually time, cost, and labor effective for short period monitoring (Ahn and Shanmugam, 2006). Cyanobacteria-related spectral characteristic is complicated, and spectral-response features compose the foundation for cyanobacterial concentration extraction (Han, 1997; Schalles, 2006). High light absorbance of the cyanobacteria-laden water causes the reflectance minimum around 440 nm (blue) and 670 nm (red) while the reflectance peaks at about 550 nm (green) due to the smaller absorbance than the blue and red spectrums. Additionally, the cyanobacteria-laden water 66

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Fig. 4. Spatial distribution of cyanobacterial concentration observed at 117 points of the study reach with cross sections (S1 through S16 after the confluence of the Kumho River) using AlgaeTorch 10 on September 08, 2016

may pose unnecessary bias in the predicted variability of water quality (Kallio et al., 2008; Kuster, 2012). In addition, atmospheric conditions would not be noticeably different across the study reach if a single satellite imagery was used (Monteys et al., 2015). For these reasons, in this study, the DN of pixels on each band of the filtered imagery was normalized by the maximum DN to represent the reflectance. As shown in Fig. 5, the reflectance of the band 2 (Green), band 4 (Red edge), band 5 (NIR) showed the strong correlation with the cyanobacterial concentration. Therefore, this study selected the reflectance of these bands as the predictors of the cyanobacterial concentration.

Table 1 Summary of hydraulic data and cyanobacterial concentration data acquired on September 08, 2016 using RiverSurvyeor M9 and AlgaeTorch 10. Section

U (m/s)

W (m)

H (m)

Cc (cells/ml)

S1 S3 S5 S7 S9 S11 S13 S15

0.114 0.122 0.119 0.096 0.093 0.094 0.094 0.094

303 365 361 377 409 388 266 292

5.79 5.65 5.79 6.08 5.97 6.73 8.01 7.48

2200 1800 2080 1675 2040 1980 2625 2580

3.3. Geographically weighted regression model exhibits the prominent secondary peak reflectance near 700 nm (red edge) which is the most significant wavelength for accurate estimation of cyanobacterial concentration in the photic zone because absorption by colored dissolved organic material (CDOM) and suspended solids is minimal in the red edge spectrum (Gitelson, 1992; Moses et al., 2012). In this study, RapidEye imagery was selected for estimating cyanobacterial concentration in the areas that were ungauged by the field survey using the boat-mounted AlgaeTorch 10. The RapidEye satellite system provides the reflectance information such as digital number (DN) of pixels on the five spectral bands covering blue (440–510 nm), green (520–590 nm), red (630–685 nm), red edge (690–730 nm), and near-infrared (NIR) (760–850 nm) corresponding to the band 1–5, respectively, on a daily basis (Wallner et al., 2014). The presence of the red edge band and NIR band is a unique feature that distinguishes the RapidEye from other multispectral satellites. These bands represent the scattering of radiation by vegetation and absorption by chlorophyll (Clevers and Gitelson, 2013), thereby facilitating an effective measure to be used in productive water bodies with relative higher cyanobacterial concentration as aforementioned. This study used the RapidEye Ortho product (Level 3A) acquired on September 08, 2016 under the condition of no cloud cover (0%). The Level 3A imagery data was ortho-rectified and resampled to a spatial resolution of 5 m with radiometric, sensor and geometric correction applied to the data using the digital terrain elevation data (DTED) Level 1 and Suttle Radar Terrain Mission (SRTM) digital elevation model (DEM) (Ramoelo et al., 2012). In the pre-processing of the satellite imagery data, the speckle noises in the RapidEye imagery were reduced by the enhanced Lee filter. In this study, the satellite imagery data were not atmospherically corrected because several studies reported that atmospheric correction

In the recent past, the multiple linear regression (MLR) model has commonly been used in order to retrieve the spatial distribution of cyanobacterial concentration with the satellite remote sensing (Simis et al., 2005; Gitelson et al., 2008; Song et al., 2013). The conventional MLR model based on ordinary least square (OLS) assumes that relationship between the inputs and outputs is consistent across the whole study reach. However, the spatially non-homogeneous relationship between the inputs and outputs has been recognized because the relationship might spatially vary because hydraulic and geological characteristics are not homogeneous in different locations (Tu, 2011). Therefore, many studies have addressed the spatial heterogeneity by adopting a GWR model in environmental remote sensing (Tu and Xia, 2008; Monteys et al., 2015; Zou et al., 2016). In this study, the GWR model was proposed to extract the spatial distribution of cyanobacterial concentration from the RapidEye imagery for the calibration of the numerical model. The GWR model is a non-homogeneous approach which is able to capture spatially-varying relationships between the independent and dependent variables by allowing different relationships at different points in space (Brunsdon et al., 1996). Unlike the MLR model, the regression coefficients of the GWR model are functions of spatial location (Lu et al., 2014). The GWR model proposed in this study included an input layer of the independent variables consisting the reflectance of the band 2, band 4, and band 5 where the peak reflectance of cyanobacteria detected, of the RapidEye imagery, and an output layer of the dependent variable, in which the observed cyanobacterial concentration from the field survey was used for the calibration of the GWR model. A general form of the GWR model can be expressed as:

yi ̂ = βi0 + βi2 x i2 + βi 4 x i 4 + βi5 x i5 + εi 67

(12)

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Concentration (cells/ml)

5,000

independent variables at i ; and εi is the random error at i . In this process, the GWR model allows coefficients to vary continuously over the study reach. Thus, a set of local regression coefficients and intercept are estimated at a location where observed data is available to represent the spatial heterogeneity. The set of local regression coefficients and intercept were estimated by weighted least squares. The matrix can be defined as:

(a) Band 2 4,000 3,000

β (i) = (XT W(i)X)−1XT W(i) y ̂(i)

2,000

where β (i) is the vector of estimated parameters including βi0 , βi2 , βi4 and βi5 ; X is the matrix of the independent variables; W(i) is the diagonal matrix denoting the geographical weighting of the dependent variables at i ; and y (̂ i) is the single column vector of the dependent variables for yi .̂ Here, W(i) is the weighting scheme calculated by a kernel function based on the proximities between the regression point i and observation point. This study adopted a Gaussian kernel function wij which can be defined as:

r = 0.70

1,000 0 0

0.2 0.4 0.6 Reflectance (Normalized DN)

1 dij wij = exp ⎡− ( )2⎤ ⎢ ⎦ ⎣ 2 b ⎥

Concentration (cells/ml)

5,000 4,000 3,000 2,000

n + tr(S) ⎫ AICc = 2nln(σ )̂ + nln(2π ) + n ⎧ ⎨ ⎩ n−2−tr(S) ⎬ ⎭

r = 0.69

3.4. Retrieval of cyanobacteria concentration

0.2 0.4 0.6 Reflectance (Normalized DN)

For evaluating the performance of the GWR model, several model evaluation statistics including AICc , as given below were used:

5,000 Concentration (cells/ml)

(15)

where n is the sample size; σ ̂ is the estimated standard deviation of the error term; and tr(S) denotes the trace of the hat matrix S.

0 0

(14)

where dij is the distance between observation point j and regression point i , and b is the kernel bandwidth. The bandwidth is the key controlling parameter and can be specified either by a fixed distance or by a fixed number of nearest neighbors. If dij is greater than b , wij approaches zero. The optimum bandwidth is often found by minimizing the corrected Akaike Information Criterion (AICc ) which accounts for model parsimony to avoid the overfitting of the GWR model (Hurvich et al., 1998). AICc can be expressed as:

(b) Band 4

1,000

(13)

CV =

(c) Band 5

1 n

n

∑

(yi −yi )̂ 2

i=1

(16)

n

4,000

∑ R2

=

∑

3,000

(yi −yi )̂ 2

1− i =n1 (yi −yi )2

i=1

2,000

MAPE =

r = 0.71

1,000

∑ i=1

yi −yi ̂ × 100% yi

(17)

(18)

where yi is the observed cyanobacterial concentration at i .Cross validation (CV ) score is the sum of the squared residuals for which the smaller the value is the closer the fit to the observed data. Coefficient of determination (R2 ) and mean absolute percent error (MAPE ) are measures of goodness-of-fit, with higher values of R2 and lower values of MAPE being preferable. As a result of prediction, the GWR model provided better model fit diagnostics compared to the MLR model, where R2 was increased to 0.719 from 0.615, and AICc was also reduced from 1735 to 1710 with 335 m of the optimum bandwidth b , as shown in Table 2. Other model evaluation statistics such as CV and MAPE were also enhanced with the GWR model. According to Fig. 6, the local regression coefficients were spatially-varying and represented the marked regional differentiation unlike the uniform coefficients of the MLR model. Before the confluence of the Kumho River, the local regression coefficients and intercept remained constant over the space whereas these values remarkably varied after the confluence due to

0 0

1 n

n

0.2 0.4 0.6 Reflectance (Normalized DN)

Fig. 5. Correlation between the observed cyanobacterial concentration and reflectance of the spectral bands following Band 2 (Green), Band 4 (Red edge), and Band 5 (NIR).

where yi ̂ is the predicted cyanobacterial concentration at a regression point i ; βi0 is the intercept at i ; βi2 , βi4 and βi5 are the local regression coefficient for the independent variables at i ; x i2 , x i4 and x i5 are the 68

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Table 2 Comparison of the prediction accuracy for cyanobacterial concentration between the GWR model and MLR model. Model

AICc

CV

MAPE (%)

R2

MLR GWR

1735 1709

158,502 124,916

17.8 15.2

0.615 0.719

mixing of two different water qualities. As aforementioned, the reason of this spatial heterogeneity in the estimated parameters can be explained by the rapid change of hydraulic and water quality conditions of the Nakdong River after the confluence. These results revealed that the GWR model can be considered as a better predictor for the spatial distribution of cyanobacterial concentration, compared to the MLR model in the study reach. To evaluate the reliability of the GWR model proposed in this study, the sensitivity and specificity were estimated. These statistical measures were widely used to detect the specific substances with the threshold to identify them using the satellite imagery (Saatchi et al., 2008; Alatorre et al., 2011). In this study, the threshold value was set to be 2000 cells/ mL of the cyanobacterial concentration, and the sensitivity and specificity were defined as followings:

Fig. 7. Spatial distribution of cyanobacterial concentration on September 08, 2016 calculated by the GWR model with the ordinary Kriging method.

Specificity = P [Prediction( < 2,000 cells/ml)|Observation( < 2,000 cells

Sensitivity = P [Prediction(⩾2,000 cells/ m)|Observation(⩾2,000 cells/ml)]

/ml)]

(19)

(20)

As a result of this analysis, the GWR model showed the fair levels of the prediction performance with 0.82 of the sensitivity, and 0.90 of the specificity. Therefore, the specific level of the cyanobacterial

(a) Band 2

(b) Band 4

(c) Band 5

(d) Intercept

Fig. 6. Spatial variations of local regression coefficient (βi2, βi4 and βi5 ) of input bands (B2, B4 and B5) and intercept (βi0 ) estimated by the GWR model on September 08, 2016. 69

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concentration was well identified by the GWR model. Fig. 7 shows the result of mapping of cyanobacterial concentration with the proposed GWR model. The local regression coefficients and intercepts at points ungaged by the field survey were generated using the ordinary Kriging method to retrieve cyanobacteria concentration from the RapidEye imagery. This figure revealed that the GWR model adequately reproduced the high accumulation of the cyanobacteria downstream of the study reach, which was also found in the field survey. Furthermore, with reference to GWR results, the relatively higher concentration of the cyanobacteria was estimated along the shoreline referred to the shallow and slow flow zone rather than the main flow zone referred to the deep and fast flow zone because the shallow and slow flow zone facilitate the higher light intensity available with less light attenuation, and even longer WRT associated with the slower flow velocity.

Table 3 Prediction accuracy of the numerical model for flow velocity, water depth and cyanobacterial concentration at cross sections. Section

MAPE (%)

S5 S7 S9 S11 S13 S15

Flow velocity

Water depth

Cyanobacterial conc.

15.6 23.2 24.2 28.2 25.1 22.3

6.5 9.1 27.6 9.2 8.8 13.6

3.03 2.55 2.51 3.93 2.27 3.71

the water depth was generally less than 15% of MAPE except the result at S9 yielding 27.6% of MAPE . This error could be explained by the local change of the river bed at this section because this study used the topography data measured in 2015. Dispersion coefficients, DL and DT that are important parameters in the water quality model based on the depth-averaged 2D advectiondispersion equation, can be related to the hydraulic characteristics such as the average shear velocity, U ∗ and the average water depth, H of the study reach, and commonly given as follows (Fischer et al., 1979):

4. Calibration and application of numerical model 4.1. Model input conditions The numerical model used in this study required several input data which includes the followings: river bathymetry of the study domain, boundary conditions, and meteorological data. The topography data with 30 × 30 m spatial resolution, as shown in Fig. 1, surveyed using RiverSurveyor M9 with RTK-GPS in 2015 (Kim et al., 2018) were used for the construction of the computational mesh of the 2D numerical model. The finite element mesh of the study reach was created by interpolating scatter points of the measured bathymetry data with the inverse distance weighting method. The generated computational mesh consisted of 10,053 nodes and 9397 elements with a combination of structured and unstructured grids, as shown in Fig. 1. For the hydrodynamic model, the average discharges measured by RiverSurveyor M9 at the cross sections of the Nakdong River before the confluence and the Kumho River were used as upstream boundaries. The water surface elevation measured at the last cross section of the Nakdong River was used as the downstream boundary. For the water quality model, water temperature, nitrate, phosphate and cyanobacterial concentrations were inputs for the upstream boundaries. The cross-sectional average values of the cyanobacterial concentration observed by AlgaeTorch 10 at the first cross section of each stream, and other water quality variables observed at the MOE monitoring stations of each stream were assigned to upstream boundaries in condition of the continuous injection for all the water quality variables from t = 0 s . Additionally, the meteorological data such as I , Td and Ws were obtained from Daegu station operated by Korea Meteorological Administration (KMA).

αL ≈

DL HU ∗

(21)

αT ≈

DT HU ∗

(22)

where αL and αT are the dimensionless longitudinal and lateral dispersion coefficients, respectively; and U ∗ can be derived from Manning’s equation for uniform flow in an open channel, given as follows:

U∗ =

n g H1/6

U

(23)

where U is the average flow velocity of the study reach. In Eq. (23), the parameters such as U , H and n were obtained from the simulation results of the hydrodynamic model. Seo et al. (2016) suggested the relation of αL and αT with the hydraulic and geometric properties of rivers based on tracer studies using the fluorescent dye, Rhodamine WT conducted in several natural streams located in South Korea. Their study showed that DL / HU ∗ and DT / HU ∗ had a strong correlation with W / H and U / U ∗, in which W is the average channel width of the study reach. Therefore, in this study, DL and DT were determined using the regression equations adapted from Seo et al. (2016). Using the flow velocity, water depth, and dispersion coefficients calculated by the hydrodynamic model, the cyanobacterial dynamics was simulated with the water quality model. Fig. 9 shows the comparison of the lateral variation of cyanobacterial concentration predicted by the numerical model with that obtained by the GWR model. The simulation results by the numerical model were in a good agreement with the GWR results that can be regarded as the observed concentration, as shown in Fig. 9. The discrepancy between the simulation and observation at all cross sections was less than 5% of MAPE , as shown in Table 3. The model accurately predicted the lateral variation of the cyanobacterial concentration especially at S9–S15, where relatively higher concentration of the cyanobacteria around the shoreline were adequately reproduced. In the section between S5 and S11, the cyanobacterial concentration gradually increased due to the channel divergence, as shown in Table 1. The widening of the channel also caused an increase in both cyanobacterial concentration and lateral variation of the concentration. This can be attributed to the decrease in the simulated flow velocity for which U decreased from 0.11 m/s to 0.07 m/s, especially along the shoreline. In the section after S11, the lateral gradient of the cyanobacterial concentration slightly decreased as the channel converged leading to an increase in the simulated flow velocity.

4.2. Model calibration Model calibration was performed by comparing the simulated results of the hydrodynamic model and water quality model with the measured hydraulic data and the cyanobacterial concentration predicted by the GWR model at several cross sections of the study reach (S5, S7, S9, S11, S13 and S15) in Fig. 4 on September 08, 2016, of which 1500 and 1300 cells/ml of the cyanobacterial concentration were introduced from Gangjeong weir and the Kumho River, respectively. The hydrodynamics model with 0.03 of n and 0.2 of Cs yielded the minimum error between the simulated values and the observed data for flow velocity and water depth, as shown in Table 3. Fig. 8 shows the comparison between the simulated and measured hydraulic variables in the lateral direction. Among the cross sections, the most upstream section, S5 showed the lowest error with 15.6% of MAPE for the flow velocity, and error for the flow velocity at the remaining cross sections was in a range of 22.3–28.2% of MAPE . The error was note to increase when the hydrodynamic model predicted low flow velocity less than 0.1 m/s. The discrepancy between the simulation and observation for 70

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J.S. Kim et al.

(a) S5 velocity (m/s)

0.2

16

0.1

8

0.0

0

-0.1

-8

0.1

8

0.0

0

-0.1

-8

-0.2 0.2

0.4 0.6 0.8 y/W from L. B.

1.0

1.2

0.2

1.2

16

-0.1

-8

-0.2

-16 0.4

0.6 0.8 y/W from L. B.

1.0

0.1

8

0.0

0

-0.1

-8

velocity (m/s)

velocity (m/s)

0

-0.2

1.2

0.2

0.2

16

0

-0.1

-8

1.0

1.0

1.2

16

(f) S15

8

0.0

0

-0.1

-8

-0.2

-16 0.4 0.6 0.8 y/W from L. B.

0.4 0.6 0.8 y/W from L. B.

0.1

velocity (m/s)

0.0

0.2

1.2

water depth (m)

8

water depth (m)

0.1

-0.2

-16 0.0

(e) S13 velocity (m/s)

1.0

water depth (m)

0.0

water depth (m)

8

0.2

0.4 0.6 0.8 y/W from L. B.

(d) S11

0.1

0.0

0.2

0.2

16

0.2

-16 0.0

(c) S9

0.0

(b) S7

-0.2

-16 0.0

16

24

water depth (m)

0.2

Sim. (vel.) Sim. (depth)

water depth (m)

Meas. (vel.) Meas. (depth)

velocity (m/s)

0.3

-16 0.0

0.2

0.4 0.6 0.8 y/W from L. B.

1.0

1.2

Fig. 8. Comparison between simulation and measurement for flow velocity and water depth at cross sections on September 08, 2016, in which L. B. and y refer to the left bank of the cross sections and distance from L. B., respectively.

upstream boundary equivalent to discharge of the Nakdong River for the hydrodynamic model varied with each scenario, as shown in Table 5 to investigate the change of the spatial distribution of cyanobacterial concentration with the increase in the inflow discharge. Fig. 10 shows that the simulated flow velocity fields for specific cases (Case 0, Case 1, Case 3 and Case 5). Similar to the calibration case, the simulated flow velocity gradually decreased from S5 to S11 owing to the channel divergence which facilitated the favorable hydraulic conditions for the cyanobacterial growth by retarding the water flow. In Case 0 and Case 1, the flow velocity was noted to be lower than 0.1 m/s where the inflow discharge was smaller than 200 m3/s whereas, in Case 3, the flow velocity along the main flow zone of the Nakdong River was faster than the critical value although some regions like the shoreline had a flow velocity lower than 0.1 m/s. In Case 5 where the inflow discharge was 300 m3/s, the velocity exceeded 0.1 m/s across the cross sections over the entire study reach. Fig. 11 shows the spatial distribution of the simulated cyanobacterial concentration accounted for the simulated flow velocity fields in Fig. 10. This figure illustrates that, for cases with higher discharges, the decrease in WRT with the increased flow velocity would not allow the cyanobacteria to be stagnant for the growth as the water flow faster than 0.1 m/s considerably contributed to flush out the accumulated cyanobacteria along the shoreline of the Nakdong River after the confluence of the Kumho River. Therefore, the area with the cyanobacterial concentration exceeding 10,000 cells/ml drastically reduced with the increase in the inflow discharge from Gangjeong weir. Additionally, the

As shown by the results obtained by the model calibration, it can be concluded that the cyanobacterial concentration higher than 2000 cells/ml was suppressed along the main flow zone with flow velocity faster than about 0.1 m/s whereas it proliferated along the shoreline with flow velocity lower than this critical value, as shown in Fig. 9. The numerical model was calibrated with parameters that provided the best fit between the observation and simulation by minimizing MAPE . The calibrated parameters are listed in Table 4. 4.3. Model application In order to evaluate the effect of inflow discharge from Gangjeong weir on the HAB control downstream of the weir, the numerical simulation with the seven scenarios in addition to the actual HAB event on August 17, 2015 referred to Case 0 was conducted using the calibrated model. In Case 0, 6550 and 9970 cells/ml of the cyanobacterial concentration were introduced from Gangjeong weir and the Kumho River, respectively, and the inflow discharge from Gangjeong weir and the Kumho River was 47.8 and 39.0 m3/s, respectively. This base discharge of the weir was close to the low flow condition corresponding to the 275-day flow of the Nakdong River before the confluence of the Kumho River during 2015–2016. In this discharge range, HAB associated with high cyanobacterial concentration usually occurred in the study reach, as illustrated in Fig. 3. The boundary and meteorological conditions for the water quality model for all scenarios from Case 1 to Case 7 were identical to those of Case 0. While on other hand, the 71

Journal of Hydro-environment Research 20 (2018) 63–76

2,250

0.15

2,000

0.10

1,750

0.05 0.00

1,500 0.0

0.2

0.4

0.6 0.8 y/W from L. B.

1.0

Concentration (cells/ml)

0.15

2,000

0.10

1,750

0.05 0.00

1,500 0.8

2,000

0.10

1,750

0.05 0.00 0.2

0.4

1.0

0.20

2,250

0.15

2,000

0.10

1,750

0.05 0.00 0.0

0.2

0.4

Concentration (cells/ml)

Concentration (cells/ml)

0.8

1.0

1.2

2,000

0.10

1,750

0.05

1,500

0.00 1.0

2,500

0.20

(f) S15

2,250

0.15

2,000

0.10

1,750

0.05

1,500

0.00 0.0

1.2

Velocity (m/s)

0.15

Velocity (m/s)

2,250

0.8

0.6

y/W from L. B.

0.20

0.6

1.2

1,500

(e) S13

0.4

1.0

(d) S11

1.2

2,500

0.2

0.8

2,500

y/W from L. B.

0.0

0.6

Velocity (m/s)

2,250

0.6

0.15

0.0

0.20

0.4

2,250

1,500

(c) S9

0.2

0.20

(b) S7

y/W from L. B.

2,500

0.0

2,500

1.2

Velocity (m/s)

Concentration (cells/ml)

0.20

Velocity (m/s)

Obs. (conc.) Sim. (conc.) Sim. (vel.)

(a) S5

Concentration (cells/ml)

2,500

Velocity (m/s)

Concentration (cells/ml)

J.S. Kim et al.

0.2

0.4

0.6

0.8

1.0

1.2

y/W from L. B.

y/W from L. B.

Fig. 9. Comparison between simulation and GWR results for cyanobacterial concentration at cross sections on September 08, 2016, in which L. B. and y refer to the left bank of the cross sections and distance from L. B., respectively.

Table 4 Calibrated parameters used in the water quality and hydrodynamic models. Parameter

Description

Range1

Calibrated value

μ max kresp

Maximum growth rate of cyanobacteria (/day) Respiration rate of cyanobacteria (/day)

0.5–3.0 0.02–0.80

0.98 0.05

kdeath k excr θ ωc K1, K2 Topt KN KP ke Is αN kN αP αL αT n Cs

Death rate of cyanobacteria (/day) Excretion rate of cyanobacteria (/day) Temperature coefficient Settling velocity of cyanobacteria (m/day) Curve parameters in water temperature limitation function (/°C2) Optimal water temperature for cyanobacterial growth (°C)

0.02–0.80 0.02–0.80 1.02–1.09 0–1 0–0.1 25–35

0.03 0.01 1.09 0.05 0.02 28

Half-saturation constant of nitrate (μg/L) Half-saturation constant of phosphate (μg/L) Light attenuation coefficient Saturating light constant (ly/day) Stoichiometric ratio of nitrate to cyanobacteria (μg nitrate/cells cyanobacteria) Denitrification rate (/day) Stoichiometric ratio of phosphate to cyanobacteria (μg phosphate/cells cyanobacteria) Dimensionless coefficient of longitudinal dispersion Dimensionless coefficient of lateral dispersion Manning’s coefficient Smagorinsky coefficient

10–200 1–70 0.22–7.31 88–300 0.08–0.09 0–1 0.012–0.015 – – 0.02–0.05 0.1–0.3

50 3 0.35 120 0.08 0.09 0.015 33.9 1.06 0.03 0.2

1

The ranges of all parameters were used with reference to Kim et al. (2018).

increase in the dispersion coefficients, especially DT with the enhanced U ∗ significantly reduced the lateral gradient of the cyanobacteria concentration because the enhanced lateral dispersion effectively acted to suppress the localized proliferation of the cyanobacteria along the shallow and slow flow zone. The blooming area (BA ), maximum concentration (MC ) of the cyanobacteria, and average lateral variance (σT2 )

of the cyanobacterial concentration with average WRT (Tr ) of the section after the confluence for each scenario are summarized in Table 5. In this table, BA was defined as the area with the cyanobacterial concentration exceeding the warning level which is 10,000 cells/ml. Tr was calculated by dividing the length of the study reach by U . This table indicates that all four key parameters calculated from the numerical 72

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usually faster than the sum of the respiration, death and excretion rates at the optimal conditions such as high water temperature and light intensity during summer, as shown in Table 4. Despite this limitation, the control of the inflow discharge can still be efficient in controlling other parameters such as MC and σT2 by shortening Tr associated with HAB reduction in the study reach of the Nakdong River.

Table 5 Summary of simulation conditions and results for each scenario. Case Case Case Case Case Case Case Case Case

0 1 2 3 4 5 6 7

QN (m3/s)

Tr (hour)

MC (cells/ml)

BA (%)

σT2

47.8 100 150 200 250 300 350 400

56.6 41.4 32.2 26.6 22.7 19.8 17.9 15.7

20,666 15,773 13,419 12,029 11,143 10,493 10,021 9664

100.0 90.2 49.8 30.4 19.3 6.1 0.2 0.0

2,256,001 2,010,713 1,470,943 1,082,204 842,386 663,544 543,910 460,213

5. Conclusions The spatial variability of HAB in the Nakdong River was investigated using the depth-averaged 2D model. The field survey was conducted to acquire cyanobacterial concentration data and hydraulic data for the calibration of the numerical model. Satellite remote sensing was also applied to retrieve a high resolution map of the cyanobacteria concentration by adoption of the GWR approach. The GWR model proposed in this study yielded more accurate results over the conventional MLR model as the prediction accuracy was enhanced to R2 = 0.719 from 0.615. The numerical model with calibrated parameters showed a satisfactory prediction level with less than 30% and 5% of MAPE for hydraulic properties measured by the field survey and cyanobacterial concentration retrieved from the GWR model, respectively. The numerical model accurately reproduced higher cyanobacterial concentration along the shoreline where the cyanobacterial growth was preferred due to longer WRT and less light attenuation caused by the

simulation results decreased as the inflow discharge increased. These findings are elucidated more clearly in Fig. 12 in which the reduction rates of these parameters according to the rate of the inflow discharge are depicted. In this figure, one can notice that BA can be reduced to less than 10% of its original area when the discharge increased up to about 6 times the original value as WRT decreased to about 37% of its original value. However, this effect on reducing BA only be valid when the cyanobacterial concentration lower than the warning level was introduced from the upstream of the study reach. This is because the cyanobacterial concentration simulated in the study reach could not be decreased to a value lower than that of the boundary condition only with the control of the inflow discharge since the growth rate was

(a) Case 0 ( QN = 47.8 m3/s)

(b) Case 1 ( QN = 100 m3/s)

(c) Case 3 ( QN = 200 m3/s)

(d) Case 5 ( QN = 300 m3/s)

Fig. 10. Spatial variability of simulated velocity for each scenario, in which QN refers to the inflow discharge from Gangjeong weir. 73

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(a) Case 0 ( QN = 47.8 m3/s)

(b) Case 1 ( QN = 100 m3/s)

(c) Case 3 ( QN = 200 m3/s)

(d) Case 5 ( QN = 300 m3/s)

Fig. 11. Spatial variability of simulated cyanobacterial concentration for each scenario, in which QN refers to the inflow discharge from Gangjeong weir.

1.2 1.0 Parameter ratio

discharge increased to about 6 times the original level, the blooming area of the cyanobacteria reduced by a small margin. Moreover, the increase in U ∗ reduced the localized accumulation of the cyanobacteria along the shoreline referred to the shallow and slow flow zone as it decreased the lateral gradient of the cyanobacterial concentration with the enhanced lateral dispersion of water quality. In the regulated rivers, the results from this study can help with decision making for the weir operation and securing water supplies by suggesting the threshold value of the inflow discharge for the HAB reduction when the additional water flow from the weir is required to reduce the intensity of HAB to the safety level.

BAR BAR MC R MCR 2 (σ T ) R VARR (Tr ) R WRTR

0.8 0.6 0.4 0.2 0.0 0

2

4

6

8

10

(QN)R

Acknowledgements

Fig. 12. Reduction efficiency of HAB with the increased rate of inflow discharge from Gangjeong weir, in which (QN )R , (Tr )R , MCR , BAR and (σT2)R refer to the ratio of QN , Tr , MC , BA and σT2 obtained from each scenario, respectively to their original values obtained from Case 0.

This research was supported by the BK21 PLUS research program of the National Research Foundation of Korea. The authors would like to express their sincere gratitude to the River Survey Team of Changwon National University for their valuable contribution to the field work. This research work was conducted at the Institute of Engineering Research and Institute of Construction and Environmental Engineering in Seoul National University, Seoul, Korea.

slow flow velocity and shallow water depth, respectively. The simulation results of HAB mitigation scenarios with the calibrated numerical model revealed that the blooming area and maximum concentration of cyanobacteria in the study reach proportionally decreased with an increase in inflow discharge from Gangjeong weir. Flow velocity faster than 0.1 m/s sufficiently suppressed HAB because the fast water flow disrupted the cyanobacterial growth. When the inflow

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