the Creative Commons Attribution 4.0 License.

the Creative Commons Attribution 4.0 License.

# Hydrodynamic and biochemical impacts on the development of hypoxia in the Louisiana–Texas shelf – Part 2: statistical modeling and hypoxia prediction

### Yanda Ou

### Bin Li

This study presents a novel ensemble regression model for forecasts of the
hypoxic area (HA) in the Louisiana–Texas (LaTex) shelf. The
ensemble model combines a zero-inflated Poisson generalized linear model
(GLM) and a quasi-Poisson generalized additive model (GAM) and considers
predictors with hydrodynamic and biochemical features. Both models were
trained and calibrated using the daily hindcast (2007–2020) by a
three-dimensional coupled hydrodynamic–biogeochemical model embedded in the
Regional Ocean Modeling System (ROMS). Compared to the ROMS hindcasts, the
ensemble model yields a low root-mean-square error (RMSE) (3256 km^{2}),
a high *R*^{2} (0.7721), and low mean absolute percentage biases for overall
(29 %) and peak HA prediction (25 %). When compared to the shelf-wide
cruise observations from 2012 to 2020, our ensemble model provides a more
accurate summer HA forecast than any existing forecast models with a high
*R*^{2} (0.9200); a low RMSE (2005 km^{2}); a low scatter index (15 %); and low mean absolute percentage biases for overall (18 %),
fair-weather summer (15 %), and windy-summer (18 %) predictions. To
test its robustness, the model is further applied to a global forecast model
and produces HA prediction from 2012–2020 with the adjusted predictors
from the HYbrid Coordinate Ocean Model (HYCOM). In addition, model
sensitivity tests suggest an aggressive riverine nutrient reduction strategy
(92 %) is needed to achieve the HA reduction goal of 5000 km^{2}.

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The Louisiana–Texas (LaTex) shelf has become a center of hypoxia (bottom
dissolved oxygen, DO *<* 2 mg L^{−1}) study since the 1980s (e.g.,
Rabalais et al., 2002, 2007a;
Justić
and Wang, 2014). Regular mid-summer shelf-wide cruises documented that the
area and volume of hypoxic bottom water could reach up to 23 000 km^{2}
and 140 km^{3}, respectively (Rabalais and Turner,
2019; Rabalais and Baustian, 2020). The aquatic environments,
fisheries, and coastal economies are under threat of recurring hypoxia in
summer (Chesney and Baltz, 2001;
Craig and Bosman, 2013;
de Mutsert et al., 2016;
LaBone et al., 2021; Rabalais and
Turner, 2019; Rabotyagov et al., 2014;
Smith et al., 2014). For example, habitats of
some fish species (e.g., croaker and brown shrimp) shift to offshore hypoxic
edges (Craig and Crowder, 2005;
Craig, 2012) during summer hypoxia events,
which may impact organism energy budgets and trophic interactions
(Craig and Crowder, 2005;
Hazen et al., 2009). The horizontal
displacement of habitats of brown shrimp in summer can also lead to changes in
the distribution of Gulf of Mexico shrimp fleets
(Purcell et al., 2017). Although an action
plan has been launched by the Mississippi River/Gulf of Mexico Hypoxia Task
Force to control the size of the mid-summer hypoxic zone below 5000 km^{2} in a 5-year running average since 2001
(Mississippi River/Gulf of Mexico Watershed Nutrient Task
Force, 2001, 2008), extents of the hypoxic area have experienced no
significant decreases in recent decades (Del
Giudice et al., 2020). An accurate prediction of the hypoxic area is
urgently needed for coastal managers and the fishery industry.

Water column stratification and sediment oxygen consumption (SOC) are two main factors regulating the formation, evolution, and destruction of bottom hypoxia from mid-May through mid-September (Bianchi et al., 2010; Conley et al., 2009; Fennel et al., 2011, 2013, 2016; Feng et al., 2014; Hetland and DiMarco, 2008; Justić and Wang, 2014; Laurent et al., 2018; McCarthy et al., 2013; Murrell and Lehrter, 2011; Rabalais et al., 2007b; Wang and Justić, 2009; Yu et al., 2015). The stratification inhibits bottom water reoxygenation, while SOC, induced by water eutrophication associated with high anthropogenic nutrient supplies by rivers, can lead to anaerobic benthic environments. Nevertheless, existing prediction models of hypoxic area (HA) rely mostly on contribution from the nutrient load rather than hydrodynamic features. Turner et al. (2006) built a multiple linear regression model for summer HA prediction using the annual and May nitrogen flux (nitrate + nitrite) of the Mississippi River as the predictors. The model provides a robust annual prediction when no strong wind is present but overestimates HA in windy years. Obenour et al. (2015) modeled HA using the empirical relationship between HA and bottom DO concentration derived from a Bayesian biophysical model. Their model accounts for primary biophysical processes solved for steady-state conditions, water transport, May total nitrogen loads by rivers, and parameterized water reaeration. Katin et al. (2022) further adjusted the Bayesian model by taking into account river flows, riverine bioavailable nitrogen loadings, and wind velocity in both summer (June–September) and non-summer (November–May) months. Summer riverine inputs are projected using non-summer riverine variables, river basin precipitation, and river basin temperature, while summer wind velocity is resampled from historical records between 1985 and 2016. Therefore, the seasonal prediction model is known as a pseudo forecast model, since predictors in future stages only include riverine inputs. This model explains 71 % and 41 %–48 % of the variability in the hindcast (Del Giudice et al., 2020) and geostatistically estimated HA (Matli et al., 2018), respectively. An additional Bayesian model applied to summer bottom DO prediction accounts for May total nitrogen loads, distance from the Mississippi River mouth, and downstream velocity (Scavia et al., 2013). The summer HA is determined by hypoxic length (HA = 57.8 hypoxic length) derived from summer bottom DO concentration. The model explains 69 % of the variability in observed HA by the mid-summer shelf-wide cruises. Mechanistic prediction methods have also been applied by Laurent and Fennel (2019) to develop a weighted mean forecast that is calibrated using May nitrate loads and three-dimensional hindcast simulations over the period 1985–2018. Once calibrated, the model only requires May nitrate loads as an input to produce the seasonal forecast for a given year. The model can explain up to 76 % of the year-to-year variability in the HA observation. However, the model is not favorable for years with strong wind events during summer.

These above-mentioned models share some similar drawbacks. (1) The effects of water column stratification are considered only implicitly by the associated wind speeds, water transport, and riverine nutrient loads (usually correlated to river discharges), although stratification is documented as a crucial factor in regulating HA variability. (2) Forecasts of the predictors are usually limited, which restricts some of these seasonal models to pseudo ones. (3) Most models are only capable of capturing interannual HA variability and are not reliable in summers when winds are strong. According to the hindcast results by our three-dimensional coupled hydrodynamic–biogeochemical model described in the accompanying paper (Part 1), strong wind events bring considerable uncertainties to monthly and daily variabilities in HA. In this study we aim to provide a novel HA prediction method that considers both stratification and biochemical effects. Our new model aims to produce daily HA forecasts based on selected predictors' forecasts with a minimum computational cost. The rest of the paper is organized as follows. Detailed descriptions of methods and data are given in Sect. 2. The implementations of generalized linear models (GLMs), generalized additive models (GAMs), and an independent model application using a global forecast product (HYbrid Coordinate Ocean Model, HYCOM; Bleck and Boudra, 1981; Bleck, 2002) are given in Sect. 3. Comparisons against existing forecast models and recommendations on nutrient reduction strategy are given in Sect. 4.

## 2.1 Data preparation

We adapted a three-dimensional coupled hydrodynamic–biogeochemical model
embedded in the framework of the Regional Ocean Modeling System (ROMS) on
the platform of Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST)
modeling system (Warner et
al., 2010) to the Gulf of Mexico (GoM; Gulf–COAWST, for detailed descriptions, validations, and results of the numerical model, see Part 1). Numerical hindcasts
(hereafter denoted as ROMS hindcasts or ROMS simulations) are output daily
from 1 January 2007 to 26 August 2020 and spatially averaged over the LaTex
shelf extending from the west of Mississippi River mouth to 95^{∘} W
with water depths ranging from 6 to 50 m (color shaded region in Fig. A1b).

### 2.1.1 Hydrodynamic-related predictors

Both water stratification and bottom biochemical processes modulate the
variability in bottom DO concentration in the LaTex shelf. Potential energy
anomaly (PEA, in J m^{−3}) is introduced as an estimate of water column
stratification according to

where *ρ* is the water density profile (estimated by water temperature and
salinity profiles) over the water column of depth $H=h+\mathit{\eta}$,
*h* is the location of the bed, *η* is water surface elevation, *g* is
the gravitational acceleration (9.8 m s^{−2}), *z* is the vertical axis, and
$\stackrel{\mathrm{\u203e}}{\mathit{\rho}}$ is the depth-integrated water density given by $\stackrel{\mathrm{\u203e}}{\mathit{\rho}}=\frac{\mathrm{1}}{H}{\int}_{-h}^{\mathit{\eta}}\mathit{\rho}\mathrm{d}z$
(Simpson and Hunter, 1974, 1978; Simpson, 1981;
Simpson and Bowers, 1981). The PEA
represents the amount of energy per volume required to homogenize the entire
water column (Simpson and Hunter, 1974). Thus, a greater PEA
value represents a more stratified water column. As a river-dominated area,
water stratification in the LaTex shelf is highly affected by
freshwater-induced buoyancy from the Mississippi and Atchafalaya rivers. Sea
surface salinity (SSS) is a good proxy for representing the distribution and
variability in river freshwater across the shelf. Indeed, the correlation of
regionally averaged PEA and SSS is significantly high as −0.87 (*p**<*0.001; Fig. 1a), which emphasizes the importance of freshwater-induced
stratification. Therefore, we considered SSS as another candidate predictor
besides PEA.

Surface heating and wind mixing are two other factors that influence water stratification (Simpson, 1981). The tidal effects considered in Simpson (1981) are neglected here due to the relatively weaker contribution in stratification in the shelf when compared to the effects of rivers and winds. The two mixing terms are quantified as follows:

where *Q* is the rate of surface heat input, *α* is the volume
expansion coefficient, *c* is water specific heat capacity, *δ* is a
coefficient of wind mixing, *k*_{a} is the drag coefficient, *ρ*_{a} is
the density of humid air near the sea surface, and *W* is the wind speed near the
sea surface. The first term on the right-hand side of Eq. (2) represents the
rate of change in water stratification due to surface heating, while the
second term is the rate of working by wind stress contributing negatively to
water stratification. Therefore, the heat-induced change in PEA is
proportional to surface heat input, which is

The total net heat flux, a sum of net shortwave and net longwave radiation
flux, is derived from the National Centers for Environmental Prediction (NCEP)
Climate Forecast System Reanalysis (CFSR) 6-hourly products
(Saha et al., 2010,
2011) in this study. The term *Q* is
added to the candidate list of predictors and is denoted as
PEA_{heat} (heat-induced PEA changes) for
simplification (Fig. 1a).

Daily variability in the term (*δ**k*_{a}*ρ*_{a}*W*^{3}) is
dominated by that of *W*^{3}, since the *ρ*_{a} fluctuates much
less than the *W*^{3} on a daily scale (Fig. A2). We obtained
*ρ*_{a} according to (Picard et al.,
2008):

where *p* represents the absolute air pressure, *M*_{d} (28.96546 g mol^{−1}) is the molar mass of dry air, *M*_{v} (18.01528 g mol^{−1})
is the molar mass of water vapor, *Z* indicates compressibility, *R* (8.314472 J mol^{−1} K^{−1}) is the molar gas constant, *T* is
thermodynamic temperature, and *x*_{v} is the mole fraction of water vapor. We
assumed that air parcels at the sea surface are ideal gases (*Z*=1) and are
always saturated with water vapor. Thus, *x*_{v} is a function of the absolute
air pressure (*p*) and saturation vapor pressure of water (*p*_{sat}) and
can be calculated as follows:

According to the adjusted Tetens equation
(Murray, 1967; Monteith and
Unsworth, 2014), *p*_{sat} (in Pa) can be estimated by

where ${T}^{\prime}=\mathrm{36}$ K. Substituting Eqs. (5)–(6) for Eq. (4) with the
assumption of *Z*=1, we obtained air density as a function of both air
pressure and air temperature in the following:

*ρ*_{a} is then estimated using sea surface air pressure and air
temperature 2 m above the sea surface provided by NCEP CFSR 6-hourly
products. The correlation of daily *ρ*_{a}*W*^{3} and
*W*^{3} (provided by NCEP CFSR 6-hourly products) is significantly
high as 0.9988 (*p**<*0.001, Fig. A2), emphasizing the importance of
term *W*^{3} in controlling the daily variability in wind-induced
PEA changes over the shelf. We, thus, approximated the relationship as

The term *W*^{3} is introduced as another candidate predictor and
is denoted as PEA_{wind} (wind-induced PEA changes)
for simplification (Fig. 1a).

### 2.1.2 Biochemical-related predictors

Sedimentary biochemical processes directly influence the bottom DO
consumption rate. However, global forecast models such as HYCOM do not cover
biochemical parameters. Therefore, the biochemical-related term SOC needs to
be replaced by an alternative term (denoted as SOCalt). According to the SOC
scheme (Eq. 9) stated in Part 1, the biochemical features are attributed to
the sedimentary particulate organic nitrogen concentration (PONsed, derived
from ROMS hindcasts). The total nitrate + nitrite loads by the Mississippi
River are used to represent the PONsed variability due to the long-term data
supports. The daily Mississippi River discharges at site 07374000 have been
updated daily by the U.S. Geological Survey (USGS) National Water
Information System (NWIS) since March 2004. The total nitrogen concentration
at site 07374000 has been provided and updated daily by USGS since November 2011.
Prior to 2011, nitrogen loads (at site 07374000) were provided monthly by
USGS and, in this study, are interpolated to daily intervals according to
the corresponding monthly loads. Although phosphate and silicate are another
two important nutrients in the shelf, daily measurements are still not
available for the Mississippi River. Monthly total nitrate + nitrite loads,
phosphate loads, and silicate loads by both the Mississippi River and the
Atchafalaya River are significantly correlated (Table A1). Therefore, the
total nitrate + nitrite loads applied here can be interpreted as total
nutrient loads by both river systems. Due to lateral transports and vertical
settling of particulate organic matter, a leading period should be
introduced to the time series of riverine nutrient loads. The optimal length
of leading days is obtained by examining the highest linear correlation of
regionally averaged ROMS-hindcast SOC and SOCalt (Eq. 10) and is
calculated as 44 d (*R*=0.7427, *p**<*0.001, Fig. A3a). The
exponential term in Eqs. (9)–(10) estimates the temperature-dependent
decomposition rate of organic matter:

where VP2N_{0} is a constant representing the decomposition rates of sedimentary
particulate organic nitrogen PON_{sed} at 0 ^{∘}C,
*K*_{P2N} is a constant (0.0693 ^{∘}C^{−1}) indicating
temperature coefficients for decomposition of PON_{sed}, and *T*_{b} is
bottom water temperature (in ^{∘}C). The *Q*_{10} (2 given the above
chosen coefficients; van 't Hoff and Lehfeldt, 1899;
Reyes et al., 2008) assumption is applied to mimic the aerobic
decomposition rate of PON_{sed}. Along with SOCalt, the
temperature-dependent decomposition rate ${e}^{\mathrm{0.0693}\cdot {T}_{\mathrm{b}}}$ is also
considered a candidate predictor in statistical models and is denoted as
DCP_{Temp} for simplification.

### 2.1.3 HA estimation

As listed in Table 1, six candidate predictors are considered in the
statistical models including four stratification-related variables (PEA,
SSS, PEA_{heat}, and PEA_{wind}) and two bottom biochemical variables
(SOCalt and DCP_{Temp}). The correlation matrix (Fig. 1a)
indicates that multicollinearity may become a problem in regression models,
since linear correlations among some predictors are significantly high,
e.g., 0.74 (*p**<*0.001) between PEA and SOCalt and −0.87 (*p**<*0.001) between PEA and SSS. The multicollinearity can violate the assumption
that predictors are independent. It can lead to difficulties in individual
coefficient tests and numerical instability (Siegel and
Wagner, 2022). The frequency distribution of HA (Fig. 1b) illustrates that
the response variable is highly skewed to the right with ∼ 42 % of
samples (2081 out of 4943) being exactly zero. HA is estimated by the
number of hypoxia cells (ROMS computational cells reaching hypoxic
conditions) times a nearly constant value (area of the computational cell),
which is 25.56 ± 0.17 km^{2} (mean ± 1 SD). Thus, HA can be
estimated by the number of grid cells when the Poisson and negative binomial
regression models are applied. However, the great portion of zero samples
leads to overdispersion (magnitude of variance ≫ magnitude of mean,
i.e., 45 730 441 ≫ 4507) and zero-inflated problems
(Lambert, 1992). The overdispersion issue
violates the mean-variance equality assumption employed in regular Poisson
regression models, while zero-inflated problems can weaken the model
performances.

## 2.2 Data pre-processes

We first spatially averaged ROMS-derived predictors (daily) over the LaTex shelf (color-shaded area in Fig. A1b) and then applied the min–max normalization (Eq. 11) to the one-dimensional time series. Predictive models can be beneficial from the min–max normalization when applying to a new dataset, since the method guarantees that the normalized predictors from different datasets range from 0 to 1 as the minimum and maximum values are prescribed. Note that the response is not normalized.

where *X*_{nor}, *X*_{org}, min_{prescribed}, and max_{prescribed}
represent the normalized value, original value, prescribed minimum, and
prescribed maximum, respectively. The daily samples are then split into a
training set (for model construction) accounting for 80 % of the total
samples and a test set (for assessment of model performances) accounting for
the remaining 20 %. To maintain the HA distribution in both sets, a
stratified random resampling method is applied in different HA intervals individually.
For example, 80 % of samples with HA = 0 are chosen randomly for the
training set out of all daily samples with HA = 0, while the rest of the
samples with HA = 0 are grouped into the test set. HA = 0 is the first
interval to which the resampling process is applied, while the remaining
samples are split at intervals of 5000 km^{2}. However, the distribution
of HA from each year is similar with a right-skewed structure and numerous
zero values. Thus, even through random processes, both the training and test
sets contain samples from each year including samples with non-peak and peak
HA. This splitting method increases the model applicability and provides a
comprehensive assessment of prediction performances on both non-peak and
peak HA.

## 2.3 Model skill assessment

The *R*^{2}, root-mean-square error (RMSE), mean absolute percentage bias
(MAPB), and scatter index (SI; Zambresky, 1989) are used to assess
the model performances in HA predictions. The SI is a normalized measure of
error or a relative percentage of expected error with respect to the mean
observation. The calculations of the statistics are given in Eqs. (12)–(15):

where *P*_{i} and *O*_{i} represent the *i*th record of prediction and
observation (or hindcast), while $\stackrel{\mathrm{\u203e}}{O}$ represents the average of all
observed (or hindcast) records.

## 3.1 Model built-up process

Several regression models are explored using the statistical programming
language R. To find the “best” model balancing both model interpretability
and prediction performance, a procedure is conducted for model selection
(Fig. 2) and is summarized below. (1) Choose a regression model. (2) Apply
an exhaustive best-subset searching approach to the chosen model. Models
with possible combinations of candidate predictors from the ROMS training
set are built. A 10-fold cross-validation (CV) method is applied to each
model, yielding 10 RMSEs and 1 corresponding mean. The candidate predictors
of PEA and SOCalt are forced into each subset. Thus, the number of fitted
models with a subset size of *k* is $C\left(\mathrm{6}-\mathrm{2},k-\mathrm{2}\right)=\frac{\mathrm{4}\mathrm{!}}{\left(\mathrm{6}-k\right)\mathrm{!}(k-\mathrm{2})\mathrm{!}}\phantom{\rule{0.125em}{0ex}},\phantom{\rule{0.125em}{0ex}}\mathrm{2}\le k\le \mathrm{6}$ (the total number of candidate
predictors is 6). The optimal subset of this size is found as the one with
the lowest mean CV RMSE among these models. The best subset is then obtained
by comparing mean CV RMSEs of the optimal subsets of different sizes. (3) Steps (1)–(2) are repeated for the selected *M* candidate regression models.
(4) Prediction performances of different models with the corresponding best
subsets are assessed by the 10-fold CV RMSEs and bootstrap (1000 iterations) aggregating (i.e., bagging) ensemble algorithms. The bagging
method builds the given model *N* (1000) times during each of which the
given model is trained using different samples chosen randomly and
repeatedly from the ROMS training set and is executed for HA prediction
using samples in the ROMS test set. The ensemble means and ensemble 95 %
prediction intervals (PIs) of forecast HA are given according to the
prediction results in the 1000 iterations. The best model (model X in
Fig. 2) is chosen according to the comparisons of the 10-fold CV RMSEs and
the bagging results.

## 3.2 Generalized linear models (GLMs)

### 3.2.1 Regular GLMs and zero-inflated GLMs

The response variable can be treated as count data. Regular Poisson
(function `glm`

in R package `stats`

version 3.6.2), quasi-Poisson (function
`glm`

in R package `stats`

version 3.6.2), and negative binomial (function
`glm.nb`

in R package `MASS`

version 7.3-54; Venables and
Ripley, 2002) GLMs are explored in this section. The latter two GLMs are
known for solving overdispersion problems by relaxing the mean-variance
equality assumption. These GLMs make use of a natural log link function.
Thus, a natural logarithm of the area of a single ROMS cell (∼ 25.56 km^{2}) is added to the models as an offset term (an additional
intercept term).

In addition, the overdispersion issue can result from the great percentage
(∼ 42 %) of zero values in the response variable (Fig. 1b). Zero-inflated GLMs (using function `zeroinfl`

in R package `pscl`

version 1.5.5; Jackman, 2020; Zeileis et al.,
2008) are developed for dealing with response variables of this kind. Rather
than resetting dispersion parameters, a zero-inflated count model is a
two-component mixture model blending a count model and a zero-excess model.
The count model is usually a Poisson or negative binomial GLM (with log
link), while the zero-excess model is a binomial GLM (with a logit link in
this study) estimating the probability of zero inflation. An offset term of
log (25.56) is also introduced into the count model. Instead of applying the
best-subset searching to the count and zero-excess models simultaneously, in
this study, the searching is conducted, respectively, for these two models to
reduce the demands of computational resources. The best subset of the
zero-excess model (binomial GLM) is given first. The best subset of the
count model (Poisson or negative binomial GLMs) is then provided blending
the zero-excess model with the corresponding selected best subset.

However, it is hard to determine whether a given zero value of HA is
excessive; instead, it is relatively easy to model hypoxia occurrence
assuming that all the zero values are excessive. A new binary response,
hypoxia, stated in Eq. (16) is introduced for modeling hypoxia occurrence
using regular binomial GLMs (function `glm`

in R package `stats`

version 3.6.2). The hypoxia is equal to 0 when HA is 0 (no hypoxia); otherwise, it is
equal to 1. The optimal model selected three predictors: PEA, SOCalt, and
DCP_{Temp} (Fig. 3b).

### 3.2.2 Performance of GLMs

The zero-inflated Poisson GLM serves as the best GLM in terms of prediction
performances, since it has the lowest mean CV RMSE (Fig. 3a) among the five
candidates GLMs. The relaxation of the mean-variance equality assumption by
the negative binomial GLM and the quasi-Poisson GLM does not guarantee
salient improvement in performances when comparing their CV RMSEs to those
of regular Poisson GLM. The zero-inflated negative binomial GLM yields
similar performances to the three regular GLMs. The mean CV RMSEs of
zero-inflated Poisson GLM hit the trough (3573 km^{2}) at the size of 4. However, the greatest drop of RMSEs (3586 km^{2}) occurs at the
size of 3 beyond which the RMSEs remain stable. It is worth considering
a model with fewer predictors satisfying model interpretability. Thus, the
best zero-inflated Poisson GLM accounts for three predictors (PEA, SOCalt,
and DCP_{Temp}) in the count model and three predictors (PEA, SOCalt, and
DCP_{Temp}) in the zero-excess model. As indicated in the correlation
matrix (Fig. 1a), the robustness of a model can be impaired by
multicollinearity which can be estimated by variance inflation factors
(VIFs). VIFs among the selected predictors are 2.15, 2.70, and 1.59 for PEA,
SOCalt, and DCP_{Temp}, respectively. The VIFs are all less than 5,
suggesting that both the count and the zero-excess models with these
predictors involved are merely violated by multicollinearity. For
simplicity, the best zero-inflated Poisson GLM is symbolized as GLMzip3.

The bagging ensemble method is implemented to estimate the prediction
performance of GLMzip3 (Fig. 4a). It is noted that the training set and
test set are resampled according to different HA intervals. Since the
distributions of HA in each year are similar (see Sect. 2.2), both
the training and test set contain peak and non-peak HA values in
each year. Therefore, samples shown in Fig. 4 are listed sequentially in
the time dimension from 2007 to 2020 but are not necessarily evenly
distributed. The listed samples should not be regarded as time series. The
bagging means of predicted HA provide an RMSE of 3614 km^{2} and an
*R*^{2} of 0.7214 against the ROMS hindcasts. The bagging 95 % PIs are
restricted within a narrow range with a slight increase at the predicted
peaks. Within different ranges of hindcast HA, the MAPB between predicted
and hindcast HA ranges from 29 % to 38 % with an average of 33 %
(Table 2). Particularly, GLMzip3 produces the lowest bias (29 %) for
the hindcast HA at ≥ 30 000 km^{2}. The results suggest that GLMzip3 is
capable of providing not only accurate but also stable HA forecasts.
Nevertheless, we noted salient overestimations (e.g., peaks around samples 30, 481, and 901) and underestimations (e.g., peaks around samples 181, 390,
and 826) at some peaks. Instead of the prediction performance at non-peak
HA, here we focused more on the forecasts at HA peaks which impose more
threats to the shelf ecosystem. In Sect. 3.3, GAMs are investigated with
an expectation of further improvements in peak predictions by considering
non-parametric or non-linear effects of the predictors.

### 3.2.3 Model interpretation for GLMzip3

We applied the complete ROMS training set to the model construction of
GLMzip3. Coefficients for PEA, SOCalt, and DCP_{Temp} (Table 3) are all
found to be significantly positive (*p**<*0.001) in the count model, while
coefficients for these predictors are significantly negative (*p**<*0.001) in the zero-excess model. The count model simulates HA, while the
zero-excess model estimates the probability of HA being zero. Higher PEA is
consistent with stronger water stratification, while higher SOCalt and
DCP_{Temp} are both corresponding to higher sediment oxygen consumption.
Therefore, there is no surprise that higher PEA, SOCalt, and DCP_{Temp}
are related to greater HA and higher hypoxia occurrence or a lower probability
of HA being zero. Results indicate that GLMzip3 essentially builds up
reasonable relationships between the response and predictor variables with
a high agreement with physical and biochemical mechanisms. Since the ranges
of normalized predictors are from 0 to 1, comparisons of regression
coefficients indicate that effects of PEA (2.8037 in the count model and
−10.4439 in the zero-excess model, same hereafter) are considered more
important than SOCalt (0.9057 and −7.3100) and DCP_{Temp} (0.8425 and
−9.5698). The result is consistent with the findings of previous studies
which emphasized that the physical impacts are stronger than the biological
impacts on HA estimates (Yu et al., 2015; Mattern et al., 2013).

## 3.3 Generalized additive models (GAMs) and the ensemble model

GAMs are explored with an expectation of improving prediction performance in
HA peaks by introducing non-parametric effects of predictors. Using function
`gam`

in R package `mgcv`

(version 1.8-36;
Wood, 2011) with smooth functions
as pure thin plate regression splines (degrees of freedom = 9;
Wood, 2003), three GAMs are studied and compared, i.e.,
Poisson GAM, quasi-Poisson GAM, and negative binomial GAM. Following the
same procedure in GLM exploration, the best-subset searching approach is
applied to the GAMs first. Although mean 10-fold CV RMSEs for the Poisson
and quasi-Poisson GAMs (Fig. 3a) exhibit insignificant differences at
sizes from 2 to 5, the CV RMSEs for the former increase dramatically at
a size of 6, which indicates that the model stability decreases with
size. The negative binomial GAM has the greatest mean CV RMSEs among the
GAMs studied and has an extremely high mean CV RMSE at the size of 6. The
quasi-Poisson GAM is considered the best GAM among the three. Although the
mean CV RMSEs for the quasi-Poisson GAM reach the lowest at the size of 6,
the best size is considered three (including PEA, SOCalt, and
DCP_{Temp}) at which CV RMSEs exhibit the most saline decline and beyond
which mean CV RMSEs stabilize around 3200 km^{2}. The quasi-Poisson GAM
with three predictors involved is symbolized as GAMqsp3.

Component plots of GAMqsp3 (Fig. 5) imply that HA generally increases
as the chosen predictors increase. Note that the summation of all smooth-function terms contributes directly to the log of fitted HA. Such results
agree with those found by model GLMzip3. However, the component plots
provide more detailed information about the rate of changes in HA. The
effective degrees of freedom range from 6.79 to 8.90, indicating strong
non-linear effects of the predictors on the variability in HA. HA is
more sensitive to the predictors in the low-value ranges but becomes nearly
stable in the medium- and high-value ranges of predictors. This implies that
bottom hypoxia develops rapidly in early summer when water stratification
and sediment oxygen demand start to increase. On the other hand, the smooth
functions of SOCalt and DCP_{Temp} have a sharper slope than that of PEA
at the low-value range. It suggests that at the first stage of hypoxia
development in late spring and early summer, sedimentary biochemical
processes contribute more than water stratification. The bottom hypoxic
water further extends with a much lower expansion rate as the
stratification and SOCalt further intensify. Nevertheless, the smooth
function of PEA is slightly greater and also has a more acute slope than those
found for SOCalt and DCP_{Temp} in the medium- and high-value regimes of
the predictors. It indicates that the HA variability is more related to the
hydrodynamic changes in the shelf than the biochemical effects during
mid-summers. The result is consistent with the findings by
Yu et al. (2015) and Mattern et al. (2013). The GAMqsp3 model
provides reasonable interpretations of the mechanisms of hypoxic area.

The prediction performance of GAMqsp3 is estimated using the bagging
ensemble method (Fig. 4b). The RMSE and *R*^{2} between the bagging mean
and ROMS-hindcast HA are 3157 km^{2} and 0.7858, respectively. They are 13 % lower and 9 % higher than the corresponding statistics found for GLMzip3, respectively. MAPB between GAMqsp3 predicted and hindcast HA ranges
from 25 % to 40 % with an average of 30 % (Table 2). Such
statistics are generally lower than those found in GLMzip3. Results suggest
that GAMqsp3 outcompetes GLMzip3 in terms of overall performance. However,
GAMqsp3 tends to underestimate HA peaks (such as the peaks around
samples 750 and 901), some of which are overestimated by GLMzip3.
Therefore, instead of determining the best model out of the two, ensemble HA
predictions blending efforts of both GLMzip3 and GAMqsp3 are carried out
with an expectation to improve model performance in the peak forecast. We
assumed that the contributions of GLMzip3 and GAMqsp3 are equally weighted
and thus averaged the predicted HA by GLMzip3 and GAMqsp3 and calculated the
95 % PIs given the bagging results of these models (Fig. 4c). As
expected, the overall performance of the ensemble forecast is somewhere
between the performance of GLMzip3 and GAMqsp3 with an RMSE of 3256 km^{2} and an *R*^{2} of 0.7721. However, some HA peak events (such as the peaks around samples 750 and 901) which are overestimated by GLMzip3 but are
underestimated by GAMqsp3 are accurately predicted by the ensemble approach.
MAPB also indicates an increase in peak prediction performance by the
ensemble model. The statistic is within a range of 25 % to 36 % with
an average of 29 %. At extreme peaks (hindcast HA ≥ 30 000 km^{2}), compared to the MAPB by GLMzip3 (29 %) and by GAMqsp3 (28 %), the statistic decreases to 25 % by the ensemble model. The
ensemble model provides a higher accuracy in peak forecast given minor
sacrifices in overall performance.

## 3.4 Application to global forecast products (HYCOM)

The power of the prediction model relies on the availability of the forecast
of predictors. In this section, we discuss the model's transferability using
an independent global ocean product. The Global Ocean Forecasting System
(GOFS) 3.1 provides global daily analysis products and an 8 d forecast
in a daily interval with a horizontal resolution of $\mathrm{1}/\mathrm{12}{}^{\circ}$. The
products (hereafter referred to as HYCOM-derived products) are derived by a
41-layer HYCOM global model (Bleck and Boudra,
1981; Bleck, 2002) with data assimilated via the
Navy Coupled Ocean Data Assimilation (NCODA) system
(Cummings, 2005; Cummings and
Smedstad, 2013). The Mississippi River total nitrate + nitrite loadings are
provided by USGS NWIS as described in Sect. 2.1.2. Daily HYCOM-derived
hydrodynamics and USGS river nitrogen loads from 1 January 2007 to 26 August 2020 are used to reconstruct predictors of PEA, SOCalt, and DCP_{Temp}.
Relationships of ROMS-derived and HYCOM-derived predictors are examined in
Fig. 6. The magnitudes of HYCOM-derived SOCalt and DCP_{Temp} match up
with the corresponding ROMS-derived predictors, respectively, although
HYCOM-derived predictors are found to be slightly greater. Simple linear
regression for these predictors illustrates that the linear relationships
between the ROMS and HYCOM products are significant with the *R*^{2} ranging
from 0.94 to 0.96. The intercept terms are at least 1 order of magnitude smaller than
the magnitudes of corresponding predictors. Therefore, the HYCOM global
products are deemed to agree with the ROMS hindcasts for SOCalt and
DCP_{Temp}. Nevertheless, the magnitude of HYCOM-derived PEA is found to be much lower than the ROMS-derived PEA (Fig. 6a). Simple linear regression
indicates a significant linear relationship between the natural log
transformation of PEA from the two datasets (*R*^{2}=0.66).

At land–sea interfaces, the HYCOM global model is forced by monthly riverine
discharges, which weaken the model performance in coastal regions. The
hydrodynamics in the LaTex shelf is highly affected by the freshwater and
momentum from the Mississippi and the Atchafalaya rivers. Monthly river
forcings in HYCOM are essentially weaker than daily forcings used in our
ROMS setups and can result in a less stratified water column (i.e., lower
PEA). Therefore, it is necessary to scale the magnitude of HYCOM-derived PEA
to that of the ROMS hindcast. It can be achieved by using the natural log
transformation and simple linear regression as discussed. We then adjusted
HYCOM-derived PEA but kept the HYCOM-derived SOCalt and DCP_{Temp}
unchanged before the application of the ensemble model.

The bagging approach is implemented again to assess the performances of the
ensemble model. During each iteration (*N*=1000), GLMzip3 and GAMqsp3
are trained using the ROMS training set and then applied to the adjusted
HYCOM-derived predictors for HA prediction from 1 January 2012 to 26 August 2020 (Fig. 7a). The ensemble method provides averages and 95 % PIs of
predicted HA blending bagging results by GLMzip3 and GAMqsp3. Compared to
observed HA by mid-summer shelf-wide cruises, the ensemble model fails in
the summers of 2013, 2014, 2017, and 2018 but provides accurate predictions
in other summers. The width of 95 % PI is larger during high-HA periods,
suggesting less stability in the HA peak forecast. The overall performance
is barely acceptable, with an *R*^{2} of 0.4242, an RMSE of 5088 km^{2},
and an SI of 38 %. The bias against the observations can be ascribed to
HYCOM's failures in reproducing the shelf hydrodynamics, although
HYCOM-derived predictors are adjusted before being applied to the model
(Fig. 6a). We noticed that among the three variables, HYCOM-derived PEA
exhibits the largest deviation from that generated by ROMS. We then applied
the model using ROMS-derived PEA, HYCOM-derived SOCalt, and HYCOM-derived
DCP_{Temp} (Fig. 7b). The performance of the ensemble model was
largely enhanced with a higher *R*^{2} (0.9255), a much lower RMSE (3751 km^{2}), and a lower SI (28 %) compared to the one using the pure HYCOM
products. These results indicate that the ensemble model can produce a
highly accurate prediction for HA summer peaks once water stratification is
well resolved. Instead of using monthly river forcings, the HYCOM model may
possibly resolve the shelf hydrodynamics by utilizing daily river discharges
of the Mississippi and the Atchafalaya rivers.

## 4.1 Model performance evaluation

To further assess the robustness of our model, we reviewed a suite of
existing forecast models that are transitioned operationally (in early June)
to the NOAA ensemble forecast for each summer (data sources are listed in
Table 4). Using the ROMS-derived predictors, daily HA predictions during the
shelf-wide cruise periods are averaged for each summer from 2012 to 2020
and are compared to the cruise observations. As shown in Fig. 8a, our
model predictions fit well with the shelf-wide observation for summers with
or without strong windy events prior to the cruises. Other seasonal forecast
models have similar performances to our model in fair-weather summers (i.e.,
2012, 2014, 2015, and 2017) but fail to produce an accurate forecast for
several summers with strong wind conditions (i.e., 2018 and 2020).
Percentage differences between predictions and observations (Fig. 8b) also
emphasize the superiority of our model with the percentages ranging from −24 % to 7 % for fair-weather summers and from 7 % to 35 % for
summers with strong winds or storms. All models either underestimate or overestimate
observed HA in fair-weather summers but overestimate HA in windy summers.
Our model provides the most accurate overall performance with the highest
*R*^{2} (0.9200, *N*=8), the lowest RMSE (2005 km^{2}, *N*=8), the lowest
SI (15 %, *N*=8), and the lowest MAPB (18 %, *N*=8) among all models
(Table 4). The multiple linear regression model developed by
Forrest et al. (2011) provides the second best
prediction. For fair-weather summers, the NOAA ensemble predictions produce
the best estimation of the observed HA with an MAPB of 9 % (*N*=4), while
our model results rank the second (15 %, *N*=4). However, our model
performs the best in windy summers with an MAPB of 18 % (*N*=4), while
other models produce an MAPB from 33 % to 74 %.

Models developed by Turner et al. (2006, 2008, 2012)
and Laurent and Fennel (2019) are calibrated on
May nitrate or nitrate + nitrite loads from the Mississippi–Atchafalaya
River basin, assuming that the predicted HA in summers is under fair
weather. It is expected that models excluding wind effects can hardly
produce accurate forecasts during summers with strong winds or storms. Wind
mixing effects on HA are considered in reaeration by introducing a wind
stress term in the mechanistic model
(Obenour et al., 2015), while in the
Bayesian model by Scavia et al. (2013), the wind
effects are considered indirectly via an estimation based on current
velocity and the reaeration rate given different wind conditions (i.e., fair
weather, strong westerly winds, and storms). However, as shown in Fig. 1a,
PEA_{wind}, which can also be interpreted as wind power, is found poorly
correlated to daily HA ($R=-\mathrm{0.2458}$) compared to other highly correlated
predictors and is dropped out of the candidate list by the best-subset
searching approach. Forrest et al. (2011) also found
that monthly wind power is not significantly correlated to summer HA due to
the short timescales of strong wind events. Therefore, the wind mixing
effects considered by Obenour et al. (2015) and Scavia et al. (2013) have limited
contribution to the prediction of the interannual variability in HA.
Indeed, our model construction process indicates that wind mixing,
freshwater plume, and water temperature jointly control the water
stratification and vertical mixing, which directly modulates the
reoxygenation of shelf water. PEA can serve better in representing such
effects rather than by wind speed or wind power alone. The daily PEA is
significantly correlated to daily HA (*R*=0.8178, *p**<*0.01; Fig. 1a),
while the non-linear effects of PEA cannot be neglected (Fig. 5a).
Therefore, an accurate forecast of shelf hydrodynamics is critical for a
robust summer HA prediction.

Data source (last access in 15 June 2022): https://gulfhypoxia.net/ (Turner et al., 2006, 2008, 2012), http://scavia.seas.umich.edu/hypoxia-forecasts/ (Scavia et al., 2013), https://www.vims.edu/research/topics/dead_zones/forecasts/gom/index.php (Forrest et al., 2011), https://obenour.wordpress.ncsu.edu/news/ (Obenour et al., 2015), https://memg.ocean.dal.ca/news/ (Laurent and Fennel, 2019), https://www.noaa.gov/news (NOAA ensemble).

## 4.2 Task force nutrient reduction

In this section we assess the effects of nutrient reductions on HA using our
model. Since 2001, the Mississippi River/Gulf of Mexico Hypoxia Task Force
has had the goal of controlling the size of the mid-summer hypoxic zone below
5000 km^{2} in a 5-year running average (Mississippi
River/Gulf of Mexico Watershed Nutrient Task Force, 2001; 2008)
by reducing riverine nutrient loads. Because the monthly riverine silicate,
phosphate, and nitrate + nitrite loads are highly correlated (Table A1),
here we refer to nitrogen load (the only nutrient that has daily
measurements) as the proxy for all riverine nutrients. The averaged summer
HA during the shelf-wide cruises in the most recent 5 years (2015, 2107,
2018, 2019, and 2020) is calculated with different nutrient reduction
scenarios and is shown in Fig. 9. The PEA, bottom temperature, and river
discharges are unchanged, while the SOCalt is altered by reducing the
nutrient concentration from 5 % to 90 %. The averaged observed HA is
14 000 km^{2}, while the averaged prediction by our ensemble model is
15 478 km^{2}, which is 11 % greater than the observation. As a leading
time of 44 d (Fig. A3a) is prescribed in SOCalt prior to shelf-wide
summer cruises in mid–late July, reduction strategies are applied to
mid-June nutrient loads rather than May loads in our model. The monthly
averaged total nitrogen loads for the 1980–1996 summers (April, May, and
June) are 1.96 × 10^{8} kg per month (Battaglin et
al., 2010). It is comparable to the June mean total nitrogen load (1.6 × 10^{8} kg per month) for the 2015–2020 period. We
find that a 92 % reduction, which corresponds to a total nitrogen load of
5.5 × 10^{5} kg d^{−1} or 1.6 × 10^{7} kg per month, is needed for the mid-June nutrient loads to achieve the
goal of a 5000 km^{2} HA.

The recommended reduction strategy of our model is much more demanding than
that of other models (Scavia et al., 2013;
Obenour et al., 2015;
Turner et al., 2012;
Laurent and Fennel, 2019), which recommend a load
reduction of 52 %–58 % related to the 1980–1996 average
(Scavia et al., 2017). A recommendation of 92 % reduction is close to that by Forrest et al. (2011) (80 %) when the coastal westerlies from 15 June to 15 July
were considered in their regression model. Since water stratification is
attributed to not only wind mixing effects but also effects from other
physical processes (e.g., riverine freshwater transports and surface
heating), models developed based solely on May nutrient loads
(Turner et al., 2012;
Laurent and Fennel, 2019) or nutrient loads and
wind mixing (Scavia et al., 2013;
Obenour et al., 2015) fail to capture
water stratification's contribution to hypoxia development. If a model
considers the variability in HA to rely highly on the nutrient loads, then a
moderate decrease in nutrient loads would result in a substantial HA
reduction. For further illustration, we reran the model without
consideration of the PEA (i.e., using DCP_{Temp} and SOCalt or using only
SOCalt). Model results show a substantial shrinking of HA with moderately
reduced riverine nitrogen loads (Fig. 9). In details, if only DCP_{Temp} and SOCalt are used as the predictors, a nutrient reduction of 60 %
will satisfy the 5000 km^{2} HA goal. And if we only use SOCalt as the
predictor, then a 55 % reduction is sufficient. These results
highlight the importance of considering PEA in HA predictions.

In this study, we present a novel HA forecast model for the LaTex shelf
using statistical analysis. The model is trained using numeric simulations
from 1 January 2007 to 26 August 2020 by a three-dimensional coupled
hydrodynamic–biogeochemical model (ROMS). Multiple GLMs (regular Poisson
GLMs, quasi-Poisson GLMs, negative binomial GLMs, zero-inflated Poisson
GLMs, and zero-inflated negative binomial GLMs) and GAMs (regular Poisson
GAMs, quasi-Poisson GAMs, and regular negative binomial GAMs) are assessed
for HA predictions. Comparisons of model prediction performance illustrate
that an ensemble model combining the prediction efforts of a zero-inflated
Poisson GLM (GLMzip3) and a quasi-Poisson GAM (GAMqsp3) provides the most
accurate HA forecast using PEA, SOCalt, and DCP_{Temp} as predictors. The
ensemble model is capable of explaining up to 77 % of the total
variability in the hindcast HA and also provides a low RMSE of 3256 km^{2} and low MAPBs for overall (29 %) and peak predictions (25 %)
when compared to the daily ROMS hindcasts.

We then applied the hydrodynamics field generated by a global model (HYCOM,
GOFS 3.1) and performed a HA hindcast for the period from 1 January 2012 to
26 August 2020. The overall performance is barely acceptable with an *R*^{2} of 0.4242, an RMSE of 5088 km^{2}, and an SI of 38 % against the
shelf-wide summer cruise observations, largely due to HYCOM's relatively
poor representation of shelf stratification. A substitution of ROMS-derived
PEA led to a pronounced improvement with an *R*^{2} of 0.9255, an RMSE of
3751 km^{2}, and an SI of 28 %.

The ensemble model also provides an efficient yet more robust summer HA
forecast compared to existing HA forecast models. Comparing against the shelf-wide
cruise observations, our model provides a high *R*^{2} (0.9200 vs.
0.2577–0.4061 by existing forecast models, same comparison hereinafter); a
low RMSE (2005 km^{2} vs. 4710–9614 km^{2}); a low SI (15 % vs.
36 %–95 %); and low MAPBs for overall (18 % vs. 44 %–132 %),
fair-weather summer (15 % vs. 8 %–46 %), and windy-summer (18 % vs. 33 %–74 %) predictions. Sensitivity tests were conducted and
suggest that a 92 % reduction in riverine nutrients related to the
1980–1996 summer average is required to meet the goal of a 5000 km^{2}
HA. These results highlight the importance of considering PEA in HA
prediction.

Model data are available at the Louisiana State University (LSU) mass storage system, and details are on the web page of the Coupled Ocean Modeling Group at LSU (https://lsu.app.box.com/folder/168361434653?s=8qhpz2glpxlbsu9z9m6g4cudcegfseh4, Ou, 2022). Data requests can be sent to the corresponding author via this web page.

BL and ZGX designed the experiments, and YO carried them out. YO developed the model code and performed the simulations. YO, BL, and ZGX prepared the manuscript.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Research support was provided through the Bureau of Ocean Energy Management (grant nos. M17AC00019 and M20AC10001). We thank Jerome Fiechter at the University of California, Santa Cruz, for sharing his NEMURO (North Pacific Ecosystem Model for Understanding Regional Oceanography) model codes. Computational support was provided by the high-performance computing facility (clusters SuperMIC and QueenBee3) at Louisiana State University.

This research has been supported by the Bureau of Ocean Energy Management (grant nos. M17AC00019 and M20AC10001).

This paper was edited by Tina Treude and reviewed by Brandon Jarvis and two anonymous referees.

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^{−1}). We developed a novel prediction model using state-of-the-art statistical techniques based on physical and biogeochemical data provided by a numerical model. The model can capture both the magnitude and onset of the annual hypoxia events. This study also demonstrates that it is possible to use a global model forecast to predict regional ocean water quality.