the regular , seasonal 
 occurrence of bottom - water hypoxia in the 
 northern gulf of mexico has been well documented over the last 25 
 years .
hypoxic extent , defined operationally 
 as the area where bottom - water dissolved oxygen ( bwdo ) concentrations 
 are below 2 mg l , has been determined primarily 
 through midsummer monitoring cruises conducted regularly since 1985 . 

these cruises demonstrate that the areal extent of hypoxia has increased 
 over time , corresponding with a period of elevated nutrient loading 
 from the mississippi river basin .
this 
 observation , along with other evidence of increasing hypoxia , has motivated development of nutrient reductions strategies for 
 the basin .
the relationship between nutrient 
 loads and the interannual ( i.e. , 
 year - to - year ) variability of the midsummer hypoxic area has been explored 
 through a range of computational models .
use a one - dimensional , simple mechanistic model that explains 
 45% of the interannual variability as a function of the may 
these results are generally consistent with the statistical 
 regressions of bianchi et al . who find 
 that the may  june nitrogen load explains 47% of the variability , 
 and of greene et al . who find that the 
 may nitrate plus nitrite ( no ) load explains 42% of this variability . 

in addition , studies by turner et al . and others have shown that model performance is improved by also accounting 
 for the long - term cumulative effects of nutrient loading .
it 
 is widely understood , however , that water column stratification 
 also affects the temporal variability of hypoxia .
stratification , 
 which inhibits the reoxygenation of bottom waters , can be particularly 
 strong in the northern gulf due to warmer surface waters significantly 
 freshened by discharges from the mississippi and atchafalaya rivers 
 overlying denser waters derived from the deep shelf .
, while acknowledging the importance of nutrient 
 loading , determined that the majority of the interannual variability 
 in the hypoxic area ( for a nine - year period ) could be explained using 
 the mean river flow from the preceding eleven months . using a more 
 expansive data set ,
demonstrate 
 that 41% of the interannual variability in hypoxic area can be explained 
 in terms of the may 
the fact that both 
 nutrients and flow can explain a large portion 
 of the variability in hypoxic extent is not surprising .
therefore , use of either of these 
 variables masks the mechanistic effect of the other , leaving room 
 for debate regarding whether eutrophication ( via nutrient loading ) 
 or stratification ( via freshwater flow ) is the primary control on 
 the interannual variability of hypoxia .
accordingly , hetland and dimarco suggest that it will be necessary to separate 
 the physical and biological causes of hypoxia to develop models with 
 greater predictive capability ; and a recent scientific assessment stresses the need to include physical factors 
 within hypoxia models .
moreover , a recent study by murphy et al . demonstrates the importance of both nutrients 
 and stratification for predicting hypoxia in the chesapeake bay .
this 
 need likely extends to other systems , as diaz and rosenberg report that there are over 400 coastal hypoxic 
 zones around the world , and that they are controlled by both biological 
 and physical factors ( generally eutrophication and stratification , 
 respectively ) . because stratification is primarily a natural phenomenon , 
 while nutrient loading is often an anthropogenic watershed pollution 
 issue , the ability to distinguish between these factors is critical 
 for managing these complex systems . in this study , we determine 
 the effect of stratification on the 
 variability of hypoxia through a geostatistical regression ( gr ) for bwdo . in the model , stratification is represented by metrics 
 derived from salinity and temperature profiles , with regression coefficients 
 determined based on how stratification explains the spatial variability 
 in bwdo .
while a portion of the interannual variability in bwdo is 
 also explained by the stratification effect , the remaining portion 
 must be explained by other factors , such as mississippi river nutrient 
 inputs .
we evaluate the efficacy of this methodology using 10 recent 
 years of midsummer cruise data ( 19982007 ) . as such
, this study 
 generally focuses on the interannual variability of the system within 
 its current state ; and it does not focus on long - term trends in the 
 system .
we use data from 
 midsummer hypoxia monitoring cruises conducted between 1998 and 2007 
 along the louisiana - texas shelf .
these cruises are performed by the 
 louisiana universities marine consortium ( lumcon ) , and the data were 
 retrieved from the national ocean data center . to help ensure a consistent spatial envelope for this study , 
 only locations sampled during at least 9 of the 10 years
were included 
 in the analysis ( figure 1 ) , resulting in 6164 
 monitoring locations for each year .
sampling locations were geo - referenced 
 using the utm zone15 projection , and water depths were determined 
 from a 3-arc - second digital elevation model ( dem ) obtained from noaa .
we use the dissolved oxygen , salinity , and temperature 
 profile data collected at these locations .
typically , data were collected 
 by two different instruments at each monitoring site : a hydrolab and 
 a sea - bird profiler . based on a comparison 
 with the dem , the hydrolab and sea - bird typically reached to within 
 zero and one meters of the sea floor , respectively , with minor variability . 
 for this study
, the bwdo values were taken from whichever instrument 
 reached the greatest recorded depth ( typically the hydrolab ) . to determine 
 salinity and temperature profiles , sea - bird data , which have better 
 vertical resolution ,
were chosen preferentially over hydrolab data ; 
 and when the hydrolab reached a greater depth , we appended these additional 
 measurements to the sea - bird profile .
the stratification intensity at each sampling location 
 was quantified 
 using metrics derived from the salinity and temperature profiles . 

because sampling intervals in the raw profile data were not uniform , 
 the profiles were first resampled by linear interpolation to 0.2 m 
 resolution .
the difference ( s ) between the 
 25th and 100th percentiles of salinity ( slo and shi , respectively ) was calculated 
 for each location , and then the maximum salinity gradient ( sg ) over a 0.4 m vertical interval , within the 
 region of s , was determined .
the thickness 
 ( m ) of the subhalocline ( hs ) , defined 
 as the region below sg , was also calculated . 

figure s1 ( supporting information ( si ) ) 
 provides an illustration of these metrics .
use of the 25th and 100th 
 percentiles for defining slo and shi was not arbitrary ; a range of percentile 
 values was considered , and the values that optimized the gr ( based 
 on bic score , described subsequently in section 2.4 ) were selected . 
 for temperature profiles ,
an identical analysis was performed , and 
 the zeroth and 75th percentiles were found to be optimal for defining tlo , thi , and t .
the maximum temperature gradient and subthermocline thickness , tg and ht , respectively , 
 were also calculated . because temperature tends to decrease with depth , 
 while salinity increases , the 25th percentile of salinity and the 
 75th percentile of temperature both generally correspond to the 25th 
 percentile of depth , suggesting that near - surface stratification conditions 
 are less important for predicting bwdo .
the mississippi and 
 atchafalaya river outfalls ( figure 1 ) provide 
 the vast majority of fresh water and nutrients 
 to the shelf .
the atchafalaya river is important because approximately 
 30% of the mississippi river flow ( and load ) enters the atchafalaya 
 river near simmesport , louisiana .
monthly 
 flow and loading data were retrieved from usgs , and we used the sum of the two river inputs .
the usgs uses 
 both an adjusted maximum likelihood estimator ( amle ) and a composite 
 ( comp ) method to estimate loads .
we used 
 amle data because they generally performed better in the modeling 
 analyses .
however , the two data sets are highly correlated , and the 
 choice does not greatly affect the results .
our geostatistical modeling approach takes into account the spatial 
 correlation of the dependent variable ( i.e. , bwdo ) , which improves 
 estimates of the model parameters relative to a regression based on 
 the assumption of independent and identically distributed residuals , 
 and allows for a more realistic assessment of model uncertainty .
the effectiveness of gr methods for modeling 
 environmental phenomena has been demonstrated in studies of rainfall , snow depth , water 
 quality , and biospheric co2 exchange . with the exception of the 
 last example , these works focused primarily on spatial interpolation , 
 and less on inference of causal factors .
as such , our work adds to 
 the limited number of studies demonstrating how geostatistical modeling 
 can be useful for confirming and quantifying causal relationships 
 within environmental systems . in the gr model , the dependent 
 variable , z ,
the deterministic 
 component , x , is the portion of z that can be expressed as a function of predictor variables and annual 
 constants ( i.e. , intercepts ) .
the stochastic component is the portion 
 of z not accounted for by the deterministic component , 
 and which can include both spatially correlated and uncorrelated parts ,  and  , respectively .
overall , the 
 gr is represented as1where z is an n  1 vector of bwdo measurements taken at different locations 
 and times .
the k  1 vector  includes the parameters of the deterministic component , which can 
 be divided into annual intercepts ( a ) and regression coefficients ( p ) ( eq 2 ) . correspondingly , 
 the n  k matrix x includes the annual classifiers ( xa ) and predictor variables ( xp ) for each observation .
each predictor variable is normalized to 
 a mean of zero and variance of one over the 10 year period.2 as discussed in the introduction , a portion 
 of the interannual variability in mean bwdo is accounted for through 
 stratification metrics ( which are included as predictor variables ) . 

the regression coefficients for these metrics are fit to the spatial 
 variability in bwdo , based on the assumption that sites which are 
 strongly stratified will have lower bwdo due to lower rates of reoxygenation . 

they are not fit to the interannual variability in bwdo because this 
 could confound the role of stratification with nutrient loading , as 
 they are temporally related , both being dependent on river flow .
this 
 approach does not , however , preclude the stratification metrics from 
 explaining a portion of the interannual variability . as the average 
 intensity of stratification varies from year to year , the predicted 
 impact of stratification on bwdo varies proportionally , as a function 
 of the regression coefficients .
this is reasonable because years of 
 intense stratification would be expected to have less reoxygenation 
 and thus lower bwdo .
the remaining interannual variability is accounted 
 for primarily through the annual intercepts , which will be discussed 
 further in section 2.6 .
 +  , was found 
 to be well represented by the commonly used exponential covariance 
 model with a nugget effect , as follows:3where the covariance ( q ) 
 between two observations ( zi and zj ) is modeled 
 as a function of the distance between the observation locations ( hi , j ) and the 
 covariance model parameters  , 
  , and r. here , r is a range parameter , and 3r is the effective 
 range of spatial correlation .
the parameter  represents the variance of the portion of the residuals 
 that is not spatially correlated ( microvariability and measurement 
 error ) , and  represents the variance 
 of the portion that is spatially correlated .
spatial correlations 
 are expected to be stronger in the east  west direction than 
 in the north  south direction due to along - shore currents . to account for this phenomenon , hi ,
j is scaled by an 
 anisotropy ratio ,  , which is the ratio of east 
we use restricted maximum likelihood ( reml ) to estimate the covariance model parameters and the anisotropy ratio . 

this method is recommended for models with strong spatial correlation 
 and/or a large numbers of predictor variables , and it has been applied in previous geostatistical studies .
the parameters are optimized by minimizing lr ( eq 4 ) with respect 
 to  ,  , r and  , which define q ( an n  n covariance 
 matrix with elements determined from eq 3 ) . 
 because the covariance between the stochastic components of the observations 
 collected in different years is assumed to be zero
4 once q is optimized , the 
 deterministic model parameters are calculated in a straightforward 
 manner:5thus , a complete set of model parameters is 
 uniquely defined .
candidate variables include the salinity stratification 
 metrics ( ln[s ] , shi , sg , and hs ) and temperature stratification metrics ( ln[t ] , tlo , tg , and ht ) .
note that slo and thi were omitted to 
 avoid issues of colinearity ; and the salinity and temperature differences 
 were log - transformed to account for an apparent nonlinearity in their 
 relationships with bwdo .
variables for water column depth , utm easting , 
 and utm northing ( d , e , n ) were also included , along with their squares ( d , e , n ) to allow for potential spatial and bathymetric trends . 

overall , there are fourteen candidate predictor variables , yielding 
 over 16  000 combinations of 114 variables to be considered . 

the challenge is to determine an optimal combination of predictor 
 variables that best describes the phenomenon of interest , without 
 resulting in overparameterization of the model .
in general , this is achieved by including only those variables 
 that have a sufficiently high degree of explanatory ability , as defined 
 by a statistical criterion . in this study
, we used the bayesian information 
 criterion ( bic ) , where models with different 
 sets of predictor variables ( xs ) are compared based on their bic scores , which quantify the 
 explanatory power of a model relative to its complexity , with the 
 lowest score indicating the model with optimal balance . assuming the 
 residuals
follow a normal distribution , the bic score is calculated 
 as follows:6 the gr model should be optimized in 
 terms of both its covariance parameters ( section 2.3 ) and its selection of predictor variables . because the covariance 
 parameters of the stochastic component depend on the selected predictor 
 variables and vice versa , an iterative approach was used .
the interannual 
 variability of midsummer hypoxic intensity can be assessed by comparing 
 the mean bwdo concentrations between years .
annual mean bwdo values 
 were determined using geostatistical kriging of the mean , which assigns lower weights to observations 
 from clustered sampling locations .
the mean bwdo for year i is calculated as7with weights , i , corresponding to observations , zi . the weights are determined 
 from the system of linear equations presented in eq 8 , where q  i is the ni  ni covariance matrix for the 
 observations from year i , with elements determined 
 from eq 3 .
the scalar , i  , is a lagrange multiplier , its square root being the 
 standard error of the estimated mean value.8 the annual mean impacts of the predictor 
 variables ( on bwdo ) are also determined geostatistically . for a given 
 year
i , the mean impact of each predictor variable 
 is calculated by applying the vector of location - specific weights , i , to the vector of location - specific 
 impacts , xi , j  j , where j refers to 
 the jth predictor variable .
linear 
 regression models were developed to explore potential relationships 
 between the annual intercepts and nutrient and flow data .
the response 
 variable is the set of 10 annual intercepts , a , determined from the gr .
candidate 
 predictor variables include the april , may , and june monthly loads 
 and concentrations for no , total kjeldahl nitrogen ( tkn ) , and total 
 phosphorus , as well as monthly flows .
these concentrations are flow - weighted 
 averages , calculated by dividing monthly load by monthly flow .
to 
 account for potential changes in the system s susceptibility 
 to hypoxia , a linear trend across years is also included as a candidate 
 variable . because of the large number of candidate variables 
 ( p = 22 ) , many of which are correlated , and relatively 
 small sample size ( n = 10 ) , the 
this method constrains the magnitude of the model 
 parameters ( and shrinks some parameters to zero , thereby eliminating 
 them ) to prevent problems commonly associated with the overfitting 
 of models .
the elastic - net method was 
 implemented using the  glmnet  package for the r statistical 
 computing program .
the degree to which 
 model parameters are constrained is determined through a 10-fold cross 
 validation routine included in this package .
we used the elastic - net 
 as an exploratory tool and to select one or more primary variables 
 from which to create a more parsimonious regression model .
the information developed above can be used to 
 predict how the intensity of midsummer hypoxia will respond ( within 
 the system s current state ) to changes in nutrient loading . 

however , while this study focuses on bwdo concentration , policy goals 
 have centered on the areal extent of hypoxia .
thus , 
 we develop a regression model for midsummer hypoxic area ( as determined 
 by lumcon ) using the annual mean stratification effects 
 ( section 2.5 ) and one or more nutrient variables 
 ( section 2.6 ) . using this model
, we can explore 
 the effect of hypothetical nutrient reduction scenarios over the 10 
 year study period .
the goal of the intergovernmental task force 
 action plan is to reduce the five - year running average 
 of hypoxic area to less than 5000 km .
thus , we develop 
 modeling results for all possible consecutive five - year periods across 
 the 10 year study period .
the consecutive five - year period which requires 
 the greatest nutrient reduction to achieve the action plan goal is 
 defined as the  critical  period .
because of the 
 non - negativity constraint on hypoxic area ( any predictions 
 of negative hypoxic area are treated as zero ) , probabilistic results 
 are best determined through monte carlo simulation ( eq 9 ) . here , sim is a 5  1 vector of simulated hypoxic 
 areas for a given five - year period ,  is the predicted 
 ( i.e. , mean ) response , u is a vector of independent samples 
 from a standard normal distribution , and c( ) is the upper - triangular matrix obtained by cholesky decomposition 
 of the covariance matrix for the predictions ( eq 10 ) . in eq 10 ,
w is the matrix 
 of predictor variables used to develop the regression ( corresponding 
 to the observed conditions ) , w is a matrix of 
 predictors with reduced nutrient levels , r is the variance of the model residuals , and i is the identity matrix.910 for each nutrient reduction scenario , 
 10  000 simulations 
 of sim were generated 
 in accordance with eq 9 , using different random 
 draws of the vector u. any simulations of negative hypoxic 
 area were replaced with a value of zero , and the mean of each sim was then determined , resulting 
 in 10  000 simulations of five - year average hypoxic area .
summary 
 statistics for each nutrient reduction scenario were then calculated 
 based on this ensemble of results .
the 
 deterministic component of the gr ( eq 2 ) was 
 optimized in terms of the regression coefficients and annual intercepts . 

the regression coefficients ( p ) indicate how bwdo is related to the various predictor 
 variables ; all parameters are significantly different from zero ( p < 0.05 , table 1 ) . because the 
 predictor variables were normalized
the regression 
 coefficients for northing ( n ) and depth ( d ) suggest that bwdo concentrations tend to be lower at 
 locations that are shallower and farther north ( i.e. , closer to shore ) . 

this is likely because the near - shore waters mix less with the more 
 oxygenated and less eutrophic deep - shelf waters .
as expected , the 
 regression coefficients for the stratification metrics all indicate 
 bwdo tends to be lower in areas of intense water column stratification . 

annual intercepts ( a ) ranged from 1.66 to 3.50 mg l , and are 
 discussed further in section 3.2 . for the 10 
 year study period , the deterministic component of the model ( x ) explains 52% of the variability in bwdo across 
 space and time . for individual years , the deterministic component 
 of the model explains from 27% to 61% of the spatial variability in 
 bwdo .
the remaining spatial variability may be due largely to the 
 effects of varying coastal current patterns that can influence transport 
 of fresh water , nutrients , and organic matter .
the stochastic portion 
 of the model , which accounts for this remaining variability , has substantial 
 spatial correlation , consistent with current patterns acting across 
 large spatial scales .
additional model details including the covariance 
 parameters , a test of the linearity assumption , and site specific 
 results are provided in the si .
the results of the gr can be summarized on an annually averaged basis 
 to analyze the interannual variability of the factors affecting mean 
 bwdo concentration .
figure 2 illustrates how 
 mean bwdo is affected by northing and bathymetry ; salinity stratification 
 ( ln(s ) , shi , and sg ) ; temperature stratification ( ln(t ) and tlo ) ; and annual intercepts . 

the combination of these effects can be used to exactly predict the 
 estimated mean bwdo ( eq 7 ) . for illustrative 
 purposes , however ,
each factor is presented as a bwdo depletion , calculated 
 by determining each effect relative to its year of minimum impact ; 
 for example , temperature stratification was least severe in 2006 and 
 most severe in 2004 .
for each factor , the standard deviation of the 
 10 annual impacts is calculated , providing a metric for assessing 
 the degree to which each factor contributes to the interannual variability 
 of bwdo , with higher standard deviations indicating greater contributions . 
 from the figure ,
it is clear that stratification has a substantial 
 impact on the interannual variability in bwdo depletion , and the standard 
 deviation of the net stratification effect ( salinity plus temperature ) 
 is 0.51 mg l bwdo .
the standard deviation of the 
 northing / bathymetry effect is only 0.05 mg l bwdo , 
 which is expected because there is little interannual variation in 
 the sampling locations used in this study .
the greatest portion of 
 the interannual variability is accounted for through the annual intercepts , 
 with a standard deviation of 0.71 mg l bwdo .
while 
 these intercepts do not have intrinsic explanatory value , they can 
 be modeled in terms of other factors , such as nutrient inputs .
bwdo depletions 
 attributed to different factors from gr model ; 
 each factor presented relative to its year of minimum impact .
the annual intercepts ( a ) were first related to candidate predictor 
 variables 
 through development of an elastic - net model ( section 2.6 ) .
, variables enclosed in brackets represent 
 nutrient concentrations , while unbracketed variables represent loads , 
 and subscripts represent months . because variables were normalized , 

the regression coefficients indicate their relative importance.11 the elastic - net model indicates may 
 no concentration has the largest 
 impact , followed by may no load , which is discussed more below .
the 
 trend with time ( year ) also has a relatively large effect , suggesting 
 that hypoxia is becoming more intense irrespective of seasonal nutrient 
 inputs and stratification .
this is consistent with previous studies 
 indicating increasing hypoxia irrespective of seasonal nutrient loading or stratification , but this is the 
 first study to suggest this trend while considering both factors in 
 combination .
june no concentration and april tkn and no loads are 
 also included , but appear to have relatively small effects .
the selection 
 of tkn only for the month of april is consistent with this more refractory 
 nitrogen fraction requiring additional time to become biologically 
 available .
the elastic - net model did not select any of the variables 
 for tp or flow , suggesting that these factors are less important for 
 predicting midsummer hypoxia .
overall , the elastic - net model explains 
 85% of the variability in the annual intercepts .
figure s4 ( si ) graphically illustrates how the various factors 
 in eq 11 affect the annual intercepts .
we also developed a simple linear regression ( slr ) for the annual 
 intercepts using may no concentration alone ( eq 12 ) .
the no concentrations were normalized so that the model coefficients 
 are comparable to those in eq 11 .
this model 
 explains 76% of the variability in the annual intercepts , indicating 
 that its performance is similar to the elastic - net model , despite 
 its relative simplicity.12 the use of may ( or may  june ) 
 nitrate data to predict hypoxia 
 has precedent in multiple previous studies , and is reasonable given the known processes of phytoplankton growth 
 and bacterial decomposition that link nitrogen inputs to bwdo depletion 
 over time .
however , while previous studies generally 
 indicate that load is the best single nutrient predictor of hypoxia , 
 this study indicates concentration .
( greene et al . also consider models using flow and concentration , but 
 the confounding correlation between flow and load was not addressed . ) 
 to explore this distinction further , figure 3 illustrates how may no loads and concentrations correlate with mean 
 bwdo ( eq 7 ) and the annual intercepts . as shown , 
 mean bwdo is somewhat correlated with no load ( figure 3a ) , and as expected , the strength of this correlation ( r = 0.41 , p = 0.045 ) is similar 
 to that of previous studies relating nitrogen loads to hypoxic area . the correlation between the annual intercepts and may no concentrations 
 ( figure 3d )
, corresponding to the slr ( eq 12 ) , is much stronger ( r = 0.76 , p = 0.001 ) .
this improvement can be attributed 
 to the fact that here we use nutrients to predict only the variability 
 in hypoxia that remains after accounting for stratification ( i.e. , 
 the annual intercepts ) , rather than the total variability in hypoxia 
 ( i.e. , mean bwdo or hypoxic area ) .
if we do not remove stratification 
 effects , nutrient load is a better predictor of hypoxia than concentration 
 ( figure 3a versus 3b ) . 

this is as expected given load is correlated with flow , and higher 
 flow tends to increase stratification , making load partially reflective 
 of both stratification and nutrient concentration .
annual mean bwdo ( top ) 
 and annual intercepts from gr ( bottom ) versus 
 may no loads ( left ) and concentrations ( right ) , with 95% confidence 
 intervals .
while these results suggest that nutrient concentration 
 is the 
 best predictor of hypoxia ( after accounting for stratification ) , nutrient 
 load may also be of some predictive importance .
the elastic - net model 
 ( eq 11 ) did include multiple nutrient loading 
 terms , though they generally had less impact than the concentration 
 terms .
similarly , figure 3c indicates that 
 there is some correlation between the annual intercepts and may no 
 load , though markedly less than with concentration . from a mechanistic 
 perspective
, nutrient load is an intuitive predictor 
 of hypoxia based on the assumption that it is proportional to the 
 primary production and oxygen demand that develops within the system . 

however , the importance of concentration ( as suggested by this study ) 
 indicates that the amount of oxygen demand generated on the shelf 
 is also affected by the degree to which that load is diluted by flow . 

the exact reasons for this are not readily apparent and could benefit 
 from further research .
we note , however , that loads are highly correlated 
 with flows , and high flows can intensify coastal current velocities , thus reducing the time available to produce 
 and settle organic matter within the study area . also , because biochemical 
 process rates are typically concentration dependent
the approach outlined in this study made it possible to isolate 
 the effects of stratification through gr , and then determine the effects 
 of nutrients based on the interannual variability in bwdo that remained . 

overall , the results suggest that both river nutrient concentration 
 and stratification play large and comparable roles in determining 
 the interannual variability of hypoxia in the northern gulf of mexico . 

the standard deviation of the net stratification effect is 0.51 mg 
 l bwdo , while the standard deviation of the may 
 no effect ( from the slr ) is 0.62 mg l bwdo , indicating 
 nutrients may play a slightly larger role .
when the annual intercepts 
 predicted by the slr are used in combination with the net stratification 
 and northing / bathymetry effects , the overall model explains a large 
 majority ( 82% ) of the interannual variability in mean bwdo .
because of its explanatory power , this approach provides a more 
 precise way to evaluate the response of gulf hypoxia to changes in 
 mississippi river nutrients .
note that when hypoxia is modeled using nutrient loads alone , the 
 interannual variability in oceanographic conditions can mask the effects 
 of changes in nutrient loading , at least in the short term .
this can 
 confound management of the system by obscuring the effect of watershed 
 management practices aimed at curtailing nutrient inputs .
however , 
 by using the approach outlined here , we separate the effects of stratification 
 from the effects of nutrients , allowing for a more detailed assessment 
 of how each is impacting hypoxia over time . although the intensity 
 of stratification can be difficult to predict in advance because it 
 varies over short time scales due to wind forcing , it can likely be approximated using river flow and climate 
 data .
for example , the may river flow alone explains 27% of the variability 
 in the net stratification effect determined by this study .
the stratification 
 effect can also be determined following each midsummer monitoring 
 cruise using the measured salinity and temperature profiles , as was 
 done here . while may no concentration and load were not well 
 correlated over 
 the period of this study ( r = 0.14 ) ; 
 longer - term trends in nitrate concentration and load have been shown 
 to be parallel .
thus , if the existing 
 action plan is successful at reducing no load , it will likely also 
 be successful in reducing concentration .
so , while we think that concentration 
 should receive more attention in future studies and in evaluating 
 year - to - year changes in hypoxic severity , we do not think this emphasis 
 on concentration is in discordance with the long - term action plan 
 goal of reducing nutrient loads .
stratification 
 metrics and river nutrient concentrations were also used to develop 
 a regression model for hypoxic area ( y , km ) , as described in section 2.7 . in the model 
 ( eq 13 ) , s is the aggregated 
 bwdo depletion due to salinity and temperature stratification ( as 
 illustrated in figure 2 ) ; and [ nomay ] is the may no concentration . both of the variables were normalized 
 so that the regression coefficients indicate their relative importance . 

overall , the model explains 79% of the variability in observed hypoxic 
 area.13 we used the model to estimate the average 
 hypoxic area for different nutrient reduction scenarios , along with 
 associated uncertainty determined through monte carlo simulation ( eq 9 ) ; and to estimate the percent nutrient reduction 
 required to consistently ( over the 10 year study period ) reduce the 
 five - year running average of hypoxic area to less than 5000 km in accordance with action plan goals .
figure 4 illustrates how nutrient reductions will affect 
 the five - year running average of hypoxic area for the critical period 
 ( 19982002 is the critical period because it requires the greatest 
 nutrient reduction to achieve the action plan goal ) .
the model suggests 
 that a 42% reduction in may no concentration is required , with a 90% 
 confidence interval of 2962% reduction .
the non - negativity 
 constraint ( section 2.7 ) had only a minor impact , 
 resulting in a recommended nutrient reduction of 42% instead of 41% . 

these results support multiple previous modeling studies suggesting 
 nutrient reductions of around 4045% , but are somewhat lower than the 71% reduction 
 recommended by liu et al . predicted average hypoxic 
 area for the critical five - year period 
 ( 19982002 ) under different levels of nutrient reduction , with 
 90% confidence intervals .
note that these predictions assume the linear relationships 
 in 
 eq 13 remain valid outside of the range of observed 
 conditions .
if the effects of stratification become less severe under 
 scenarios of reduced nutrient inputs , this would make the estimated 
 loading reductions somewhat conservative .
it should also be noted 
 that this study used recent data ( 19982007 ) , so the results 
 generally reflect the system at its current state . if the system becomes 
 more or less susceptible to hypoxia over time , as a result of long - term 
 trends in nutrient loading , climate change , or other factors , then 
 the reductions required to meet the action plan goal would also change .
 stratification and nutrient loading are two primary factors 
 leading 
 to hypoxia in coastal systems 
 . however , where these factors are temporally 
 correlated , it can be difficult to isolate and quantify their individual 
 impacts . 
 this study provides a novel solution to this problem by determining 
 the effect of stratification based on its spatial relationship with 
 bottom - water dissolved oxygen ( bwdo ) concentration using a geostatistical 
 regression . 
 ten years ( 19982007 ) of midsummer gulf of mexico 
 bwdo measurements are modeled using stratification metrics along with 
 trends based on spatial coordinates and bathymetry , which together 
 explain 2761% of the spatial variability in bwdo for individual 
 years . because stratification effects explain only a portion of the 
 year - to - year variability in mean bwdo ; 
 the remaining variability is 
 explained by other factors , with may nitrate plus nitrite river concentration 
 the most important . 
 overall , 82% of the year - to - year variability in 
 mean bwdo is explained . 
 the results suggest that while both stratification 
 and nutrients play important roles in determining the annual extent 
 of midsummer hypoxia , reducing nutrient inputs alone will substantially 
 reduce the average extent . 
Introduction
Materials and Methods
Results and Discussion