Montclair State University Digital Montclair State University Digital Commons Commons Statistical Analysis of Nutrient Loads from the Mississippi- Statistical Analysis of Nutrient Loads from the Mississippi-Atchafalaya River Basin (MARB) to the Gulf of Mexico Atchafalaya River Basin (MARB) to the Gulf of Mexico

: This study investigated the annual and seasonal variations in nutrient loads (NO 2 − + NO 3 − and orthophosphate) delivered to the Gulf of Mexico from the Mississippi-Atchafalaya River Basin (MARB) and examined the water quality variations. The results indicate that (1) annually, the mean NO 2 − + NO 3 − and orthophosphate loads showed a steady increase during 1996–1999, a persistent level during 2000–2007, and a moderate increase during 2008–2016; (2) seasonally, NO 2 − + NO 3 − and orthophosphate in MARB in spring and summer were higher than those in autumn and winter. Analysis of variance (ANOVA) identiﬁed highly signiﬁcant di ﬀ erences among seasonal loads; and (3) the median value of NO 2 − + NO 3 − in normal weather conditions were higher than that during and right after the hurricanes, while the median value of orthophosphate loads in normal weather conditions was higher than that during the hurricanes, but higher than that right after hurricanes. The two-sample t-test indicates a signiﬁcant di ﬀ erence ( p < 0.046) in orthophosphate loads before and after Hurricane Katrina. Moreover, it is found that there is a signiﬁcant ( p < 0.01) increase in nutrient loads during normal weather conditions. The results indicate that hurricane seasons can signiﬁcantly inﬂuence the nutrient loads from the MARB to the Gulf of Mexico.


Introduction
The "hypoxic zone" refers to a specific water area where the dissolved oxygen concentration is less than 2 mg/L, and to hypoxia associated with excess nutrient input, such as nitrogen and phosphorus, which can yield serious environmental, economic, and social impact. A variety of sources, which are related to economic activities and population growth, can contribute to the elevated nutrient concentrations in rivers (e.g., agricultural activities, industrial point-discharge, urban runoff, natural deposition, and domestic waste, such as household cleaning products; [1][2][3][4][5][6]. Water quality from the Mississippi-Atchafalaya river basin to the Northern Gulf of Mexico has been improved since the enactment of the 1972 Clean Water Act (CWA) and other regulations by the Environmental Protection its distributary, the Atchafalaya River. The Mississippi River either borders or passes through ten states starting from Minnesota through Wisconsin, Iowa, Illinois, Missouri, Kentucky, Tennessee, Arkansas, Mississippi, and Louisiana into the Gulf of Mexico. The Atchafalaya River is located within the Mississippi River delta plain in south Louisiana. The Atchafalaya River is 137 miles long (220 km), and a distributary of the Mississippi River and the Red River in south central Louisiana [33,34]. The Mississippi-Atchafalaya River Basin (MARB) is shown in Figure 1. The Mississippi River empties into the Gulf of Mexico and the Atchafalaya River is a distributary of the Mississippi River and Red River in south central Louisiana in the United States. The Atchafalaya River meets up with Mississippi River before reaching the Gulf of Mexico.
Environments 2020, 7, x FOR PEER REVIEW 3 of 13 Mississippi River delta plain in south Louisiana. The Atchafalaya River is 137 miles long (220 km), and a distributary of the Mississippi River and the Red River in south central Louisiana [33,34]. The Mississippi-Atchafalaya River Basin (MARB) is shown in Figure 1. The Mississippi River empties into the Gulf of Mexico and the Atchafalaya River is a distributary of the Mississippi River and Red River in south central Louisiana in the United States. The Atchafalaya River meets up with Mississippi River before reaching the Gulf of Mexico.

Materials
The data used in this study, including the annual total loads of inorganic nitrogen and orthophosphate, were collected from the United States Geological Survey (USGS) archive data (https://toxics.usgs.gov/hypoxia/mississippi/flux_ests/delivery/index.html). The data were analyzed for annual and seasonal variation patterns of NO2 − + NO3 − and orthophosphate loads from the Mississippi-Atchafalaya River Basin that were delivered to the Gulf of Mexico during 1996-2016. Nutrient load data used for analysis were the sample data of total inorganic nitrogen (NO2 − + NO3 − ) and total orthophosphate. The load estimator (LOADEST)data adequately reflect the effect of nutrient loads on water quality from its source to the gulf mouth, particularly with respect to the influence of agricultural activities on the Mississippi-Atchafalaya River Basin on hypoxia in the northern Gulf of Mexico. The composite data were used for autoregressive integrated moving average (ARIMA) analysis.

Data Processing and Statistical Analysis
A long-term time series analysis was performed on the USGS nutrient load dataset, which were estimated by the adjusted maximum likelihood estimation (AMLE) method using the LOADEST program and by the composite method. The annual and monthly loads were used to reveal annual and seasonal characteristics of the loads, respectively. Specifically, annual loads of inorganic nitrogen (NO2 − + NO3 − ) and orthophosphate from 1996 to 2016 were used to study the nutrient variations. Monthly net loads of inorganic nitrogen (NO2 − + NO3 − ) and orthophosphate during 1996 to 2016 were used to examine the nutrient seasonal variations. Statistical analysis was carried out to examine the rise, peak, and impact of storm flow conditions and seasonal conditions on nutrients loads. The seasons were defined as winter (December-February), spring (March-May), summer (June-August), and autumn (September-November) [35,36]. Two-sample t-tests and analysis of variance (ANOVA) were applied to identify the significant variations in the mean nutrient loads among different seasons and weather conditions. A forecasting NO2 − + NO3 − and orthophosphate model of net nutrient loads

Materials
The data used in this study, including the annual total loads of inorganic nitrogen and orthophosphate, were collected from the United States Geological Survey (USGS) archive data (https://toxics.usgs.gov/hypoxia/mississippi/flux_ests/delivery/index.html). The data were analyzed for annual and seasonal variation patterns of NO 2 − + NO 3 − and orthophosphate loads from the Mississippi-Atchafalaya River Basin that were delivered to the Gulf of Mexico during 1996-2016. Nutrient load data used for analysis were the sample data of total inorganic nitrogen (NO 2 − + NO 3 − ) and total orthophosphate. The load estimator (LOADEST)data adequately reflect the effect of nutrient loads on water quality from its source to the gulf mouth, particularly with respect to the influence of agricultural activities on the Mississippi-Atchafalaya River Basin on hypoxia in the northern Gulf of Mexico. The composite data were used for autoregressive integrated moving average (ARIMA) analysis.

Data Processing and Statistical Analysis
A long-term time series analysis was performed on the USGS nutrient load dataset, which were estimated by the adjusted maximum likelihood estimation (AMLE) method using the LOADEST program and by the composite method. The annual and monthly loads were used to reveal annual and seasonal characteristics of the loads, respectively. Specifically, annual loads of inorganic nitrogen (NO 2 − + NO 3 − ) and orthophosphate from 1996 to 2016 were used to study the nutrient variations.
Monthly net loads of inorganic nitrogen (NO 2 − + NO 3 − ) and orthophosphate during 1996 to 2016 were used to examine the nutrient seasonal variations. Statistical analysis was carried out to examine the rise,

Annual Variation
The composite method load estimate was reported when there were 10 or more nutrient concentration measurements for that year. The nutrient loads were calculated using a 5-year moving calibration method to investigate the annual and seasonal variations in the nutrients loads to the Gulf of Mexico delivered from the Mississippi-Atchafalaya River Basin. Method comparison between the LOADEST and composite methods for the nutrient loads was made and the results are shown in Figure 2. The two-sample t-test showed that there is no statistically significant difference (p > 0.05) between the two methods for the nutrient loads. The annual nutrient loads estimated by the LOADEST method show that the nutrient loads from 1996 to 2016 were 892,286 t/yr with a range of 671,000 t/yr for NO 2 − + NO 3 − , and 44,324 t/yr with a range of 39,700 t/yr for orthophosphate, respectively. In the meantime, the annual nutrient loads given by the composite method for the same time period were 898,143 t/yr with a range of 755,000 t/yr for NO 2 − + NO 3 − , and 44,319 t/yr with a range of 41,100 t/yr for orthophosphate, respectively. It is found that, for the LOADEST method, the NO 2 − + NO 3 − loads increase from 827,000 t/yr in 1996 to 1,110,000 t/yr in 1999, and then declined to 539,000 t/yr and remained constant at around 800,000 t/yr during 2001 and 2007, then increased to 1,210,000 t/yr and persisted at around 1,000,000 t/yr during 2008 and 2011, and then decreased to 571,000 t/yr in 2012 and increased again to 1,100,000 t/yr in 2016. The annual predicted nutrient loads indicate that the peak  Figure 3. A two-sample t-test was performed to compare the mean NO2 − + NO3 − and orthophosphate loads before and after Hurricane Katrina in 2005. The t-test results indicate a statistically significant increase in the mean orthophosphate load after Hurricane Katrina (p < 0.05). The mean load increased from 39,888.89 t/yr to 48,800.00 t/yr . A Wilcoxon rank-sum test was performed to detect significant difference in monthly NO2 − + NO3 − and orthophosphate loads before and after a hurricane and the results indicated that there was no statistically significant difference (p > 0.05) between a month before and after the hurricane for both NO2 − + NO3 − and orthophosphate loads, respectively. A two-sample t-test was performed to compare the mean NO2 − + NO3 − and orthophosphate loads before and after Hurricane Katrina in 2005. The t-test results indicate a statistically significant increase in the mean orthophosphate load after Hurricane Katrina (p < 0.05). The mean load increased from 39,888.89 t/yr to 48,800.00 t/yr . A Wilcoxon rank-sum test was performed to detect significant difference in monthly NO2 − + NO3 − and orthophosphate loads before and after a hurricane and the results indicated that there was no statistically significant difference (p > 0.05) between a month before and after the hurricane for both NO2 − + NO3 − and orthophosphate loads, respectively.

Seasonal Variation
Variations in nutrient loads can be significantly affected by meteorological conditions, biomass productivity, and land-use activities, of which the severe weather involving strong winds and waves also yield a great impact [37,38]. The seasonal variations in the mean loads are summarized in Figure 4, which show that the mean loads of spring and summer are higher than those in autumn and winter.

Seasonal Variation
Variations in nutrient loads can be significantly affected by meteorological conditions, biomass productivity, and land-use activities, of which the severe weather involving strong winds and waves also yield a great impact [37,38]. The seasonal variations in the mean loads are summarized in Figure  4, which show that the mean loads of spring and summer are higher than those in autumn and winter.  One-way ANOVA was conducted to identify the significant difference in seasonal NO2 − + NO3 − and orthophosphate loads. The ANOVA results indicate that there is significant difference existing in seasonal NO2 − + NO3 − load (p < 0.01). A multiple comparison Tukey's test indicates that winter load is significantly different from spring and autumn loads (p < 0.05); spring load is significantly different from summer load and autumn load (p < 0.05); and summer load is significantly different from autumn load (p < 0.05). Among the four seasonal periods, the mean NO2 − + NO3 − load is in the order of Spring > Summer > Winter > Autumn. For orthophosphate load, statistical results indicate a significant difference (p < 0.05) in nutrient load among four seasons. In contrast, the mean orthophosphate load is in the order of Summer > Spring > Winter > Autumn. The load in the summer season made up the largest proportion (33.6%), followed by spring (29.7%), winter (19.5%), and autumn (17.1%) under normal weather conditions. The seasonal cycle that mostly reflects freshwater discharge of NO2 − + NO3 − loads in Mississippi river is summer. Highest loads of nitrogen usually occur in May/June, while loads are lowest in September/October [39].
Under hurricane weather conditions, however, spring season made up the largest proportion (30.    Figure 5. ANOVA was performed on these three categories of NO 2 − + NO 3 − and orthophosphate loads, respectively, to detect if there is statistically significant difference among the mean loads of the three groups in order to assess the impact of extreme weather conditions on variations of nutrient loads. varied. It is interesting to find that hurricane flow seems to be associated with an increase in nutrient loads during winter. ANOVA was performed on these three categories of NO2 − + NO3 − and orthophosphate loads, respectively, to detect if there is statistically significant difference among the mean loads of the three groups in order to assess the impact of extreme weather conditions on variations of nutrient loads. The ANOVA results indicated there is no statistically significant difference (p > 0.05) among the three categories of weather condition for both NO2 − + NO3 − and orthophosphate loads. The mean loads under different weather conditions indicate that NO2 − + NO3 − load under hurricane conditions was about 1.24 times greater than that under normal weather conditions. The relative contributions of seasonal loads to the total loads of NO2 − + NO3 − under normal weather and hurricane conditions varied. It is interesting to find that hurricane flow seems to be associated with an increase in nutrient loads during winter.

Nutrient Load Prediction
An autoregressive integrated moving average (ARIMA) model was constructed for the nutrient loads forecast. The Dickey-Fuller test results showed that both NO2 − + NO3 − and orthophosphate annual loads from 1996 to 2016 were not stationary data series with p > 0.05 in both cases. Therefore, the ARIMA method is not suitable for the annual dataset. Nevertheless, an augmented Dickey-Fuller Test on the monthly NO2 − + NO3 − loads did not detect any non-stationarity data in the data set (p < 0.05). The decomposition analysis suggests a seasonal component for the model. The monthly observation of NO2 − + NO3 − load is shown in Figure 6. (a)

Nutrient Load Prediction
An autoregressive integrated moving average (ARIMA) model was constructed for the nutrient loads forecast. The Dickey-Fuller test results showed that both NO 2 − + NO 3 − and orthophosphate annual loads from 1996 to 2016 were not stationary data series with p > 0.05 in both cases. Therefore, the ARIMA method is not suitable for the annual dataset. Nevertheless, an augmented Dickey-Fuller Test on the monthly NO 2 − + NO 3 − loads did not detect any non-stationarity data in the data set (p < 0.05). The decomposition analysis suggests a seasonal component for the model. The monthly observation of NO 2 − + NO 3 − load is shown in Figure 6.
The autocorrelation function (ACF) and the partial autocorrelation function (PACF) for the monthly data set were computed. As shown in Figure 6, the ACF plot suggests a possibility of MA (1) and MA (2) terms and the PACF plot indicates AR (1), AR (2), AR (3), and AR (4) terms for the model, respectively. Based on the AIC value of the models, ARIMA (1,0,2) ×(0, 1, 1) 12 is selected as the final model which is expressed as follows: where B is the backshift operator, B S is the seasonal backshift operator, φ 1 = 0.8013 is the coefficient of AR (1) term, θ S 1 = −0.960 is the coefficient of the seasonal MA (1) term, and θ 1 = −0.1799 and θ 2 = −0.1790 are coefficients of the MA (1) and MA (2) terms ( Table 1).
The residuals plot indicates that the model captures the time series attributes of the observations. The monthly NO 2 − + NO 3 − forecasting load is shown in Figure 6 along with observations in the testing dataset. loads forecast. The Dickey-Fuller test results showed that both NO2 − + NO3 − and orthophosphate annual loads from 1996 to 2016 were not stationary data series with p > 0.05 in both cases. Therefore, the ARIMA method is not suitable for the annual dataset. Nevertheless, an augmented Dickey-Fuller Test on the monthly NO2 − + NO3 − loads did not detect any non-stationarity data in the data set (p < 0.05). The decomposition analysis suggests a seasonal component for the model. The monthly observation of NO2 − + NO3 − load is shown in Figure 6. The autocorrelation function (ACF) and the partial autocorrelation function (PACF) for the monthly data set were computed. As shown in Figure 6, the ACF plot suggests a possibility of MA (1) and MA (2) terms and the PACF plot indicates AR (1), AR (2), AR (3), and AR (4) terms for the model, respectively. Based on the AIC value of the models, ARIMA (1,0,2) × (0,1,1) is selected as the final model which is expressed as follows:  For the monthly data of the orthophosphate loads, the ARIMA model is established on the logarithm-transformed data set. The augmented Dickey-Fuller test confirms the stationarity of the data set (p < 0.05). The decomposition analysis suggests a seasonal component for the model. The monthly observation of orthophosphate load is shown in Figure 7.
The ACF and PACF of logarithm-transformed data were computed and shown in Figure 7. In Figure 7, it can be seen that the ACF and PACF suggest the possibility of MA (1), MA (2), and MA (3) terms, as well as an AR (1) term for the model, respectively. Based on the AIC value of the models, the final model is defined as ARIMA (1,0,0) ×(0, 1, 1) 12 : where B is the backshift operator, B S is the seasonal backshift operator, φ 1 = 0.7213 is the coefficient of AR (1), and θ S 1 = −0.8996 is the coefficient of the seasonal MA (1) term (Table 2).   Figure 7.
The mean annual nutrient loads (10 3 t/yr) observed during 1996-2016 and predicted for 2017-2022 are summarized in Table 3.
Statistically, there is no significant difference (p > 0.05) between the observed and the predicted dataset. The residuals of ARIMA (1,0,2) × (0,1,1) for the NO2 + NO3 loads are shown in Figure 6. The residuals plot indicates that the model captures the time series attributes of the observations. The monthly NO2 − + NO3 − forecasting load is shown in Figure 6 along with observations in the testing dataset.
For the monthly data of the orthophosphate loads, the ARIMA model is established on the logarithm-transformed data set. The augmented Dickey-Fuller test confirms the stationarity of the data set (p < 0.05). The decomposition analysis suggests a seasonal component for the model. The monthly observation of orthophosphate load is shown in Figure 7. The ACF and PACF of logarithm-transformed data were computed and shown in Figure 7. In Figure 7, it can be seen that the ACF and PACF suggest the possibility of MA (1), MA (2), and MA (3) terms, as well as an AR (1) term for the model, respectively. Based on the AIC value of the models, the final model is defined as ARIMA (1,0,0) × (0,1,1) : where B is the backshift operator, is the seasonal backshift operator, = 0.7213 is the coefficient  The standard deviation of the predicted loads is 89% lower than that of the observed loads. The monthly mean loads of orthophosphate loads from 2017 to 2022 are predicted from ARIMA (1,0,0) ×(0, 1, 1) 12 .
The annual predicted mean loads of the orthophosphate loads are obtained by addition of the predicted loads of twelve months. The prediction for annual mean orthophosphate loads is 41.7 ± 5.25 t/yr, which is 5.8% lower than the actual observations of 44.3 ± 10.5 t/yr. The two-sample t-test for observed and predicted annual mean nutrient loads indicate that there is no statistically significant difference (p > 0.05). Therefore, this model has significance to apply in other regions with similar settings.

Conclusions
The results from this study suggest that the mean orthophosphate load is more sensitive to changes in weather conditions than mean NO 2 − + NO 3 − load in the Mississippi-Atchafalaya River Basin. The monthly observations of nutrient loads exhibit obvious seasonal variation. The loads showed a trend of being maximum in spring and minimum in autumn during the hurricane seasons. Time series analysis indicate that the NO 2 − + NO 3 − load in the Mississippi-Atchafalaya River Basin has a significant seasonal attribute, strong correlations among annual and monthly loads, as well as considerable sensitivity to weather conditions, which is consistent [40]. Overall, the results suggest that hurricane seasons significantly influence the nutrient loads from the Mississippi-Atchafalaya River Basin (MARB) to the Gulf of Mexico.