Forecasting future estuarine hypoxia using a wavelet based neural network model

Ocean Modelling 96 (2015) 314–323

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Forecasting future estuarine hypoxia using a wavelet based neural network model Andrew C. Muller a,∗, Diana Lynn Muller b,1 a b

United States Naval Academy, Oceanography Department, Annapolis, MD 21402, USA 859 Selby Blvd., Edgewater, MD 21037, USA

a r t i c l e

i n f o

Article history: Received 28 December 2014 Revised 4 October 2015 Accepted 2 November 2015 Available online 6 November 2015 Keywords: Hypoxia Estuarine dynamics Neural network models El Niño Wavelet coherence Chesapeake Bay

a b s t r a c t Ecosystem based modeling and predictions of hypoxia in estuaries and their adjacent coastal areas have become increasingly of interest to researchers and coastal zone managers. Although progress has been made in modeling oxygen dynamics and short-term predictions, there is still a lack of long-term forecasts that incorporate multiple inputs including climatological effects such as El Niño-Southern Oscillation (ENSO) events. In this study, we first develop a hypoxic volume index (HVI) using 26-years of hypoxic volume (<62.5 μm g l−1 ) measurements from the main-stem of the Chesapeake Bay. Then a cross-wavelet analysis is used to identify and weight input parameters in order to build a neural network model of future hypoxic volume. The timeforward dynamic model uses cross-bay winds along with the Oceanic Niño Index (ONI), and Susquehanna River flow indexes to predict a hypoxic volume index over the next several years. Wavelet analysis indicates an anti-phase relationship between southwesterly winds and hypoxic volume index, and an 18-month phase lag between Susquehanna River index and hypoxic volume index. The neural network model results yield R-values of 0.99, and 0.91 for training, and validation and an R2 of 0.68 for predictions illustrating the usefulness and promise of these types of models for long-term predictions of hypoxic volume. Model results could be used as a climatologically based hypoxic volume baseline for comparing actual hypoxic volume response to nutrient load reductions. Published by Elsevier Ltd.

1. Introduction Sufficient levels of dissolved oxygen are critically important to the sustainability of aquatic organisms in marine habitats such as estuaries and their adjacent coastal environments. Numerous reports and studies have documented both spatial and temporal expansions of hypoxic conditions within coastal habitats worldwide over the last several decades (Bricker et al., 1999; Diaz and Rosenberg, 1995, 2008). Severe hypoxia is typically defined as dissolved oxygen content below 62.5 μm l−1 (2.0 mg l −1 ), and has been attributed to eutrophic environments (Kemp et al. 2005). Nixon (1995) has defined eutrophication as an overabundance of nutrients to an ecosystem. Protracted summer-time hypoxia and anoxia, which can last from days to months, appear to have become the new normal condition in sections of many estuarine environments (Boesch et al. 2001; Dybas 2005; Hagy et al. 2004; Kemp et al. 2005; Officer et al. 1984; Rosenberg, 1990; Paerl et al. 1998; Testa and Kemp 2008). Kuo and Neilson (1987) have shown that deep-water hypoxia is controlled by

∗

Corresponding author. Tel.: +1 410 293 6569; fax: +1 4102932131. E-mail addresses: [email protected], [email protected] (A.C. Muller), [email protected] (D.L. Muller). 1 Tel.: +1 443 534 2847. http://dx.doi.org/10.1016/j.ocemod.2015.11.003 1463-5003/Published by Elsevier Ltd.

pycnocline strength, which is governed by the strength of the estuaries gravitational circulation and the diffusion of dissolved oxygen across the pycnocline. The coupling of severe eutrophic conditions and strong water column stratification has been identified as the primary factors in the occurrence of prolonged deep-water hypoxia within the Chesapeake Bay (Kuo and Neilson 1987; Boicourt 1992; Shen et al. 2008). The effects of massive nutrient loading in aquatic systems may lead to numerous deleterious consequences including large algal blooms, reductions in water clarity, decreased acreage of submerged aquatic vegetation (SAV) beds, hypoxia, anoxia and in some cases fish kills (Fallesen et al. 2000; Lowery 1998; Medine 1983; Orth and Moore 1983; Orth et al. 2010). Prolonged exposure to hypoxic conditions may decrease the ability of fish larvae to capture their prey, and could leave them more vulnerable to predators (Breitburg et al. 1997; Malone 1992; Purcell et al. 2014; Taylor and Eggelston 2000). A few studies also suggest that long-term effects of eutrophication may even cause disruptions to estuarine food webs (Baird and Ulanowicz 1989; Livingston 2007; Ludsin et al. 2009). In response to the increased prevalence of hypoxia throughout the world’s coastal zones, many state and federal agencies have migrated to an ecosystem based management approach. The ecosystem-based approach strives to integrate monitoring and environmental assessment with scientific knowledge in order to drive policies that are

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more effective. This usually includes an adaptive management approach in order to reduce the major input stressors such as nutrients and sediment loading (Boesch 1996, 2006; Fletcher et al. 2014; Loomis and Patterson 2014). Much of the recent ecosystem based management has focused on the use of models as decision and policymaking tools, including predictions of hypoxia (Borsuk et al. 2002; Evans and Scavia 2011). Recent studies on hypoxia within the Chesapeake Bay have identified several important environmental factors. These forcing elements include total nitrogen loading, total phosphorus loading, annual Susquehanna River flow, chlorophyll a concentrations, as well as wind speed and direction (CENR, 2003; Liu and Scavia, 2010; Malone et al., 1986; Scully, 2010; 2013; Zhou et al. 2014). Several models ranging from simple linear regression to complex three-dimensional process based models have been applied to the Chesapeake Bay in order to predict near-future summer-time hypoxic/anoxic volume or future conditions based on nutrient load reductions (Bever et al., 2013; Cerco and Cole, 1993; Haggy et al., 2004; Lee et al., 2013; Murphy et al., 2011). While each of these approaches has their own inherent strengths and weaknesses, there is still much debate over the utility of each as effective adaptive management tools (Borsuk et al. 2001; Stow and Scavia 2009). Although progress has been made in modeling oxygen dynamics and short-term predictions, there is still a lack of long-term forecasts especially those that incorporate multiple inputs including climatological effects such as El Niño-Southern Oscillation (ENSO) events. Many water quality variables such as dissolved oxygen, nutrients, chlorophyll a and turbidity display large temporal swings in estuarine environments resulting in non-normal distributions (Boyer et al. 2000; Christian et al. 1991; Muller and Muller 2014; Ortega et al. 2009). These variables as well as river discharge and winds may also contain non-stationary signals (Kundzewicz 2011; Ragavan and Fernandez 2006). Several climatic indices and signals also tend to have non-stationary distributions (Molinos and Donohue 2014). In fact, many of the physical and biological process have quasi-periodic characteristics. Therefore, it is important to characterize the dominant frequencies over which these processes occur and the potential coherent structures in time. An emerging technique for environmental time series data is the continuous-wavelet transform. This technique can identify the dominant frequencies, and if energy shifts have occurred between frequencies during the sampling period. Crosswavelet and wavelet-coherence allows for the detection of cyclical coherence of multiple variables Lee and Lwiza (2008). This can then be used to identify the dominant processes or input variables to a particular model. Over the last several years, water resource managers and environmental scientists have turned to artificial neural network (ANN) models in order to develop new predictions and forecasting of environmental variables (Maier and Dandy, 2001; Palani et al. 2008). Artificial neural network models have become a popular tool for environmental modeling due to their non-linearity and the fact that they perform well with noisy and limited data sets (Chakraborty et al. 1992; Tang et al. 1991). Several recent studies have illustrated the value of neural network models in the prediction of nutrient inputs from rivers, salinity, wind-driven waves, dissolved oxygen as well as other ecosystem and atmospheric variables (Areerachakul et al. 2011; Bajo and Umgiesser 2010; Clalr and Ehrman 1996; DeSilets et al. 1992; Boznar et al. 1993; Paruelo and Tomasel 1997; Whitehead et al. 1997). Some researchers have recently recognized the value of coupling the individual strengths of wavelets and neural networks to develop various types of wavelet based neural network models (Prakash et al. 2011; Shoaib et al. 2014). The goals of this study were to first identify major variables that contribute to hypoxic volume in estuarine environments including large-scale climatological effects using spectral techniques, rather than regression analysis techniques. This will allow for the identification of the dominant frequencies in each of the input parameters and

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Fig. 1. Map of the Chesapeake Bay, illustrating the long-term fixed stations of the U.S. Environmental Protection Agencies Chesapeake Bay Program used in this study to determine the annual hypoxic volume index.

which parameters demonstrate coherent frequencies with measured hypoxic volume. Secondly, to develop a predictive tool that will make yearly summertime hypoxic volume predictions over the next several years using a dynamic feed forward neural network model. The ultimate goal is to create a climatological hypoxic volume benchmark to be used in order to determine how successful the current nutrient reduction strategies used in the Chesapeake Bay are in reducing the average spatial extent of hypoxia during summertime conditions. 2. Methods 2.1. Data collection The study was conducted in the main-stem of the Chesapeake Bay, using hydrographic data collected by the Chesapeake Bay Program on a monthly to biweekly bases from 1985 to 2014. The average summer time (May–September) hypoxic volume was determined by interpolating vertical profiles of dissolved oxygen at 31 fixed stations throughout the Chesapeake Bay (Fig. 1). Interpolations were performed using an inverse distance squared algorithm in SURFER 11. The monthly May–September calculated volumes were then averaged to produce a yearly hypoxic volume for the central

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portion of the Chesapeake Bay. Hydrographic data from the Chesapeake Bay program can be found at http://www.chesapeakebay.net. data/. Data collected for potential model inputs for this study included annual Susquehanna River flow, cross-bay wind speed and direction, an ENSO index and an NAO index. These specific parameters were chosen based on previous work indicating that these parameters may strongly influence Chesapeake Bay climatology and the development of hypoxic conditions. Annual mean January through May Susquehanna River discharge (m3 s−1 ) was calculated using data from the United States Geological Survey (USGS) station 01578210 (http://www.waterdata.usgs.gov/nwis). Susquehanna River discharge was used as an input variable because it represents 45% of the freshwater flow to the Chesapeake Bay, and therefore the largest contribution of nutrients (Hagy, 2002). The large influx of freshwater leads to increased buoyancy, and therefore, increased stability of the water column, which is expressed as a stronger pycnocline. Annual averaged Cross-Bay (February–April) winds have also been shown to have a large influence on hypoxia structure (Scully, 2010). Cross-bay wind (m s−1 ) data was derived from the Patuxent River Naval Air Station historical records following the methods of Lee et al. (2013). In this study, positive cross-bay wins are from the southwest, while negative values represent winds from the northeast. The Oceanic Nino Index (ONI) was used as an input parameter over the 26-year period of 1985–2010. The ONI is a threemonth moving average index, which is based on sea surface temperature anomalies from a 30 year mean in the Nino 3.5 region (5°N–5°S; 120°–170°W) and used primarily to identify warm and cold phase ENSO events. ONI values were obtained from the National Weather Service’s Climate Prediction Center (http://www.cpc.ncep. noaa.gov/products/precip/CWlink/MJO/enso.shtml;). Annual values for the January–March (JFM) index were used to capture the ENSO signature of the study period. This period tends to have a strong signal and therefore potentially the greatest influence over climate variables such as precipitation. Annual precipitation and chlorophyll a values along with annual nutrient fluxes were not used in this study because they are typically affected by the other variables and thus their signal is captured. Yearly (January–March) averaged seasonal NAO or North Atlantic Oscillation index values were also retrieved from the Climate Prediction Center (http://www.cpc.ncep.noaa.gov/ products/precip/CWlink/pna/nao.shtml). Each of the individual indexes along with cross-bay winds was then subjected to continuouswavelet transform and cross-wavelet transforms with HVI in order to determine which parameters to use in the neural network model. 2.2. Index creation Since more than two decades of direct measurements have been collected throughout the Chesapeake Bay, it is now possible to construct a Bay Hypoxic Climatology. In order to match the scaling of the ONI and NAO inputs, a hypoxic volume index was developed using yearly (May–September) averages of hypoxic volume calculated from the monthly to biweekly vertical profiles taken at the fixed stations. The hypoxic volume index is calculated as the yearly deviation from the long-term mean (1985–2010). Positive values indicated larger than average summer-time hypoxic volume, while negative values represent years of below average hypoxic volume in the main-stem of the Chesapeake Bay. A Susquehanna River index was also developed using similar practices as the previous indexes.

mother wavelet ( sτ ) This can be seen in Eq. (1):

sτ (t ) =

1

|s|



1 2

t − τ 

(1)

s

where s =0, −∞ < τ < ∞. The continuous-wavelet transform can then be written as follows in Eq. (2):



1

Xω (s, τ ) =

|s|

1 2

∞ −∞

X (t ) 

t − τ  s

dt

(2)

In this form,   is the complex conjugate of  . Therefore, the continuous-wavelet transform is suited for extracting information on power shifts at different frequencies within a time series record, thus allowing one to examine the non-stationary signals within the series and may be useful in interpreting physical processes (Liu and Miller, 1996; Emery and Thomson, 1997; Haus et. al., 1999). The main advantage using wavelets is that you get good time resolution for high frequency events and good frequency resolution for low frequency events, which makes this technique attractive for geophysical processes hidden within this noise. In this study, we employ a continuous wavelet transform known as the Morlet wavelet. The Morlet wavelet can be described as a simple sinusoidal modified by a Gaussian, and is defined in Eq. (3):

ψ0 (η) = π −1/4 eiω0 η e− 2 η , 1

2

(3)

where ω0 represents the dimensionless frequency, which for Morlet is 6 and η is dimensionless time. The normalized CWT of a time series is then defined by the equation below:



Wn (s) = x

δt s



N  n =1

Xn ψ0



δt (n − n) s

(4)

In Eq. (4), Wnx (s) is the transformed time series for scale s; δt is the time step, while n is the time. The wavelet power is therefore computed from |Wnx (s)|2 , and the then signal variance is used to normalize the power. A cone of influence is also determined in order to define areas where edge effects may become significant (Farge, 1992; Torrence and Compo, 1998; Flinchem and Jay, 2000; Grinsred et al., 2004). A more complete description of the continuous wavelet transform and the properties of several mother wavelets can be found in Torrence and Compo (1998). Recent developments include the introduction of cross-wavelet and wavelet coherence analysis, increasing the spectral tools available to aide in the analysis of non-stationary signals. These techniques allow one to analyze two time series together and to determine potential relationships between them. The cross-wavelet transform (XWT) consisting of time series χn and γn is described in Grinsred et al. (2004) as W XY = W X W Y ∗ , where ∗ depicts complex conjugation. Torrence and Compo (1998), further define the theoretical distribution of the cross wavelet power given two time series as:



  Zν ( p) |WnX (s)WnY ∗ (s)| D

(5)

where PkX and PkY are the background power spectra of the respective time series, and Zν ( p)is the confidence level, which for all cases was at the 95% level as compared against background red noise. Wavelet coherence has been characterized by Torrence and Webster (1998) as essentially a localized correlation coefficient in time-frequency space, and is defined in Eq. (6):

|S(s−1WnXY (s))|2 )|WnX (s)|2 )  S(s−1 )|WnY (s)|2

2.3. Continuous wavelet methodology

R2n (s) =

Continuous-wavelet transforms are essentially a wave-like family of functions, known as the analyzing wavelet ( sτ ). This analyzing wavelet is used to convert one dimensional functions of time into two dimensional functions consisting of both time and frequency (scale), and is accomplished through dilations s, and translations τ from a

S in this equation is a smoothing factor. A detailed description of the cross wavelet transform and wavelet coherence can be found in Grinsred et al. (2004). All continuous wavelet, cross wavelet and wavelet coherence calculations and graphics were performed using MATLAB 2013a. The resultant Cross-Wavelet and Wavelet Coherence

S(

s−1

(6)

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errors cannot be reduced any further. At this point, the connection weights are saved, and the process moves to the last step. The initial weights used in this model are the continuous wavelet transform values for the input variables and the target. Once satisfactory meansquare errors and regressions between the outputs and the target values are achieved, the feed-forward loop is closed and the NARX model will make predictions. For this particular model, we used the first 22 years (1985–2006) of input parameters and targets to train, and validate the NARX performance before predictions were made. The NARX model actually projects the same number of years into the future as the input data. Therefore, the model predicts hypoxic volume index 22 years in the future. However, we do not have 22 years of future data to test model predictions and as a result we only reported the first 11 years. Current predictions go out to 2017, which is the date for the Chesapeake Bay Program’s mid-term review of the effectiveness of the EPA’s (Environmental Protection Agencies) Total Maximum Daily Load (TMDL) management plan to reduce nutrients to the Chesapeake Bay. As a final test of model capability to accurately predict hypoxic volume several years in the future, we compared measured hypoxic volume to predicted hypoxic volume using data from 2007 to 2014. Fig. 2. Schematic of a simplified neural network model architecture.

3. Results analysis produces phase-arrows. Phase-arrows pointing to the right indicate an in-phase relationship, while arrows directed to the left illustrate an anti-phase relationship. Arrows pointing directly up or down indicate one series leads the other. Actual phase angles are essentially the angle between the imaginary and real components of the cross-wavelet transform. The phase-angle between the two series is then used to calculate the lag time between the processes. 2.4. Neural network model A nonlinear autoregressive Neural Network with Exogenous Inputs (NARX) model was designed in order to forecast future hypoxic volume several years in the future. The NARX model is a recurrent dynamic network that contains feedback connections encompassing several layers within the network and is based on the linear ARX model. These models are thought to be well suited for predicting time series of chaotic dynamic systems (Haykin 1999; Lin et al. 1996). NARX models predict future values of a time series y(t) using previous values of that time series also known as the target series along with values of a second time series x(t). Eq. (7) illustrates the basic equation for the NARX model:

y(t ) = f (y(t − 1), y(t − 2), y(t − 3), . . . y(t − ny ), x(t − 1), x(t − 2), x(t − 3), . . . x(t − nx ))

(7)

In this model, future values y(t) are regressed on previous values of the dependent input and the exogenous inputs. The NARX model was designed and implemented in MATLAB 2013a using a two-layer feed-forward neural network to approximate the function (ƒ). The basic architecture is shown in Fig. 2. In our version of the NARX model, the exogenous inputs x(t) are multidimensional, in that more than one input is used along with the target input (hypoxic volume index). Calibration and validation of the NARX model was accomplished by first dividing the data into two groups and randomly selecting data to be used for training and validation. Seventy percent of the data was used for training, and the remaining 30% was used for validation purposes. Training and validation involves deploying an open loop back-propagation algorithm. At these steps, the neural network uses an iterative process in order to reduce the mean square errors between the model output and the target output. As a result, the connection weights are continuously changed until the mean square

3.1. Continuous wavelet analysis The Chesapeake Bay climatologic indices that were created for this study included the hypoxic volume index (HVI), the Susquehanna River index (SQI) and the cross-bay wind. Together along with the Oceanic Nino index (ONI) and the North Atlantic Index (NAO) it is now possible to describe the Chesapeake Bay in terms of a Bay climatology as it relates to the condition of the ecosystem. The hypoxic volume index over the 26-year interval illustrates several years when the hypoxic volume was either significantly above normal or significantly below normal conditions. In this study, deviations of +0.5 or −0.5 indicate higher or lower than usual hypoxia respectively. Twelve years ranked as extreme conditions; five of which (1986, 1989, 1993, 1997 and 2003) are times when the hypoxic volume was significantly larger than the 26-year average, especially 1997 and 2003. Seven years (1985, 1991, 1996, 1999, 2001, 2004 and 2006), have below average hypoxic volume (Fig. 3a). The continuous-wavelet transform (CWT) for the hypoxic volume index from 1985 to 2010 is shown in Fig. 3b. Analysis indicates a dominant 5–6 year periodicity and a minor 3-year periodicity. The dominant period is significant at the 95% confidence interval, which is indicated by the black circle. The dark hyperbolic line is the cone of influence showing areas where edge effects may become important. Peak energy appears to have occurred between 1997 and 2004 for both the dominate 5–6 year period and the minor 3-year period. This is coincident with the information gleaned in Fig. 3a. CWT of the ONI index suggests significant peak energy at the 3–4 year period, which is consistent with wavelet results of other ENSO indexes. There also appears to be a minor 5–6 year periodicity (Fig. 4a). For the ONI, peak energy occurs between 1996 and 2001, and is significant at the 95% confidence level. Spectral results of the Susquehanna River Index (SQI) reveal peak energy in the 3–4 year band most notably between the years 1995 and 1998. This dominant periodicity is also significant at the 95% confidence level (Fig. 4b). The cross-bay wind spectral patterns are illustrated in Fig. 4c, and reveal a dominate periodicity of 3 years and a minor periodicity between 5and 6 years. The weaker spectral energy dominates the record period from 1990 to 2000, while the larger spectral peak occurs between the years 2000 and 2010. The NAO index over this period shows a very weak nonsignificant spectral peak at the 5–7 year band between 1995 and 2000 (Fig. 4d). Each of the parameters examined; HVI, ONI. SQI, cross-bay

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Fig. 3. Plot of the hypoxic volume index from 1985 to 2010 (a), and the continuous wavelet transform of the hypoxic volume index (b) indicating the dominate periodicity around the 6-year mark. The black circle represents the 95% confidence interval, while the hyperbolic curve represents the cone of influence. The color map displays the normalized wavelet power.

winds, and the NAO clearly demonstrate quasi-periodic structures, many of which are non-stationary.

shows that a linear relationship does not exist between these variables (R2 = 0.18, P > 0.05). Conversely, if HVI and ONI are plotted on top of each other, it appears that there are times when these waves are in-phase and out of phase, suggesting a coherence in-time between these variables (Fig. 5b). As a result, wavelet coherence analysis was performed between HVI and the other variables used in this study as a way to determine which variables should be used in the neural network model. The cross-wavelet and wavelet-coherence between the hypoxic volume index and ONI indexes suggests a significant coherence at the 95% confidence level around the 5–6 year period and a minor coherence around the 2–3 year band. This is consistent with the results displayed in Fig. 5b. Right pointing arrows indicate an in-phase relationship between hypoxic volume and the ENSO signal (Fig. 6a). The results of the cross-wavelet coherence analysis between HVI and SQI reveal that a significant coherence at the 95% confidence level exists within the 5–6 year spectral band, and a minor coherence exists at the 2–3 year periodicity. Phase arrows indicate SQI leading HVI with an average phase angle of 94°. This phase angle yields an 18-month phase lag between annual Susquehanna River flow and the hypoxic volume index in the Chesapeake Bay (Fig. 6b). Analysis of cross-bay winds and hypoxic volume index indicate a significant coherence at the 95% confidence level within the 5–7 year spectral band, as well as a minor significant energy peak at the 3-year period. Phase arrows are pointed to the left, indicating an anti-phase relationship between cross-bay winds and hypoxic volume (Fig. 6c). The NAO signal shows very little Cross-Wavelet Coherence with the HVI. Phase angles in different spectral bands are in opposite directions suggesting that any coherence is coincidental (Fig. 6d). 3.3. Neural network diagnostics and prediction

3.2. Cross-wavelet coherence analysis ENSO processes have typically been left out of hypoxic volume modeling for the Chesapeake Bay due to the lack of their linear correlation. However, if hypoxic volume is treated like a quasi-periodic wave, a new pattern emerges. Fig. 5a illustrates the linear regression analysis between hypoxic volume index and the ONI. The plot clearly

Based on the cross-wavelet coherence analysis, three exogenous inputs were fed into the NARX model along with the corresponding target values y(t). The inputs included the ONI index, the Susquehanna River index and the Cross- Bay wind data. Since the NAO index showed very little cross-wavelet coherence with the HVI, it was excluded from this model. Fig. 7 provides a schematic of the dynamic

Fig. 4. Morlet continuous wavelet analysis of the hypoxic volume index (a), the Susquehanna River index (b), cross-bay winds (c) and the NAO index (d). The black circle represents the 95% confidence interval, while the hyperbolic curve represents the cone of influence. The color map represents the normalized wavelet power.

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Fig. 5. Regression analysis between HVI and ONI (a) and HVI and ONI curves plotted on the same graph (b); note the appearance of “in-phase and” “out of phase” coherent structures in (b).

Fig. 6. Cross wavelet coherence plots for HVI and ONI (a); HVI and Susquehanna river index (SQI), (b); HVI and cross Bay winds (c); and HVI and then NAO index (d). Thick black outlined areas are periods of high coherence at the 95% confidence level. Arrows indicate phase angle relationships; where arrows pointed to the right are indicative of an inphase relationship; left pointing arrows are out of phase; and up or down arrows suggest one property leading or being led by the other. The color map indicates the normalized cross-wavelet power.

feed-forward (NARX) model used in this study. Step one of the calibration process revealed that the best results occurred using a sigmoidal function with five hidden layers and 20 neurons. The calibration process produced very good training and validation responses with an R of 0.99 and 0.94 respectively. The mean square error (MSE) for the training phase is 2.4 × 10−14 , and 0.47 for the validation phase. Fig. 8 illustrates the overall NARX model performance over the 22year data set used for learning and calibration. Regression analysis on the total data inputs used yielded an R-value of 0.92. After completion of the NARX model calibration and validation, the model loop is closed and predictions of the hypoxic volume index are projected into the future from 2007 to 2017. The long-term average of 5 km3 , which was used to create the HVI is then added to the predicted index to recover the predicted hypoxic volume. A regression analysis of the 2007–2014 predictions versus calculated hypoxic volume was performed in order to determine how well the NARX model predicted actual annual average hypoxic volumes in the Chesapeake Bay (Fig. 9). The NARX model produced reasonable results with an R2 of 0.68 and a P-value equal to 0.02. The results yielded deviations between predicted and measured hypoxic volume mostly in the 0.2–0.4 km3 range, with an MSE of 0.5. The first 3 years

(2007–2009) show modest under predictions, while the next three years have mostly slight over predictions. The deviation between the predicted and measured hypoxic volume for 2012 is much larger than any other year, as the NARX model over predicted the hypoxic volume by 1.2 mg l−1 (Fig. 9). The NARX model did well in predicting the large hypoxic volume in 2011, especially since a significant amount of rainfall occurred in early spring resulting in the opening of the Conowingo dam to reduce flooding in Pennsylvania, and two tropical storms in late summer. NARX model predictions for 2013 and especially 2014 have excellent predicted to measured hypoxic volume agreement. Despite poorer model results in 2012, all predicted values lie well within the 95% prediction band (dashed lines in Fig. 9). 4. Discussion The Cross-Wavelet Coherence Analysis was able to detect significant coherences between ONI, SQI, cross bay winds and HVI. The inphase relationship between ONI and HVI indicates that ENSO does have an effect on hypoxia on the 5–7 year scale, with ENSO warm phase related to an increase in hypoxic volume. Other studies imply that ENSO events do not affect hypoxia in the Chesapeake Bay at all

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Fig. 7. Schematic of the dynamic feed-forward neural network model used in this study. The model contains 5 hidden layers and 20 neurons in each layer.

Fig. 8. Plot of the NARX model performance during the training, and validation phases.

Fig. 9. Regression analysis between NARX model results of hypoxic volume and actual annual hypoxic volume (2007–2014). Dotted lines represent the upper and lower 95% confidence interval, while the dashed lines signify the 95% prediction bands. All predictions lie well within the 95% prediction band.

(Constantin de Magny et al., 2010; Lee and Lwiza, 2008). We suggest that this is not a direct relationship but rather ENSO events may enhance the development of hypoxic volume when the warm phase is in phase with the more dominating variables that control hypoxia. We hypothesize that the main ENSO effect is rooted in increased precipitation within the Chesapeake Bay watershed. This is most likely in the form of snow. In their study of ENSO phase effects on regional snowfall frequency in the continental United States, Pattern et al. (2003) found significant differences between ENSO phase extremes

related to light, medium and heavy snowfall. In particular, they concluded that within the Northeast corridor region which included the Chesapeake Bay watershed, ENSO warm phase was associated with an increase in heavy snowfall days, while ENSO cold phase was more closely associated with increases in light and moderate snowfall days as compared to neutral phase snowfall patterns. In contrast, Seager et al. (2010) found an increase in total snowfall during ENSO cold phase and a reduction during ENSO warm phase in the Northeast. They also found increased snowfall in the Southeastern United States during ENSO warm phase events. It is important to note that this particular study contained a preponderance of their stations located inland from the coast. Smith and O’Brian (2001) used a completely different method to investigate snowfall pattern and ENSO events. This study focused on normalized quartiles of seasonal snowfall distributions to define regions with similar patterns in the continental United States. The authors of this study determined that warm phase ENSO events in the Northeast coincided with significant increases in snowfall at all quartiles as compared to neutral phase events during midwinter (D, J, F). The opposite trend was also found during cold phase events for mid-winter. Pattern et al. (2003) suggest that subtle differences in coastal cyclone intensity and track may be responsible for snowfall frequency variability between inland and coastal stations in the Northeast. In a study on the occurrence of East Coast winter storms, Hirsch et al. (2001) found in general a 44% increase in East Coast storms during ENSO warm phase as compared to ENSO neutral phase events. The basic mechanism driving differences between inland and coastal station snowfall frequencies appears to be that when East Coast storms track close to the coast, the warmer conditions lead to light and medium snowfall near the coast and an increase in heavy snowfall occurrences inland. Conversely, when East Coast winter storms track further offshore they tend to produce heavier snowfall in the Northeast corridor (Pattern et al. 2003). If in fact, subtle changes in East Coast storm

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tracks and intensity are influenced by ENSO phase, then ENSO phase may have an indirect relationship to hypoxic volume in the Chesapeake Bay, which was detected by the cross wavelet analysis of this study. Heavy snowfall in the upland regions of the Chesapeake Bay watershed could lead to a large spring melt carrying higher concentrations of nutrients. The increased discharge of freshwater would enhance stratification and deliver a higher concentration of nutrients in time for the development of larger and potentially earlier algal blooms eventually leading to a larger average hypoxic volume for the summertime. Another important aspect that is not directly included in the NARX model is that a significant amount of water enters the bay from non-point sources making it difficult to include in models in general. Zhou et al. (2014) also point to the problem of non-point source freshwater entering the bay and suggest including other major river inputs such as the James and the Potomac rivers. The NARX model would most likely improve with other discharge sources. The anti-phase relationship detected by the Cross-Wavelet Coherence between cross bay winds and the hypoxic volume index suggest that positive deviations of hypoxia from the long term average are more closely associated with North-easterly winds, whereas negative values of the hypoxic volume index are associate most often with South-westerly winds for the Chesapeake Bay. These results are consistent with results of Lee et al. (2013) and Zhou et al. (2014), illustrating the importance of treating these variables as quasiperiodic functions. This is in contrast to Scully (2013), which suggested that westerly winds increased hypoxia due to seiching effects. North-easterly winds increase flow out of the bay, acting like an enhanced discharge, leading to increased saltwater intrusions from the Atlantic Ocean to the bottom waters of the bay. This will increase stratification and hence strengthen or enlarge hypoxic volumes. Typically the largest portion of the hypoxic volume occurs in the upper section of the bay, which is also the narrowest cross-section of the bay. It is unlikely that seiching is a dominant factor in this area, and Scully’s model is actually only relevant to the southern portion of the bay, which is the widest section. Lee et al. (2013) used the ChesROMS model to hypothesize that cross bay winds were responsible for transporting algal biomass to the western side of the upper bay as a mechanism for enhanced hypoxic volume. We suggest that this is not a plausible mechanism due to the fact that the ROMS models include a Coriolis parameter which would transport the biomass to the west. However the narrow cross sectional area does not allow for a sufficient Rossby Radius of Deformation to allow Coriolis to be a significant forcing factor in this area. The enhanced discharge concept is supported by a few studies on wind forcing of non-tidal circulation in estuarine environments. Weisberg (1976) discovered a high anti-phase coherence between longitudinal winds and bottom currents in the Providence River. A similar baroclinic response to wind forcing was also found in the Potomac River, Chesapeake Bay (Elliott 1978). Atmospherically induced exchanges between local estuaries and their adjacent coastal oceans were found in the Potomac River (Elliott (1978), Chesapeake Bay and the Atlantic Ocean (Wang and Elliott (1978) and Corpus Christi Bay, Texas (Smith 1977). Further evidence of axial wind influences on gravitational circulation in estuarine environments has been provided by Scully et al. (2005) and Chen and Sanford (2009). In their 2005 paper, Scully et al. were able to show that stratification and flow patterns in the York River are highly related to episodic axial winds. Both flow exchange and stratification tended to increase under moderate down-stream winds, while flow reversals occurred under moderate up-stream winds. Several studies have reported increased mixing in estuarine environments under strong wind conditions (Goodrich et al. 1987; Blumberg and Goodrich 1990; Li et al. 2007, Scully et al. 2005; Wang 1979) also proposed wind induced straining and mixing mechanisms to explain the axial wind effects observed in the York River. In an attempt to further understand wind effects on stratification intensity and salt transport, Chen and Sanford (2009)

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Fig. 10. Plot of predicted hypoxic volume for the main-stem of the Chesapeake Bay (2007–2017).

Fig. 11. Plot of average monthly temperatures (1985–2012) and average monthly temperatures during 2012 for mid bay station CB 4.1c, indicating that 2012 was warmer than usual for most of the year.

constructed an idealized model of the Chesapeake Bay. The model used confirmed the results of Scully et al (2005) and that their results are applicable in general to partially-mixed estuaries. Since the NARX model provides yearly predictions of the hypoxic volume index over the next several years, it is also possible to determine the predicted hypoxic volume for each year. Fig. 10 illustrates the predicted average (June–September) hypoxic volume for the main stem of the Chesapeake Bay from 2007 to 2017. In general the NARX model performed well especially capturing the extreme hypoxic volume of 2011 and the near average conditions of 2013 and 2014. However, the NARX model was not able to account for the higher bay temperatures and the much drier conditions in 2012 (Fig. 11). The drier conditions led to a smaller than average Susquehanna River flow which ultimately resulted in a below average hypoxic volume. Consequently, the NARX model over predicted the hypoxic volume for 2012. The cross wavelet analysis also suggested an approximate 18 month lag between Susquehanna River flow and the Hypoxic volume index. Although the reasons for this lag have not been fully resolved, one possible reason may be related to river flow and phytoplankton biomass in the Chesapeake Bay. Boynton and Kemp (2000) reported that there appears to be a strong relationship between phytoplankton biomass and Susquehanna River flow, and a moderate relationship between flow and production. In this study, it was also determined that the highest degree of correlation between biomass and flow occurred when using the annual Susquehanna River flow plus the previous year’s annual flow suggesting lag periods in the order of about a year. The authors suggest that this may be due to residual nutrients or a “nutrient pool” in the bottom sediments of the bay (Boynton and Kemp 2000; Boynton et al. 1995).

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In this model we excluded NAO as a factor mainly because the cross-wavelet analysis suggested a weak coherence with the HVI. Scully (2010) suggested that a regime shift in the climate occurred during the later years of our study period, in which the NAO became important. Our cross wavelet analysis did detect this and it is possible the NAO could aid in our predictions but its signal is not as strong as the ENSO signal we used. Interestingly, Seager et al. (2010) suggests that the anomalously high snowfall during the 2009–2010 Winter in the Northeast and Mid-Atlantic regions was mainly a consequence of a strong ENSO warm phase coupled with a negative NAO index. One of the main advantages of this type of model is that it can be a predictive tool similar to a weather forecast, where actual measurements are made, and are re-fed back into the model updating the predictions annually. The ten-year forecast would be then analogous to a 10-day forecast for meteorology in which the 3–4 year forecasts are more accurate and the future years less accurate. However, since the Neural Network model is self training the predictions will improve as new information is fed into the model (actual hypoxic volume measured). 5. Conclusions The research presented in this paper highlights the importance of analyzing environmental data as wave properties rather than purely linear functions, and that the predictive power comes from determining the constructive and destructive interference patterns of the input parameters. Furthermore, while numerical models are useful in investigating the primary physical forcing and responses in an estuarine system, the combined Wavelet-Neural Network Models, especially the NARX dynamic systems method is a useful tool in the prediction of environmental stressors, such as dissolved oxygen. While the wavelet coefficients provided the initial guess to train the neural network model, the biggest strength of the wavelet analysis was in the ultimate choice of the input variables. These types of models should be used in conjunction with other tools to create sound adaptive management practices and policies in coastal regions. This Neural-Network model is a tool to predict hypoxic volume several years into the future, which can have a significant impact on adaptive management procedures, such as marine spatial planning, fisheries, and restoration in coastal environments. This model can be thought of as a “climate-based” hypoxic volume benchmark for future hypoxic volume in Chesapeake Bay. We use the term climate based model to reflect the entire climatology of the bay which includes forecasts of river discharge, cross-bay winds, ENSO events and anthropogenic effects. The model can also be used to “test” the effectiveness of the nutrient or sediment reductions required by the Chesapeake Bay TMDL. If no reductions occur, hypoxic volume with continue to grow and expand, and if nutrient/sediment reductions are real, then the actual measurements should be below the predictive model outputs. In this way the model forecast acts as a bay climatology measuring stick to interpret bay restoration advances. Acknowledgments We would like to thank the Naval Academy Research Council, the United States Naval Academy Oceanography Department, and the Paul and Maxine Frohring Foundation for their support on this project. We would also like to thank the two anonymous reviewers for helping to greatly improve the manuscript. References Areerachakul, S., Junsawang, P., Pomsathit, A., 2011. Prediction of dissolved oxygen using artificial neural network. In: 2011 International Conference of Computer Communication and management, Proceeding of CSIT, vol. 5. IACSIT Press, Singapore.

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