Nitrogen prediction in the Great Barrier Reef using finite element analysis with deep neural networks
Introduction
The Great Barrier Reef (GBR) is the world's largest coral reef system, located off the east coast of Queensland, Australia. This world heritage site is facing severe threats that challenge its resilience, including extreme weather events and climate change, agricultural pollutants, coastal activities, surface runoff associated with the catchment areas, etc. Among these threats, land and agricultural activities are the main sources of pollutants from GBR catchments (Steven et al., 2019).
Nutrients, fine sediments, and pesticides are considered to be the primary land-based pollutants that significantly reduce ocean water quality (Waterhouse et al., 2020). According to the Australian and Queensland Government's long-term sustainability plan for the GBR (Reef 2050 Plan) (Reef-2050, 2021), excess nitrogen is particularly challenging in the GBR. High rainfall, flash floods, numerous short river basins, and the close proximity of the reef to the Wet Tropics of Queensland mean nutrients are flushed to the reef lagoon quickly.
Accordingly, the total nitrogen is amongst the most commonly measured and monitored water quality variables worldwide. In coastal and marine waters, nitrogen is usually considered the primary limiting nutrient. In other words, there is a strong consensus that it is the limited supply of nitrogen that limits marine ecosystem productivity in most cases, although phosphorus, silica, and iron may co-limit productivity in some situations (Howarth and Marino, 2006). When the total nitrogen increases, the growth and productivity of marine algae and other photosynthesising organisms increases, often to the detriment of marine ecosystems. This process is known as eutrophication and there is an extensive literature assessing its prevalence, causes, and management (Smith et al., 1999).
There is extensive evidence that the coastal waters of the GBR have been subject to some degree of eutrophication due to changes in its catchment land use since European settlement (Kroon et al., 2012; Bell et al., 2014; McCloskey et al., 2021) and that this has had a negative effect on GBR ecosystems (De'ath and Fabricius, 2010; MacNeil et al., 2019), though the offshore GBR and much of the midshelf remain oligotrophic (i.e., has low nitrogen and phosphorus concentrations) in absolute terms (McKinnon et al., 2017).
Management of nitrogen loads to the GBR in order to improve GBR water quality has been the focus of major investments by state and federal governments, not-for-profit organizations and farmers for many years (Kroon et al., 2016; Coggan et al., 2021; Waltham et al., 2021). Towards this end, a greater focus on experimentation, evaluation, and modelling to understand future nitrogen scenarios could further support water quality programs (Najafzadeh et al., 2019). In particular, predictive models can be used to forecast and manage the high risk areas in the coral reef ecosystems (Waterhouse et al., 2020).
However, implementing an accurate nitrogen predictor for the vast areas of the GBR is a challenging task. Nitrogen values in the GBR form a big frame (matrix) that vary with both spatial coordinate (x, y) and the time. One technique to handle this giant time-varying frame is to transform it into a timeseries by averaging all nitrogen values on each day.
This technique has been employed by many predictive models for a variety of target parameters, e.g., physical, chemical, and biochemical characteristics of water (Najafzadeh and Niazmardi, 2021), water quality index (Najafzadeh et al., 2021), nitrogen uptake in crops (Sharifi, 2020), marine environment salinity, O2, NO3, phosphorus, silicon, chlorophyll, and alkalinity (Wen et al., 2021), etc. The employed timeseries forecasting models in these published works range from decision tree and multivariate regression in statistical models to support vector regression in shallow neural networks, and further to the Long Short-Term Memory (LSTM) in deep neural networks. For example, one of the most recent models that has used this averaging technique is the fuzzy partitioning LSTM model introduced by Wen et al. (2021). In this model, the data attributes are partitioned by fuzzy c-means before feeding to an LSTM network for supervised learning. This architecture makes the model ready for high-speed distributed learning, as well as inference.
As opposed to the above technique, there is a second approach to design a next-frame predictor. In this approach, nitrogen values of each day across the GBR form a frame. The goal is to forecast future frames from the historical frames. This approach is referred to as next-frame prediction in parlance (Zhou et al., 2020). While time series forecasting could be applied to predict a value for each pixel separately, next frame forecasting has the great advantage of incorporating both spatial and time-series information rather than considering the history of each pixel in isolation. This provides a much richer source of information for each prediction.
It is worth mentioning that next-frame prediction is a type of forecasting problem, which is different from simulation problems widely carried out by hydrodynamic models (Huang et al., 2021). Standalone hydrodynamic models cannot forecast unless future boundary conditions can be reliably predicted, except by coupling with a data-driven surrogate model. For this reason, hydrodynamic models for water quality forecasting are rarely reported in the literature, are mainly timeseries forecasting models, and typically have high errors (Khan et al., 2020).
To the best of our knowledge, all existing data-driven next-frame predictors in the literature treat each frame as a whole. In other words, they simply stack up historical 2D frames, making a 3D matrix, and then feed the resulting 3D matrix to their Deep Neural Network (DNN) models to output a 2D prediction frame. Some of the commonly used DNNs are recurrent neural networks (Wang et al., 2019), 3D Convolutional Neural Network (Conv3D) (Mathieu et al., 2016), Convolutional Long Short-Term Memory (ConvLSTM) (Hong et al., 2018; Guen and Thome, 2020), etc.
One of the most successful next-frame predicting models in the literature is PhyDNet proposed by Guen and Thome (2020). PhyDNet disentangles physical knowledge described by partial differential equations from data, before feeding it to the ConvLSTM model. The experiments with sea surface temperature data showed the ability of PhyDNet to outperform state-of-the-art methods. In ensuing sections, we will apply PhyDNet to our nitrogen distribution dataset for comparison. We will show that the main disadvantage of these next-frame predictors is their low coefficient of determination (R2). In other words, frames predicted by these models are blurred (i.e., reduced R2) to reduce their overall prediction error (as measured by the mean squared error (MSE)). To address this problem, we propose a new DNN inspired by the Finite Element analysis (FE-DNN). By dividing the GBR study area into small elements, and by introducing the so-called stiffness matrices concept from the finite element analysis into the proposed FE-DNN model, prediction accuracy is increased, while the details of data variations are preserved.
To investigate the performance of the proposed FE-DNN model, we employ it to forecast nitrogen distribution frames in the GBR from hindcast distributions provided by an existing Partial Differential Equations (PDE) based simulation model. This distribution follows a complicated set of PDEs (Baird et al., 2020). The eReefs modelling suite (Steven et al., 2019) provides plenty of simulated nitrogen distribution data based on biogeochemical transformations and the spatial distribution of total nitrogen across the GBR but does not forecast future values. In addition, there are some sparsely collected nitrogen measurements across the GBR, which are useful in understanding and predicting nitrogen distribution in the GBR. These criteria make nitrogen prediction a good case study for FE-DNN implementation.
The rest of this article is organized as follows. In Section 2, nitrogen in the GBR will be defined, and challenges in high-resolution nitrogen prediction will be discussed. Section 3 will describe FE-DNN as our proposed solution to the problem of next-frame nitrogen prediction in the GBR. This data is introduced in Subsection 4.1. We will then evaluate the accuracy of the FE-DNN model for nitrogen distribution forecasting in the rest of Section 4, where a detailed investigation of both the computational complexity and the ablation properties of our model is also provided. The paper is concluded in Section 5.
Section snippets
Background and problem definition
The GBR is recognized by UNESCO as a World Heritage Area of “Outstanding Universal Value” due to its great cultural and natural significance and unmatched biodiversity. As stated in the previous section, reduced water quality since European settlement has been identified as a key threat to the health and resilience of GBR ecosystems (De'ath and Fabricius, 2010). While climate change is the single greatest threat to the world heritage status of the GBR, water quality adds cumulative pressure,
Proposed model
As discussed in Section 1, there is no high-resolution model in the literature that is able to forecast TN distribution over the GBR. In our proposed model, shown in Fig. 1a, we solve the TN forecasting problem by meshing the GBR study area into small overlapping elements. To elaborate, each day in N days of the input frames consists of a frame of TN values of all the meshes. The TN value for each mesh is termed a pixel, which represents the average TN in a 16 km2 mesh area. Several pixels are
Results and discussions
In this section, we will start by introducing the measured TN data, along with the PDE simulation results for TN in the GBR. We will then optimize the element size, before proceeding to the accuracy analysis, computational complexity, and ablation studies.
Conclusion
Inspired by the well-known FEA, we proposed the FE-DNN model for next-frame prediction of physical parameters in wide spatial coordinates. Our model is applicable to any environmental modelling scenarios, which are governed by underlying PDEs. We applied our novel model to the problem of TN distribution prediction in the GBR. To the best of our knowledge, our study is the first to use a data-driven machine learning approach for nitrogen prediction in the GBR. One challenge in training our
Software and data availability
The observational TN values are gathered from the GBR Marine Park Authority MMP, which is led by Australian institute of marine science (AIMS-MMP, 2021). The PDE solutions for the TN distribution in the GBR are obtained from the eReefs modelling suite. To elaborate, the eReefs regional GBR4 biogeochemical simulation data are downloaded from the AIMS website (AIMS-eReefs, 2021). The proposed FE-DNN model is implemented by Keras APIs of TensorFlow 2.5.0 in Python 3.8.
Funding
This work is funded by the Australian Government Research Training Program Scholarship.
This research was supported partially by the Australian Government through the Australian Research Council's Discovery Projects funding scheme (project DP220101634).
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
The eReefs model simulations were produced as part of the eReefs project (eReefs.info), a collaboration between the Science Industry Endowment Fund (SIEF), the Commonwealth Scientific Industrial Research Organisation (CSIRO), the Australian Institute of Marine Science (AIMS), the Bureau of Meteorology (BOM), and the Great Barrier Reef Foundation (GBRF), with support from BHP Billinton Mitsubishi Alliance, the Australian and Queensland governments, and with observations obtained through the
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