Peter Borgen Sørensen, Christian Frølund Damgaard, Poul Løgstrup Bjerg, Hans Estrup Andersen, Peter Engelund Holm, Henrik Tornbjerg, Jesper Leth Bak, Goswin Johann Heckrath, Ane Kjeldgaard, Patrik Fauser. 2022. Udvikling af model til understøttelse af vandplanlægningen i fastlæggelsen af koncentrationsniveauer af metaller i danske vandløb. Aarhus Universitet, DCE – Nationalt Center for Miljø og Energi, 70 s. - Videnskabelig rapport nr. 484.
https://dce2.au.dk/pub/SR484.pdf

Summary

This project aims to develop a test model for predicting the presence of metals in running waters and is structured as a test project that uncovers the applicability of various descriptive data for use in any future modeling projects for other groups of substances as well. The project is a first attempt to use NOVANA data in combination with descriptive data to set up a model for estimating environmentally hazardous pollutant concentrations in running waters.

As spatial resolution, ID 15 catchments have been selected, which are topographic catchments of approx. 1500 ha each. These catchments are already defined based on topography and are connected hydrologically for the whole of Denmark. Therefore, they form a natural basis for a spatial modelling, where a spatial analysis must be related to upstream ID 15 catchments along the running water. The established stations under NOVANA are all typically located close to the outlet of an ID 15 catchment area. Thus, some ID 15 catchments will feed water to stations measured for metals in NOVANA, while other ID 15 catchments will be outside these areas.

A data-driven (statistical) approach has been used, where existing data from the NOVANA program controls the set-up and parameterization of the model. The model can handle both the uncertainty related to the sampling, the chemical analysis as well as the uncertainty in the model's predictions of concentration levels for unmonitored watercourses. There are two main sources of input:

• Measurements of metal concentrations in the water phase at selected stations under NOVANA, divided into season and year.
• Information (attributes) on conditions in all ID 15 catchments that have been assessed to have a potential effect on the metal concentration in the water phases, e.g. agricultural activities, soil type and wastewater outlets.

The model can be continuously updated with data and knowledge and can, thus, be improved both in relation to new measurements and in relation to the new information from the catchments that enter the ID 15 catchments. Due to its statistical structure, the model has been named MetalStat.

The calculation work for MetalStat can be divided into a phase, where the model predictions must converge towards the most realistic relation between model and measurements, and then a simulation phase, where the model yields result, cf. the queries that may be interesting. Since there are many variables in the model, it takes a long time for it to converge, but once this is completed, the model will be able to give results instantly. The long time it takes for the model to converge has made the development work more difficult in the relatively short project period, as any correction and change means that the model has to start converging from scratch, and ongoing adjustments have been made as a natural part of the development work. But for the project, this has meant that only the 3 metals lead, cadmium and nickel are about to converge by report submission, as the model was adjusted in its structural equation towards project completion in December and therefore is not completely converged in relation to this new condition. Another run with lead, cadmium, nickel, copper and zinc is also converging, but will require at least one month of extra calculation time, which will continue into 2022, as it will be an advantage to have a finished converged mode as a starting point for a possible operating phase. So, after the initial list of metals was reduced to the 5 metals lead, cadmium, nickel, copper and zinc, and to get calculations as close to converging as possible, these 5 metals have further been reduced to lead, cadmium and nickel in this report. It is recommended not to include the other metals barium, chromium, mercury and arsenic in the model till after the first 5 metals have been put into operation. The convergence calculations continue after the submission of this report to support an upcoming modeling activity. The concrete calculation results in this report must, therefore, not be taken as a realistic interpretation of the occurrence of metals, as the model is still converging at the time of writing.

The project has focused on the water concentration of metals, as this is where most data are available, but other matrices, such as sediment, could be included in the model once the modeling of the water concentration has been implemented. The model's multivariate structure means that measurements in different environmental matrices can support each other with combined knowledge and the presence of a substance.

The following four main questions were posed from the beginning of the project:

1. To what extent can the model predict concentration levels for uncontrolled watercourses? Based on the monitored areas, the concentration levels can be predicted for the whole of Denmark as distributions that reflect the uncertainty.
2. With what certainty are the predictions obtained by such modeling determined? The certainty of a prediction outside monitored areas will depend on how well it is possible to describe important mechanisms in a nationwide catchment area model, and the uncertainty thus highly depends on the substance. The uncertainty will be greatest outside monitored areas, in which the uncertainty is primarily due to the analytical technique and the capability of the water sampling to reflect the conditions in the sampling station. In both places, there is uncertainty, but it is greatest outside the monitored areas. The report illustrates how MetalStat can map the uncertainty related to a prediction of a concentration level outside the monitored range so that a false certainty does not arise in relation to predicted values.
3. An assessment of how the present model can be applied beneficially in the preparation of a future monitoring program for metals in running waters. MetalStat can improve the ability to find correlations in monitoring data that can support a better understanding of the fate of the metals and their supply to the aquatic environment. This type of analysis could be part of the planning of a future monitoring program. It is also natural to prioritize a future monitoring program to have focus on the non-monitored areas that MetalStat predicts are most likely to have the highest concentration levels.
4. An evaluation of the project to highlight attention and learning points for possible future model projects. Models for environmentally hazardous pollutants are typically very complex, and predictions from these are subject to considerable uncertainty. If it is subsequently decided to use the developed model for decision support, a version must be made for the operational phase, which places specific requirements partly for optimal operation and partly for extra quality assurance of the coding itself, which can otherwise be supported by comparing results from the pilot model with results from the operating model. MetalStat sets new standards for what can be concluded based on monitoring data and, thus, also requirements for the competencies required from those who will be using the model. This means that it is advantageous to create a professional structure behind the model, which processes results and seeks operation and improvements. The professional structure around the model could be built up in four groups that work in synergy:

• A user group that is responsible for disseminating the model to all relevant parties in the Danish Environmental Protection Agency and formulates the specifications that the model must meet.

• An environmental science group that continuously discusses the model's results in relation to whether they appear to be environmentally credible. In addition, this group must ensure that the model is updated with new knowledge about the processes that the model describes. The environmental scientist group may publish a condition report with conclusions based on model simulations, including monitoring data.

• An operating group that is responsible for the computational connection to data sources as well as documentation of the model's calculations and ensures that the model meets the desired specifications. The operating group must ensure that the model delivers results corresponding to the expectations of the user group. The extracted calculations can be processed with descriptive statistics such as histograms or fractional values shown for each ID 15 catchment in GIS. These extracts are specified by the user group.

• A development group that combines environmental chemical professional knowledge with mathematical and arithmetic knowledge in consultation with the environmental professional group and comes up with project proposals for possible development projects. Evaluates and monitors the model's results and makes suggestions for improvements and adjustments in relation to new data sources and improvements in the model's mathematical structure. This group could possibly also assess the possibilities of extending the modeling to other substances and issues.

As MetalStat is a multivariate model in terms of metals, knowledge of one metal's concentration level will automatically be able to contribute knowledge of another metal's concentration level in the same place and at the same time. In the same way, an auxiliary variable can be used if there is a connection between e.g., the lithium content and a metal, and if the lithium concentration is measured, then it will be possible to contribute knowledge about the metals, given the lithium auxiliary variables are included in the model in line with the metals. It should be considered whether such auxiliary variables should be included in the first operating version of MetalStat.

The current calculations in this project have uncovered some important points that should be addressed when setting up a model for operation: (1) the X matrix should be thoroughly evaluated based on the results of this project when the model is converged to optimize the linear catchment model. Especially in relation to the strongly nonlinear attributes, e.g. the clay content and pH. Because it seems possible to eliminate some of the selected attributes to a smaller number, it should be considered whether others should be tested, e.g. areas of industry, city and fresh water. It should be investigated whether it is possible to maintain β to be only positive, as it will counteract the estimation of negative concentrations and the formation of fictitious opposite +/- effects from different attributes. The database should be continuously updated with the latest NOVANA data as they become available, which means that an operating model must expand its data base to also include NOVANA data from 2021.

MetalStat uses estimated groundwater supply in a rather simplified description, where a better description would be based on a statistical model of the groundwater concentration that utilizes knowledge of groundwater concentration from the catchment area's drilling samples. In this way, groundwater monitoring can be integrated into watercourse monitoring. In the same way as described for groundwater, other matrices, such as sediment-bound metal, are coupled to MetalStat through a new latent variable for sediment concentration, if a credible function can be found that links adsorbed phase to dissolved phase, possibly based on equilibrium chemistry or first-order exchange between sediment and water phase.