# Water pollution forecasting model

*Figure 1: Assoc. Prof. Dr. Tran Thu Ha*

Predicting water pollution is an important task for the safety of human life and living species. It is imperative to be able to identify uncertainty in a model prediction. That is the task of sensitivity analysis whose role is to determine the uncertainty in the model's outputs according to the model's inputs (the parameters in this case). The ability to predict with high accuracy the impact of changes in pollutant emissions from one domain to another will help researchers make decisions that improve public health and the environment.

The objective of the project is to provide an effective tool based on the conjugate equation approach to calculate the sensitivity of input parameters to the output (system feedback), for allowing to obtain information about how the output is performed by each input parameter.

The conjugate equation approach method is computationally efficient for solving sensitivity analysis problems. It allows, in a single run of conjugate equation approach, to generate the sensitivity of a given response function (defined over a point or a region over a period of time) to the domain-wide distribution of the sources. The main difficulties in the conjugate equation approach are related to the construction of the conjugate variable for the related linearization system in a nonlinear dynamical system, especially for high-dimensional systems.

The project presents the theoretical aspects of the method related to the sensitivity of the response function to the observed pollution locations, within the general framework of the water pollution problem. Furthermore, a simulation model is presented that is the application of these theoretical aspects. In this part of the application, 2D hydraulic and pollution models are used to describe the transport of pollutants. By constructing a sensitive problem using the optimal variable, the problem aims to show the best measurement domain for calculating water pollution to determine the pollution source. On the basis of the theoretical problem, numerical models are established, model-testing calculations provide a theoretical method and a calculation program for the sensitivity function that depends on the measurement location. From there, we can show that the measurement location should be the most suitable to calculate the source of pollution emission.

The main objectives are to find the source of pollution through the value distribution of the response function gradient (or sensitivity function) over the domain, through this functional gradient calculation model for the inverse problem of pollution source.

By using current calculation methods and developing new modern mathematical methods, the topic develops better sets of calculation subroutines to improve the quality of flow simulation, and improve the ability to calculate water quality, to use these programs as a calculation support tool for future practical problems

Through the research process, the team presented a new correction method to find the pollution source by the variable optimization method. With the new method of sensitive function theory, the implemented calculation program has successfully calculated the pollution problem of Thanh Nhan Lake in Hanoi.

Thanh Nhan lake is located behind Thanh Nhan hospital with an area of 8.1 hectares, a depth of 1.5m -3m, an average capacity of 162000m3. The amount of wastewater poured into the lake is about 2100m3/day-night. Thanh Nhan lake is meshed into unstructured triangular grids (Figure 2 left).

*Figure 2. Grid diagram of Thanh Nhan lake (left), pollution field at a time calculated T3=T2+20 s (reference model as measured) (Right)*

Through the calculation results (Figure 3), it can be seen that the sensitivity is stronger when the measurement area is close to the polluted area. Furthermore, as shown in Figure 3.c and Figure 2 (on the right), we can see the maximum sensitivity function value when the measurement area is in the pollution source domain. From there, by changing the different measurement locations to calculate the sensitivity function, we can determine the area with the source of pollution emission. That helps us to have an additional method of detecting contaminated areas through the change of measurement locations in the simulation, then the sensitivity function value will change. This sensitivity function will be greatest when coincides with the source of pollution emission.

*Figure 3. Error of pollution field with reference pollution field (a); Gradient of response function (called sensitivity function) for Cobs with different measurement positions (b)-(e)*

The project has published 01 article in the high-quality ISI journal and 01 article in the SCIE journal. With the obtained results, the team hopes to continue to develop a calibrated prediction method based on a new technology, adaptive artificial intelligence, called ANN.

Translated by Phuong Huyen

Link to Vietnamese version