Reduction of variable nitrogen river water loading model by variance based sensitivity analysis, Case Study: Tweedriverbasin

The nitrogen cycle may be affected by chemical fertilization and industrial waste water. Nitrate can affect the human body through water and food, which can be transformed into nitrate and nitrosamine as a threat for humans and aquatic life. Therefore, detecting the influential elements and factors on this cycle, are essential from the environmental protection point of view. Many of scientists utilize mathematical models for these kind of problems. These models encompass linear and nonlinear differential equations that aresolved by numerical computer cods. The numerical codes are called “Deteministic computer models”, and running the model with different input values is called a computer experiment. One of the most famous models for the estimation of nitrogen river load is INCA-N (Integrated Nitrogen in Catchments).
INCA-N is a semi-distributed, process-based deterministic model of the flow of water and nitrogen through catchments. It simulates the key factors and processes that affect the amount of NO3 and NH4 stored in the soil and groundwater systems, and it feeds the outputs from these systems into a multi-reach river model. INCA-N has different input variables, thus detection of inactive variables of INCA-N is important. Because of reducing the input variables and simplifying of model, sensitivity analysis methods are used.
Sensitivity analysis involves sampling based, screening based and monte-carlo based and variance based method. Variance based method, which us used in this paper, detectsthe important variable and interaction effects. The main effect (first-order index) and total effect are most popular and important indices in variance based sensitivity analysis. These indices are multiple integrals based on the concepts of conditional mathematical expectation and conditional variance.The first-order index represents the main effect contribution of each input factor to the variance of the output. The total effect index accounts for the total contribution to the output variation due to factor Xi, i.e. its first-order effect plus all higher-order interaction effects. These indices are defined based on multidimensional integral which is estimated by simulation techniques.
In this paper, after introducing variance based approach and estimation of sensitivity indices with Monte Carlo and quasi random number, our attention is focused onsensitivity analysis of ofINCA-N model in the Tweed river. In this study the derived output is the average annual riverine load of inorganic nitrogen over a period of seven years.
The results of sensitivity analysis in optimized sample size showed that four variables, out of seven, of INCA-N are important:1." Plant nitrate uptake." The average main effect and total effect of this variable are 0.44 and 0.49, respectively. The difference between the total effect and main effect, which is 0.051, indicates that this factor does not have any significant interaction with other input variables in the model.
2. "Denitrification rate". The mean and standard deviation for the main effect were 0.247 and 0.189, whereasthese two measures for the total effect are 0.248 and 0.366, respectively.
3. " Immobilization ". The mean and standard deviation of immobilization were 0.182 and 0.787 for the main effect, and they are 0.227 and 0.3736 for the total effect respectively.
4. "Mineralization rate". The mean and standard deviation of this variable were 0.072 and 0.268 for the main effect, and 0.106 and 0.391 for the total effect,respectively .
The main and total effect of thesefour variables are (0.44,0.49), (0.247,0.248), (0.182,0.227), (0.072,0.106). It can be mentioned that, the interaction between these variable are so weak (maximum= 0.059). Three other variables nitrogen fixation, ammonium planet uptake and maximum nitrogen uptake is not important. Thus the sensitivity analysis method has good efficiency in the reduction of variation.
To manage the riverine load of inorganic nitrogen in the Tweed River at least fourfactors, including nitrate uptake rate by plants, denitrification rates, immobilization and mineralization, should be controlled. The variance based method makes it possible to detect the important variables. In the other words, the sensitivity analysis lts of INCA-N model showed that for controlling the nitrogen entering the Tweed River, at least three factors of "plants nitrate uptake," "denitrification rate" and "immobilization" should be taken into consideration. In addition to these three factors, mineralization can be considered as the fourth factor affecting the nitrogen load.