Study On The "Dose-loss" Response Model For Acid Deposition On Typical Crops

In 1872, the English Chemist R.A.Smith, first proposed the term of "acid rain" in the book "air and precipitation: the Beginning of the Chemical Climate ". Acid rain is the precipitation which pH value is less than 5.6, including thunder storm, fog, hail and the other forms of precipitation. Acid deposition consists of wet deposition and dry deposition. Natural source and man-made source are the two sources of acidic materials which lead to the formation of acid rain.The chemical composition of acid deposition are sulphur oxides (about 60%), nitrogen oxides (about 21% 23%), chloride (about 10% 12%), carbon dioxide, ammonia and organic acids. Human activities have significant impact on the formation of acid deposition. Because of the serious environmental damage caused by acid deposition, it has now become one of the ten problems threatening the world's environment. It only occurred in the industrialized countries of Europe and the United States in the past, now extended to the developing countries. China has become the third largest acid rain area of the world inferior to North America and Europe. According to the scholars'research on acid deposition samples of the chemical analysis, the acid deposition's chemical compositions classify in general: H⁺,Ca²⁺,NH₄⁺,Na⁺,K⁺,Mg²⁺,SO₄^2-,NO₃^-,Cl^-,HCO₃^-。This research builds "dose - loss" response model for acid deposition on typical crops by combining an example and using of single dependent variable partial least squares (PLS) regression method. Whereafter, the research analyzes the predicting product results, tests the effectiveness of fitting equation and facilitates more visible and easily operated "dose - loss" response model prediction software by using Visual Basic 6.0. Therefore, it eventually establishes model prediction system.Partial least squares regression (PLS) method was first drew by S. Word and C. Albano, who proposed in 1983. Later, PLS was concerned by the statisticians and used to solve many of problems which are difficult to solve by using multiple linear regression. This method not only can be applied to analyze single-variable regression, but also can be used for multi-variable regression analysis.PLS could effectively extract the strongest integrated and variable explained information of the system, delete the multiple correlative and unmeaning information interference. Thereby it overcomes the multiple correlation of the variation in the system modeling of adverse effects. PLS provides a regression modeling method between multi-dependent variable and multi-independent variable, especially when there is a highly relativity among the variables. By adopting PLS modeling, the analysis conclusion would be more reliable and more holistic. PLS could effectively solve the problems of multiple correlations among the variables and carry out the comprehensive application of a variety of multivariate statistical analysis methods, which is especially suitable when sample size is less than the number of variables.This study chooses vegetable crops as typical samples which has more sensitive response to acid deposition. 12 sets of collected samples data are divided into two groups, eight samples for analysis modeling, the other four for predicting. This study considers pH,Ca²⁺,NH₄⁺,Na⁺,,K⁺,Mg²⁺,SO₄^2-,NO₃^-,Cl^- as the influencing factors, which is marked as x₁ ,…,x₉.It also considers acid deposition losses as the target function, which is marked as y . Then , we could obtain the "dose - loss" response model through PLS1, which could be analyzed specifically.From the correlation coefficient between independent variables x₁～x₉ and dependent variable y ,we could judge that multiple correlation exists between x₁～x₉ and y . We can draw the conclusion that there are strong multiple correlation-ships between them, especially there is a strong negative correlation (correlation coefficient -0.936) between x1 and y (pH and acid deposition losses).By using cross-validation method to estimate the reliability of model system and to determine the optimum number of principal components, we can get the results which are calculated as: PRESS3=PRESSmin =1.477. Thus, it is adequate that taking three principal components to generalize the information of the original sample.According to partial least squares regression algorithm, the PLS1 solution can be stated as follows.â‘´the first component: t₁ = -0.7897x₁^* + 0.1255 x₂^*-0.3857 x₃^*+ 0.2155 x₄^* + 0.0429 x₅^* + 0.3727x₆^*- 0.0196 x₇^* + 0.0040 x₈^* - 0.1559x₉^* The PLS1 solution is given by t₁ as : (y|^)= r₁t₁ = 0.7686 t₁ = - 0.6070 x₁^* + 0.0964 x₂^* - 0.2965 x₃^* + 0.1657x₄^*+ 0.0330 x₅^* + 0.2865 x₆^* - 0.0151x₇^* + 0.0031x₈^* - 0.1198x₉^*⑵the second component: t₂ = -0 .2981x₁^* - 0.3986 x₂^* - 0.6029 x₃^* - 0.3646 x₄^* - 0.1622 x₅^* - 0.1779x₆^*- 0.4212 x₇^* - 0.1445 x₈^* - 0.3233x₉^* The PLS1 solution is given by t1 and t 2 as : (y|^)^*= r₁t₁ + r₂t₂ = 0.7686 t₁ + 0.0692t₂ = - 0.6276 x₁^* + 0.0689 x₂^* - 0.3382x₃^*+ 0.1404 x₄^* + 0.0217x₅^* + 0.2742 x₆^* - 0.0442 x₇^* + 0.0069 x₈^* - 0.1422x₉^*⑶the third component: t₃ = - 0.0299 x₁^* - 0.2636 x₂^* - 0.5099 x₃^* - 0.3013 x₄^* + 0.4897 x₅^* - 0.0047x₆^*- 0.1499 x₇^* + 0.5624 x₈^* + 0.3165x₉^* The PLS1 solution is given by t₁ , t₂ and t₃ as : (y|^)^* = r₁t₁ + r₂ t₂ + r₃ t₃ = 0.7686 t₁ + 0.0692t₂ + 0.2271t₃= - 0.6344 x₁^* + 0.0090 x₂^* - 0.4540 x₃^* + 0.0720 x₄^* + 0.1329x₅^*+ 0.2731x₆^* - 0.0783 x₇^* - 0.1280 x₈^* - 0.0703x₉^*â‘·Finally, the PLS1 model can be expressed as: Standardization variable regression equation: (y|^)^* = - 0.6344 x₁^* + 0.0090 x₂^* - 0.4540 x₃^* + 0.0720 x₄^* + 0.1330x₅⁺ 0.2731x 6^* - 0.0783 x₇^* - 0.1280 x₈^* - 0.0703x₉^*Origin variable regression equation: y = 7.3050 - 0.7910 x₁ + 0.0244 x₂ - 0.7747 x₃ + 0.0194 x₄ + 0.2770x₅+ 0.1645 x₆ - 0.0054 x₇ - 0.0501x₈ - 0.1742x₉Precise analysis shows that the correlation between y and t₁ is strong, so it is between x₁ and t₁ , which performs the strong interpretation ability of x₁ to explain y . From the correlation coefficient matrix of dependent and independent variables, we can see that between x₁ and y there is a strong negative correlation (correlation coefficient -0.936), which fixes the actual situation.Through precise analysis, the first principal component t₁ explains 18.92% variability information of the original dependent variable system and 91.01% variability information of the original independent variable system. The second principal component t₂ explains 67.25% variability information of the original dependent variable system and 2.65% variability information of the original independent variable system. The third principal component t₃ explains 5.83% variability information of the original dependent variable system and 2.62% variability information of the original independent variable system. Component t₁,t₂,t₃ totally explain 91.99% variability information of the original dependent variable system, and they have a good representation for the original variables system. Component t₁ makes a greater contribution to the dependent variable system. However, component t₂ and t₃ seperately explain 2.65% and 2.62% variability information of the original dependent variable system, which make less contribution to the dependent variable system.From the charts- t₁ /u₁ , t₂ /u₁ , t₃ /u₁ , we can see that there is an obvious linear relationship between t₁ and u₁ , and it further confirms the conclusions reached from the analysis of Rd (Y;t₁)= 91.01%. The linear relationship among t₂, t₃ and u₁ are weakened in turn.Thought the variable important in projection histogram, we observe and compare with the important effect of x_j to explain y . It can be directly seen that the explanation of x₁ for y still has the strongest effect.According to partial least squares regression equation, we can draw the conclusion which use a full set of eight-samples data for model fitting analysis that the regression equation fitting error range from -8.08% to 9.68%, the maximum relative error is 9.68%, while the minimum relative error is 0.07% . From the contrastive curve of fitting value and the observed value, we can see the absolute error of regression equation directly and there is a similar trend between them. Finally, the regression equation fits better, and the equation is feasible. Testing the quality of the regression model in use of 4 samples data, we can see the regression equation prediction error range from -2.25% to 4.32%. The maximum relative error is 4.32 %, while the minimum relative error is -2.25%. Through the contrastive curve of predictive value and observed value, we can see there is an absolute error between regression equations predicted value and observed value. The regression equation predicts fine results.Finally, by using Visual Basic 6.0, we could build the more visible and easily operated "dose - loss" response model prediction software for acid deposition on typical crops.