Optimization and Evaluation of Environmental Operation for Three Gorges Reservoir

Optimization and Evaluation of Environmental Operation for Three Gorges Reservoir

Ming Hu1,2, Guo H. Huang 2*, WeiSun 3,**, YongpingLi2, Bin Fan1

1State Key Laboratory of Environmental AquaticChemistry, Research Center for Eco-EnvironmentalSciences, Chinese Academy of Sciences, Beijing100085, China

2MOE Key Laboratory of Regional Energy and Environmental Systems Optimization, S-C Resources and Environmental Research Academy, North China Electric Power University, Beijing 102206, China

3Environmental Systems Engineering Program, Faculty of Engineering and Applied Science, University of Regina, Regina, Saskatchewan S4S 0A2, Canada

Correspondence: *Dr. G.H. Huang

Faculty of Engineeringand Applied Science

University of Regina, Regina,

Saskatchewan,

Canada S4S 0A2

Tel: (306) 585- 5631;
Fax: (306) 585-4855;

E-mail:

**Dr. Wei Sun

Institute for Energy, Environment and Sustainable Communities

University of Regina,

Regina, Saskatchewan S4S 7H9, Canada

E-mail:

Annex A: Statistical water quality response models of studied rivers

Statistical water quality response models of XXR

(1a)

(1b)

(1c)

(1d)

(1e)

(1f)

(1g)

(1h)

Statistical water quality responsemodels of DNR

(2a)

(2b)

(2c)

(2d)

(2e)

(2f)

(2g)

(2h)

Statistical water quality response models of XJR

(3a)

(3b)

(3c)

(3d)

(3e)

(3f)

(3g)

(3h)

(3i)

(3j)

where i is the period (10days); is the water release in period i; is the water head in period i; is the inflowin period i;is the total nitrogen concentrations of the XXRin period i; is the total phosphorus concentrationsof the XXRin period i;is the total nitrogen concentrations of the DNRin period i; is the total phosphorus concentrationsof the DNRin period i;is the total nitrogen concentrations of the XJRin period i; is the total phosphorus concentrationsof the XJRin period i.

Annex B: Processes of TOPSIS

(1) The decision matrixis polarized to make all decision variables with the same tendency. Not the positive decision variablesbutthe negative onesneed to be processed:

(4a)

(2) The decision matrix is normalized through the following equation:

(4b)

whereis the normalized value.

(3) The weightis determined and the weighted normalized decision matrix iscalculated.

Firstly, the weight of every decision criterion iscalculated;

(4c)

where and .

Secondly, the weight is normalized:

(4d)

Thirdly, the weighted normalized decision matrixis determined

(4e)

(4) The ideal and negative-ideal solutions aredetermined:

(4f)

(4g)

whereandare the sets of benefit and cost criteria/attributes, respectively.

(5) The Euclidean distances of each alternative fromthe ideal and the negative-ideal solutions are calculated,respectively:

(4h)

(4i)

(6) The relative closeness of each alternative to theideal solutionis obtained.

(4j)

(7) The alternativesare ranked according to the relative closeness tothe ideal solution. The bigger is the, the better is thealternative. The best alternative is the one with thegreatest relative closeness to the ideal solution.

Annex C: Processes of fuzzy TOPSIS

(1) The fuzzy decision matrix is normalizedaccording to equations (5b) and (5c). Then the ideal and negative-ideal solutionsare obtained by equations (5d) to (5g):

(5a)

(5b)

(5c)

(5d)

(5e)

(5f)

(5g)

whereand are the lower and upper bound of , respectively; is the core of ;;; represents the normalized performance; I and NI are the ideal and the negative ideal solutions, respectively.

(2) The following non-linear programming model is solved ateach alpha-cut level to compute the fuzzy relative closeness of each alternative;

(5h)

where

(5i)

(5j)

(5k)

where , and are the fuzzy decision matrix, fuzzy weight and fuzzy relative closeness, respectively; , and are the elements of , and at the-cut level of ; and are the lower and upper bounds of ; and are the lower and upper bounds of ;and are the lower and upper bounds of .

(3) The fuzzy relative closeness is defuzzified as follows:

(5l)

Where is the relative closeness represented by averaging level cuts (Fortemps and Roubens, 1996);are alpha levels (); k is the index of -cut level; N is the total number of -cut levels.

(4) The alternatives in terms of their defuzzified relative closeness are ranked. The alternative with the highest ratio is deemed the best option.

Annex D: Processes of AHP

(1) A hierarchy structure of the problem isconstructedwith different levels:the goal, criterion, sub-criterion and scheme levels.

(2) A set of pair-wise comparison matrices are completedforlower levels with one matrix for each element at theimmediately abovelevel by using the standardpreference scale.

(3) The single hierarchy sequencing and consistency check is conducted.

Single hierarchy sequencing is to both find the maximal eigenvalue and normalize thecorresponding eigenvector of the judgment matrixA.

(6a)

where, .The normalized W is as follows:

(6b)

where is the weight vector of certain sequencing, corresponding to A.

The consistency index can be calculated by

(6c)

(6d)

where CI is the consistency index; is the largest or principal eigenvalue of the matrix; n is the order of the matrix; RI is the random index. If CR0.10, the degree of consistency is satisfactory; otherwise, serious inconsistencymay exist so that the AHP may not yield provide meaningful results.

(4) The rating of each alternative is multipliedby the weights of the sub-criteria and aggregated to determinethe ratings.

Annex E: Processes of fuzzy AHP

(1) A triangular fuzzy number is assigned to an indexdenoting the relative strength of each pair of indicesin the hierarchy.

(2) Afuzzy judgment matrix using these triangular fuzzy numbers is constructed to represent the pair-wisecomparison of the indices at a certain level.

(3) The consistency of fuzzy judgment matricesis corrected by the optimal transfer matrix.

(4) The comprehensive importance of differentcriteriais determined by the following equation.

(7a)

(5) A proximity coefficient is defined to obtain the defuzzified rankingorder of the decision elements(Chen, 2000).

(7b)

(7c)

(7d)

Where is the weight for decision element j, and and are the distances between two fuzzy numbers.

(6) The priority weight of each alternative is obtainedby synthesizing the priority at each level using fuzzyaddition and multiplication.

Table S1.Correlation analysis between the water-quality indices and operational variablesin the three rivers

River / Water-quality index / Sample size / Period / Operational parameters / r / pt / Correlation?
XXR / TN / 38 / 1-16 / Water level-Zup / 0.465 / 0.001 / Y
Inflow-I / 0.015 / 0.635 / N
Water release-Q / 0.522 / 0.002 / Y
17-24 / Water level-Zup / -0.056 / 0.886 / N
Inflow-I / -0.053 / 0.805 / N
Water release-Q / -0.529 / 0.004 / Y
25-36 / Water level-Zup / -0.553 / 0.003 / Y
Inflow-I / -0.419 / 0.002 / Y
Water release-Q / 0.024 / 0.851 / N
TP / 41 / 1-16 / Water level-Zup / -0.593 / 0.001 / Y
Inflow-I / 0.014 / 0.856 / N
Water release-Q / -0.032 / 0.791 / N
17-24 / Water level-Zup / 0.051 / 0.556 / N
Inflow-I / 0.479 / 0.012 / Y
Water release-Q / 0.506 / 0.011 / Y
25-36 / Water level-Zup / -0.652 / 0 / Y
Inflow-I / -0.435 / 0.008 / Y
Water release-Q / 0.863 / 0 / Y
DNR / TN / 27 / 1-15 / Water level-Zup / 0.537 / 0.001 / Y
Inflow-I / 0.021 / 0.604 / N
Water release-Q / -0.563 / 0.002 / Y
16-25 / Water level-Zup / 0.656 / 0.002 / Y
Inflow-I / -0.042 / 0.782 / N
Water release-Q / 0.604 / 0.003 / Y
26-36 / Water level-Zup / 0.553 / 0.002 / Y
Inflow-I / 0.019 / 0.761 / N
Water release-Q / -0.624 / 0.001 / Y
TP / 32 / 1-18 / Water level-Zup / 0.593 / 0.001 / Y
Inflow-I / 0.014 / 0.856 / N
Water release-Q / -0.641 / 0.002 / Y
19-25 / Water level-Zup / -0.671 / 0.003 / Y
Inflow-I / 0.021 / 0.614 / N
Water release-Q / 0.606 / 0.011 / Y
26-36 / Water level-Zup / 0.652 / 0.001 / Y
Inflow-I / 0.041 / 0.754 / N
Water release-Q / -0.863 / 0.002 / Y
XJR / TN / 32 / 1-15 / Water level-Zup / 0.526 / 0.002 / Y
Inflow-I / 0.019 / 0.593 / N
Water release-Q / -0.551 / 0.001 / Y
16-30 / Water level-Zup / -0.612 / 0.002 / Y
Inflow-I / -0.042 / 0.782 / N
Water release-Q / 0.598 / 0.002 / Y
31-36 / Water level-Zup / 0.541 / 0.003 / Y
Inflow-I / 0.249 / 0.761 / N
Water release-Q / -0.632 / 0.001 / Y
TP / 41 / 1-18 / Water level-Zup / -0.582 / 0.001 / Y
Inflow-I / 0.011 / 0.783 / N
Water release-Q / 0.694 / 0.002 / Y
19-25 / Water level-Zup / 0.537 / 0.001 / Y
Inflow-I / 0.069 / 0.716 / N
Water release-Q / -0.497 / 0.011 / Y
26-36 / Water level-Zup / -0.652 / 0.002 / Y
Inflow-I / 0.027 / 0.671 / N
Water release-Q / 0.682 / 0.001 / Y

Table S2. Regression coefficientssignificance tests of statistical models

River / Water-quality index / Sample size / Period / P (x0, x1, x2, x3) / Feasibility?
XXR / TN / 38 / 1-9 / 0.002, 0.001, 0.002, 0.629 / Y, Y, Y, N
10-16 / 0.004, 0.002, 0.002, 0.519 / Y, Y, Y, N
17-24 / 0.001, 0.398, 0.003, 0.413 / Y, N, Y, N
25-36 / 0.003, 0.002, 0.283, 0.003 / Y, Y, N, Y
TP / 41 / 1-9 / 0.004, 0.003, 0.193, 0.206 / Y, Y, N, N
10-16 / 0.001, 0.002, 0.381, 0.417 / Y, Y, N, N
17-24 / 0.003, 0.517, 0.003, 0.001 / Y, N, Y, Y
25-36 / 0.002, 0.001, 0.003, 0.002 / Y, Y, Y, Y
DNR / TN / 27 / 1-15 / 0.003, 0.002, 0.003, 0.472 / Y, Y, Y, N
16-25 / 0.005, 0.003, 0.002, 0.339 / Y, Y, Y, N
26-36 / 0.004, 0.001, 0.006, 0.501 / Y, Y, Y, N
TP / 32 / 1-15 / 0.002, 0.005, 0.001, 0.548 / Y, Y, Y, N
16-18 / 0.004, 0.001, 0.005, 0.617 / Y, Y, Y, N
19-25 / 0.001, 0.008, 0.003, 0.712 / Y, Y, Y, N
26-30 / 0.002, 0.005, 0.001, 0.569 / Y, Y, Y, N
31-36 / 0.003, 0.001, 0.005, 0.441 / Y, Y, Y, N
XJR / TN / 32 / 1-15 / 0.002, 0.004, 0.001, 0.511 / Y, Y, Y, N
16-18 / 0.001, 0.004, 0.005, 0.635 / Y, Y, Y, N
19-25 / 0.005, 0.003, 0.002, 0.716 / Y, Y, Y, N
26-30 / 0.001, 0.002, 0.005, 0.528 / Y, Y, Y, N
31-36 / 0.002, 0.001, 0.004, 0.618 / Y, Y, Y, N
TP / 41 / 1-15 / 0.003, 0.002, 0.005, 0.735 / Y, Y, Y, N
16-18 / 0.005, 0.007, 0.004, 0.491 / Y, Y, Y, N
19-25 / 0.006, 0.004, 0.001, 0.592 / Y, Y, Y, N
26-30 / 0.002, 0.003, 0.001, 0.514 / Y, Y, Y, N
31-36 / 0.001, 0.004, 0.003, 0.816 / Y, Y, Y, N

x0 is the constant term.

Table S3. Multicollinearity analysis of explanatory variables

River / Water-quality index / Sample size / Period / /
XXR / TN / 38 / 1-9 / 0.142, 0.115, 0.891 / 1.2, 1.1, 9.2
10-16 / 0.212, 0.312, 0.912 / 1.3, 1.5,11.4
17-24 / 0.904, 0.291, 0.911 / 10.4, 1.4, 11.2
25-36 / 0.331, 0.884, 0.279 / 1.5, 8.6, 1.4
TP / 41 / 1-9 / 0.189, 0.921, 0.909 / 1.2, 12.7, 11.0
10-16 / 0.412, 0.917, 0.941 / 1.7, 12.0, 16.9
17-24 / 0.933, 0.442, 0.511 / 14.9, 1.8, 2.0
25-36 / 0.479, 0.399, 0.614 / 1.9, 1.7, 2.6
DNR / TN / 27 / 1-15 / 0.581, 0.481, 0.939 / 2.4, 1.9, 16.4
16-25 / 0.533, 0.612, 0.924 / 2.1, 2.6, 13.2
26-36 / 0.601, 0.511, 0.941 / 2.5, 2.0, 16.9
TP / 32 / 1-15 / 0.421, 0.483, 0.908 / 1.7, 1.9, 10.9
16-18 / 0.501, 0.602, 0.893 / 2.0, 2.5, 9.3
19-25 / 0.396, 0.448, 0.927 / 1.7, 1.8, 13.7
26-30 / 0.551, 0.611, 0.921 / 2.2, 2.6, 12.7
31-36 / 0.499, 0.553, 0.897 / 2.0, 2.2, 9.7
XJR / TN / 32 / 1-15 / 0.612, 0.461, 0.883 / 2.6, 1.9, 8.5
16-18 / 0.391, 0.332, 0.908 / 1.6, 1.5, 10.9
19-25 / 0.402, 0.551, 0.914 / 1.7, 2.2, 11.6
26-30 / 0.386, 0.449, 0.931 / 1.6, 1.8, 14.5
31-36 / 0.271, 0.331, 0.895 / 1.4, 1.5, 9.5
TP / 41 / 1-15 / 0.522, 0.443, 0.941 / 2.1, 1.8, 16.9
16-18 / 0.601, 0.599, 0.938 / 2.5, 2.5, 16.1
19-25 / 0.377, 0.422, 0.935 / 1.6, 1.7, 15.4
26-30 / 0.427, 0.481, 0.942 / 1.7, 1.9, 17.2
31-36 / 0.604, 0.571, 0.879 / 2.5, 2.3, 8.3

FigureS1. The boxplot of water quality data for TN (a) and TP (b)