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Modelling the Effect of Weather Conditions on Cyanobacterial Bloom Outbreaks in Lake Dianchi: a Rough Decision-Adjusted Logistic Regression Model

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Abstract

Lake Dianchi, one of the main water sources for Kunming, China, experiences severe cyanobacterial blooms due to rapid urbanization and local industrial development. Scientific interest in the mechanisms that cause blooms has been increasing. An integrated model combining rough set theory with binary logistic regression was used to examine the correlation between weather conditions and cyanobacterial blooms in Lake Dianchi based on daily monitoring data. The binary logistic regression yielded quantitative correlations between cyanobacterial blooms and the assessed meteorological variables, including temperature, wind velocity, and wind direction. The rough decision process connected the weather conditions and cyanobacterial blooms, which were used to verify the binary regression model results. It was shown that by comparing the methods, the rough decision-adjusted binary logistic regression model significantly improved model accuracy. The integrated model of cyanobacterial blooms in Lake Dianchi may inform decision-makers at local water purification plants of the water quality in the lake and assist them in making more cost-effective decisions.

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Acknowledgments

This research was conducted with the support of the “China National Water Pollution Control Program” (2008ZX07102-001) and the National Natural Science Foundation of China (grant no. 41101567 and no. 40701066).

Author information

Authors and Affiliations

  1. College of Environmental Science and Engineering, Peking University, Beijing, China, 100871

    Yong Liu, Huaicheng Guo & Hu Sheng

  2. School of Resource and Environmental Science, Hubei Biomass-Resource Chemistry and Environmental Biotechnology Key Laboratory, Wuhan University, Wuhan, China, 430072

    Zhen Wang

  3. College of Resource and Environment, Huazhong Agricultural University, Wuhan, China, 430070

    Shuxia Yu

Authors
  1. Yong Liu
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  2. Zhen Wang
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  3. Huaicheng Guo
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Corresponding author

Correspondence to Zhen Wang.

Appendix

Appendix

1.1 Twenty-five Rules Used in RDALR Model

  1. 1.
    $$ {\text{A}}{{\text{T}}_{{3}}} \wedge {\text{H}}{{\text{T}}_{{2}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{2}}} \wedge {\text{W}}{{\text{D}}_{{2}}} \wedge {\text{S}}{{\text{D}}_4} \to {y_0} $$
  2. 2.
    $$ {\text{A}}{{\text{T}}_{{4}}} \wedge {\text{H}}{{\text{T}}_{{2}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{3}}} \wedge {\text{W}}{{\text{D}}_{{2}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_0} $$
  3. 3.
    $$ {\text{A}}{{\text{T}}_{{3}}} \wedge {\text{H}}{{\text{T}}_{{1}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{3}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{5}}} \to {y_0} $$
  4. 4.
    $$ {\text{A}}{{\text{T}}_{{3}}} \wedge {\text{H}}{{\text{T}}_{{1}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{2}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_0} $$
  5. 5.
    $$ {\text{A}}{{\text{T}}_{{4}}} \wedge {\text{H}}{{\text{T}}_{{3}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{3}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{5}}} \to {y_0} $$
  6. 6.
    $$ {\text{A}}{{\text{T}}_{{2}}} \wedge {\text{H}}{{\text{T}}_{{3}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{1}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{5}}} \to {y_0} $$
  7. 7.
    $$ {\text{A}}{{\text{T}}_{{4}}} \wedge {\text{H}}{{\text{T}}_{{3}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{2}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{5}}} \to {y_0} $$
  8. 8.
    $$ {\text{A}}{{\text{T}}_4} \wedge {\text{H}}{{\text{T}}_3} \wedge {\text{L}}{{\text{T}}_2} \wedge {\text{HV}}{{\text{V}}_1} \wedge {\text{W}}{{\text{D}}_2} \wedge {\text{S}}{{\text{D}}_4} \to {y_1} $$
  9. 9.
    $$ {\text{A}}{{\text{T}}_{{4}}} \wedge {\text{H}}{{\text{T}}_{{3}}} \wedge {\text{L}}{{\text{T}}_2} \wedge {\text{HV}}{{\text{V}}_{{1}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_1} $$
  10. 10.
    $$ {\text{A}}{{\text{T}}_{{2}}} \wedge {\text{H}}{{\text{T}}_{{1}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{1}}} \wedge {\text{W}}{{\text{D}}_1} \wedge {\text{S}}{{\text{D}}_3} \to {y_1} $$
  11. 11.
    $$ {\text{A}}{{\text{T}}_{{2}}} \wedge {\text{H}}{{\text{T}}_{{1}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{1}}} \wedge {\text{W}}{{\text{D}}_{{2}}} \wedge {\text{S}}{{\text{D}}_{{3}}} \to {y_1} $$
  12. 12.
    $$ {\text{A}}{{\text{T}}_{{1}}} \wedge {\text{H}}{{\text{T}}_{{1}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{2}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_0} $$
  13. 13.
    $$ {\text{A}}{{\text{T}}_{{3}}} \wedge {\text{H}}{{\text{T}}_{{1}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{3}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_0} $$
  14. 14.
    $$ {\text{A}}{{\text{T}}_{{4}}} \wedge {\text{H}}{{\text{T}}_{{2}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{2}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_0} $$
  15. 15.
    $$ {\text{A}}{{\text{T}}_{{3}}} \wedge {\text{H}}{{\text{T}}_{{2}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{1}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_0} $$
  16. 16.
    $$ {\text{A}}{{\text{T}}_{{4}}} \wedge {\text{H}}{{\text{T}}_{{1}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{2}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_0} $$
  17. 17.
    $$ {\text{A}}{{\text{T}}_{{4}}} \wedge {\text{H}}{{\text{T}}_{{3}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{1}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_1} $$
  18. 18.
    $$ {\text{A}}{{\text{T}}_4} \wedge {\text{H}}{{\text{T}}_{{3}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{1}}} \wedge {\text{W}}{{\text{D}}_{{2}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_1} $$
  19. 19.
    $$ {\text{A}}{{\text{T}}_{{3}}} \wedge {\text{H}}{{\text{T}}_{{1}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{1}}} \wedge {\text{W}}{{\text{D}}_{{1}}} \wedge {\text{S}}{{\text{D}}_{{3}}} \to {y_1} $$
  20. 20.
    $$ {\text{A}}{{\text{T}}_{{2}}} \wedge {\text{H}}{{\text{T}}_{{2}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{2}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_0} $$
  21. 21.
    $$ {\text{A}}{{\text{T}}_{{2}}} \wedge {\text{H}}{{\text{T}}_{{1}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{3}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{2}}} \to {y_0} $$
  22. 22.
    $$ {\text{A}}{{\text{T}}_{{3}}} \wedge {\text{H}}{{\text{T}}_{{2}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{3}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_0} $$
  23. 23.
    $$ {\text{A}}{{\text{T}}_{{4}}} \wedge {\text{H}}{{\text{T}}_{{1}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{3}}} \wedge {\text{W}}{{\text{D}}_{{3}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_0} $$
  24. 24.
    $$ {\text{A}}{{\text{T}}_{{2}}} \wedge {\text{H}}{{\text{T}}_{{1}}} \wedge {\text{L}}{{\text{T}}_{{1}}} \wedge {\text{HV}}{{\text{V}}_{{2}}} \wedge {\text{W}}{{\text{D}}_{{2}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_1} $$
  25. 25.
    $$ {\text{A}}{{\text{T}}_{{4}}} \wedge {\text{H}}{{\text{T}}_{{2}}} \wedge {\text{L}}{{\text{T}}_{{2}}} \wedge {\text{HV}}{{\text{V}}_{{2}}} \wedge {\text{W}}{{\text{D}}_{{2}}} \wedge {\text{S}}{{\text{D}}_{{4}}} \to {y_0} $$

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Liu, Y., Wang, Z., Guo, H. et al. Modelling the Effect of Weather Conditions on Cyanobacterial Bloom Outbreaks in Lake Dianchi: a Rough Decision-Adjusted Logistic Regression Model. Environ Model Assess 18, 199–207 (2013). https://doi.org/10.1007/s10666-012-9333-3

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