Inductive reasoning and prediction of population dynamics of Cylindrospermopsis in the Wivenhoe Reservoir by means of evolutionary computation

Inductive reasoning and prediction of population dynamics of Cylindrospermopsis in the Wivenhoe Reservoir by means of evolutionary computation Friedrich Recknagel 1, Philip Orr 2 and Hongqing Cao 1 1 School of Earth and Environmental Sciences, University of Adelaide 2 South East Queensland Water, Brisbane

Background The presentation is based on outcomes of the ARC Linkage Project LP99453 Early warning of cyanobacteria blooms in drinking water reservoirs by means of evolutionary algorithms in collaboration with South East Queensland Water and the SA Water Corporation The research is focusing on predictive modelling of population dynamics of Anabaena, Microcystis and Cylindrospermopsis in the Myponga Reservoir, South Australia and the Wivenhoe Reservoir, Queensland We show only results for Cylindrospermopsis raciporskii in the Wivenhoe Reservoir.

Key hypotheses of the project are: - early warning of cyanobacteria blooms requires operational models driven by in situ data from online monitoring - operational in situ models can be developed by nonlinear inductive evolutionary computation - nonlinear inductive models reveal predictor variables as well as relationships and thresholds triggering cyanobacteria blooms

Inductive versus deductive modelling REALISM Explanatory Models Linear Induc.ve Deduc.ve Predictive Models Nonlinear Induc.ve Analy.cal Models Generic Models Levin, R., 1966. The strategy for model building in population biology. American Sc. 54, 421-431.

Nonlinear inductive modeling by evolutionary computation

Nonlinear inductive modeling by evolutionary computation

Wivenhoe Reservoir, Queensland 146 1825 219 2555 292 3285 365 415 438 2 1 1 365 73 195 146 1825 219 2555 292 3285 365 415 438 15 1 1 5 1 365 73 195 146 1825 219 2555 292 3285 365 415 438.15.1.5.5 365 73 195 146 1825 219 2555 292 3285 365 415 438 25 12 1 15 8 1 6 4 5 14 2 2 365 1999 73 195 21 146 1825 23 219 2555 25 292 3285 27 365 29 415 438 DO mg/l 195 Silica mg/l 73 TP mg/l WT C Turb NTU 365 2 2 TN mg/l ph 5 EC µs/cm 5 3 Chl_a μg/l max vol: 1165 Gl, max depth: 79 m; thermally stratified Dam Wall Station: historical Data 1/1999 12/21 1

365 73 195 146 1825 219 2555 292 3285 365 415 438 365 73 195 146 1825 219 2555 292 3285 365 415 438 365 73 195 146 1825 219 2555 292 3285 365 415 438 365 73 195 146 1825 219 2555 292 3285 365 415 438 (including Chl_a) 7- DAYS- AHEAD (excluding Chl_a) 7- DAYS- AHEAD Historical Data All Inputs (1/99 12/21) 2 15 1 5 Measured Predicted r 2 =.58 18 16 14 12 1 8 6 4 Measured Predicted r 2 =.57 2 Historical Data Electron. Meas. Inputs(1/99 12/21) 18 16 14 12 1 8 6 4 2 Measured Predicted r 2 =.57 18 16 14 12 1 8 6 4 2 Measured Predicted r 2 =.57

Historical Data All Inputs (1/99 12/21) (including Chl_a) IF WT>26.3 THEN Cylindrospermopsis=exp(pH+pH*81.1/(Cond+pH)) ELSE Cylindrospermopsis=(Cond+5.6)*(Chla- TP) r 2 value=.58 (excluding Chl_a) IF Turb<=57.4 AND Turb>=23.44 THEN Cylindrospermopsis=exp(WT/2.979)+WT ELSE Cylindrospermopsis=exp(WT/(11.4- ph))*(exp(turb/49.5)- TN*silica+silica) r 2 value=.57 Historical Data Elec. Meas. Inputs (1/99 12/21) IF WT<=25.5 THEN Cylindrospermopsis=(Cond*Turb/192.2- Turb)*Chla*82.5 ELSE Cylindrospermopsis=exp(pH)*exp(pH)/(Cond*Cond)*147.9 r 2 value=.57 IF WT>25.6 AND WT<32.7 THEN Cylindrospermopsis=exp(pH)*pH/(Cond- 198.8)*1.2 ELSE Cylindrospermopsis=(ln( DO )*Turb/WT+.3)*exp(pH) r 2 value=.57

365 73 195 146 1825 219 2555 292 3285 365 415 438 365 73 195 146 1825 219 2555 292 3285 365 415 438 365 73 195 146 1825 219 2555 292 3285 365 415 438 365 73 195 146 1825 219 2555 292 3285 365 415 438 Historical Data All Inputs (1/99 12/21) 8 7 6 5 4 3 2 1 (including Chl_a) THRESHOLDS WT>26.3 WT<=26.3 14 12 1 8 6 4 2 (excluding Chl_a) THRESHOLDS 23.3<=TURB<=57.4 23.3>TURB>57.4 Historical Data Elec. Meas. Inputs (1/99 12/21) 1 8 6 4 2 WT<=25.5 WT>25.5 1 8 6 4 2 25.6<WT<32.7 25.6<=WT>32.7

Historical Data All Inputs (1/99 12/21) Historical Data Elec. Meas. Inputs (1/99 12/21) 1 8 6 4 2 25 2 15 1 5 (including Chl_a) THEN- Branch ELSE- Branch Cond:22.7~477.3 ph:7.7~9 6 5 4 3 2 1 Cond:23.6~54.4 Chla:.4~15.3 TP:~.5 5 1 5 1 Cond:195.2~51.1 & 6 Cond:244.9~486.5 Chla:.1~15.6 ph:7.8~8.8 5 Turb:~38.7 4 5 1 3 2 1 5 1 14 12 1 8 6 4 2 8 7 6 5 4 3 2 1 (excluding Chl_a) THEN- Branch ELSE- Branch WT:14.2~27.9 25 2 15 1 5 5 1 16 Cond:245.1~486.3 14 ph:7.8~8.8 12 5 1 1 8 6 4 2 ph:7.4~8.7 Turb:~39.4 WT:16.6~3.2 silica:~8.5 TN:.3~.7 5 1 DO:5.3~11.8 ph:7.3~8.9 Turb:~38.8 WT:15.2~27 5 1

4 ph 36 72 2 18 DO mg/l 2 1 1 36 72 5 18 4 4 3 3 2 2 1 1 36 72 18 7 6 5 4 3 2 1 36 27 72 28 18 29 21 Chl_a μg/l WT C 5 2 5 Turb NTU 1 6 3 max vol: 1165 Gl, max depth: 79 m; thermally stratified Dam Wall Station: Online Data 9/27 12/21 EC µs/cm Wivenhoe Reservoir, Queensland

365 73 195 146 1825 219 2555 292 3285 365 415 438 365 73 195 146 1825 219 2555 292 3285 365 415 438 36 72 18 365 73 195 146 1825 219 2555 292 3285 365 415 438 365 73 195 146 1825 219 2555 292 3285 365 415 438 36 72 18 (including Chl_a) 7- DAYS- AHEAD (excluding Chl_a) 7- DAYS- AHEAD Historical Data All Inputs (1/99 12/21) 2 15 1 5 Measured Predicted r 2 =.58 18 16 14 12 1 8 6 4 Measured Predicted r 2 =.57 2 Historical Data Electron. Meas. Inputs(1/99 12/21) 18 16 14 12 1 8 6 4 2 Measured Predicted r 2 =.57 18 16 14 12 1 8 6 4 2 Measured Predicted r 2 =.57 Online Data (9/27 to 12/21) 8 7 6 5 4 3 2 1 Measured Predicted r 2 =.65 8 7 6 5 4 3 2 1 Measured Predicted r 2 =.68

Historical Data All Inputs (1/99 12/21) (including Chl_a) IF WT>26.3 THEN Cylindrospermopsis=exp(pH+pH*81.1/(Cond+pH)) ELSE Cylindrospermopsis=(Cond+5.6)*(Chla- TP) r 2 value=.58 (excluding Chl_a) IF Turb<=57.4 AND Turb>=23.44 THEN Cylindrospermopsis=exp(WT/2.979)+WT ELSE Cylindrospermopsis=exp(WT/(11.4- ph))*(exp(turb/49.5)- TN*silica+silica) r 2 value=.57 Historical Data Elec. Meas. Inputs (1/99 12/21) IF WT<=25.5 THEN Cylindrospermopsis=(Cond*Turb/192.2- Turb)*Chla*82.5 ELSE Cylindrospermopsis=exp(pH)*exp(pH)/(Cond*Cond)*147.9 r 2 value=.57 IF WT>25.6 AND WT<32.7 THEN Cylindrospermopsis=exp(pH)*pH/(Cond- 198.8)*1.2 ELSE Cylindrospermopsis=(ln( DO )*Turb/WT+.3)*exp(pH) r 2 value=.57 Online Data (9/27 to 12/21) IF WT_online<25.7 THEN Cylindrospermopsis=(WT_online- 25.2)* (ph_online+chla_online)*98.5+3868.6 ELSE Cylindrospermopsis=(exp(pH_online)+562.1)* ln( (Chla_online- 14) )- (Conduc.vity_online- ph_online* 44.5-68.3)*115.3 r 2 value=.65 IF Conduc.vity_online<=296.5 THEN Cylindrospermopsis=(((Conduc.vity_online+ Turbidity_online)+Turbidity_online)*(WT_online- 16.1)) ELSE Cylindrospermopsis=((((WT_online+(- 1.9))*82.5)- (Conduc.vity_online+(Conduc.vity_online+135.1)))*(WT_online+ (exp(ph_online)/(conduc.vity_online+ph_online)))) r 2 =.68

365 73 195 146 1825 219 2555 292 3285 365 415 438 365 73 195 146 1825 219 2555 292 3285 365 415 438 36 72 18 365 73 195 146 1825 219 2555 292 3285 365 415 438 365 73 195 146 1825 219 2555 292 3285 365 415 438 36 72 18 (including Chl_a) THRESHOLDS (excluding Chl_a) THRESHOLDS Historical Data All Inputs (1/99 12/21) 8 7 6 5 4 3 2 1 WT>26.3 WT<=26.3 14 12 1 8 6 4 2 23.3<=TURB<=57.4 23.3>TURB>57.4 Historical Data Elec. Meas. Inputs (1/99 12/21) 1 8 6 4 2 WT<=25.5 WT>25.5 1 8 6 4 2 25.6<WT<32.7 25.6<=WT>32.7 Online Data (9/27 to 12/21) 6 5 4 3 2 1 WT<25.7 WT>=25.7 5 4 3 2 1 EC > 296.5 EC <= 296.5

Historical Data All Inputs (1/99 12/21) Historical Data Elec. Meas. Inputs (1/99 12/21) Online Data (9/27 to 12/21) 1 8 6 4 2 25 2 15 1 5 7 6 5 4 3 2 1 (including Chl_a) THEN- Branch ELSE- Branch Cond:22.7~477.3 ph:7.7~9 6 5 4 3 2 1 3 2 1 Cond:23.6~54.4 Chla:.4~15.3 TP:~.5 5 1 5 1 Cond:195.2~51.1 & 6 Cond:244.9~486.5 Chla:.1~15.6 ph:7.8~8.8 5 Turb:~38.7 4 5 1 WT_online:15.1~27.1 5 ph_online:7~9 Chla_online:.8~11.7 4 5 1 3 2 1 5 1 Conduc.vity_online: 241~498 ph_online:7.7~9.4 Chla_online:~17.5 5 1 14 12 1 8 6 4 2 8 7 6 5 4 3 2 1 4 3 2 1 (excluding Chl_a) THEN- Branch ELSE- Branch WT:14.2~27.9 25 2 15 1 5 5 1 16 Cond:245.1~486.3 14 ph:7.8~8.8 12 5 1 WT_online:15.1~26.4 Conduc.vity_online: 24~311 Turbidity_online:~7.4 5 1 1 8 6 4 2 4 3 2 1 ph:7.4~8.7 Turb:~39.4 WT:16.6~3.2 silica:~8.5 TN:.3~.7 5 1 DO:5.3~11.8 ph:7.3~8.9 Turb:~38.8 WT:15.2~27 5 1 WT_online:16.1~3.7 Conduc.vity_online: 269.8~54.6 ph_online:7.3~9.1 5 1

Towards in situ operational models for early warning of cyanobacteria blooms Early Warning Horizon Operational Control Horizon Strategic Control Horizon Sampling Time days weeks seasons/years t t + T s Nonlinear Inductive Models Deductive Models

Towards in situ operational models for early warning of cyanobacteria blooms Data Archiving in the Ecological Data Warehouse On-line Data Historical Data Water Temperature C Diss. Oxygen mg/l Real-time in situ Water Quality Measurements by Hydrolab DataSonde 5X Turbidity NTU ph Ammonium NH 4 mg/l Conductivity ms/cm Total Chlorophyll µg/l Data Acquisition by Hydrolab Process Monitor On-line Data Data Merger and Validation Phycocyanoin µg/l Early Warning for Operational Raw Water Control if Algal Bloom is Imminent Chlorophyll-a µg/l Anabaena circinalis cells/ml Microcystis cells/ml Data Preprocessing Module Real-Time Forecasting Forecasting Module Model Model Design Time Series

Towards operational models for early warning of cyanobacteria blooms http://lakedataweb.services.adelaide.edu.au/ldw.aspx

What s next? Spatially-explicit forecasting of cyanobacteria assemblages in drinking water reservoirs by multi-objective evolutionary computation Turb NTU Wivenhoe Reservoir: 6 monitoring stations

What s next? Spatially-explicit forecasting of cyanobacteria assemblages in drinking water reservoirs by multi-objective evolutionary computation

Conclusions: -Nonlinear inductive models by evolutionary computation inform about ecological relationships and thresholds determining cyanobacteria population dynamics - Nonlinear inductive models by evolutionary computation provide short-term forecasting of cyanobacteria population dynamics - Nonlinear inductive models by evolutionary computation suit as in situ operational models for early warning of outbreaks of cyanobacteria blooms -Multi-objective evolutionary computation allows to develop models for spatially-explicit forecasting of cyanobacteria assemblages across sampling stations in lakes

Acknowledgements: We thank the ARC, SEQWater and SA Water for providing funding, and thank SEQWater and SA Water for their constructive support.

Early Warning of Cyanobacteria Blooms NORMAL WARNING ALARM

Early Warning of Cyanobacteria Blooms NORMAL WARNING ALARM

Early Warning of Cyanobacteria Blooms NORMAL WARNING ALARM

Inductive versus deductive modelling Ecological, Economic and Social Sciences Medicine Engineering Physics Nonlinear Inductive Models Deductive Models Electrical Circuits Inductive Models Karplus, W.J., 1983. The spectrum of mathematical models. Perspectives in Computing 3, 2, 4-13.