# Integration of GIS and a Lagrangian Particle-Tracking Model for Harmful Algal Bloom Trajectories Prediction

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model Descriptions

_{1,}U

_{2}and V

_{1,}V

_{2}are the pre-calculated velocities of winds or currents in x- and y-directions, respectively, at t

_{1}and t

_{2}computational time steps. The $\Delta {\mathrm{x}}_{\mathrm{i}}^{\prime}$ is the particle displacement due to turbulent motion which is simulated according to the based fBm Equation (4) and its derivative formulation [22,23,24,25], where ${\mathrm{B}}_{\mathrm{H}}$(t) is a continuous function with zero-mean increments and variances, which scale as ~t

^{2H}, and H(0 < H < 1) is called the Hurst parameter. $\mathsf{\Gamma}\left(\mathrm{H}+1/2\right)$ is a gamma function introduced to ensure that the fractional integral becomes an ordinary integral when H + 1/2 is an integer [21]:

## 3. GIS-Based Simulation Tool

#### 3.1. The Conceptual Framework of the Model and GIS Integration

#### 3.2. GIS Interface

#### 3.3. Pre-Processor Component

#### 3.4. fBm Based LPTM Engine Component

#### 3.5. Post-Processor Component

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The schematic diagram of the general architecture of the GIS-based simulation tool. U and V are the pre-calculated velocities of winds or currents in x- and y-directions.

**Figure 3.**The generated convex (blue line) and concave (red line) hulls of particle clouds (black points).

**Figure 4.**Comparison between the simulation results 53 hours after initial release and the observed data. The coefficient H is the Hurst value adopted in model runs. The yellow polygon is the initial red tide location (on 2 July 2013), while the orange polygon is the observed data obtained on 4 July 2013 The red tide was regarded as 2000 particles (red circle points), and the blue arrows and black arrows show the direction and magnitude of current vector fields and the wind vector fields, respectively.

Coefficients | Remark |
---|---|

H | The Hurst value generally is around 0.79$\pm $0.07 [23]. |

M | The limited memory M value is recommended at least 10 times of total simulation time steps or a larger one [25]. |

${\mathrm{C}}_{\mathrm{d}}$ | Wind drag coefficient, the optimal value is between 3–3.5% [19]. |

Number of particles | A set of released particles. |

Intervals | The expected time-step of a simulation. |

Date-time | The start date time and end date time of a simulation. |

Forced | Concave Hull Area (km^{2})H ^{1} = 0.76 | Concave Hull Area (km^{2})H = 0.5 | Observations (km^{2}) |
---|---|---|---|

Currents Currents and winds | 1150 1390 | 912 | 1230 1230 |

^{1}is the Hurst value.

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**MDPI and ACS Style**

Qin, R.; Lin, L.
Integration of GIS and a Lagrangian Particle-Tracking Model for Harmful Algal Bloom Trajectories Prediction. *Water* **2019**, *11*, 164.
https://doi.org/10.3390/w11010164

**AMA Style**

Qin R, Lin L.
Integration of GIS and a Lagrangian Particle-Tracking Model for Harmful Algal Bloom Trajectories Prediction. *Water*. 2019; 11(1):164.
https://doi.org/10.3390/w11010164

**Chicago/Turabian Style**

Qin, Rufu, and Liangzhao Lin.
2019. "Integration of GIS and a Lagrangian Particle-Tracking Model for Harmful Algal Bloom Trajectories Prediction" *Water* 11, no. 1: 164.
https://doi.org/10.3390/w11010164