# CaMEL and ADCIRC Storm Surge Models—A Comparative Study

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## Abstract

**:**

## 1. Introduction

^{SWE}or CaMEL from here after) is a recently developed storm surge model [8,16] that uses an implicit solver, primarily developed with the capability to use larger time step sizes with great numerical stability. CaMEL uses a hybrid finite element (FE) and finite volume (FV) technique to implicitly solve the conservation equations. CaMEL is parallelized in the present study with the objective of studying its storm surge simulation feasibility and capability in comparison to ADCIRC.

## 2. Governing Equations

## 3. CaMEL Model Approach

#### 3.1. Predictor

#### 3.2. Corrector

#### 3.3. CaMEL Finite Volume Method for Momentum Equation

**u**and h (i.e., those without superscripts or tilde) are used in the above equation for the purpose of better convergence. Following standard finite volume discretization, Equation (11) can be integrated over the i

^{th}element volume and use the divergence theorem to obtain

#### 3.4. CaMEL Finite Element Formulation

#### 3.5. CaMEL Solution Strategy

^{−8}. There is no convergence criterion set for nonlinear Newton Raphson (NR) iteration loop, which includes Steps 1 through 5, but the total iteration number is set to 5. By end of the NR iterations, the residuals for both water elevation and velocity solutions typically went down to 1.0 × 10

^{−10}or less.

## 4. ADCIRC Model Approach

## 5. CaMEL Parallel Implementation

## 6. Benchmarking of Parallel CaMEL Model

## 7. Model Comparison Using Katrina Storm Surge Hindcast

#### 7.1. Solver Effects

#### 7.2. Time Step Effects

#### 7.3. Buoy Time Series and High Water Mark Comparison

^{2}value of 0.716. Note that Ike had a storm surge with a maximum value of over 5 m. For Hurricane Katrina, the maximum surge was well above 8 m. Therefore, when put into perspective, a R

^{2}value of 0.71 for Katrina can be considered very good.

## 8. Model Execution Time and Parallel Scalability

## 9. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Problem Description (to be used for CaMEL only; consult ADCIRC Theory Guide [7] for ADCIRC description).

**Figure 2.**Comparison of the serial and parallel CaMEL models for a quarter annulus problem (

**a**) at 20.37 min of simulation time; and (

**b**) maximum elevation and velocity.

**Figure 3.**Computational domain and bathymetry at the region of interest with NOAA tide and current stations during Hurricane Katrina (2005).

**Figure 4.**Comparison of maximum elevation (hmax) and maximum velocity (vmax) using ADCIRC Lumped Explicit (Case 2), ADCIRC Semi Implicit (Case 4), and CaMEL Fully Implicit (Case 10) models in hindcast of Hurricane Katrina; (

**a**) maximum elevation Case 2 vs. Case 4; (

**b**) maximum velocity Case 2 vs. Case 4; (

**c**) maximum elevation Case 10 vs. Case 4; and (

**d**) maximum velocity Case 10 vs. Case 4.

**Figure 5.**A time-snap and maximum water elevation and velocity magnitude differences of Hurricane Katrina storm surge hindcast using ADCIRC and CaMEL models, (

**a**) Case 4 vs. Case 2 at 10 a.m. on 29 August 2005 UTC; (

**b**) Case 4 vs. Case 2 for maximum elevation and velocity; (

**c**) Case 4 vs. Case 10 at 10 a.m. on 29 August 2005 UTC; (

**d**) Case 4 and Case 10 for maximum elevation and velocity; (

**e**) Case 7 vs. Case 10 at 10 a.m. on 29 August 2005 UTC; and (

**f**) Case 7 and Case 10 for maximum elevation and velocity.

**Figure 6.**Time series of average, standard deviation, maximum and minimum of water elevation and velocity components differences between ADCIRC Lumped Explicit Case 2 and ADCIRC Semi Implicit Case 4 results, (

**a**) difference of elevation; (

**b**) maximum and minimum elevation; (

**c**) difference of velocity; (

**d**) maximum and minimum velocity.

**Figure 7.**Time series of average, standard deviation, maximum and minimum of water elevation and velocity components differences between ADCIRC Semi Implicit Case 4 and CaMEL Fully Implicit Case 10 results, (

**a**) difference of elevation; (

**b**) maximum and minimum elevation; (

**c**) difference of velocity; (

**d**) maximum and minimum velocity.

**Figure 8.**Time series of average, standard deviation, maximum and minimum of water elevation and velocity components differences between CaMEL Semi Implicit Case 7 and CaMEL Fully Implicit Case 10 results, (

**a**) difference of elevation; (

**b**) maximum and minimum elevation; (

**c**) difference of velocity; (

**d**) maximum and minimum velocity.

**Figure 9.**Comparison of maximum elevation and velocity using ADCIRC Semi Implicit (Cases 3 and 5) and CaMEL Fully Implicit (Cases 9 and 11) models in hindcast of Hurricane Katrina storm surge using smallest (Case 3 or 9) and largest (Case 5 or 11) time step sizes; (

**a**) maximum elevation Case 3 vs. Case 5; (

**b**) maximum velocity Case 3 vs. Case 5; (

**c**) maximum elevation Case 9 vs. Case 11; and (

**d**) maximum velocity Case 9 vs. Case 11.

**Figure 10.**A time-snap and maximum water elevation and velocity magnitude differences of Katrina storm surge hindcast using ADCIRC Semi Implicit and CaMEL Fully Implicit models, (

**a**) Case 3 vs. Case 2 at 10 a.m. on 29 August 2005 UTC; (

**b**) Case 3 vs. Case 5 maxele/maxvel; (

**c**) Case 9 vs. Case 11 at 10 a.m. on 29 August 2005 UTC; and (

**d**) Case 9 and Case 11 maxele/maxvel.

**Figure 11.**Time series of average, standard deviation, maximum and minimum of water elevation and velocity components differences between CaMEL Fully Implicit Case 9 and Case 11 results, (

**a**) difference of elevation; (

**b**) maximum and minimum elevation; (

**c**) difference of velocity; (

**d**) maximum and minimum velocity.

**Figure 12.**Katrina storm surge simulated water elevation time series compared with observed data at four NOAA buoy stations, (

**a**) Station ID 8735180 Dauphin Island AL; (

**b**) Station ID 8735180 Pilots Station East SW Pass LA; (

**c**) Station ID 8747766 Waveland MS (Note that the buoy broke and failed to record data after 9 a.m. on 29 August 2005); and (

**d**) Station ID 8761724 Grand Isle.

**Figure 13.**Comparison of modeled Katrina storm surge maximum water elevation against the 59 wet HWMs. (

**a**) Measured vs. Case 11 (CaMEL Fully Implicit); (

**b**) Case 3 (ADCIRC Semi Implicit) vs. Case 11 (CaMEL Fully Implicit). (OP: Over Predicted; UP: Under Predicted)

**Figure 14.**Parallel comparison between CaMEL and ADCIRC models for Hurricane Katrina storm surge hindcast, (

**a**) Scaling using the same time step for all models (see Table 3); (

**b**) Scaling using different model setups (see Table 4); (

**c**) Wall time using the same time step for all models (see Table 3); (

**d**) Wall time using different model setups (see Table 4). Parity line represents the perfect scaling theoretically possible.

Case # | Time Step (s) | Wall Time (s) | Solver | Comments |
---|---|---|---|---|

1 | 2.0 | 773 | ADCIRC Lumped Exp | Ran Successful |

2 | 4.0 | 672 | ADCIRC Lumped Exp | Ran Successful |

3 | 2.0 | 1150 | ADCIRC Semi-Imp | Ran Successful |

4 | 4.0 | 738 | ADCIRC Semi-Imp | Ran Successful |

5 | 8.0 | 547 | ADCIRC Semi-Imp | Ran Successful |

6 | 2.0 | 30,881 | CaMEL Semi-Imp | Ran Successful |

7 | 4.0 | 10,846 | CaMEL Semi-Imp | Ran Successful |

8 | 40.0 | 2125 | CaMEL Semi-Imp | Ran Successful |

9 | 2.0 | 33,852 | CaMEL Fully-Imp | Ran Successful |

10 | 4.0 | 10,283 | CaMEL Fully-Imp | Ran Successful |

11 | 100.0 | 1655 | CaMEL Fully-Imp | Ran Successful |

12 | 8.0 | N/A | ADCIRC Lumped Exp | Did not Run |

13 | 16.0 | N/A | ADCIRC Semi-Imp | Did not Run |

14 | 80.0 | N/A | CaMEL Semi-Imp | Did not Run |

15 | 120.0 | N/A | CaMEL Fully-Imp | Did not Run |

**Table 2.**ADCIRC and CaMEL Model High Water Mark Statistics (for only the 59 locations wet stations; Y-axis intercept forced to zero).

Case # | R^{2} | Slope |
---|---|---|

1 (ADCIRC Lumped Exp) | 0.6706 | 0.8802 |

3 (ADCIRC Semi-Imp) | 0.6686 | 0.8808 |

6 (CaMEL Semi-Imp) | 0.6624 | 0.8844 |

8 (CaMEL Semi-Imp) | 0.6623 | 0.8843 |

9 (CaMEL Fully-Imp) | 0.6635 | 0.8838 |

11 (CaMEL Fully-Imp) | 0.6638 | 0.8844 |

Computing Units | CaMEL Fully Implicit | ADCIRC Semi Implicit | ADCIRC Lumped Explicit | |||
---|---|---|---|---|---|---|

Procs. (x) | Scaling (y) | Wall Time (s) | Scaling (y) | Wall Time (s) | Scaling (y) | Wall Time (s) |

1 | 1.00 | 247,747 | 1.00 | 35,176 | 1.00 | 25,188 |

2 | 2.03 | 122,157 | 1.71 | 20,559 | 1.19 | 21,195 |

4 | 3.83 | 64,604 | 2.51 | 14,009 | 4.62 | 5451 |

8 | 7.25 | 34,162 | 8.60 | 4,090 | 7.95 | 3168 |

16 | 14.06 | 17,622 | 15.14 | 2324 | 16.86 | 1494 |

32 | 33.45 | 7407 | 32.27 | 1090 | 32.93 | 765 |

64 | 43.47 | 5699 | 60.86 | 578 | 53.25 | 473 |

128 | 68.12 | 3637 | 92.81 | 379 | 121.10 | 208 |

256 | 83.11 | 2981 | 147.80 | 238 | 206.46 | 122 |

**Table 4.**Model execution times and scaling factors for the same hindcast simulation using different model setups (i.e., time steps are different according to the cases defined in Table 1).

Computing Units | ADCIRC Lumped Explicit (Case 2) | ADCIRC Semi Implicit (Case 5) | CaMEL Semi Implicit (Case 8) | CaMEL Fully Implicit (Case 11) | ||||
---|---|---|---|---|---|---|---|---|

Procs. (x) | Scaling (y) | Wall Time (s) | Scaling (y) | Wall Time (s) | Scaling (y) | Wall Time (s) | Scaling (y) | Wall Time (s) |

1 | 1.00 | 23,817 | 1.00 | 24,282 | 1.00 | 112,418 | 1.00 | 70,894 |

0.91 | 26,101 | 1.11 | 21,917 | 0.97 | 116,225 | 1.86 | 38,159 | |

4 | 1.43 | 16,704 | 1.49 | 16,331 | 1.89 | 59,423 | 3.51 | 20,203 |

8 | 5.71 | 4168 | 4.02 | 6035 | 3.93 | 28,616 | 6.43 | 11,019 |

16 | 11.87 | 2007 | 7.11 | 3415 | 6.15 | 18,282 | 12.38 | 5728 |

32 | 24.38 | 977 | 19.30 | 1258 | 21.34 | 5267 | 23.05 | 3076 |

64 | 49.01 | 486 | 63.57 | 382 | 32.95 | 3412 | 33.19 | 2136 |

128 | 77.83 | 306 | 94.12 | 258 | 50.84 | 2211 | 42.76 | 1658 |

256 | 105.38 | 226 | 121.41 | 200 | 57.18 | 1966 | 58.83 | 1205 |

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**MDPI and ACS Style**

Akbar, M.K.; Luettich, R.A.; Fleming, J.G.; Aliabadi, S.K.
CaMEL and ADCIRC Storm Surge Models—A Comparative Study. *J. Mar. Sci. Eng.* **2017**, *5*, 35.
https://doi.org/10.3390/jmse5030035

**AMA Style**

Akbar MK, Luettich RA, Fleming JG, Aliabadi SK.
CaMEL and ADCIRC Storm Surge Models—A Comparative Study. *Journal of Marine Science and Engineering*. 2017; 5(3):35.
https://doi.org/10.3390/jmse5030035

**Chicago/Turabian Style**

Akbar, Muhammad K., Richard A. Luettich, Jason G. Fleming, and Shahrouz K. Aliabadi.
2017. "CaMEL and ADCIRC Storm Surge Models—A Comparative Study" *Journal of Marine Science and Engineering* 5, no. 3: 35.
https://doi.org/10.3390/jmse5030035