# Assessment of Sea Level Rise at West Coast of Portugal Mainland and Its Projection for the 21st Century

## Abstract

**:**

## 1. Introduction

## 2. Data and Methods

#### 2.1. Sea Level Data

^{2}(±0.0095 mm/year

^{2}) for 1970 to 2008 (second derivative of MSL), given by linear regression estimation. A similar acceleration estimate was retrieved by [14] from the GMSL series using the same approach. The same procedure applied over the GMSL satellite-based series (in Figure 3) returns identical results, with an MSL acceleration of 0.18 mm/year

^{2}from 2006 onwards.

#### 2.2. Methods of MSL Projection

_{0}).

_{0}), initial velocity (or rate) and acceleration, must be determined using numerical estimation methods based on MSL data series. Therefore, the empirical models will only depend on the data used and on the method applied for the parameter’s estimation. Since these parameters are unknowns of an undetermined problem, due to data redundancy, any estimation returns a possible solution for the SLR projection models, depending on the method, type of data, time scale, and resolution. Hence, the final SLR projections are probabilistic rather than deterministic models based on physical basics.

#### 2.2.1. Method One

_{1}, Δt

_{2}), from two consecutive times series (e.g., Table 1), and applying an LR to both, two slope estimations are obtained, corresponding to the two consecutive rates of an accelerated SLR (r

_{1}, r

_{2}). Then, by applying a numerical derivative by finite differences to the estimated rates, the SLR acceleration is then obtained by Equation (3).

_{1}) used for the estimation of the acceleration (Equation (3)), which means that v

_{0}= r

_{1}.

_{1}, r

_{2}) are estimated by a Least Square Adjustment (LSA), it has its own standard deviation estimated by the respective stochastic model. Thereby, by applying the variance propagation law, the variance of the acceleration in Equation (3) is also estimated.

#### 2.2.2. Method Two

#### 2.2.3. Method Three

_{k}is computed continuously using a 10-year baseline through Equation (5).

## 3. Numerical Estimations

#### 3.1. Uplift Rate

#### 3.2. SLR Rates

#### 3.3. SLR Acceleration

^{2}to be compatible with WCPM relative SLR rates.

## 4. The Ensemble of Empirical SLR Projections for the 21st Century

#### 4.1. Relative SLR Models for the West Coast of Portugal Mainland (WCPM)

#### 4.2. Probabilistic Ensemble of Empirical SLR Projections and Respective PDF

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location of Cascais tide gauge (TG). The old analog TG is operating since 1882, and the new acoustic TG with the digital record and with an internet connection is working since November 2003.

**Figure 2.**Cascais TG secular series of monthly MSL, from 1882 to 2017, relative to the national vertical datum, and a moving average (MovAver) of the 10-year base period.

**Figure 3.**Satellite altimetry GMSL anomalies from three international data centers, NASA, CNES (global and North Atlantic region), and CSIRO, superimposed to the Cascais MSL trend adjusted to 2000 reference.

**Figure 4.**SLR rate of the 10-year moving average over the Cascais TG secular series (Figure 2).

**Figure 5.**Daily mean sea level series (in meters) at Cascais TG, from 2000 to 2016, relative to the national vertical datum (in red), corrected from inverse barometric effect, vertical displacement, and mean seasonal oscillation, with a 6-months base period moving average (in blue). Analog TG data from Jan/2000 to Nov/2003 and from new acoustic TG data from Nov/2003 to Dec/2016.

**Figure 6.**MSL of Cascais (in mm), modeled by a 20-years moving average of the secular series (Figure 2), adjusted to the GMSL from [9] by a rate of 0.43 mm/year (left graph) and fitted to the GMSL from [10] by a rate of 0.2 mm/year (right graph), both with rotation points at epoch 2000 and an adequate vertical shift to overlay the curves.

**Figure 7.**Relative SLR projection models for the WCPM (in meters), superimposed with observed MSL at Cascais TG.

**Figure 8.**Relative SLR projection of Mod.FC_2b (in meters) with probability limits of 95% confidence, superimposed with a PDF at epoch 2100 (fitted to the MSL y-axis) and observed MSL at Cascais TG, relative to the national vertical datum of Cascais 1938 (13 cm at epoch 2000).

**Figure 9.**Histogram of the relative frequency of the ensemble projections at epoch 2100 (left) and the standard adjusted PDF (right) with a standard deviation of 38 cm.

**Figure 10.**The ensemble of 147 relative SLR projections (in meters) for the 21st century of the WCPM, superimposed with PDF for 2100 (fitted to the MSL y-axis) and relative to the national vertical datum of Cascais 1938 (13 cm at epoch 2000).

**Figure 11.**Relative SLR projections (in meters) for the 21st century of the WCPM, corresponding to a discrete set of percentiles, from 1 to 99% (probability of not being exceeded). The PDF curve is fitted to the MSL y-axis.

**Figure 12.**Absolute SLR projections (in meters) for the 21st century of the WCPM, relative to 2000, and with the local vertical velocity removed, corresponding to a discrete set of percentiles, from 1 to 99%, or the probability of not be exceeded.

**Table 1.**SLR rates and respective standard deviation (SD) for different periods (in mm/year), 1992 to 2004 from secular monthly mean series, and 2000 to 2016 from decadal daily mean series.

Period | 1992–2004 | 2000–2016 | 2001–2016 | 2003–2016 | 2005–2016 |
---|---|---|---|---|---|

SLR rate | 2.2 | 3.0 | 3.2 | 3.4 | 4.1 |

Standard Deviation | 0.07 | 0.09 | 0.10 | 0.11 | 0.14 |

**Table 2.**Global SLR rates and respective standard deviation (SD) for two different periods (in mm/year), obtained with satellite altimetry MSL anomalies from three international data centers.

Series | 1993–2016 | SD | 2007–2016 | SD |
---|---|---|---|---|

NASA | 3.16 | 0.02 | 4.37 | 0.07 |

CNES | 3.27 | 0.01 | 4.17 | 0.06 |

CSIRO | 3.36 | 0.03 | 4.46 | 0.11 |

**Table 3.**List of SLR accelerations and respective standard deviation (SD) obtained with different methods, using the relative Cascais TG MSL and the satellite altimetry MSL anomalies of near the WCPM.

Series & Period | Method | Model | Acceleration (mm/year^{2}) | SD (mm/year^{2}) |
---|---|---|---|---|

Cascais MSL (2007–2016) | Linear Regression | Mod.FC_0 | 0 | - |

Cascais MSL (1980–2017) | 2nd order polynomial | Mod.FC_1 | 0.100 | 0.030 |

Cascais MSL (1976–2016) | LR of SLR Velocity | Mod.FC_2a | 0.127 | 0.031 |

Cascais MSL (1992–2016) | Finite Differences | Mod.FC_2b | 0.152 | 0.032 |

NASA-NearCASC (1995–2017) | Finite Differences | Mod.FC_2c | 0.186 | 0.038 |

CNES-North Atl. (1996–2017) | Finite Differences | Mod.FC_3a | 0.209 | 0.038 |

NASA-WCPM (1995–2017) | Finite Differences | Mod.FC_3b | 0.263 | 0.038 |

**Table 4.**Set of relative empirical SLR models for the WCPM, velocity and acceleration parameters, MSL projections for the middle (2050) and the end of the century (2100), and the respective exceeding probability at epoch 2100.

SLR Model | Initial Velocity (mm/year) | Acceleration (mm/year^{2}) | MSL 2050 (m) | MSL 2100 (m) | Exceeding Probability |
---|---|---|---|---|---|

Mod.FC_0 | 4.10 | 0 | 0.34 | 0.54 | 94% |

Mod.FC_1 | 2.72 | 0.100 | 0.39 | 0.90 | 72.9% |

Mod.FC_2a | 3.35 | 0.127 | 0.46 | 1.10 | 53.7% |

Mod.FC_2b | 2.20 | 0.152 | 0.43 | 1.11 | 52.7% |

Mod.FC_2c | 1.98 | 0.186 | 0.46 | 1.26 | 37.5% |

Mod.FC_3a | 2.49 | 0.209 | 0.52 | 1.43 | 22.4% |

Mod.FC_3b | 2.08 | 0.263 | 0.56 | 1.65 | 8.8% |

**Table 5.**Intervals of confidence for the WCPM relative SLR at epoch 2100 based on the cumulative density function of the PDF in Figure 9.

Confidence Level | Lower Limit (m) | Upper Limit (m) |
---|---|---|

30% | 0.94 | 1.34 |

60% | 0.74 | 1.54 |

90% | 0.51 | 1.77 |

95% | 0.39 | 1.89 |

99% | 0.16 | 2.12 |

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**MDPI and ACS Style**

Antunes, C. Assessment of Sea Level Rise at West Coast of Portugal Mainland and Its Projection for the 21st Century. *J. Mar. Sci. Eng.* **2019**, *7*, 61.
https://doi.org/10.3390/jmse7030061

**AMA Style**

Antunes C. Assessment of Sea Level Rise at West Coast of Portugal Mainland and Its Projection for the 21st Century. *Journal of Marine Science and Engineering*. 2019; 7(3):61.
https://doi.org/10.3390/jmse7030061

**Chicago/Turabian Style**

Antunes, Carlos. 2019. "Assessment of Sea Level Rise at West Coast of Portugal Mainland and Its Projection for the 21st Century" *Journal of Marine Science and Engineering* 7, no. 3: 61.
https://doi.org/10.3390/jmse7030061