# MEC: A Mesoscale Events Classifier for Oceanographic Imagery

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## Abstract

**:**

## 1. Introduction

#### 1.1. State of the Art

#### 1.2. Proposed Approach

## 2. SST Satellite Data

## 3. Types of Patterns

- A filament of cold water originating from the upwelling jet, going westwards;
- A filament of cold water going southwards, extending the upwelling jet beyond Cape St. Vincent;
- A stream of cool water that bends eastwards from the upwelling jet, overtaking Cape St. Vincent and running along the southern coast of the Iberian peninsula;
- A warm countercurrent originating in the Gulf of Cádiz and running westwards along the southern Iberian coast, eventually reaching Cape St. Vincent and turning northwards.

## 4. MEC Explained

#### 4.1. Spaghetti Plot Generation

- Choose a resolution $r>0$, such that the numbers $\ell =({\varphi}_{\mathrm{max}}-{\varphi}_{\mathrm{min}})/r$ and $m=({\lambda}_{\mathrm{max}}-{\lambda}_{\mathrm{min}})/r$ are integers (typical values for r lie between 0.01 and 0.25 degrees in latitude and longitude) and divide the area A in $\ell \times m$ squares$${a}_{i,j}=[{\varphi}_{\mathrm{min}}+ir,{\varphi}_{\mathrm{min}}+(i+1)r]\times [{\lambda}_{\mathrm{min}}+jr,{\lambda}_{\mathrm{min}}+(j+1)r]$$
- For each satellite image with timestamp t and for all squares ${a}_{i,j}$, compute the spatial average of the SST at time t in the square. This step is performed to mitigate the effects of possible outliers and noise within the square. Formally, let ${X}_{i,j}\left(t\right)$ be the set of points with coordinates $(\varphi ,\lambda )\in {a}_{i,j}$ that have a recorded SST in the image, i.e.,$${X}_{i,j}\left(t\right)=\{(\varphi ,\lambda )\in {a}_{i,j}\mid T(t,\varphi ,\lambda )\mathrm{is}\mathrm{recorded}\};$$$${\overline{T}}_{i,j}\left(t\right)=\frac{1}{\left|{X}_{i,j}\left(t\right)\right|}\sum _{(\varphi ,\lambda )\in {X}_{i,j}\left(t\right)}T(t,\varphi ,\lambda )$$
- Let ${t}_{1},\cdots ,{t}_{N}$ be the timestamps of the images belonging to the time interval $\tau $. For each square ${a}_{i,j}$ compute the time series$${p}_{i,j}=\{({t}_{k},{\overline{T}}_{i,j}\left({t}_{k}\right))\mid k=1,\cdots ,N\mathrm{such}\mathrm{that}{\overline{T}}_{i,j}\left({t}_{k}\right)\mathrm{is}\mathrm{defined}\}.$$
- The spaghetti plot is obtained by plotting all the time series ${p}_{i,j}$ simultaneously within the same time–temperature coordinate system.

- Resolution $r=0.25{}^{\circ}$;
- Time interval $\tau =15\mathrm{days}$, which is the typical temporal scale at which the sought mesoscale events appear and fade;
- Data abundance threshold (used in step 2 above): we require $\left|{X}_{i,j}\left(t\right)\right|\ge 100$ for ${\overline{T}}_{i,j}\left(t\right)$ to be defined (i.e., about 16% of the expected amount of data in a square).

#### 4.2. Features Extraction

- The temporal mean of ${p}_{i,j}$$${\mu}_{i,j}=\frac{1}{{n}_{i,j}}\sum _{k=1}^{{n}_{i,j}}{\overline{T}}_{i,j}\left({t}_{k}\right);$$
- The standard deviation of ${p}_{i,j}$$${\sigma}_{i,j}=\sqrt{\frac{1}{{n}_{i,j}}\sum _{k=1}^{{n}_{i,j}}({\overline{T}}_{i,j}\left({t}_{k}\right)-{\mu}_{i,j}){)}^{2}};$$
**Figure 3.**Event of 13 August 2016 at around 21:40 UTC. (**a**) SST map at the date of the event; (**b**) detail of the SST in the reference area for the spaghetti plot (latitude between 37° and 37.75° N, longitude between 9.5° and 8.75° W, resolution 0.25°); (**c**) reference grid; and (**d**) generated spaghetti plot. - The linear regression coefficient ${\theta}_{i,j}$, defined as the slope of the straight line that better interpolates the points in ${p}_{i,j}$.

#### 4.3. Classification Rules

- Increase ${e}_{i,j}^{1}$ if:
- (a)
- The SST trend ${\theta}_{i,j}$ inside ${a}_{i,j}$ is negative;
- (b)
- The SST trend of the eastern neighbouring squares (see Figure 5b) is lower than ${\theta}_{i,j}$;
- (c)
- The SST mean value ${\mu}_{i,j}$ is lower than the averages of the mean values of the SST in the northern and southern neighbouring squares (the two neighbourhoods are tested separately, each increasing the score if the outcome is positive, and an extra increase is awarded if both are verified).

- Increase ${e}_{i,j}^{2}$ if:
- (a)
- The SST trend ${\theta}_{i,j}$ inside ${a}_{i,j}$ is negative;
- (b)
- The SST trend of the northern neighbouring squares (see Figure 5c) is lower than ${\theta}_{i,j}$;
- (c)
- The SST mean value ${\mu}_{i,j}$ is lower than the averages of the mean values of the SST in the eastern and western neighbouring squares (the two neighbourhoods are tested separately, each increasing the score if the outcome is positive, and an extra increase is awarded if both are verified).

- Increase ${e}_{i,j}^{3}$ if:
- (a)
- The SST trend ${\theta}_{i,j}$ inside ${a}_{i,j}$ and the $\theta $-values of all the full neighbourhood squares of ${a}_{i,j}$ (Figure 5a) are negative;
- (b)
- The SST in the northwestern neighbourhood (see Figure 5d) of ${a}_{i,j}$ decreases before the one in ${a}_{i,j}$, and the SST in the southeastern neighbourhood of ${a}_{i,j}$ either decreases after the one in ${a}_{i,j}$ or increases (this condition is tested for all the relevant squares in the neighbourhoods separately);
- (c)
- ${a}_{i,j}$ is warmer, on average, than the squares in its northwestern neighbourhood and colder, on average, than the ones in its southeastern neighbourhood (the two conditions are tested separately, each increasing the score if the outcome is positive, and an extra increase is awarded if both are verified).

- Increase ${e}_{i,j}^{4}$ if:
- (a)
- The SST trend ${\theta}_{i,j}$ inside ${a}_{i,j}$ and the $\theta $-values of all the full neighbourhood squares of ${a}_{i,j}$ (Figure 5a) are positive;
- (b)
- The SST in the northwestern neighbourhood (see Figure 5d) of ${a}_{i,j}$ either increases after the one in ${a}_{i,j}$ or decreases, and the SST in the southeastern neighbourhood of ${a}_{i,j}$ increases before the one in ${a}_{i,j}$ (this condition is tested for all the relevant squares in the neighbourhoods separately);
- (c)
- ${a}_{i,j}$ is warmer, on average, than the squares in its northwestern neighbourhood and colder, on average, than the ones in its southeastern neighbourhood (the two conditions are tested separately, each increasing the score if the outcome is positive, and an extra increase is awarded if both are verified).

- Additional conditions may modify the final scores (these are checked after the previous four points):
- (a)
- If the SST variation ${\sigma}_{i,j}$ is large (namely ${\sigma}_{i,j}\ge 1{}^{\circ}\mathrm{C}$, which is considered a very large value with respect to the typical standard deviation within the chosen time frame—see also Figure 4), then increase either ${e}_{i,j}^{1}$, ${e}_{i,j}^{2}$ and ${e}_{i,j}^{3}$ (if the SST in ${a}_{i,j}$ decreases) or ${e}_{i,j}^{4}$ (if the SST increases);
- (b)
- If ${a}_{i,j}$ is either globally “cold” (for events E1, E2, and E3) or globally “warm” (for E4), meaning that ${\mu}_{i,j}$ is smaller (respectively, larger) than the average of the $\mu $-values of all the squares in the area of interest, boost the corresponding scores;
- (c)
- If ${a}_{i,j}$ is too near the coast (within about 75 $\mathrm{k}$$\mathrm{m}$ away from it, that is a threshold to distinguish between inshore and offshore upwelling events, given their typical spatial extension), penalize the scores ${e}_{i,j}^{1}$ and ${e}_{i,j}^{2}$; if it is too far from the coast (further than about 75 $\mathrm{k}$$\mathrm{m}$ away), penalize ${e}_{i,j}^{3}$ and ${e}_{i,j}^{4}$.

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

MEC | Mesoscale Events Classifier |

EBUE | Eastern Boundary Upwelling Ecosystem |

ICCS | Iberia/Canary Current System |

SST | Sea Surface Temperature |

AVHRR | Advanced Very High Resolution Radiometer |

MODIS | Moderate Resolution Imaging Spectroradiometer |

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**Figure 2.**

**Left**: depth map of the Atlantic Ocean around the southwestern coast of the Iberian peninsula. The arrows show the direction of the water currents during a mesoscale event.

**Right**: examples of SST maps with recognisable events patterns (highlighted in the rectangles).

**Figure 5.**Neighbouring squares of ${a}_{i,j}$ used in the classification rules. (

**a**) Full neighbourhood of ${a}_{i,j}$; the values of the statistics for the squares in it are used in at least one of the rules for the computation of ${e}_{i,j}$. (

**b**) Squares used in the rules for ${e}_{i,j}^{1}$: eastern squares (orange), northern squares (green), and southern squares (purple). (

**c**) Squares used in the rules for ${e}_{i,j}^{2}$: northern squares (green), eastern squares (orange), and western squares (blue). (

**d**) Squares used in the rules for ${e}_{i,j}^{3}$ and ${e}_{i,j}^{4}$: the northwestern (respectively, southeastern) neighbourhood of ${a}_{i,j}$ is composed of the teal (respectively magenta) non-land squares that have the same distance from the coast as ${a}_{i,j}$.

**Figure 9.**Same as Figure 7, but for each type of event only the labels fulfilling the geographical constraints are kept.

**Figure 10.**

**Left**: event of 16 September 2017, classified as E1 in the ground truth (but images with events classified as E3 are present around that day in the dataset).

**Right**: heatmap generated by MEC. The figures are cropped to the area between 36° and 39° N and between 11° and 7° W for a better visualisation.

**Figure 11.**

**Left**: event of 7 October 2017, classified as E4 in the ground truth (but images with events classified as E1 are present around that day in the dataset).

**Right**: heatmap generated by MEC. The figures are cropped to the area between 36° and 39° N and between 11° and 7° W for a better visualisation.

Satellite | Sensor | Resolution | Temperature |
---|---|---|---|

(at Nadir) | Accuracy | ||

Metop-A _{(2009–2016)} | AVHRR | 1 $\mathrm{k}$$\mathrm{m}$ | $0.01$${}^{\circ}\mathrm{C}$ |

Metop-B _{(2017)} | |||

Aqua | MODIS | 1 $\mathrm{k}$$\mathrm{m}$ | $0.005$${}^{\circ}\mathrm{C}$ |

**Table 2.**Times required for each step of the classifier at different resolutions, for the analysis of an area of $1{}^{\circ}\times 1{}^{\circ}$ for 15 days. All computations were performed on a processor Intel® Core™ i5-8250U @ 1.60 GHz with 8 GB RAM.

Resolution | Spaghetti Plot | Statistics | Application |
---|---|---|---|

Generation | Extraction | of Rules | |

$0.05$${}^{\circ}$ | $261.363$$\mathrm{s}$ | $0.114$$\mathrm{s}$ | $0.216$$\mathrm{s}$ |

$0.125$${}^{\circ}$ | $44.872$$\mathrm{s}$ | $0.026$$\mathrm{s}$ | $0.037$$\mathrm{s}$ |

$0.25$${}^{\circ}$ | $14.812$$\mathrm{s}$ | $0.010$$\mathrm{s}$ | $0.014$$\mathrm{s}$ |

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## Share and Cite

**MDPI and ACS Style**

Pieri, G.; Janeiro, J.; Martins, F.; Papini, O.; Reggiannini, M.
MEC: A Mesoscale Events Classifier for Oceanographic Imagery. *Appl. Sci.* **2023**, *13*, 1565.
https://doi.org/10.3390/app13031565

**AMA Style**

Pieri G, Janeiro J, Martins F, Papini O, Reggiannini M.
MEC: A Mesoscale Events Classifier for Oceanographic Imagery. *Applied Sciences*. 2023; 13(3):1565.
https://doi.org/10.3390/app13031565

**Chicago/Turabian Style**

Pieri, Gabriele, João Janeiro, Flávio Martins, Oscar Papini, and Marco Reggiannini.
2023. "MEC: A Mesoscale Events Classifier for Oceanographic Imagery" *Applied Sciences* 13, no. 3: 1565.
https://doi.org/10.3390/app13031565