# Spatial Probability Characteristics of Waves Generated by Polar Lows in Nordic and Barents Seas

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## Abstract

**:**

## 1. Introduction

## 2. Data: PL Climatology

## 3. Method

#### 3.1. Model of Wave Evolution

#### 3.2. Examples of Model Performance

#### 3.3. Calculation Procedure

- If the distance traveled by the PL, ${T}_{life}V$, is less than the distance D adjusted for $2{R}_{m}$ (as mentioned above, the area covered by the most developed waves has a scale of approximately $2{R}_{m}$): ${T}_{life}V<D-2{R}_{m}$, then the waves reach the point $({x}_{0},{y}_{0})$ as swell with parameters prescribed by Equation (8), with $l=D-2{R}_{m}-{T}_{life}V$ and ${H}_{i}$, ${L}_{i}$ obtained at $t=min({t}_{max},{T}_{life}+{t}_{0},D/V+{t}_{0})$.
- If the PL track is masked by the land, the term (${N}^{i}\xb7{P}_{\varphi}^{i}\xb7{P}_{u}^{j}\xb7{P}_{R}^{k}\xb7{P}_{V}^{m}\xb7{P}_{T}^{n}$) is set to zero (ice coverage is not considered in present study).
- The result of wave parameter calculation at each iteration is compared with each of the specified threshold values in the range from 2 to 15 m for SWH and from 100 to 500 m for wavelength. If H or L exceeds a given threshold, the respective number of events, (${N}^{i}\xb7{P}_{\varphi}^{i}\xb7{P}_{u}^{j}\xb7{P}_{R}^{k}\xb7{P}_{V}^{m}\xb7{P}_{T}^{n}$), is summarized with the number accumulated at earlier iterations for this threshold.
- Finally, the total annual numbers of cases of occurrence the waves with SWH and wavelength exceeding specified levels are obtained for each of the 75 × 75 km grid points $({x}_{0},{y}_{0})$.

## 4. Results

#### 4.1. Significant Wave Height Probability Distributions

#### 4.2. Comparison with Observations

#### 4.3. Wavelength Probability Distributions

## 5. Discussion

#### 5.1. Accuracy of Predictions

#### 5.2. Waves Not Associated with PLs

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Statistical distributions of PL parameters: (

**a**) mean annual spatial distribution of PL origins in 75 × 75 km grid cells [3]; (

**b**) mean annual distribution of maximum wind speed from ASCAT [31] and its correction suggested by Polverari et al. [32], Equation (1); (

**c**) mean annual distributions of PL diameter and traveled distance; (

**d**) lifetime and (

**e**) translation speed; data taken from [3].

**Figure 2.**Color: joint probability of PL lifetime and translation speed. Dotted lines: time of wave development to reach a steady solution in a stationary, Equation (6), and (solid lines) moving, Equation (5), cyclone with diameter 300 km and maximum wind speed 15, 25 and 35 m/s (white, grey and black lines correspondingly.

**Figure 3.**ERA5 fields of (

**a**–

**d**) wind speed and (

**e**–

**h**) SWH during PL#1 lifetime. Maximum (

**i**) wind speed and (

**k**) SWH observed at every point during the PL lifetime. Self-similar model (

**j**) wind speed for PL#1 and (

**l**) SWH obtained using Equations (7) and (8). Black solid lines mark the PL trajectory; black circle is the PL origin.

**Figure 4.**ERA 5 fields of (

**a**–

**d**) wind speed and (

**e**–

**h**) SWH during PL#2 lifetime. Maximum (

**i**) wind speed and (

**k**) SWH observed at every point during the PL lifetime. Self-similar model (

**j**) wind speed for PL#2 and (

**l**) SWH obtained using Equations (7) and (8). Black solid lines mark the PL trajectory; black circle is the PL origin.

**Figure 5.**Spatial distribution of the annual number of events when SWH of PL-generated waves exceeds the specified threshold values: 2 m, 4 m, 6 m, 8 m, 10 m and 12 m. Black triangles are location of maritime stations 76,925, 76,928 and 76,930; squares are stations 76,923, 76,931 and 76,932.

**Figure 6.**Spatial distribution of the annual number of events when wavelength of PL-generated waves exceeds the specified threshold values: 100 m, 200 m, 300 m and 400 m.

**Figure 7.**Spatial distribution of the annual number of events when the SWH of PL-generated waves exceeds the specified threshold values: 2 m, 4 m, 6 m, 8 m, 10 m and 12 m. Black triangles are location of maritime stations 76,925, 76,928 and 76,930; squares are stations 76,923, 76,931 and 76,932. The calculation using the wind distribution without correction of scatterometer data.

**Figure 8.**(

**a**) Spatial distribution of the annual number of days when maximum wind speed exceeds 15 m/s, estimated from ERA5 for 2012–2022. (

**b**) Spatial distribution of the annual number of PL passages in a given point.

**Figure 9.**Spatial distribution of the annual number of days when SWHs (either PL-associated, or not) exceed 2 m, 4 m, 6 m, 8 m, 10 m and 12 m from ERA5 data for 2012–2022.

**Table 1.**Number of cases of PL-associated waves in two locations of maritime stations, data from Rojo et al. [28].

Stations 76,925, 76,928, 76,930 | Stations 76,923, 76,931, 76,932 | |||
---|---|---|---|---|

SWH Threshold | Total Number of Events | Annual Number of Events | Total Number of Events | Annual Number of Events |

>2 m | 22 | 1.6 | 6 | 0.43 |

>4 m | 20 | 1.4 | 6 | 0.43 |

>6 m | 12 | 0.86 | 4 | 0.29 |

>8 m | 5 | 0.36 | 1 | 0.07 |

>10 m | 1 | 0.07 | 1 | 0.07 |

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**MDPI and ACS Style**

Yurovskaya, M.; Kudryavtsev, V.; Chapron, B.
Spatial Probability Characteristics of Waves Generated by Polar Lows in Nordic and Barents Seas. *Remote Sens.* **2023**, *15*, 2729.
https://doi.org/10.3390/rs15112729

**AMA Style**

Yurovskaya M, Kudryavtsev V, Chapron B.
Spatial Probability Characteristics of Waves Generated by Polar Lows in Nordic and Barents Seas. *Remote Sensing*. 2023; 15(11):2729.
https://doi.org/10.3390/rs15112729

**Chicago/Turabian Style**

Yurovskaya, Maria, Vladimir Kudryavtsev, and Bertrand Chapron.
2023. "Spatial Probability Characteristics of Waves Generated by Polar Lows in Nordic and Barents Seas" *Remote Sensing* 15, no. 11: 2729.
https://doi.org/10.3390/rs15112729