# Characteristics of Gravity Waves over an Antarctic Ice Sheet during an Austral Summer

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Site and Instrumentation

**Figure 1.**Satellite image of Victoria Land in West Antarctica. The star indicates the position of the micrometeorological tower located in the middle of a flat snowy homogeneous area on the Nansen Ice Sheet (NIS). The coloured lines bound the wind direction sectors used to classify the analysed data as defined in Section 3.1.

## 3. Method of Analysis

#### 3.1. Preliminary Data Processing and Selection

#### 3.2. Identification and Filtering of Wave Activity

_{ab}) and its integral represents the covariance $\overline{a\prime b\prime}$; its imaginary part (Q

_{ab}) is designated as the quadspectrum (or quadrature spectrum) and represents the spectrum of the product of a and b shifted by 90°. Moreover the phase spectrum, defined as

_{ab}(f)= tan

^{−1}(Q

_{ab}(f) /C

_{ab}(f))

## 4. Results

^{−1}.

**Table 1.**Classification of the selected 30-min time series based on different wind direction sectors (see Figure 1). N refers to the number of runs exhibiting a wavelike pattern; (%)

_{TOT}and (%)

_{GW}refer to the percentage of runs exhibiting a wavy pattern relative to the total number of runs in each sector and relative to the total cases of GW, respectively; U represents the average mean wind associated with the wavy selected events for each sector at z = 10 m.

Sectors | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

Wind direction (°) | 330–10 | 10–35 | 45–60 | 60–150 | 150–210 | 210–260 | 260–330 |

N | 19 | 13 | 19 | 5 | 11 | 1 | 12 |

(%)_{TOT} | 8.0 | 9.0 | 6.8 | 1.8 | 3.2 | 0.9 | 4.9 |

(%)_{GW} | 23.8 | 16.2 | 23.8 | 6.2 | 13.8 | 1.2 | 15.0 |

U (m·s^{−1}) | 2.3 ± 1.6 | 3.0 ± 0.9 | 2.2 ± 1.1 | 2.1 ± 1.7 | 2.4 ± 1.7 | 2.3 | 2.2 ± 1.5 |

**Figure 2.**Time series of longitudinal (

**a**) and vertical velocity components (

**b**), sonic anemometer air temperature (

**c**) and fluctuations in water vapour concentration (

**d**) for a selected but uncommon case of a “cleaner” wave (Wave 1). The time series were collected on the 24 November 1993 at 18:00 (local time) and were associated with a drainage wind from the Priestley glacier (Sector 1). The different colours refer to the different levels of measurement: red (10 m), green (4.5 m), blue (2 m). The black dashed lines refer to the mean values. Note that in Figure 2a,b, the time series relative to the lowest levels (green and blue lines) have been artificially shifted for better visualisation purposes.

_{C}: [9]) were computed at the highest level for sensible heat flux (RN = 28, NR = 0.9, I

_{C}= 1) and latent heat flux (RN = 8, NR = 0.9, I

_{C}= 1), indicating stationarity of the corresponding time series. The period and amplitude of the wave changed slightly during the analysed episode. Moreover, the wave period did not differ at the three measurement heights even if the amplitude tended to be attenuated closer to the ice sheet surface. This is mainly true for the vertical velocity component that is characterised by smaller wave amplitude superimposed onto increasing levels of turbulence activity near the ground. Spectral and cospectral analyses (Figure 4 and Figure 5) further highlight the presence of a well-defined spectral gap between the turbulence and the wave frequency range. In fact, the spectra of the wind components and the scalars exhibited a secondary maximum at f~0.0025 Hz, corresponding to the same wave period observed in the time series (6–7 minutes). This low frequency maximum is well separated from the turbulence frequency range by a gap at f~0.01 Hz. At the frequency of the wave maximum quadspectra, the phase spectrum approaches −90° for w-T cross-spectrum and +90° for the w-q cross-spectrum, indicating the small diffusive characteristic of this detected wave.

**Figure 3.**As per Figure 2 but for a selected case of a “dirty” wave (Wave 2). The time series were collected on 28 December 1993 at 00:30 (local time) and were associated with a drainage wind originating from the Browning pass (Sector 3).

_{C}= 0.87, and for latent heat flux were RN = 31, NR = 1.7, I

_{C}= 0.91 indicating a weaker stationarity of the corresponding time series with respect to the case shown in Figure 2 (Wave 1).

**Figure 4.**Spectra (in pre-multiplied form) computed for the longitudinal and lateral wind velocity components (

**a**), for vertical wind component (

**b**) and for temperature and water vapour (

**c**) versus the natural frequency (f) relative to the time series shown in Figure 2 and sampled at the highest level (10 m).

**Figure 5.**Cospectra (black lines) and quadrature spectra (grey lines) for the w-T cross-spectrum (

**a**) and the w-q cross-spectrum (

**b**); phase spectra for the w-T cross-spectrum (

**c**) and the w-q cross-spectrum (

**d**) versus the natural frequency (f) relative to the time series shown in Figure 2 and sampled at the highest level (10 m).

**Figure 8.**Triple decomposition of longitudinal (

**a**) and vertical wind velocity components (

**b**), sonic anemometer temperature (

**c**) and water vapour concentration (

**d**) relative to the case of the “cleaner” gravity wave shown in Figure 2 (Wave 1) and sampled at the highest level (10 m). The time series were filtered using the MR decomposition technique based on the Haar wavelet. The threshold frequency used to separate wavy and turbulent components (f~0.01 Hz) was selected on the basis of the spectral analyses shown in Figure 4 and Figure 5. The red lines represent the original fluctuations $\left(x-\overline{x}\right)$, the black lines represent the filtered wavy components $\left(\tilde{x}\right)$, and the grey lines represent the wave-corrected fluctuations $\left(x-\overline{x}-\tilde{x}\right)$. Note that red lines have been artificially shifted for better visualisation purposes.

**Figure 10.**Scatter plot of unfiltered turbulent statistics versus the same statistics corrected for the wave effect: standard deviation of the longitudinal (

**a**), lateral (

**b**) and vertical wind velocity component (

**c**), and friction velocity (

**d**). The different colours and symbols refer to the different levels of measurement: red stars (10 m), green points (4.5 m), blue diamonds (2 m). Coloured dotted lines represent the linear best-fit regression lines whereas the black dotted line represents the 1:1 line.

_{u}and σ

_{v}with respect to the unfiltered values (Figure 10a,b). On the other hand, σ

_{w}slightly decreased after the wave filtering (less than 10%) (Figure 10c), suggesting that the pancake nature of eddies in a highly stratified SBL flow may be linked to some wave effects. A large wave impact was also observed in the standard deviations of the scalars that appear to be reduced by about 50%–60% (Figure 11a,b), commensurate with σ

_{u}and σ

_{v}.

**Figure 11.**Same as Figure 10 but for the standard deviation of air temperature (

**a**) and water vapour (

**b**), sensible heat flux (

**c**), and latent heat flux (

**d**).

**Table 2.**Linear regression analysis of turbulent statistics and fluxes computed by using the original fluctuations and corrected for the wave effect shown in Figure 10. The subscribed numbers refer to different levels of measurements (1 → 10 m; 2 → 4.5 m; 3 → 2 m). R

^{2}is the coefficient of determination associated with the regression analysis.

Linear Fit | R^{2} |
---|---|

σ_{u1f} = 0.34 σ_{u1} + 0.01 | 0.75 |

σ_{u2f} = 0.36 σ_{u2} + 0.00 | 0.75 |

σ_{u3f} = 0.38 σ_{u3} + 0.00 | 0.73 |

σ_{v1f} = 0.29 σ_{v1} + 0.02 | 0.64 |

σ_{v2f} = 0.32 σ_{v2} + 0.01 | 0.75 |

σ_{v3f} = 0.30 σ_{v3} + 0.02 | 0.71 |

σ_{w1f} = 0.92 σ_{w1} - 0.01 | 0.98 |

σ_{w2f} = 0.95 σ_{w2} + 0.00 | 0.99 |

σ_{w3f} = 0.93 σ_{w3} + 0.00 | 0.98 |

u_{*1f} = 0.75 u_{*1} + 0.00 | 0.64 |

u_{*2f} = 0.75 u_{*2} + 0.00 | 0.63 |

u_{*3f} = 0.73 u_{*3} + 0.00 | 0.80 |

Linear Fit | R^{2} |
---|---|

σ_{T1f} = 0.49 σ_{T1} − 0.01 | 0.92 |

σ_{T2f} = 0.50 σ_{T2} + 0.00 | 0.87 |

σ_{T3f} = 0.48 σ_{T3} + 0.01 | 0.85 |

σ_{q1f} = 0.42 σ_{q1} + 0.00 | 0.85 |

σ_{q2f} = 0.40 σ_{q2} + 0.00 | 0.92 |

σ_{q3f} = 0.44 σ_{q3} + 0.00 | 0.88 |

H_{1f} = 0.47 H_{1} − 0.76 | 0.67 |

H_{2f} = 0.66 H_{2} − 0.67 | 0.68 |

H_{3f} = 0.69 H_{3} − 1.53 | 0.78 |

Le_{1f} = 0.35 Le_{1} + 0.60 | 0.45 |

Le_{2f} = 0.41 Le_{2} + 0.80 | 0.53 |

Le_{3f} = 0.48 Le_{3} + 0.38 | 0.46 |

_{*}appears reduced after the wave filtering (by about 25%). The waves have a larger impact on the turbulent fluxes of scalars. Figure 11 confirms that waves often produce counter-gradient positive values of sensible heat flux (H). In reality, the surface H should be negative in a stably stratified boundary layer experiencing wavy motion. The wave filtering corrects the turbulent H sign (that becomes negative), but the magnitude is reduced (also as expected for weak turbulence conditions). On the other hand, in the negative quadrant (H < 0 and H

_{f}< 0) where both unfiltered and filtered fluxes are negative, the filtered flux appears less negative than the uncorrected total flux. The percentage of sensible heat flux magnitude reduction due to filtering apparently increased with increasing measurement height (from 30% at 2 m to 50% at 10 m), as reported in Table 3.

**Table 4.**Wind speed (U) and contributions of the wavy and turbulent fluctuations to the total fluxes of momentum ($\overline{u\prime w\prime}$) and sensible heat (H) relative to the time series shown in Figure 2 (Wave 1) and Figure 3 (Wave 2) at the three measurement heights. Values in bold and underlined characters indicate counter-gradient fluxes.

Wave 1 | |||

Height | 10 | 4.5 | 2 |

U (m·s^{−1}) | 3.2 | 2.5 | 2.3 |

$\overline{u\prime w\prime}$ (m·s^{−1})^{2} | |||

total wave turbulence | −0.7 × 10^{−3}+3.6 × 10^{−3}−4.3 × 10 ^{−3} | −12.0 × 10^{−3}−7.0 × 10 ^{−3}−7.0 × 10 ^{−3} | −16.0 × 10^{−3}−8.0 × 10 ^{−3}−8.0 × 10 ^{−3} |

H (W·m^{−2}) | |||

total wave turbulence | −1.0+0.5−1.5 | −6.7 −3.3 −3.4 | −1.5 −0.7 −0.7 |

Wave 2 | |||

Height | 10 | 4.5 | 2 |

U (m·s^{−1}) | 1.9 | 1.5 | 1.1 |

$\overline{u\prime w\prime}$ (m·s^{−1})^{2} | |||

total wave turbulence | −6.3 × 10^{−4}−5.9 × 10 ^{−4}−0.4 × 10 ^{−4} | −6.7 × 10^{−4}−5.0 × 10 ^{−4}−1.7 × 10 ^{−4} | +8.0 × 10^{−4}+9.7 × 10^{−4}−1.7 × 10 ^{−4} |

H (W·m^{−2}) | |||

total wave turbulence | +1.6+1.7−0.1 | −8.6 −7.7 −0.9 | +3.9+4.7−0.8 |

**Figure 12.**Wavelength of detected waves (GW) versus the atmospheric stability parameter (z/L, where z is the measurement height and L is the Obukhov length), measured at the highest level (=10 m) and computed after the wave-filtering process. Different colours and symbols refer to data belonging to different wind direction sectors. The continuous black line refers to the exponential regression: y = 1287 e

^{(−0.56x)}(R

^{2}= 0.64); the dashed and dotted black lines refer to the power-law regressions: y = 592 x

^{−0.47}(R

^{2}= 0.47) and y = 5687 x

^{−0.06}− 5018 (R

^{2}= 0.62), respectively.

## 5. Conclusions

- -
- Wavelike motions on the NIS were probably excited by the complex topography surrounding the area, as frequently observed in the Antarctic coastal regions. In fact, the detected waves were prevalently associated with moderate or low drainage winds from inland towards the coast. During conditions of weak atmospheric stratification (z/L < 1), the wavelengths were of the order of a few kilometres (1000–2000 m), comparable to the height of the surrounding orography. When stability increased, the GW wavelengths rapidly decreased and assumed extremely small values (~100 m) for strong stability conditions.
- -
- The observed wavy patterns were seldom monochromatic. They were frequently characterised by variable amplitude and period and persisted only for few cycles in the time series. The wave period remained unchanged with the measurement heights, but the pattern and amplitude tended to be attenuated closer to the ground surface due to the increasing levels of turbulence mixing [17]. Recall that mechanical production of turbulent kinetic energy is highest near the ground. Moreover, observed “dirty” waves often produced non-stationarity and large intermittency in turbulent fluctuations that can significantly alter the estimation of turbulence statistics in general and fluxes in particular.
- -
- The impact of the wavelike patterns on turbulence statistics and fluxes was different for different flow variables, but showed only a weak dependence on different measurement heights.
- -
- Turbulence statistics can be overestimated without a proper filtering of wavy oscillations. One of the most impacted parameters is TKE. In particular, the longitudinal and lateral components are more impacted than the vertical (already suppressed due to buoyancy). A reduction of approximately 60% in σ
_{u}and σ_{v}was noted after the wave filtering was applied. A modest decrease in σ_{w}(10%) was also noted, which is consistent with other studies [18,19]. - -
- The effect of wave activity on momentum and scalar fluxes is more complex because waves can produce large errors in sign and magnitude of computed turbulent fluxes [14] or they themselves can contribute to intermittent turbulent mixing [17]. The filtering procedure used here based on the MR decomposition restored the correct sign in the sensible heat flux values. Both u
_{*}and H were reduced in absolute value after the wave filtering, which is consistent with the weak turbulent states.

## Acknowledgments

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**MDPI and ACS Style**

Cava, D.; Giostra, U.; Katul, G.
Characteristics of Gravity Waves over an Antarctic Ice Sheet during an Austral Summer. *Atmosphere* **2015**, *6*, 1271-1289.
https://doi.org/10.3390/atmos6091271

**AMA Style**

Cava D, Giostra U, Katul G.
Characteristics of Gravity Waves over an Antarctic Ice Sheet during an Austral Summer. *Atmosphere*. 2015; 6(9):1271-1289.
https://doi.org/10.3390/atmos6091271

**Chicago/Turabian Style**

Cava, Daniela, Umberto Giostra, and Gabriel Katul.
2015. "Characteristics of Gravity Waves over an Antarctic Ice Sheet during an Austral Summer" *Atmosphere* 6, no. 9: 1271-1289.
https://doi.org/10.3390/atmos6091271