Vertical Spectra of Temperature in the Free Troposphere at Meso-and-Small Scales According to the Flow Regime: Observations and Interpretation
oleh: Richard Wilson, Hiroyuki Hashiguchi, Masanori Yabuki
| Format: | Article |
|---|---|
| Diterbitkan: | MDPI AG 2018-10-01 |
Deskripsi
This article addresses the properties of stably-stratified and unstable layers in the free troposphere. Thorpe’s method of analysis has been applied to potential temperature (PT) profiles obtained from the raw measurements of operational radiosondes. In principle, this method distinguishes stably stratified and unstable regions. The background static stability, quantified by the square Brunt-Väisälä frequency estimated on the sorted PT profiles (stable everywhere), is observed to be significantly smaller in the unstable regions, likely due to turbulent mixing. The vertical power spectral densities (PSDs) of temperature fluctuations are shown to be proportional to <inline-formula> <math display="inline"> <semantics> <msup> <mi>m</mi> <mrow> <mo>−</mo> <mi>p</mi> </mrow> </msup> </semantics> </math> </inline-formula>, where <i>p</i> is in the average <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2.8</mn> <mo>±</mo> <mn>0.2</mn> </mrow> </semantics> </math> </inline-formula> in the stably stratified regions, and is <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1.7</mn> <mo>±</mo> <mn>0.3</mn> </mrow> </semantics> </math> </inline-formula> in the unstable regions, for wavenumbers <i>m</i> in the range <inline-formula> <math display="inline"> <semantics> <mrow> <mo>[</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mo>,</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>]</mo> </mrow> </semantics> </math> </inline-formula> m<inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics> </math> </inline-formula>. Such findings validate the Thorpe analysis when applied to radiosondes. Also, the distribution of thicknesses <i>h</i> of unstable layers is observed to approximately follow a power law, varying as <inline-formula> <math display="inline"> <semantics> <msup> <mi>h</mi> <mrow> <mo>−</mo> <mi>r</mi> </mrow> </msup> </semantics> </math> </inline-formula> with <inline-formula> <math display="inline"> <semantics> <mrow> <mi>r</mi> <mo>≈</mo> <mn>2.1</mn> <mo>±</mo> <mn>0.1</mn> </mrow> </semantics> </math> </inline-formula>. PT profiles for the entire troposphere have also been analyzed as the sum of a sorted profile and an anomaly profile. The PSDs of the sorted PT profiles are scaled as <inline-formula> <math display="inline"> <semantics> <msup> <mi>m</mi> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics> </math> </inline-formula> down to a few meters on the vertical scale. Simple stochastic models based on random walks with increments having the property of flicker noise are shown to reproduce the spectral properties of the sorted PT profiles, i.e., of the vertical stratification of the free atmosphere.