Max H. Balsmeier
© Max H. Balsmeier 2020 - 2026
This work most likely contains errors and inaccuracies. It is under permanent revision. Some parts are incomplete or only headings have been inserted so far. Commercial use is prohibited. All rights reserved.
There are many good textbooks in the different areas of meteorology, especially in dynamics the amount of literature is large and constantly growing. But there are also extensive standard works on cloud physics and radiation and a certain number of books that are somewhat thin in terms of content, but have been prepared in a didactic manner. However, as is typical of textbooks, some derivations are presented in simplified or at least shortened form, just like in many lectures. This can leave a theoretically interested reader or listener with a feeling of doubt about the correctness of the theory. In addition, there are numerous different notations of the quantities, so that a literature search, for example on the derivations and prerequisites of certain concepts, sometimes does not provide any clarity. This book aims to close this gap. It should not be understood as a pure textbook, because in such a book the linguistic explanations would probably have been a little less condensed; on the other hand, it is not a pure collection of formulas, because such a collection would not contain any derivations.
The reader should find answers to questions like
and will find a mathematically rigorous (at least for a physicist) but not didactically broken down presentation of the content; all requirements and limitations of a concept are clearly stated as such. The derivations are so small that additional calculations should not be necessary for a reader who is confident in high school mathematics.
Dynamics, radiation, cloud microphysics and numerical science are covered. In part I the physical basics that are important for understanding the atmosphere are compiled. In part II an attempt is made to put together a system of equations that describes all processes in the atmosphere. The basic knowledge gained is then applied to specific areas of atmospheric theory. In part III, theoretical tools are prepared for the treatment of air flows in a planetary atmosphere, which is referred to as dynamics. In the following part IV this theory is applied to concrete atmospheric and oceanic problems. In contrast to this, part V deals with the additional areas of radiation and cloud microphysics. Numerical problems are discussed in the sixth part. In the seventh part a dynamic core is developed. Mathematical basics are explained in the appendix.
The SI system is used as the system of units.
| Symbol / Bezeichnung | Bedeutung | evtl. Wert |
|---|---|---|
| $k_B$ | Boltzmann-Konstante | $1,380649\cdot 10^{-23}$ JK$^{-1}$ [15] |
| N$_A$ | Avogadro-Konstante | $6,0221409\cdot 10^{23}$ mol$^{-1} = 1$ [15] |
| $R = k_B\cdot N_A$ | universelle Gaskonstante | $8,314463$ Jmol$^{-1}$K$^{-1}$ |
| $R_s$ | spezifische Gaskonstante | |
| $c^{(p)}$ | isobaric specific heat capacity | |
| $c^{(V)}$ | isochoric specific heat capacity | |
| Index $d$ | Bezug auf trockene Luft | |
| Index $v$ | Bezug auf Wasserdampf | |
| index $g$ | reference to the gaseous portion of the air | |
| $M_d$ | molare Masse trockener Luft | $0,028964420$ kg/mol [22] |
| $M_v$ | molare Masse von Wasser | $0,01801527$ kg/mol [28] |
| $\omega$ | Winkelgeschwindigkeit der Erdrotation | $7,292115\cdot 10^{-5}$ 1/s [29] |
| $a$ | Earth's radius at the equator | $6378137.0$ m [40] |
| $1/\newtilde{f}$ | Abplattung | $298,257223563$ [40] |
| $\beta$ | Obliquity of the Earth's axis | $23.439279^\circ$ [29] |
| $S_0$ | Solarkonstante | $1361$ W/m$^2$ [31] |
| $\Omega$ | Winkelgeschwindigkeit der Erdrevolution | $1,99099\cdot 10^{-7}\text{s}^{-1}$ [31] |
| $M$ | Masse der Erde | $5,9723\cdot 10^{24}\:\text{kg}$ [31] |
| spezifisch | pro Masse |
The following books are relevant in the different areas:
| name | alternative name | length scale / m | time scale / s | typical phenomena |
|---|---|---|---|---|
| synoptic scale | large scale | $> 1\cdot 10^6$ | $> 1\cdot 10^5$ | Rossby waves, extratropical depressions |
| Meso$-\alpha-$Skala | $2\cdot 10^{5}$ - $2\cdot 10^6$ | $2\cdot 10^{4}$ - $2\cdot 10^5$ | tropische Zyklonen, Fronten | |
| Meso$-\beta-$Skala | $2\cdot 10^{4}$ - $2\cdot 10^5$ | $2\cdot 10^{3}$ - $2\cdot 10^4$ | Land-Seewind-Zirkulation | |
| Meso$-\gamma-$ scale | storm scale, convective scale | $2\cdot 10^{3}$-$2\cdot 10^4$ | $2\cdot 10^{2}$-$2\cdot 10^3$ | convection, leeward waves, Kelvin-Helmholtz instability |
| microscale | $2\cdot 10^{-3}$-$2\cdot 10^3$ | $2\cdot 10^{-4}$ - $2\cdot 10^2$ | turbulence, flow around houses and trees etc. | |
| molekulare Skala | $< 2\cdot 10^{-3}$ | $< 2\cdot 10^{-4}$ | Impuls- und Stoffdiffusion, Strahlung |
| size | magnitude |
|---|---|
| synoptic length scale $L$ | $10^6$ m |
| Horizontalwind $u, v$ | $10^{1}$ ms$^{-1}$ |
| Vertikalwind $w$ | $10^{-2}$ ms$^{-1}$ |
| Schwere $g$ | $10^{1}$ ms$^{-2}$ |
| characteristic height $H$ | $10^{4}$ m |
| Zeitskala $T = L/u$ | $10^5$ s |
| Erdradius $a$ | $10^7$ m |
| Dichte $\rho$ | $10^0$ kgm$^{-3}$ |
| Coriolis-Parameter $f$ | $10^{-4}$ s$^{-1}$ |
| horizontale Druckschwankung $\delta p$ | $10^{3}$ Pa |
| vertikale Druckschwankung $\delta p$ | $10^{5}$ Pa |
| Rossby-Parameter $\beta$ | $10^{-11}$ m$^{-1}$s$^{-1}$ |
| relative Vorticity $\zeta$ | $10^{-5}$ s$^{-1}$ |
| Horizontaldivergenz $\delta$ | $10^{-5}$ s$^{-1}$ |
| $p-$Vertikalgeschwindigkeit $\omega$ | $10^{-1}$ Pas$^{-1}$ |
The word scales denotes orders of magnitude. The goal of scale analysis is to simplify equations. Different scales are characterized by different phenomena that typically occur on them. Tab. 1.3 provides an overview of the time and length scales typically used in meteorology, their names and typical phenomena. Some important quantities of the synoptic scale are listed in table 1.3.
| Abk. | Aussprache | Bedeutung |
|---|---|---|
| P | peta | $10^{15}$ |
| T | tera | $10^{12}$ |
| G | giga | $10^{9}$ |
| M | mega | $10^{6}$ |
| k | kilo | $10^{3}$ |
| h | hekto | $10^{2}$ |
| da | deka | $10^{1}$ |
| d | dezi | $10^{-1}$ |
| c | zenti | $10^{-2}$ |
| m | milli | $10^{-3}$ |
| $\mu$ | mikro | $10^{-6}$ |
| n | nano | $10^{-9}$ |
| p | piko | $10^{-12}$ |
| f | femto | $10^{-15}$ |
| a | atto | $10^{-18}$ |