Appleman v2.1
Ordunque, in
Appleman 2.0
Thursday, September 11, 2008
European Nursery Rhymes
What has been highlighted in the previous article is the fact that one of the key ingredients for the construction of the graph of temperature is the saturation pressure of water vapor. Now the trail so that instead of "evaporate" or sublimate (transition from solid to gas) form a beautiful cloud of ice crystals should be that the relative humidity in the atmosphere relative humidity is higher than the ice.
What are these sizes? The first is a law that describes the dynamic equilibrium of ice vapor interface (the saturation vapor pressure than ice). The second is a formula that defines the relative humidity over ice. We use again the model of Murphy-Koop to the saturation pressure of vapor on ice
e_ {i} (T) = \\ frac {1} {100} and {^ (9.550426 - \\ frac { 5723.265 + 3.53068} {T} \\ cdot \\ log (T) - 0.00728332 \\ cdot T)}
and where the is the saturation pressure of steam on the ice in [hPa] and T is the temperature in [ K].
A trick that point, the 'RH (relative humidity) and the RH
(RH ice) which is defined in analogy to the relative humidity as normal:
RH = \\ frac {e (T)} {e_ {w} (T)}
RH_ {i} = \\ frac {e (T)} {e_ {i} (T)}
with
, RH and RH RH_ {i} = \\ frac {e (T)} {e_ {i} (T)}
with
belonging to the interval [0,1], and (T) the partial pressure of steam,
and w (T) saturation pressure of steam and water and the (T) saturation pressure of steam on the ice.
At this point do not seem to know how to get out, because trying to impose the condition RH> RH
the this is always trivially falsa, dal momento che e i
(T) w (T) per ogni T. Ci viene in aiuto una grandezza che abbiamo già visto in precedenza e che ci consente di determinare direttamente la pressione parziale del vapore e(T) direttamente dai dati: il mixing ratio. Ricordiamo che il mixing ratio r [g/Kg] è legato alla pressione p [hPa] (mb) e ad e(T) con la seguente formula: r = 621.97\frac{e(T)}{p-e(T)}
che rigirata con un "ardito" passaggio matematico diventa:
che rigirata con un "ardito" passaggio matematico diventa:
\frac{r}{621.97}(p-e(T)) = e(T)
da cui segue che: e(T)= \frac{rp}{621.97+r} sostituendo e(T) così trovato nell'espressione per RH i , questa diventa:
RH_{i} = \frac{rp}{e_{i}(T)(621.97+r)}
A questo punto il gioco è fatto: e
i
è disponibile dal modello come funzione della temperatura, r è fornito dai dati della sonda, così come la temperatura e la pressione.
I dati con i quali le seguenti analisi vengono condotte sono relativi al giorno 11 settembre 2008 ore 12Z (+2 GMT) prelevati dalla stazione di osservazione di Pratica di Mare (RM).
Ecco un grafico che mostra l'evoluzione dell'umidità relativa non interpolata (Blue dots) and the RH
(purple dots): 
now imposing conditions (T
the
> RH will show the following ranges of heights:
Now the area is highlighted in green on the intervals in which the relative humidity is higher relative humidity in the ice ( and therefore in this region if there is formation of contrails, contrails will persist and give rise to cirrus clouds), while the highlighted area in blue on the range of heights to which it provides for the formation of persistent contrail. As you can see there is an area large enough (from about 12000 to 18000 m) where contrail formation is expected to give rise to the clouds. Today nothing to do for the contrail to 3000 m. : D Analyzed briefly this theory to the completion of Appleman treated so far, let us analyze another important aspect: the sensitivity to parameter variation. Now, as I have often been pointed out, measurements of the probes are not completely reliable. I am not is because the probe does not move only along the z axis but in all three dimensions (also present These motions of spin and nutation on the model of a complete meteorological probe will have to wait a little, but I am committed to firn well that if you make good;)), but mostly because the probe at fairly low temperatures makes mistakes on the relevant calculation relative humidity, which together with the pressure un'ingrediente is essential for calculating the critical temperature. Now let 's see what happens when disturbed, the relative humidity of 0.1 (10%). Normally you would have done regardless of the expression derived for this, but since there is an explicit formulation we must be content (at least at first) to consider that simply ΔTc si viene a creare a causa di una variazione del 10% (incremento) dell'umidità relativa alla pressione di 1000 hPa:
Circa gli errori sulla pressione la situazione è molto più tranquilla. For example, let 's see what happens by calculating the same mistake with the same first-perturbazioe for different pressures: It shows a lack of pressure dependence of the error (it remains practically constant along the axis of pressure) which instead is dominated But from the relative humidity.
Moral of the story: watch where the probe made measurements (in space (RH, T) temperature and humidity), but do not worry too much confusion about the pressure, so that even if a little sgarra not change much. Much more dangerous uncertainty about relative.
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