Pseudoadiabatic chart / sonde diagram

Transcription

1 Pseudoadiabatic chart / sonde diagram T = T θ 0 R c = θ const R c This can be lotted with a logarithmic scale for the ressure. The lines for constant otential temerature is following the dry adiabatic lase rate. We are most interested in the stiled area in Fig. 2.6.

2 Temerature Entroy (ot.tem.) diagram The chart in Fig. 2.6 may be lotted as a temeratureentroy diagram (Fig. 2.20a). Again, we are only interested in the atmosheric temerature interval (stiled), which is usually rotated (ca. Fig. 2.20b). Skew-T ln diagram (Fig. 2.20b)

3 Saturated air When saturated air is lifted adiabatically, water vaor will condense. All the heat formed in the hase change is assumed to warm the air arcel and the liquid water removed. The lase rate for this rocess is called seudoatiabatic lase rate (fuktigadiabat). Γ s = dt dz = 1+ Γ L c d dw dt s It is a good idea to lot both adiabats in the same diagram! And they are, as a function of ressure and temerature in the chart in the back of the book. Also lotted are the saturated mixing ratios at given T and.

4 Stability Why do we want both adiabats in the same chart? Because dry/unsaturated air follows the dry adiabat, while saturated air follows the moist (seudo) adiabat.

5 Unsaturated air 1 dθ 1 θ dz T dθ < 0 dz dθ = 0 dz dθ > 0 dz = d ( Γ Γ) Unstable Neutral Stable Saturated air Condensing water will free energy: dq = -Ld Where L is latent heat, and d is the amount condensed. But we have dθ = θ And it can be shown (Ex.2.33) that L Lws dw = s d c T c T So that Lws c T dq c T L = c T dw θ = lnθ + const = ln θe w / T 0 θ θ s s e

6 Convective instability We have convective instability when Conditional instability We have conditional instability when dθ e dz < 0 Γs < Γ < Γ d or when dθ w dz < 0

7 The Amble sonde diagram 1050hPa 500hPa: Skew-T ln diagram 500hPa 20hPa: Skew-T diagram Height of the standard atmoshere Pot.tem. on the dry adiabat Thickness of layer Moist adiabat Dry adiabat Temerature Sat. mix. rat. Pressure

8 Exercise 2.48 Pressure 200hPa, temerature T=-60 C. Find the otential temerature using a sonde diagram. θ =70 C Aroximately θ =66 C 200hPa T=-60 C θ = T R c = 213K = 337K = 200 o 64 C θ =60 C

9 Exercise 2.49a =1000hPa T=15 C Td=4 C Mixing ratio (w) Relative humidity (RH) Potential temerature (θ) Wet-bulb temerature (T w ) Wet-bulb otential temerature (θ w ) T d (T d ) (T) T Relative Potential Wet-bulb Dew oint humidity temerature RH We The are = temerature final 100% temerature 1000hPa, w(t)/w we s (T) so get after when evaorating cooling air water θ = T = = 100% 15 Cw constant ressure s (T d )/w untill s (T) into the air until it saturation. is saturated. = 100% x 5.1/10.8 The = saturated 47% mixing This ratio is at easily T d is then done the on this chart, mixing lifting ratio the of the air air. along the w(t) dry = wadiabat s (T d ) = until 5.1g/kg saturation, and then along Must NOT the seudoadiabat be confused on with its saturated way down. mixing ratio at T: (T). T w = θ w = 9.3 C

10 Exercise 2.49b =1000hPa T=15 C, Td=4 C Lift the air to 900hPa. w = 5.1g/kg RH = 100% x 5.1/6.8 = 73% θ = 15 C as before. (Conserved) T w = 4.7 C θ w = 9.3 C as before. (Conserved) T w (900hPa) T d (900hPa) 900hPa T d T w T (T d ) (T)

11 Exercise 2.49c =1000hPa T=15 C, Td=4 C Lift the air to 800hPa. w = 4.4g/kg RH = 100% x 4.4/4.4 = 100% θ = 17 C. (Not conserved for moist adiabatic rocesses) T w = -1 C θ w = 9.3 C as before. (Conserved) 800hPa T d T w T (T d (800hPa) (T d ) (T)

12 How to find different roerties on the chart Potential temerature: Follow the dry adiabat to 1000hPa and read off the temerature. Mixing ratio: At the dew oint temerature, follow the lines for constant water vaor content downwards. Saturation mixing ratio: At the actual temerature, follow the line for w downwards. Wet-bulb temerature: Follow the dry adiabat from the actual ressure uwards until saturation (the lifting condensation level), and then downwards along the moist adiabat to the starting ressure level. Wet-bulb otential temerature: From the wet-bulb temerature, follow the moist adiabat to 1000hPa. Equivalent otential temerature: Lift the arcel to saturation, and then along the moist adiabat until there is no water vaor left (where only the dry adiabat is lotted), and then downwards along the dry adiabat. Static stability: Look at the lase rate comared to the dry adiabat. Or look at otential temerature. Stable means θ increase with height. Conditional instability: If the lase rate is between the dry and the moist adiabat, we have conditional instability. Level of free convection: In case of conditional instability only. Lift the arcel to saturation, and uwards along the moist adiabat.

13 Convective instable air: If θ e or θ w decreases with height. When this occurs, an initially stable layer will destabilize as it is lifted, since the to of the layer will cool faster than the bottom, thereby steeening the lase rate. In reality, whole layers may not be lifted at once; instead, arcels often lift from the boundary layer to their level of free convection (LFC) to form thunderstorms. Thus, the hysical rocess that otential instability reresents may or may not occur often during convection. However, θ e (which is more sensitive to moisture than temerature) decreasing with height IS imortant, since it reresents the resence of dry air above moist air which enhances downburst and ossibly hail otential if thunderstorms develo. htt://

14 Exercise 2.52 =1000hPa T=20 C w=10g/kg Air is lifted when assing a mountain to 700hPa. T d = 13.9 C Liquid water: (T)- (T 2 ) = 10-6 = 4g/kg Lose 80% of water: w=10-0.8*4 = 6.8g/kg T(900hPa) = 19.5 C T 2 700hPa T d T (T 2 ) (T)