Introduction to thermodynamic diagrams • As discussed in last chapter, as an air parcel rises, it cools at the dry adiabatic lapse rate • As the air parcel cools, its RH increases • When RH reaches 100%, water starts to condense (LCL) • Above the LCL, temperature decreases at the saturated adiabatic lapse rate • All these different processes can be followed quite easily on a thermodynamic diagram (Stull Fig. 6-2; see also Ahrens Ch. 6 p. 162-163) Summary of procedure • Below LCL (T > Td) – T follows a dry adiabat (constant line) –Td follows an isohume (constant r line) – The level at which T = Td is the LCL • Above LCL – T follows a saturated adiabat –Td = T – Total water content (liquid + vapor) • Follows isohume (constant r line) if no precipitation • Follows saturated adiabat if all liquid water rains out Worked example • Use Stull Fig. 6.2 to solve the following problem • An air parcel at 1000 hPa has a temperature of 10 °C and a dew point of 0.5 °C – Plot the state of the air parcel on the figure – What is r and rs of the air parcel? • r: read from Td: 4 g/kg •rs: read from T: 8 g/kg – What is its RH? • RH = r/rs x 100% = 4/8 x 100% = 50% Continuation of previous example • If the air parcel is lifted to 900 hPa, what will its new temperature and dew point be? – Below LCL (when air parcel is unsaturated), T follows dry adiabat (tilted solid line), hence T ~ 2 °C – Below LCL, Td follows isohume (constant r line, dotted line), hence Td ~ -1 °C • What is the RH of the air parcel at 900 hPa? – r: read from Td = 4 g/kg (note unchanged below LCL) –rs: read from T ~ 5 g/kg (note decreased) – RH = r/rs x 100% = 4/5 x 100% = 80% Continuation of previous example • If the air parcel is lifted further, at what pressure is its LCL? What is the temperature, dew point, r, rs, and RH at that level? – LCL is when T = Td (air parcel becomes saturated) • From figure, it occurs at P ~ 870 hPa. • At that level: T ~ -2 C, Td ~ -2 C • r = 4 g/kg, rs = 4 g/kg • RH = r/rs x 100% = 100% Continuation of previous example • If the air parcel is lifted further to 700 hPa, what is its new temperature, dew point, r, rs, and RH? – Above the LCL, air parcels are saturated, hence both T and Td follow the saturated adiabats (thick dashed lines) – Hence at 700 hPa, T ~ -13 °C, Td ~ -13 °C – At that level, r ~ 2 g/kg, rs ~ 2 g/kg, and RH = 100% – Question: If all the condensed water stays in the cloud, what is the liquid water content? • Starts with r = 4 g/kg, now r ~ 2 g/kg, hence liquid water content = 4 g/kg – 2 g/kg = 2 g/kg • Make sure you are able to do all these correctly before you attempt similar problems in the next homework. Above LCL, T (and Td) follows saturated adiabats (dashed lines) LCL: when T = Td (or when the 2 arrows meet) Below LCL: Td follows constant r line T follows dry adiabat.