The altimeter measures air pressure and converts it to altitude using the standard atmosphere. When the real atmosphere differs, the altimeter is wrong. Here you can see how much, and why.
The aircraft flies with a constant altimeter reading, which means it follows a surface of constant pressure. When the pressure at sea level drops, or the air gets colder, that surface sinks, and the aircraft sinks with it without the altimeter showing it.
The number in the window on the altimeter (the subscale) decides what the altimeter measures from. Change the setting and watch what the instrument shows.
Shows altitude above mean sea level. On the ground it shows the aerodrome elevation. Used below the transition altitude, and the setting charts and terrain heights are built around.
Shows height above the aerodrome. On the runway it shows zero. Used by some operators and in some circuits, and with military traffic.
Shows pressure altitude, used for flight levels. Everyone uses the same setting, so aircraft stay separated from each other even though nobody shows their true altitude.
Climbing: set standard when passing the transition altitude. Descending: set QNH when passing the transition level. The layer in between is the transition layer, where you do not level off.
Each pilot sets the baro reference on the EFIS control panel: pull the knob for STD, push for QNH. The PFD altitude tape shows the setting below it, and it flashes if you pass the transition altitude or level without changing. The standby instrument (ISIS) has its own baro setting.
The wings and the engine feel the density of the air, not the altitude on the chart. Density altitude is the altitude in the standard atmosphere that has the same density as the air you are in.
The A320's CFM56 or LEAP engines are flat rated: take-off thrust stays roughly constant up to a corner temperature (typically about ISA+15 °C) and then falls as the air gets hotter. Lower pressure reduces thrust at any temperature.
V1, VR and V2 are indicated speeds. On a hot, high day the same VR of about 145 kt means a higher true and ground speed, so the take-off run gets longer even if the thrust were unchanged.
When there is margin, the A320 takes off with reduced thrust (FLEX, an assumed temperature higher than the real one). A high density altitude uses up that margin, so FLEX gets smaller and TOGA may be required.
Take-off distance factor is a rough teaching estimate for a jet like the A320: true airspeed at the same indicated speed rises with 1/σ, and thrust falls with pressure and, above the flat-rating temperature (typical ISA+15 °C), by about 0.8 % per °C. Real take-off performance comes from the aircraft performance software (FCOM/EFB), not from this model.
Published minimum altitudes assume the standard atmosphere. In cold air the aircraft is lower than the altimeter shows, so the correction is added to the published altitudes. The colder it is and the higher above the aerodrome, the bigger the correction.
Calculated with the ICAO formula (Doc 8168), the same one behind the ICAO correction tables. Many operators apply cold temperature corrections at aerodrome temperatures of 0 °C and below. Check the AIP and your operations manual.
Teaching model. Use the numbers to understand relationships, not for operational decisions. Always follow the AIP, the aircraft flight manual and your instructor.