LCL is the height where air has cooled to the dew point. We can calculate LCL using temperature and dew point at the surface. Like temperature dew point also decreases with height because of decreasing pressure. Ew point drops at the "de Point Lapse Rate (DPLR) of 0.2 degrees C/100m (1.0 degrees C/500m)
What is the Air Temperature and Dew Point at the following heights? 2000m, 1500 m, 1000 m, and 500 m if at the surface (sea Level) it is 26 degree C air temperature and 10 degrees C dew point?
To calculate the air temperature and dew point at different heights (2000m, 1500m, 1000m, and 500m) using the given surface values (air temperature: 26°C and dew point: 10°C), we need to consider the environmental lapse rate and the dew point lapse rate.
The environmental lapse rate is the rate at which temperature decreases with increasing altitude. Typically, it is about -6.5°C per 1000 meters or -3.57°F per 1000 feet.
Given that the dew point decreases at a lapse rate of 0.2°C per 100m, we can use this information to calculate the air temperature and dew point at each height.
Let's start with the calculations:
1. Calculate the change in temperature due to the environmental lapse rate:
Change in temperature = (altitude / 1000) * environmental lapse rate
Change in temperature at 2000m = (2000 / 1000) * -6.5 = -13°C
Change in temperature at 1500m = (1500 / 1000) * -6.5 = -9.75°C
Change in temperature at 1000m = (1000 / 1000) * -6.5 = -6.5°C
Change in temperature at 500m = (500 / 1000) * -6.5 = -3.25°C
2. Calculate the change in dew point due to the dew point lapse rate:
Change in dew point = (altitude / 100) * dew point lapse rate
Change in dew point at 2000m = (2000 / 100) * 0.2 = 4°C
Change in dew point at 1500m = (1500 / 100) * 0.2 = 3°C
Change in dew point at 1000m = (1000 / 100) * 0.2 = 2°C
Change in dew point at 500m = (500 / 100) * 0.2 = 1°C
3. Calculate the air temperature at each height:
Air temperature at 2000m = surface temperature + change in temperature
Air temperature at 2000m = 26°C + (-13°C) = 13°C
Air temperature at 1500m = surface temperature + change in temperature
Air temperature at 1500m = 26°C + (-9.75°C) = 16.25°C
Air temperature at 1000m = surface temperature + change in temperature
Air temperature at 1000m = 26°C + (-6.5°C) = 19.5°C
Air temperature at 500m = surface temperature + change in temperature
Air temperature at 500m = 26°C + (-3.25°C) = 22.75°C
4. Calculate the dew point at each height:
Dew point at 2000m = surface dew point + change in dew point
Dew point at 2000m = 10°C + 4°C = 14°C
Dew point at 1500m = surface dew point + change in dew point
Dew point at 1500m = 10°C + 3°C = 13°C
Dew point at 1000m = surface dew point + change in dew point
Dew point at 1000m = 10°C + 2°C = 12°C
Dew point at 500m = surface dew point + change in dew point
Dew point at 500m = 10°C + 1°C = 11°C
So, at the given heights:
- Air temperature at 2000m is 13°C, and dew point is 14°C.
- Air temperature at 1500m is 16.25°C, and dew point is 13°C.
- Air temperature at 1000m is 19.5°C, and dew point is 12°C.
- Air temperature at 500m is 22.75°C, and dew point is 11°C.
To calculate the air temperature and dew point at different heights, we need to consider the dew point lapse rate (DPLR) of 0.2 degrees C/100m (1.0 degrees C/500m). Let's start by determining the LCL, which is the height where air has cooled to the dew point.
LCL Calculation:
1. Convert the surface air temperature and dew point values to degrees Kelvin (K) by adding 273:
Surface air temperature: 26°C + 273 = 299 K
Surface dew point: 10°C + 273 = 283 K
2. Calculate the temperature decrease from the surface to the LCL using the DPLR:
Temperature decrease = DPLR x (Height / 100)
Assuming the LCL is at height 'H':
Temperature decrease = 1.0°C/500m * (H / 100)
3. Subtract the temperature decrease from the surface air temperature to get the LCL temperature:
LCL temperature = Surface air temperature - temperature decrease
Now, let's calculate the air temperature and dew point at different heights using the LCL temperature:
At 2000m:
Temperature decrease = 1.0°C/500m * (2000 / 100) = 4.0°C
LCL temperature = 299 K - 4.0°C = 295 K
Air temperature at 2000m = 295 K - 273 = 22°C
Dew point at 2000m = 10°C (as it remains constant below the LCL)
At 1500m:
Temperature decrease = 1.0°C/500m * (1500 / 100) = 3.0°C
LCL temperature = 299 K - 3.0°C = 296 K
Air temperature at 1500m = 296 K - 273 = 23°C
Dew point at 1500m = 10°C (as it remains constant below the LCL)
At 1000m:
Temperature decrease = 1.0°C/500m * (1000 / 100) = 2.0°C
LCL temperature = 299 K - 2.0°C = 297 K
Air temperature at 1000m = 297 K - 273 = 24°C
Dew point at 1000m = 10°C (as it remains constant below the LCL)
At 500m:
Temperature decrease = 1.0°C/500m * (500 / 100) = 1.0°C
LCL temperature = 299 K - 1.0°C = 298 K
Air temperature at 500m = 298 K - 273 = 25°C
Dew point at 500m = 10°C (as it remains constant below the LCL)
Therefore, the air temperature and dew point at different heights are as follows:
- At 2000m: Air temperature = 22°C, Dew point = 10°C
- At 1500m: Air temperature = 23°C, Dew point = 10°C
- At 1000m: Air temperature = 24°C, Dew point = 10°C
- At 500m: Air temperature = 25°C, Dew point = 10°C