## Description

A dropsonde undergoes an extreme change in environment when exiting the aircraft. At release, the sonde will experience essentially a step change in the environment that it is sensing, and will require a period of time to equilibrate to the ambient conditions. This equilibration time is calculated to be 7 times the time constant of the sensor, and data within this period is discarded. The dropsonde is also moving at the aircraft’s speed when it is launched, so it needs time to slow before winds will be accurate. The wind equilibration time is set at 10 seconds.

The temperature time constant is dependent on the ventilation rate (which is the fall rate), and the air density. Right at the dropsonde launch, the pressure sensor is undergoing extreme changes, and cannot be used to determine the dropsonde fall rate. For this reason, a theoretical fall rate is calculated, which is based on the force balance between the parachute drag and the mass of the sonde. This fall rate has been shown to be reasonably accurate. The aircraft measured temperature and pressure, or the first observed values in the sounding, are used to calculate the density, and the temperature time constant at launch is computed using these parameters. The ambient equilibration region for pressure is set equal to the temperature region, so that pressure and temperature have the same data coverage at the top of the sounding.

## Formula

### Temperature

The temperature sensor time constant is dependent on its ventilation rate, which is simply the dropsonde fall rate.

The following inputs are used:

• $$P_a$$ = ambient (outside) pressure, supplied by the aircraft flight level sensors (mb).
• $$T_a$$ = ambient (outside) temperature, supplied by the aircraft flight level sensors (°C).
• $$T_i$$ = assumed (inside) launch temperature (°C) of the sensor, in the cabin or launch tube, just prior to launch. It defaults to 25°C, but this can be changed using the CabinTemp config parameter.
• $$a$$ = parachute area (cm2).
• $$C_d$$ = parachute drag coefficient.
• $$m$$ = sonde mass (g).
• $$\delta T$$ = desired accuracy (°C).

The following are computed:

### Pressure

The pressure equilbration time is set to the same value as the temperature equilibration time. This approach was adopted from Editsonde.

### Relative Humidity

#### RS41 sondes

The following inputs are used:

• $$T_a$$ = ambient (outside) temperature, supplied by aircraft flight level sensors (°C)
• $$T_i$$ = assumed prelaunch temperature of sonde, i.e. cabin or launch tube temperature of the aircraft. It defaults to 25°C, but this can be changed using the CabinTemp config parameter.

The following are computed:

• The temperature of the RH sensor $$T_s = e^{0.00684T_a + 3.057}$$
• The temperature change between aircraft and atmosphere: $$dT = T_i + 4.5 - T_a$$
• The RH sensor time constant $$\tau_{RH} = -0.1416T_a + 25.385$$
• The number of time constants to reach desired accuracy: $$n_\tau = -\ln \frac{T_s}{dT}$$
• The time to reach desired accuracy $$t_a = \tau_{RH} * n_\tau$$

#### All other sondes

An empirically determined formulation for the RH time constant is used.

$$numTC = -\log{\frac{RHAccuracy} { (ambientRH * deltaTdry *17.67 * 243.5) / (ambientTdry + 243.5)^2 } }$$

### Winds

A fixed wind equilibration time is used. This defaults to 10 seconds and can be set using the WindEquilTime config parameter.

## Source

• Temperature: NCAR/EOL (Charles Martin).
• Relative Humdity:
• RS41 sensor: NCAR/EOL (Holger Vomel)
• All other sensors: NCAR/EOL (Junhong Wang)

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