# Internal Calibration

The process of using a reference load for internal calibration is explained.

### Gain Calibration

The RF switch uses a Dicke switch method to measure the signal power coming from the antenna and the reference signal from a 50-ohm load (resistor). The switch alternates between the two signals. Each setting has an integration time of 350 ms.

During data acquisition, the physical temperature of the reference signal may vary, causing the noise power generated by the load to fluctuate as well. A precise temperature sensor is placed next to the resistor to keep track of the physical temperature of the load accurately. The noise power generated by a load is directly proportional to its physical temperature, which makes it essential to monitor the temperature of the load during data acquisition.

For the calibration, the correlation products of the signal from the antenna (the soil signal) are divided by the reference signal and then multiplied by the physical temperature $T_\mathrm{phys}$ of the resistor:

$\mathrm{HH}' (K) = T_{\mathrm{phys}}(K) \cdot \dfrac{\mathrm{HH}_{\mathrm{ant}}}{\mathrm{HH}_{\mathrm{ref}}}$,

$\mathrm{VV}' (K) = T_{\mathrm{phys}}(K) \cdot \dfrac{\mathrm{VV}_{\mathrm{ant}}}{\mathrm{VV}_{\mathrm{cal}}}$,

and a complex division for the cross-correlation product:

$(\mathrm{HV})' (K) = T_{\mathrm{phys}}(K) \cdot \dfrac{\mathrm{HV}^*_{\mathrm{ant}}}{\mathrm{HV}^*_{\mathrm{cal}}}$.

This results in the radiometer rawdata being calibrated as a noise temperature in Kelvin.

### Receiver Noise Variability

As previously stated, the amount of noise produced by each electronic receiver component is affected by its physical temperature. Even though we conduct gain calibration, the varying noise contributions of the components can still impact the sensor output levels. To calculate the "noise offsets" caused by temperature variations, we use the following equation (with the same equation for HH and VV correlation products):

$\mathrm{Offset}(\mathrm{T}_\mathrm{phys}, \mathrm{HH}') = \mathrm{T}_\mathrm{phys}\,(\degree \mathrm{C}) \left( -4.132\cdot 10^{-4} \cdot \mathrm{HH}' + 0.4057 \right)$

Note: This is an empirically determined equation, and the physical temperature here needs to be supplied in degrees Celsius!

This offset is then subtracted from the gain-calibrated products as follows:

$\mathrm{HH}_\mathrm{corr}' = \mathrm{HH}' - \mathrm{Offset}$

### Calculation of Soil Brightness Temperature

To obtain $T_\mathrm{soil}$, $T_\mathrm{rec}$ needs to be known.

$T_\mathrm{sys}=T_\mathrm{soil}+T_\mathrm{rec}$

Now, the receiver contribution to the total system temperature can be subtracted and the output scaled in absolute brightness temperature:

$T_\mathrm{soil}\,(\mathrm{K}) = 1.778 \cdot \mathrm{HH}_\mathrm{corr}'\,\mathrm{(K)} - 175.9\,\mathrm{K}$

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