# Presentation: 490094

## MSU - Brightness Temperature Adjustments

**	****	****    ****( *****Listed in chronological order of discovery *****)**
**Instrument Bias** adjustment*
**2.**  **Diurnal Variation** adjustment for different satellites.
**3.**  **Orbital Height** adjustment of weighting function.
**4.**  **Instrument Body Effect** adjustment.
-          * *Largest effect, which is assumed constant*

- The following  presentation  discusses the last item, the
** ****Instrument Body Effect** which is the least understood.

## Adjustment Procedures for  MSU + AMSU  Measurements

-     Adjustment

- Orbital Height
- Adjustment

- Instrument Body Effect
- Adjustment

- X-Scan Measurements (Christy)
-                       or
-        Climate Model (Wentz)

- Using A-Priori Satellite
- Information

- Using Overlapping Satellite
- Measurements

**Adjustment Procedures for  MSU + AMSU  Measurements**

- Instrument Bias
- Adjustment

- Using Overlapping Satellite
- Measurements

_*Adjustment*_

_*Procedure*_

## Instrument Body Effect (IBE)

- 2.   Antenna side lobe contributions

- John Christy found that the  MSU  measurements varied slightly, and
- diurnally, with instrument temperature and adjusted the measurements.*  *

_**Possible sources of Instrument Body Effect**__  _

- 1.   Radiometer nonlinearity

- 3.   Residual diurnal temperature variation

**IBE adjustment** **:   *********T******b  ********************T **********T******************** *****= constant,**
***                                ******T*********warm load temperature,*****  T******o*****=fixed reference**

## Microwave Radiometer

- Scan

- Motor

- Cold Space
-   Radiation

- Mixer

- Local

- Oscillator

-   Video Amplifier

- Square
-   Law

***RECEIVER  SYSTEM***

***ANTENNA  SYSTEM***

***Microwave Radiometer***

- Warm
-  Load

-    Earth
- Radiation

*T**c*

*V**b*

*T**b*

*T**w*

*V**w*

*V**c*

- IF
-  Amp

- RF
- Amp

- IF = *Intermediate Frequency*

- RF =  *Radio Frequency*

- z

_**Detector Response**_
*<V> = a**2**<I**2**> +  a**4**<I**4**> + **• • •*
***  ****where  ****a**4** KBG /a**2** ** *
* **K=Boltzman’s constant, B=Bandwidth,  G =IF-Amplifier Gain*

-  Detector

******

***G***

***V***

***I***

## Nonlinear Radiometer Response

- Square
-   Law

-  Detector

******

***V***

***I***

*V*

*I*

_***Nonlinear Radiometer Response***_

**Time-averaged voltage :**

**Nyquist theorem :**

**Combining [1] and [2] :**

*                       **K=Boltzman’s constant              *
*                 **G=Amplifier gain,  B=Bandwidth*
*T=Amplifier temperature,  T**S** = Radiometric temperature**  *

**Two-point radiometer calibration eliminates *****b******o****** *****and***** b******1****** *****from*****  <V >  *****so that**

- [1]

- [2]

- [3]

*Output *
*Voltage**                 *

*  **Input *
*Current*

## Nonlinear Calibration Equation

- The brightness temperature viewed by the radiometer  *T**b*  is

- where  *V**b**  * is  the  corresponding  output  voltage  or  counts.  The first
- bracketed  term  is  the  linear  term;  it  is  directly  proportional  to the
- output voltage.   The second term contains  the  nonlinear parameter  **
- resulting from an imperfect square-law detector; **is proportional to the
- amplifier gain *G* which is temperature dependent.  Both the slope *S *and
- intercept *I *are obtained from the two-point radiometer calibration,  *i.e.,*

- where  *T**c** *is the temperature and *V**c* is the voltage for the cold space
- observation and *T**w**  *and *V**w* are the corresponding warm target data.

## The nonlinear term is a function of (Tb-Tc)(Tw-Tb)  - Tb.  The graphs below show the MSU - laboratory measurements of (Left) and the changes in both   () and Tb (Right) resulting from a 5K change in instrumental temperature. 

- By approximating *T**b* by the linear term, the calibration equation becomes

##    Tbo  = [I + S Vb] - Tb - TcTw - Tb

- The  parameter is approximated as a linear function of instrument temperature, *T *,

- where

*   **T**bo  *= [*I* + *S V**b*] - *****T**b *- *T**c**T**w *- *T**b*

*T**b**= T**bo **+ **T**b*

- and

- *T**b  *-*********T *-*T**T**b *- *T**c*)(*T**w *- *T**b*)

**********- **

- 

- 

-  Christy and Wentz use  *T**b ****** ****T****T**o *with *T * *T**w* and *T**o  *has
-  fixed values* *between* 274 *and* 280 K *depending on the satellite.** **

**1.  **_**Nonlinearity Temperature Correction**_

## 2.  Side Lobe Temperature  Correction

- A major portion of the antenna side lobes, ***C *, “sees”
- the cold-space radiation, *T**c*. A smaller portion of the side lobes, ***S* , sees the solar radiation, *T**SL *, reflected with reflectivity *R* from materials on the spacecraft.

*Earth*

- The brightness temperature can also be written as

- where

- This adjustment is very different than that used by Christy & Wentz,  *i.e.,*

## Summary of Indirect Diurnal Sources of Radiation

-    Christy and Wentz refer to these corrections as an Instrument Body Effect
-    and express the correction as  *T**b  ****T**T*where  *T **T**w *

- 1. Detector Nonlinearity*        *T**b  ******T**T**T**b *- *T**c*) (*T**w *- *T**b*)        0.1  to  + 0.3 K

_**Source **_                       _**Brightness Temperature Correction**_**            **_**Estimate**_

- 2. Antenna Side Lobes

** This source contains the instrument temperature, T.*

**** *= nonlinearity at temperature* *T**o         ****‘= nonlinear temperature* *parameter*
*T**c   **= cold space temperature*                 *T**w **= warm load temperature** *
*T   = instrument temperature                 T**b  **= brightness temperature*
***S  **= fraction of solar radiation**	**      ****C **= fraction of cold-space radiation*
*T**SL**= solar radiation temperature*          *R   *=  s*pacecraft* r*eflectivity*

- ? ?

## Appendices

## Slide 12

## Slide 13

## Slide 14

## Effects of Calibration on Derived Temperature Dependence and Trend (Wentz) 

**Effects of Calibration on Derived Temperature Dependence and Trend (Wentz) **

- “**Linear Calibration**” (My Comment)

- “**Linear calibration results in the smallest temperature dependence**** “**

- “**Trend is independent of calibration algorithm”     **
**  ****What is the source of target factor in the case   **
**  ****of the linear calibration?**

- “**Used by Vinnikov”**

## Nonlinear parameter as a function

**of instrument temperature.**
**Solid-Line:** Laboratory Measurements
- Mo, T, *et al*., *JGR*-106, 10145-10150, 2001
**  ****Dashed-Line:** Satellite Derived (Wentz)

## Nonlinear minus Linear TB  plotted against  TB  for

**              ****different nonlinear parameters.**

## Slide 18