# Presentation: 060031

## Basic structure of the 2A25 algorithm and its improvement for V7 

- Toshio Iguchi (NICT)
- with much help from
- John Kwiatkowski (George Mason University)
- Toshiaki Kozu (Shimane University)
- February 6, 2008
- The Third TRMM Conference, Las Vegas

## Rain Retrieval as Parameter Estimation

- Remote sensing is an ill-posed inverse problem.
- There are more unknowns than measurable parameters.
- MWR researchers take this position from the beginning.
- Radar researchers’ approach has been different.
- A single parameter (Z) determines almost everything.
- Other parameters are treated as corrections.
- The key of the algorithm development is to build a good model of rain storms that gives the values of the unknown parameters or the inter-relationships among them.
- Once the model is chosen, the rest is a numerical techinique.

## Basic Idea of Rain Retrievals with a Single-frequency Radar 

- Deterministic approach
- Calculate radar reflectivity factor (dBZ) from received power (Pr) using a radar equation.
- The radar equation usually neglects non-uniformity of scatterers within a scattering volume.
- Parameterize DSD’s variation with a single parameter
- Z-R relationship, k-Z relationship
- Attenuation correction (if necessary)
- Convert Z into R
- Errors in measurement and DSD parameterization are often ignored.

## The approach in 2A25 algorithm development

- Rain retrieval is equivalent to the DSD parameter estimation. (a microphysical approach)
- Assume that DSD can be parameterized with two parameters.
- Two-scale model: one parameter changes at each gate and the other changes by footprint.
- Errors in DSD model and measurements are considered.
- Non-uniformity of rain distribution and attenuation due to CLW and WV are deterministically calculated from rain distribution.
- All other parameters are deterministically chosen.

## DSD parameter estimation in 2A25

- DSD is parameterized with two parameters
- Gamma DSD model with **=3 fixed
- A default *Z-R* relation defines *N*0=*f*(*D*0)
- The second parameter **modifies this relation: *N*0=*f*(*D*0,**)
** changes by footprint
**  is related to the attenuation deviation from the default model.
- If there is no independent attenuation estimate, there is no way to estimate **. (Or need to use the a priori pdf *p*(**))
- The PIA estimate from SRT is used to estimate **.
- In 2A25, **, which is a multiplicative adjustment parameter of  in *k*=*Z*e***,***corresponds to **.

## There are two observables (x and y) that are related to PIA (). 

- A general form of ** estimation

* **x*: ln(***m*) where
* **y*: PIA estimate from SRT in dB
** true attenuation to the top of surface clutter
**: ln(**), ** is a multiplicative adjustment parameter of  in *k*=*Z*e**
**x: error in measurement of *x*
***y*: error in measurement of *y*

- where

- The problem is to find ** and ** for given x and y.

- Att. in surface clutter

## Estimation of attenuation

- Since ** corresponds to the uncertainty of ln(**), we can combine **x and ** to **x’ and eliminate ** from the equations.

- If we know the probability distribution of **x’ and **y,
- we can calculate the a posteriori pdf of ** for given x and y.

- Or we can calculate the likelihood of ** for given x and y.

- Find an estimate of ** as
- the maximum likelihood estimate,
- the expected value of ** or
- the mode of the a posteriori pdf.

- Note that we only need ** for attenuation correction.

- Functions becomes more complicated if NUBF corrections are included, but the structure of the problem remains the same..

## Assumptions we can adjust

- NUBF model
- How to estimate fine scale inhomogeneity from coarse scale inhomogeneity
- Initial default DSD model
** in the current model, which corresponds to the  relationship between the Z-R and k-Z relations
- Particle type and DSD profile model (**(*h*))
- Errors in these models (pdf of **x’)
- Errors in PIA from SRT (pdf of **y)
- Attenuation by CLW and WV

## Test Runs (1/2)

- Adjustment of particle model above FL
- 100% ice above -15C level.
- Less attenuation above FL
- decreases **: (unless SRT is effective, less att. correction and decreases *Ze* and *R* estimates)
- increases ** if SRT is effective: increases *R* in heavy rain
- Increases R where storm height is high.
- Implementation of NUBF correction
- Increases att. correction in heavy rain cases
- Little effect in light rain

## Effect of NUBF correction

- No NUBF correction

- With NUBF correction

## Test Runs (2/2)

- Adjustment of the DSD model
- default stratiform Z-R relation: increase Z by 1dB and 0.5 dB
- increases R for stratiform rain
- Non-spherical drop shape is taken into account
- deceases R in heavy rain
- Adjustment of the error model of DSD
- Inclusion of other error sources in determining **
- Rayleigh fading in *Z**m* is considered.
- error in NUBF correction is considered.
- decreases the modification of the *R-Z* relation

## Test runs already tried

## Results of test runs

- (Look at the poster)

## Example of the overall effect on R and Z in convective rain

- (Look at the poster)

- Percentage increase of *R* from V6

- Increase of dBZ from V6

## Summary

- The rain estimation algorithm is formulated with consideration of errors in measurement and models.
- Adjustable parameters are identified.
- Selection or determination of actual values of the parameters is a difficult job.
- We try to choose the values that give consistent results with other measurements.
- Model validation with other satellite-borne and ground-based instruments is desired.
- V7 of 2A25 should be improved from V6 and more reliable.

## Surface Reference Technique (SRT)

- A surface echo appears behind rain echoes when observed from space.
- The surface echo suffers rain attenuation.
- A change in surface echo intensity gives an estimate of rain attenuation down to the surface range (*r**s*). The value of this change 0 is denoted by *y* here.

- y is an estimate of -10log10(*A**t*(*r**s*))

**1: true attenuation to *r**b*

**3: true attenuation from* r**b* to *r**s*

**3=10log10(*A**t*(*r**b*))-10log10(*A**t*(*r**s*))

- y is an estimate of **1+**3

## Example of a vertical profile of Zm

- 0 km

- 5 km

- レンジビン番号(80が標高0、1レンジビン250m)

## Relationship between p(1|y) and p(2|x,y)

## Non-Uniform Rain Distribution & PIA

- dBZm

- dBZm

- Height

- Height

**Uniform**

**Non-uniform, but **
**vertically uniform**

- PIA(U)

- PIA(NU), SRT

- PIA(V6)

- Cs(V5)

- Cs(V6)

- V5:
- Cs(V5) = PIA(U) - PIA(NU)
- dBZe(surf)=dBZm(surf)+PIA(U)

- V6:
- Cs(V6) = PIA(V6) - PIA(NU)
- dBZe(surf)=dBZm(surf)+PIA(V6)

- Ze

## Effect of Non-Uniform Rain Distribution