# Presentation: 492950

## Standard Retrieval Algorithms 	GPM Core (DPR)Issues in DPR algorithm 

- Toshio Iguchi (NICT)
- 4th GPM Planning Workshop
- 15-17 June 2004
-  Marriott Hotel, Greenbelt, Maryland, USA

## Roles of DPR in GPM

- To provide vertical profiles of precipitation
- To provide the ice/water transition altitude
- To provide DSD information
- To provide accurate rainfall rate
- To provide reference data for other sensors & satellites
- calibration standard
- statistics of profiles and rain structure
- Data base

## Review

- In the last two GPM WS, I showed:
- Dual-frequency algorithms exist.
- can estimate two DSD parameters at each range bin.
- generally work well under the given assumptions.
- Random noise does not create biases.
- Issues:
- multiple solutions possible for liquid particles
- choice of two (DSD) parameters
- separation of solid (ice) phase from liquid phase
- inhomogeneity of rain within footprint
- beam mismatching
- attenuation caused by CLW and water vapor

## Summary in 2003

- Separation of the liquid phase region from the solid phase region seems possible.
- Uncertainty in the shape parameter of DSD has little effect in rain rate estimation.
- A DF algorithm provides better estimates of RR than a SF algorithm for 2 < RR <15 mm/h
- The assumption that N0 is constant near surface gives very reasonable profiles in most of stratiform rain cases. If this works, we do not need SRT. Good news over land.
- Quantization error in Pr does not cause a serious bias error in retrieval.

## Remaining Issues in 2003

- Unknown attenuation by cloud water
- for R < 1 mm/h (no DF algo or SRT usable)
- Uncertainty in DSD for R<1 mm/h
- Effect of non-uniform rain distribution
- How to use overlapping IFOV data effectively to extract inhomogeneity information?
- Effect of Beam mismatching
- Validation and verification (verifiability)

## Basic Idea of DF Algorithm

- 2N(+2) observables (2N of Zm (and 2 of )) to estimate RR at N range gates.
- If the relations among Z, R and k were constant, R would be overdetermined.
- In fact, Z, R and k are functions of many parameters (DSD, phase, shape, temp., vertical air velocity, non-uniformity, etc.)
- Parameterize DSD with two variables.
**E.g., N0 and D0****、****N0* and D0**
- Estimate these two parameters at each gate.
**2N estimates from 2N(+2) observables**
- All other parameters are fixed.
**E.g. shape parameter in DSD, phase, temp, etc.**
- Calculate R with the estimated parameters.

## Assumptions

- DSD is parameterized by 2 parameters.
- e.g., N0,  with known  in -distribution
- Phase state of particles is known.
- Phase state is likely to be estimated from data.
- Temperature of rain drops is known.
- Uncertainty of temperature is a source of error but not large.
- Rain is uniformly distributed in IFOV.
- Attenuation is only caused by precipitating particles. (No attenuation by water vapor, cloud particles, etc. are considered.)
**Cloud liquid water: Att(Ka) = 10 * Att(Ku), up to 5 dB**
**Water vapor: Att(Ka) =  5 * Att(Ku), up to 1.5 dB near surface**
**Oxygen: Att(ka) = 5 * Att(Ku), 0.4 dB near surface**

## How to solve issues

- use surface reference technique.
- How well does it work over land?
- Does difference between Ka and Ku help?
- Database?
- only one or two constraints.
- abandon to estimate 2N parameters at N range bins.
- e.g., one DSD parameter at each bin + one DSD parameter over a given (long) interval.
- use information from other data and models, e.g., GMI, IR data, model profiles of CLW, WV, O2.

## Combined H-B method

- Similar to TRMM PR algorithm, but use both Ka and Ku-band data.
- Uncertain attenuation to the boundary of integration.
- New constraint: RR estimates at two channels must be the same.

##  adjustment with HB solution for DPR

## Beam mismatch and inhomogeneity of rain distribution

- If rain distribution is horizontally uniform, beam mismatch does not cause any error.
- Horizontal non-uniformity and beam mismatch are closely related issues.
- High wavenumber components of fluctuation whose corresponding wavelengths are less than the footprint dimension are smeared out in measurement and cannot be retrieved.
- non-linear effect
- Rain with a constant gradient
- beam mismatching is a issue
- A sharp narrow peak within the footprint

## Future research topics

- good models of solid particles (snow, graupel, hail)
- drop size and density distribution
- spatial distribution
- Validation is very difficult.
- rain distribution model
- inhomogeneity model
- characterization of rain systems from the viewpoint of remote sensing
- information on the stage of rain system evolution from IR, model, etc.

## Summary

- NUBF effect is a big issue.
- Denser samples of KaPR (than KuPR or TRMM PR) will provide better information of inhomogeneity, but its degree is yet to be examined.
- NUBF problem remains even if the two beams are perfectly matched.
- NUBF problem is closely related to beam mismatching issue.
- Attenuation correction, DSD parameter retrievals, beam mismatching, and NUBF corrections are all entangled.  How to disentangle each effect is a challenge.
- More simulation studies are required to evaluate each effect and how they are coupled.
- More probabilistic or deterministic constraints from other data or models will help reduce the estimation error.  However, use of other data sources makes the validation of the algorithm more difficult. (better to keep at least one algorithm that is independent of the consensus algorithm.)