# Presentation: 791494

##  An Empirical Cloud Development Model for Satellite Precipitation Estimation 

-  ***An Empirical Cloud Development Model ******for Satellite Precipitation Estimation ***

***The 3******rd****** NASA/JAXA International TRMM Science Conference****** ******Las Vegas, Nevada, February 4-8, 2008***

***1******Center for Hydrometeorology and Remote Sensing, UC Irvine, USA***

***2******Geography Department ******University of Hull, UK***

***Kuolin Hsu******1******, Tim Bellerby******2******, and Soroosh Sorooshian******1***

## Satellite Precipitation Monitoring

***Satellite Precipitation Monitoring***

- Geostationary IR
- Cloud top heights only
- 15-30 minute data

- Passive Microwave (SSM/I)
- Some characterisation of
- rainfall
- ~2 overpasses per day per spacecraft, moving to 3-hour return time (GPM)

- TRMM precipitation RADAR
- 3D imaging of rainfall
- 1-2 days between overpasses
- (35°N-35°S only)

- Meteosat 7 (EUMETSAT)

- TRMM PR (NASA/NASDA)

- SSMI 85GHz (DMSP)

## 3-hour Precipitation

## Interpolation of 3-hour Precipitation

***Interpolation of 3-hour Precipitation***

*T*

*T+3hr*

*T+6hr*

*t-hr*

*t+3hr*

## Objectives

- How can we more effectively integrate LEO and GEO satellite information to improve short-term rainfall estimation?

## Outline

***Motivation/Objective***
***Lagrangian Cloud Development Model (LMODEL)***
***▪******	******Dynamic cloud tracking***
***▪ ******	******An Empirical Cloud Model for Rainfall Generation***
***▪ ******	******State Adjustment using Kalman Filter***
***Case Study***
***	******▪ ******	******Data***
***	******▪ ******	******Simulation***

***Outline***

##  LMODEL: 2D Lagrangian Cloud Model

*** ******LMODEL: 2D Lagrangian Cloud Model***

***Important features:***
***High resolution cloud advection tracking***
***Synchronisation of PMW Precipitation to IR clouds***
***Linear conceptual model of precipitation development***
***Linear updating states based on PMW observations***

- Time

## Conceptual Cloud Model

**Outputs:**
*R(t)* = Rainfall
**States:**
*C(t) *= Convective Potential
*Q(t)* = Cloud Precipitable Water

**Forcing:** (from cloud imagery):
*f(t)* = 	Convective Rainfall
*g(t)* = 	Accumulation of Cloud Precipitable 	Water
**Parameters:**
*a* = Stratiform rainfall fraction
*e* = Evaporation and dispersal fraction

## GOES-East TIR (Band 4) 

- GOES-East TIR (Band 4)
- Hurricane Georges,
- 17:02-17:15 GMT, 28th September 1998.

- (above) GOES-East IR image for 17:02 GMT
- (right) Forward displacement vectors, scaled to 40% of their true magnitudes

## High Resolution 2D Cloud Advection Tracking

**Correlation search**
**Replace  mesh**
**(check consistency)**
**Interpolate**
**(untangle)**

**Bellerby, *****TGARS*****, 2006**

***High Resolution 2D Cloud Advection Tracking***

## Conceptual  Cloud Model

**States:**
*C(t) *= Convective Potential
*Q(t)* = Cloud Precipitable Water
**Outputs:**
*R(t)* = Rainfall

**Forcing:** (from cloud imagery):
*f(t)* = Convective Rainfall
*g(t)* = Accumulation of Cloud Precipitable Water
**Parameters:**
*a* = Stratiform rainfall fraction
*e* = Evaporation and dispersal fraction

- In cloud free regions *(T**b**>265K) *: *R(t)=Q(t)=0*

## Model Forcing from GEO Imagery

- Derive *h(t)* - rainfall estimate based on 2D histogram match
- Marzano *et al.* *TGARS*, 2004
- Assumes monotonic relationship of input variables to rainfall
- Solve *P(R>R*)=P(X<X*,Y<Y*)*
- Yields *R*=h(X*,Y*)*
- Input variables:
*T**b**(t)  **	*(GOES Channel 4)
- Cold cloud indicates convection
***T**b**(t) =T**b**(t)-T**b**(t-****t)*
- Rapidly cooling cloud indicates convection
*h(t)* provides a normalised variable
- used as the basis for *f(t)* and *g(t)*

- Expand *f(t)* and *g(t)* as Taylor series of *h(t):*
*f(t)=**α**1**h(t)+**α**2**h(t)**2**+**α**3**h(t)**3*
*g(t)=**β**1**h(t)+ **β **2**h(t)**2**+ **β **3**h(t)**3*

## Parameter Calibration

## f(t) and g(t)

- Expand *f(t)* and *g(t)* as Taylor series of *h(t):*
*f(t) =**α**1**h(t)+**α**2**h(t)**2**+**α**3**h(t)**3*
*g(t)=**β**1**h(t)+ **β **2**h(t)**2**+ **β **3**h(t)**3*
- Parameter calibration: 	*{a, e, **α**i**, **β**i**} for i=1..3*

## Linear Dynamic System

*System State Model:*
- 	xt=Axt-1 + wt-1	where wt ~ N(0, Qt)
*Measurement Model:*
- 	Zt = Hxt + vt	where vt ~ N(0, Rt)

## LMODEL as Linear Dynamic System

- State vector:	*x**t**=(**C**t**, Q**t**)**T*
- Output vector:	*z**t**=(R**t**)*
- State model:	*x**t+1**=A**t**x**t**+w**t**	** **	**(w**t**=error)*
*	**	**	**	*
*	**	**	**	**A**t**=*
- Measurement model:	*z**t**=H**t**x**t**+v**t**	**(v**t **= error)*
- Update of state when PMW-RR observation is available

## Kalman Filter

- Prediction Equations *(t=k-1,  predict t=k)*

- Correction Equations *(t=k, when z**k** is known )*

- -- Project the state ahead

- -- Project the state error covariance ahead

- -- Measurement prediction

- -- Compute the Kalman Gain

- -- Update state with measurement zk

- -- Update the state error covariance

## Dataset

-  0.04 30-minute IR Imagery
-  0.25 30-minute PMW imagery
-  0.04 60-minute ground radar
-  Continental USA
-  June - August 2006

## Subgrid Model

- Microwave data spatial resolution: ~25km
- Rescale PMW rainfall to ~4km
- Geostationary imagery spatial resolution: ~4km

- Use 4km spatial resolution
- Avoids aliasing in tracking cloud motion at lower cloud advection speeds

## Simulation Results:	July 4, 2006

## Simulation Results:	6:45, July 4, 2006

## Simulation Results:	06:45, July 4, 2006

***Simulation Results:******	******06:45, July 4, 2006***

## Simulation Results:	07:45, July 4, 2006

***Simulation Results:******	******07:45, July 4, 2006***

## Simulation Results:	07:45, July 4, 2006

***Simulation Results:******	******07:45, July 4, 2006***

## Simulation Results:	13:45, July 5, 2006

***Simulation Results:******	******13:45, July 5, 2006***

## Simulation Results:	13:45, July 5, 2006

***Simulation Results:******	******13:45, July 5, 2006***

## Simulation Results:	14:45, July 5, 2006

***Simulation Results:******	******14:45, July 5, 2006***

## Simulation Results:	14:45, July 5, 2006

***Simulation Results:******	******14:45, July 5, 2006***

## Conclusion

*A satellite-based cloud development model is proposed.*
*The model integrates GEO-IR image and LEO PMW rainfall for real-time rainfall estimation*
*This model consists of three components:*
*A cloud tracking system to capture cloud advection vector at fine scale*
*A dynamic cloud evolution model to include forcing vectors described by GEO IR information*
*An effective updating scheme based on Kalman filter when PMW rainfall observation is available*
*Case study shows potential of providing effective rain estimation between two MW overpass period*