# Presentation: 020695

## Satellite and Ground-based Estimates of Instantaneous Rainfall Intensities

**Satellite and Ground-based Estimates of Instantaneous Rainfall Intensities**

**Eyal Amitai**
***George Mason University, Fairfax, Virginia & ***
***NASA Goddard Space Flight Center, Greenbelt, Maryland***
- Eyal.E.Amitai@nasa.gov
**&**
**Xavier Llort**
***GRAHI/Universitat Politecnica de Catalunya, Barcelona, Spain***

***3******rd****** Int’l TRMM Science Conference, Las Vegas, NV, 4-8 February 2008***

## Estimates of Instantaneous Rain Rate (R) and

**Estimates of Instantaneous Rain Rate (*****R*****) and**
** ****Distribution of *****R***** are significant ...**

**Hydrological applications **
**	****flood forecasting**
**	****runoff accommodation****	**
**	****erosion prediction**
**	****urban hydrological studies**
**Fraction of rainfall likely to be available for crop growth**
**Radio wave propagation; Design of communication systems operating at microwave signals**

- Rain Intensity Sensing Wipers
-  Speed automatically varies depending on rainfall intensity

**However, efforts to evaluate quantitative *****R***** estimates/forecasts, as opposed to rainfall-accumulated amounts, are surprisingly rare**

**Notes:**
Information on surface rain rate is important in many fields. The distribution of instantaneous rain rates (R) is of great interest in many hydrological applications such as flood forecasting (which depends on an accurate representation of the excess rainfall that does not infiltrate the soil and controlled by R). The design of communication systems operating at microwave signals depends on our knowledge of R distribution.  
And even today we have some car models with rain intensity sensors to control automatically the speed of the wipers... 
but this is to get your attention; not really a reason for why R estimates are so important.

For the last 10 years R can be obtained from spaceborne radar observation (TRMM PR).
How accurate are these estimates?
In this presentation I’ll concentrate on the evaluation of rain rate estimates from the TRMM PR using ground reference data (GV).
I’ll present some results, but emphasize on opportunities & challenges that this effort provides..
----

The evaluation of instantaneous rainfall products and rain rate estimates from space is quite a challenge.  
Scatter plots of pixel-by-pixel comparisons of space-based R estimates with ground-based radar R estimates are extremely noisy because of sample volume discrepancies, timing and navigation mismatches, and uncertainties in the observed-radar reflectivity rain-rate Ze-R relations.
Furthermore, comparisons of rainfall over daily, weekly or even monthly time scales suffer from the temporal sampling errors of the satellite where the revisit time is on the order of hours or days. Consequently, an alternative approach of comparing space-based radar pdfs with pdfs derived from co-located ground-based radar observations is attractive for evaluating satellite-based precipitation products, such as those from TRMM precipitation radar (PR).

## TRMM PR-WSR88D (GV) Rain Rate Comparison

*Comparison of rain rate fields and their associated pdfs for the February 17, 1998 TRMM overpass over central Fl: PR V5 (upper left), PR V6 (upper right), GV at approximately 1-min before the overpass (lower left) and their corresponding pdfs (lower right).  Is PR V5 better than V6 as suggested by the GV estimates? *(Amitai et al. 2006, *MZ*)

***TRMM PR-WSR88D (GV) Rain Rate Comparison***

**Notes:**
Here is a example based on one TRMM overpass (O/P)....
TRMM...
PR V6 includes modification (hopefully improvements) to the Z attenuation correction algorithm
The pdfs are based on data in a common grid & resolution

Surprisingly, GV estimates agree better with PR V5 than with PR V6
Is PR V5 better than V6?  Quite disturbing news...  
Is this is the general case?

## TRMM PR-GV Comparison  -Melbourne, FL

- 2A25 V6/2A53 V5: **0.93**  (209 OP)
- 2A25 V5/2A53 V5: **1.03**  (209 OP)

**Advantage of PDF comparisons**
** ****Free of large uncertainties associated with pixel by pixel comparisons**
-   **Free of  satellite temporal sampling errors associated with the monthly products**
** ****PDF of rain *****volume***** by *****R***** are less sensitive to instrument thresholds and with a direct hydrological significance**

** ****How accurate is the GV PDF?**
**Are TRMM PR curves represent the general case?**

***TRMM PR-GV Comparison  -Melbourne, FL***

**Notes:**
Distribution of rain volume by rain rate for the Melbourne, Fl., WSR-88D (GV) and TRMM PR datasets based on 209 rainy overpasses during 1998-2005 and co-located GV data within 15-100 km of Melbourne. 

The reduction in rain amount (PR V6-V5) was observed in other locations (e.g. Cyprus) as well.  Is this the general case over coast/land?
PR(V6)-GV differences between the maxima of the pdfs (~7 dBR) are very large for hydrological applications.  

Which of the curves better represents the true distribution of R and whether the answer applies only to the data presented here or represents the general case?
This presentation is not aimed at providing answers to these questions, but rather presents challenges and opportunities

## Sensitivity of the PDFs to Different Gauge Adjusted Schemes 

***Sensitivity of the PDFs to Different Gauge Adjusted Schemes****** ***

- Uncertainties in derived PDFs are likely to be smaller using gauge rates (I.e., WPMM) compared to those based on applying an adjusted power law

**Dense gauge networks required for better estimation of the rain rate distribution at the scale of a radar pixel.**

**C**

- (Amitai et al. 2006, *JTECH,* 23, 1492–1505)

**Notes:**
Sensitivity of the radar pdfs to ...
In general, the pdfs based on different gauge adjusted power low Z-R are very sensitive to the selected power low parameters...
We can also match the distribution of the radar reflectivities to the distribution of the gauge rates to have PMM Z-R relations, in which by definition upon application of such Z-R relations the pdf of the radar rain rates are identical to the pdf of the gauge rates (for the pixels over the gauges).  However, the pdf of the gauge rates not necessarily represent the distribution of R at the scale of a radar pixel.  We test the sensitivity of the gauge pdf to different time periods in which we averaged the gauge rates, simulating different domain sizes.

## TRMM PR-GV Comparison  -Melbourne, FL

***GV V4: Gauge adjusted Z=AR******1.4***
***GV V5:  WPMM Z-R***

***TRMM PR-GV Comparison  -Melbourne, FL***

**Which curve better represents the truth?**
- While GV V4-V5 similarities may increase our confidence that major PR-GV differences are due to satellite algorithm errors, determination of the accuracy of the GV pdf is still required

**Notes:**
For 1998 we had also the previous GV version (V4).  The pdfs are based on 24 o/p.

The GV R estimates are taken from TRMM standard product 2A-53 version 4 (Power law Z-R; V4) and version 5 (WPMM Z-R; V5) with 2x2 km2 pixel resolution, and are averaged to 4x4 km2.
The PR R estimates are taken from TRMM standard product 2A-25 version 5 and version 6 averaged to 4x4 km2.
The PR/GV rain volume ratios are indicated in the legend.
All PR figures presented here are based on the near-surface R products.

## A Framework for Statistical & Physical Verification

**Comparing PDFs after rain type classification**
**Combining**
***Hydrological***** validation approach that uses **
***statistical***** properties of precipitation **
**with**
***Meteorological***** approach that uses **
***physical *****properties of precipitation**
**Classification will allow **
**evaluation of the satellite algorithms under different conditions (*****Physical validation*****); **
**extrapolation of uncertainties to regions not covered by validation data sets, but characterized by same rain types (*****Globalization*****)**

- Amitai et al. 2005: Accuracy verification of spaceborne radar estimates of rain rate.  *The Royal Meteorological Society Atmospheric Science Letters* (ASL), 6, 2-6.

***A ******Framework for ******Statistical & Physical Verification***
*** ******of Space-borne Radar Estimates of Rainfall***

**Notes:**
The pdf comparisons are part of a new framework for global verification of space-based estimates of precipitation. The framework includes the use of pdf comparisons before and after rain type classification.  The classification allows for  ...

The figure presents the pdf comparisons for the14 rain types of Amitai (1999) classification scheme using data from all 105 overpasses.  The classification scheme is applied to the PR data set, while the GV data set is classified based on PR-GV matched-pixels.  For most rain types, the PR pdfs are shifted toward low R relative to the GV pdfs (i.e., PR overestimates probabilities of low R, and underestimates probabilities of high R).  PR overestimation at high R (i.e., PR pdf shifted toward high R relative to the GV pdf) is found only in three of the rain types (types # 2, 4 and 7).  In these rain types the echo top heights usually exceeded 9 km, always exceeded 5-km, a bright-band signature did not exist (i.e., very convective cells), but with weak horizontal gradients.  Weak horizontal gradients suggest that partial beam filling is not an issue.  On the other hand, in heavy convection, a significant contribution to the total attenuation can arise from mixed phase particles; underestimating the fraction of the attenuation caused by the mixed phase region and overestimating the attenuation caused by the cloud water can yield overestimates of the near-surface rain.   This was corrected in version 6 of the PR algorithm 2A-25 ((next slide).

## Comparison of NSSL Q2 and TRMM PR near surface rain rates using the original resolution over a portion of Tile 7 (green square in right panel).  

**Utilizing U.S. national network (Q2)**
**to identify and resolve significant discrepancies: When, Where & Why large discrepancies exist**

*Comparison of NSSL Q2 and TRMM PR near surface rain rates using the original resolution over a portion of Tile 7 (green square in right panel).  *

***NOAA Q2**** *

***TRMM PR***

*May 12, 2007 @ 22:30 UT*

**Notes:**
Utilizing the National Network for statistical verification of TRMM estimates of Ze & R

 will significantly increase sample size of data available for verification of instantaneous satellite rainfall estimates (at central FL 2 rainy TRMM O/P per month)
 will permit classification by rain type, topography, geographic region, climate regime, season, weather extreme, distance from the nadir-line
 will allow to identify and resolve significant discrepancies: When, Where & Why large discrepancies exist
 potentially to generalize the results; to predict algorithm performance globally under similar conditions

TRMM flew over this area exactly at the same minute of the Q2 product

## TRMM PR-NOAA Q2 Comparison

*Distribution of rain volume by rain rate (R) for TRMM PR V6 near surface R and NOAA Q2. *
*Data from TRMM orbit 54068 over Tile 7 and Q2 rain rates within the PR swath on May 12, 2007 @22:30*

***TRMM PR-NOAA Q2 Comparison***

**Notes:**
All PR and Q2 rainy values within the PR swath regardless whether both observed rain at the same pixel are used to generate the pdfs.  Data are matched-up into a common grid and resolution of 0.04 deg pixel. 
The number of rainy pixels and their averaged rain rate are indicated in the legend.

## May 2007: 34 rainy overpasses

*May 2007: 34 rainy overpasses*
**(with more PR rainy pixels than from Florida TRMM GV site during the entire mission)**

**Are Rain Rates Distributed Log-normal?**
**Our expectation for a log-normal distribution of rain rate *****occurrence *****does not mean we shall expect a log-normal *****volumetric***** pdf.**

**Notes:**
Distribution of rain volume by rain rate (R) for TRMM PR V6 near surface R and NOAA Q2.  
Data from 34 TRMM orbits during May 2007 and co-located Q2 rain rates during the overpasses.
All PR and Q2 rainy values within the PR swath regardless whether both observed rain at the same pixel are taken to generate the pdfs.  Data are matched-up into a common grid and resolution of 0.04o pixel. 
The number of rainy pixels and their averaged rain rate are indicated in the legend.

## Hurricane Humberto

*TRMM PR*
*09:10Z*
*Image from trmm.gsfc.nasa.gov*

*Hurricane Humberto*
*September 13, 2007*

*NOAA Q2*
*09:10Z *
*Image from www.nmq.nssl.noaa.gov*

## Hurricane Humberto: September 13, 2007

*Distribution of rain volume by rain rate (R) for TRMM PR V6 near surface R and NOAA Q2.  *
*Data from TRMM orbit 55992 over Tile 6 at 09:10Z *
*and Q2 rain rates within the PR swath on September 13, 2007 at 09:10Z.*

**2% of PR rainy pixels (area) have no Q2 rain; they contribute to 0.4% of the total PR rain amount.**
** ****11% of Q2 rainy pixels (area) have no PR rain; they contribute to 0.6% of the total Q2 rain amount.**

*Hurricane Humberto: September 13, 2007*

**Notes:**
Distribution of rain volume by rain rate (R) for TRMM PR V6 near surface R and NOAA Q2.  
Data from TRMM orbit 55992 over Tile 6 at 09:10Z 
and Q2 rain rates within the PR swath on September 13, 2007 at 09:10Z.

All PR and Q2 rainy values within the PR swath regardless whether both observed rain at the same pixel are used to generate the pdfs.  
Data are matched-up into a common grid and resolution of 0.04 deg pixel. 
The number of rainy pixels and their averaged rain rate are indicated in the legend.
Note, dBR=10 log(R/ 1 mm h-1) | [R]=[mm h-1].

## Hurricane Humberto:  September 13, 2007

*Q2 pdfs during one hour centered at the time of the overpass (9:10Z) [right panel] compared to a sharp drop*
* **in the Q2-PR pixel-by-pixel scatter-plot correlation (9:10Z=Mintue 550) [left pane]*

*Hurricane Humberto:  September 13, 2007*
**Advantage of pdf comparison over scatterplots**

- The pdfs become even more similar (stable) when including Q2 data outside the PR swath (not shown) since some rain features of the hurricane system moves in/out of the swath within the hour

## Gauge correction of Q2 radar rain rate estimates

*The pdf before and after gauge correction for the May 2007 and Hurricane Humberto case studies*

*Gauge correction of Q2 radar rain rate estimates*

**Notes:**
Note: PR pdf, pixel numbers and mean rain rate may change upon using Q2 gauge corrected data.  
See report for more information.

## Challenges & Opportunities

***Challenges & Opportunities***
**toward determining and reducing uncertainties in GV PDFs**
** ****(and thereby space-based pdf estimates)**
** **

**1. Understanding the underlying processes that lead to uncertainties**
**2. Establishing rain type classification scheme in which the GV pdfs for a given type are stable in time and space --> evaluate satellite algorithms under different conditions; extrapolate uncertainties in satellite estimates to non-GV monitored regions**
**3. Utilizing dense gauge networks**
**4. Keeping the ground radar calibration stable.  **
**(A 1-dB undetected reflectivity shift, that is quite common, corresponds to 15%-25% *****R***** uncertainty)**
**5. QC, QC, QC! **
**6. Improving *****Z******e******-R***** relations for *****instantaneous***** products**
**7. Improving space/ground volume-matching procedures**
**8. Establishing uncertainty values for the satellite estimates independently of the reference (GV) products**

**Notes:**
The list is limited to non-polarimetric radar observations adjusted to gauge measurements.  However, dual-polarization radars are important for the validation effort, in particular, for estimation of the dsd, which in turn is very important for physical validation of the satellite algorithms.  They are also important for overcoming radar calibration issues (point c) and for rain type classification that is required for improving Ze-R relations for instantaneous rainfall products (point e).

Non-polarimetric radar obs adjusted to gauge measurements

1. Establishing rain type classification scheme in which the GV pdfs of R for a given type are stable in time and space (location-to-location) --> extrapolating uncertainties in satellite estimates to non-GV monitored regions. 

2. Utilizing dense gauge networks for determining and reducing uncertainties in the GV radar pdf estimates.

3. Keeping the ground radar calibration stable.  A 1-dB undetected reflectivity shift (that is quite common) corresponds to 15%-25% R uncertainty.

4. Ensuring the quality of radar and gauge datasets.  When adjusting the radar estimates to the gauges the most significant decision to make could easily be which gauges to use 

5. Improving Ze-R relations for instantaneous rainfall products.

6. Improving volume-matching procedures between the ground and the space observations

7. Establishing uncertainty values for the satellite rainfall estimates based on the satellite algorithms and their assumptions independently of the reference (GV) products.

## For more information...

***For more information...***

- Amitai E., X. Llort, and D. Sempere-Torres, 2006: **Opportunities and challenges for evaluating precipitation estimates during GPM mission**.  *Meteorol. Zeitschrift, *15(5), 551-557.
- Amitai E., D. A. Marks, D. B. Wolff, D. S. Silberstein, B. L. Fisher, and J. Pippitt, 2006: **Evaluation of radar rainfall products: Lessons learned from the NASA TRMM validation program in Florida.** *J. Atmos. Ocean. Technol., *23, 1492–1505.
- Amitai E., L. Liao, X. Llort, and R. Meneghini, 2005: **Accuracy verification of spaceborne radar estimates of rain rate. ***The Royal Meteorological Society Atmospheric Science Letters (ASL),* **6**, 2-6.
- Wolff D. B., D. A. Marks, E. Amitai, D. S. Silberstein, B. L. Fisher, A. Tokay, J. Wang, and J. L. Pippitt, 2005: **Ground validation for the Tropical Rainfall Measuring Mission (TRMM).**  *J. Atmos. Ocean. Technol.* **22**, 365-380.
- Amitai E., J. A. Nystuen, L. Liao, R. Meneghini, and E. Morin, 2004: **Uniting space, ground and underwater measurements for improved estimates of rain rate.**  *IEEE Geoscience and Remote Sensing Letters,* 1(2), 35-38.

***...******ask Eyal for a copy***
**Eyal.E.Amitai@nasa.gov**

## Backup slides

***Backup slides***

## Distribution of rain volume by rain rate for the Melbourne, Fl., WSR-88D (GV) and TRMM PR datasets based on 313 rainy overpasses during 1998-2006 and co-located GV data within 15-100 km of Melbourne. 

*Distribution of rain volume by rain rate for the Melbourne, Fl., WSR-88D (GV) and TRMM PR datasets based on 313 rainy overpasses during 1998-2006 and co-located GV data within 15-100 km of Melbourne.** *

- 2A25 V6/2A53 V5: **0.95**  (313 OP)
- 2A25 V5/2A53 V5: **1.03**  (209 OP)

***TRMM PR-GV PDF(R) Comparison  -Melbourne, FL***

**Notes:**
PR(V6)-GV differences between the maxima of the pdfs (~7 dBR) are very large for hydrological applications.  
Again, GV estimates agreed better with PR V5 than with PR V6, for most rain rates.  

## Utilizing the 

**Utilizing the **
**National Network for statistical verification of TRMM estimates of *****Z******e***** & *****R***
-  will significantly increase **sample size** of data available for verification of instantaneous satellite rainfall estimates (at central FL 2 rainy TRMM O/P per month)
-  will permit **classification** by rain type, topography, geographic region, climate regime, season, weather extreme, distance from the nadir-line
-  to identify and resolve significant discrepancies:
***When*****, *****Where***** & *****Why*** large discrepancies exist
-  potentially to generalize the results; to **predict algorithm performance** globally under similar conditions

## Hurricane Humberto: September 13, 2007

*0.04**o **x 0.04**o*

*Hurricane Humberto: September 13, 2007*
*TRMM PR 09:10Z*

*PR original resolution*

## Hurricane Humberto: September 13, 2007

*Hurricane Humberto: September 13, 2007*
*Before and After regridding PR original data*

*The pdfs for the PR images in the previous slide (blue) and for Q2 (red)*
- The smoothing of the precipitation field due to regridding, and how this affects the pdf is taken into consideration when comparing PR-Q2 products.
-  For this event, regridding decreases the PR rain amount by 0.5% and increases the rainy area by 8%
- (rainy area increases by additional 11% according to Q2; see Slide 10).

## May 2007: Before and After regridding PR original data

*May 2007: **Before and After regridding PR original data*

- The smoothing of the precipitation field due to regridding, and how this affects the pdf is taken into consideration when comparing PR-Q2 products.
-  For this event, regridding decreases the PR rain amount by 0.9% and increases the rainy area by 31%

## Utilizing the National Network for Statistical Verification of Satellite Rainfall Estimates

**Utilizing the National Network for Statistical Verification of Satellite Rainfall Estimates**

**PI: Eyal Amitai (George Mason University)**
**U.S. Collaborators: Steven Vasiloff (NOAA/NSSL), David Kitzmiller (NOAA/OHD), Robert Meneghini (NASA/GSFC)**
**Foreign Collaborators: Daniel Sempere-Torres (UPC, Spain), Xavier Llort (UPC, Spain)**

**NASA Grant NNX07AK47G (2007-2010)**

*TRMM PR  09:10Z*

- Hurricane Humberto: September 13, 2007

*NOAA Q2  09:10Z** *

** ****Evaluating the potential use of existing U.S. national network of radars and rain gauges for statistical verification of TRMM and future GPM estimates**
** ****Identifying and resolving significant discrepancies between the U.S. national network and satellite estimates: When, Where and Why**

**Notes:**
Information on surface rain rate is important in many fields. The distribution of instantaneous rain rates (R) is of great interest in many hydrological applications such as flood forecasting (which depends on an accurate representation of the excess rainfall--driven by R--that does not infiltrate the soil).

For the last 10 years probability distribution functions (pdf) of R can be obtained from spaceborne radar observation (TRMM PR).
How accurate are they?
----

Recent effort to evaluate such pdfs by comparing to ground observations reveals large discrepancies

The evaluation of instantaneous rainfall products and rain rate estimates from space is quite a challenge.  Scatter plots of pixel-by-pixel comparisons of space-based R estimates with ground-based radar R estimates are extremely noisy because of sample volume discrepancies, timing and navigation mismatches, and uncertainties in the observed-radar reflectivity rain-rate Ze-R relations.  Furthermore, comparisons of rainfall over daily, weekly or even monthly time scales suffer from the temporal sampling errors of the satellite where the revisit time is on the order of hours or days (e.g., the Tropical Rainfall Measuring Mission [TRMM] satellite, the future Global Precipitation Measurement [GPM] mission satellite).  Consequently, an alternative approach of comparing space-based radar pdfs with pdfs derived from co-located ground-based radar observations is attractive for evaluating satellite-based precipitation products, such as those from TRMM precipitation radar (PR).

## Utilizing the National Network for Statistical Verification of Satellite Rainfall Estimates

**Utilizing the National Network for Statistical Verification of Satellite Rainfall Estimates**

**NASA Grant NNX07AK47G (2007-2010)**

*Comparison of NSSL Q2 and TRMM PR near surface rain rates using the original resolution over a portion of Tile 7 (green square in lower right panel).  *

***NOAA Q2**** *

***TRMM PR***

*May 12, 2007 @ 22:30 UT*

**Notes:**
Information on surface rain rate is important in many fields. The distribution of instantaneous rain rates (R) is of great interest in many hydrological applications such as flood forecasting (which depends on an accurate representation of the excess rainfall--driven by R--that does not infiltrate the soil).

For the last 10 years probability distribution functions (pdf) of R can be obtained from spaceborne radar observation (TRMM PR).
How accurate are they?
----

Recent effort to evaluate such pdfs by comparing to ground observations reveals large discrepancies

The evaluation of instantaneous rainfall products and rain rate estimates from space is quite a challenge.  Scatter plots of pixel-by-pixel comparisons of space-based R estimates with ground-based radar R estimates are extremely noisy because of sample volume discrepancies, timing and navigation mismatches, and uncertainties in the observed-radar reflectivity rain-rate Ze-R relations.  Furthermore, comparisons of rainfall over daily, weekly or even monthly time scales suffer from the temporal sampling errors of the satellite where the revisit time is on the order of hours or days (e.g., the Tropical Rainfall Measuring Mission [TRMM] satellite, the future Global Precipitation Measurement [GPM] mission satellite).  Consequently, an alternative approach of comparing space-based radar pdfs with pdfs derived from co-located ground-based radar observations is attractive for evaluating satellite-based precipitation products, such as those from TRMM precipitation radar (PR).

## Estimates of Instantaneous Rain Rate (R) and

**Estimates of Instantaneous Rain Rate (*****R*****) and**
** ****Distribution of *****R***** are significant ...**

**Hydrological applications **
**	****flood forecasting**
**	****runoff accommodation****	**
**	****erosion prediction**
**	****urban hydrological studies**
**Fraction of rainfall likely to be available for crop growth**
**Radio wave propagation; Design of communication systems operating at microwave signals**

**Notes:**
Information on surface rain rate is important in many fields. The distribution of instantaneous rain rates (R) is of great interest in many hydrological applications such as flood forecasting (which depends on an accurate representation of the excess rainfall--driven by R--that does not infiltrate the soil).

For the last 10 years probability distribution functions (pdf) of R can be obtained from spaceborne radar observation (TRMM PR).
How accurate are they?
----

Recent effort to evaluate such pdfs by comparing to ground observations reveals large discrepancies

The evaluation of instantaneous rainfall products and rain rate estimates from space is quite a challenge.  Scatter plots of pixel-by-pixel comparisons of space-based R estimates with ground-based radar R estimates are extremely noisy because of sample volume discrepancies, timing and navigation mismatches, and uncertainties in the observed-radar reflectivity rain-rate Ze-R relations.  Furthermore, comparisons of rainfall over daily, weekly or even monthly time scales suffer from the temporal sampling errors of the satellite where the revisit time is on the order of hours or days (e.g., the Tropical Rainfall Measuring Mission [TRMM] satellite, the future Global Precipitation Measurement [GPM] mission satellite).  Consequently, an alternative approach of comparing space-based radar pdfs with pdfs derived from co-located ground-based radar observations is attractive for evaluating satellite-based precipitation products, such as those from TRMM precipitation radar (PR).