Stage II and III Post Processing of NEXRAD Precipitation Estimates in the Modernized Weather Service

1. INTRODUCTION

  The National Weather Service (NWS) has developed a set of post processing algorithms for
NEXRAD precipitation estimates which have been referred to as Stage II and Stage III.   Starting
in 1992, NWS River Forecast Centers (RFCs) have been using a prototype Stage II algorithm to
combine hourly Stage I radar rainfall estimates with raingage observations.  The Stage II
multisensor rainfall estimation has been upgraded to use an optimal estimation technique to
account for "local biases" in the vicinity of individual raingages in addition to the mean field bias. 
The Stage III algorithm currently used at RFCs takes the Stage II multisensor estimates from
multiple radars and mosaics them together to provide hourly estimates of rainfall which cover the
entire RFC area of responsibility.  Stage III also allows user interaction with radar and gage data
for manual quality control purposes.  Here we give a general overview of Stage II and Stage III
and plans for implementation in AWIPS.  


2. STAGE II

  The main purpose of Stage II is to provide an optimal estimate of the rainfall that has fallen
during a given clock hour using a combination radar and hourly raingage observations.   The
procedure is carried out on the Hydrologic Rainfall Analysis Project (HRAP) grid which is a polar
stereographic map projection with approximately 4 km resolution in mid-latitudes (Schaake 1989). 
The multi-sensor estimate of rainfall is computed out to a radius of 230 km 
from the radar using the hourly digital precipitation (HDP) product from the Stage 1 
Precipitation Processing System (PPS) as the only input from the radar.    

  The first step in creating this radar-gage multisensor estimate is to compute the mean bias in
the HDP product using a Kalman filter approach (Smith and Krajewski 1991) similar to that used in
Stage I.  In Stage II, however, the Kalman filter approach has been modified to incorporate the
use of a "memory span" parameter which essentially represents the length of a moving window
from which to calculate a mean field bias (Seo et al., 1997).  When the memory span parameter is
set to large values, the computed bias approaches climatology.  Conversely, smaller settings
allow the computed bias to respond quickly to the current sample bias or that of recent hours. 
Since the Stage II algorithm will be re-run several times as more gage data become available,
there will be more gages to use than were available for the bias adjustment procedure in the
Stage I PPS, and hence, a better estimate of the bias should be made.  The HDP rainfall estimate
is then multiplied by the computed bias.  

  Biases in radar-derived rainfall tend to vary non-uniformly over the radar domain both as a
function of range and rainfall type (i.e. convective vs. stratiform).  To account for this
inhomogeneity, local adjustments to the bias-adjusted radar field are made near gage
locations through an optimal estimation procedure (Seo, 1997).  In the optimal estimation 
proceedure, the weights for radar and gage values are determined such that their linear
combination minimizes the expected error variance of the analysis.  Since a gage observation
is considered to be "truth", the optimal estimate matches the gage value at the gage location
and places a heavy weigh on the gage value in the vicinity of the gage location.
The amount of weight placed on the radar estimate at a given grid point increases as a
function of distance from the nearest gage.  An example illustrating the result of Stage II
multisensor analysis is shown in Fig. 1.  For comparison, the estimates from Stage 1 PPS,
and a gage-only analysis are also shown in Fig 1.  Note how the Stage II multi-sensor
estimate incorporates many of the details in the convective portion of the heavy rainfall
which are not detected or properly resolved by the gage network. 
 
This Stage II estimate is further improved by the location of gages at far ranges and in the
stratiform portion of the storm where the radar was under-estimating actual rainfall.  When verified
with independent gage data, Stage II estimates are superior to  unadjusted Stage I estimates
(Seo, 1997).




                     Figure 1.  One hour rainfall accumulation (inches) ending at
                     0600 UTC 7 November 1996 for the Tulsa, OK WSR-88D (INX)
                     estimatedl from (a) Stage I radar only (i.e, the HDP product)
                    (b) rain gages only, (c) Stage II bias-adjusted radar only, and
                    (d) Stage II radar-raingage multisensor optimal estimate.


3. Stage III

     Stage III was created specifically for the NWS river forecast centers which need rainfall
estimates over a much larger area than covered by an individual radar.  Stage III mosaics
together Stage II estimates from multiple radars onto a subset of the national HRAP grid covering
the river forecast center area of responsibility.   In areas where two or more radars overlap, the
user has the option to use either the mean or maximum value.  An example of a Stage III rainfall
estimate is shown in Fig 2.

     
           Figure 2.  Stage III one-hour accumulation (inches) ending at 
           0600 UTC 7 October 1996 covering the Tulsa RFC forecast area.
           This composite was constructed by mosaicking Stage II
           multisensor estimates from 18 overlapping radars.  The rings
           represent the 230 km range limit of Stage II processing for each
           of these radars.

     Stage III also provides a graphical user interface to display rainfall estimates and to allow
interactive quality control of both gage and radar data.  Gage values may be manually edited or
set to missing if the data is deemed questionable.  The radar may also be edited to remove areas
contaminated by anomalous propagation or other sources of error.  After a gage value or radar
field has been edited, the Stage II algorithm is re-run and the data is re-mosaicked to provide a
manually improved Stage III estimate.


4. STAGE II AND III IN THE AWIPS ERA

     In the AWIPS era, NWS Weather Forecast Offices (WFOs), which have not had the capability
to merge radar and raingage observations to date, will also be able to run the Stage II algorithm
locally. Stage II will be perfomed at forecast offices in the WFO Hydrologic Forecasting System
(WHFS) which is currently scheduled for implementation in AWIPS Build 3, in the fall of 1997 (Roe
et al. 1998).  Once in place, the Stage II algorithm will run in an automated mode, producing
rainfall estimates for a single radar to a radius of 230 km.  

     Stage III will continue to run at RFC's in AWIPS, however the current paradigm of computing
Stage II multisensor estimates for individual radars and then mosaicking will be changed to an
approach where a single multisensor estimate is computed globally over the entire RFC domain. 
This new approach, which will still use optimal estimation,  should be computationally less
expensive, as well as make better use of the overlapping WSR-88D coverage within the RFC area
of responsibility.

     Even though Stage II will be run primarily for WFO use, and a modified Stage III will be run for
RFC wide precipitation estimation, parallel improvements will be made to both Stage II and Stage
III.   For example, an option to use a double optimal estimation procedure (Seo, 1997) has already
been implemented in the software so that precipitation estimates from satellite can eventually be
incorporated into the multi-sensor precipitation estimate.  The incorporation of satellite-derived
precipitation estimates will improve Stage II and Stage III estimates where there is missing data or
radar beam blockage by terrain, and in other areas where radar estimates perform poorly such as
at long ranges from the radar.

     Satellite will also be used for quality control of Stage II/III precipitation estimates.   
A prototype automated quality control procedure to check for areas which may be contaminated by 
anomalous propagation has also been developed and tested for Stage II (Fiore et al. 1986).  This simple
algorithm looks for areas that are likely to be cloud-free by computing the difference between the
infrared satellite-derived brightness temperature and the surface temperature.  Areas where the
difference between these two fields is greater than an adaptable threshold are considered cloud
free, and any radar measured rainfall is considered to be caused by anomalous propagation of the
radar beam.   While the prototype algorithm which functioned using GOES 7 data at a 40 km
resolution was not used operationally, an improved version of the algorithm using 4 km GOES 8 /
GOES 9 data will be considered in the AWIPS era. 
 
  
5. References

Fiore. J.V., Farnsworth, R.K. and Huffman. G.J.,  1986: Quality Control of 
Radar-Rainfall Data with VISSR Satellite Data, Preprints of the 23rd Conference 
on Radar Meteorology, American Meteorological Society, Snowmass, Colorado. 
September 1986 pp. JP15-JP18.     

Schaake, J., 1989: Importance of the HRAP grid for operational hydrology.  
Preprints, U.S/People's Republic of China Flood Forecasting Symp., Portland, OR,
NOAA/NWS, 331-355.

Seo, D.J., 1997: Optimal Estimation of Rainfall Fields Using Radar Rainfall and
Rain Gage Data., (Submitted to Journal of Hydrology)

____,R. Fulton, and J. Breidenbach, 1997: Final Report, Interagency Memorandum of
Understanding among the NEXRAD Program, WSR-88D Operational Support Facility, and
the NWS/OH Hydrologic Research Laboratory. [Available from NWS/OH/HRL, 1325 East-
West Hwy., W/OH1 Silver Spring, MD 20910]

Smith,J.A., and W.F. Krajewski, 1991: Estimation of the Mean Field Bias of Radar
Rainfall Estimates. J. Appl. Meteor., 30, 397-412.

Roe, J., M. Glaudemans, C. Gobs, P. Taylor, and J. Zimmerman, Special Symposium
on Hydrology, Pheonix, AZ, Amer. Meteor. Soc., Jan 11-16, 1998.

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