A Pilot Study Examining Model Derived Precipitation Efficiency for Use in
Precipitation Forecasting in the Eastern United States

James Noel
NOAA/NWS Forecast Office, Atlanta, Georgia

Jeffrey C. Dobur
NOAA/NWS Forecast Office, Atlanta, Georgia

ABSTRACT

In 1996, the Ohio River Forecast Center(OHRFC) implemented
model-derived Precipitation Efficiency to assist in evaluating the
expected spatial and temporal distribution of precipitation.
Precipitation Efficiency(PE) is derived from any atmospheric numerical
weather prediction model where precipitable water for the entire
atmospheric column and mean relative humidity for the 1000 to 700 hPa
layer are computed. The goal of this paper is to describe a technique by
which precipitation forecasting skills can be improved using PE.

The PE model-derived parameter has proven to be a useful
tool in refining the probability, timing, duration, coverage, and
intensity of precipitation. PE was shown to provide
value-added information to assist the hydrometeorologist in preparing
precipitation forecasts. Results using the National Weather Service
(NWS) Eta model show that as the value of PE increases, the percent of
precipitation occurrences also increases. In addition, results indicate
that the onset of precipitation is tied to critical PE values and
temperatures.

1. Introduction

Quantitative Precipitation Forecasts (QPF) have been an integral part of
the river and flood forecast program in the National Weather Service
(NWS) Eastern Region since 1977 (Opitz et al. 1995) and NWS-wide since
the 1990s (Fenbers 1995). Forecasts of precipitation amounts and
onset are critical to the achievement of the greatest possible hydrologic
forecast accuracy and longest possible lead-times (Georgakakus and Hudlow
1984). As part of the National Weather Service(NWS) modernization
program, a Hydrometeorological Analysis and Support (HAS) function was
created at the NWS River Forecast Centers (RFC) to maintain the QPF
process. The HAS function utilizes the 6-hour national QPF guidance from
the Hydrometeorological Prediction Center(HPC) in addition to examining
an array of meteorological model and mesoscale parameters in formulating
the 12-24-hour HAS QPF. The HAS QPF is completed twice daily
around 0000 UTC and 1200 UTC and is incorporated into the NWS River
Forecast System(NWSRFS) to produce river forecasts out to three to five
days. In addition to addressing the spatial and temporal challenges of
precipitation forecasting at RFCs, there is a continuing need to
improve the Probability of Precipitation (POP) forecasts at NWS Weather
Forecast offices (WFOs). Improved methods for precipitation forecasting
could benefit both NWS, RFCs and WFOs. One such method is presented here.

2.Background

Precipitable water (PW) and mean relative humidity (RH) have been derived
using real-time satellite estimates at the National Oceanic and
Atmospheric Administration (NOAA) National Environment, Satellite, Data
and Information Service since the early 1980s. These parameters are then
used to estimate how efficient the precipitation process is and
adjustments to rainfall estimates can be subsequently made (NESDIS)
(Scofield 1987; Vicente andScofield 1998). In 1996, the OHRFC
applied the NESDIS PW/RH method to model-derived precipitation forecasts.
In order to apply a real-time technique to model-based forecasts, there
was a need to use model-derived weather parameters to approximate
precipitation efficiency (PE). Precipitation Efficiency is defined as
the ratio of the total rainfall to the total condensation (Weisman and
Klemp 1982 and Ferrier et al. 1996). While the former can be derived from
standard numerical models, the latter is not available. Another
approximation is needed.

Several factors affect PE, including saturation ratio, production rate of
condensate, residence time of droplets in clouds, dry air entrainment,
vertical wind shear, and precipitable water (Doswell et. al. 1996). A
requisite for high rainfall intensity is a large production rate
of condensate. The rate at which the condensate is produced in a column
of cloudy air is directly proportional to air density, updraft speed,
cloud thickness, and the vertical gradient of the saturation mixing
ratio. The density and vertical gradient of the saturation mixing ratio
terms act to produce larger condensate rates in the lower part of the
cloudy column. In general, the greatest rates of condensate production
are found in the lower half of the cloudy column. The residence time
of droplets in clouds also plays a critical role in increasing PE. With
increased vertical motion and increased depth of clouds, cloud droplets
are allowed longer residence time in the cloud to grow large enough to
produce rain droplets. Vertical wind shear plays a critical role since
the shear often produces dry air entrainment, reducing PE. Finally, a
high amount of precipitable water usually increases PE. Typically,
precipitable water values range from 1.50 and greater during the warm
season (Junker 1997) to around 0.80 or more in the cool season.

For the operational hydrometeorologist, a simple relationship related to
precipitation efficiency is defined as PE = PW x RH; where RH is the
average lower tropospheric relative humidity and PW is the precipitable
water through the entire column (Scofield 1987). PW and RH are easily
obtainable from numerical weather prediction models, although
the usefulness of gridded data is limited by the model from which it is
derived (Scofield and Kusselson 1996). The PW/RH relationship indicates a
potential efficiency of the environment for producing precipitation at
specific times in the future.  Thus,this model-derived PW/RH parameter
is referred to as Precipitation Efficiency (PE) for the operational
forecast process at NWS WFOs and RFCs. It must be emphasized that this
model-derived PE is only an approximation of PE, using only PW and RH,
not actual PE, discussed earlier.

3. Data and methodology

This section discusses ways PE can be implemented into the precipitation
forecasting process,and a description of data sources and analysis
techniques used.

PE is calculated as follows:

PE = PW * (1000-700 MRH)

where PE = Precipitation Efficiency, PW = Precipitable Water through the
entire depth of the atmosphere, in inches, and 1000-700 MRH is the mean
relative humidity expressed as a decimal value. The 1000-700 hPa layer
was chosen since the deep moisture is mainly contained in the lowest 3-4
km of the atmosphere (Junker 1997).

PE can be displayed as an added volume browser customization within the
Advanced Weather Interactive Processing System (AWIPS) D2D meteorological
display software (Biere1998). Readily-available software such as General
Meteorological Data Assimilation, Analysis and Display Software Package
(GEMPAK) (desJardins 1985), NWS National Centers Translator (Ntrans),and
GEMPAK Analysis and Rendering Program (GARP) are also capable
of integrating PE into their list of precipitation forecasting
parameters. This allows for widespread use of the PE parameter in all
sectors (government, university, and private).

We examined twenty-seven cases from March 1997 through June 1998 (Table
1)  in which precipitation occurred within the OHRFC
hydrologic service area. An additional four cases occurring from
May 2001 through September 2001 were examined.

In the cases for March 1997 through June 1998, PE values were taken from
the NWS NCEP50 layer, 29-km Eta numerical weather model using GARP. PE
values were determined for each six-hour interval of the 48-hour model
forecast for six different cities in the Ohio Valley region (Table 2)
. Six-hour intervals were chosen due to the limits of
model output intervals and resolution at the time of data collection. In
addition, six-hour intervals allow you to capture model temporal and
spatial uncertainty. Furthermore, occurrence of precipitation forecasts
are usually made in six-hour intervals or greater. This data set provided
a total of 1296 forecast times and locations against which observed
precipitation could be compared. These forecast values were compared to
the monthly Local Climatological Data (LCD)hourly rainfall amounts at
each location. In addition, a warm season case from June 29th , 2001
and a transition season case from March 9th, 2002 are shown. Using the
NWS AWIPS D2D meteorological analysis software, a comparison was made
between PE and the Ohio Valley regional 0.5 reflectivity radar mosaic to
show the utility of PE.

The PE values (inches) derived from the Eta model were
compared against the percentage of observed precipitation
occurrences(PPO). The PPO was calculated by dividing the number of
occurrences by the total number of 6-hourly intervals for each location.
An occurrence is defined as when 0.01 precipitation or greater was
recorded at a particular location during any hour of the 6-hour interval.
The 6-hour intervals were grouped into three categories to account for
seasonal moisture influences driven by temperature and amount of
available moisture in the atmospheric column. To do this, a mean
temperature was calculated for all the 6-hour intervals from May 1997 to
June 1998. The first category,called the mean transition season
category, was defined as those 6-hour intervals with a mean surface
temperature within one standard deviation of the overall mean surface
temperature (54 F). The second category, called the cool season
category, was defined as those 6-hour intervals with a mean surface
temperature more than one standard deviation cooler than the overall
mean. The final category, called the warm season category,was defined
as those 6-hourly intervals with a mean surface temperature more than one
standard deviation warmer than the overall mean temperature. A linear
regression line was computed for all groups *(Figure 1)*
.

4. Results

In *Figure 1* , results show the plot of the three
categories linear regression lines. The PE values associated with the 80
PPO for the cool, transition, and warm season categories were 0.75,
1.15, and 1.90 , respectively. The PE value associated with the 50 PPO
for the cool, transition, and warm season categories were 0.50, 0.75,
and 1.30, respectively. The PE value associated with the 20 PPO for the
cool, transition, and warm season categories were 0.25, 0.30, and
0.65, respectively. These differences between cool, transition, and
warm season categories can be attributed to seasonal variations in
moisture and the random nature of scattered afternoon convection,
especially during the warm season. Correlation coefficients for the
cool, transition, and warm season of 0.93,0.92, 0.90 respectively,
provide confidence in the utility of this parameter. Based on these
results, OHRFC and WFO ATL have developed monthly
precipitation thresholds *(Figure 2)* .

PE has also shown the capability to indicate precipitation
intensity. High values of PW and instability are often collocated and
become antecedent conditions prior to the development of heavy rainfall
and flash floods (Scofield et al. 1996,2000). High values of PW can
produce high values of PE if 1000-700 MRH is high. Data from March 1997
through June 1998 show evidence that the proportion of heavier
precipitation occurrences (greater than 0.25 in a 6-hour period)
to total occurrences is larger with higher PE values *(Figure 3)*
.

In addition to providing some level of confidence in the PPO,
PE has displayed the ability to detail the axis of precipitation
development and movement. This is especially important when a
precipitation forecast is made for input into a hydrologic model.
Spatially centering the axis of precipitation is critical in projecting
which locations on certain rivers will rise, recess, or remain steady.
During times of high flow, such a prognosis in determining the axis of
precipitation can mean the difference between issuing and not issuing a
flood forecast.

Comparisons of PE to radar reflectivity during the summer of
2001 and spring of 2002 have shown the ability of PE values to highlight
the axis and areal coverage of precipitation. Spring and summer
cases were chosen to show PE performance in both a synoptic case (spring)
and a local forcing case (summer). On June 29, 2001,scattered convection
developed in an area from Indianapolis, Indiana eastward to near Dayton,
Ohio during the morning hours. Evaluating the 0000 UTC June 29th Eta
PE forecast valid at 1200 UTC overlaid with the 1130 UTC June 29th
Ohio Valley regional 0.5 reflectivity mosaic *(Figure 4)*
, it is evident that PE provided a fair
solution in portraying the areal coverage and axis of precipitation. In
examining the 1200 UTC Eta PE forecast valid at 1800 UTC overlaid with
the 1800 UTCï June 29th Ohio Valley regional 0.5reflectivity mosaic
*(Figure 5)* , PE provided an indication
of the shift in developing convection by the afternoon across the
Cumberland river valley. PE performance is illustrated in a third
example dealing with a cold front pushing across the Ohio and Tennessee
valleys on March 9th, 2002. PE 1200 UTC Eta-model values for the
1800 UTC period highlighted the impending coverage and axis of
precipitation when compared to the 0.5 reflectivity near the same time
period *(Figure 6)* .

Finally, *Figure 7*  shows how PE can be
used to better forecast precipitation than the individual components used
to derive it. The four panel image displays Eta-model derived PW,
Eta-model PE, Eta-model 1000-700 hPa mean RH, and an IR picture for 0600
UTC March 30^th 2002. The main convection was occurring across northern
Mississippi, Alabama and Georgia into eastern Tennessee. PW focused on
northern Mississippi and Alabama while 1000-700 hPa relative humidity
focused over eastern Tennessee.When combining PW/RH together, PE focused
on the area where the strong convection occurred.

5. Conclusions and Future Research

PE is not a stand-alone indicator for precipitation, but it
has been proven as a very useful tool in evaluating the spatial and
temporal distribution of precipitation. This parameter can assist in
refining probability of precipitation forecasts. When applied alongside
other traditional or useful parameters such as950-850 hPa low level jet
convergence, 300-200 hPa upper level jet divergence,950-850 hPa theta-e
advection, 850-500 hPa omega, and other indices, PE can be a more
valuable tool than relying on its foundational components individually.

Additional case studies are needed to further examine the threshold criteria
for heavy rainfall during different times of the year
and at different surface temperatures and dew points. Further study will
substantiate additional value in using the PE parameter for other regions
across the United States.

Acknowledgments.

The authors would like to thank Rod Scofield of NESDIS,
Gary Beeley from WFO ATL, Wes Junker and Charlie Chappell from
COMET training, and Dave Ondrejik from WFO CTP for ideas on improving the
parameter and manuscript and to the reviewers for their suggestions.� A
special thanks also goes to Mark Fenbers from OHRFC for the founding idea
to implement PE into a forecast mode.

Authors

James Noel currently serves as the Senior Service Hydrologist at the
National Weather Service Forecast Office (WFO) in Peachtree City,
Georgia. Prior to this, he served as a Public and Aviation Forecaster at
the WFO Peachtree City, GA, a Hydrometeorologist at the Ohio River
Forecast Center in Wilmington, Ohio,and Developmental Meteorologist at
the Techniques Development Lab at National Weather Service Headquarters
in Silver Spring, Maryland. His education includes a BS in
Meteorology with a minor in Math from Northern Illinois University (1992)
and studies inHydrology/Civil Engineering from the Ohio State University.

Jeff Dobur currently serves as a Public and Aviation Forecaster at the
National Weather Service Forecast Office (NWSFO) in Peachtree City,
Georgia. Prior to this, he has worked at the NWSFO and the Ohio River
Forecast Center in Wilmington, Ohio and with the State Climatologist in
Ohio. His educational background includes a BS in Atmospheric Science
from the Ohio State University (1997) and additional graduate course work
in Hydrology/Civil Engineering from the University of Cincinnati.

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