Polar Algorithm 

Note: all numerical values given in this
guide are Default Adaptable Parameters (DAP). 
1.0 
Data Quality 

Functional description 

The algorithm, DATA QUALITY, removes
bad data due to residual ground clutter and anomalous propagation (AP).
There are 2 modes of checking for AP. The first, "Reflectivity_mode," requires
a reflectivity vertical continuity test using the hybrid scan. If there
is a decrease in reflectivity from the first to the second tilt IN
THE HYBRID SCAN of more than 90%, then the reflectivity is flagged
as missing. It is important to keep in mind that the hybrid scan is
used (as opposed to the lowest 2 elevation angles); this test MAY use
elevation angles of 2.4 deg and 3.3 deg to perform this test. (SV comment:
seems like this test could overdo removal since there very well could
be a large decrease from 2.4 to 3.3 deg, even from .4 to 2.2 deg; only
1st 2 tilts should be used in stratiform rain/snow).
The second "Velocity_mode" checks for nearzero velocity.
The gate spacing is 250 m for velocity and 1 km for reflectivity. A
4bin average velocity is computed, each having one corresponding reflectivity
value. If that average velocity is less than 2.5 m s1, then the reflectivity
is set to missing.
Either one or both modes can be selected. 

return to top 
2.0 
Convective/Stratiform
Precipitation Typing and Rain Rate Computation 

Functional description 

The algorithm, CONVECTIVE/STRATIFORM
PRECIPITATION TYPING and rain rate computation, examines a volume of
reflectivity to determine what precipitation type and precipitation
rates are occurring at each range bin. 
2.1 
Convective vs. stratiform 

First, convection is checked for at all
elevation angles. The check for convection is based on reflectivity
thresholds and bright band vertical depth dimensions. If the reflectivity
in any bin for a vertical column of data bins is greater than 50 dBZ
then precipitation is tagged as "convective," unless that
bin is within the bright band layer.
If the upper reflectivity value is not exceeded, then the highest
bin in the vertical column with reflectivity above 30 dBZ is found.
If the second threshold value is found at or above the 10 deg C height,
then the precipitation is tagged "convective." 
2.2 
Checking for other precipitation types 

If the initial identification is that
stratiform is present, i.e., not convective, then further typing is
done. If the hybrid tilt reflectivity is located below the bright band
layer, then the precipitation is tagged "good rain." If the
hybrid tilt reflectivity is located within 1200 m distance above the
bright band, then the precipitation is tagged as "good snow." (Click
here for an example how good rain and snow are determined.)
Reflectivity measured within the bright band and at heights greater
than 1200 m above the bright band top are deemed "bad rain" and "bad
snow" respectively. 
2.3 
Rain rates 

The hybrid bin precipitation rates for convective
rain, good stratiform rain, or good snow are determined using appropriate
ZR or ZS relationships (see Symbolic Formulas). Precipitation rates
associated with "good rain" and "good snow" are used
in conjunction with satellite IR data to determine final precipitation
rates (see Section xx). 

return to top 
3.0 
Bright Band Detection 

Functional Description 

Section 2 above uses
output from the bright band detection algorithm, which identifies a
horizontallyuniform layer of contaminated reflectivity due to melting
hydrometeors (see linked document). 
3.1 
Initialization 

Check to see if there are previous BB
detections. 
3.2 
Processing a volume scan 

Only data within the range interval 1030
km (for VCP 11) or 2030 km (for VCP 21) are examined to determine the
existence of a bright band. For each grid point, columns of reflectivity
at each azimuth and range location are checked to see if there is sufficient
data to determine the vertical extent of a potential bright band. If
there is terrain blockage and the hybrid scan tilt angle is greater
than or equal to 2.4 deg, then data in the vertical column are not used.
The number of vertical columns used to locate the bright band is tracked
by the variable "good_points." If there is an insufficient
number of "good_points," there is no test for a bright band.
The column is then searched for the maximum reflectivity. If the
maximum is greater than 30 dBZ, the data value and location are stored.
The column reflectivity values are normalized by dividing each reflectivity
by its column maximum. The heights at which normalized reflectivity
decrease by 20%, above and below the maximum value, are then the bright
band top and bottom, respectively. The tops and bottoms for each column
are averaged and the standard deviation of the tops is calculated. 
3.3 
Checking for a bright band 

The existence of a bright band is determined
using two criteria. The first is the ratio of points with reflectivity
greater than the threshold to the value of "good_points." The
second is the standard deviation of the bright band tops found above.
The existence of a bright band is declared if the ratio is greater than
10% and the standard deviation is less than 500 m.
If a bright band is detected then the top and bottom heights are
averaged with the heights from the previous 30 minutes. These data
are then used in the PRECIP TYPING algorithm. 

return to top 
RadarOnly
Accumulation Algorithm 

Overview 

(Note: Several of these routines are
also used in the multisensor algorithm.)
Now that the precip rates and types have been determined in polar
coordinates, they are now combined on a common grid to produce accumulations.
Gridding also allows rates to be compared with satellite data to verify
that there is really precip occurring and to be compared to lightning
data to determine if convection is occurring. Development of additional
tools is underway. 
4.0 
Create Radar Coverage
Maps 

Functional Description 

This routine determines which radar has
the lowest hybrid scan bin (HSB) height for each grid point. A look
up table contains the names of radars associated with each grid point.
Some grid points may have 2 or more associated radars. Each radar is
checked for availability. The name of the available radar having the
lowest (HSB) height is saved for that grid point. If the lowest HSB
is greater than 5000 m AGL, there will be no radar coverage for that
grid point. The radar coverage map shows each grid point color coded
according to which radar has the lowest HSB height. 
5.0 
Remap Rates and Types
to Cartesian Grid 

Functional Description 

Polar data for each radar with the lowest
hybrid scan bin (HSB) height are remapped to a Cartesian grid. The remapped
data are hybrid scan reflectivity, rain rate, and precipitation type.
The data nearest to a grid point is assigned to that grid point. 

return to top 
6.0 
Mosaic Radar Data 

Functional Description 

Remapped Cartesian data for each radar
are combined for the entire QPESUMS domain. 
7.0 
Clear Air QC 

Functional Description 

Model surface and satellite cloud top
temperatures are used to eliminate nonprecipitation echoes. The temperature
difference is calculated. If the difference is less than 8 C (adaptable),
then no clouds are believed to be present and the rate is set to zero. 

return to top 
8.0 
Convective Precipitation
Check Using Lightning Data 

Functional Description 

If lightning occurs at a grid cell within
a 5 minute period, the precip type at that grid cell is assigned as
convective and the rate is recalculated. Lightning data for the QPESUMS
grid are computed as a flash density (e.g., strikes in 5 minutes at
each grid point). Lightning data for the previous 15 minutes are searched.
A 100 mm hr^{1} cap is placed on convective rain rates. 
9.0 
Precipitation Accumulation 

Functional Description 

There are various accumulation periods.
The frequency of updating the accumulations depends on the period. One
hour accumulations are updated every 5 minutes. Three, six, and 24 hour
accumulations are updated once an hour. The 72 hour accumulation is
updated every 24 hours. 

return to top 
MultiSensor
Accumulation Algorithm 
10.0 
Satellite QPE 

Functional Description 

This algorithm is designed to provide
rain and snowfall (SWE) based on satellite IR data alone. Precipitation
rates are derived from the latest satellite IR data using a climatological
regression curve that relates IR temperatures and precipitation rates.
This algorithm is used primarily for development purposes. 
10.1 
Reading in data 

Satellite data are read in and scaled
by multiplying each value by 10. A QC check is done whereby values not
between 163K and 330K are set to missing.

10.2 
Remapping 

The satellite grid resolution is coarser
than the QPESUMS grid. The satellite cloudtop temps are sampled on
the common QPESUMS grid using a nearest neighbor approach. 
10.3 
Reprojection 

Radar data are reprojected in a series
of calculations that determine new spacing intervals and dimensions
for the QPESUMS grid. The reprojection is used in the output of the
NIDS formatted files which use different dimensions than the QPESUMS
grid. If new satellite data are found within a 15 minute time window,
NIDS and binary files of precip accumulations are output as specified
in a configuration file. 
10.4 
Precipitation derived from climatological
regression 

Rain rates are calculated from the IR
temperatures. The exponential curve or equation used was derived from > 160
hours of data consisting of radarderived rain rates and cloudtop temperatures.
Using precipitation type flags, a rain regression coefficient is used
for rain (good, bad, or convective) and convection and a snow coefficient
is used in snow (good or bad). 
10.5 
Accumulation 

Precipitation accumulations are produced
for the different time periods (see Section 9). 

return to top 
11.0 
MultiSensor QPE 

Functional Description 

This algorithm prepares data points for
use in a realtime regression calculation between satellite cloud top
temperatures and good rain/snow. The user may choose if regressions
will be built for individual radars or for the entire domain.
Separate equations are derived for rain and snow. Various quality
control checks are done on the data range and correlation coefficients
to ensure that the regression equation fits the data appropriately.
(See Section 11.2.) 
11.1 
Generate realtime regression data 

First, since there are more grid points
in the QPESUMS grid than there are in the satellite grid, QPESUMS precipitation
rates are averaged to correspond to the satellite grid scale. Averaging
precipitation types is more complicated and relies on a priority system
in lieu of averaging. If a convective type is found to be associated
with a satellite grid point, then the satellite grid obtains convective
type. If a satellite grid point contains both good rain and good snow,
the satellite grid point assumes the majority type. If the grid point
contains both bad rain and bad snow, the majority of bad snow or bad
rain is assigned to the satellite grid point.
A satelliteradar pair is accepted if there is a) no missing satellite
temperature, or b) either good rain or good snow associated with the
pair. Any grid cells that are deemed convective are not used in the
regression. This technique applies to stratiform rain and snow only.
Valid pairs are used in the regression technique if they are less than
one hour old. Data older than one hour are purged and no longer used. 
11.2 
Update regression function 

Several quality control criteria must
be met when deriving realtime satelliteradar regressions. When regressing
two variables, stable relationships may be found when there is a) a
sufficient number of satelliteradar pairs, b) variety in the satelliteradar
pairs. The technique described herein assesses these criteria by initially
placing each satelliteradar pair in 1 K temperature "bins".
A temperature bin is said to have enough data if there are five or more
pairs that fall into the bin. The radar rain (or snow) rates are then
averaged for each temperature bin having five or more pairs. The second
criterion is evaluated by calculating the number of temperature bins
that have five or more pairs. If ten or more bins satisfy this criterion,
then there is sufficient variety of satelliteradar pairs and a regression
may be derived.
A regression is fit to the data using a decaying exponential equation.
This equation was found to fit the data most accurately. Two parameters
that describe the steepness of the curve and the yintercept are optimized
using a leastsquares fit. Finally, a correlation coefficient describing
the "goodness of fit" to the data is calculated. If this
value is 0.5 or greater, then the realtime regression is used. Otherwise,
the technique reverts to a climatological regression for both rain
and snow. 
11.3 
Correlation coefficients for cloud top
temperature/precipitation rate regressions 

The algorithm 'Multisensor QPE' derives
a regression between satellite cloud top temperature (K) and radar derived
precipitation rates (mm/hr) using data from areas identified as "good" rain
or "good" snow.
If there are not enough temperature bins in the regression (a valid
temperature bin contain > 5 precipitation rates) then a check is
done to see if the there is a 'flat' distribution of data points. If
the maximum 'mean' precipitation rate for bins is less than the 1mm/hr
threshold, the distribution is considered flat and the correlation
coefficient is set to 4 meaning that the climatological regression
is used. If the maximum 'mean' precipitation rate associated with any
cloud top temperature bin is greater than 1mm/hr then the correlation
coefficient is set to 3 and the most recent good regression (".latest")
is used.
If there are enough data points (i.e. sufficient number of cloud top
temperature bins and associated precipitation rates) then the following
regression relationships are calculated to determine whether the regression
is good enough to be used.
The equation below describes the relationship of the regression curves:
R = alpha * exp ( beta * CTT )
Where R is the precipitation rate (mm/hr), CTT is cloud top temperature
(K) and alpha and beta are regression function coefficients.
Regression function coefficients (alpha and beta) and the correlation
coefficient (CCOEFF) are calculated for each regression every 5 minutes. In
order to derive the regression, mean precipitation rates for each CTT
bin must be calculated. If the maximum mean precipitation rate corresponding
to a CTT bin is less than 1mm/hr then the CCOEF is instantly set to
'2' and the regression is not used and a climatological regression
is used instead.
If the alpha and beta coefficients produce a precipitation rate less
than 1mm/hr from the following equation:
Rate = alpha * exp ( beta * 200K )
the regression is given a correlation coefficient of 2 and again
a climotological regression is applied for that time.
If the alpha and beta calculated for a regression are not found to
be in the following range then the CCOEF is set to zero and the most
recent good regression is applied instead
0 < alpha < 1 * 10^{30}
1 * 10^{30} < beta < 0
If the regression passes all the checks listed above then the CCOEFF
is calculated for the regression. If the correlation coefficient is
greater than 0.5 the regression is used. If the correlation coefficient
is below 0.5 then the regression is not used and the most recent good
regression is applied instead.
See figures below for examples of regression with each of the correlation
coefficients discussed above (0, 2, > 0.5 and < 0.5). The red
line is the mean precipitation rate and the blue line is the regression
fit to the data.

Figure 1. CCOEFF=0; alpha and/or beta are out of
range 


Figure 2. CCOEFF=2. Alpha and beta produce rates < 1mm/hr
at 200K
or maximum mean precipitation rate < 1mm/hr 


Figure 3. CCOEF = 3. There are not enough temperature
bins with greater than 5 precipitation rates to fit a regression
with and the maximum "mean" precipitation rate > 1mm/hr
so '.latest' good regression is used. 


Figure 4. CCOEF = 4 . There are not enough temperature
bins to fit a regression and the maximum "mean" precipitation
rate for temperature bins is less than 1mm/hr so a climatological
regression is used. (In this case there are not enough rates i.e. >5
in ANY bin so "mean" rates cannot be calculated) 


Figure 5. CCOEFF=0.77. Good regression, used in
real time 


Figure 6. CCOEFF=0.32. Bad regression, not used 

11.4 
Regression application 

The parameters derived in the regression
process are used to supply rain and snow rates to the cloudtop temperature
map only for those grid cells that have bad rain or bad snow precipitation
types. The calibrated satellite precip rates are thus applied to grid
cells where the quality of radar data is in question due to overshooting
and/or bright band contamination.
For the entire grid, hourly RUC data are used to determine a rain/snow
line. At a bad snow grid point, the snow regression is used, while
a rain regresison is used at bad rain grid points. The user can specify
in a configuration file whether the regression is derived from satellite
and individual radars or with satellite and all radars combined. 

return to top 
Gauge Algorithm 
12.0 
GaugeOnly QPE 

Functional Description 

The gaugeonly analysis incorporates
all available rain gauge observations in a domain. Initially, a simple
quality control (QC) step is applied to the data. The QC routine is
capable of checking the magnitude, temporal consistency, and spatial
consistency of each rain gauge report. Currently, only the magnitude
check is applied to the data such that gauge accumulations are ignored
if the accumulations exceed 8"/hour (203 mm/hr). If the reporting
interval of the gauges is more frequent than one hour, then the accumulations
are aggregated to produce hourly accumulations. The point estimates
are analyzed on the 1x1 km QPESUMS common grid using a Barnes objective
analysis scheme. The two parameters optimized in the gridding process
are the weighting function and the radius of influence. Initial values
for these parameters are chosen according to the distribution of the
gauge spacing for a given gauge network. Further refinement of the parameters
is accomplished by examining both widespread and scattered rainfall
events. Expert analysis is used to determine the quality of the gridded
gauge product and thus the final values for the Barnes objective analysis
parameters. The hourly accumulations are aggregated to produce longterm
accumulation products. 

return to top 
13.0 
Mean Field Bias QPE 

Functional Description 

The multisensor and radaronly products
are both adjusted using a mean field bias correction based on the comparison
of the nearest grid point values to the gauge locations. This adjustment
technique is intended to remove domainwide biases on an hourly basis
that may be due to improper ZR equations, overestimation from hail
contamination, or underestimation from virga. The mean field bias is
computed as follows:
where is the bias factor, R_{i} is the hourly multisensor
or radaronly accumulation, G_{i} is the hourly gauge accumulation
and N is the number of gauges reporting for that hour. Some checks are
placed on the bias value to ensure that no unreasonable biases are computed.
If the mean of the gauge accumulations (G_{i}) over the entire
domain is zero and the mean of the estimator (R_{i}) at the
gauge locations is zero, then the bias factor is set to a value of one.
If the mean of the gauge accumulations (G_{i}) is zero and the
mean of the estimator (R_{i}) at the gauge locations is nonzero,
then the bias factor is set to a value of zero. Otherwise, the entire
grid of radaronly and multisensor hourly rainfall is divided by the
bias factor to produce the radarmean field bias adjusted and multisensormean
field bias adjusted products. Like all other QPE products, these are
aggregated to produce longterm accumulations. 
14.0 
LocallyAdjusted QPE 

Functional Description 

The multisensor and radaronly products
are adjusted on an hourly basis using a spatially nonuniform bias adjustment
technique. This adjustment is intended to remove nonuniform biases that
may be due to improper ZR relationships, rangedependency in QPEs from
reflectivity profiles that decrease with height, and contamination from
hail, birds, ground clutter, chaff, and other echoes from nonweather
targets. First, the difference between the gauges and the estimators
is computed at each gauge location (e.g., GR). A local bias field is
then computed for the 1x1 km QPESUMS common grid using the point (GR)
values. The parameters used in the Barnes objective analysis scheme
discussed in section 12.0 are used here to analyze the point (GR) values
at the gauge locations to the entire grid. The weighting parameter and
radius of influence are dependent on the gauge spacing with a given
gauge network. Finally, the local bias field is added to the multisensor
and radaronly hourly products to yield the radarlocal bias adjusted
and multisensorlocal bias adjusted QPE products. 