1.
Introduction
The Local Analysis and
Prediction
System (LAPS) analyzes three-dimensional moisture and other state
variables
each hour (or less) over a high resolution relocatable domain. LAPS analyses have been used to initialize
local-scale, high-resolution models such as the Colorado State
University's
Regional Atmospheric Modeling System (RAMS) model and NCAR's MM5
(mesoscale
model, version 5) on a routine basis as a means to utilize local data
in the
forecast model. LAPS has been integrated into the Advanced Weather
Information
Processing System (AWIPS) as part of the National Weather Service (NWS)
modernization.
Research to expand LAPS capabilities is one avenue toward providing
advanced
technologies and new innovations to the operational forecaster.
This paper describes work
in progress and the next step
toward advancing the variational technique in the LAPS moisture
analysis. To date, the variational step
has been used
only with GOES sounder radiances. Other
moisture variables were analyzed separately and either merged with that
variational
result or with the background field prior to the variational step
(Birkenheuer 2000, 1999).
This change will enable the use of more data in the variational
framework. The solution strategy allows
different data sources to be represented by different terms in the
minimized
functional. The functional can be
automatically adjusted to match the datasets present.
More important, this approach accommodates nonlinear functionals.
1.1
Brief History
of LAPS
Under development since
1990, LAPS combines nationally
disseminated data with local data for real-time objective analyses of
all data
available to the local weather forecast office. LAPS
analyses are of suitable quality to initialize local-scale
forecast models. Such models can
address specific problems of a small forecast domain with greater
detail than
can be achieved with nationally disseminated model guidance (Snook et
al.
1998).
The LAPS system is
routinely tested with new data sources
and innovative improvements, using more "conventional" data, which
have potential for national dissemination.
During the 1980s FSL
conducted forecast exercises to test
its workstation prototypes. Forecasters
were burdened with the impossible task of reviewing all the incoming
data made
possible through new technologies, while producing timely forecasts. It
became
obvious that local data needed to be objectively analyzed in
conjunction with
nationally disseminated data. Conceived
as a resolution to this challenge, LAPS was designed to analyze all
local data
in real time on an affordable computer workstation and use its own
output
fields to initialize local-scale forecast models. So
far LAPS has been interfaced with RAMS and MM5, but it can
function with any weather prediction model.
A more detailed review of LAPS is available in McGinley et al.
(1991).
LAPS integrates all
state-of-the-art data as they become
routinely available to a field forecast office. Advanced
data include Doppler reflectivity and velocity fields,
satellite observations including GOES infrared (IR) image data in AWIPS
format,
wind profiler data, automated aircraft reports, and dual-channel
ground-based
radiometer data. New data sources
included here are GOES-derived layer precipitable water data (GVAP),
and Global
Positioning System (GPS) data.
2. LAPS
Moisture analysis
The specific humidity (SH)
module is one of 17 LAPS
algorithms that span everything from data preparation and quality
control (QC)
to actual analysis. In addition to
state variables, LAPS also produces highly specific analyses of special
interest, such as aircraft icing threat and relative humidity, both
with
respect to mixed and liquid phases.
2.1 Background
Setup
Like most analysis
systems, LAPS needs a starting field,
which it later modifies by adding information from other datasets. This background or first-guess field for
the test discussed here is FSL's Mesoscale Analysis and Prediction
System
(MAPS) analysis. Updated each hour,
MAPS is the development model of the operational Rapid Update Cycle
(RUC-2) at
the National Center for Environmental Prediction (NCEP).
The background model moisture data are
interpolated to the denser LAPS grid and reconciled with the LAPS
temperature
analysis to avoid supersaturation.
2.2 Boundary
Layer Moisture
The boundary layer
moisture module utilizes surface humidity
and mixes this into the calculated boundary layer by augmenting the
moisture in
the low levels of the 3-D grid. In the
new system, the variational adjustments are allowed to modify the
low-level
moisture values, a change from the earlier algorithm.
2.3 GVAP
and GPS Pre-analysis
The GVAP and GPS fields
are individually preanalyzed prior
to the variational step. This is done
to specify data at all grid points. The
preanalysis consists of a simple nearest grid point assignment of the
observation, and a smoothed interpolated field between observation
locations. In addition to the three
GVAP fields (one for each sigma layer) and the one GPS field, each
field has a
corresponding weighting function. The
spatial weight controls the horizontal influence of the data field at
grid
points near the one that represents the observation.
This includes the spatial influence of observations and other
error factors (i.e., limb effects for microwave data, a possible future
consideration). In addition, data
latency (temporal considerations) can be set up to modify data source
influence
in the variational step in this same function.
2.4
The
Expanded Variational Adjustment
The variational adjustment
using GOES radiances (Birkenheuer
1999) is being expanded to include GVAP layer precipitable water (over
the
column water previously analyzed), GPS total column water, and cloud
information in one step. The cloud
information is made available from the LAPS cloud analysis (Albers et
al.
1996). The cloud analysis utilizes
aircraft and surface reports, in addition to GOES visible and infrared
satellite image data,and describes cloud vertical extent and horizontal
distribution. In this newly revised
variational approach, the cloud analysis is allowed to influence
utilization of
other data, specifically IR radiances.
2.5 Cloud
Saturation
As a safeguard to assure
consistency, a final check is made
to the field to make sure that moisture is saturated in 100% cloudy
areas with
respect to the applicable water phase.
2.6 Quality
Control
The final step in the SH
algorithm is quality control. Each
moisture value is compared to the LAPS
analyzed temperature, and if supersaturated, it is reported and reduced
to
saturation. Typically, supersaturation
rarely occurs.
3.
data
sources
3.1 GVAP Data
GVAP data were obtained
from the University of Wisconsin -
Madison in real time on a daily basis (Menzel et al. 1998). The new variational scheme scales the
appropriate parts of the LAPS moisture column to fit each of the three
layers
provided by GVAP data. The prior LAPS
system only utilized total column GVAP water vapor data.
The GVAP layers (defined as surface to 0.9
sigma, 0.9 to 0.7 sigma, and 0.7 to 0.3 sigma) are converted to a
pressure
coordinate system as part of the GVAP preanalysis.
GVAP data have a nominal latency of 2 h at the current time.
3.2 GPS
Data
GPS data are
acquired from derived
total column
water vapor from signal delay (Wolfe et al., 2000).
These data are real-time with a characteristic latency of 20
min. GPS data are immune from cloud
effects, and therefore can be used where clouds are present. This capability is incorporated in the new
functional of the variational analysis.
3.3 Cloud
Data
Cloud data are obtained
from the LAPS cloud analysis, which
relies on satellite image data in addition to Doppler radar, ACARS,
surface-based observations of sky conditions, and pilot reports. These data define clear fields of view for
the variational adjustment, help saturate the atmosphere in cloudy
regions, and
influence the moisture analysis in partly cloudy regions.
4. VARIATIONAL Formalism
The mathematical formalism
of the variational procedure is
presented in equation 1. The
advantage
of this approach is that it offers a robust method for operational
application
and can accommodate nonlinear terms.
(1)
Each
term in (1) is modified by the variable S, which is a switch
(with the
exception of the background term which is always on).
Thereby, the terms can be used or not used depending on whether
or not data are available or if clouds are present.
Furthermore, a user can easily add terms for new data sets by
simply
creating a new term. Here the variables
are as follows:
·
Ci the coefficient vector
applied to
q to adjust the moisture field.
Ideally this would have the same dimensions as q has
levels, but may be reduced depending on computer
horsepower. Adjustment of this
parameter is in essence the variational fit to the solution, i.e., ciq becomes the adjusted q
field. The adjustment coefficient is a
scalar with a lower limit of 0 (never negative). A
value of 1 indicates no change to the background. Because
of this, the system will only work
with a quantity such as temperature or humidity that uses absolute
units. For example, using this approach
to analyze temperature in degrees F will fail.
·
q the specific humidity
profile at one LAPS grid point
·
R the forward-modeled
radiance or radiance observation
with the superscript o.
·
i index for the LAPS
vertical (vector dimension of q), with a current
maximum of 40
(accommodating the climatological stratospheric layers needed for the
forward
radiance model).
·
k the index indicating the
satellite sounder or imager
channel used.
·
QGPS the total precipitable
water
measurement from GPS.
·
E the error function
(squared quantity) that describes
the observation or background error, subscripted by observation type.
·
L spatial weighting term
subscripted by observation
type. This weights the smoothed
(preanalyzed) field value by its proximity to the observation and
reflects the
horizontal influences of the measurement.
Each data source has an associated gridded field of
spatial-weighting
terms characterizing its proximity to the observation and its spatial
representation.
·
P the function to convert
from pressure to sigma coordinates
·
QGVAP the GOES vapor total
precipitable water layer data. The
layers are defined in sigma coordinates and vary grid point to grid
point.
·
j the index of the GVAP
layer, with a current maximum
of 3 (1 is lowest, 3 is highest).
·
Cld cloud function
designating cloudy
regions in the vertical, with dimensions of q.
·
J the functional to be
minimized.
·
t is the temperature profile
(LAPS) at the same
location as q.
·
S logical switch for the
observation type to be present
or not. Each term in the functional can
be easily included or excluded depending on the presence of the data
source. Also new data sources can be
added by including new terms.
·
qs(t) saturated q
as a function of temperature.
·
g cloud fraction indicator
as a function of level.
·
G a function of g
such that it indicates cloud in the column. For radiance measurements,
this has
the advantage of disabling IR terms including GVAP.
Finally, the GPS term would be unaffected by clouds in principle
since the data source can deliver data in cloudy areas.
However, the analysis needs to probably give
more credence to the cloud field since it is vital the cloud field
complements
the moisture field ensuring that two fields don’t conflict. G
can be a linear function of cloud such that it might serve to help
define
partly cloudy regions by allowing a smooth gradient from total through
partly
cloudy to clear air.
·
GT is a similar function to G, but it may be nonlinear and can match
the satellite radiometer’s field of view.
5.
Solution
methodology
The
minimization of (1) is accomplished using the same methods as the prior
moisture analysis. The Powell method
(Brent 1973) employs a multidirectional search to seek out a solution. Typically two to five calls of the algorithm
are required to solve the function.
Each call to the numeric method involves 25 or so functional
calls. Although more efficient methods are
available, this technique has worked reliably to date.
Model adjoints are not required for this
technique.
6. Example
A qualitative example of the new analysis is shown in Figs. 1 and 2. Figure 1a, shows a midlevel com-parison (600-hPa relative humidity plot) of the
Fig. 1a. The older analysis of the 600 hPa RH (contours at 10% intervals) showing analyzed cloud (grayscale) over the LAPS Regional Observing Cooperative (ROC) domain (17 April 2001).
former analysis with the newer adaptation of the variational method (Fig. 1b). Similarly, Figs. 2a and 2b show a high-level example at 400 hPa from the same time. Note that the cloud field is denoted as a white area, contours are at 10% RH intervals. The newer variational approach appears to capture more humidity structure away from the cloud. Furthermore, the gradient about the cloud appears more gradual
Fig. 1b Same as Fig. 1a with the newer variational method using clouds and GVAP data.
and perhaps
is more realistic. More validation is
required to establish that the new method is rendering a more accurate
analysis.
Fig. 2a Older analysis of 400-hPa RH for the same time as in Fig. 1.
Fig. 2b Similar to Fig. 1b except at 400 hPa.
7. Summary
The new functional
solution is now being tested with broader
focus on the run times and feasibility of real-time operation. These aspects of the algorithm look
promising, even for AWIPS-type resources.
Error functions are currently approximated and will require
refinement. For this case GPS data were
not used since they remain under development.
6. REFERENCES
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J. McGinley, D. Birkenheuer, and J. Smart 1996: The Local Analysis and
Prediction System (LAPS): Analyses of clouds, precipitation, and
temperature. Wea.
Forecasting, 11, 273-287.
Birkenheuer,
D., 2000: Progress in applying GOES-derived data in local data
assimilation, 10th
Conf. on Satellite Meteorology and Oceanography, Amer. Meteor.
Soc.,
Long Beach, CA, 70-73.
________,
1999: The effect
of using
digital satellite imagery in the LAPS Moisture Analysis. Wea.
Forecasting, 14,
782-788.
Brent, R.P., 1973: Algorithms
for Minimization without
Derivatives. Prentice-Hall, Chapter
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McGinley, J. A., S.
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