1.
Introduction
The Local Analysis and
Prediction
System (LAPS) analyzes three-dimensional moisture and other state
variables
hourly (or more frequently) over a high-resolution relocatable domain. LAPS analyses have been routinely used to
initialize local-scale, high-resolution models such as the Colorado
State
University's Regional Atmospheric Modeling System (RAMS) model and the
National
Center for Atmospheric Research’s MM5 (mesoscale model, version 5) 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
progress 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
automatically adjust to match the datasets present.
More important, this approach accommodates nonlinear functionals.
1.1
Brief History
of LAPS
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
available local
data in real time on affordable computer workstations and utilize the
analyses
to initialize local-scale forecast models.
So far LAPS has been interfaced with RAMS and MM5, but in
principle it
can function with any weather prediction model. 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). A
more detailed review of LAPS is available in McGinley et al. (1991).
The LAPS system is
routinely tested with new data sources
and innovative improvements, using more "conventional" data, which
typically are nationally disseminated.
Advanced data include Doppler reflectivity and velocity fields,
satellite observations including GOES infrared (IR) sounder data, 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.
data
sources specific to this
upgrade
2.1 GOES-Derived Layer Precipitable Water 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.
Also as part of this step, data are distributed on an analysis
grid with a radial influence corresponding to the field of view. In this case, 30 km GVAP data have a nominal
latency of 2 h at the current time.
2.2 Global
Positioning System Vapor Delay Data
GPS data
refer to derived
total column
water vapor (zenith) from GPS signal delay
(Wolfe et al., 2000). These data are
obtained in 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. A
horizontal influence of 12 km was applied to the GPS data.
Similar to the GVAP data treatment, these
data are distributed on an analysis grid.
2.3 Cloud
Data
Gridded 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
utilizing satellite radiance data and help identify regions that
require
saturation due to complete cloudiness.
In partly cloudy regions, the scheme relates cloud fraction to
RH and
influences the variational result. The partial cloud enhancement starts
at 0.6
cloud fraction assigning a 60% RH at that point, and ramps linearly to
saturation at total cloud cover.
3. 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 with
respect to
both mixed and liquid phases. The SH
module is one of the last analyses run, prior to the new mass balance
scheme. It incorporates many fields
that have already been processed such as clouds and surface moisture.
3.1 Background
Setup
Like most analysis
systems, LAPS requires 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 Centers 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.
Additionally, LAPS can
also use a previous short-range
forecast (i.e., MM5 1-h forecast initialized with LAPS) and uses this
as the
background for the next analysis in the cycle.
This four-dimensional data assimilation (4DDA) scheme is
currently being
tested using an hourly update cycle.
3.2 Boundary
Layer Moisture
Since the surface analysis
uses hourly observations, its
representation of surface moisture is possibly the most up-to-date
moisture
field attainable using conventional data sources, and is key to
tracking
moisture changes in the boundary layer.
The boundary layer moisture module mixes surface humidity into
the
calculated boundary layer by adjusting the moisture in the low levels
of the
3-D grid.
3.3 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 and assure they have a
spatial influence related to instrument
characteristics. The preanalysis
consists of a simple nearest gridpoint 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
surrounding
those that represent 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.
3.4
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). In this newly revised
variational approach, cloud fraction is included in the moisture
solution.
3.5 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.
With the variational step now including cloud influence, this
adjustment
is invoked less often.
3.6 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.
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 ignored depending on whether
or not
data are available or if clouds are present.
Furthermore, a user can easily add terms for new datasets by
simply
creating a new term. 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. 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 find a solution.
Each call to the numeric method involves approximately 25 calls
to the
functional. Although more efficient
methods are available, this technique has worked reliably to date. Model adjoints are not required for this
technique.
6. Example
The
very deep and premature monsoon flow over the regional observation
cooperative
(ROC) domain in early July 2001 provided a very good signal for
moisture
study. Figures 1 and 2 contrast the old
and new analysis schemes. Both figures
depict a cross section of relative
humidity from west to east through Boulder, Colorado.
Fig.
1. Cross section through 40° N latitude showing
relative humidity
and cloud fraction through the ROC domain.
Fig.
2. Same as Fig. 1 except using the newer variational
analysis.
For the most part, the two
analyses are very similar with
the newer scheme possibly showing more detail.
The cloud field is the same in both sets and is depicted by
shaded
features. The lighter shades indicate
low cloud fraction while black would show 100% cloud.
It is apparent that very low cloud fractions existed; therefore,
clouds had minor impact on the RH adjustment.
Even so, the analysis shows higher RH values in partly cloudy
areas. A quantitative evaluation of the
scheme is currently being performed.
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.
When running the system in
4DDA mode, it quickly becomes
apparent that model and analysis moisture components must be compatible. For example, the model may base RH
computations on the liquid phase for all temperatures while the
analysis may
use ice as a reference below some threshold temperature.
Such discrepancies can lead to artificial
“generation” of water or chronic drying of the atmosphere as these
discrepancies are compounded in the 4DDA cycle. The
new variational scheme has demonstrated a resistance to this
effect during ongoing 4DDA tests.
8. REFERENCES
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J. McGinley, D. Birkenheuer, and J. Smart 1996: The Local Analysis and
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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
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derivatives. Prentice-Hall, Chapter
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