1. science
2. weather
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o,and ocoanss
ELSEVIER
Dynamics of Atmospheres and Oceans 27 (1997) 439-470
The impact of Global Positioning System data on
the prediction of an extratropical cyclone: an
observing system simulation experiment
Y.-H. Kuo, X. Zou *, W. Huang
MPG / MMM / NCAR, P.O. Box 3000, Boulder, CO 80307-3000, USA
Received 8 February 1996; revised 18 July 1996; accepted 29 July 1996
Abstract
In this paper, we report a series of observing system simulation experiments that we conducted
to assess the potential impact of Global Positioning System/meteorology (GPS/MET) refractivity
data on short-range numerical weather prediction. We first conducted a control experiment using
the Penn State/NCAR mesoscale model MM5 at 90-km resolution on an extratropical cyclone
known as the ERICA (Experiment on Rapidly Intensifying Cyclones over the Atlantic) IOP 4
storm. The results from the control experiment were then used to simulate G P S / M E T refractivity
observations with different spatial resolution and measurement characteristics. The simulated
refractivity observations were assimilated into an 180-km model during a 6-h period, which was
followed by a 48-h forecast integration, Key findings can be summarized as follows:
• The assimilation of refractivity data at the 180-km resolution can recover important atmospheric structures in temperature and moisture fields both in the upper and lower troposphere,
and, through the internal model dynamical processes, also the wind fields. The assimilation of
refractivity data led to a considerably more accurate prediction of the cyclone.
• Distributing the refractivity randomly in space and applying a line averaging did not alter the
results significantly, while reducing the spatial resolution from 180 km to 360 km produced a
moderately degraded result. Even at the 360-km resolution, the GPS-type refractivity data still
have a notable positive impact on cyclone prediction.
• Restricting the refractivity data to altitude 3 km and above considerably degraded its impact on
cyclone prediction. This degradation was greater than the combined effects of distributing the
refractivity data randomly, performing line averaging, and reducing the resolution to 360 km.
These results showed that the G P S / M E T refractivity data is likely to have a significant impact
on short-range operational numerical weather prediction. The random distribution and line
* Corresponding author.
0377-0265//97/$17.00 © 1997 Elsevier Science B.V. All rights reserved.
PII S0377-0265(97)00023-7
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Y.-H. Kuo et al, / Dynamics ~f Atmospheres and Oceans 27 (1997) 439-470
averaging associated with the inherent GPS occultation do not pose a problem for effective
assimilation. On the other hand, these results also argue that we need to improve the GPS/MET
retrieval algorithm in order to recover useful data in the lower troposphere, and to increase the
number of low-earth-orbiting satellites carrying GPS receivers in order to increase the density of
GPS soundings, so that the potential impact of GPS/MET refractivity data on numerical weather
prediction can be fully realized. © 1997 Elsevier Science B.V.
1. Introduction
The radiosonde, a balloon-borne system that sends temperature, humidity, and
pressure data to the ground by radio signal, is the basis for operational analysis and
prediction at most weather forecast centers worldwide. Contemporary radiosonde instruments measure temperature and relative humidity with an accuracy of about 0.2°C and
3.5%, respectively (Elliot and Gaffen, t991). Their performance diminishes in cold, dry
regions or at high altitudes for relative humidity fields. Although the value of in situ
measurements that provide good vertical resolution is clear, radiosonde measurements
also have some serious disadvantages. Radiosondes are expendable, and the cost of these
devices restricts the number of launches to twice daily (00:00 and 12:00 UTC) at a
limited number of stations. Therefore, radiosonde measurements have inadequate temporal and spatial resolutions for mesoscale study. This is especially true for water vapor,
which has a scale much finer than those of temperature or winds (Anthes, 1983). In fact,
uncertainty in the analysis of water vapor is one of the key factors limiting the accuracy
of short-term (0-24 h) precipitation forecasts.
As part of the NASA Earth Observing System, the Jet Propulsion Laboratory
suggested to apply the radio occultation or limb sounding technique to studies of the
earth's atmosphere. Radio occultation studies of the terrestrial atmosphere make use of
signals transmitted by satellites of the Global Positioning System (GPS) and received by
one or more other satellites in low earth-orbit (LEO). With the receiver orbiting at a
height of about 800 km and the GPS satellites at about 2t 000 km, the duration of a
complete occultation (surface through ionosphere) is about 1 min. Vertical profiles of
refractivity, to a height of about 60 km, can be retrieved from the data obtained by a
receiver aboard an LEO satellite as it rises or sets as viewed from the GPS satellites. On
April 3 1995, the first GPS receiver aboard the MicroLab- 1 spacecraft, capable of earth
radio occultation observations, was successfully placed in orbit. One of the goals of this
'proof of concept' satellite experiment is to assess the accuracy of such active limb
sounding measurements and their potential utility for operational weather prediction and
climate-change research. Over 10 000 GPS/meteorology ( G P S / M E T ) occultations were
received by the end of 1995. Early results, as reported by Ware et al. (1996), indicate
that G P S / M E T temperature profiles typically compare within 1-2 K with other
observing systems, such as radiosondes, in the 5-40-km altitude range where moisture
effects are negligible. In the lower troposphere, there is ambiguity in deriving separate
temperature and moisture information. However, this does not present a problem if the
G P S / M E T data are directly assimilated into numerical models through adjoint techniques. G P S / M E T proves to be a promising technology that deserves further assessment
of its accuracy and impact on numerical weather prediction.
Y.-H. Kuo et a l . / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
441
Zou et al. (1995) developed a 4-D variational data assimilation (4DVAR) system
based on an adiabatic version of the Penn State/NCAR mesoscale model (MM5) and
conducted a series of observing system simulation experiments (OSSEs) to assess the
impact of GPS-derived atmospheric refractivity data. The results showed that the
assimilation of atmospheric refractivity was effective in recovering the vertical profiles
of water vapor. The accuracy of the derived water-vapor field was significantly better
than that obtained through the traditional retrieval technique. The assimilation of
atmospheric refractivity also provided useful temperature information.
Although these results are encouraging, one needs to be aware of the inherent
limitations associated with the experiment design. The simulated GPS observations were
evenly distributed over a limited domain at 60-km grid intervals. The inherent averaging
associated with GPS occultation was not taken into consideration. Also, both the control
simulation and the assimilation experiment used an adiabatic model without the complication associated with precipitation and latent heat release. These conclusions need to be
re-examined with simulated data having measurement characteristics more resembling
the actual GPS observations, and using a model and data-assimilation system including
moist physics.
It is important to bear in mind that the 'raw' observation from G P S / M E T system is
the refractive angle of the radio signals passing through the atmosphere. The atmospheric refractivity is derived from the refractive angle through an inversion algorithm
using the local spheric symmetry assumption (Gurvich and Sokolovskiy, 1985). As a
result, the derived refractivity represents an average over the path tangent to the
atmosphere with a characteristic scale, which is approximately 500-600 km in the upper
atmosphere and 200-300 km in the lower atmosphere. Because of the differences in the
characteristic spatial scale of the actual and simulated GPS refractivity measurements,
the OSSE results of Zou et al. (1995) may be overly optimistic. Moreover, the GPS
occultation has a global coverage. We thus need to perform a data-assimilation study on
a larger domain to better assess the impact of G P S / M E T measurements.
Baroclinic waves propagate around the globe at middle and high latitudes continuously. These waves drive surface cyclogenesis and its associated frontogenesis, and are
responsible for the production of clouds and precipitation. The structure of these waves
is usually better captured over land where there are adequate observations. Over the
ocean, these waves are poorly sampled, which often contributes to forecast failures.
Evidence supporting this argument can be found in the comparison of the forecast skill
of NGM (Nested Grid Model) in the prediction of rapid cyclogenesis over the western
Atlantic versus eastern Pacific. Sanders (1987) showed that the correlation coefficient
between predicted and analyzed 12-h deepening for the NGM model was 0.78 for
western Atlantic storms for the winter of 1986-1987. The same model had a correlation
coefficient of 0.03 over the eastern Pacific. A challenge to the operational numerical
weather prediction community is to improve the quality of the initial condition,
particularly in its description of the baroclinic wave structure that is important to surface
cyclogenesis. The key question to be addressed in this study is: Will the assimilation of
G P S / M E T data improve the description of the structure of baroclinic waves and its
associated surface cyclogenesis?
In this paper, we conduct a series of OSSEs to examine the potential impact of the
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Y.-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
G P S / M E T refractivity data on the prediction of an extratropical cyclone, known as the
ERICA (Experiment on Rapidly Intensifying Cyclones over the Atlantic) lOP 4 storm.
Specifically, we will address the following questions: (i) What is the impact of
atmospheric refractivity on the prediction of an extratropical cyclone? (ii) Will the
impact degrade substantially as the resolution of the GPS measurements is decreased?
(iii) Does the line-averaging characteristic of the refractivity observations influence the
assimilation results? Section 2 provides a short description of the lOP 4 storm. Technical
details on how to generate simulated GPS measurements and the experiment design are
provided in Section 3, along with a brief description of the model. Numerical results are
presented in Section 4. Section 5 gives a summary and a discussion.
2. Case description
An extreme case of an extratropical marine cyclone took place over the Northwestern
Atlantic Ocean on 4 - 5 January 1989. This storm was the most intense one among the
eight cases studied in ERICA, with an estimated minimum pressure of 936 mb at 00:00
UTC 5 January, and a 24-h deepening of 60 rob. The storm started as a 996-mb low off
Cape Hatteras, North Carolina, embedded within a broad baroclinic zone with a
moderate thermal gradient. During the ensuing 24 h, with the approach of an intense
upper-level short wave, the storm went through rapid intensification along the warm
Gulf Stream. Detailed synoptic and mesoscale analyses of this case can be found in
Wakimoto et al. (1992), Neiman and Shapiro (1993), Neiman et al. (1993). A numerical
simulation of the airflow and frontal evolution was presented by Reed et al. (1994). All
these studies focused on the 24-h period of rapid intensification, ending at 00:00 UTC 5
January.
Davis et al. (1996) studied the dynamics of this cyclone, and concluded that the storm
evolves from a disturbance with maximum amplitude at the tropopause to a maximum
amplitude at the surface as the system moves offshore. They explained the cyclogenesis
in terms of a baroclinic wave propagating through a varying basic state, in which the
surface development is rapid because of the sudden response of the wave structure to a
changing environment. Kuo and Low-Nam (1990) examined the predictability of this
storm using a 120-km hemispheric version of the MM4 model. They showed that the
upper-level short wave and its associated potential vorticity (PV) anomaly can be traced
back to the Gulf of Alaska. Rapid cyclogenesis took place as the PV anomaly moved off
shore to interact with the low-level baroclinic zone over the western Atlantic (Reed et
al., 1994). This case is ideally suited to examining the impact of G P S / M E T refractivity
data on the description of atmospheric structures that are crucial to cyclone prediction.
3. Model and experiment design
3.1. MM5 and its adjoint model
In this study, we utilize adiabatic version of the Penn State/NCAR non-hydrostatic
mesoscale model version 5 (MM5) with relatively simple physics. It includes model
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443
dynamics, diffusion, bulk planetary-boundary-layer (PBL) processes, surface frictions
grid-resolvable non-convective precipitation, Kuo-type cumulus convection, and a split,
semi-implicit time integration scheme. The model uses a terrain-following g-coordinate.
For a detailed description of MM5 and its adjoint model, see Grell et al. (1994) and Zou
et al. (1995), respectively. Problems related to the use of the adjoint of moist physical
parameterization in 4DVAR are discussed in a separate paper by Zou (1996).
In order to simulate G P S / M E T observations, we first conducted a control experiment
(CTRL), which had a horizontal resolution of 90 km with 20 levels in the vertical. This
experiment was initialized at 00:00 UTC 3 January 1989 (defined as t = - 12 h), and
was integrated for 60 h. It covered the northern hemisphere (outer domain in Fig. 1)
with a mesh of 197 × 197 × 20. The initial conditions (ICs) was obtained from an
objective analysis of rawinsonde and surface observations using the NMC global
analysis as the first guess. The lateral boundary conditions were obtained by linear
interpolation of these analyses at 12-h intervals.
It is well known that when the same model is used for both creating the 'simulated'
observations and for testing their impact, the results tend to be overly optimistic. This is
known as the 'identical-twin' problem, because model-created atmospheres tend to be
alike, but different from the real atmosphere. In order to partially remedy the identicaltwin problem, we used a 180-km, ten-level MM5 model with a smaller mesh size of
160E
150E
140E
130E
120E
110E
100E
90 E
80 E
?0 E
170 E
60 E
m
50E
I?0 W
40 E
160 W
30 E
150 W
20 E
140 W
10 E
130 W
GM
120 W
10 W
110 W
I00 W
9Q W
80 W
?0 W
60 W
50 W
40 W
30 W
20 W
Fig. 1. Illustration of model domains used for C T R L (outer domain) and 4 D V A R experiments (inner domain).
444
Y.-H. Kuo et al. / Dynamics c~'Atmospheres and Oceans 27 (1997) 439-470
61 x 51 X 10 as the assimilation and forecast model, which covered all of North
America and part of the western Atlantic and eastern Pacific (see the inner domain in
Fig. 1). Both the forward integration of MM5 and the backward integration of its adjoint
are performed with a 7.5-min time step.
3.2. Assimilation of GPS / MET data
3.2.1. 4DVAR problem
4DVAR minimizes an objective function which measures the distance between the
model-predicted refractivity (180-kin resolution) and the observed refractivity N °bs
(extracted from the 90-km simulation) in the 6-h time window [t 0, tR]. This objective
function is given by
R
J(xo) = ~ (CN(x(t,.)) - N"h~(t,.)) -~
(l)
r= 0
where x(t r) is the model prediction at time t r representing the wind components (u, u,
w), the temperature T, specific humidity q, and the pressure perturbation p', N is an
operator calculating the model refractivity from model variables, N°bS(t r) is the
refractivity observation at time t~, and C is an operator mapping the model-predicted
refractivity from model grids to observational points. For example, if N°b~(tr) is
distributed on each model grid, C is merely a unit matrix. If N°b~(tr) is randomly
distributed with line averaging, C will contain operations of line averaging and
interpolation. The operator N is based on the atmospheric refractivity N which is given
by
N = 77.6 £ + 3.73 X 105P~
T -~
T
where p is pressure in mb, T is temperature in degrees Kelvin, and p~ is water-vapor
pressure in mb. The atmospheric refractivity is a non-dimensional quantity.
Minimizing the cost function defined by Eq. (I) is an under-determined problem
since the dimension of the control variables xt) is much larger than the number of
observations. However, here we seek modification to the guess field from the refractivity assimilation, instead of determining a unique solution of the IC independent of initial
guess fields. Therefore, our results are limited to the assessment of the individual impact
of refractivity on the cyclone prediction in an OSSE mode. In a more complete system, a
background term should be included, with addition of some dynamical or physical
constraints, or a measure of distance to other possible source of information in an
additional weak constraint term jc in Eq. (1) of Courtier et al. (1993). Such an effort
will be reported in a forthcoming paper.
3.2.2. Simulated GPS measurements
Assuming 12 (50) LEO satellites in orbit simultaneously, about 3000 (12500)
atmospheric refractivity soundings can be expected every 12 h (Hardy et al., 1992).
These soundings will possess a horizontal resolution of 367 km (180 km) and a vertical
resolution of about 1 km in the upper atmosphere and a few hundred meters in the
Y.-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
445
troposphere. In some experiments in order to more closely simulate the G P S / M E T
refractivity measurements, we distribute such measurements randomly in space. Each
simulated atmospheric refractivity observation at random points represents a line average along a random direction over a distance of about 200-300 km.
For example, for simulated G P S / M E T observations having an averaged resolution of
360 km, four random points are generated within an area of 720 × 720 km following the
formula:
x=j+4×ranf, y = i + 4 × r a n f
(3)
where ran f represents a random number ranging between 0 and 1 and (j, i) represents
the grid index for the lower-left point of the selected 720 km × 720 km domain. A
random direction is then generated at each observational point:
2~a = 180 × ran f
(4)
where c~ represents the angle between the averaging line and the x-axis. The hemispheric distribution of the soundings over a 12-h period following Eqs. (3) and (4)
(which represents observations of 12 LEO satellites over a 12-h period) is shown in Fig.
ID
170 E 160 ~ 5 0 B 0 1 E C I 2 r l R I ~
~0 ET0 E
60 E
170 W
50 E
40 E
160 W
30 E
20 E
150 W
10 E
GM
140 W
tO W
20
130 W
W
30 W
120 W
110 W
40 W
100 W
90 w
ao w
70 w
so w
50 w
Fig. 2. R a n d o m distribution o f N °bs at 3 6 0 - k m resolution, with a line associated with e a c h observational point
on w h i c h a line a v e r a g i n g is taken.
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2. In order to simulate line-averaged observations along a random direction tan a , we
first calculate two ending points of the line as follows:
L
xj=x+--cosa,
2
/~
x 2 = x - --cos ce,
2
L
y~=y+--since
2
C
y: = y - --sin ce
2
(5)
where L is the averaging length, which has a value of about 180 km. Then a weighted
averaging is taken to obtain the simulated refractivity observations N °b~ from the
refractivity N derived from the 90-km control run:
N(obs
x,,.,
= N~ ~.,.~ + 0.25 × (N¢.,~.~,, + N~,_~,,.,- 2 × N~.....7)
(6)
No errors are added to the simulated N °b~.
3.3. Experiment design
All the 4DVAR experiments were conducted in a 6-h time window from t o = 0 h
(12:00 UTC 3 January 1989) to t R = 6 h (18:00 UTC 3 January 1989). The first-guess
fields for the assimilation experiments were generated from the control run, except that
the horizontal resolution was degraded by a factor of 8. Specifically, we extracted model
soundings at every eighth grid point from the 90-km control simulation. A bi-parabolic
interpolation was then employed to interpolate these data to the 180-km grid of the
assimilation model. This represents a first-guess field having a horizontal resolution of
720 km, not atypical for global analysis, particularly over the ocean. Obviously, the
small-scale atmospheric structures are largely removed through this resolution reduction
process. The question is, can assimilation of refractivity data recover important atmospheric structures that are crucial for a successful prediction of cyclones? As a
benchmark for the subsequent 4DVAR experiments, we conducted a no-assimilation
experiment based on this initial-guess field, which is termed the NO4DVAR experiment.
Five 4DVAR experiments have been conducted (see Table 1). The G P S / M E T
refractivity data are assumed to be available at both the beginning and ending times of
Table 1
Summary of numerical experiments
Experiment
CTRL
NO4DVAR
E1
E2.upper
E3.random
E4.random360
E5.180terrain
4DVAR (12:00-18:00 UTC 3
refractivity obs. from CTRL)
Forecast
Vertical level
IC
Model
90-km 00:00 UTC 3
720-km 12:00 UTC3
~Optimal'
'Optimal'
' Optimal"
'Optimal'
90-km
180-kin
180-km
180-km
180-km
180-km
Random distribution
1-10
No
1-7
No
1-10
Yes, 180-km
1- 10
Yes, 360 km
Same as E1 except that CTRLgenerated OBS used 180-km terrain
Y.-H. Kuo et aL / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
447
the 6-h assimilation window. The first experiment (El) assumes that refractivity
observations ( N °bs) are available on all model grids. The second experiment (E2.upper)
is similar to E1 except that N °bs are available only at levels from 1 to 7 ( = 3 km above
the ground). In E3.random N °bS is randomly distributed with a 180-km line-averaging
taken along a random direction for each observation. Such N °b~ are available with an
averaged horizontal resolution of about 180 km. The fourth experiment (E4.random360)
is similar to E3.random except that the horizontal resolution of randomly distributed
N °bs is reduced from 180 km to 360 km. The last experiment (E5.180terrain) is the same
as E1 except that the 180-km terrain (instead of 90-km terrain) is used in CTRL, which
provides N °b~. It is designed to eliminate errors due to inconsistency in terrain between
CTRL and all 4DVAR experiments (El, E2.upper, E3.random, and E4.random360). The
results after 4DVAR experiments in which simulated N observations assume various
spatial and temporal distributions are compared with NO4DVAR and CTRL to assess
the impact of G P S / M E T data assimilation on cyclone development.
4. Numerical results
4. l. Evolution o f the control simulation
An important prerequisite for a meaningful observing system simulation experiment
is the success of the control simulation in capturing the essential dynamics of the
atmosphere. In this section, we will examine the evolution of the 90-km control
experiment. Fig. 3 shows the predicted surface temperature and sea-level pressure at
06:00 UTC 4, 12:00 UTC 4, 18:00 UTC 4, and 12:00 UTC 5 January 1989, which are
30-h, 36-h, 42-h, and 60-h forecasts. At 06:00 UTC 4 January, the simulated lOP 4
storm was located off Cape Hatteras, with a central pressure of 987 mb. No sharp fronts
could be seen at that time. A preceding storm, known as the IOP 3a storm, located at
50°W, 45°N, was at its late stage of development. Six hours later, the IOP 4 storm
deepened to 973 mb (a 14-mb deepening in 6 h), and began to develop distinct cold and
warm fronts. By 18:00 UTC 4 January, the storm reached 961 mb (another 12-mb
deepening in 6 h). A pocket of warm air was found to the southwest of the low center.
The storm continued to deepen with time, and by the end of the simulation, the storm
had a minimum central pressure of 938 rob. An occluded front with extremely strong
temperature gradients developed. This front linked the low center to the triple point
where cold and warm fronts intersected, with structures similar to the observations. Cold
air from behind the cold front surged to the east of the low center, producing an
accentuated tongue of warm air near the low center. The evolution of these frontal
structures compares favorably with analyses presented in Wakimoto et al. (1992) and
Neiman and Shapiro (1993). The ability of the model to simulate the depth of this storm
is particularly impressive (938 mb versus observed value of 936 mb). A criticism can be
made regarding the timing of the simulated deepening. The observed storm reached its
minimum pressure at 00:00 UTC 5 January, while the model storm's minimum pressure
was delayed by about 12 h. Given the fact that the model had relatively coarse
horizontal and vertical resolutions, and was initialized 24 h before the start of rapid
E-H. Kuo et al. / Dynamics q/Atmospheres and Oceans 27 (1997) 439-470
448
w
'~o w
ao w
~o w
40 w
'i ~, .....~,
~o w
'-
ao w
~o w
Bo w
~o w
,..i,.,
, .......
?0 W
eo w
~o w
~,,
eo w
-'
eo w
~o w
~
'
"
~,~
4e N
!3o
~
~o w
30 w
io w
~o w
~ '.)-,.-
40 ~
.
~,o w
~
k
~o w
~o w
70 •
~o w
80 w
V/
~o w
~o w
40 w
~o
t/.I///~/gd-:,'? t
,,o w
60W
~W
c!
d~f/.::i,'\d i
( ~
L
/
?0 w
,
L
/
/
,
~o w
~
,,,
,
5o w
Fig. 3. Surface temperature (solid lines, c.i. = I~C) and sea-level pressure (dotted lines, c.i. = 4 rob) from a
60-h high-resolution (90-kin) numerical simulation (CTRL) of the lOP 4 marine cyclone by the MM5 at (a)
06:00 UTC 4 January, (b) 12:00 UTC 4 January. (c) 18:00 UTC 4 January, and (d) 12:00 UTC 5 January
1989.
intensification, these results are considered quite good. The ability of the control
simulation to capture the rapid intensification of the storm and its frontal evolution
allows us to use the results of this e x p e r i m e n t to "simulate' the G P S observations with
confidence.
4.2. Impact o f GPS / M E T data on cyclone prediction
In E l , G P S / M E T refractivity data ( N °bs) are assumed to be available at the
beginning (12:00 U T C 3 January) and ending (18:00 U T C 3 January) time o f the
Y.-H. Kuo et aL / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
449
assimilation period. The N °b~ is available at every grid point of the 180-km model. No
line averaging is performed. Therefore, this simulates a condition that is more optimistic
than what would be possible with actual G P S / M E T data. This represents an upper
bound for the potential impact of a G P S / M E T system having a spatial resolution of 180
km and a temporal resolution of 6 h.
In 4DVAR, we seek possible improvement of the analyzed IC, which is used as the
initial guess for the minimization. The cost function and the norm of the gradient
decreased from 902 and 57.03 to 5.799 and 1.880 in 38 iterations, respectively. This
shows that the refractivity data can be successfully assimilated into the model. In order
to examine where major changes occur, we plot in Fig. 4 the refractivity differences
between model and simulated observations at 300 mb, 500 mb, and 850 mb for
NO4DVAR and E1 at the end of the assimilation window (18:00 UTC 3 January 1989).
We observe that refractivity errors in NO4DVAR at 300 mb, 500 mb, and 850 mb (Fig.
4(a), (c), (e)) are significantly reduced after data assimilation (Fig. 4(b), (d), (f)). The
improvements over the Mexican Plateau and the Gulf of Mexico at 500 mb and 850 mb
are particularly impressive. At 300 mb, an error maximum in NO4DVAR was located at
the southern tip of Lake Michigan. This refractivity error maximum is associated with an
upper-level disturbance which is responsible for the development of the lOP 4 cyclone.
Since there is little water vapor at this level, the error must be caused by errors in the
temperature field in the initial condition. This error was nearly completely eliminated
after 4DVAR. We note, however, large errors over Greenland in both NO4DVAR and
El, with the latter being larger than the former. As will be discussed later, this is caused
by incompatibility in model terrain between the CTRL and 4DVAR assimilation model.
In CTRL, a 90-km terrain is used while a 180-km terrain is used in El.
The 'observed' (derived from the control simulation) 500-mb temperature and
850-mb specific humidity at 18:00 UTC 3 January are shown in Fig. 5(a) and (b). The
errors in these fields for NO4DVAR and E1 are shown in Fig. 5(c) and (d) and Fig. 5(e)
and (f), respectively. We note that errors in the 500-mb temperature (Fig. 5(c)) and
850-mb humidity fields (Fig. 5(d)) in NO4DVAR occurred mainly over regions with
sharp gradients (Fig. 5(a), (b)). The 500-mb temperature error of 2.5°C took place over
Wisconsin, where there was a temperature trough. The positive temperature error over
Wisconsin, and the negative error immediately to its west and east, suggest that the
amplitude of the temperature trough was weakened in NO4DVAR. The assimilation of
refractivity data reduced the temperature error over Wisconsin by I°C, and nearly
completely eliminated the negative temperature error to its west. As a result, the
amplitude of the temperature trough was recovered. However, large temperature errors
over Greenland (northeast corner) and southern Mexico remain large after data assimilation (Fig. 5(e)). Errors in the low-level moisture fields (NO4DVAR, Fig. 5(d)) exhibit a
significant reduction after refractivity assimilation (El, Fig. 5(f)). A 4-g kg-l reduction
is observed over the Mexican Plateau. These results show that errors in temperature and
specific humidity fields in the ICs of NO4DVAR due to reduction of horizontal
resolution, which occur in regions with a sharp gradient of atmospheric state, could be
reduced through assimilation of atmospheric refractivity data with a spatial resolution of
180 km.
In El, only N °b~ data are assimilated; the minimization problem is thus an under-de-
Y.-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
450
/
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Fig. 4. Difference fields of atmospheric refractivity at 300 mb ((a) and (b), c.i. = 5 NU), 500 mb ((c) and (d),
c.i. = 10 NU), and 850 mb ((e) and (f), c.i. = 50 NU) for NO4DVAR (left column) and El (right column) at
18:00 UTC 3 January 1989. verified against CTRL, where NU represents refractivity unit.
Y.-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
l~W
i~w
iltlwlOOIOimtvollolSOw4~l~ll
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Fig. 5. 'Observed' (a) 500-mb temperature (c.i. = 2°C) and (b) 850-mb specific humidity (c.i. = 1 g k g - t ), and
the difference fields of (c) 500-mb temperature (c.i. = I°C) and (d) 850-mb specific humidity (c.i. = 1 g k g - t )
for N O 4 D V A R at 18:00 UTC 3 January 1989, verified against CTRL. (e) and (f) are the same as (c) and (d)
except for El.
Y.-H. Kuo et al. / Dynamics o/Atmospheres and Oceans 27 (1997) 439 470
452
termined problem. Without additional constraints, adjustments in the ICs could be rather
arbitrary, especially those fields not directly related to N °bs such as wind fields. It will
be interesting to examine the changes in wind fields as a result of refractivity data
assimilation. Fig. 6 shows the 300-mb wind speed (Fig. 6(a)) of El and the difference
field between El and NO4DVAR (Fig. 6(b)) at 18:00 UTC 3 January. We observe a
consistent increase of wind speed along the upper-level jet with a magnitude of about
130~
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m s
i ) at 1 8 : 0 0 U T C
3 January
1989.
(c.i. = i
E-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
453
3.5 m s - 1. The change in wind speed suggests a strengthening of relative vorticity over
Illinois associated with the upper-level disturbance (figure omitted). Since the model is
used as a constraint during the process of N °b~ assimilation, such adjustment is realized
through the model's internal dynamics.
It should be kept in mind that the extracted data on the 180-km grid may not be in
dynamical balance since the 90-km terrain is used in CTRL to generate simulated
observations (OBS) while the 180-km terrain is used for all the data-assimilation
experiments. The differences in model terrains are caused by reduction in grid resolution. Because of differences in model terrain, the simulated refractivity observations can
become inconsistent with the assimilation model (for example, there can be differences
in the elevation of a given sigma level between simulated observations and the
assimilation model).
In seeking reasons why errors over Greenland remain large after data assimilation, we
re-run CTRL using 180-km terrain, re-generate N °bs, and repeat E1 (now called
E5.180terrain). Results are shown in Fig. 7. We observe that errors of 300-mb
refractivity (Fig. 4(b)) and 500-mb temperature (Fig. 5(e)) over Greenland are eliminated after data assimilation (Fig. 7(a), (b)).
As shown earlier there is a significant improvement in the temperature and moisture
analyses as a result of refractivity data assimilation in El. An important question is: Will
these improvement last during the course of model prediction? To answer this question,
we present the vertical profiles of root-mean-square (r.m.s.) errors of temperature (Fig.
8(a)-(i)) and specific humidity (Fig. 8(j)-(r)), calculated for the entire model domain,
for E5.180terrain at 6-h intervals from 12:00 UTC 3 to 12:00 UTC 5 January. The time
evolution of r.m.s, errors for these two fields is quite different. The impact of
G P S / M E T data assimilation on temperature shows up most distinctly in the middle and
upper troposphere. More importantly, this impact appears to increase with time. In
contrast, the impact on water vapor occurs mainly in the lower and middle troposphere,
and it diminishes quickly with time. For example, the water-vapor r.m.s, error was
reduced by as much as 0.8 g kg -j at ~ = 0.85 at 18:00 UTC 3 January as a result of
refractivity data assimilation. This improvement was reduced to 0.2 g kg-1 by 00:00
UTC 4 January, in just 6 h. The impact then gradually diminishes with time. By the end
of the 48-h forecast, it was negligible. This shows that the water vapor is more
'transient' and 'passive' than temperature. The GPS data assimilation has a significant
impact on the moisture analysis, but, because moisture distribution changes quickly in
response to dynamic forcing in the course of model forecast integration, this impact does
not last very long (less than 24 h). Fig. 8 also shows that the model forecast errors
continued to increase with time, even for the experiment with data assimilation. The
forecast error growth is considerably larger than the impact due to refractivity assimilation. This suggests that there is much room for model improvement at such a resolution
(180 km). It should be noted that the forecast central pressure in the 180-kin model in
El (963 mb) is considerably higher than that of the 90-km control (938 mb). As will be
shown later, this difference can be significantly reduced by using a higher resolution
model for forecast integration following data assimilation.
As mentioned earlier, there was a significant reduction of errors in 300-mb refractivity over Illinois and Indiana after data assimilation (see Fig. 4). This is also the region
E-H. Kuo et al./ Dynamics of Atmospheres and Oceans 27 (1997) 439-470
454
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Fig. 7. Difference fields of (a) atmospheric refractivity (c.i. = 5 NU) at 300 mb and (b) temperature
(c.i. = I°C) at 500 mb at 18:00 UTC 3 January 1989 for E5.180terrain, verified against CTRL in which a
180-kin terrain is used as opposed to a 90-kin terrain.
where there existed a prominent PV anomaly. This PV anomaly provided the upper-level
forcing for the development of the surface cyclone. It is interesting to examine the
impact of refractivity assimilation on the structure of the PV anomaly. Fig. 9 shows a
cross-section of potential temperature (Fig. 9(a) and (b)) and PV (Fig. 9(c) and (d)) for
both NO4DVAR (left column) and E1 (right column) along the line A - B on Fig. 4(a).
Also shown are their errors (differences from CTRL; thick lines). Without refractivity
assimilation, the temperature error was as large as 3°C at 500 mb, directly under the PV
Y.-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
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Fig. 8. The r.m.s, errors o f temperature ((a)-(i), unit: °C) and specific humidity ((j)-(r), unit: g k g - 1) at 6-h
intervals from 12:00 UTC 3 January to 12:00 UTC 5 January 1989 for E5.]80terrain (solid line) and
N O 4 D V A R (dashed line).
456
:3oo
K-H. Kuo et al. / Dynamics qf Atmos '~heres and Oceans 27 ( 19971 439-470
: i~-328 ~
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Fig. 9. (a), (b) Cross-section along the line A--B in Fig. 4(a) of the potential temperature (thin lines, c.i. = 2 K)
and the potential temperature difference (thick lines, c.i. = I K) and, (c) and (d), potential vorticity (thin lines,
c.i. = I PVU) and its difference field (thick lines, c.i. = 0.6 PVU) for NO4DVAR (left column) and E1 (right
column) at 18:00 UTC 3 January, verified against CTRL
anomaly. The negative temperature error (cooling) above and on both sides of the
positive temperature error clearly suggests that the temperature perturbation associated
with the upper-level disturbance has a broader scale than the control and has a lower
static stability, which contributes to a weaker potential vorticity in N O 4 D V A R . Indeed,
the PV in the N O 4 D V A R experiment was weaker than C T R L by nearly 2 P V U
(potential vorticity units). The assimilation of refractivity significantly reduced the errors
in both the temperature and PV fields. As a result, the PV in E1 is sharper, stronger, and
extends deeper into the lower troposphere, and has a stronger influence on the surface
cyclogenesis.
Y.-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
-'t'
+
t'
,'-r-"
457
i4 "
.. l 'K
Fig. 10. Difference fields of SLP (shaded, c.i. = 2 mb) and PV on the 315-K isentropic surface (contour lines,
c.i. = 0.2 PVU) between E1 and NO4DVAR, and the wind vectors on the 315-K isentropic surface for El at
(b) 00:00 UTC 4 January, (c) 12:00 UTC 4 January, (d) 00:00 UTC 5 January, and (e) 12:00 UTC 5 January.
Fig. 10 shows the differences of PV (thin lines) on the 315-K isentropic surface and
sea-level pressure (heavy lines) between E1 and NO4DVAR for the period of 00:00
UTC 4 to 12:00 UTC 5 January at an interval of 12 h. At 00:00 UTC 4 January, the
sea-level pressure of the IOP 4 storm near Cape Hatteras in El was deeper than that in
NO4DVAR by 2.91 mb. Further downstream, a difference of 2.66 mb was found at
47°N, 44°W for the IOP 3a storm. In between these two storms, the sea-level pressure
was higher in E1 as compared with NO4DVAR. The difference in PV on the 315-K
surface was about 0.6 PVU at 00:00 UTC 4 January, and it was located over eastern
Ohio immediately to the northwest of the lOP 4 cyclone. A similar PV difference with
smaller magnitude (0.4 PVU) was found upstream of the lOP 3a storm. Twelve hours
458
Y.-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
later, the lOP 4 storm in E1 was deeper than that in NO4DVAR by 5.2 mb, and that for
the IOP 3a storm by 4 mb. In between the two storms, the ridge was enhanced by 4.3
mb. This clearly shows an amplification of the surface pressure wave. An interesting
pattern in the PV difference field began to develop directly above the surface cyclone at
this time, with a positive PV difference behind the storm, and a negative PV difference
ahead of the storm. The negative PV anomaly was produced by the rising low PV air
originating in the boundary layer (Reed et al., 1992). By 00:00 UTC 5 January, the
difference in sea-level pressure for the IOP 4 storm was as large as 10.9 rob. The
upper-level PV couplet above the surface cyclone also intensified. The surface cyclone
and the upper-level baroclinic wave amplified together during the next 12 h, ending with
a difference of 13.8 mb in pressure and 1.3 and - 2 . 1 PVU in PV. This figure shows
that the relatively small difference in the initial conditions between El and NO4DVAR
as a result of refractivity assimilation grows rapidly with time, and causes a major
difference in the development of surface cyclones and the amplification of the baroclinic
wave.
As discussed by Reed et al. (1992), the three building blocks tot surface cyclogenesis, from the PV perspective (Hoskins et al., 1985), consist of (1) PV with its origin in
the jet-stream-tropopause region, (2) surrogate PV associated with a surface warm
anomaly, and (3) low- to mid-level PV formed by diabatic heating due to condensation.
The previous section has demonstrated that refractivity assimilation improves the
analysis of the upper-level PV at the jet-stream level, and that it has a significant
influence on the subsequent evolution of the upper-level PV anomaly and surface
cyclogenesis. Does refractivity assimilation have a significant impact on the description
of the surface thermal anomaly (surrogate PV)? The answer is clearly affirmative. Fig.
11 shows the surface temperature of E1 and NO4DVAR and their differences at 00:00
UTC 4 January. Temperature differences of several degrees are found near the coast,
with the positive anomaly located to the south and the negative anomaly to the northeast.
These 'perturbations' create a stronger baroclinic zone over the western Atlantic ocean
in El, as compared with NO4DVAR, which is a necessary ingredient for surface
cyclogenesis.
The interaction of an upper-level PV anomaly and a low-level thermal anomaly in the
development of a baroclinic cyclone has been discussed by Davis and Emanuel (1991).
For the tOP 4 storm, the upper-level PV anomaly propagated from the vicinity of Lake
Michigan southeastward toward North Carolina during the 12-h period ending at 00:00
UTC 4 January, while the low-level thermal anomaly migrated from Georgia northeastward toward the same region. By 00:00 UTC 4 January, the upper-level PV anomaly
became interlocked with the low-level thermal anomaly. Subsequently, rapid cyclogenesis took place. The assimilation of refractivity data through a better definition of the
upper-level PV anomaly and the low-level thermal anomaly helped enhance this
coupling process, and produced a stronger cyclone. This process can be illustrated by
examining the PV and temperature differences between E1 and NO4DVAR from 18:00
UTC 3 January to 00:00 UTC 4 January at 2-h intervals along the path (line C - D in Fig.
5(c)) of the upper-level disturbance (Fig. 12). At 18:00 UTC 3 January, the PV
difference (thin lines) was as large as 1 PVU at 400 mb. Large positive temperature
differences (heavy lines) are found above the PV anomaly, with negative temperature
Y.-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
9O W
8O W
459
7O W
klJ!' ' , " i : " - ~ ................... / . . . . .
BOW
~OW
8O w
?ow
eow
7ow
?o w
Fig. 11. Surface temperature in (a) NO4DVAR and (b) E1 (thin line, c.i. = 2°C) at 00:00 UTC 4 January. The
differences of surface temperature between E1 and NO4DVAR are also plotted in (b) (thick lines, c.i. = I°C).
differences below. Such structure is consistent with the relationship between PV and
static stability. In the lower troposphere, a positive temperature difference of 2°C can be
found near the coast. This temperature 'perturbation' does not extend above 800 mb. At
18:00 UTC 3 January, the PV perturbation and the low-level temperature perturbation
(as a result of refractivity assimilation) are separated by as far as 1400 km. During the
next 4 h, the upper-level anomaly travels at a speed of 30 km in 2 h (about 50 m s -1)
toward the low-level thermal anomaly. The thermal anomaly itself does not move much,
except it intensifies with time. By 22:00 UTC 3 January, the thermal anomaly reaches a
magnitude of 3°C, and the PV anomaly moves to within 900 km of the temperature
anomaly. The distance between these two anomalies continues to shrink with time. By
00:00 UTC 4 January, the two anomalies are interlocked, and they both move eastward
together as the cyclone begin its course of rapid development.
460
K -H. Kuo et al. / Dynamics Of Atmospheres and Oceans 27 (1997) 439-470
I/--~+,
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.
t',
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z
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; 3 January
/
" -2
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,ooi) ~ ,
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~¢
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400 1
.,"
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0000UTC
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D
Fig. 12. Cross-section of differences m potential temperature (thick line, c.i. = I K) and PV (thin line,
c.i. = 0.2 PVU) between El and NO4DVAR along the line C-D in Fig. 5(c) from 18:00 UTC 3 January to
00:00 UTC 4 Januaryat 2-h intervals.
These results clearly show that the assimilation of G P S / M E T refractivity data can
recover atmospheric structures in temperature and wind fields (as reflected in the PV
and thermal anomalies), both in the upper and lower troposphere, that are highly
important to the prediction of surface cyclogenesis. Although the adjustments to the
initial condition are small, they grow rapidly as the baroclinic wave amplifies, and
consequently result in major differences in the surface cyclone. This suggests that
providing critical observations in the baroclinic unstable region (particularly over the
ocean) can be a key contribution of G P S / M E T refractivity data to numerical weather
prediction.
Y.-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
461
4.3. The importance of G P S / M E T data in the lower troposphere
Retrieval of occultation data obtained by the first low-earth-orbiting satellite carrying
a GPS receiver, MicroLab-1, showed that accurate vertical temperature profiles can be
obtained from approximately 40 km to about 5 kin. Below 5 km, multipath effects
caused by large gradients in refractivity, primarily due to water-vapor distribution,
reduced the signal-to-noise ratio significantly, and usually prevent an accurate retrieval
(Ware et al., 1996). Before an improved algorithm is developed for tracking the
low-level GPS signals, it is desirable to evaluate the relative importance of the low-level
refractivity data. To address this issue, we perform an experiment, E2.upper, in which
simulated refractivity data are assumed to be available only above tr = 0.7 (roughly 3
km). A comparison with E1 will illustrate the importance of the low-level refractivity
data.
Fig. 13 shows the difference fields in sea-level pressure and PV on 315-K isentropic
surface between E2.upper and NO4DVAR. A comparison between Figs. 13 and l0
shows notable differences. The change in cyclone pressure as a result of G P S / M E T
refractivity assimilation is considerably reduced if the low-level data are not used. On
the other hand, the adjustment in the upper-level PV field is increased. The positive PV
change at 00:00 UTC 4 January reaches a value of 0.88 PVU on the 315-K isentropic
surface for E2.upper as compared with 0.58 PVU in El. However, during the subsequent
36-h forecast period, there is no amplification of the PV difference between E2.upper
and NO4DVAR. By 12:00 UTC 5 January, it has a value of 0.7 PVU, while that in E1 is
1.3 PVU. The negative PV anomaly ahead of the storm is also similarly weak. The
difference in sea-level pressure grows only to a value of - 5 . 9 rob, far short of that in
E1 ( - 13.8 mb).
A cross-section of PV and temperature differences between E2.upper and NO4DVAR
along the path of the upper-level disturbance is shown in Fig. 14. No low-level thermal
anomaly can be identified east of the Appalachian Mountains at 18:00 UTC 3 January.
The PV difference exceeds 1 PVU and is located at about 350 mb, slightly higher than
that in El. A stronger negative temperature anomaly below the PV anomaly is retrieved
in E2.upper. Without the constraints of the lower-level refractivity data, the 4DVAR has
more degrees of freedom in making adjustments in the upper levels. The PV anomaly
continues to migrate toward the east coast at a speed similar to that in El. However,
even by 00:00 UTC 4 January, the E2.upper fails to create any appreciable thermal
anomaly.
These results illustrate the importance of low-level refractivity data. Without the
low-level thermal anomaly, recovered by assimilation of low-level refractivity data, the
PV aloft is far less effective in spinning up the low-level cyclogenesis.
4.4. The impact of horizontal resolution and line averaging
The previous experiments (El and E2.upper) assume that the G P S / M E T refractivity
data are available at every grid point of the 180-km model. No line averaging was
performed on the simulated data. This is considerably more optimistic than what is
available from the actual G P S / M E T occultation. In order to simulate the G P S / M E T
E-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
462
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measurements in a more realistic manner, we conducted an experiment (E3.random) by
distributing the refractivity measurements randomly in space, while keeping the averaged resolution at 180 km. In addition, a line averaging was performed along a random
direction for each measurement (see Section 3.1 for details).
The difference fields of sea-level pressure and PV on a 315-K surface between
E3.random and NO4DVAR are shown in Fig. 15 for the period of 00:00 UTC 4 January
to 12:00 UTC 5 January at 12-h intervals. The initial difference in sea-level pressure was
about 1 mb at 00:00 UTC 4 January. It grew rapidly with time, and by 12:00 UTC 5
January, it was as large as 14.6 mb, a magnitude very similar to that of El. The PV
perturbations also amplified with time, and reached a value of 1.1 PVU and - 2 . 1 PVU,
respectively, for the positive and negative anomalies. This shows that the random
distribution and line averaging did not degrade the impact of the simulated G P S / M E T
refractivity data.
Y.-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
463
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Fig. 14. Cross-section of differences in PV (thin line, c.i. = 0.2 PVU) and potential temperature (thick line,
c.i. = 1 K) between E2.upper and NO4DVAR at 18:00 UTC 3 and 00:00 UTC 4 January along the line C-D in
Fig. 5(c).
Fig. 16 compares the 12-h accumulated rainfall ending at 12:00 U T C 4 January for
E l , E3.random, and N O 4 D V A R . The rainfall distribution was nearly identical between
E1 and E3.random (particularly for precipitation associated with the lOP 4 storm),
Y.-H. Kuo et al. / Dynamics ~g'Atmospheres and Oceans 27 (1997) 439-470
464
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showing that distributing the refractivity observations randomly in space did not alter the
rainfall forecast. Another interesting finding is the similarity between El and NO4DVAR
in the rainfall prediction. Despite significant differences in sea-level pressure between
these two experiments, the differences in rainfall are not large. Although the maximum
rainfall ending at 12:00 UTC 4 January in NO4DVAR was 28.7 mm, slightly less than
that of E1 (35 ram), the rainfall pattern is highly similar. The similarity is even greater
for the next 12-h period (figure omitted). This leads us to believe that latent heat release
(and the diabatically generated PV) is not a crucial factor differentiating these two
180-km experiments. It is the difference in the baroclinic structures (as reflected in the
PV and thermal anomalies) with or without the G P S / M E T refractivity data assimilation
that causes the cyclone to behave differently in these two experiments.
In the final experiment, E4.random360, we reduce the spatial resolution of the
Y.-H, Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
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Fig. 16. Twelve-hour rainfall ending at 12:00 UTC 4 January for (a) NO4DVAR, (b) El, and (c) E3.random.
466
Y.-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
1010 ~
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Fig, 17. Time series of central pressure (in rob) for the simulated lOP 4 at 6-h intervals from 00:00 UTC 4
January to 12:00 UTC 5 January 1989 for NO4DVAR (dashed line), El (solid line), E2.upper (long and
short-dashed line), E3.random (dotted line), and E4.random360 (dash-dotted line).
G P S / M E T data to 360 km, tbllowing the same procedure as that of E3.random.
Examination of difference fields in sea-level pressure and upper-level PV between this
experiment and NO4DVAR indicates that despite the reduction of horizontal resolution
to 360 km, the assimilation of refractivity data still produces a notable impact on the
cyclone deepening (not shown).
Fig. 17 compares the time series of central pressure of the IOP 4 storm as simulated
in various experiments during the 36-h period ending at 12:00 UTC 5 January. At the
incipient stage of cyclogenesis, there is no significant difference in cyclone central
pressure (less than 2 rob). By the end of the simulation, E1 has a central pressure of 963
rob, while that of NO4DVAR is 975 mb. E3.random has nearly an identical pressure
trace to that of El. The final pressure of E4.random360 is 969 rob. The worst
data-assimilation experiment is E2.upper, which had a central pressure of 971 mb. It is
very instructive to see that the removal of the low-level G P S / M E T data has a greater
impact on the cyclone deepening than the combined effects of reducing the spatial
resolution of refractivity data to 360 km, distributing it randomly in space, and
performing line averaging. This again shows the importance of extending the G P S / M E T
data down to the lowest level possible. The significant difference between E3.random
and E4.random360 also suggests that horizontal resolution of G P S / M E T refractivity
data does have a noticeable impact on the quality of data assimilation and prediction. It
is important that we continue to increase the number of low-earth-orbiting satellites
carrying GPS receivers so that the potential value of G P S / M E T occultation data to
operational numerical weather prediction can be fully realized.
There might be a concern that the cyclones predicted by these 180-km data
assimilation experiments are all considerably weaker than that simulated by the 90-km
control experiment. For example, at 12:00 UTC 5 January, E1 produced a storm with a
central pressure of 963 mb, while that in the control was 938 mb. One should recognize
that although 4DVAR data assimilation often has to be performed on a model with
Y.-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
1010
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Fig. 18, Same as Fig. 17 except that a 90-km ten-level model is used for the forecast integrations after data
assimilation.
coarser resolution (or simpler physical parameterization) due to computational constraints, there is no reason not to use a higher-resolution model for forward integration
after the assimilation process. To demonstrate this point, we interpolated the optimal
initial conditions obtained after the refractivity assimilation to the 90-km grid, while
keeping the vertical levels at ten, and carried out the forward integration for all the
experiments. The results are shown in Fig. 18. It is interesting to note that almost all
experiments have produced an additional deepening in the range of 12-15 mb with the
use of higher resolution model for forward integration. On the other hand, there is no
change in the relative performance of these experiments. The cyclone in 90-km E1 is
now 948 mb, 15 mb deeper than the NO4DVAR experiment. With the use of higher
resolution prediction model, the distance between E4.random360 and E3.random became
smaller, arguing for the value of a G P S / M E T system with a limited number of LEO
satellites. Still, the E2.upper produced worse results than that of E4.random360 confirming the importance of the low-level refractivity data.
5. Summary and discussions
In this paper, we conducted a series of observing system simulation experiments to
assess the potential impact of G P S / M E T refractivity data on the prediction of an
extratropicat cyclone. We first conducted a 90-kin control simulation of an intense
marine cyclone, known as the ERICA IOP 4 storm, which deepened rapidly over the
western Atlantic Ocean with a pressure fall of 60 mb in 24 h. The 90-km control
experiment successfully simulated the observed storm, both in terms of cyclone intensity
and position. The results obtained from the control experiment were then used to
simulate G P S / M E T refractivity profiles with different spatial distributions and measurement characteristics. The simulated observations were assimilated into an 180-km model
during a 6-h period prior to the rapid cyclogenesis stage. The first-guess fields for the
468
E-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
180-km model were provided by degrading the control 90-km experiment results to a
horizontal resolution of 720 km. Forward model prediction was performed for each
assimilation experiment, and the results were compared with the no-assimilation experiment to assess the impact of G P S / M E T refractivity data on short-range prediction of an
extratropical cyclone.
In the first assimilation experiment, we assume that the G P S / M E T refractivity data
are available at every grid point of the 180-km model. No measurement errors are
added, and no line-averaging is performed. This experiment represents an upper bound
for the impact of G P S / M E T data assimilation. The assimilation of refractivity data
produced a significant improvement both in the temperature and moisture fields. The
initial improvement in the water vapor field in the lower troposphere is particularly
impressive. However, we observe a significant difference between the behavior of
temperature and moisture fields. The improvement in the humidity field caused by
incorporating G P S / M E T refractivity was largely lost within 12 h of the forecast. In
contrast, the improvements in the temperature field were retained through the forecast.
This suggests that the moisture field is passive and dynamically driven (at least in this
case). The value of G P S / M E T refractivity data in the improvement of moisture analysis
and precipitation is likely to be confined to very short-range mesoscale prediction.
An interesting result from this experiment was the improvement in potential vorticity
and the forecast winds. Even though the refractivity data are not directly related to the
wind field, through internal model dynamics, improvements in the temperature induced
improvements in the wind fields. Analysis of the PV and temperature fields shows that
the assimilation of G P S / M E T refractivity data produced a considerably improved
description of the upper-level potential vorticity anomaly, which is the primary upperlevel forcing mechanism for the low-level cyclogenesis, and the low-level thermal
anomaly, which is also an essential ingredient for cyclogenesis. Although the initial
changes due to refractivity assimilation in upper-level potential vorticity and sea-level
pressure are small and subtle, they grow rapidly as the baroclinic wave develops. By the
end of the forward integration, the experiment with refractivity assimilation has produced a surface cyclone 13 mb deeper than that of the no-assimilation experiment.
If one views the adjustments due to refractivity assimilation as perturbations in the
initial conditions, this shows that there is significant predictability error growth associated with the development of the baroclinic cyclone. We note that the error growth is
much less, or does not exist, outside the region of cyclone development. This suggests
that the 'importance' of data is not uniform across the model domain. Critical observations that help better define the structure of the upper atmospheric baroclinic wave and
the lower-level thermal structure will have the most positive impact on the prediction of
the storm. The importance of the low-level thermal structure is illustrated by a second
experiment, in which we assume that the refractivity data are limited to 3 km and above.
Even though the refractivity data are distributed evenly at every grid point, the lack of
lower tropospheric observations prevented a proper definition of the low-level thermal
structure. The improved definition of upper-level disturbance in itself was insufficient to
bring the cyclone to a proper depth. As a result, the impact of refractivity data on
cyclone deepening was reduced from 13 mb in 36 h to 6 mb in 36 h, less than 50% of
the improvement in the experiment in which all-level data were assimilated.
Y.-H. Kuo et al. / Dynamics of Atmospheres and Oceans 27 (1997) 439-470
469
There is a concern that distributing the refractivity evenly at every grid point is overly
optimistic for an operational G P S / M E T system. Moreover, the inherent horizontal
averaging associated with the ray path of GPS signals needs to be taken into consideration. Therefore, we performed a third experiment, in which the G P S / M E T data were
randomly distributed at the horizontal resolution of about 180 km. Also, a line averaging
was performed along a randomly determined direction with a length scale of 180 km.
Interestingly, we found few differences between this experiment and the one in which
refractivity data were distributed at every grid point and without averaging. We conclude
that the random distribution and the line averaging associated with the inherent nature of
GPS occultation data do not pose a particular problem for an effective assimilation of
such data into a weather-prediction model.
In the final experiment, we relaxed the spatial resolution from 180 km to 360 km.
The impact on cyclone deepening was reduced by 6 mb in 36 h. However, even at a
360-km horizontal resolution, with line averaging and random distribution, the GPS-type
refractivity data still produced a notable impact on the prediction of this cyclone. This
shows that even with a moderate number (i.e. a dozen) of low-earth-orbiting satellites, a
G P S / M E T system is likely to have a positive impact on global numerical weather
prediction.
Acknowledgements
The authors are grateful to R. Anthes, M. Exner, B. Gall, R. Serafin, and R. Ware,
for their continuous support. They especially thank S. Sokolovskiy for the discussions
related to the G P S / M E T refractivity observational characteristics and R. Anthes, R.
Reed, and S.-W. Yang for their valuable and constructive comments. This research was
supported by the National Science Foundation and the Federal Aviation Administration
through a corporate agreement with NCAR and UCAR, ATM9209181 under scientific
program order EAR9405501 and the Department of Energy's Atmospheric Radiation
Measurement Program (DOE/ARM) grant number DE-A105-90ER1070.
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