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INCLUDING
IMPLEMENTATION OF THE GFDL/URI HURRICANE-OCEAN COUPLED MODEL
Morris
A. Bender
Isaac Ginis *
Timothy P. Marchok **
Robert E. Tuleya
Geophysical
Fluid Dynamics Laboratory, NOAA
Princeton, New Jersey 08542
(Tel. 609-452-6559; FAX 609-987-5063, e-mail: mb@gfdl.gov)
Graduate
School of Oceanography *
University of Rhode Island
Since
1995, the GFDL Hurricane Prediction System has provided operational guidance
for forecasters at the National Hurricane Center (NHC) in both the Atlantic
and East Pacific basins (Kurihara, Tuleya and Bender 1998, hereafter referred
to as KTB). In addition, a version of the GFDL model (GFDN) has been used
by the Navy to provide operational guidance for storms in most of the other
ocean basins as well (Rennick 1999). Although the model has shown great
skill in track prediction, the GFDL Hurricane Prediction System exhibits
small track biases and rather large intensity biases (Bender and Ginis
2000). Indeed, in spite of a steady improvement in tropical cyclone track
forecasting over the last two decades (Lawrence et al. 1997), there still
appears to be little skill in predicting hurricane intensity changes.
To
help reduce the large intensity errors in the GFDL prediction system, an
improved version of the GFDL model has been developed in which the forecast
model has been coupled with a high-resolution version of the Princeton
Ocean Model (POM). This new model has been run in parallel with the operational
GFDL model during the past three hurricane seasons, and has demonstrated
substantial improvements in the prediction of storm intensity, particularly
measured by the storm's minimum sea level pressure, with a reduction of
nearly 26% in the mean error.
Another
intensity-related problem is that in strong wind conditions, the GFDL model's
prediction of the low level wind has exhibited a large negative bias and
poor pressure wind relationship, as the model tends to under-predict surface
wind speeds for a given central pressure. To address this problem, another
important change will also become operational in the 2001 hurricane season
in which an equation for the prediction of turbulent kinetic energy is
added to the diffusion parameterization. Tests have indicated that this
results in a significantly improved vertical profile of wind speed in the
boundary layer and a much improved pressure wind relationship. Finally,
changes were also incorporated into the initialization of the model's specified
vortex (Kurihara, Bender and Ross 1993; hereafter referred to as KBR),
which has lead to an initial storm intensity that more closely matches
the observed value and has also decreased the tendency of the model to
over-intensify weak systems during the first 12-24 hours of the forecast.
Besides
improving intensity forecasts, it is important that any changes do not
lead to an appreciable degradation in the track forecasts. It is encouraging
that tests with this entire package have shown a decrease in the average
track error of 5-10% in the 24 to 72h hour time period.
2.) Outline of Atmospheric Model and changes implemented in 2001
The
GFDL multiply-nested moveable mesh model has been described in previous
publications (e.g., Kurihara et. al 1995; Kurihara et. al 1998) and will
only briefly be outlined here. The model is a primitive equation model
formulated in latitude, longitude, and sigma coordinates, with 18 vertical
sigma levels. The grid system for each of the triply nested meshes is summarized
in Table 1.
The
model physics of the current operational hurricane model include cumulus
parameterization described by Kurihara (1973) with some additional modifications
(Kurihara and Bender, 1980, appendix C); a Monin-Obukhov scheme for the
surface flux calculation; and the Mellor and Yamada (1974) level-two turbulence
closure scheme for the vertical diffusion, with a background diffusion
coefficient added. As described by Tuleya (1994), the Schwarzkopf and Fels
(1991) infrared and Lacis and Hansen (1974) solar radiation parameterization
were also incorporated, with interactive radiative effects of clouds and
a diurnal radiation cycle. The land surface temperature is computed by
an energy equation containing a soil layer.
In
the upgraded 2001 system, the vertical diffusion will be upgraded to
a level 2.5 Mellor-Yamada turbulent closure scheme. In this formulation,
an equation for the prediction of turbulent kinetic energy is added to
the diffusion parameterization. The diffusion coefficients KM
and KH are then computed using the turbulent
kinetic energy (b2) computed by equation
(4:23) of Miyakoda and Sirutis (1977). Near the region of maximum winds
this scheme significantly enhances the transfer of momentum from above,
leading to a more vertically mixed hurricane boundary layer with higher
surface winds. This corresponds more closely with recent results observed
using GPS sondes. In addition, in the upgraded system model surface winds
will again be estimated by the lowest model layer as in TPB # 424
(1995), since it is evident that the reduction to 10m by the Monin-Obukhov
formulation is not valid. Together, these changes lead to a much improved
pressure-wind relationship and improved wind forecasts as will be shown
later
3.) Outline of Atmospheric Initialization and changes implemented in 2001
In
this section, changes that will be made to the atmospheric initialization
will be described in detail. As outlined in KTB, the initial condition
for the atmospheric model is obtained from the current AVN which is interpolated
onto each of the three nested meshes. Two filters are used to remove the
original vortex from the AVN analysis following the procedure outlined
in KBR and modified by Kurihara, Bender, Tuleya, and Ross 1995 (hereafter
referred to as KBTR).
First,
using a scale selective filter, the AVN fields (A) of wind, temperature
and surface pressure are partitioned into a large-scale component called
the basic field (B) and the deviation field denoted as the disturbance
field (D):
Next,
using a second filter, the disturbance field is separated into the hurricane
component (H) which will be removed from the analysis and a non-hurricane
component (NH) that should be retained. The environmental field is then
obtained by combining the non-hurricane component of the disturbance field
with the basic field over the entire model domain.
In
the filtering technique it is assumed that the hurricane component (H)
that is to be removed is entirely confined within a filter domain (ro)
so that the region of the global analysis beyond ro by definition remains
unchanged. The extent of the filter domain (ro) is computed at 24 radial
points surrounding the AVN vortex, determined by testing the radial profiles
of the tangential component of the disturbance wind, from the vortex center
outward. Once ro is determined at each of the 24 azimuthal angles, it was
then multiplied by 1.25 (rfact) to guarantee
that the hurricane component is entirely contained within the filter domain.
It was found that with the new AVN analysis, the value of rfact,
could be reduced with the analysis vortex still adequately removed. The
obvious advantage of reducing the size of the filter domain is to lessen
the possibility of removing important features from the original global
analysis. In extensive tests it was determined that a value of 1.1 appeared
optimal for rfact both by the reduction
of the track error in the test cases and in careful analysis of the resulting
fields in these cases. Hence, in the new upgraded GFDL forecast system,
we have changed the value of rfact
from
1.25 to 1.1.
As
summarized in KBR, during the next step of the initialization, a model-compatible
specified vortex is generated and inserted back on to the environmental
field at the correct storm position. The specified vortex is generated
from the time integration of an axi-symmetric version of the hurricane
prediction model. During the integration, the tangential component of wind
is gradually forced over a 60h time period toward a target profile based
on the storm observations provided by the National Hurricane Center (NHC)
in 4 quadrants surrounding the storm. Four modifications were made to enable
the initial wind field to more closely match with the correct observed
storm intensity.
(1.)
The
tangential wind is forced toward the target profile at the model level
ktop (defined as the model sigma level closest to 850 hPa). The environmental
flow at each observation location is subtracted from the total observed
wind to obtain the wind component related to the vortex. However, since
the observed wind data available are reported surface values, in the present
system they are multiplied by an empirically obtained factor f (presently
1.30) to estimate the tangential component at level ktop. However, the
value of f tended to be too large and a more reasonable value of 1.20 has
been tested and found to yield positive improvements. In the new upgraded
GFDL forecast system, the value of f has been changed from 1.30 to the
new value of 1.20.
(2.)
In
the previous system, the forcing of the tangential component to the target
value was eliminated during the last hour of the time integration of the
axi-symmetric model, to reduce any imbalance that may have developed in
the model fields due to the forcing. However, careful analysis indicated
that this could cause a large spin-up or spin-down of the vortex due to
the absence of any environmental conditions in the vortex spin-up that
may impact the storm intensity in the three dimensional model. By retaining
the forcing throughout the entire period of the integration, it was found
that the final winds were closer to the targeted values. In the new
upgraded GFDL forecast system, the forcing of the tangential winds to the
target profile is retained throughout the entire axi-symmetric integration.
(3.)
In
general, the axi-symmetric model is integrated to 60h. The integration
is terminated earlier if the surface pressure difference (pdiff
) between the minimum surface pressure and the value in the
outer region of the storm exceeded the observed pressure difference plus
an additional factor Dp where
Dp=
min (pmax , a + b ppiff
)
a = 1 hPa; b = .25,
pmax = 10 hPa
(2)
However,
it was found that in some cases this lead to storms that were initially
much deeper then observed. To correct this problem, in the new upgraded
GFDL forecast system, we have reduced this correction factor (Dp) by changing
the values of the constants b and pmax
to the values .05
and
4 hPa, respectively.
(4.)
At
the beginning of the current initialization, the axi-symmetric vortex was
initialized with the environmental values of the moisture (ME
=MBasic
+ MDis - MHurr);
and temperature at the storm center. At the end of the axi-symmetric spin-up,
the deviation of the water vapor mixing ratio at each point from the value
at the outer storm region (MAxi ) was then
computed (e.g., Fig. 3 of KBR). This value was added entirely back onto
the environmental moisture field as a function of distance from the storm
center to obtain the final moisture (MF)
at the start of the integration:
MF
= b * MAxi + ME
(b = 1 over water: b =.5 over land)
(3)
However,
it was found that this often lead to excessive amounts of humidity in the
storm region initially, especially for weak storms. This likely contributed
to the positive intensity bias during the first 12-24 hours of the forecast,
as the vortex often began to rapidly spin-up at the start of the forecast.
To help reduce this false spin-up, the value of b was reduced so that the
initial humidity fields in the storm region would have more reasonable
values. For well developed and more intense storms, the value of b would
be expected to be larger which was confirmed by examining the storm structure
of mature storms after many hours of integration. Since the actual value
of b is somewhat arbitrary, the most reasonable approach was to make it
a function of the observed intensity tendency over the previous 6 hours
as well as the storm's current intensity determined by the central surface
pressure. Taking these considerations into account we obtained the following
formula for b as a function of the current observed storm intensity pcur
(hPa)
and the observed intensity tendency over the last 6 hours (ptend):
bi
= max (.35 , pbase + ptend
*
a )
ptend = pold
- pcurr ; a = .035
(4)
b
= min (1.0, bi)
pbase
= .5 + bint
(5)
bint
=
.4
pcur < 960 hPa
bint
= .4 * (985. - pcur )/25.
960 < pcur
< 985 hPa
bint
=
0.0
pcur > 985 hPa
As
seen in equation 4, b is bounded by the values of .35 and 1.0.
4.) Outline of the Ocean Coupled Model
The
most substantial change to be implemented in the 2001 hurricane forecast
system is the coupling of the GFDL forecast model with a high-resolution
version of the Princeton Ocean Model (POM). The specific model details
and experimental design have been outlined extensively in Bender
and Ginis (2000), hereafter referred to as BG. For proper simulation
of the ocean interaction, the ocean model should have a highly accurate
representation of the upper ocean mixed layer physics, which has been clearly
demonstrated by the Princeton Ocean Model (e.g., Blumberg and Mellor 1987).
POM is a three-dimensional, primitive equation model with complete thermohaline
dynamics, formulated with an ocean-bottom following, sigma vertical coordinate
system and a free surface. The model employs a second-order turbulence
closure scheme (Mellor and Yamada 1982). The momentum and thermodynamic
equations are solved with the prognostic variables of free surface, potential
temperature, salinity and velocity computed.
In
the current model configuration, three ocean model domains are used (Fig.
1). The grid resolution of each domain is 1/6o
which matches the finest resolution of the innermost nest of the hurricane
model. The first domain spans the region from 15o
to 31oN and from 75 to 98oW
and includes all of the Gulf of Mexico, the northwestern portion of the
Caribbean Basin, and the southwest portion of the South Atlantic Bight.
The second domain covers the western and central Atlantic area from 10o
to 47oN and 48o
to 82oW. The third domain covers the eastern
most Atlantic, from 10o to 40oN
and from 60o to 30oW.
Most of the Atlantic basin in which NHC has forecast responsibility, is
covered by one of the three forecast domains. At the start of each forecast
cycle, one of the three ocean domains is selected, based on the initial
and 72h forecasted storm position. A summary of the vertical sigma levels
for each of the three domains is presented in Table 2.
The ocean interaction is only implemented in the Atlantic basin.
During
the coupled forecast, the ocean model is integrated with a 1350 second
time step while the three atmospheric meshes (Table
1) are integrated with time steps of 90, 30 and 15 seconds, respectively.
Thus, the inner nest of the atmospheric model, with a corresponding 1/6o
grid resolution, is integrated 90 times during one ocean time step. In
the present system, the atmospheric wind stresses, the surface radiative
fluxes and fluxes of sensible and latent heat are interpolated to a uniform
1/6o resolution and then passed from the
atmospheric to the ocean domain. The ocean model is then integrated one
time step in parallel with the atmospheric model which uses SSTs from the
previous ocean step. At the time step in which synchronization of the atmospheric
and the ocean model occurs the forecasted oceanic SSTs are passed to the
atmosphere and interpolated to the nested grid domain and the updated atmospheric
fluxes are passed to the ocean. In the present system, changes of surface
stresses due to oceanic waves are ignored.
5.) Ocean model initialization
A
realistic ocean and hurricane initialization is critical for proper simulation
of the ocean response in the coupled hurricane-ocean system. The current
operational GFDL hurricane model uses the real-time SST data used in the
operational AVN global analysis. The current resolution is too coarse to
capture the large horizontal gradients of surface temperature on smaller
spatial scales. In addition, the interaction between the ocean and the
hurricane is also largely controlled by other properties of the upper ocean
such as the mixed layer depth and stratification of the upper thermocline
and upper ocean currents. Since there is no real-time sub-surface ocean
data in advance of the hurricane operationally available, the ocean initialization
relies on a diagnostic and prognostic spin-up of the ocean circulation
using available climatological ocean data in combination with the real-time
SST data. The initialization procedure, as outlined in detail in BG,
consists of four steps. The ocean model is initialized by utilizing the
monthly averaged profiles of temperature and salinity produced by the NAVOCEANO
Generalized Digital Environmental Model (GDEM). GDEM is an ocean climatology
from the U.S. Navy observational database. The GDEM data provides the starting
fields of temperature and salinity for the ocean model while the initial
velocity field is set to zero. The ocean model is then integrated for one
month in diagnostic model without surface forcing (e.g., holding the temperature
and salinity constant while allowing the velocity field to evolve). This
is followed by a three month prognostic run in which climatological GDEM
temperatures and salinity at the sea surface is fixed in time and wind
stress forcing from the Comprehensive Ocean-Atmosphere Data Sat is applied.
In the operational implementation, the ocean condition at the end of this
second step provides the data sets for each domain and for each month in
which a hurricane forecast will be made. Next, once a day and for each
of the three ocean domains, the upper ocean structure is adjusted to a
more realistic pre-storm condition by assimilating the current sea surface
temperature form the NCEP operational global analysis. In this step, the
GDEM temperatures are replaced by the NCEP SSTs and a prognostic model
integration is continued for 2 additional days, keeping the temperatures
at the surface constant.
In
the final ocean initialization step, the cold wake produced by the hurricane
during the three-day period prior to the start of the forecast is generated.
This step is necessary since the cold wake is not resolved is the current
NCEP SST analysis. In this step the ocean model is forced by prescribed
hurricane wind stress forcing using a hurricane axi-symmetric surface wind
field generated from the National Hurricane Center storm message files.
The surface stress is calculated using a simple bulk transfer formula with
a drag coefficient. The ocean model is simply integrated with the above
mentioned forcing, with the final ocean condition serving as the initial
condition for both the atmospheric and ocean parts of the coupled model.
As
mentioned previously, a coupled version of the previous operational GFDL
system has been run in parallel with the operational uncoupled model during
the past several years. This model has demonstrated significant improvement
in storm intensity prediction, particularly in the forecast of the storm's
minimum sea-level pressure compared to the current operational model. Fig.
2 shows an example of the improved intensity prediction during the
very active 1999 hurricane season. Improvement in the intensity prediction
is seen at each forecast time level, with an average reduction of 25% in
the error of the forecasted central pressure. A similar result was found
for the 1998 season, as well as in a limited number of test cases during
the 1995-1997 season (Bender and Ginis 2000). Although
some improvement in the prediction of the maximum low-level winds occurred
with the coupled model, the overall improvement was limited because of
the tendency to under-predict the low-level wind in strong wind conditions
with the present atmospheric model. However, this will be remedied with
implementation of the changes outlined in sections 2 & 3 as shown in
Fig.
3. Here the pressure wind relationship is shown (forecasted minimum
pressure vs. forecasted low-level winds) for both the current operational
GFDL model (blue) and the new system (red) tested from cases from the 1999
and 2000 hurricane season. The predicted low-level winds are now much closer
to the observed values for a given central pressure, particularly for winds
greater than 90 knots. In this set of cases, the model intensity prediction
exhibited skill relative to SHIFOR at 24h, while the old GFDL system had
skill only at the 72h time level (Fig. not shown).
Improvements
in track were also demonstrated with the new GFDL system (Fig.
4) at all forecast time levels in test cases for storms that occurred
during the two past hurricane seasons. In this first set of cases, both
the new and old GFDL forecast systems were run from the current AVN global
analysis. This enabled us to see the impact of the new changes to the GFDL
model in 2001 in a wide variety of cases over the past two hurricane seasons.
The improvements were statistically significant at the 24, 36 and 48h time
period at the 95% confidence level, with a reduction in the average track
error of about 10% at these time levels and 6% at 72h. It is interesting
to note that in the homogenous comparison with several of the global models
that also provided track guidance to NHC, some of these models did slightly
better then the old GFDL system (bottom) particularly at the later forecast
periods. However, the new GFDL system performed better then all of the
other models at every time period for this limited set of cases.
The
new GFDL package was also tested for 51 cases during the 2000 hurricane
season, using the new AVN global analysis that will be operational during
the 2001 season. The results for the track error, normalized with respect
to CLIPER, are shown next (Fig. 5) both for the Atlantic
and Eastern Pacific basin. Since the coupling with the ocean in the new
GFDL model only occurs in the Atlantic basin, the East Pacific results
were run uncoupled but with all the changes outlined in sections 2 and
3. In the Atlantic very little difference in track performance is
noted with the new system. However, the model performance in this basin
was already quite skillful, as seen in the comparison with the official
forecast. In contrast, in the East Pacific, the new GFDL system run from
the new AVN global model exhibited considerable improvement at all time
levels beyond 24h. The improvement was statistically significant both at
48 and 72h time periods, with reduction in track error of about 20%, with
reduced track error for 66 and 70% of the cases, respectively.
The
48h track error for each of the individual storms in this test set is presented
next in Fig. 6. Much of the poor performance of the
GFDL model for Hurricane Keith was dramatically reduced with the new system.
Fig.
7 shows one example from the forecast at the 0000 UTC 1 October initial
time. The model also performed better for Hurricanes Olivia,, Gilma and
Hector in the East Pacific which had large errors in several of the operational
GFDL forecasts.
Finally,
the improvements in the intensity forecast with the new system are shown
in Fig. 8 for the test cases in the Atlantic. The very
poor performance of the GFDL model during the 12-36h forecast period is
dramatically reduced with the new system. Although the model still exhibited
problems at forecast hour 12, the GFDL model showed skill relative to SHIFOR
by 24h with the new system with skill of over 20% relative to SHIFOR at
36h. This is particularly encouraging considering the difficultly in the
intensity prediction that occurred during the 2000 season. It is also encouraging
that the new GFDL model performed better than the SHIPS intensity prediction
model in the 36 to 72h forecast period. However, by 72h the new GFDL model
performed slightly worse than the operational GFDL model. This was because
of over-prediction of the storm intensity which was greater in the new
system due to the improved pressure-wind relationship for strong storms.
This indicates that further refinements to the model physics, particularly
in the parameterization of convection and moist processes are necessary
before the GFDL can be relied on for consistently skillful intensity prediction,
particularly in sheared situations where the model usually tends to greatly
over intensify storms. Nevertheless, it is anticipated that the new model
will provide useful intensity prediction particularly in storms that are
not undergoing strong vertical shear. This should make it a valuable tool
to the National Hurricane Center, particularly in conjunction with other
intensity prediction models such as SHIPS.
Bender, M.A. and I. Ginis, 2000: Real-case simulations of hurricane-ocean interaction using a high-resolution coupled model: effects on hurricane intensity. Mon. Wea. Rev., 128, 917-946.
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Kurihara, Y., M.A. Bender, R.E. Tuleya and R.J. Ross, 1995: Improvements in the GFDL hurricane prediction system. Mon. Wea. Rev., 123, 2791-2801.
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Figure 1 The three ocean model domains used in
the GFDL hurricane-atmosphere coupled system.
Figure 2 Average error in central pressure (hPa) at each forecast period
for forecasts run during the 1999 hurricane system both for the operational
(blue) and coupled (red) GFDL model.
Figure 3 Plot of the pressure wind relationship (forecasted minimum
pressure vs. forecasted low-level winds) for both the operational GFDL
model (blue) and the new 2001 system (red) for test cases from the 1999
and 2000 hurricane season. The forecasted values at each of the forecasted
time levels are plotted.
Figure 4 Plot of the track forecast skill relative
to CLIPER (top), for both the operational (old) GFDL model (black), the
new GFDL forecast system (red) and the official forecast (blue dashed)
run for 44 test cases from the 1999 and 2000 hurricane season using the
current 2000 AVN global analysis. A homogenous comparison (bottom) of the
track forecast skill compared to several of the operational global models
is also presented. The official forecast shown in this figure and in subsequent
ones is presented as reference since it is based on 6 hour earlier model
guidance.
Figure 5 Plot of the track forecast skill relative to CLIPER (top),
for both the operational GFDL model (black), the new GFDL forecast system
(red) and the official forecast (blue dashed) for test cases from the 2000
hurricane season using the new 2001 AVN global analysis both for the Atlantic
(top) and Eastern Pacific (bottom).
Figure
6 Scatter diagram of the 48 forecast error (nautical miles) for each of
the test cases in Fig. 5 for both the Atlantic (top) and Eastern Pacific
(bottom), comparing the current operational GFDL model and new 2001 version.
Figure
7 Forecasted storm tracks for Hurricane Keith using the operational GFDLforecast
system (red) and the new GFDL forecast system (greeen dashed) compared
to the observed track (black), starting from the 0000 UTC 1 October initial
time.
Figure 8 Plot of the intensity error relative to SHIFOR for the operational
GFDL model (black), the new GFDL forecast system (red), the official forecast
(blue dashed) and the SHIPS intensity model (green), for test cases from
the 2000 hurricane season in the Atlantic basin using the new 2001 AVN
global analysis.
TABLE 1. Grid system of the triply-nested mesh
hurricane model.
|
|||||||
Mesh | Grid
resolution (degree) |
Longitude (deg) |
(points) |
Latitude (deg) |
(points) | Time
step (sec) |
|
|
|||||||
1 | 1 | 75 | (75) | 75 | (75) | 90 | |
2 | 1/3 | 11 | (33) | 11 | (33) | 30 | |
3 | 1/6 | 5 | (30) | 5 | (30) | 15 | |
|
TABLE 2 Summary of vertical sigma levels in the ocean model and depths (m) in the deepest regions of the Gulf of Mexico and Eastern and Western Atlantic
|
|||||
Gulf of Mexico
|
Western and Eastern Atlantic
|
||||
k level | sigma | depth | sigma | depth | |
|
|||||
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 |
-0.0017
-0.0050 -0.0083 -0.0117 -0.0150 -0.0183 -0.0217 -0.0250 -0.0283 -0.0317 -0.0417 -0.0583 -0.0833 -0.1250 -0.1833 -0.2583 -0.3667 -0.5167 -0.7000 -0.9000 -1.0000 |
-5
-15 -25 -35 -45 -55 -65 -75 -85 -95 -125 -175 -250 -375 -550 -775 -1100 -1550 -2100 -2700 -3000 |
-0.0009
-0.0027 -0.0045 -0.0064 -0.0082 -0.0100 -0.0118 -0.0141 -0.0168 -0.0200 -0.0245 -0.0318 -0.0455 -0.0682 -0.1000 -0.1409 -0.2000 -0.2818 -0.3818 -0.5091 -0.6727 -0.8818 -1.0000 |
-5
-15 -25 -35 -45 -55 -65 -77.5 -92.5 -110 -135 -175 -250 -375 -550 -775 -1100 -1550 -2100 -2800 -3700 -4850 -5500 |