an efficient and effective explicit damping time
TRANSCRIPT
U.S. DEPARTMENT OF COMMERCENATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION
NATIONAL WEATHER SERVICENATIONAL METEOROLOGICAL CENTER
OFFICE NOTE 249
An Efficient and Effective ExplicitDamping Time Integration Scheme
Clifford H. DeyDevelopment Division
DECEMBER 1981
This is an unreviewed manuscript, primarilyintended for informal exchange of informationamong NMC staff members.
. i
An Efficient and Effective Explicit DampingTime Integration SchemeS .w~ ; -~~~by Clifford Dey
I. Introduction
There are two general classes of solutions permitted by the set of
primitive equations we use to describe atmospheric motions -- meteorological
modes and gravity-inertia modes. The meteorological modes most closely
;describe the atmospheric motions that produce most of our everyday weather
and are therefore the ones we seek to predict. Gravity-inertia motions,
although present in the atmosphere, are generally of much less importance.
By - In numerical prediction models, however, the amplitudes of the gravity-
inertia modes can become abnormally large and interfere with the prediction
of the more important synoptic-scale meteorological motions. One method
of dealing with this problem has been to develop time integration schemes
that reduce the amplitudes of the gravity-inertia motions while leaving
_ 00 the meteorological motions relatively untouched.
There are two general types of selectively damping time integration
schemes. One type are those whose damping is frequency-dependent. They
rely on the fact that many of the most offensive gravity-inertia motions
have much higher frequencies than do the meteorological modes in order
to achieve their selectivity. Examples of frequency-dependent damping
integration schemes are the Euler-backward method (Matsuno, 1966) and the
Robert time filter (Robert, 1966). The second type of damping time inte-
gration schemes achieve their selectivity by treating the linear terms
of the model equations, which are most closely associated with gravity-
inertia motion, differently from the nonlinear advection terms. The
best-known scheme of this type is the semi-implicit backward method
2
(Kurihara, 1965). The only explicit technique in this class is a vari-
ation of the Euler-backward scheme described by Kurihara and Tripoli
(1976).
All of the explicit damping time integration schemes require more
computer time than the nondamping methods. This seems a rather high
price to pay for noise control. In this paper, an explicit, selectively
damping time integratfon scheme is described that requires substantially
less computer time than simple centered differences. The computational
economy is achieved by incorporating into the centered time integration
method a damping procedure originally conceived by Okamura (see Nitta,
1969) and later generalized by Grant (1974). The next section describes
the basic concept of incorporating the generalized Okamura technique
into the centered time difference scheme. The integration method itself,
the Semi-Interative Method, is presented and analysed in Section III.
W~ 0Simple numerical tests of the Semi-Iterative Method are described in the
fourth section. Section V contains some concluding remarks.
II. Application of the generalized Okamura procedure to centered dif-
ferences in time
The basic idea behind the semi-iterative method, which will be
discussed in the next section, is to incorporate the generalized Okamura
technique into the centered difference time integration scheme in a
particular way. Before considering the semi-iterative scheme in its
entirety, however, it will be instructive to consider the effects of
introducing the generalized Okamura technique into centered time dif-
ferences with a simple example.
Consider the oscillation equation
(1) a i k b
where is any variable, t is time, k the wave number, and c is
3
the phase speed. A centered difference representation of this
equation is
(2) - I 2Lcec t
where CtGkCt ,/4tis the time step, and tAtis the time level. The
generalized Okamura technique applied to is represented by the equa-
tions A
c4) = c4) -0
A A A* (3) ( 4) = V .4 LC -
0 Qt = t14 d+ ) ¢t_ fQ Elimination of reference to ) in (3) gives
(4)
" can be positive number. The first way of incorporating this potr
damping device into (2) is to replace ~ with its damped counterpart.
Using (4) one then obtains
, 0- R t t e~~~~~~It -1 (5) = - L _o. B
in which B = 1-oa C, (note that this can be done n times. Then
B= (i - *CC) . In this note, only n=l will be considered).
In order to analyze the effect of this substitution, let ) be
represented by
Let , the time-dependent part of , be given by
- -L - e Cq At
where c* is the numerical phase velocity. Thus,t~~~~~-i [kC~At
where X = . Furthermore,
(6) L~~~
ent
,j ·V
I -, I I~f:: :r: I
.. .,. - V ,_ .; .' - ,- ? , . .. £ ,, ,,_. . . " ,, , ! --- * . , -.; i .V.-.,I .i, :..r
4
In general, X is a complex number (+ +r+- L) . The magnitude
of the time-dependent part of the solution is
(7) V =
while the numerical phase angle (e) is given by
However, it will be more convenient to refer to the ratio (R) of the
numerical to the analytic (-a) phase angle. R is given by
(8) R =Substituting (6) into (5), multiplying through by , and rearranging
terms results in
(9) X LZ -I = O
The roots of (9) are given by /
(10) X - CO -{--
When _-C i t'L'O , at least one root of (9) will always be
unstable. However, when - + t C- , the magnitude of
both roots is unity. Recalling the definition of B, the stability
requirement becomes
considering the equality and expanding in terms of A, one finds
CILc -Z C4.a((11) H iZ2. 2.i+t AD
The two solutions for c( in (11) are:
(12) i = 2{1+ &4Graphs of a4_ and d_-are given in Fig. 1. The i root reaches a maximum
somewhere around a=3/2, then decreases. The 4 root, on the other hand,
decreases monotonically, reaching the maximum value of d- around a=3.
To fix these values with more assurance, note that
co5 -: SC)_ OT GY 0~~0 ~L
5
Since d;/. is zero when a=3/2, the maximum value ofc_ is indeed reached
at that point. From (12), = / when a=3/2. Since, also from
12), d+ 7 when a=3, the maximum time step in this case is
three times as long as the usual centered difference time step. Every-
where in the stable region, the amplitude response is neutral. Graphs
of l and R are given as a function of a for O< = 4/27 in Figs. 2 and
3, respectively. 7.
Another way to incorporate the genralized Okamura technique into centered
time differences is to replace A with its damped counterpart. Then, (2) becomes
where, as before, = 1- h. Proceeding as in the previous case, (13)
becomes
(14) AZ 4 2L c - SC 0
The roots of (14) are
(15) .A _o- * t -ca i '/2:2.Here, stability will always occur for - . Then,
(16) lxi =
The magnitude can be made less than 1 for any value of a by an appropriate
choice of i. The question is for what values of a will the inequality
hold. Utilizing the definition of B, the inequality can be written as-C + t -door
(17) -
Since o must be positive, the maximum value of a for which (17) will
hold is 1. As -d increases, damping increases but the maximum allowable
value of a decreases. The region for which- C+ 20 is shown in Fig. 4.
6
However, the scheme is not always unstable when-0-i-5<O. In the narrow
strip between the solid and dashed lines in Fig. 4, the scheme is stable
even though-&-e Q<. Graphs of 1\\ and R are given as a function of a
for C =1.0 in Figs. 5 and 6, respectively.
The third way of incorporating the generalized Okamura technique
into centered time differences is to replace both 4 and 4 with their
damped counterparts. Here, (2) becomes
(18) 4 13 _ 2aJ3 .a
where B is defined as before. Proceeding as in the previous cases, (18)
becomes
(19) - z22ci % --
The roots of (19) are
(20) X = - - +
In this case, stability always occurrs for-15 6 . Then, the magnitude
of both roots is given by
: :E i htxl = { -d
which is the same as in the previous case. Once again, the question is
for what values of a will the inequality hold. Recalling the definition
of B, the requirement becomes
::: ( dt< CL-G ) o:
Proceeding as with the first case, consider now the equality and expand
in terms of d. Then,
(21) ? (Z + (a-Z - <) -+ = 0The two solutions for c in (21) are
(22) c+ = - ; _ = -
Graphs of C+ and ~ are given in Figure 7. (As in Fig. 4, in the narrow
strip between the solid and dashed lines, the scheme is stable even though
7
--.. a I : ~ 0- ). Note the similarity between Figs. 7 and 1. In
contrast with the first case, however, this scheme is a damping one
everywhere within the stable region. In order to determine the maximum
allowable time step, note that
+ 4
The maximum value of i_ occurrs for Q= t , at which point c_( . The
value of a for L=i is 2, or twice that of the usual centered difference
formulation (actually because of the stable region for - +[ 3 , 0
the maximum value of a when is nearly 2.2). Graphs of i} and R are
given as a function of a for = LJin Figs. 8 and 9, respectively.
To summarize the results of this section, there are three basic
ways of incorporating the generalized Okamura technique into a centered
time difference scheme. If the technique is applied only to thetAttime
level, the time step may be increased by up to a factor of three, but no
damping results. If the technique is applied only to theCt-- 6t time level,
strong damping results, but the maximum allowable time step is reduced.
If the scheme is applied to both the tht and (M-)Attime levels, on the other
hand, the maximum allowable time step is increased by over a factor of 2
yet strong damping is still achieved. In the latter two cases, the
amount of damping may be selected by varying the parameter i
Although each of these three choices results in a scheme with interesting
characteristics, none is very practical. First, all the tendency terms
must be computed an extra two times for each iteration of the generalized
Okamura technique. Second, the damping is frequency-dependent and therefore
not very selective. Third, an extra set of fields is required. In each
case, however, the generalized Okamura technique can be applied to centered
8
time differences in such a way that the first two objections are removed.
The result, referred to as the semi-iterative scheme, features both
computational efficiency and highly selective damping. The next section
describes and analyzes the semi-iterative scheme and suggests that
it is a very attractive alternative to existing explicit time integration
schemes.
III. The Semi-Iterative Method
In order to illustrate the semi-iterative method, consider the
following system of linear equations:
(23) - +
(24) E + , +
(25) + _ + = 0in which U is a constant zonal current, h is the mean depth of the
fluid varying only in the y direction such that
(26) -_
and u,v, and h are pertubation wind components and height, respectively.
Assume the solutions to (23)-(25) are of the form
(27) = o e :
where c is the phase speed, k is the wave number (k= Zt-, L=wavelength), and
uo,vo, and ho are unknown amplitudes. Substitution of (27) into
(23)-(25) and requiring the determinant of the resulting system of linear
equations to vanish produces an equation for the phase speed c;
(28) (U-c) ( + C - ) + W- ' = oThere are three real roots of (28), given by
(29) Ci = + 3 CS-
(30)= -L A- CA D +c[ + - j
(31). C3 U +2 t 4
".. - 'I �, - - I., -�- $ 1 � f% - ; I- �.'- � � � - , ' � �� wl�'�v . c �� �':� '�::_ ;. . 1; . -�'m .�-� - , . .4 ; 11-1,�A." "'..'�'..: _� - ;�-. , ... . � � % ml . -,, -_
9
where
(32) CL = [- =cu
C1, C2 , and C3 denote the phase velocity of a meteorological wave,
an eastward moving external gravity-inertia wave, and a westword moving
external gravity-inertia wave, respectively.
Referring to C1, C2, and C3 as Cj, j=l,3 and expressing uo and vo 0
in terms of ho, the solutions to (25) may be written as
-3 ~~~~~Z'3(33) ' .-& C)X
4-I V j _c) 7
(35) =j-I
It can be shown (Kurihara, 1965, op. cit) that with substitution of
~ ~(33)-(35) into the original system, any one of (23)-(25) can be written
:-* in the form
"~ +4 K~h-+L L.j-)h=o,,¼:.]h(36) Am ~ D"=
where hj represents uj,vj, or j. This fact allows the analysis of
the semi-iterative method to proceed by considering only one equation of
the form of (27) rather than to the original system of three equations.
Using centered differences in time, equation (36) may be written as
0 hj = h/ -21.< CZ At h -ZLK ¢ C A-F)Athj )
or letting CL - K J t Cak b- K (C -) t , as
(37) 1- - J '
_ .- The semi-iterative method consists of applying the generalized Okamura
technique to the terms associated with gravitational oscillations (those
. . - .. I r � - I - . - ' 1 � , 11 �_ -, I ' . ' I . .1 .1 . 6' ".. , _1 . , - - . . .. , , :1 � .� � : - . - I . . - .� . . � � � . .�� . , .- - r �� , - .I - - - I - , 4 , - .- , � 4 - ; -.1 � 1, .� � -- . - , 1- . ---- '-'.� 11 � '; �-"- I � -
10
involving b), then using the resulting damped fields for the tendency
~* calculations and/or to step from when making a centered time step. In
this case, the generalized Okamura technique applied to the fields at the
time level is written as
a 4-ib%:
::0ff ~ ~ ~ k -;0 :o0I : : i-- h 7;b0Jor;0 ~ ~ 04i i0t-t=O fL J - a t = -b ) J :. :
If this proces is iterated n times, then one finds
(38)
where it is entirely permissible for i to be different (but always positive)
on each iteration. In a similar manner, m generalized Okamura iterations
on the -(i fields results in
-T-~ ~ ~ ~ ~ tI(39) =
Once again, p may differ on each iteration. Replacing j and hj in (37)
by their damped counterparts given by (38) and (39) produces the semi-
iterative method. The result is
(40) PK = J- ) s - WThe analysis of (40) proceeds as in the previous section. Thus
(40) becomes
(41) -X + ' a, b5'- 7)'>- (!-i b) - o
However, rather than evaluating the roots of (41) as in the previous
section, a computer program was used. There are many combinations of
, m, and n that could be examined. By way of example two categories
of combinations will be described in this section. They are:
Category 1: m=l,cK= 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, n=O, =O.
Category 2: m=n-l,o( i = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5.
Category 1 is one iteration of the generalized Okamura procedure
applied only to j , using six different values of c( (when o =0
11
in category 1, the system reduces to simple centered differences in
time). Using the results of the previous section as a guide, we would
expect this to provide an increased time step but no damping. Category
2 is one generalized Okamura iteration applied to both V and using
six different values for o and (when o= P Oin category 2, the system
reduces to simple centered differences in time). By setting = , a
separate iteration of the generalized Okamura procedure would not need
to be performed on the %- fields in actual practice. Again using the
previous section as a guide, we might expect the combinations in this
category to result in an increased time step (although less than in
category 1) and strong damping. As before, the effect of finite differences
in space is not considered in this simple analysis. In all the graphs
shown in this section, both the amplitude of X and the ratio of the numerical
to the analytical phase speed are given as functions of a (CO4CAt)
where the wave length is assumed to be 2000 km.
The six category 1 configurations are described in Figures 10-15. The
behavior of the meteorological mode is shown in Figures 10 and 11. The most
important thing to note here is that the graphs are the same for all
values of i. The effect of the semi-iterative method for category 1
configurations is thus restricted to the gravity-inertia modes, which are
described in figures 12-15.
The gravity-inertia modes are shown for various values of (, with a
mean geopotential of 8x104 m2s- 2 in figures 12 fnd 13. Note there is no
damping in the stable region for any choice of o<c. Wheno( =0.1, a large
unstable region appears at a=l.0 and continues to a=3.1. Then there is
another stable region that extends to a=4.1. However, little or no
12
increase in the time step is allowed until the intermediate instability area
is eliminated. As a increases, the unstable region separating the two
stable regions shrinks, and the limit (in terms of a) on the second stable
region shrinks as well. By the time c =0.3, the intermediate unstable
region disappears, and the stability limit is at a=2.5. The comparison
to the results of Section II can be seen by recalling Figure 1. There,
the Q curve rose above zero for a >1.0. This is the same (intermediate)
unstable region that can be seen in Figure 12. In both figures, the
intermediate unstable area was avoided by making d sufficiently large.
Figure 13 shows that whenci=0.3, the gravity-inertia wave phase speed is
reduced for all values of a below the stability limit. The graphs terminate
when the physical and computational mode curves meet, for the computer
program is unable to distinguish one from the other thereafter. This
should be of little importance, however, because this point is very
close to the stability limit.
Figures 14 and 15 describe the effect of reducing the mean geopotential
while holding o(fixed at 0.25. At first, as the mean geopotential is
reduced, the stability limit increases. However, by the time 4 becomes,2,% 1 l m~ - , the intermediate instability area noted in Figure 12
appears, substantially reducing the maximum allowable time step. The
intermediate instability area for small values of ) can be eliminated
by increasing o< . We note from Figure 12 that this reduces the maximum
allowable time step somewhat. In effect, the maximum allowable time
step for this use of the semi-iterative method will be determined by the
internal gravity-inertia modes, for they will require the largest values
of d to eliminate the intermediate instability area. As expected, there
is no damping when the semi-interative method is applied only to theZfields.
� -�' %�� �' �' , �wz� " ; ;- , : -- , , -�v��: .. ..' I a- - �: a' � ... - '� �;'% : �� 1_ 11 I I :J� 11. .� � - p -- �` :�� - � jc -: , ; -, .. , -� �; I '�' - � : I � '� 'f :� ". .� - ' 1."t : -".1 " -- � ..
13
The behavior of six category 2 configurations are described in Figures
16-21. The meteorological modes are shown in Figures 16 and 17. There is
no effect on the meteorolgical modes when the semi-iterative method is applied
to both the L and -0Ifields. One of the goals of this use of the semi-
iterative method has therefore been attained-there is neither damping
nor phase speed changes of the meteorological modes.
Figures 18 and 19 describe the behavior of the gravity-inertia
modes for various values of c( , where C is held constant at 8x104 m2 s-2.
In this case, there is strong damping of the gravity-inertia modes throughout
the stable regions. These graphs are similar to those in Figure 12
in that the intermediate instability area is once again present. It is
eliminated when d and are >O©J(not the actual minimum value needed).
When oand = 0.4, very strong damping of the gravity-inertia modes
occurrs for a < 1.86. Thereafter, the computational mode quickly becomes
unstable while the physical mode continues to be damped. Therefore,
the other two goals of this use of the semi-iterative method are also
achieved - strong damping of the gravity-inertia modes and an increased
time step. As before, the phase speeds of the gravity-inertia modes are
reduced everywhere in the stable region for ' of (Figure 19).
Figures 20 and 21 illustrate the effect of reducing the mean geopotential
while keeping d and fixed at 0.35. As in the category 1 configuration,
the intermediate instability area appears for small values of
Here, the values of a and ( needed to eliminate the undersired behavior
is larger than the value a needed in the category 1 use. This is also
in accordance with the results of Section II, for the requirement was ( 7
for category 1 type use (Figure 1) whiled=>> Ywas needed for category
2 type use (Figure 7). Application of the generalized Okamura procedure
14
to both 7 and' O fields thus appears to be an attractive choice, for
strong, highly selective damping achieved while the time step may increased.
Both uses of the semi-iterative method are testing using a free-surface
barotropic model in the next section.
IV. Tests of the Semi-Iterative Method in a Free-Surface Barotropic
Model
1. Experimental-Design
The semi-iterative method was tested using a free-surface barotropic
model. The finite difference equations are
- - -L&~Y :~Ky77Y
(42) U>- 1 - y x,~ ~ Yx(43) V t 4 _____I - - X 7 IV V -__ + ~ ~ - - x¥ --___
(44) k + h yI - h -
where u and v are the horizontal wind components, h is the height, f is the
coriolis parameter, and g is gravity. During the generalized Okamura iteration
of the semi-iterative method, the right-hand side of (42)-(44) are set to zero.
In two of the experiments, the Robert time filter was used. The time filter is of
the form
(45) S -i -
where S is u, v, or h. The model was integrated on a 65x65 point Northern
Hemisphere polar stereographic grid true at 60° north latitude. The
grid interval was 381km.
A case was selected in which a closed cyclonic circulation developed
over the western United States during a 5-day period. The initial time
of the case was 1200 GMTt, 17 May, 1981. The initial analyses of u,v,
and h were provided by the Hough global spectral analysis (Flattery,
1971). As a consequence, the initial mass and motion fields were related
quasi-geostrophically and the initial divergence was nearly zero.
15
Initial imbalances between the mass and motion fields lead to generation
of gravity-inertia wave noise. The various schemes were examined with
respect to their comparative handling of both gravity-inertia wave noise
and synoptic-scale meteorological scale motions.
Five 120 hour forecasts were made, differing only in the time integration
method used. The five different time schemes were
Control: centered differences, At =10 min.
Comparison: centered differences, time filter with
H=0.115) t= 8 min.
Experiment 1: Semi-Iterative Method, m=l, ( =0.30, n=0,P?=0,Xt=30 min.
Experiment 2: Semi-Iterative Method, m=l, o( =0.30, n=O0, =0,
time filter with O =0.90, t=30 min.
Experiment 3: Semi-Iterative Method, m=n=l,o:P= 0.45, b = 20 min.
2. Experimental Results
Consider first the graphs of RMS divergence and absolute vorticity
shown in Figures 22 and 23. In the control run, the RMS divergence
maintains a level of from 4x10- 6 to 5x10-6 S- 1 throughout the five
days of the forecast. The use of the time filter with a strongly damping
coefficient of 0.15 in the comparison run very effectively controls the
gravity-inertia wave noise that was present in the control run. In Exp.
1, the RMS divergence decreases at first, then increases slowly. This
is somewhat puzzeling, since the analysis of Section III indicated no
damping for this choice. As will be seen shortly, the five day forecast
maps produced by Exp. 1 were extremely noisy in appearance, much more so
than in the control run. For this reason, the forecast was rerun using
the time filter with a coefficient of 0.9. This forecast is designated
16
S_ Exp. 2. Note that this did not necessitate a reduction of the 30 min.
time step of Exp. 1. It did, however, control the noise. In Exp. 3,
the noise was controlled slightly better than even in the comparison
run. The RMS absolute vorticity decreased in Exps. 2 and 3 and the
comparison run more than in either the control run or Exp. 1, although
the amount was small. The increased reduction of RMS absolute vorticity
was to be expected in the comparison run and Exp. 2 due to use of the
time filter, which is not a very selective noise damper. It was not
expected in Exp. 3.
The forecast 500mb height maps are shown in Figures (24)-(29) (for
a portion of the grid). Here, we note a noisy map from the control run
(figure 24) and an extremely noisy map from Exp. I (Figure 26). The
noise is completely eliminated by use of the time filter in Exp. 2 (Figure
27). The maps from the comparison run and Exp. 3 are also noisefree.
The central depth of the closed circulation is lowest in Exp. 2 and
highest in Exp. 1. It is disappointing to note that the low is not as
deep in Exp. 3 (Figure 28) as in the control run or even the comparison
run (Figure 25). The maps of wind speed and absolute vorticity (not
shown) confirm a slight but consistent loss of amplitude in the five day
forecast of the synoptic-scale features in Exp. 3. This is both puzzeling
and disturbing, for it seems to disagree with the analysis in Section
III. The maximum allowable time step, however, was determined experimentally
to agree quite well with the indications in Section III in all five
forecasts.
3. Assessment of the Experimental Results
Use of the semi-iterative method can provide either an increased
B .~time step with no damping or a smaller increase time step with strong
1. - . ~ 1..1 . I - 1- . - . , :~" .. 'I fl ;IT I - - q '> .V A.-. .. . *A ' , r..
17
damping. The computer time (CPU) required for each 120 hour forecast
was:
Control Run 96 sec.
Comparison Run 121 sec.
Experiment 1 65 sec.
Experiment 2 65 sec.
Experiment 3 99 sec.
Thus, the Semi-Iterative Method proves to be quite efficient. The
saving of computer time would be even greater in a complex baroclinic
model, for the physics would only have to be computed one-half (Exp. 3)
or one-third (Exps. 1 and 2) as often as normally. The damping of the
Semi-Iterative Method is also substantial, whether provided by the time
filter, as in Exp. 2, or by the choice of parameters, as in Exp. 3. In
this sense, the Semi-Iterative Method indeed proves to be an efficient
and effective noise control device, as suggested in Section II.
Several notes of caution must, in fairness, be added to this assessment.
First, the damping in Exp. 3 does not seem to be as selective as was
hoped at the outset and indicated by the linear analysis, for there was
a disturbing amount of damping of the synoptic-scale meteorological
motions. Furthermore, although use of the time filter in Exp. 2 did
control the extreme amount of noise noted in Exp. 1, it must be remembered
that this is only a barotropic model. The noise apparently present in Exp.
1 could therefore be easily controlled by the time filter. It- is possible
that application of this form of the Semi-Iterative Method to a baroclinic
model would result in internal gravity-inertia wave noise that could not
be so easily controlled with the time filter. One more factor must
also betpointed out. The Semi-Iterative Method requires an extra set
18
of fields. This would increase the storage requirements of a model unless
w ~some appropriate reading in and writing out of fields was used.
V. Concluding Remarks
The generalized Okamura procedures is a potent damping device.
This paper described a methodd of incorporating this device into centered
time differences. The result is an increased time step and strong damping.
One drawback lies-in increased storage requirements, although creative
programming might at least alleviate this. A more serious problem lies
in the selectivity of the damping. The results of Experiments 1, 2, and
3 suggest to me that the source of the problem might lie in an imprecise
identification of the terms driving the gravity-inertia wave motions to
which the generalized Okamura technique is applied. If future research
could eliminate this drawback, the Semi-Iterative Method would become a
very attractive candidate for numerical weather prediction models.
19
REFERENCES
Flattery, T., 1971: Spectral models for global analysis and forecasting:
Proc. Sixth AWS Technical Exchange Conference, U.S. Naval Academy,
Annapolis, MD., 21-24 September 1970. Air Weather Service Tech Re.
242, 42-54.
Grant, W.F.K., 1974: On initialization of primative equation models,
M.S. Thesis, Mass. Institute of Technology, 67pp.
Kurihara, Y., 1965: On the use of implicit and iterative methods for
the time integration of the wave equation, Mon. Wea Rev., 93, 33-46.
, and G. J. Tripoli, 1976: An iterative time intergration
scheme designed to preserve a low-frequency wave, Mon. Wea. Rev.,
104, 761-764.
Matsuno, 1966: Numerical integrations of the primitive equations by a
simulated backward difference method, J. Meteor. Soc Japan, 44,
76-84.
Nitta, T., 1969: Initialization and analysis for the primative equation
model. Proc. Int. WMO/IUGG Symp Numerical Weather Prediction,
Tokyo, Meteor. Soc. Japan, pp. VI-11 to VI-20.
Robert, A., 1966: The integration of a low order spectral form of the
primitive meteorological equations, J. Meteor. Soc. Japan, 44, No. 5.
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.16 + 17 +Ai +19 +20 +Z1 +22 23 +24 +25 +26 +27 +28 +29 +30 +11 +32 +33 +34 +35 +36 +37 +38
+ 28 +5899+ 8b4+58Do+5Jid`~+574 8+~c^d+.,40+5C88+55 .+.5490+549i+S 95+5502+5516+552 +55C5i+5465+5397+533j+528$+5 06+5383+544 +28*~ ~~ ~~~~b SESS P~. ,-Il-iF . X,;i .C.~ ,,ur.. HUS ~G J0GG L ;G,~JG G05G..,ju;G GG ~FFF .EEEECEECEE c E1f 653k 344- 151+ '0 ZG0544 3s8o4JooEF22051
AA ~~~~~~~~~~~~~~~~~~~EE+2? +5906+589 5878+55 7u+5 53 335+5 5539b +21
+26 +5063+901+ 58 3+5873 +5 +5810I, 772+52 5 6 51+5634+5t835 i565 2+54 +5 +5382
~'~~~~~~~AA 5329AI2
*tHH I8 888 r 18C,2G'80 .8;GuGG3 ' 7 4 t~HHHHt.HH-HnHHht-ilnIIIHHH HHHHHHhHHhH G FE83888888883668 A8AAAA,. IHHIk Fb4B8182 666-1G, . "GG/ IF H Hr-HHHEHHHHH HH+25.. +5899+5896+58+5875+5855 823+57 6+5745+5 12 5690+5' 7 1+5693 55+ 04+ 40+5 5+ 26+53 1+5362-5+53' +25
·' ·' :-~~~~~~~~~~~~~~~~~~AAA 'i IHH H J
8882826'3u- *886 HHIIHH.lHtHH+H 0G FIF EEEIE- 85888888656 64*A HtiH HH HH./n -+24 +5896+5- 58 5865+58 5 69+572 59t5688 698+5711+571 569 5 55+561 557 3 +24* r ~~~~~~~~~~~~~~~~~~~~~~468A468 H HIArIIH.'ihinH iI5-ItitillM ,G G 55 6FE - 9 37 2
A966AA HFHHH'1-IIHH-HHHHtHifiIIHHH 1IHHHHHH
·- BBBB~b~ . : .5M~AA A A1 HS HI1 HHHHHHHH -023 ·.:C .. .. GG H. · GGGGG- , 66666 8-In 000000 00300 I1I~~~~~~~HIIHH;-IHHH HHIIIHHH -IIHHHHHHL-HIGHG G-I-H+20 +5863+5860+5850+584 9+560-i-576+5 7+ 5915+565+559 1+5 9+6 9+5655+5660i-582+6+56055673+567662i +5658563549 +20
AAAA ~ ~ ~ ~ ~ ~~- ,,,O -fHHH l-ItHH HH F1IGHHGHhGGHHI-~Hkfi-HAAA8 -IH 0030, 000IHHHHHHLHHHHHHHHHHEHHI-GIH
.+219 +5851+5852+5846+584 +5165771 706 +563' 583+5556+5 55895 ,63+5905110+5665 151i57i 65625685689 +19L
0 5.
........H64. +r5 8 .- A+,tAAAAAAAAA AAA '-. ;... ...+17 +5885+5886+5+5759+5851+55 +578+0594+5+55+ 5++559+5682+5803+56+5 + 9+5798+ 62+5935 +10
* 888888883882888 , ..~~~~~~~~AAA H AAAAAAAAAA AAAAAAAAAAA -AAAAAAA -888888888882888888LA A H 'r6GUGAAGGAAAAGAA6AAAHHHH.HH '+16 +5889+589615+86+S893 7715 7+88+bt 7+5837+849+580+51515851+sa+ 814+860+58 +53+85H1
* . 8588886888888828885666 . 8~~~~AA 7+,20+1115888118718888 62869 +1 58 5B88788+57+8 598888 .. - . J-
-- +5+582 9+90+9350+589 574 0+58256+8951+80 ~ +8559+9551+9050+8258 j-
8888 88888B88888B888 8 588888o1
1 88885 5 B585888888B 8Bu - B 8688 8888858888888888885 8 B88B8838 B88 888B63B5888 888s8888...........
- 8888 182 5'5+5 +1 +85+90+90+v1i-913791+56+502522595559+57+suŽ503soesss59o701+97i591s57537+92 1
* '-T' ..... 88888BB88b8888888888~BB~BS688856888683sB3BBsB~sa8BBB~B~aeosBB8gaBBs~a2 E81B088888888888888882BBBB8888B88 '. -,*..... +13.- +5139+5699+5906+-5908+5916+5916+5922+59i8+592+591 5+5915+5909+5911+5911+5917+5S18+5925+5928+5934+5938+5936+5932+5922 +1]3-.
BBBB~~~BBBB] B8BBBBBBBBB~BBBBBDBB BBB BBGBBBBBBBBBBBBB BBBBABB8BBB
* 88881826888 8888866883866855 8i18886886886.85656886688668830668665,886B688885888682218686 88 08 888BB 88 66 8B88 8E 8 88B88 888 8 B8 B 8...
- 8888868888$68688581811A1168886686tA88888083550A8A888 AAAAAAAAAAAAAA888858A888888888858
+12 +58~9 + 5899+5907?+5909+ 5915-+5 916+59 21+5921I+5924+5920+592o+591 1+5912i-5'11 +5920+ 5S23+-5931i+593J3+ 5y3gi5938+59 39+5934+593o +12
41~ 15~~~~~~~BBBBBBB B BFBBBBB/+ BBBBBBB BBBBBBB+BEBBBBEB~ BBB tBBBBBB E ~ 1+78P`1 6+1 f I BE-,BBBBBBBB BB UBB
,SBB BB BEE B~.BBBPBB0 B B BBBBBBBBB B EBBBBB'D B E BB BB B BB8 8 LNBBBBB~,, ABB BiB. AAA AABBAAA*16 38888888 9 8 +596589388 82888888568338888 58888837+8498885082851+5861858 888 850$888888&8BB88eB82B8B8858881808888888888888-68868888838888 -t5BI88 IBSE N 8 J'5 8 B8B5 6A 8o888
+1e . +5895+5t98+5902+59U5+591i+591I'+5920+5921+5924+592-2+592 9+5 +16+5911 +5910+695+5528+5910 +5919+5942+53L8+5941+5934+5934 +11
+16 +19+186 +19 +20 +21 +22 +23 +24 +.255 +26 +21 +218 +"9 +30 +31 +32 +33 +34 +3,5 +36 +3,7 +380J ..............
HE·HS* j ... ....... :551
BaBEIBBBBBB I' 88b8BBI3Uf3PB8 E E E EBBBEEBBBEBBBB585BBBBB OBB868BBBBO~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+16 +17 +18 +19 +20 +21 +22 +Z3 424 +25 +26 +27 +28 +29 30 +3] +32 +33 +3 +35 +36 +38+29 +30 +21 + 3 2 +33 34 + 3375++B
+28 +5906 +5950+5939 5873 58C4 5749+ 70 +56-26+5522+5458+54B8548+5 6+5514 556 +55 + .5499+5438+5369+5309+5269 +527 +5B 51I+5440 +288§' 8,88 AABAA HH GG ' 'GGGGG GG FF EEEEEEEEEE
888 AA AAAA- EEEE+27 +.5/931+5962+59T;[+59Z~k+587B + 50<AA[57637. ' -+ -- ',:5 +5622+5 6 56-7~-'4+- +538Z+%""E3'J~37+537 L+54'6 *-27
5BBB\ AAAAA HHHH G FFF+26 +5945+595+75275 +5755+ +569+5 5 46+ 35+5375+5353+5357 +26B B B B E B _E b-'"'B-,,_,,,, 8 B BBBB B AAAAA HHHHHHHHHHHHHHH *HHHHHHI H FF GGG FFF E
+88 8 3BBBBBBB AAAAA: HHHHHHHHHHHH HHHH~HH G FB BB8888 tAAAAAHiHHH GG fB5 +5906+5912B5935+591575 0 +56 97 00+5 9+5 06+5 6+55]-5 40+53 E+5328 +5* B888888B8888~~~~~~~B58888858 AAAAAAAGGI HH 0A53HHI 3- GGGG FE588BB8B88B88B8BBBBB8888 AAAAAAAA H14 HFFGFBBBBEBBBBBBBBB888 AAAAAAAA H HHHH) GGGG G G FF
+24 +i76 B 888+59285929 A AAAA H HGGG HHHH GGGGGGGGG FFFFFFF *~ HH-.HHH GGJ j..G GGGGGG G: F= "22 +591 +586t81+84+864 + 83 5'z 5+ + 6550z635 65 +54+ 4~151+56504 9 2+4358.
* BBB AAA~ HH l-IHHHHHH HGG HHHHGGGG' HBb%~.~~~~~~~~ HEBB GG BGF FFFFFFFF "+23 8 +58 + 46+ 55+56 96+9958+561 +23
+20 +5850+5833+583.4+587 5816 +/825775654 +0 0f 619+78+554+575 68 91++., .56 82+563+55+ 57 +20
0 AAA IHHHH ~ GGGGGGGGG HHHHHHHHHHGGHHHHHHHHG -IHHHHGHH* AAAAAAAAA AA k-I+ HHHH HHHHH HI--HGHH
+2 J5891 5878+5847+5a6A A 3 HBBB 15+5600 4 8 + 60 548~~~~~~~~~~~~~~~~~~~~.56i3 22
BB ,1AA AAA HAHH18~ +58 G58 580257835 4 522- 7 H5 15 + 5658 7+5H76+5724+5738+06+5 7 15530+5 6 +581H +218AA AA HGGGHHI- AM GGG GAA GAGGGGGG8AA A A A AA, HH HHHIH AAAGGAG AGAHAAGAGA888 +58505833AA583A58-H7HHAA HHHH AHAGA H AAA AAG HHAHHHHHHHHHHHHH AHIA A H H+17 +5903+5833+5873+5840¥ 18t6¥5 817 7'1-5+<~ 6 7796644 12+5560+5544+8 +5 98+5682+5691+5.75+5692+5675+5 6+ 59 Z71 1 ' I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I
~AA/A \HHHHH~ CGGGGGG~ I HHHHHHHHHHHHFHHHHHHHHHHHHHHHHHHHHH HHHJ: .: 'QGGGGGGG .,G" HHHHHHHHHHHHH~FFHHHHHHHHHHHHHHHHHHHHH HH]tt. +19 t5884+5 49+5786 5+ 8+ 26+ 94+ 70~ 642 +2609~' ~ 7+6859+63S8+69S~+~7JOSg+6 ¥b75Z HHHH'19H ,= ,,,'HHHHHH..H
ql~ ~ '~~~~~~~~~~AAAAAAAAAA ' A~ . HHHH[.J HHHHt~U lHHfH PFH"HiHHHlH H ' '. BE~~k ~,~AAA/~AAAAA~. '~AAA~~ N~ HH H1[, J'HHbU " " - '"HHHHHHHY~- '..... BBAAAA ,AA ,8 8+iS5 +5894573+ 065~1154+ 65781' +18
+16 +B953+584+5814+5871+5866+5829+584,2+5857+ 816+5831+5989+5893+5905+558+5890+591-5861+5871+5865+5858 +16-+15 B-5 BB5 58B + +15
'~~~~~~B BBB% A
........ 888888888888 88B88B8 BB88B B8888 - 8....BB8B 8888A 8 8 BB88EEBBB 8 8 888888888.
BBBBBBB T. +17~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ r' :'+16 93+5 5842+53 .:
· .- 888 8888 88888 888888 88 8 88 -' +[1 +59 59 4+584+571+5860+5829+5951+950+5921+59 +459 538+5928946+85+596+13 +5855+ 593'5 +530 5 4 + 955+5898+5002+5939 + 5+56946 +13+12 +59 5+r8 4+ 78+ +5 l +593+592+58 5+5964+5 1+515+5 +5942 +3o 5944+5557+59 +5'6;+3596+57+53+3 '412
BB 0
+16 +17 +18 +19 +20 +21 B+22 +2 +4 25 +2 +2B+8 29 +3B+3 +2 33 +3 +35 +3 +3 5938·~~~~~~~~~~~B BEB~B BBBBB BBBBBBBBBEBB BBBBB~~~~~~~~~~~~ BB':BB B
+14 B I 1 113 B B BBBBBBBBB ~B' B~B;B,~BSEEBBBBB BBBBBB
*
+16 +L7 +17 +19 +20 +21 +22 +23 3 24 +25 +26 +27 +28 +29 +30 +31 +32 +33 +34 +j5 +36 +37 +38+25 +5921+5904+5875+5825+ 758+k694+5 49+55_575535t 5494+ 4 + 0+55085513+552 5507+ 469 400. 5333+5292 + 313+5390 +5453 +28
HH L 494+54~~~96+55_9508 95 tE87EE.Q8888388Bb8 4&Ai t-IHH >~~~~~~~~~~S~ GG$i LGG G - LGL~GGGGG G GG GGG GO 1--1 EEEEE?1-
B~56BE866\6 6.AAA '"*Lt18t '- tiGGGGGUGGGgGGGGGGGGGGLG~Gtg-GGGGGGGG-: ~, FFF1- "EEEEEEEE EKJ -ISE~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~F F 46FF-S88 88888BB 8bB .I AAIW 888H8i'f,~ C GG~GG&'GJ~GGGt'~£ -'GGGGGC1-1-C~_ ~FFP._' EEEEEEEJ 'R8F 0
88186366566888B£~\ "AAAA H8HH
* ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ d 8d8688o8 H6 H HH HHH HI .IJHHh-Ht~-IHH8i-~'t-,%1188 - '0GG0 %FFFF~ /1EEE0& B 8251 dBOM686 6 ~AAAAAA EHrHr-II-1888HHhFHHHHH8'HHH HH1-1- FF E.,8888E1E2E88E888BB6 6666 _ HAAAAAsh1tHH 8HH8 r~HHHHHHr~ _ GGG& ~FF1 ' EEEE-'.
+25 +5915+5911+507 +5 7+5868+5 327+57 5754+5 +2
8883888888AAAA
+24 +5902+5902+5890587878+56 58L+5 81+5734555+65561.3..5580 26+ 466'+ 6+53 5337 +26
BBBB 25 BeEE8§ B SE~ / AA AAAX e~r hHH -el HE HHtlJ J
8888886638858 33H36 hH-HHHHHHHH *1888,8G GOG,. r F F1F F ""-.. 88E883 E E888888 6AAAAAAAFF FF EE6AM? 888,, 8iHHH H HH 8888H8H88H1-8 8HHHHHHHH HHHHH ~GG~GGG, ':jl:FF 't',F .; '+235 +5981+591+5880+5886+5868+57 3+5795754+5884+567s 5639+50 565 5 +57+5440 5415 +23+22 +90+5 81 5102+5810+5867+5t5 + 78+5 16+5 74+56+566 5634+5606++560 +555 +55 5 N 543 +f2 ·*B B~I~,.~
~AAM AA, 6-
6636 ~ /tHHHH HH81H GGHHH~ HHHHH HHHF~GGG~ JF .. ' G', H--8888----I18-H888-8
BBBB~~bH688BB/ AAA .~ .HHHHHH GG'G A .,, t H H HHHHHHHHHhHHHH1HHHG F
a AMAAA /Id H H H H,'' H H H HH HHHHHHHHH H -HH .GGGG -"+20 +5868+5835+5 582 + 573++57'0 5+ 250+5497+5661+561 :5 +5656+5685+5639+5678+5635+556 567+56 5641 +23B AA~~~I /AJ HHh iHHHHHH-~---=H-HHHH.... HHHHHHiHHHHHHHHk ""~GGGGGGGG~...
AAAA H HH HG"HHHHHHHHHHHH "" GGGG GGG G . ....+18 588258865A65816584A521375H"H77 G 43, . 51 69G57 58+ 5HHHHHHHHHHHH?04+5,_5'"GG '- ·8AA8A8 A . 6AAAAAAAA6AAAAAAA....AAAAAAAAAAMHHHHHHHHHHHHH A....... .'
~AA~AJ JH~ GG' ~'GG ~ HHHH J HH H HHHHHHHHHHH ''
* 5888856166188 AJAAAAH GG 3GG6 3 -GG SHHHHHHHHHH+21 +58692+5894+580 J586 584 513+ 5+ 65 +5560+5750+ 73+5+87+565+5822+ 583+13 7 5875 +21 -8A8AAI8HH8888GGGBV( GG6 4AAGA AAMAHH -H6H-'H.:.' . .. A AAA A GGGG,,,GGG AHH-HH', HHHHHHH '.8888 88 AAAA A -HH G "GG SHHHH 'HHHH HHHHHH . . .+16 +5869+5871+5865+585916+ 7+58 + 8 + 1 8+583+58 1+5655+5856+582+5788+57+5672+5645+58646 +29
AAA ~ ~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~HGGGGHHHHHHJ;L .......H:' .HH.H , HH'. HH.HHHHHH
888, 8288228EB8 8888 88858888 - '1:!-! -;? : ' i888888B88888888888888888888 888B6885888888888B8B888B88888HH 88HHHH +15 +58973+5904+590+90+89+92+85+ + 589 6 +5+2882 9589+58924+5724+5706+5710+5728+591+56912+56047512 +19+! H
+13 +58.8_+5911+592+5903+589 1+5919+5926+5920+5920+591 852+599+5917/+5916+5925+53638+__-585 0+5960+5485+65'13 ;7 :.1 5,+888888E888888 B8B8u888888888B888888su8882+5886 69+5 575 475t
*8B88E8E88588888888BBBB S 8-'8.,,,88888...8.-88BBB5BBasBBBBBBJT'-. 8888888858 'S._,,d,:..:,:
BBBBBBBB__BBBBBBBBBB ' ' ' BBBBBEEEBBBBBBBBBBBBBBBEBBB AA'-WAAA.AAAAAA!.':a'"A~&A& :A'A ....A ' A"
+12 +5892+59824+591+5906+5893 +5929+5595+5"27+592 +5 ;.805+s91+5892+58 4+S90875940+Sg54+sg58+5952+5go4+5947 +1'B88B BB8 8 88 ~868888BBBBB _k.-.A-AA :,..;5 -.;;,,-:A...A -
B8~888888888 88 8B55B8B8668888B8B8838.B88BB888888B8B88888888888BB~~~~B888868B 8B B8 8B88BB8B88..,. ';r ,,$_88 B88 B_82 882 86 88B8BB 8 B8B8888 B688888BBB B8BB8BB8E8B8BS8BS8BB8BS8S888B5B888BBBBSBBB8BS 888BB '8;,88 :8 ,88.8.88' ;78
+11 +5894+5906+5894+58924+5907+592593+5926+599+592+5933+5925+5924+5915+5924+5925+37+38+5950+550+5948+5934+5940+ :,.
B~80 jBBB8EEEEEE B 58 B BBB B BBB8 8 B B8 8 BBBBB8 88B EjB 'B888 -~.(',. ~B 8EEEBBBBB6BBB~BBBBBBB~BBb8BBB3~B8BBBBBB B ~ i8 B BBB8BBBBBBB.``BBBB-
BBBBBSOBBBBBBBB'BBBB BBB - ~'~-,;J , ,"~BI E~BBBB ~ ~~B3BB 888B8B8IbBB8B~8b~Bs BBBBbB88~ b~bBbBBBB88BBj61- . L " , -:
+1 16 +5 1 9 8+59+591 +59 +590 +591 + 59 +592 +524 +59 +59 +51 5+52 6 +529 0 +51 +2 4 + 3+59 5 +35659 +5934 +534 -
TBBBBBBS EB.BBBB.BBBEBBBB BBBBBBBBBBBBBBBBBBBBBEBBBBBBBzBBByBBBBBBBBB:BBBBm .BBBB
+13 +5 89+ 59 112+59112+5 900i+5 9179+ 5925+59326+59 20+5 9 275 9122759281+59129+59 17+59 16+59 256+51+93- 5+9438+5594.5 592+59 50+594-2+5940' +13'..BBB8 38 BBE B8 8 8d J~dB B B BB BBB B II88USU BB 8886888888888888 888888888 8 88888 BIB88888888888 8 BB. ..,':,B ~_BB888 8888888882 88 88886888888 88888888888888888888E8I88 88E IO BB~ JBBB] 8-~' .... ' -. 3B 38BBBB3 1 B BBII B8BB16B BBBB8BPb$BBB~B/ BBbBd BBBUBB~dBHBB BBBBBBBBBB~BB~ BB BBBB~BLB~8BBBBBBBBEBBBBBB 888BB.'-- : ' ~§[Bi',' = '
+1./ +5894+59U/.+5894+5892+5907+5924+5931+5926+5929+5929+5933+5 925+5924+5915+5924+5925+5937+5g36+5950+5950.''594,6+'-5g]'9E34+5940 +11
+16 +17 +18 +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +]1 +32 +33 +34 +35 +36 +37 +38 :.
* ~~~~~4%+16 +11 +1I +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +31 +32 +33 +34 +35 +36 +37 +38
·* +28 +5902+5881+5858+5807+5743 568+I-635 +5282+55+5489+5490+5492 5499+5517+552 5509+541+'402.5335+5292+510+ 35+5452 +idBBB8 BBB8888A A AA"~ F~,,i HHH ·GG.-G GGGGUGGGGGGG- FF EEEEEEEEEE FFF88BBBEBE . A .AL. HHHH 00G 0' ;'00G.G0 G - 5FF EEEEEEEEEEI : FF8Bbb8s88 AAAA HHHH "GOGGGFGGGGGGOOGG."'-G0GG FFF EEEEEEEE+ +5908+589 5879+ -0 156 4+5 07+56+ 556+552. +545'+39 5 1340+5323+536-5402 +21*BBB EB AAAAA HHH EEEEhIBB5588888 8 AAAA HHH-G8888882eb8bb AAAAIHH-HH-HHHHH00F:!f · +26 +59085903+5 + 838+535 5336 +. BBABEBEA A AH HEEEEE88!:888 8 AAAAAA B H - HHFF [EEEEEEEB88B8B885888B8 58 AA AAAA HH HH -II-HHHHH HHhHHHI 00 FFFF~ lESEEBBBB589 6 EEEEEE
* +25 +5903+5825+579+545+ 11566+5 +595+ 59+ 0 + 2+53 +5329530 +25 B8BB8B 88B 88 AAAAAA HH I-HH fHHH HH-HHHHI- G080 FFEEEBB'r"B~~~~~~~~~~~AA GB " FE EEEBBBBBBB E AA AHH HH HHH . H HH 0 FFBBBBEBE 88 8 8 8 AAAAAAH HHHtHHHHH-IHHH
* +24 +5892+585511+584 811 3+5728 96 5681+5 +5690 51+5619 558 32+ 5343 +ZiSBB BB] .. AAAA HHHHHHH hHHHHHHH
+23 +878+583+586a+5855+ 79 5749 0295674+5665+5661+5661+56765686679 5405606.5 3+556 517+ 95438+5416 .23.AA' H' · H GG..HHHHHHHHHHH HH
ALALA 8111-18 00000000 ~~~~~~~~~HH-HHHHHHHI-HI -GG . G0000
· +21, +5863+5856+S5849.5843 5819+ /510 0-569 +5622+ 153+5551+5553:1581+5+1 1g+56/+8+5662 .+5e?,4..5. 56344 a 33+5620+560 +5568 +21/
- - . LALA 88 OOGGOGOOOOGGOAAOGHHHt-IHHH1-HHI-FHHHIHHHHHHIGHH.GGG,..* +20 +5 868T+5863+5855+5846 5821+ 111 56+6655+5352+ +6 +551+675+57+67+61+56957+6 +67+0--
AAA . H HHGHHGHGHO-OHHG H I 1 H GGGGGH"
+21 +5816+5813+5865 58-50+ 2 85 86+ 11 64 6+ 93+5561+55 519+ 8+5648+5110+5145+5610+1619+5623+5688+1 +5693 +129IAAAI IH GGGGGGGG GGGGGG7 ,-HHHHHHHHH-HHHHHH HHHHHHHHHHHHH H HHHH HHHHHH......' . . -- ' ALA 1,188,LAA A GGGGGG8HHHHHHH8H8 . HHH.HHHHV HH HH ' .* j0 +5868458265+58586+58584 58 81 1 +61 12505+5 +6157+68+6157+67+6p+-5AA -IHH \ 'GG GGCGGGG GGG GGG GGG HHrHH H H H H HHHi~iiJL HH H HHH HH H HHH HH HH HHH HH HHH HHHH
88888888. , ~AAA AA~ N H8888881- IHH AA ALGAGGGGGAGGGGG G GAAA HAH HA A HA"' "HAHA HIHAHAHAHHHHHHH
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