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Use of data from meteorological satellites in long-range weather forecasting
Adv.
Space Res.
© COSPAR, 1981.
Vol. 1, pp.315—318. Printed in Great Britain.
02731177/81/0301—0315$05.OO/O
USE OF DATA FROM METEOROLOGICAL SATELLITES IN LONG-RANGE WEATHER FORECASTING SILA. Musaelyan Hydrorneteorological Research Center of USSR, Moscow, USSR ABSTRACT
In the Soviet Union experiments on obtaining meteorological information by means of man—made Earth’s satellites were initiated in 1966 (the “Lleteor” meteorological system). Starting with 1975 the launches of the “Meteor—2” updated meteorological satellites of the second generation were carried out. The detailed information about the Soviet meteorological satellite system can be found in 19). Below, the problems concerning the use of satellite data in schemes of long— range weather forecasts are considered. Particular attention is paid to the role of external sources of energy. The role of cloud cover over the oceans is emphasized as a heat influx regulator in the process of absorption radiant solar heat by the ocean. The dynamic and statistical method of ocean heat memory parameterization is stated. II~TRODUCTION Theory. Contributions of initial data and external energy sources to the numerical weather prediction over various time scales were studied by some authors [1,4]. The contributions can also be investigated directly on the basis of the first principle of thermodynamics, which can be written in the following form: =
E+J,
(1)
a where V
6
J(O,~,t)
~T
-——-
a
V _____
~e
—
asinO
~?A
e=½~9
t is the time, 2~—the geographical lon~itude, and ~“ for the latitude, v0(O, ~,t) and v, ,~,t) - velocity components along the ~ and 2.~ axes respectively, T( 8, ?.,t) is the temperature, a is the mean radius of the Earth, K is the coefficient of horizontal macroturbulent
(e
315
316
Sh.A. Musaelyan
exchange,
U
function
E
being the Laplacian operator in spherical coordinates, (C,
A ,t)
the
describes integrally all the heat influxes.
Let us assume that it is necessary to obtain a solution of Eq. Ci) which would be periodic in A , symmetrical With respect to the equator, restricted on the pole and, at the same time, would satisfy the following initial condition:
(~, ~,t)~:
T
(e,’)
T
(2)
The solution to the problem (l)—(2) can be written in the following spectral form
m T(t)
=
+
where
Tm (t),
functions
a2(~+?~) r m n I 1K 1l—exP~——~-n(n÷l)tp.÷ Kn(n+l~ ~ a )
T~’ exp
—
n (n ÷i) t
J
,
(3)
E~(t), J~(t), T~~(t)are the expansion coefficients at the
T, E, J, T
on spherical harmonics,
the ~joint Legendre polynomial,
~
ered time interval, values of the Porecast classification. latitude cyclone waves following conclusions:
, Em(t)
n
and
m
—
are indexes of
are the averaged, over the considand
,r°1(t) respectively.
On the basis of formula (3) analysis for the mid (n~5) and with K 10 62—1 m s one can draw the
1. Over the time scale 0 to 5 days the skill score is mainly determined by the quality of initial fields analysis, the contribution of energy sources being of secondary importance, i.e. in this case the forecast problem can in a first approximation be regarded as a classical problem with initial data In accordance with the currently adopted terminology the forecasts up to 5 days are called short—range forecasts. 2. Over the time scale from 1 to 2 weeks the role of the above mentioned factors is approximately equally impOrtant. In this case the forecast problem should be regarded as the Cauchy problem with source. This is the case of medium—range weather forecasting. 3. Over the time scale from 2 weeks to 1—2 months the role of initial data continues to decrease and the energy sources contributiOn increases. In this case the forecast problem seems to present the Cauchy problem with source, the main role being played by the energy sources. This is the case of long— range weather forecasting up to a month or a season. 4. Finally, for the time scales greater than 1—2 months the role of initial data becomes negligible and everything (or almost everything) is determined by the external sources of energy. This is the case of extra—long—range
METEOSAT Data in Long—range Weather Forecasting
317
weather forecast. The limit of predictability can be also deduced from (3). consistently viith[6J. OBSERVIVPICNS AID) TH~I1I STATIS~IlCALMU~LYSI$ In developing the long—range weather forecast methods for cold half—year it is essentially important to paranleterjze the oceanic heat memory, The papers [5] and [7Jpresent a certain phenocienological approach to this problem which envisages using satellite data on the oceanic cloud cover instead of the sea
water temperature. It is shovrn, in particular, that there exists a cipse enough negative asynchronous relationship between the anomalies in the summer cloudiness over the ocean averages over the three month time intervals and the deviations from the normal continental winter air temperature. The subsequent studies showed that
such relationship also exists with the two month averaging of the anomalies in the above mentioned meteorological elements. Those results were presented in papers [21 and [8]. In these papers there are presented cross—correlation matrices for some stations of the European territory of the USSR produced with the help of the isocorrelate systems. The character of the field of isocorrelates of the above mentioned cross—correlation matrices are approximately the same as in the case of three—month averaging (3], [5], [7].
PRELIMINARY RESULTS OP THS LONG—RANGE FORECASTING An analysis of these matrices allowed us to select the most informative predictors for drawing up the statistical scheme of the air temperature anomaly forecasting for the European area of the USSR using the data on cloudiness over the North Atlantic (Table 1). TABLE 1
Months—Predictors on the Basis of the Anomaly in Cloudiness for the Anomaly in Temperature
Forecast Months
Months—Predictors
January
February
April
March
August
-
February
-
Nay
-
September
-
March
-
April
September
—
October
April
-
May
September
—
October
May
February
June
-
June
-
July
-
August
July August September
—
September
—
October
November
-
October
-
March
February - March January — February June
July
—
April
—
May
June —July
November
—
December
May
December
—
January
July
June
—
-
August
On the basis of this table a prognostic regression equation was made.
As a
318
Sh.A. Musaelyan
rule, the forecasts prove to be quite satisfactory with respect to the sign. At present the forecasting methods undergo operational tests. The preliminary test results are encouraging (see Table 2). C0NCLU5IOI~
Thus, both the papers published earlier (5, 7J and the results cited in this article convincingly show that there exists a rather close negative asynchronous relationship between the summer Verification Score Percentage of Two—months Air—temperature Anomaly Forecasts with Respect to Sign for the European Area of the USSR
TABLE 2
Average for 1975 — 1977
Period of Advance (in months)
Months of Forecast
1977
January - February February — March
71 65
64 80
9 6
March
-
April
93
96
6
April
-
May
65
70
7
May—June
70
70
3
June-July
64
56
4
40
63
6
67
86
2
93
57
5
45
56
4
July
—
August
August
September
—
September
—
October
November
—
October
November
-
December
85
79
4
December
—
January
40
56
5
66
70
5
Mean
anomalies in cloudiness over the North Atlantic and the deviations from the normal winter air temperatures over the European area of the USSR. This property of the ocean—atmosphere system can be used in developing of statistics
to long—range weather forecasts. REFERENCES 1. E. N. 2. T. H. 3. G. I. (1974) 4. A. S.
Blinova, DAN, SSSR, ~ N°2, (1960) Zadorozhnaya, Trudy Gidromettsentra SSSR, 192, 62. (1977) Marchuk and Sh. A. Musaslyan, Meteorologiya I Gidrologiya,
N 8,
10.
Monin, Meteorologiya i Gidrologiya, N 8, 43. 1963 5. Sh. A. Musaelyan, On Character of Seine Super-long Atmospheric Processes, Gidrometizdat, Leningrad, 1978, (in Russian) 6. E. N. Lorenz, in: The Predictability of Hydrodynamic Flow. Trans. New York Acad. Sd., Ser. 2, 1963, 25, p. 409. 7. Sh. A. Musaelyan, Space Research XIX, 271, (1977) 8. Sh. A. Musaelyan, Space Research XXI, 63, (1979) 9. I. P. Vetlov, in: Proc. of a Techn. Conf. Lannion, Prance, 1979, ESA,p.l5.
Space Res.
© COSPAR, 1981.
Vol. 1, pp.315—318. Printed in Great Britain.
02731177/81/0301—0315$05.OO/O
USE OF DATA FROM METEOROLOGICAL SATELLITES IN LONG-RANGE WEATHER FORECASTING SILA. Musaelyan Hydrorneteorological Research Center of USSR, Moscow, USSR ABSTRACT
In the Soviet Union experiments on obtaining meteorological information by means of man—made Earth’s satellites were initiated in 1966 (the “Lleteor” meteorological system). Starting with 1975 the launches of the “Meteor—2” updated meteorological satellites of the second generation were carried out. The detailed information about the Soviet meteorological satellite system can be found in 19). Below, the problems concerning the use of satellite data in schemes of long— range weather forecasts are considered. Particular attention is paid to the role of external sources of energy. The role of cloud cover over the oceans is emphasized as a heat influx regulator in the process of absorption radiant solar heat by the ocean. The dynamic and statistical method of ocean heat memory parameterization is stated. II~TRODUCTION Theory. Contributions of initial data and external energy sources to the numerical weather prediction over various time scales were studied by some authors [1,4]. The contributions can also be investigated directly on the basis of the first principle of thermodynamics, which can be written in the following form: =
E+J,
(1)
a where V
6
J(O,~,t)
~T
-——-
a
V _____
~e
—
asinO
~?A
e=½~9
t is the time, 2~—the geographical lon~itude, and ~“ for the latitude, v0(O, ~,t) and v, ,~,t) - velocity components along the ~ and 2.~ axes respectively, T( 8, ?.,t) is the temperature, a is the mean radius of the Earth, K is the coefficient of horizontal macroturbulent
(e
315
316
Sh.A. Musaelyan
exchange,
U
function
E
being the Laplacian operator in spherical coordinates, (C,
A ,t)
the
describes integrally all the heat influxes.
Let us assume that it is necessary to obtain a solution of Eq. Ci) which would be periodic in A , symmetrical With respect to the equator, restricted on the pole and, at the same time, would satisfy the following initial condition:
(~, ~,t)~:
T
(e,’)
T
(2)
The solution to the problem (l)—(2) can be written in the following spectral form
m T(t)
=
+
where
Tm (t),
functions
a2(~+?~) r m n I 1K 1l—exP~——~-n(n÷l)tp.÷ Kn(n+l~ ~ a )
T~’ exp
—
n (n ÷i) t
J
,
(3)
E~(t), J~(t), T~~(t)are the expansion coefficients at the
T, E, J, T
on spherical harmonics,
the ~joint Legendre polynomial,
~
ered time interval, values of the Porecast classification. latitude cyclone waves following conclusions:
, Em(t)
n
and
m
—
are indexes of
are the averaged, over the considand
,r°1(t) respectively.
On the basis of formula (3) analysis for the mid (n~5) and with K 10 62—1 m s one can draw the
1. Over the time scale 0 to 5 days the skill score is mainly determined by the quality of initial fields analysis, the contribution of energy sources being of secondary importance, i.e. in this case the forecast problem can in a first approximation be regarded as a classical problem with initial data In accordance with the currently adopted terminology the forecasts up to 5 days are called short—range forecasts. 2. Over the time scale from 1 to 2 weeks the role of the above mentioned factors is approximately equally impOrtant. In this case the forecast problem should be regarded as the Cauchy problem with source. This is the case of medium—range weather forecasting. 3. Over the time scale from 2 weeks to 1—2 months the role of initial data continues to decrease and the energy sources contributiOn increases. In this case the forecast problem seems to present the Cauchy problem with source, the main role being played by the energy sources. This is the case of long— range weather forecasting up to a month or a season. 4. Finally, for the time scales greater than 1—2 months the role of initial data becomes negligible and everything (or almost everything) is determined by the external sources of energy. This is the case of extra—long—range
METEOSAT Data in Long—range Weather Forecasting
317
weather forecast. The limit of predictability can be also deduced from (3). consistently viith[6J. OBSERVIVPICNS AID) TH~I1I STATIS~IlCALMU~LYSI$ In developing the long—range weather forecast methods for cold half—year it is essentially important to paranleterjze the oceanic heat memory, The papers [5] and [7Jpresent a certain phenocienological approach to this problem which envisages using satellite data on the oceanic cloud cover instead of the sea
water temperature. It is shovrn, in particular, that there exists a cipse enough negative asynchronous relationship between the anomalies in the summer cloudiness over the ocean averages over the three month time intervals and the deviations from the normal continental winter air temperature. The subsequent studies showed that
such relationship also exists with the two month averaging of the anomalies in the above mentioned meteorological elements. Those results were presented in papers [21 and [8]. In these papers there are presented cross—correlation matrices for some stations of the European territory of the USSR produced with the help of the isocorrelate systems. The character of the field of isocorrelates of the above mentioned cross—correlation matrices are approximately the same as in the case of three—month averaging (3], [5], [7].
PRELIMINARY RESULTS OP THS LONG—RANGE FORECASTING An analysis of these matrices allowed us to select the most informative predictors for drawing up the statistical scheme of the air temperature anomaly forecasting for the European area of the USSR using the data on cloudiness over the North Atlantic (Table 1). TABLE 1
Months—Predictors on the Basis of the Anomaly in Cloudiness for the Anomaly in Temperature
Forecast Months
Months—Predictors
January
February
April
March
August
-
February
-
Nay
-
September
-
March
-
April
September
—
October
April
-
May
September
—
October
May
February
June
-
June
-
July
-
August
July August September
—
September
—
October
November
-
October
-
March
February - March January — February June
July
—
April
—
May
June —July
November
—
December
May
December
—
January
July
June
—
-
August
On the basis of this table a prognostic regression equation was made.
As a
318
Sh.A. Musaelyan
rule, the forecasts prove to be quite satisfactory with respect to the sign. At present the forecasting methods undergo operational tests. The preliminary test results are encouraging (see Table 2). C0NCLU5IOI~
Thus, both the papers published earlier (5, 7J and the results cited in this article convincingly show that there exists a rather close negative asynchronous relationship between the summer Verification Score Percentage of Two—months Air—temperature Anomaly Forecasts with Respect to Sign for the European Area of the USSR
TABLE 2
Average for 1975 — 1977
Period of Advance (in months)
Months of Forecast
1977
January - February February — March
71 65
64 80
9 6
March
-
April
93
96
6
April
-
May
65
70
7
May—June
70
70
3
June-July
64
56
4
40
63
6
67
86
2
93
57
5
45
56
4
July
—
August
August
September
—
September
—
October
November
—
October
November
-
December
85
79
4
December
—
January
40
56
5
66
70
5
Mean
anomalies in cloudiness over the North Atlantic and the deviations from the normal winter air temperatures over the European area of the USSR. This property of the ocean—atmosphere system can be used in developing of statistics
to long—range weather forecasts. REFERENCES 1. E. N. 2. T. H. 3. G. I. (1974) 4. A. S.
Blinova, DAN, SSSR, ~ N°2, (1960) Zadorozhnaya, Trudy Gidromettsentra SSSR, 192, 62. (1977) Marchuk and Sh. A. Musaslyan, Meteorologiya I Gidrologiya,
N 8,
10.
Monin, Meteorologiya i Gidrologiya, N 8, 43. 1963 5. Sh. A. Musaelyan, On Character of Seine Super-long Atmospheric Processes, Gidrometizdat, Leningrad, 1978, (in Russian) 6. E. N. Lorenz, in: The Predictability of Hydrodynamic Flow. Trans. New York Acad. Sd., Ser. 2, 1963, 25, p. 409. 7. Sh. A. Musaelyan, Space Research XIX, 271, (1977) 8. Sh. A. Musaelyan, Space Research XXI, 63, (1979) 9. I. P. Vetlov, in: Proc. of a Techn. Conf. Lannion, Prance, 1979, ESA,p.l5.