Universal Frequency Spectra of Surface Meteorological Fluctuations

Chikara Tsuchiya Department of Earth and Planetary Science, The University of Tokyo, Tokyo, Japan

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Kaoru Sato Department of Earth and Planetary Science, The University of Tokyo, Tokyo, Japan

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Tomoe Nasuno Japan Agency for Marine-Earth Science and Technology, Kanagawa, Japan

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Akira T. Noda Japan Agency for Marine-Earth Science and Technology, Kanagawa, Japan

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Masaki Satoh Japan Agency for Marine-Earth Science and Technology, Kanagawa, and Atmosphere and Ocean Research Institute, The University of Tokyo, Chiba, Japan

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Abstract

Statistical characteristics of surface meteorology are examined in terms of frequency spectra. According to a recent work using hourly data over 50 yr in the Antarctic, the frequency spectra have a characteristic shape proportional to two different powers of the frequency in the frequency ranges lower and higher than a transition frequency of (several days)−1. To confirm the universality of the characteristic spectra, hourly data—including surface temperature, sea level pressure, and zonal and meridional winds—collected over 45 yr at 138 stations in Japan were analyzed. Similar spectral shapes are obtained for any physical quantities at all stations. The spectral slopes clearly depend on the latitude, particularly for sea level pressure, which in the high-frequency range are steeper at higher latitudes. Next, the analysis was extended using realistic simulation data over one month with a nonhydrostatic model to examine the global characteristics of the spectra in the high-frequency range. The model spectra accord well with the observations in Japan. The spectral slopes are largely dependent on the latitude—that is, shallow in the low latitudes, and steep in the middle and high latitudes for all the physical quantities. The latitudinal change of the spectral slope is severe around 30°, which may be due to the dynamical transition from nongeostrophy to geostrophy. The longitudinal variations are also observed according to the geography. The variance is large in the storm-track region for surface pressure, on the continents for temperature and over the ocean for winds.

Corresponding author address: Chikara Tsuchiya, Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113–0033, Japan. E-mail: chikara@eps.s.u-tokyo.ac.jp

Abstract

Statistical characteristics of surface meteorology are examined in terms of frequency spectra. According to a recent work using hourly data over 50 yr in the Antarctic, the frequency spectra have a characteristic shape proportional to two different powers of the frequency in the frequency ranges lower and higher than a transition frequency of (several days)−1. To confirm the universality of the characteristic spectra, hourly data—including surface temperature, sea level pressure, and zonal and meridional winds—collected over 45 yr at 138 stations in Japan were analyzed. Similar spectral shapes are obtained for any physical quantities at all stations. The spectral slopes clearly depend on the latitude, particularly for sea level pressure, which in the high-frequency range are steeper at higher latitudes. Next, the analysis was extended using realistic simulation data over one month with a nonhydrostatic model to examine the global characteristics of the spectra in the high-frequency range. The model spectra accord well with the observations in Japan. The spectral slopes are largely dependent on the latitude—that is, shallow in the low latitudes, and steep in the middle and high latitudes for all the physical quantities. The latitudinal change of the spectral slope is severe around 30°, which may be due to the dynamical transition from nongeostrophy to geostrophy. The longitudinal variations are also observed according to the geography. The variance is large in the storm-track region for surface pressure, on the continents for temperature and over the ocean for winds.

Corresponding author address: Chikara Tsuchiya, Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113–0033, Japan. E-mail: chikara@eps.s.u-tokyo.ac.jp

1. Introduction

The statistical characteristics of the atmosphere have been examined in terms of wavenumber and frequency spectra in many previous studies. It was shown that the spectra in the free atmosphere tend to have characteristic shapes proportional to a power of the wavenumber and/or frequency. In addition, there are several studies on the persistence of the surface temperature. The persistency characteristics are related to the spectral ones.

VanZandt (1982) first reported that the spectra in the free atmosphere have universal shapes, regardless of the season, meteorological conditions, and geographical location. Nastrom and Gage (1985) showed, using aircraft data in the upper troposphere, that the horizontal wavenumber spectra of wind and temperature fluctuations are proportional to a power of of the horizontal wavenumber in the wavelength range from about 2.6 to 400 km and to a power of −3 in the range from about 400 to 104 km. These results are frequently used for the validation of atmospheric general circulation models (AGCMs) (Koshyk and Hamilton 2001; Takahashi et al. 2006; Watanabe et al. 2008; Terasaki et al. 2009). Ecklund et al. (1985) showed that the frequency spectra of vertical wind fluctuations observed by a very high frequency (VHF) clear-air Doppler radar are categorized into two groups as follows: one proportional to a power of of the frequency in active periods and the other to a power of zero in quiet periods. Sato (1990) showed that the vertical wind spectra proportional to the power of of the frequency in the active periods are likely due to phase modulation of topographically forced gravity waves in slowly varying background winds. Tsuda et al. (1989) showed that vertical wavenumber spectra of horizontal wind fluctuations in the troposphere, stratosphere, and mesosphere obtained by the middle and upper atmosphere (MU) radar, which is a VHF clear-air Doppler radar, are proportional to a power of −3 of the wavenumber.

VanZandt (1982, 1985) discussed the relation among various kinds of spectra under the assumption that fluctuations are due to internal gravity waves, following the works by Garrett and Munk (1972, 1975) and Munk (1981) for the spectra in the ocean. Using linear theory of atmospheric gravity waves, the horizontal (k) and vertical wavenumber (m) and intrinsic frequency spectra of the same physical quantities are connected by the dispersion relation, and the spectra of different quantities are connected by the polarization relation. However, deducing particular spectra from observed spectra using these relations is not a simple matter. The observed frequency (ωobs) is usually Doppler shifted by the mean wind, and hence it is different from the intrinsic frequency that appears in the dispersion and polarization relations. The deduction of particular spectra from observations is possible only when the mean wind is so weak that the Doppler shift is negligible.

Great efforts have been made to explain the m spectra of temperature and horizontal winds that have a characteristic shape proportional to m−3, as frequently observed by high-resolution radiosondes, VHF radars, and lidars. Previous studies attempted to explain the shape and amplitude of the characteristic spectra in terms of saturated gravity waves. Gravity wave saturation is a hypothesis in which gravity wave amplitudes are limited so as to make static stability, including gravity wave fluctuations, neutral (Lindzen 1981). Smith et al. (1987) derived the spectral amplitudes of horizontal winds assuming saturated gravity waves. The spectral shape proportional to m−3 was a priori given in their study. They also explained that the characteristic vertical wavenumber—that is, the smallest wavenumber of the spectral range proportional to the minus third power of the wavenumber—decreases as the altitude increases, which is consistent with all previous observations. Sato and Yamada (1994) theoretically derived the m spectra of horizontal wind and temperature fluctuations for a monochromatic saturated gravity wave propagating vertically in the linear horizontal wind shear. The derived spectra are consistent with observations regarding both amplitudes and shapes. Several other studies also tried to explain the characteristic spectra (Weinstock 1990; Hines 1991). Subsequent observational studies show that the power of m depends to some extent on the latitude (Allen and Vincent 1995; Tsuda and Hocke 2002; Sato et al. 2003).

Conversely, another type of analysis has been made to show statistical characteristics of the surface meteorological parameters, in particular for the surface temperature, in terms of the persistence of the temperature. This persistence is characterized as the fluctuation function F(s) in a given time window of length s, using the profile y(n), which is defined as
e1
where T is an anomaly from an average year and n is a time step. The fluctuation function F(s) of y(n) with respect to a straight line z(n) = an + b is defined as
e2
It was shown that when F(s) is proportional to a power of s, the autocorrelation function C(τ) and frequency spectrum S(ω) are also proportional to a power of lag τ and frequency ω, respectively. The three functions F(s), C(τ), and S(ω) are related to one another as follows (Talkner and Weber 2000):
e3
e4
e5
e6
Koscielny-Bunde et al. (1998) analyzed daily maximum temperature data for a typical period of 100 yr at various stations and showed that F(s), when s is greater than 10 days, is proportional to s0.65 irrespective of the location.

Such persistence is also observed in the temperature fluctuations simulated by AGCMs. Using reanalysis data and GCM simulation data, Fraedrich and Blender (2003) and Blender and Fraedrich (2003) showed that the power γ of s in the range of 1–5 yr depends on the surface condition: γ = 1 over the ocean and γ ≈ 0.5 over the inner continents. They indicated that the observed value γ ≈ 0.65 is due to the location of the stations in coastal regions, whereas Eichner et al. (2003) and Bunde et al. (2004) showed that the power γ of the observed data over the inner continents remains about 0.65 regardless of the distance to the ocean, instead of 0.5. However, this issue is still controversial.

Manabe and Stouffer (1996) showed that the spectral densities of surface air temperature (SAT) fluctuations are larger at lower frequencies over the ocean, while they are more or less independent of frequency over the continents. They attributed this feature to the difference in the thermal inertia between the mixed layer of the ocean and the continents. Moreover, the spectral density of sea surface temperature (SST) fluctuations decreases as the frequency increases in the range greater than (three years)−1, whereas the SAT spectral density at the same location is almost independent of frequency and hence larger than the SST spectral density. These SST spectra were consistent with the probabilistic formulation for the fluctuations by Hasselmann (1976): the SST spectrum as a response to the atmospheric thermal forcing having a white-noise spectrum becomes
e7
where F0 is the amplitude of the white-noise forcing by the atmosphere, C is the effective heat capacity of the mixed layer, and λ is the rate of thermal dumping for SAT. Equation (7) indicates that the SST spectrum has a transition frequency around λ/C.

These studies on the surface meteorology mainly make use of daily data or data with longer time intervals. Since the International Geophysical Year (IGY; 1957/58), the data showing short time intervals have been obtained and accumulated for a half century. Sato and Hirasawa (2007) examined the frequency spectra of the surface meteorological parameters over a wide range of (20 yr)−1 to (2 h)−1 at Syowa Station in the Antarctic and showed that the spectra of the surface temperature, sea level pressure (SLP), and zonal and meridional winds have a shape proportional to two different powers of the frequency with a transition frequency of (several days)−1 as well as isolated peaks corresponding to annual and diurnal frequencies and their higher harmonics. The existence of the transition frequency in the spectra was first detected in their work by using hourly data.

The purpose of the present study is to examine whether the characteristic frequency spectra of surface meteorological parameters shown by Sato and Hirasawa (2007) are universal. First, a similar spectral analysis was made of the surface observation data at 138 stations in Japan to observe the geographical variation of the spectral characteristics. Second, the analysis was extended for realistic simulation data by a cloud-system-resolving nonhydrostatic model, to examine the global characteristics of the spectra for the high-frequency range from (3 days)−1 to (6 h)−1. Details of the analyzed data and definition of parameters characterizing frequency spectra are described in section 2. The results of the analysis for the surface meteorological observation and for the simulation data are shown in section 3 and section 4, respectively. A discussion is presented in section 5. A summary and concluding remarks are given in section 6.

2. Data description and spectral parameter definition

a. Surface observation data

The data analyzed are the time series of the surface temperature, SLP, and zonal and meridional winds observed at 138 stations in the period from 1 January 1961 to 31 December 2005 by the Japan Meteorological Agency (JMA) (Fig. 1). The intervals of archived observation data vary depending on the period, namely, 4 or 8 times a day before 1991 and 24 times a day after 1991 at all stations. Thus, two time series from the original data were made: one is a six-hourly time series for the period from 1961 to 2005 and the other is an hourly time series for the period from 1991 to 2005. Then, frequency spectra of respective time series from which linear trends are removed are estimated by the maximum entropy method (MEM). Figure 2 shows the frequency spectra of temperature, SLP, and zonal and meridional wind fluctuations at Wakayama (34°N, 135°E) as a typical example. Note that spectra calculated using the 6-hourly time series and the hourly time series are closely overlapped in the frequency range of (50 days)−1 to (3 days)−1. Two different slopes in the frequencies, lower and higher than the transition frequency of (several days)−1, are observed in the spectra of all the physical parameters. This characteristic spectral shape is similar to that at Syowa Station. Similar characteristics are also observed at all other stations in Japan. The transition frequencies are about (five days)−1 for all spectra at Wakayama, but they vary slightly from each other. It is also noted that isolated peaks corresponding to annual and diurnal frequencies and their higher harmonics are observed in the spectra of all the physical quantities at all stations.

Fig. 1.
Fig. 1.

Stations of the surface meteorological observation operated by JMA, from which the data are used in this study. Symbols and notes at the right side of (a)–(e) show the stations that are used for averaged spectra shown in Fig. 5, but for Kumejima station (26°N, 126°E).

Citation: Journal of Climate 24, 17; 10.1175/2011JCLI4196.1

Fig. 2.
Fig. 2.

Frequency spectra of (top left) the surface temperature, (top right) the SLP, (bottom left) the zonal wind, and (bottom right) the meridional wind at Wakayama (34°N, 135°E). Dotted straight lines show the frequencies of (11 yr)−1, (1 yr)−1, and (1 day)−1, and their higher harmonics.

Citation: Journal of Climate 24, 17; 10.1175/2011JCLI4196.1

The spectral densities of all the physical quantities in Fig. 2 are relatively large around the isolated spectral peaks at annual and diurnal frequencies, although these for SLP around the diurnal frequency are obscure. This spectral foot of each peak is likely due to a slight departure from regular annual and diurnal variations and different from the spectral slopes. The foot should not to be taken into consideration to estimate the spectral shape. Thus, in this paper, two spectral slopes and variances in the low- and high-frequency ranges, and the transition frequency are estimated mainly for the SLP spectra in a range of (90 days)−1 to (6 h)−1, thus effectively eliminating the problem of the foot of each spectral peak.

Another problem in examining the statistical characteristics of the spectra comes from the relocation, urbanization, and/or other environmental changes (e.g., local vegetation change, volcanic eruption, desertification, and accompanying topographical change) of the observational stations. This problem causes disagreement between the two spectra in the overlapping frequency range calculated for different periods. Such disagreement is observed at 23 out of 138 stations for zonal and meridional wind fluctuations, and at Kumejima station (26°N, 126°E) for temperature and SLP fluctuations. According to the historical records of the stations, most problems of the two spectra that are not overlapped come from the relocation and/or urbanization. The spectra displaying such problems were not used in the analysis of the present study.

b. Definition of spectral parameters

To examine statistically the geographical variations of the spectral characteristics with a shape proportional to a power of the frequency, several parameters are defined as follows: Figure 3 is the same SLP spectra at Wakayama as shown in Fig. 2 but without the isolated spectral peaks. The ranges of ωL1 ≡ (90 days)−1 to ωL2 ≡ (6 days)−1 and of ωH1 ≡ (3 days)−1 to ωH2 ≡ (6 h)−1 are defined as the low- and high-frequency ranges, respectively. The spectra in the low- and high-frequency ranges fit to the functions
e8
e9
by the least squares method. The variances for the respective frequency ranges, υL and υH, are obtained as
e10
e11
The transition frequency ωt is analytically obtained as ωt = (CH/CL)1/(βHβL). Then, five spectral parameters—the spectral slopes βL and βH, the variances υL and υH, and the transition frequency ωt—are analyzed statistically.
Fig. 3.
Fig. 3.

Frequency spectrum of SLP at Wakayama and the definition of spectral parameters. Isolated peaks around (one year)−1, (one day)−1, and their higher harmonics were removed. Thin curves show the fitted spectral shapes in the low (high)-frequency range of (90 days)−1 to (6 days)−1 [of (3 days)−1 to (6 h)−1], respectively. Hatched areas denote the variances for frequency ranges υL and υH. Dotted–dashed line indicates the transition frequency, ωt.

Citation: Journal of Climate 24, 17; 10.1175/2011JCLI4196.1

c. Simulation data of a cloud-system-resolving model

Data from simulations for two periods by a global nonhydrostatic cloud-system-resolving model called the Nonhydrostatic Icosahedral Atmospheric Model (NICAM) (Satoh et al. 2008; Tomita and Satoh 2004) are also analyzed: one period is from the experiment for boreal winter (BW) over one month from 15 December 2006 (Miura et al. 2007) and the other period is from the experiment for boreal summer (BS) over 160 days from 1 June 2004 (Oouchi et al. 2009; Noda et al. 2010). In the experiments, the moist process is explicitly calculated without using cumulus parameterization and the improved version of the Mellor and Yamada (1974) level 2 turbulence scheme is used. Although both experiments were made without nudging observation data, realistic atmospheric fields were successfully simulated. See Satoh et al. (2008) for details of NICAM.

The physical quantities analyzed in the present study are the 2-m temperature, surface pressure (SP), and 10-m zonal and meridional winds from the 7- and 14-km BW experiments over the entire simulation period and those from the 14-km BS experiment over one month from 21 June 2004. Time intervals of these simulation outputs are 1.5 h.

3. Latitudinal variation of frequency spectra observed in Japan

Analysis was mainly made for SLP spectra because spectral peaks in many temperature and zonal and meridional wind spectra have spectral feet, as described at the end of section 2a. Figure 4 shows estimated spectral parameters βL, βH, ωt, υL, and υH as a function of the latitude for the SLP spectra. Clear dependence on the latitude is observed. A monotonic increase with latitude is observed in βH, while there is a local minimum for βL near 35°N. The inverse of the transition frequency (ωt)−1 decreases as the latitude increases at the latitudes lower than 35°N and is almost constant (about four days) at higher latitudes. The variances υL and υH increase monotonically with latitude. The spectral parameters at Syowa Station (69°S, 39°E) are βL = 0.88, βL = 4.34, and (ωt)−1 = 3 days (Sato and Hirasawa 2007), which are within the extrapolated latitudinal variations seen in Fig. 4.

Fig. 4.
Fig. 4.

Observed spectral parameters as a function of the latitude. (a) Slope βL (βH) for the low (high)-frequency range is shown as cross marks (circles); scale is shown on the left (right) side. (b) Inverse of the transition frequency (ωt)−1. (c) Variance for the low (high)-frequency range υL (υH) is shown as cross marks (circles); scale is shown on the left (right) side. Dashed curve in (b) is mentioned in section 5.

Citation: Journal of Climate 24, 17; 10.1175/2011JCLI4196.1

To examine the latitudinal variation of the SLP spectra in more detail, the spectra were averaged for five latitudinal ranges shown as marks and notes in Fig. 1: latitudes higher than 42°, 38°–42°, 34°–38°, and 30°–34° and latitudes lower than 30°N. The numbers of the spectra used for the average are 20, 15, 67, 29, and 6, respectively. The results are shown in Fig. 5. These profiles are shifted by one digit so as to see the characteristics more easily. The scale of the left axis is for the spectra of 34°–38°N. The fitted shape of the spectrum at Wakayama is plotted for reference together with each spectrum. In the low-frequency range, the spectral amplitudes around relatively low frequencies increase as the latitude increases, while those around relatively high frequencies only to the south of the region 34°–38°N increase with latitude. These latitudinal variations of the spectral amplitudes result in the βL minimum around 35°N in Fig. 4.

Fig. 5.
Fig. 5.

Frequency spectra of the SLP averaging (a) 20 spectra at stations located to the north of 42°N, (b) 15 spectra for the latitudinal range of 38°–42°N, (c) 67 spectra for 34°–38°N, (d) 29 spectra for 30°–34°N, and (e) 6 spectra to the south of 30°N. Scale on the left axis is shown for the spectrum in (c). Other spectra are shifted by one digit to make comparison easier.

Citation: Journal of Climate 24, 17; 10.1175/2011JCLI4196.1

Analysis was also made for the temperature spectra to compare with the results of previous studies for persistence. The spectral slope in the low-frequency range, βL, is in the range of 0.32–0.68, which corresponds to γ = 0.66–0.84. These values are consistent with previous studies on the surface temperature persistence, that is, γ = 0.65(β = 0.3) for s above 10 days [for the frequency lower than (10 days)−1] by Koscielny-Bunde et al. (1998) and γ in 0.5–1 (β in 0–1) for s in the 1–5-yr range by Fraedrich and Blender (2003).

4. Global variation of simulated frequency spectra by a cloud-system model

Next, the global variation of the spectral characteristics is examined using simulation data from a high-resolution global nonhydrostatic model, NICAM. The use of a nonhydrostatic model is important for the analysis because the assumption of hydrostatic balance used in the primitive equations may not hold in the high-frequency range that is analyzed in this section.

After removing a linear trend from the data series, frequency spectra were calculated by MEM similarly to the observation data analysis. To reduce statistical noise, a smoothing was made by averaging the spectra at nine adjacent grids. A comparison of simulated spectra and the actual observation was made. A thick solid curve in Fig. 6a shows the SP spectrum obtained using the 7-km BW experiment data near Wakayama. The spectral peaks at the diurnal frequency and its higher harmonics were removed. A dotted curve is the observation at Wakayama as in Fig. 3 but only for the high-frequency range. A thin solid curve shows an average of the spectra at Wakayama obtained using observation data only in the winter (0100 LT 15 December–2400 LT 15 January) over 14 consecutive years. It is clear that the model spectra accord quite well with the observations. Figure 6b shows the same as Fig. 6a, but for Syowa Station. The simulated spectrum obtained using the 7-km BW experiment data agrees well with the observed winter spectrum in terms of the slope and spectral amplitude. Figure 6c shows the same as Fig. 6a, but for Batavia in the tropical region. Hamilton and Garcia (1986) showed a frequency spectrum observed at Batavia in their Fig. 3 in the linear plot. Here we made a spectral calculation for the same time series as used in Hamilton and Garcia. The slopes and amplitudes of these spectra are quite similar.

Fig. 6.
Fig. 6.

(a) Comparison of observed and simulated frequency spectra of the SP without peaks. Observed spectra of SLP at Wakayama (dotted curve), observed spectra calculated using data in the winter only (thin solid curve), and simulated spectra of the SP at the location closest to Wakayama by BW experiment with the 7-km mesh model (thick solid curve). (b) As in (a), but for Syowa Station. (c) As in (a), but for Batavia in the tropics.

Citation: Journal of Climate 24, 17; 10.1175/2011JCLI4196.1

Spectral parameters were obtained as follows: First, isolated peaks at the diurnal frequency and its higher harmonics were removed. Second, the spectra were fitted to the shape of (9) in the high-frequency range of ωH1 = (3 days)−1 to ωH2 = (6 h)−1, as denoted by a straight line (Fig. 7) to estimate the spectral parameters βH (spectral slope) and υH (variance).

Fig. 7.
Fig. 7.

Simulated spectrum from the 7-km BW experiment data of the surface pressure closest to Wakayama without peak at (one day)−1 and its higher harmonics, and definition of spectral parameters for the simulated frequency spectrum.

Citation: Journal of Climate 24, 17; 10.1175/2011JCLI4196.1

Figure 8 shows the global map of βH and υH of the SP spectra obtained using simulation data. For the BW experiment from December to January with the 7-km mesh model, the spectral slope βH clearly depends on the latitude: the βH values are smaller in the low-latitude region and maximized around 50°–60° latitudes in both hemispheres. Slight longitudinal dependence is also observed: gentle on the maritime continents and steep in the subtropical regions around the Andes in the austral summer (BW experiment) and around North America in the boreal summer (BS experiment). The variance υH also exhibits clear latitudinal dependence: small in the low latitudes and maximized in 40°–70° in both hemispheres. In addition to such latitudinal dependence, longitudinal variation is also seen. Large υH values are observed in the storm-track region over the North Pacific and the North Atlantic. Similar variations of spectral characteristics are observed in the BW experiment with the 14-km mesh model, except for a slight difference in the magnitude of each spectral parameter. The results from the BS experiment from June to July with the 14-km mesh are also similar, but they have some differences: The large βH values are distributed at higher latitudes than those for the BW experiments. The υH values are smaller in the Northern Hemisphere and larger in the storm-track region in the Indian Ocean and the east Pacific in the Southern Hemisphere.

Fig. 8.
Fig. 8.

Global distribution of the spectral parameters (left) βH (slope) and (right) υH (variance) for the high-frequency range for the SP. Result from the (top) BW experiment (December 2006–January 2007) with the 7-km mesh model, (middle) BW experiment with the 14-km mesh model, and (bottom) BS experiment (June–July 2004) with 14-km mesh model.

Citation: Journal of Climate 24, 17; 10.1175/2011JCLI4196.1

The parameters βH and υH for the SLP spectra obtained using observation data and for the SP using simulation data are shown as a function of the latitude in Fig. 9. Cross marks, thick solid, thick dotted, and thin dotted curves show results for the observation, 7- and 14-km BW experiments, and 14-km BS experiment, respectively. The βH values for the BW experiment with the 14-km mesh model are smaller than those with the 7-km mesh model in almost all latitudes. The shaded region for βH shows 3 times the standard deviation for the 7-km BW experiment. It is clear that the observation and model experiment results match very well within the three standard deviations. The βH value of the simulations at around 70°S is slightly smaller than the observation at Syowa Station (βH = 4.34). The model variances υH have strong seasonal dependence in the middle and high latitudes, and the observations are within the range of the seasonal variation.

Fig. 9.
Fig. 9.

Spectral parameters (a) βH and (b) υH as a function of latitude for observed SLP (cross marks) for simulated SP from the BW experiments with the 7-km mesh model (thick solid curves) and with the 14-km mesh model (thick dotted curves), and from the BS experiment with the 14-km mesh model (thin dotted curves). Shading in (a) denotes three standard deviations for βH from the 7-km BW experiment.

Citation: Journal of Climate 24, 17; 10.1175/2011JCLI4196.1

It is interesting that the latitudinal increase of spectral slope βH around the latitude of 30° is quite large. This severe change may be owing to the difference in dominant physics, such that the geostrophic balance holds in the middle and high latitudes but not in the low latitudes. The βH curve for the BS experiment shifts to the north (toward the summer hemisphere) by about 10° in the low and middle latitudes compared with the BW experiment. This feature is probably related to the seasonal variation of the latitudinal dependence of the solar radiation. The υH peak around 50° latitude is clear in both hemispheres for the BW experiment and only in the Southern Hemisphere for the BS experiment. This antisymmetry is likely related to the difference in the storm activity between the two hemispheres.

Figure 10 shows the zonal-mean SP spectra from the 7-km BW experiment data for the respective latitudes from which the isolated peaks at the diurnal frequency and its higher harmonics are removed. Spectral densities at frequencies lower than about (1 day)−1 are larger for the middle and high latitudes than those for the low latitudes. Conversely, the spectral densities at the frequencies higher than about (1 day)−1 are larger for the low latitudes than those for the middle and high latitudes. These latitudinal dependences are consistent with the smaller spectral slopes at the low latitudes than those at the middle and high latitudes.

Fig. 10.
Fig. 10.

Zonal-mean frequency spectra of the SP as a function of latitudes in the range from (a) 80°S to (i) 80°N with the 20° latitudinal interval. Thick solid curves show the results from the 7-km BW experiment, thick dotted curves from the 14-km BW experiment, and thin dotted curves from the 14-km BS experiment.

Citation: Journal of Climate 24, 17; 10.1175/2011JCLI4196.1

The foot of the diurnal peak is observed in the spectra at the low latitudes. However, these shapes do not affect greatly the estimation of the spectral slope because the frequency range of such a spectral foot is relatively narrow.

Analysis was also made for the frequency spectra of 2-m temperature and 10-m zonal and meridional winds. Results are shown in Figs. 11 and 12, for the 7-km BW experiment and for the 14-km mesh BS experiment, respectively. The spectral slopes βH of both temperature and winds depend on the latitude: they are gentler in the low latitudes than in the middle and high latitudes. On the whole, the variances υH of the 2-m temperature are large over the continents and small over the ocean. Conversely, υH of the 10-m winds is dominant in the storm-track regions and the precipitating region in the tropics over the ocean. In Fig. 12, the shallow slope region migrates northward compared to Fig. 11, and the variances reduce in the Northern Hemisphere.

Fig. 11.
Fig. 11.

Global distribution of the spectral parameters (left) βH (slope) and (right) υH (variance) for the high-frequency range for the (top) surface temperature, (middle) zonal wind, and (bottom) meridional wind, from the 7-km BW experiment.

Citation: Journal of Climate 24, 17; 10.1175/2011JCLI4196.1

Fig. 12.
Fig. 12.

As in Fig. 11, but from the 14-km BS experiment.

Citation: Journal of Climate 24, 17; 10.1175/2011JCLI4196.1

The large variances over the continents for the 2-m temperature and on the ocean for the winds may be partly explained by the properties of the surface: Temperature fluctuations may be large due to small heat capacity of the surface of the continents. Small roughness of the surface of the ocean may cause large wind fluctuations.

5. Discussion

An important characteristic seen in the frequency spectra of surface meteorological parameters—including SP, temperature, and zonal and meridional winds—is their strong latitudinal dependence (Figs. 8, 11, and 12). In particular, the slope is much different between the two regions of latitudes lower and higher than about 30°. The slopes and spectral amplitudes are maximized around the latitudes of 40°–60°. Two explanations are possible for such variations. First, in the middle and high latitudes, large amplitudes of pressure disturbances could be maintained through balancing with the Coriolis force. Second, there is an energy input around the frequency of (several days)−1 in the middle latitudes that originates from baroclinic instability owing to the large latitudinal gradient of temperature. The feature of larger variance in the winter than in summer is consistent with this inference because the baroclinic wave activity is very weak in summer in the Northern Hemisphere. The large SP variances in the storm-track region (Fig. 8) are also consistent with the importance of baroclinic instability.

It is likely that the latitudinal dependence of the transition frequency is related to that of the frequency of the most unstable mode of baroclinic instability. The frequency of the most unstable mode of the Eady problem (Eady 1949), ωm (day−1), is
e12
where cr, km, μm, LdNH/f0, U, f0 ≡ 2(2π sinϕ) (rad day−1), N, H, and ϕ are the real part of phase speed, wavenumber, nondimensional wavenumber, Rossby radius of deformation, wind speed at the top boundary (i.e., the tropopause), Colioris parameter, buoyancy frequency, scale height, and latitude, respectively. The subscript m denotes the most unstable mode. A dashed curve in Fig. 4b shows (ωm)−1 as a function of latitude when U = 23 m s−1, N = 1.2 × 10−2 rad s−1, H = 8 × 103 m, and μm = 1.61, which are reasonable values of the real atmosphere. This accords well with the latitudinal variation of observed (ωt)−1.

The latitudinal variations of the variance and spectral slopes are similar for pressure. However, this is not the case for temperature and winds. The spectral slopes are mainly dependent on the latitude for both temperature and winds, while the variance seems strongly affected by geographical features. The variance of temperature is larger over the ocean than over the continents, while that of winds is larger over the region with strong precipitation in the tropics and the storm-track region over the ocean. These facts suggest that the spectral slopes of the temperature and winds are controlled by a mechanism that is not the same for the variance.

6. Summary and concluding remarks

Statistical characteristics of the surface meteorology were examined in terms of the frequency spectra, to confirm the universality of the spectral shape at Syowa Station shown by Sato and Hirasawa (2007). First, the frequency spectra were examined using hourly surface meteorological data—including the SLP, temperature, and zonal and meridional winds—over 45 yr at 138 stations in Japan. The spectra obtained were in a five-digit range from (20 yr)−1 to (2 h)−1.

Spectral densities of all the physical quantities were proportional to two different powers of the frequency in the ranges higher and lower than a transition frequency of (several days)−1 at all stations. Note that the transition frequency could be detected only by using this high time resolution data. Isolated spectral peaks corresponding to annual and diurnal frequencies and their higher harmonics were embedded in the continuous spectra for all the physical quantities. These characteristics were consistent with the spectra at Syowa Station. To estimate objectively and quantitatively the spectral shape in terms of the spectral slopes, variances, and transition frequency, the least squares fitting method was applied to the spectra in the respective lower- and higher-frequency ranges than the transition frequency, and the geographical variations of the spectral shape were examined.

  • Clear latitudinal dependence is observed in the spectral slopes and variances in the low- and high-frequency ranges and the transition frequency for the SLP spectra. The spectral parameters at Syowa Station are in the extrapolated range of the latitudinal variation.

  • The transition frequency of the SLP spectra is in a range of (8 days)−1 to (4 days)−1.

  • The latitudinal dependence for the temperature and wind spectra in Japan is not very clear.

To investigate the global variation of the spectral shape in the high-frequency range from (3 days)−1 to (6 h)−1, realistic simulation data over one month by a nonhydrostatic model data for the boreal winter (the BW experiment) and for the boreal summer (the BS experiment) were used. Analyzed quantities were the 2-m temperature, SP, and 10-m zonal and meridional winds:

  • The model spectra accord well with the observation in terms of both shapes and amplitudes.

  • Clear dependency on the latitude is observed for the spectral slope of the temperature, SP, and wind fluctuations. The slope is shallow in the low latitudes and steep in the middle and high latitudes. The latitudinal variation around 30° is severe.

  • The latitude region with small spectral slopes for SP shifts to the summer hemisphere by about 10°.

  • The variances in the high-frequency range depend on the climate and surface condition. Large variances are observed in the storm-track regions for the SP—on the continents for the 2-m temperature, and over the rainy regions in the tropics and storm-track regions over the ocean for the 10-m winds.

It may be interesting to examine how spectral characteristics are different between the simulations by nonhydrostatic and hydrostatic models. Although hydrostatic models are capable of simulating realistic baroclinic waves as a possible energy input, spectral shape at the high-frequency region may be affected by nonlinear processes, including nonhydrostatic motions. Thus, the difference in the spectra between hydrostatic and nonhydrostatic models may give us a hint to explain the mechanism to form the characteristic spectra. Moreover, vertical dependence of the frequency spectra is another interesting topic. Observations with fine time and height resolution by VHF/UHF clear-air Doppler radars and boundary layer radars, and simulations by high-resolution models would be useful to deepen our understanding of the spectra regarding the three-dimensional structure in the atmosphere.

Acknowledgments

We thank Michio Yamada and Hisashi Nakamura for their fruitful discussion. Data at Batavia was kindly provided by Kevin Hamilton. This study is supported by Grant-in-Aid for Scientific Research (B) 22340134 of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. The NICAM simulations were performed using the Earth Simulator at the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) under the support by the Core Research for Evolutional Science and Technology (CREST) of the Japan Science and Technology Agency (JST). Figures were drawn using the GFD-DENNOU library. This manuscript was proofread by a proofreading/editing assistant from the Global COE program From the Earth to “Earths.”

REFERENCES

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    • Export Citation
  • Nastrom, G. D., and K. S. Gage, 1985: A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J. Atmos. Sci., 42, 950960.

    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Oouchi, K., A. Noda, M. Satoh, H. Miura, H. Tomita, T. Nasuno, and S. Iga, 2009: A simulated preconditioning of typhoon genesis controlled by a boreal summer Madden-Julian oscillation event in a global cloud-system-resolving model. SOLA, 5, 6568, doi:10.2151/sola.2009–017.

    • Search Google Scholar
    • Export Citation
  • Sato, K., 1990: Vertical wind disturbances in the troposphere and lower stratosphere observed by the MU radar. J. Atmos. Sci., 47, 28032817.

    • Search Google Scholar
    • Export Citation
  • Sato, K., and M. Yamada, 1994: Vertical structure of atmospheric gravity waves revealed by the wavelet analysis. J. Geophys. Res., 99 (D10), 20 62320 631.

    • Search Google Scholar
    • Export Citation
  • Sato, K., and N. Hirasawa, 2007: Statistics of Antarctic surface meteorology based on hourly data in 1957–2007 at Syowa Station. Polar Sci., 1, 115, doi:10.1016/j.polar.2007.05.001.

    • Search Google Scholar
    • Export Citation
  • Sato, K., M. Yamamori, S.-Y. Ogino, N. Takahashi, Y. Tomikawa, and T. Yamanouchi, 2003: A meridional scan of the stratospheric gravity wave field over the ocean in 2001 (MeSSO2001). J. Geophys. Res., 108, 4491, doi:10.1029/2002JD003219.

    • Search Google Scholar
    • Export Citation
  • Satoh, M., T. Matsuno, H. Tomita, H. Miura, T. Nasuno, and S. Iga, 2008: Nonhydrostatic Icosahedral Atmospheric Model (NICAM) for global cloud resolving simulations. J. Comput. Phys., 227, 34863514, doi:10.1016/j.jcp.2007.02.006.

    • Search Google Scholar
    • Export Citation
  • Smith, S. A., D. C. Fritts, and T. E. Vanzandt, 1987: Evidence for a saturated spectrum of atmospheric gravity waves. J. Atmos. Sci., 44, 14041410.

    • Search Google Scholar
    • Export Citation
  • Takahashi, Y. O., K. Hamilton, and W. Ohfuchi, 2006: Explicit global simulation of the mesoscale spectrum of atmospheric motions. Geophys. Res. Lett., 33, L12812, doi:10.1029/2006GL026429.

    • Search Google Scholar
    • Export Citation
  • Talkner, P., and R. O. Weber, 2000: Power spectrum and detrended fluctuation analysis: Application to daily temperatures. Phys. Rev., 62, 150160, doi:10.1103/PhysRevE.62.150.

    • Search Google Scholar
    • Export Citation
  • Terasaki, K., H. L. Tanaka, and M. Satoh, 2009: Characteristics of the kinetic energy spectrum of NICAM model atmosphere. SOLA, 5, 180183, doi:10.2151/sola.2009–046.

    • Search Google Scholar
    • Export Citation
  • Tomita, H., and M. Satoh, 2004: A new dynamical framework of nonhydrostatic global model using the icosahedral grid. Fluid Dyn. Res., 34, 357400, doi:10.1016/j.fluiddyn.2004.03.003.

    • Search Google Scholar
    • Export Citation
  • Tsuda, T., and K. Hocke, 2002: Vertical wave number spectrum of temperature fluctuations in the stratosphere using GPS occultation data. J. Meteor. Soc. Japan, 80, 925938, doi:10.2151/jmsj.80.925.

    • Search Google Scholar
    • Export Citation
  • Tsuda, T., T. Inoue, S. Kato, S. Fukao, D. C. Fritts, and T. E. VanZandt, 1989: MST radar observations of a saturated gravity wave spectrum. J. Atmos. Sci., 46, 24402447.

    • Search Google Scholar
    • Export Citation
  • VanZandt, T. E., 1982: A universal spectrum of buoyancy waves in the atmosphere. Geophys. Res. Lett., 9, 575578.

  • VanZandt, T. E., 1985: A model for gravity wave spectra observed by Doppler sounding systems. Radio Sci., 20, 13231330, doi:10.1029/RS020i006p01323.

    • Search Google Scholar
    • Export Citation
  • Watanabe, S., Y. Kawatani, Y. Tomikawa, K. Miyazaki, M. Takahashi, and K. Sato, 2008: General aspects of a T213L256 middle atmosphere general circulation model. J. Geophys. Res., 113, D12110, doi:10.1029/2008JD010026.

    • Search Google Scholar
    • Export Citation
  • Weinstock, J., 1990: Saturated and unsaturated spectra of gravity waves and scale-dependent diffusion. J. Atmos. Sci., 47, 22112226.

Save
  • Allen, S. J., and R. A. Vincent, 1995: Gravity wave activity in the lower atmosphere: Seasonal and latitudinal variations. J. Geophys. Res., 100 (D1), 13271350.

    • Search Google Scholar
    • Export Citation
  • Blender, R., and K. Fraedrich, 2003: Long time memory in global warming simulations. Geophys. Res. Lett., 30, 1769, doi:10.1029/2003GL017666.

    • Search Google Scholar
    • Export Citation
  • Bunde, A., J. F. Eichner, S. Havlin, E. Koscielny-Bunde, H. J. Schellnhuber, and D. Vyushin, 2004: Comment on “Scaling of atmosphere and ocean temperature correlations in observations and climate models.” Phys. Rev. Lett., 92, 039801, doi:10.1103/PhysRevLett.92.039801.

    • Search Google Scholar
    • Export Citation
  • Eady, E. T., 1949: Long waves and cyclone waves. Tellus, 1, 3352, doi:10.1111/j.2153-3490.1949.tb01265.x.

  • Ecklund, W. L., B. B. Balsley, D. A. Carter, A. C. Riddle, M. Crochet, and R. Garello, 1985: Observations of vertical motions in the troposphere and lower stratosphere using three closely spaced ST radars. Radio Sci., 20, 11961206, doi:10.1029/RS020i006p01196.

    • Search Google Scholar
    • Export Citation
  • Eichner, J. F., E. Koscielny-Bunde, A. Bunde, S. Havlin, and H.-J. Schellnhuber, 2003: Power-law persistence and trends in the atmosphere: A detailed study of long temperature records. Phys. Rev., 68, 046133, doi:10.1103/PhysRevE.68.046133.

    • Search Google Scholar
    • Export Citation
  • Fraedrich, K., and R. Blender, 2003: Scaling of atmosphere and ocean temperature correlations in observations and climate models. Phys. Rev. Lett., 90, 108501, doi:10.1103/PhysRevLett.90.108501.

    • Search Google Scholar
    • Export Citation
  • Garrett, C., and W. Munk, 1972: Space-time scales of internal waves. Geophys. Astrophys. Fluid Dyn., 3, 225264, doi:10.1080/03091927208236082.

    • Search Google Scholar
    • Export Citation
  • Garrett, C., and W. Munk, 1975: Space-time scales of internal waves: A progress report. J. Geophys. Res., 80 (3), 291297.

  • Hamilton, K., and R. R. Garcia, 1986: Theory and observations of the short-period normal mode oscillations of the atmosphere. J. Geophys. Res., 91 (D11), 11 86711 875.

    • Search Google Scholar
    • Export Citation
  • Hasselmann, K., 1976: Stochastic climate models part I. Theory. Tellus, 28, 473485, doi:10.1111/j.2153-3490.1976.tb00696.x.

  • Hines, C. O., 1991: The saturation of gravity waves in the middle atmosphere. Part I: Critique of linear-instability theory. J. Atmos. Sci., 48, 13481360.

    • Search Google Scholar
    • Export Citation
  • Koscielny-Bunde, E., A. Bunde, S. Havlin, H. E. Roman, Y. Goldreich, and H.-J. Schellnhuber, 1998: Indication of a universal persistence law governing atmospheric variability. Phys. Rev. Lett., 81, 729732, doi:10.1103/PhysRevLett.81.729.

    • Search Google Scholar
    • Export Citation
  • Koshyk, J. N., and K. Hamilton, 2001: The horizontal kinetic energy spectrum and spectral budget simulated by a high-resolution troposphere–stratosphere–mesosphere GCM. J. Atmos. Sci., 58, 329348.

    • Search Google Scholar
    • Export Citation
  • Lindzen, R. S., 1981: Turbulence and stress owing to gravity wave and tidal breakdown. J. Geophys. Res., 86 (C10), 97079714.

  • Manabe, S., and R. J. Stouffer, 1996: Low-frequency variability of surface air temperature in a 1000-year integration of a coupled atmosphere–ocean–land surface model. J. Climate, 9, 376393.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., and T. Yamada, 1974: A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci., 31, 17911806.

    • Search Google Scholar
    • Export Citation
  • Miura, H., M. Satoh, T. Nasuno, A. T. Noda, and K. Oouchi, 2007: A Madden-Julian oscillation event realistically simulated by a global cloud-resolving model. Science, 318, 17631765, doi:10.1126/science.1148443.

    • Search Google Scholar
    • Export Citation
  • Munk, W., 1981: Internal waves and small-scale processes. Evolution of Physical Oceanography, B. A. Warren and C. Wunsch, Eds., The MIT Press, 264–291.

    • Search Google Scholar
    • Export Citation
  • Nastrom, G. D., and K. S. Gage, 1985: A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J. Atmos. Sci., 42, 950960.

    • Search Google Scholar
    • Export Citation
  • Noda, A. T., K. Oouchi, M. Satoh, H. Tomita, S.-I. Iga, and Y. Tsushima, 2010: Importance of the subgrid-scale turbulent moist process: Cloud distribution in global cloud-resolving simulations. Atmos. Res., 96, 208217, doi:10.1016/j.atmosres.2009.05.007.

    • Search Google Scholar
    • Export Citation
  • Oouchi, K., A. Noda, M. Satoh, H. Miura, H. Tomita, T. Nasuno, and S. Iga, 2009: A simulated preconditioning of typhoon genesis controlled by a boreal summer Madden-Julian oscillation event in a global cloud-system-resolving model. SOLA, 5, 6568, doi:10.2151/sola.2009–017.

    • Search Google Scholar
    • Export Citation
  • Sato, K., 1990: Vertical wind disturbances in the troposphere and lower stratosphere observed by the MU radar. J. Atmos. Sci., 47, 28032817.

    • Search Google Scholar
    • Export Citation
  • Sato, K., and M. Yamada, 1994: Vertical structure of atmospheric gravity waves revealed by the wavelet analysis. J. Geophys. Res., 99 (D10), 20 62320 631.

    • Search Google Scholar
    • Export Citation
  • Sato, K., and N. Hirasawa, 2007: Statistics of Antarctic surface meteorology based on hourly data in 1957–2007 at Syowa Station. Polar Sci., 1, 115, doi:10.1016/j.polar.2007.05.001.

    • Search Google Scholar
    • Export Citation
  • Sato, K., M. Yamamori, S.-Y. Ogino, N. Takahashi, Y. Tomikawa, and T. Yamanouchi, 2003: A meridional scan of the stratospheric gravity wave field over the ocean in 2001 (MeSSO2001). J. Geophys. Res., 108, 4491, doi:10.1029/2002JD003219.

    • Search Google Scholar
    • Export Citation
  • Satoh, M., T. Matsuno, H. Tomita, H. Miura, T. Nasuno, and S. Iga, 2008: Nonhydrostatic Icosahedral Atmospheric Model (NICAM) for global cloud resolving simulations. J. Comput. Phys., 227, 34863514, doi:10.1016/j.jcp.2007.02.006.

    • Search Google Scholar
    • Export Citation
  • Smith, S. A., D. C. Fritts, and T. E. Vanzandt, 1987: Evidence for a saturated spectrum of atmospheric gravity waves. J. Atmos. Sci., 44, 14041410.

    • Search Google Scholar
    • Export Citation
  • Takahashi, Y. O., K. Hamilton, and W. Ohfuchi, 2006: Explicit global simulation of the mesoscale spectrum of atmospheric motions. Geophys. Res. Lett., 33, L12812, doi:10.1029/2006GL026429.

    • Search Google Scholar
    • Export Citation
  • Talkner, P., and R. O. Weber, 2000: Power spectrum and detrended fluctuation analysis: Application to daily temperatures. Phys. Rev., 62, 150160, doi:10.1103/PhysRevE.62.150.

    • Search Google Scholar
    • Export Citation
  • Terasaki, K., H. L. Tanaka, and M. Satoh, 2009: Characteristics of the kinetic energy spectrum of NICAM model atmosphere. SOLA, 5, 180183, doi:10.2151/sola.2009–046.

    • Search Google Scholar
    • Export Citation
  • Tomita, H., and M. Satoh, 2004: A new dynamical framework of nonhydrostatic global model using the icosahedral grid. Fluid Dyn. Res., 34, 357400, doi:10.1016/j.fluiddyn.2004.03.003.

    • Search Google Scholar
    • Export Citation
  • Tsuda, T., and K. Hocke, 2002: Vertical wave number spectrum of temperature fluctuations in the stratosphere using GPS occultation data. J. Meteor. Soc. Japan, 80, 925938, doi:10.2151/jmsj.80.925.

    • Search Google Scholar
    • Export Citation
  • Tsuda, T., T. Inoue, S. Kato, S. Fukao, D. C. Fritts, and T. E. VanZandt, 1989: MST radar observations of a saturated gravity wave spectrum. J. Atmos. Sci., 46, 24402447.

    • Search Google Scholar
    • Export Citation
  • VanZandt, T. E., 1982: A universal spectrum of buoyancy waves in the atmosphere. Geophys. Res. Lett., 9, 575578.

  • VanZandt, T. E., 1985: A model for gravity wave spectra observed by Doppler sounding systems. Radio Sci., 20, 13231330, doi:10.1029/RS020i006p01323.

    • Search Google Scholar
    • Export Citation
  • Watanabe, S., Y. Kawatani, Y. Tomikawa, K. Miyazaki, M. Takahashi, and K. Sato, 2008: General aspects of a T213L256 middle atmosphere general circulation model. J. Geophys. Res., 113, D12110, doi:10.1029/2008JD010026.

    • Search Google Scholar
    • Export Citation
  • Weinstock, J., 1990: Saturated and unsaturated spectra of gravity waves and scale-dependent diffusion. J. Atmos. Sci., 47, 22112226.

  • Fig. 1.

    Stations of the surface meteorological observation operated by JMA, from which the data are used in this study. Symbols and notes at the right side of (a)–(e) show the stations that are used for averaged spectra shown in Fig. 5, but for Kumejima station (26°N, 126°E).

  • Fig. 2.

    Frequency spectra of (top left) the surface temperature, (top right) the SLP, (bottom left) the zonal wind, and (bottom right) the meridional wind at Wakayama (34°N, 135°E). Dotted straight lines show the frequencies of (11 yr)−1, (1 yr)−1, and (1 day)−1, and their higher harmonics.

  • Fig. 3.

    Frequency spectrum of SLP at Wakayama and the definition of spectral parameters. Isolated peaks around (one year)−1, (one day)−1, and their higher harmonics were removed. Thin curves show the fitted spectral shapes in the low (high)-frequency range of (90 days)−1 to (6 days)−1 [of (3 days)−1 to (6 h)−1], respectively. Hatched areas denote the variances for frequency ranges υL and υH. Dotted–dashed line indicates the transition frequency, ωt.

  • Fig. 4.

    Observed spectral parameters as a function of the latitude. (a) Slope βL (βH) for the low (high)-frequency range is shown as cross marks (circles); scale is shown on the left (right) side. (b) Inverse of the transition frequency (ωt)−1. (c) Variance for the low (high)-frequency range υL (υH) is shown as cross marks (circles); scale is shown on the left (right) side. Dashed curve in (b) is mentioned in section 5.

  • Fig. 5.

    Frequency spectra of the SLP averaging (a) 20 spectra at stations located to the north of 42°N, (b) 15 spectra for the latitudinal range of 38°–42°N, (c) 67 spectra for 34°–38°N, (d) 29 spectra for 30°–34°N, and (e) 6 spectra to the south of 30°N. Scale on the left axis is shown for the spectrum in (c). Other spectra are shifted by one digit to make comparison easier.

  • Fig. 6.

    (a) Comparison of observed and simulated frequency spectra of the SP without peaks. Observed spectra of SLP at Wakayama (dotted curve), observed spectra calculated using data in the winter only (thin solid curve), and simulated spectra of the SP at the location closest to Wakayama by BW experiment with the 7-km mesh model (thick solid curve). (b) As in (a), but for Syowa Station. (c) As in (a), but for Batavia in the tropics.

  • Fig. 7.

    Simulated spectrum from the 7-km BW experiment data of the surface pressure closest to Wakayama without peak at (one day)−1 and its higher harmonics, and definition of spectral parameters for the simulated frequency spectrum.

  • Fig. 8.

    Global distribution of the spectral parameters (left) βH (slope) and (right) υH (variance) for the high-frequency range for the SP. Result from the (top) BW experiment (December 2006–January 2007) with the 7-km mesh model, (middle) BW experiment with the 14-km mesh model, and (bottom) BS experiment (June–July 2004) with 14-km mesh model.

  • Fig. 9.

    Spectral parameters (a) βH and (b) υH as a function of latitude for observed SLP (cross marks) for simulated SP from the BW experiments with the 7-km mesh model (thick solid curves) and with the 14-km mesh model (thick dotted curves), and from the BS experiment with the 14-km mesh model (thin dotted curves). Shading in (a) denotes three standard deviations for βH from the 7-km BW experiment.

  • Fig. 10.

    Zonal-mean frequency spectra of the SP as a function of latitudes in the range from (a) 80°S to (i) 80°N with the 20° latitudinal interval. Thick solid curves show the results from the 7-km BW experiment, thick dotted curves from the 14-km BW experiment, and thin dotted curves from the 14-km BS experiment.

  • Fig. 11.

    Global distribution of the spectral parameters (left) βH (slope) and (right) υH (variance) for the high-frequency range for the (top) surface temperature, (middle) zonal wind, and (bottom) meridional wind, from the 7-km BW experiment.

  • Fig. 12.

    As in Fig. 11, but from the 14-km BS experiment.

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