Topographic Effects on the Solar Semidiurnal Surface Tide as Simulated in a Very Fine Resolution...

Topographic effects on the solar semidiurnal surface

tide simulated in a very fine resolution general

circulation model

Kevin Hamilton,1 Steven C. Ryan,2 and Wataru Ohfuchi3

Received 13 March 2008; revised 9 June 2008; accepted 20 June 2008; published 6 September 2008.

[1] We present an examination of the solar tidal variation of surface pressure inintegrations conducted with the Atmospheric GCM for the Earth Simulator (AFES) globalgeneral circulation model run at very fine resolution (roughly 10 km horizontal gridspacing and 96 numerical levels from the ground up to 0.1 hPa pressure). The basicfeatures of the observed diurnal and semidiurnal surface pressure oscillations arereasonably well simulated by the model, although simulated amplitudes of the semidiurnaloscillation have an overall enhancement of about 25% over those observed, adeficiency which is reasonably attributed to the effects of the upper boundary condition inthe model. The focus of our analysis is the local-/regional-scale modulation of thesemidiurnal tidal oscillation in the tropics and subtropics associated with high and steeptopography. The results show that the first-order effect of high topography is a reductionin the semidiurnal pressure amplitude with surface elevation, a feature that isconsistent with our understanding of the semidiurnal tide as a vertically propagatinginertia-gravity wave primarily excited in the ozone layer. We also find evidence in themodel for systematically weak semidiurnal pressure amplitudes to the west of veryhigh and steep topography, which is reasonably attributed to a shadowing effect oftopography on the global-scale westward propagating tide. Support for these effects ispresented in our analysis of previously published station observations of the semidiurnalpressure oscillation. In addition, we present new determinations of the semidiurnalpressure oscillation based on barometric data from a special array of nine sensorsestablished on the island of Hawaii, representing an unprecedented sampling of surfacetides over a large range of elevations in a relatively small geographical region. Theresults of the AFES simulations agree quite well with these new detailed observations inHawaii.

Citation: Hamilton, K., S. C. Ryan, and W. Ohfuchi (2008), Topographic effects on the solar semidiurnal surface tide simulated in a

very fine resolution general circulation model, J. Geophys. Res., 113, D17114, doi:10.1029/2008JD010115.

1. Introduction

[2] The daily cycle of solar radiation has important effectson atmospheric circulation. On a local scale, variations in theeffective surface heating over land and ocean produce thefamiliar land-sea breeze, while diurnal heating over topo-graphic slopes produces mountain-valley breezes. Thedynamics of these local diurnal circulations typically involvea rough balance between the radiatively driven horizontalpressure gradients and small-scale turbulent ‘‘friction’’. Suchcirculations are generally restricted to the lowest 2–3 km of

the atmosphere and have rather small pressure signals. On alarger horizontal scale the pressure gradients caused bydiurnal heating variations are balanced by Coriolis andacceleration terms, and the response can be regarded aslarge-scale inertia-gravity waves. On the global scale thisproduces a large Sun-following wave that can propagatevertically upward and/or downward from its forcing altitudes.This wave is conventionally resolved into diurnal (24 h),semidiurnal (12 h), terdiurnal (8 h) etc. components. Theseare the Sun- synchronous or ‘‘migrating’’ components of theatmospheric solar tide. The solar tide has an amplitude insurface pressure generally less than 30 Pa peak to peak.This tidal variation of barometric pressure contributes onlymodestly in the extratropics, but at low latitudes this pressurevariation exceeds typical day-to-day synoptic changes [e.g.,Chapman and Lindzen, 1970].[3] In addition to the Sun-synchronous components, any

zonal modulation of the local time diurnal cycle of heatingor of the lower boundary can excite other components of thediurnal and semidiurnal tides, the non-Sun-synchronous

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, D17114, doi:10.1029/2008JD010115, 2008

1International Pacific Research Center, University of Hawai’i, Honolulu,Hawaii, USA.

2Mauna Loa Observatory, Global Monitoring Division, Earth SystemResearch Laboratory, NOAA, Hilo, Hawaii, USA.

3Earth Simulator Center, Japan Agency for Marine-Earth Science andTechnology, Yokohama, Japan.

Copyright 2008 by the American Geophysical Union.0148-0227/08/2008JD010115

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components (we prefer this terminology, introduced byWilson and Hamilton [1996], to the more familiar ‘‘migrating/nonmigrating components’’). These are presumably forcedparticularly by regional variations in the daily cycle of latentheat or of turbulent sensible heat transport and by thetopographic effect on the tide.[4] There are extensive single station observational deter-

minations of the amplitude and phase of the solar diurnalsurface pressure oscillation, S1(p), and the solar semidiurnalsurface pressure oscillation, S2(p). Such determinations arebased on a simple Fourier analysis of long records of hourlybarometric observations, and can be expressed as an ampli-tude and a local time phase (time of maximum) for theS1(p), S2(p) etc. components. If only Sun-synchronouscomponents are present, the amplitudes and phases will bezonally symmetric. Analysis of the available data shows thatS1(p) has a strong geographical modulation with muchlarger amplitudes over land than over ocean, while S2(p)is more strongly dominated by the Sun-synchronous com-ponent, at least in the tropics and midlatitudes. This behavioris now understood in terms of the vertical structure of theresponse to diurnal and semidiurnal thermal forcing. Thetidal response is reasonably well represented by the so-calledclassical tidal theory [e.g., Chapman and Lindzen, 1970]which solves for the small amplitude response to mono-chromatic forcing assuming a motionless base state withtemperature only a function of height. The main Sun-synchronous component of the semidiurnal tide is associatedwith a very long vertical wavelength and is very efficientlyexcited by the deep solar heating of the ozone layer. Bycontrast the diurnal tide is associated with components thatare either trapped in the vertical or have short verticalwavelengths. Thus, to first order, S2(p) is the result of aglobal Sun-synchronous inertia-gravity wave propagatingdownward from the ozone layer, while S1(p) is much morethe result of tropospheric forcing (mainly from solarabsorption by water vapor and from latent and sensibleheating) which is much more regionally varying.[5] An interesting implication of our theoretical under-

standing of S2 as a vertically propagating wave in acompressible atmosphere is that the amplitude of the pres-sure perturbations should vary roughly as the square root ofthe mean density [e.g., Chapman and Lindzen, 1970]. Thissuggests a first-order effect of topography on S2(p) maysimply be a reduction of amplitude over that at sea level atthe same latitude. Haurwitz [1956] noted that in severalcases he found the S2(p) determinations at high-altitudestations to be anomalous relative to other nearby lower-elevation stations, although this apparently has not beenexplored systematically in earlier studies.[6] While S2(p) is dominated by the Sun-synchronous

component, the regional-scale deviations from purely Sun-synchronous behavior in S2(p) have attracted some atten-tion. Spar [1952] discussed results of determination ofannual mean S2(p) amplitude and phase at about 100 stationsin the continental USA. This revealed interesting geograph-ical variations, with notably weaker amplitudes and laterphases along the west coast. This was also found in a moremodern study of the observed S2(p) over the USA by Masset al. [1991]. Haurwitz [1956] in his global study of S2(p)noted Spar’s observations in the USA and also ‘‘similarirregularities over the Andes region of South America. . .

although [this] is not so well supported because fewerobservations are available than over North America’’. Thepossibility that steep topography is responsible for thesegeographical modulations of S2(p) was raised in thesepapers, but not pursued theoretically.[7] Fels [1977] noted that the topographic effect on the

semidiurnal tide can be regarded as the scattering of the(largely Sun-synchronous) downward propagating inertia-gravity wave. He noted that the effect would be to scatterenergy out of the large-scale Sun-synchronous componentsinto other components with smaller horizontal scales andpresumably very small (or even imaginary) vertical wave-lengths, that likely would not propagate to high altitude.Thus from the point of view of the upper atmosphere theeffects of relatively small-scale topography could be to actas an effective dissipation of the downward propagatingcomponent incident at the surface. Most theoretical/numericalmodels of the tide have assumed a flat, perfectly reflectinglower boundary, but it is possible that, via the mechanismdiscussed by Fels, the topographic irregularities couldaffect the tide in the upper atmosphere. However, Felsnoted that, at least in certain limits, the scattering efficiencyof isolated topographic features is proportional to the ratioof the height of the topography to the vertical wavelengthof the incident tide, which for the semidiurnal tide is quitesmall.[8] There have been a number of earlier modeling studies

of the diurnal and semidiurnal tides which have considerednon-Sun-synchronous components. Some studies haveemployed linear models of varying sophistication [e.g.,Giwa and Hussain, 1978; Hagan and Forbes, 2002] andothers have used comprehensive global general circulationmodels (GCMs [e.g., Zwiers and Hamilton, 1986; Tokiokaand Yagai, 1987; Miyahara et al., 1999]). The models in allcases have been run with fairly coarse spatial resolution(horizontal grid spacing of 300 km or more), and regionalfeatures such as those discussed by Spar [1952] or Haurwitz[1956] are not well simulated.[9] Recently there has been increasing interest in studying

the behavior of global GCMs run at rather fine spatialresolution. Such studies are principally motivated by suchissues as simulation and forecasting of tropical cyclones[e.g., Yoshioka et al., 2005; Oouchi et al., 2006], simulationof narrow quasi-permanent frontal zones [e.g., Kawataniand Takahashi, 2003; Ohfuchi et al., 2004], understandingthe spatial spectrum of atmospheric motions [e.g., Takahashiet al., 2006]. Simulating tides has not been a major concernso far, but these high-resolution GCMs are of interest fromthe point of view of tides since they incorporate thedetailed steep topography that has been speculated to bethe cause of significant regional-scale variations in S2(p).Certainly the S2(p) observational database represents aparticularly rich source of detailed information aboutatmospheric behavior and it is of interest to see how wellour increasingly detailed and powerful numerical modelscan simulate the observations.[10] The present paper examines the surface tidal baro-

metric signal, particularly S2(p), as simulated in a very fineresolution global GCM, one that can resolve rather steeptopographic slopes. We will show that this model is able tosimulate some of the more prominent regional geographicalvariations observed in S2(p). Notably we will make a case

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for the existence of a ‘‘shadowing’’ effect accounting forregions of reduced amplitude to the west of steep topogra-phy. Because of the limited length of the very fine resolu-tion integrations that are available, the analysis is focussedon low latitudes where the signal-to-noise ratio for S2(p) islargest.[11] Section 2 briefly reviews available observations of

S2(p) and some relevant experience from earlier compre-hensive GCM studies of S2(p). Section 3 describes theGCM used in the present investigation. Results for thelarge-scale features of S1(p) and S2(p) in the simulationare described in section 4. Section 5 examines the simula-tion of S2(p) in the vicinity of two particularly steeptopographic features in South America and Hawaii, andcompares with available observations in these regions. Wealso present here new observational determinations of S2(p)from a special network of 9 stations established on the BigIsland of Hawaii in 2004. Conclusions are summarized insection 6.

2. Brief Review of S2(p) Observations and anEarlier GCM Study

[12] In his classic study of the global distribution of S2(p),Haurwitz [1956] presented annual mean S2(p) determina-tions at 296 stations throughout the world, most based on atleast several years of hourly barometric observations andtypically published earlier as results from individual researchprojects focused on one or a few stations. He producedhand-drawn maps of the S2(p) amplitude and local timephase that showed the dominance of the Sun-synchronouscomponent in the tropics.Dai and Wang [1999] used 3-hourlysurface pressure data taken from the Global Telecommuni-cation System (GTS) reports at 7553 land stations, alongwith ocean reports from the Comprehensive Ocean-Atmosphere Data Set (COADS) binned into 3083 2 � 2.5�latitude-longitude boxes. These determinations of S2(p) at thelarge number of locations were then objectively interpolatedonto a regular grid. Dai and Wang’s Figures 8 and 10 presenttheir global pictures of the annual mean S2(p) amplitude andphase and are the counterparts of the hand-drawn maps ofHaurwitz [1956]. Ray [2001] discusses the relative merits ofusing the large number of arguably less-than-optimal qualityGTS and COADS data versus using just the more restrictedhigher-quality data as in Haurwitz’s [1956] analysis. In anyevent, the large-scale features of the S2(p) are similar in theHaurwitz subjective analysis and the objective interpolationof Dai and Wang.[13] As mentioned earlier, studies of the solar tides

including S1(p) and S2(p) have been performed using outputfrom free running climate GCMs. Zwiers and Hamilton[1986] (hereinafter referred to as ZH) analyzed S1(p) andS2(p) in a control simulation of an 11-level model with arigid lid upper boundary at about 10 hPa and with verycoarse horizontal resolution (about 600 km horizontal gridspacing). The model was able to reproduce reasonably wellthe observed large-scale features of S1(p), notably theintensification of amplitude over the continents. The modelalso did a good job of reproducing the main features ofS2(p) including the overall amplitudes. As noted by ZH, atfirst glance this is somewhat surprising given the truncationof the domain at 10 hPa. This limitation of the domain

results in a model that does not include a large region of theozone layer that is thought to be important for the excitationof S2. ZH performed some linear classical tidal theorycalculations of S2 and found that omitting the ozone heatingabove 10 hPa resulted in about a 40% reduction in theamplitude of S2(p) in a standard calculation that solves forthe tidal fields up into the thermosphere and includes aradiation condition at the top. However, when the linearcalculations were performed subject to a rigid lid boundarycondition at 10 hPa the S2(p) amplitudes became about 30%larger (and so close to those of the most realistic calcula-tion). Thus ZH concluded that the realistic S2(p) amplitudein their GCM simulation resulted from a cancelation oferrors: omission of the ozone heating above 10 hPa com-pensated by an unrealistic intensification of the tide causedby reflection from the artificial upper boundary.

3. AFES Model and Integrations

[14] The AFES model is a standard global atmosphericmodel and was adapted from the CCSR/NIES AGCM [e.g.,Numaguti et al., 1997] to run efficiently on the EarthSimulator [Ohfuchi et al., 2004]. The version of AFESemployed here is a spectral GCM with standard semi-implicit time-marching formulation and spectral advectionscheme. A fourth-order horizontal subgrid-scale hyperdiffu-sion is employed in the momentum, thermodynamic andwater vapor and cloud water equations. The results shownhere were obtained employing the Emanuel scheme [e.g.,Emanuel, 1991] for parameterizing subgrid-scale moistconvection. Ohfuchi et al. [2004] discuss integrations witha version of the model with triangular 1279 horizontalresolution and 96 levels in the vertical (T1279L96) up toa pressure of about 0.1 hPa (about 60 km). The modelphysics at the T1279 resolution is computed using fieldsreconstructed on a 3840 � 1920 latitude-longitude grid,corresponding roughly to a 10 km horizontal grid spacing.The ozone distribution is specified as a function of height,latitude and time of year based on observed climatology.The model is formulated in standard sigma coordinates, sothe lower boundary condition of no normal flow into thesurface is included exactly. The component of the windparallel to the surface at the lowest model level interactswith the surface via a standard drag parameterization. Themodel used here employs a slightly filtered version of rawT1279 topography [see Ohfuchi et al., 2004]. Yoshioka et al.[2005] presented limited results for the tidal pressureoscillation in this model as part of a study of the effectsof the diurnal cycle on tropical cyclones.[15] The present paper analyzes the surface tides in the 3

integrations of the AFES version with the T1279L96resolution reported by Ohfuchi et al. [2004]. TheseT1279L96 runs were control integrations with prescribedclimatological values of the sea surface temperature, sea icecover and ozone concentrations. Each integration beganfrom initial conditions interpolated from a snapshot froma multiyear control run of a T319L24 version of AFES. Thethree experiments began from 7 January, 21 June and6 September, and lasted 10, 10 and 16 days, respectively.The brevity of the available integrations limits our ability toreliably determine the tidal signal, particularly in the extra-tropics where the signal/noise ratio for the tidal variations is


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much lower [e.g., Chapman and Lindzen, 1970]. In order tomaximize the signal/noise ratio most of the analysisreported will be performed for data spanning all of days4–16 of the September run, days 4–10 of the January runand days 4–10 of the June run, for a total of 27 days of data.Results obtained by analysis of this combination of 7 daysnear the boreal winter solstice, plus 7 days near the borealsummer solstice plus 13 days of near-equinox are thencompared with annual mean observations. Three-hourlysnapshots of the surface pressure were saved from themodel run and are analyzed here.

4. Results for the Large-Scale Structure of S1and S2

[16] Figure 1 shows the 27-day mean Sun-synchronousamplitude of S1(p) from the AFES results compared with avery simple analytical fit to the station data produced byHaurwitz [1965]. The result shows that the overall ampli-tude of the diurnal pressure oscillation is reasonably wellsimulated in AFES. The simulated Sun-synchronous com-ponent of S1(p) has phases around 0500–0600 local time inthe tropics, in agreement with observations as well. As inobservations, the simulated S1(p) has strong non-Sun-synchronous components with stronger amplitudes overcontinents than over ocean areas (not shown).[17] Figure 2 shows a map of the amplitude of S2(p)

determined from the 27 days of AFES data (this has beenslightly smoothed to make plotting easier). The overallpattern is similar to that observed, with high amplitudes inthe tropics which decrease away from the equator. The peakamplitudes are larger than observed, however, exceeding1.6 hPa in some locations. By contrast, the Haurwitz [1956]map indicates no region with S2(p) amplitude exceeding

1.4 hPa. This discrepancy is understandable in light of theearlier results of ZH. The AFES model extends to 0.1 hPaand thus includes virtually all the ozone heating responsiblefor generating the semidiurnal tide. The AFES modelincludes a sponge layer near the model top imposed aslinear damping on winds and temperatures. However, whilethe sponge is perhaps adequate for low-frequency planetarywaves, the large amplitude of S2(p) in the simulationsuggests that the model lid does reflect significant amountsof the relatively high-frequency semidiurnal tide.[18] The overall east-west variation near the equator is

similar in Figure 2 and the Haurwitz [1956] observations,with minima over parts of the equatorial Pacific and Atlanticand maxima over South America and the Indian Ocean/maritime continent region. Figure 3 shows the amplitude ofthe Sun-synchronous component of S2(p) determined sepa-rately for the 7 days in January, 7 days in June and the 13 daysin September. These are compared with Haurwitz andCowley’s [1973] simple analytical fit to the observations forNovember-February, May-August and the 4 months closestto the equinoxes (March, April, September, October). Themodel overpredicts the amplitude in all seasons, but the senseof the overall annual cycle is reproduced, with highestamplitudes near equinox and lowest in boreal summer.[19] Figure 4 shows the counterpart of Figure 2 for the

local time phase of S2(p). Over most of the tropics the phaseis around or slightly earlier than 9.5 h. This is close to, butsomewhat earlier than, the observed phases which typicallyvary between 9.5 and 9.8 h. At higher latitudes the phase inthe AFES simulation is more variable. Although the resultspoleward of 30� are quite noisy, the tendency for the localtime phase to become later east to west across the USA isevident, in overall agreement with observations [Spar,1952; Haurwitz, 1956; Mass et al., 1991].

Figure 1. The 27-day mean amplitude of Sun-synchronous S1(p) from the AFES simulations (solidcurve) compared with the simple analytical fit to annual mean station data by Haurwitz [1965] (dashedcurve).


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Figure

2.

Theam

plitudeofS2(p)determined

from

the27daysofAFESdata.

Resultsareslightlysm

oothed

inspace.

Contours

labeled

inhPawithacontourinterval

of0.2

hPa.


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Figure 3. The solid curves show the amplitude of the Sun-synchronous component of S2(p) determinedseparately for the 7 days in January, 7 days in June, and 13 days in September. The dashed curves showthe Haurwitz and Cowley [1973] simple analytical fit to the observations for November-February (green);May-August (red); and March, April, September, and October (black).


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Figure

4.

Asin

Figure

2butforthelocaltimephaseofS2(p).Contoursarelabeled

inhoursafterlocalmeansolarmidnight

(andnoon).


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Figure 5. Scatterplots of a measure of the local amplitude of 27-day mean S2(p) at individual gridpoints in the AFES simulation versus the topographic height. Specifically plotted is the S2(p) amplitude ateach grid point divided by the zonal mean value of the amplitude at its latitude. Results only for locationswith topography greater than 500 m are plotted. (top) Points equatorward of 15� and (bottom) pointsbetween 15 and 30� latitude.


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[20] Each point in Figure 5 shows the S2(p) amplitude atone grid point divided by the zonal mean value of theamplitude at its latitude, plotted against the topographicheight of the grid point. For readability, results only forlocations with topography greater than 500 m are plotted(even with this restriction there are over 250000 pointsplotted in Figure 5). There is a great deal of scatter in Figure 5,but an overall negative correlation of the S2(p) amplitudewith height can easily be discerned. As noted in theIntroduction this overall behavior (a decrease in pressureperturbation with height) is consistent with the expectationsif the semidiurnal tide can be considered as a verticallypropagating inertia-gravity wave in a compressible atmo-sphere. This effect will be seen in more detail in the regionalanalyses presented in the next section.

5. Regional Results for S2(p)

5.1. West Coast of South America

[21] Examination of the S2(p) amplitude results in Figure 2in the tropics shows that there are some notable zonalvariations on a subcontinental scale. For example, theamplitude drops off over the mountains of East Africa.However, the most obvious disruption to zonal symmetry inthe tropics are the variations over the Andean region and offthe west coast of South America. As noted earlier, Haurwitz[1956] flagged the west coast of South America as a regionwith possibly interesting S2(p) variations. Figure 6 showsthe T1279 AFES model topography over the western part ofSouth America between 24�S and 12�S. The very steepslopes on the western side of the Andes are reasonably wellcaptured in the AFES topography. For example, Figure 7shows a cross section of the topography along 17.1�S in the

model and in the US National Geophysical Data CenterETOPO5 5-min observed topography data set. The averageslope in the east-west direction from the coast at 72�W tonear the peaks at 70�W is about 0.02. Figure 8 shows theunsmoothed results for the S2(p) amplitude for this part ofSouth America. Comparing this with Figure 6 a negativecorrelation between topographic height and the amplitude isapparent. However, in addition there is a strong east-westasymmetrywith lower amplitudeswest of theAndes than eastof the Andes. For example at 17�S the simulated S2(p)amplitude is 1.1 hPa at the coast at 72�W, but is near1.8 hPa at 64�W to the east of the Andes. The region ofanomalously small amplitude extends westward off the coastfor �300–500 km before amplitudes return close to thosetypical of the rest of the latitude band (see Figure 2). This is akind of ‘‘hole’’ in the amplitude relative to the typical valuesat sea level at the same latitude.[22] The suggestion of Haurwitz [1956] that the west

coast region of South America might be anomalous in termsof its S2(p) appears to be based on data at just two stations,Mollendo (17.1�S, 72�W) on the coast and Arequipa(16.4�S, 71.6�W) at 2451 m elevation. These locations aremarked as ‘‘M’’ and ‘‘A’’ on Figure 8. Note that Haurwitzgives the longitude of Mollendo incorrectly as 73�W andalso plots the corresponding point on his station map at73�W (over the ocean rather than on the coast!). Table 1shows the results for amplitude and phase of S2(p) atMollendo and Arequipa together with those from otherstations within a narrow latitude band (15.9�S–18.3�S)taken from Haurwitz [1956] and Ray [1998]. The observedamplitudes of 0.889 at Mollendo and 0.641 at Arequipa areconsiderably lower than any of the other stations in thelatitude band. These low values have no counterpart in anyof the other stations near 17�S.[23] We suggest a simple explanation for the low S2(p)

amplitudes on the west side of the Andes in terms of wavescattering from topography. Figure 9 shows a schematic ofthe group velocity associated with a large-scale inertia-gravity wave directed downward and westward towarda topographic feature. At low latitudes the semidiurnaltide incident at the ground could be roughly consideredan inertia-gravity wave with angular frequency about1.5 � 10�4 s�1. Assuming a tropospheric Brunt-Vaisalafrequency of 0.01 s�1 and ignoring rotation, simple planewave theory would predict a slope of a = 0.015 from thehorizontal for the group velocity vector. Classical tidaltheory, which takes into account the rotation and sphericityof the earth, predicts a main meridional mode for the Sun-synchronous semidiurnal tide with vertical wavelengthexceeding 200 km which is 0.01 times the equatorial horizon-tal wavelength of 20,000 km [Chapman and Lindzen, 1970],providing another estimate for the effective slope, a, for thegroup velocity. In the geometrical optics limit one mightexpect to see a completely shadowed region to the west ofthe topography depicted in Figure 9 extending H/a where His the height of the topography. For the Andes in the regionaround 16�S the relevant value of H is about 4.5 km andso the extent of the shadow would be predicted to beabout 300 km. Of course the tide is very far from thegeometric optics limit since both the vertical and hori-zontal wavelengths of the incident wave are much largerthan the vertical and horizontal scales of the topography

Figure 6. Topographic heights as represented in theT1279 AFES model for a region in South America. Thethin contours are for 200, 400, 600, and 800 m. The thickcontours are for 1000, 2000, 3000, and 4000 m. The red lineis a low-resolution representation of the coastline.


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Figure 7. Topographic heights along a zonal section through the Andes near 16.1�S in the ETOP05 dataset and as represented in the T1279 AFES model.


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considered. However, it is reasonable to expect that steeptopography could cast a long ‘‘shadow’’ to the west, albeitwithmuch diffraction of the incident wave to contribute to theS2(p) amplitude in the shadow region.

5.2. Hawaii Simulation

[24] Another example of localized very high and steeptopography at fairly low latitude is provided by the BigIsland (BI) of Hawaii. The representation of the topographyin the AFES model for all the main Hawaiian islands isshown in Figure 10. The model topography on each of theislands is unrealistically smooth because of the limitedspectral resolution. Figure 11 shows the realistic topographyfor the BI. The model representation of the BI topography isas a single ridge oriented roughly north-south with a peak

height of about 2200 m. The real topography is closer to asaddle shape with two peaks separated by about 30 km:Mauna Loa (4150 m) in the south and Mauna Kea (4200 m)in the north with a valley between them dropping to about2000 m right between the peaks. In both the real world andthe model topography there is roughly 50 km from thehighest points to sea level on the west coast of the island,resulting in quite steep mean slopes in the east-westdirection (about 0.05 – 0.1). Figure 12 shows theunsmoothed amplitude of S2(p) determined from the 27 daysof AFES simulation for the Hawaiian region. In the 19–20�N latitude band the amplitude in the far field east or westfrom the BI is about 1.4 hPa. On the BI itself the simulatedamplitude drops off to less than 1.1 hPa at the summit.There is an east-west asymmetry of the simulated amplitudewith higher amplitudes (by �0.05–0.10 hPa) over the oceanon the east side than on the west side. Looking atFigures 8 and 2 one sees a region of reduced amplitude(relative to typical values at sea level for this latitude)extending about 200 km to the west of the BI.[25] Each circle in Figure 13 shows normalized 27-day

mean S2(p) amplitude as simulated at one grid point, plottedas a function of the topographic elevation of the grid pointin the model. The values are normalized by the mean of theamplitudes at the grid points closest to Hilo (model gridpoint at 19.72�N, 154.97�W) and Kona (model grid point at19.72�N, 156.0�W) which are on the east and west coast,respectively (and marked on Figure 12). Results are shownfor points in the box 19–20�N, 155–156�W, whichincludes almost all the BI land mass and a small amountof surrounding ocean. Values for the points in the easternhalf of the box are shown in red and in the western half areshown in black. Very roughly this divides the grid pointsinto those on the eastern slopes (and to the east of the highesttopography) and those on the western slopes. The generaldecay of amplitude with height is very evident. The contrastof higher amplitudes on the eastern slopes and loweramplitudes on the western slopes is also quite apparent.

5.3. Hawaii Station Observations

[26] The overall pattern of S2(p) amplitude on the BIsimulated in the model has some observational support,notably from new results obtained with instrumentsdeployed in a network of 9 stations on the BI by the NOAAEarth Systems Research Laboratory, Global MonitoringDivision Mauna Loa Observatory [Ryan, 2004]. Eachstation consists of an Onset Computer Corporation four-channel micro–data logger equipped with pressure, temper-

Figure 8. The amplitude of S2(p) determined from the27 days of AFES data. Results are unsmoothed. Contoursare labeled in hPa. The contour interval is 0.1 hPa, and the1.0 hPa contour is thick. The letters ‘‘M’’ and ‘‘A’’ mark thelocations of the Mollendo and Arequipa stations for whichHaurwitz [1956] reported observations.

Table 1. S2(p) Determinations for Stations Near 17�Sa

Station Name Latitude Longitude Altitude (m) Record (years) Amplitude (hPa) Phase (hours) Source

St. Helena 15.9�S 5.7�W – 7 1.100 9.67 RChirundu 16.0�S 28.9�E 390 1 1.37 9.87 HArequipa 16.4�S 71.6�W 2451 4 0.641 9.84 HMollendo 17.1�S 72.0�W 24 4 0.884 9.55 HMtoko 17.4�S 32.2�E 1262 8 1.04 9.69 HTahiti 17.5�S 149.6�W – 7 1.158 9.37 RLivingstone 17.8�S 25.8�E 964 7 1.16 9.74 HSalisbury 17.8�S 31.0�E 538 17 1.050 9.79 HFiji 18.1�S 178.4�E – 6 1.123 9.50 RGatooma 18.3�S 29.9�E 1174 4 1.06 9.87 HaThe source of the values is denoted by ‘‘H’’ [Haurwitz, 1956] or ‘‘R’’ [Ray, 1998].


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ature and humidity ‘‘smart sensors’’. The pressure data werecalibrated against yearly comparisons with a ParascientificDigiquartz Pressure Standard (SN 63724) operated by theUS National Weather Service Hilo office. The averageabsolute drift of the network pressure sensors was0.16 hPa per year. The sensors were sampled at 1 Hz and1-min averages for the pressure were recorded at a resolutionof 0.1 hPa. Hourly mean pressures were computed from the1-min values and then used in calculations of S2(p) followingthe procedure outlined by Chapman and Lindzen [1970].[27] The coordinates of the stations in the network and

their elevation above sea level are given in Table 2. Station1 is at Hilo Airport and station 8 is at Keohole Point, closeto Kona Airport. Station 7 is at the Mauna Loa Observatory(MLO) which is on the north slope of Mauna Loa, almostdue north from the summit. Stations 2–6 lie in a very roughline between Hilo and MLO ascending the northeast slopeof Mauna Loa, and station 9 is on the south slope of MaunaKea, almost due south of the summit.[28] Table 2 presents the results for S2(p) amplitude and

phase for the station network determined from two fullyears of observations (May 2004 to April 2006). Theamplitude for each station normalized by the mean of thevalues at Kona and Hilo is plotted as a function of elevationin Figure 13. A tendency for the amplitude to drop off withheight is apparent in the station observations, and the rate ofdecrease with height is comparable to that in the AFESsimulation. Also the contrast in amplitude between Hilo andKona provides some observational support for the east-westasymmetry of S2(p) across the BI in the AFES simulation.Specifically the ratio of the present observed S2(p) ampli-tude at Hilo to that at Kona is 1.08; the AFES simulatedamplitudes at the grid points near Hilo and Kona are1.23 hPa and 1.14 hPa, respectively, for a ratio also of1.08. The simulated local time phases of S2(p) are 9.44 h atthe grid point near Hilo and 9.64 h at the grid point nearKona, showing a similar contrast as the observed stationvalues (9.50 and 9.60, respectively).[29] Ray [1998] presented results for the annual mean

S2(p) at Kawaihae (20.0�N, 155.8�W) on the west coast,about 15 km north of Kona, based on 7 years of data. Hisamplitude of 1.027 hPa is fairly close to the present resultfor Kona (1.009 hPa) and still substantially less than theHilo value (1.092 hPa) on the east coast. Ray’s S2(p) phase

for Kawaihae is 9.47 h which compares to 9.60 h in thepresent determination for Kona.

6. Conclusions

[30] This paper has documented the simulation of thesolar tidal variation of surface pressure in the T1279L96AFES GCM. The main focus of the analysis has been onS2(p) and notably on regional-scale features that may beassociated with high topography. Extremely fine resolutionmodels are needed to resolve the topography well enough toadequately investigate these regional features. As an inter-esting aside, we estimate that integrating the present fineresolution GCM requires roughly two million times thecomputational effort per day of simulation as the modelused by ZH (which represented the state of the art 2 decadesago). Even a more idealized global linear model thatexplicitly included the small-scale topography wouldinvolve very considerable computation effort for obtainingsolutions.[31] Our analysis was based on a total of 27 days of

integration and was focussed on the tropics where signal-to-noise is large enough to allow fairly stable S2(p) determi-nations. The model was shown to simulate large-scalefeatures of S2(p) reasonably well, although with overallamplitudes typically 20–30% larger than observed, a defi-ciency which we believe is reasonably attributed to theeffect of the rigid lid in the model.[32] The first-order effect of high topography in the

model is a reduction in S2(p) amplitude with surfaceelevation, a feature that is consistent with our understandingof the semidiurnal tide as a vertically propagating inertia-gravity wave primarily excited in the ozone layer. Beyondthis we see evidence in the model results for weak S2(p)amplitudes to the west of very high and steep topography,which we attribute to a simple shadowing effect on the

Figure 9. A schematic of a large-scale inertia-gravitywave directed downward and westward toward a topo-graphic feature.

Figure 10. Topographic heights as represented in theT1279 AFES model for the Hawaiian Islands region. Thethin contours are for 200, 400, 600, and 800 m. The thickcontours are for 1000 and 2000 m. The red lines are a low-resolution representation of the coastlines.


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Figure 11. Topographic map of the Big Island of Hawaii with the positions of the barometric stationsmarked as squares. Station numbers correspond to those in Table 2.


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global-scale propagating tide. This accounts for the S2(p)anomaly noted half a century ago by Haurwitz along thewest coast of South America, as well as the ‘‘hole’’ in S2(p)amplitude extending over the ocean off the coast in the Daiand Wang [1999] global observational interpolation.[33] The very steep mountains of the Big Island of Hawaii

present another test for both the elevation effect on S2(p)and our proposed topographic shadowing effect. We pre-sented here for the first time a set of S2(p) determinationsusing barometric data from a special array of 9 sensorsestablished on the Big Island, representing an unprecedentedsampling of S2(p) over a large range of elevations in arelatively small geographical region. The comparison ofAFES simulations and the detailed observations are quiteimpressive. The simulated S2(p) amplitudes decline withheight at a rate very similar to that seen in the observations.Both model and observations support the idea that the steeptopography induces a contrast in the S2(p) amplitude on theeast versus the west side of the island.[34] This study used the availability of the AFES simula-

tions to investigate long-standing issues in the regional mod-ulation of the semidiurnal tide, but it also provides a chance toevaluate the model itself. It is encouraging that at least thishigh-resolution model is able to successfully simulate somedetailed regional structure in S2(p). Numerical weather pre-diction models are being run in major operational centers atincreasingly fine horizontal resolution. A realistic simulation

Figure 12. The amplitude of S2(p) determined from the27 days of AFES data. Results are unsmoothed. Contoursare labeled in hPa. The contour interval is 0.05 hPa, and the1.05, 1.15, 1.25. . . hPa contours are dashed. The letters‘‘K’’ and ‘‘H’’ mark the locations of the Kona and Hilostations.

Figure 13. Circles represent a plot of a measure of the local amplitude of 27-day mean S2(p) atindividual grid points in the AFES simulation versus the topographic height. Specifically plotted is theS2(p) amplitude at each grid point divided by the sum of the amplitudes at grid points close to Hilo andKona (see text for details). Results are shown for points in the box 19–20�N, 155–156�W, whichincludes almost all the BI land mass and a small amount of surrounding ocean. Results for the points inthe eastern half of the box are shown in red and in the western half are shown in black. The blue numbersare placed at the normalized 2-year mean S2(p) amplitude from observations at a network of nine stations.The observations are normalized by the average of the station results at Hilo and Kona.


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of the topographic modulation of the daily pressure variationin such models will be helpful for accurately assimilatingsurface pressure observations.

[35] Acknowledgments. This research was supported in part by NSFaward ATM02-19120. This research was also supported by the JapanAgency for Marine-Earth Science and Technology through its sponsorshipof the International Pacific Research Center. The model integrations wereperformed on the Earth Simulator of the Japan Agency for Marine-EarthScience and Technology.

ReferencesChapman, S., and R. S. Lindzen (1970), Atmospheric Tides, 200 pp.,Gordon and Breach, New York.

Dai, A., and J. Wang (1999), Diurnal and semidiurnal tides in global surfacepressure data, J. Atmos. Sci., 56, 3874–3891.

Emanuel, K. A. (1991), A scheme for representing cumulus convection inlarge-scale models, J. Atmos. Sci., 48, 2313–2335.

Fels, S. B. (1977), Momentum and energy exchanges due to orographicallyscattered gravity waves, J. Atmos. Sci., 34, 499–514.

Giwa, F. B. A., and L. A. Hussain (1978), A theory of atmospheric tidesgenerated by the differential heating between land and sea, Pure Appl.Geophys., 116, 56–65.

Hagan, M. E., and J. M. Forbes (2002), Migrating and nonmigrating diurnaltides in the middle and upper atmosphere excited by tropospheric latentheat release, J. Geophys. Res., 107(D24), 4754, doi:10.1029/2001JD001236.

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Haurwitz, B. (1965), The diurnal surface pressure oscillation, Arch.Meteorol. Geophys. Bioklimatol., Ser. A, 14, 361–379.

Haurwitz, B., and A. D. Cowley (1973), The diurnal and semidiurnalbarometric oscillations, global distribution and annual variation, PureAppl. Geophys., 102, 193–222.

Kawatani, Y., and M. Takahashi (2003), Simulation of the Baiu front in ahigh-resolution AGCM, J. Meteorol. Soc. Jpn., 81, 113–126.

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Ohfuchi, W., H. Nakamura, M. K. Yoshioka, T. Enomoto, K. Takaya,X. Peng, S. Yamane, T. Nishimura, Y. Kurihara, and K. Ninomiya (2004),10-km mesh mesoscale resolving simulations of the global atmosphere onthe Earth Simulator—Preliminary outcomes of AFES (AGCM for theEarth Simulator), J. Earth Simulator, 1, 8–34.

Oouchi, K., J. Yoshimura, H. Yoshimura, R. Mizuta, S. Kusunoki, andA. Noda (2006), Tropical cyclone climatology in a global-warming climateas simulated in a 20-km mesh global atmospheric model, J. Meteorol. Soc.Jpn., 84, 259–276.

Ray, R. D. (1998), Diurnal oscillations in atmospheric pressure at twenty-five small oceanic islands, Geophys. Res. Lett., 25, 3851–3854.

Ray, R. D. (2001), Comparisons of global analyses and station observationsof the S2 barometric tide, J. Atmos. Sol. Terr. Phys., 63, 1085–1097,doi:10.1016/S1364-6826(01)00018-9.

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��K. Hamilton, International Pacific Research Center, University of

Hawai’i, Honolulu, HI 96822, USA. ([email protected])W. Ohfuchi, Earth Simulator Center, Japan Agency for Marine-Earth

Science and Technology, Yokohama 236-0001, Japan.S. C. Ryan, Mauna Loa Observatory, Global Monitoring Division, Earth

System Research Laboratory, NOAA, Hilo, HI 96720, USA.

Table 2. S2(p) Determinations for Stations on the Big Island of Hawaiia

Station Number Latitude (�N) Longitude (�W) Altitude (m) Amplitude (hPa) Phase (hours)

1 (Hilo) 19.72183 155.0505 11 1.092 9.502 19.68401 155.1827 590 1.025 9.463 19.69267 155.2842 1176 0.972 9.394 19.67933 155.3773 1709 0.887 9.515 19.62033 155.4750 2270 0.851 9.476 19.57333 155.5088 2831 0.829 9.647 (MLO) 19.53917 155.5792 3396 0.756 9.748 (Kona) 19.72583 156.0573 5 1.009 9.609 19.76267 155.4580 2797 0.768 9.68aThe results at each location are 2 year means from measurements taken in the network operated by the Mauna Loa Observatory (MLO). See text for

details.


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