Implementation of Bessel's method for solar eclipses prediction in the WRF-ARW model

19 Pages·2016·2.12 MB·English

Atmos.Chem.Phys.,16,5949–5967,2016
www.atmos-chem-phys.net/16/5949/2016/
doi:10.5194/acp-16-5949-2016
©Author(s)2016.CCAttribution3.0License.
Implementation of Bessel’s method for solar eclipses prediction in
the WRF-ARW model
AlexMontornès1,BernatCodina1,JohnW.Zack2,andYolandaSola1
1DepartmentofAstronomyandMeteorology,UniversityofBarcelona,Barcelona,Spain
2MESOInc.,Troy,USA
Correspondenceto:AlexMontornès([email protected])
Received:3October2015–PublishedinAtmos.Chem.Phys.Discuss.:18January2016
Revised:17April2016–Accepted:23April2016–Published:17May2016
Abstract.Solareclipsesarepredictableastronomicalevents in the period 1950–2050, by comparing the shadow trajec-
that abruptly reduce the incoming solar radiation into torywithvaluesprovidedbyNASA.Latitudeandlongitude
the Earth’s atmosphere, which frequently results in non- aredeterminedwithabiaslowerthan5×10−3degrees(i.e.,
negligiblechangesinmeteorologicalfields.Themeteorolog- ∼550m at the Equator) and are slightly overestimated and
icalimpactsoftheseeventshavebeenanalyzedinmanystud- underestimated,respectively.Thesecondpartincludesavali-
iessincethelate1960s.Therecentgrowthinthesolarenergy dationofthesimulatedglobalhorizontalirradiance(GHI)for
industryhasgreatlyincreasedtheinterestinprovidingmore four total solar eclipses with measurements from the Base-
detailinthemodelingofsolarradiationvariationsinnumer- line Surface Radiation Network (BSRN). The results show
ical weather prediction (NWP) models for the use in solar an improvement in mean absolute error (MAE) from 77 to
resource assessment and forecasting applications. The sig- 90%undercloudlessskies.Loweragreementbetweenmod-
nificant impact of the recent partial and total solar eclipses eledandmeasuredGHIisobservedundercloudyconditions
that occurred in the USA (23 October 2014) and Europe becausetheeffectofcloudsisnotincludedinthesimulations
(20 March 2015) on solar power generation have provided for a better analysis of the eclipse outcomes. Finally, an in-
additional motivation and interest for including these astro- troductorydiscussionofeclipse-inducedperturbationsinthe
nomicaleventsinthecurrentsolarparameterizations. surfacemeteorologicalfields(e.g.,temperature,windspeed)
Althoughsomestudiesaddedsolareclipseepisodeswithin is provided by comparing the WRF–eclipse outcomes with
NWP codes in the 1990s and 2000s, they used eclipse pa- controlsimulations.
rameterizationsdesignedforaparticularcasestudy.Incon-
trast to these earlier implementations, this paper documents
a new package for the Weather Research and Forecasting–
AdvancedResearchWRF(WRF-ARW)modelthatcansim- 1 Introduction
ulate any partial, total or hybrid solar eclipse for the period
1950 to 2050 and is also extensible to a longer period. The Solar eclipses are predictable astronomical events that mo-
algorithmanalyticallycomputesthetrajectoryoftheMoon’s mentarily reduce the incoming radiation to the Earth’s at-
shadow and the degree of obscuration of the solar disk at mosphere, inducing a significant change in the meteorolog-
eachgridpointofthedomainbasedonBessel’smethodand ical fields. The impact of the shadow of the Moon on the
the Five Millennium Catalog of Solar Eclipses provided by Earth’satmospherehasawakenedtheinterestofmanyscien-
NASA, with a negligible computational time. Then, the in- tists since the second part of the 20th century. Solar eclipse
coming radiation is modified accordingly at each grid point episodes are excellent experiments for analyzing the re-
ofthedomain. sponseoftheatmosphere(e.g.,surfaceandplanetarybound-
Thiscontributionisdividedinthreeparts.First,theimple- ary layer, PBL) and for testing the response of the physi-
mentation of Bessel’s method is validated for solar eclipses calschemesinnumericalweatherprediction(NWP)models.
During a solar eclipse, the region under the shadow experi-
PublishedbyCopernicusPublicationsonbehalfoftheEuropeanGeosciencesUnion.
5950 A.Montornèsetal.:SolareclipsesinWRF-ARWmodel
encesasimilarphysicalprocesstothatwhichoccursatsun- ing the late 1990s along with the dense network of weather
riseandsunsetbutabruptlyandonashortertimescale(An- stations across Europe facilitated a large number of publi-
derson,1999). cations on this event. In general, these studies focused on
The first modern studies related to the relationship be- the impact on near-surface variables. For example, Hanna
tweentheatmosphereandthesolareclipsesappearedinthe (2000)analyzedthemeasuredvariationatstationsacrossthe
late1960smainlyfocusedontheozonevariationsandtheir UnitedKingdom,whileAplinandHarrison(2003)provided
impact on the stratosphere and mesosphere (Bojkov, 1968; a broader-scale analysis of the variations across the conti-
Randhawa,1968;Ballardetal.,1969). nent. Other relevant studies in other areas of interest were
Atthebeginningofthe1970s,ChimonasandHines(1970, performedbyAbrametal.(2000),Zerefosetal.(2001)and
1971) suggested that the cooling produced by the lunar Anfossietal.(2004),amongothers.Abrametal.(2000)mea-
shadow, crossing the atmosphere of the Earth at supersonic sured the effect of the solar reduction on the tropospheric
speeds, should produce gravity waves in the upper layers, chemistry,particularlyonthehydroxylradicalandozonein
measurable as surface pressure fluctuations. Based on this England.Zerefosetal.(2001)examinedtheinducedthermal
discussion, many studies were published that tried to detect fluctuations in the ozone layer, ionosphere and troposphere
these waves such as Davis and Da Rosa (1970), Anderson at stations in the Balkans, observing the existence of domi-
etal.(1972)andChimonas(1973)orlaterpublicationssuch nantoscillations inthe parameters relatedto theionosphere
as Fritts and Luo (1993), Altadill et al. (2001) and Zerefos and the ozone layer. Anfossi et al. (2004) used a three-axis
etal.(2007). propeller anemometer (Gill-type) and a fast-response tem-
Although several early studies (e.g., Stewart and Rouse, perature sensor in a mast located in France for measuring
1974; Antonia et al., 1979) examined the impact of solar theturbulencevariationduringtheeclipse.Inthatstudy,they
eclipsesonsurfaceprocesses,itwasnotuntilthelate1990s documentedarapidturbulentkineticenergydecayintime.
andearly2000sthatthefocusshiftedtothevariationsintem- More recently, other studies such as Founda et al. (2007)
perature,humidity,windspeed,turbulenceandatmospheric and Gerasopoulos et al. (2008) have been focused on the
chemistry. Fernández et al. (1993a, b) analyzed the varia- total solar eclipse which occurred on 29 March 2006 over
tions produced by the total eclipse of 11 July 1991 on dif- eastern Europe and particularly in Greece. Subrahamanyam
ferent meteorological fields using a set of surface stations et al. (2011) analyzed the behavior of the atmospheric sur-
and radio soundings for different sites in Costa Rica. The face layer, comparing the eclipse observations for the event
firststudyconcernedtheimpactontheglobalhorizontalir- on15January2010,withsimilarmeasurementsrecordedon
radiance (GHI) measurements, while the second one ana- non-eclipsecloudlessdaysinIndiausedasabaseline.
lyzed the effect on temperature, humidity and wind speed Giventhelowfrequencyofsolareclipsesinregionswith
on the ground and in the free atmosphere. Fernández et al. meteorological stations, atmospheric models are suitable
(1993b) observed negative temperature deviations ranging tools for analyzing the response of the atmosphere during
from2to5◦Creachingtheminimumvaluebetween10and a solar eclipse episode. The first studies with models ap-
30minafterthemaximumobscurationofthesolardisk.Sur- peared during the 1990s. Segal et al. (1996) used a bound-
face wind speed experienced a noteworthy reduction some ary layer version of the model described in Arritt (1989) in
minutes after reaching the lowest temperature in those sites order to evaluate the spatial and temporal effects on shel-
not dominated by the large-scale patterns. In the free atmo- tertemperatureusingthetotalsolareclipseof10May1994.
sphere, the highest temperature and wind speed variations Thegeneralfeaturesoftheeclipsewerequantifiedusingdata
were observed at ∼13km (i.e., 175hPa), with thermal dif- from the ephemerides and then refined by direct computa-
ferencesfrom−2to−6◦Candahighdeviationinwinddi- tionoftheSunandMoongeometrybasedonstandardmeth-
rection compared with soundings on similar days. Fernán- ods of celestial mechanics with a suitable accuracy. Gross
dez et al. (1996), Segal et al. (1996) and Anderson (1999), andHense(1999)presentedanNWPmodelstudyusingthe
among others, reported similar results, focusing on surface Deutschland-Modell (DM) from the German Weather Ser-
temperature. Meanwhile, Eaton et al. (1997) examined the vice (DWD) for analyzing the meteorological effects of the
effects of a solar eclipse on the PBL using the episode of 11 August 1999 eclipse. In this case, the episode was pa-
10May1994forthestudy.Theanalysisshowedaclearim- rameterizedintermsoftheshadow’strajectoryandapprox-
pactontheheatexchange(sensibleandlatent),areductionin imating thereduction in thesolar insolation. Thesolar con-
theturbulenceprocessesandasignificantnegativedeviation stant S wasmodified as0.01S in thecenter andassuming
0 0
intherefractiveindexstructureparameter.Moreover,usinga a linear increase in the north–south direction. This parame-
frequency-modulated,continuous-wave(FM-CW)radarop- terizationproducedasufficientaccuracyforthepurposesof
eratingat2.9GHz,Eatonetal.(1997)reportedthedevelop- theexperimentwith5minintimeand10%intheamplitude
mentofKelvin–Helmholtzwavesduringtheeclipse. of the eclipse. Vogel et al. (2001) used the Karlsruhe At-
The most meteorologically analyzed eclipse event is the mospheric Mesoscale Model (KAMM; Adrian and Fiedler,
total solar eclipse that occurred over Europe on 11 Au- 1991)forstudyingtheperturbationintemperatureandwind
gust1999.TheexpandeduseofmesoscaleNWPmodelsdur- driven by the eclipse of 11 August 1999 in southern Ger-
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A.Montornèsetal.:SolareclipsesinWRF-ARWmodel 5951
many. In this case, the solar constant was modified using a umbralshadowswithrespecttothecenteroftheEarth.The
mathematical expression referred as “obscuration function” use of this simpler description does not lose accuracy and
derived from geometric relationships in terms of the solar, it becomes independent of the observer coordinates. These
lunarandobserverpositions.Zanisetal.(2001)usedasim- variables are used to evaluate the eclipse conditions at each
plephotochemicalboxmodelforinvestigatingtheresponse gridpointrepresentedbythedegreeofobscurationandmod-
of the tropospheric ozone variations during a photolytical ifyingtheincomingradiationaccordingly.
perturbation as in the case of that European eclipse. Sza- Thestudyhastwomajorcomponents.Inthefirstpart,the
łowski (2002) built a basic model of local soil and air tem- algorithmimplementedtomodelsolareclipsesintheWRF-
perature changes in Poland for the same episode. The solar ARWisdescribedinSect.2andtheresultsofavalidationof
obscurationwasevaluatedfollowinggeometricrelationships thesolareclipsetrajectoriescomputedbythealgorithmwith
as a function of the topocentric coordinates of the centers respect to published NASA values are presented in Sect. 3.
of the solar and lunar disks in the equinoctial system and The second component of the paper presents results from
the angular radii of both celestial bodies. Eckermann et al. tests of the new WRF-ARW algorithm and code in simula-
(2007)investigatedtheatmosphericresponsetothetotalso- tions of four eclipse cases. The validation of the simulated
lareclipseof4December2002withthehigh-altitudeglobal globalhorizontalirradiancewithdatafromtheBaselineSur-
NWP model (Navy’s Operational Global Atmospheric Pre- faceRadiationNetwork(BSRN;Ohmuraetal.,1998)ispro-
dictions System – Advanced-Level Physics, High-Altitude, vided in Sect. 4 and the simulated eclipse-induced temper-
NOGAPS-ALPHA). In this experiment, the obscuration of ature as well as wind speed and direction perturbations are
thesolardiskwasevaluatedassumingalinearvariationfrom describedinSect.5.
the center of the eclipse to the penumbra region. Related to
the Weather Research and Forecasting–Advanced Research
2 ImplementationintheWRF-ARWmodel
WRF (WRF-ARW) model, Founda et al. (2007) parameter-
izedtheeclipseof29March2006assumingavariationinthe
The conceptual idea for including the solar eclipses within
solar constant proportional to the distance from the shadow
theWRF-ARWmodelissimilartothepreviousattemptsper-
axis, considered as a point moving on Earth with a specific
formedbyGrossandHense(1999)orFoundaetal.(2007),
velocity. More recently, Wu et al. (2011) used the WRF-
among others, as we have explained in the “Introduction”.
ARW coupled with the WRF-CHEM module for analyzing
ThesolareclipseoccurswhenthediskoftheSunishidden
the sensitivity of the tropospheric ozone and other chemi-
partially or totally by the Moon. Consequently, this process
calspeciesaswellastheeffectsonmeteorologicalvariables
producesareductionintheincomingradiationatthetopof
to the limb darkening effect as well as the effects on mete-
theatmosphere(TOA),S .
orological and other chemical species during the eclipse of in
Themagnitudeiscomputedintermsofthesolarconstant,
22July2009overChina.Thesolareclipseeffectwasadded,
S ,andthecosineofthesolarzenithangle,µ ,as
modifying the solar radiation and photolysis rates using a 0 0
scaling factor as a function of the latitude, longitude, time
S =S µ . (1)
in 0 0
andwavelength.Thedegreeofobscurationwasevaluatedas
proportionaltothedistancetothecenterofthetotaleclipse
InthedefaultversionoftheWRF-ARWmodel,S iseval-
0
trackprovidedbyNASA.
uatedatthemodulenamed“radiation_driver”ateachradia-
Therecentgrowthinthesolarenergyindustryhasgreatly
tivecallandsharedwithallshortwaveparameterizationrou-
increased the interest in including more detail in the mod-
tines as an input variable. Given one day of the year, this
eling of solar irradiance variations in NWP models for the
variableisassumedasaconstantatallgridpointsofthedo-
use in solar resource assessment and forecasting applica-
main(i.e.,scalarmagnitude).Thisnumberisdeterminedus-
tions. Regarding the resource forecasting, solar eclipses are ingabaselinesolarconstantof1370Wm−2modulatedbyan
episodes that increase errors significantly because the oper-
eccentricityfactor,determinedfollowingthemethodologyof
ational shortwave schemes implemented within NWP mod-
PaltridgeandPlatt(1976)asafunctionofthedayoftheyear.
elsneglecttheseastronomicalevents.Weproposeageneral
On the other hand, µ is calculated using spherical astron-
0
approach for modeling the eclipse effects within the WRF-
omyequationsintermsofthedate,timeandthegeographic
ARW model based on Bessel’s method (e.g., Chauvenet,
coordinates of the current grid point. Therefore, Eq. (1) has
1871) and the Five Millennium Catalog of Solar Eclipses
adependenceongridpointi,j andontimet as
providedbyNASA(EspenakandMeeus,2008).Themethod
is widely used in many astronomical applications related to
occultationsandeclipsesasaparticularcase.Thisapproach S =S µ . (2)
in,tij 0,t 0,tij
replacesthehighlycomplexequationsdescribingtheorbital
motionsoftheSun,MoonandEarthwithasimplerequation AsdiscussedinpreviouspublicationssuchasFoundaetal.
setexpressedintermsofthelocationontheEarth’ssurface (2007),thekeypointinmodelingtheimpactofsolareclipses
and the position and motion of the Moon’s penumbral and in the WRF-ARW radiation physics is the modification of
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5952 A.Montornèsetal.:SolareclipsesinWRF-ARWmodel
the incoming radiation by a spatially dependent (i.e., a 2-D eachradiationcall.Then,theincomingradiationismodified
array) degree of obscuration D. This variable takes into ac- followingEq.(3)beforecallingtheconfiguredsolarparam-
count the part of the solar disk that is hidden by the Moon eterization.
withageographicalandtemporaldependenceduetotheob-
server perspective (i.e., position within the model domain)
3 Algorithmvalidation
and the solar and lunar motions with respect to the Earth.
Thus,givenonetimet,wecanrewriteEq.(2)as
In order to evaluate the degree of accuracy and reliabil-
ity in the eclipse computation, the proposed algorithm has
S =S µ (cid:0)1−D (cid:1). (3) beenvalidatedwithrespecttoNASA’svalues(Espenakand
in,tij 0,t 0,tij tij
Meeus, 2008). As the lunar shadow has a circular shape
Whenthegridpointisnotundereclipseconditions,D =
tij (Eq. A17) in which each Earth point is separated by a dis-
0andEq.(3)becomesEq.(2).Bycontrast,whenagridpoint
tance(cid:49)fromthecenter,theevaluationoftheshadow’saxis
isunderthetotality,D =1andS becomeszero.
tij in,tij isenoughfordeterminingthedegreeofaccuracyofthenew
TheeclipsetrajectoryisdeterminedusingBessel’smethod
algorithm.
broadly explained in several manuals, such as Chauvenet
The validation includes all total, annular and hybrid
(1871), and briefly presented in Appendix A for readers
episodes for the period between 1950 and 2050. Partial
withsomeastronomicalbackground.Althoughthisapproach
eclipses cannot be validated because the trajectory is not
dates from the 19th century, it is still used by many institu-
well-defined on the Earth’s surface (Appendix A). More-
tions,suchasNASA.
over,therearesomeparticularcasesnearthepolesinwhich
Bessel’smethodisageneralapproachusedtopredictthe
the axis of the shadow does not cross the Earth’s surface
place and time for observing all celestial phenomena as oc-
and hence they are mathematically undefined. The follow-
cultationsandeclipses.Inthecaseofthesolareclipses,this
ing instances of such cases are not included in the valida-
approach projects the Sun and Moon orbit trajectories onto
tion:30April1957(annular,NorthernHemisphere),23Oc-
aplanepassingthroughtheEarth’scenterandperpendicular
tober1957(total,SouthernHemisphere),2November1967
totheaxisoftheMoon’sshadow;thisplaneisdefinedasthe
(total,SouthernHemisphere),29April2014(annular,South-
“fundamentalplane”.Onit,aCartesiancoordinatesystemin
ernHemisphere),9April2043(total,NorthernHemisphere)
R3 is used, with the X and Y axes constructed on the fun-
and3October2043(annular,SouthernHemisphere).
damentalplaneandwiththeoriginattheEarth’scenter.By
The results show a bias less than ±5×10−3 degrees for
construction the Z axis is normal to the fundamental plane
latitude and longitude, and in many cases even lower than
and parallel to the axis of the shadow. This new reference
±1×10−4 degrees(Fig.1),withtheerrorsinlongitudebe-
systemisusefulbecausewecandefineasetofvariablesthat
ing significantly higher than in latitude. In general, latitude
areonlyrelativetothefundamentalplaneandinvarianttothe
shows positive biases, while longitude tends to be underes-
observer. These magnitudes are denoted as “Besselian ele-
timated in other words, the modeled eclipse experiences a
ments”andtheyaredetailedinAppendixA.AstheBesselian
smalltemporaldelaywithrespecttotheNASAvalues.There
elements only depend on the fundamental plane and the as-
arenorelevantdifferencesbetweeneclipsetypes.
tronomicalephemerideoralmanac,theycanbeevaluatedbe-
Thesedifferencesaremostlikelyassociatedwiththevari-
fore an eclipse without considering the point of view of the
ationsintheaccuracyofphysicalconstantsandtheprecision
observer.
ofthecalculationsduetocompilerandcodinglanguagedif-
There are several catalogs for eclipses and occultations
ferences. On the one hand, the results by using double pre-
providingtheBesselianelementsbasedontheastronomical
cision instead of single precision show a near-zero bias in
ephemerides.Fortheparticularcaseofsolareclipses,NASA
latitude, while in longitude the bias is reduced by a factor
providestwocatalogs:theFiveMillenniumCatalogofSolar
of5(i.e.,110masamaximum).Foreconomytheseresults
Eclipses(EspenakandMeeus,2008)thatcontainsallpartial,
arenotincludedinthepresentstudy.Furthermore,thereare
annular,totalandhybrideclipsesfrom2000BCEto3000CE
two constants that may disturb the result: (i) the Earth’s ec-
andtheTenMillenniumCatalogofLongSolarEclipses(Es-
centricityand(ii)thecorrectingfactorforthetruelongitude
penak and Meeus, 2009) with a period from 4000BCE to
consideringthenonuniformrotationoftheEarth(Eq.A35).
6000CE.
The degree of accuracy shown in Fig. 1 (i.e., bias less
We store these Besselian elements in a WRF file named
than±550mintheEquatoranddecreasingwithlatitude)is
“eclipse_besselian_elements.dat”thatmustbepresentinthe
enough for most of the mesoscale applications. Moreover,
running folder for the model. This file contains a database
thepotentialimprovementaddedbyfeaturesdescribedinthe
ofallpartial,annular,hybridandtotaleclipsesfrom1950to
previous paragraph does not justify the increase in memory
2050(bothincluded)basedontheFiveMillenniumCatalog
resources.
ofSolarEclipses(EspenakandMeeus,2008).
Following the set of equations described in Appendix A,
thedegreeofobscurationisevaluatedforeachgridpointat
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A.Montornèsetal.:SolareclipsesinWRF-ARWmodel 5953
ahorizontalresolutionof27kmandthetopofthemodelat
Annular latitude Annular longitude
0.0050 50hPa.AllsimulationsareinitializedusingtheERA-Interim
0.0025 reanalysisat0.7◦×0.7◦ (Polietal.,2010)at18:00UTCon
the day before the date of the eclipse in order to minimize
0.0000
theimpactofmodelspin-upandupdatingtheboundarycon-
−0.0025
ditionsevery6h.Othersettingsrelatedtothemodelconfigu-
−0.0050
rationaredescribedinAppendixBbecausethisinformation
Hybrid latitude Hybrid longitude
0.0050 isnotrelevanttotheexperimentspresentedhere.
g) 0.0025 Althoughthenewcodehasanimpactonallshortwavepa-
e
Bias (d 0.0000 rhaima,e1te9r8iz9a)tifoonrst,wwoerreeadsuocnes:th(ie) dthisecuecssliiposnetomoDduifidhesiath(Deuidn--
−0.0025
coming radiation that is the same for all schemes (Sect. 2),
−0.0050
and (ii) Dudhia is the simplest shortwave parameterization
Total latitude Total longitude
0.0050 availableinthemodelandthereforesuitablefortheseinitial
0.0025 experiments.
0.0000 For each case, we run two simulations, one using the de-
fault version of the WRF-ARW model (release 3.6.1) used
−0.0025
asa “controlsimulation” andone usingthe newimplemen-
−0.0050
tation. In both cases, the cloud interaction within the so-
19501955196019651970197519801985199019952000200520102015202020252030203520402045205020551950195519601965197019751980198519901995200020052010201520202025203020352040204520502055 lar scheme is disabled using the parameter “icloud” in the
Episode
“namelist.input”file.Therearetworeasonsfordisablingthe
Figure 1. Bias in the eclipse’s track computed by WRF-ARW in cloud effects. On the one hand, cloud determination is one
comparisontotheNASAvalues.
ofthemostimportantsourcesoferrorinmesoscalemodels,
andhencetheyonlyaddnoisetothediscussion.Ontheother
hand, the main goal of this study is the implementation of
4 Casestudies Bessel’smethod, shifting cloudstoasecondary role.More-
over, the horizontal resolution used for these experiments
TheproposedimplementationwithintheWRF-ARWmodel cannot produce the desirable cloud granularity to be com-
istestedinfourrealsimulationswithtwogoals:(i)toevalu- paredwithon-siterealtimeseries.Nevertheless,themicro-
atethedegreeofimprovementintheGHIoutcomesrequired physicsschemeisenabledtoobtainamorerealisticresponse
forsolarenergyindustryapplicationsand(ii)toobservethe ofthemodel.Inthefollowingsections,thebaselineversion
degree of realism of the WRF-ARW model response nec- of the model without the eclipse physics will be referred to
essary for future scientific research in the line of previous as“WRF3.6.1”andthemodelversionwiththeeclipsealgo-
workssuchasFoundaetal.(2007). rithmwillbecalled“WRF–eclipse”.
As real measurements, we use data from the BSRN net- Thesetofresultspresentedinthisstudyisprovidedwith
work(Ohmuraetal.,1998)becausethisdatasetprovidesra- a1mintimeresolutioninordertocapturetherelevantvaria-
diation, surface and upper-air measurements for 58 stations tionsduringthesolareclipse.Spatially,thenearestgridpoint
aroundtheworldinmanyclimatezonesand,insomecases, isselectedtorepresenteachBSRNsite.
covering periods longer than 20 years. Moreover, the solar
radiationmeasurementsareprovidedwithahightimereso-
lution (1 to 3min), which is convenient for evaluating GHI 5 Results
performance.
Thecasestudiesarechosenintermsofthespatialandtem- This section includes a discussion of the results produced
poralcoverageoftheBSRNstationsandthedataavailability. by the simulations described in Sect. 4. The analysis is di-
After a previous analysis of the data sets, four total-eclipse vided into two parts. First, the skill of the new algorithm
episodesarepresented:3November1994(SouthAmerica), in reproducing the impact of the eclipse on the solar radia-
11August1999(Europe),29March2006(northernAfrica) tionreceivedatthegroundfordifferentlocationsandeclipse
and 22 July 2009 (eastern Asia). The location of the BSRN events will be evaluated (Sect. 5.1). In the second part, we
stations used for each episode is included in Fig. 2. These will present an initial discussion about the model response
stationsareFlorianopolis(FLO)inSouthAmerica;Carpen- comparing the study cases presented in this paper with the
tas(CAR),Lindenberg(LIN)andPayerne(PAY)inEurope; previousresultsdescribedinEatonetal.(1997)andFounda
Tamanrasset (TAM) in northern Africa; and Tateno (TAT) etal.(2007),amongothers(Sect.5.2).
andXianghe(XIA)ineasternAsia. Beforepresentingtheresultsoftheanalysis,threeparam-
Foreachepisode,wecreateasingledomaincomposedof eters used in the discussion should be defined. The first is
200×200 grid points (Fig. 2) and 50 vertical levels, with the “First Contact Time in Domain” (FCTD), described as
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5954 A.Montornèsetal.:SolareclipsesinWRF-ARWmodel
Figure2.Domainsusedforeachcasestudy.Sitesareindicatedinorange.Theeclipsetrackisrepresentedbythecentralgraypoints.The
redpointsindicatesomeoftheeclipsetimesinUTC.Thedarkgraypointsshowtheboundsofthe90%obscuration.
thetimestampinwhichonenodeinthedomainhasanob- the shadow. When the episodes are sorted chronologically
scurity degree different than zero. From that moment, both (i.e.,3November1994,11August1999,29March2006and
simulationsarenotstrictlyequalbecausetheincomingradi- 22July2009),theFCTDisobservedat11:08,08:39,07:41
ationinWRF–eclipsehasbeenmodified.Thisvariationhas and00:06UTC,respectively(Table1).
a direct impact on the solar heating rate profile as well as Thesecondtermthatwillbeusefulfordescribingthere-
on the GHI and consequently on the other meteorological sultsisthe“MaximumObscurationTime”(MOT),thetime
fieldsthrough(i)theEulerequationsand(ii)thelandsurface inwhichtheobscurationdegreereachesthemaximumvalue
modelandsurfacelayerparameterizations(Montornèsetal., ateachsiteandthuswhentheGHIreachesthelowestvalue
2015). Trivially, as FCTD is a property of the episode, the under the cloudless-sky assumption. This magnitude is cer-
magnitudeisthesameforallsitesinthesamedomain. tainlysite-dependent.
In the case studies presented in this paper, we observe Finally, the “Last Contact Time in Domain” (LCTD) de-
that the FCTD occurs ∼1h earlier than the first contact of finesthelasttimestampinwhichsomegridpointhasade-
the axis of the eclipse in the domain represented in Fig. 2. gree of obscuration different from 0. As in the case of the
The physical reason can be easily interpreted considering FCTD, this variable depends on the episode, with 15:16,
the velocity of the axis across the Earth and the radius of
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A.Montornèsetal.:SolareclipsesinWRF-ARWmodel 5955
Time series for WRF–eclipse are well synchronized with
1994−11−03 | FLO 1999−08−11 | CAR
respect to the real data sets. The MOT (Table 1) in FLO is
Max. obs. Max. obs.
900 reachedat13:01UTC.CAR,LINandPAYshowthelowest
97.0% 85.6%
GHI at 10:28, 10:42 and 10:31UTC, respectively. TAT and
600
XIA have the lowest GHI at 02:14 and 01:33UTC. Finally,
300 TAM experiences the MOT at 09:53UTC, with a delay of
∼1minwithrespecttotherealmeasurements.Thisdelayis
0
04:00 10:00 16:00 22:00 04:00 10:00 16:00 22:00 produced because we are considering the nearest grid point
1999−08−11 | LIN 1999−08−11 | PAY inanequatorialregion.
Max. obs. Max. obs. The amplitude of the GHI reduction shows good agree-
900
89.3% 94.3% mentinthosesitesshowingclear-skyconditionsinrealmea-
600 surements (e.g., FLO, TAM), while those sites with clouds
(e.g., PAY, TAT) show a tendency to overestimate the GHI
300
because we are not considering the effect of clouds on ra-
)
-2m 0 diativetransferintheseexperiments.Asimilarcloudimpact
W 04:00 10:00 16:00 22:00 04:00 10:00 16:00 22:00
( HI 2006−03−29 | TAM 2009−07−22 | TAT wasreportedbyFoundaetal.(2007)whencomparingWRF-
G simulated GHI with real observations during the total solar
Max. obs. Max. obs.
900 eclipseof29March2006.
80.5% 72.1%
The accuracy is quantified in terms of the bias and the
600
meanabsoluteerror(MAE),definedas
300
1 XN
0 Bias= (f −o ), (4)
i i
04:00 10:00 16:00 22:00 04:00 10:00 16:00 22:00 N
2009−07−22 | XIA i=1
900 Ma7x2.. 8o%bs. MAE= N1 XN |fi−oi|, (5)
i=1
600
respectively.Thevalidationperiodconsistsofalltimeswith
300
obscuration greater than zero in WRF–eclipse and a solar
0 zenith angle less than 80◦ (i.e., it excludes times when the
04:00 10:00 16:00 22:00
Time (UTC) sun is just above the horizon). Hence, N is the number of
validframes,whilef andoarethemodeledandrealvalues,
Legend Real WRF 3.6.1 cloudless WRF-eclipse cloudless
respectively. These metrics are not normalized with respect
Figure3.GHIoutcomesforeachepisodeandsite.Eachtotalsolar totheradiationatTOAasisusuallydonebecausethisvari-
eclipseeventislabeledwiththedate.Plotsshowrealmeasurements ableisnotthesameinWRF3.6.1asinWRF–eclipse.
(inblack),thecontrolsimulation(red)andthenewimplementation Sites under cloudless conditions show the highest im-
(blue). The first and second vertical gray solid lines indicate the provements in MAE (Table 2). In FLO, the use of WRF–
time of FCTD and LCTD, respectively. The dashed vertical gray eclipserepresentsanimprovementof90%intheMAEwith
line shows the time of maximum obscuration. All results are ex- respecttoWRF3.6.1simulations.TAMshowssimilarresults
pressedwith1mintimeresolution.
withadecreaseof77%intheMAE.Bothsitesshowahigh
reductioninthebias:inFLO,from438to−34Wm−2 and,
13:10, 12:18 and 04:29UTC being the times of occurrence in TAM, 348 to −82Wm−2. This high underestimation is
(Table1)foreachcasestudy. associatedwiththeneargridpointissuementionedbefore.
Incontrast,lowerimprovementisobservedincloudycon-
5.1 Globalhorizontalirradiance ditions. The best results are detected in CAR with an en-
hancement of 86%, drifting from a high positive bias of
The study of the GHI shows a similar behavior throughout 364Wm−2 to a slightly negative one of −42Wm−2. LIN
all analyzed sites (Fig. 3). Before and after the eclipse, the
and PAY show a similar improvement of 73 and 71% in
WRF3.6.1 and the WRF–eclipse show identical outcomes,
theMAE,respectively.Finally,aminorimprovementisob-
while the first one reproduces the expected cloudless daily
served in the Asian stations, with variations in the MAE of
patternduringtheeclipseandtheseconddecreasesabruptly
+50%inTATand+64%inXIA.Thebiasdriftsfrom493
reaching the minimum value at MOT and increasing again to176Wm−2inXIAandfrom798to395Wm−2inTAT.
later.ThereductionintheGHIdependsontheeclipsecondi-
tionsineachplace.
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5956 A.Montornèsetal.:SolareclipsesinWRF-ARWmodel
Table1.Overviewoftheparametersthatdescribetheeclipseepisodesattheselectedsites.FCTDistheFirstContactTimeinDomain,
LCTDistheLastContactTimeinDomain,MOTistheMaximumObscurationTimeandObscreferstothedegreeofobscuration.
Episode Region FCTD(UTC) LCTD(UTC) Site MOT(UTC) Obsc(%)
3Nov1994 S.America 11:08 15:16 FLO 13:01 97.0
11Aug1999 Europe 08:39 13:10 CAR 10:28 85.6
LIN 10:42 89.3
PAY 10:31 94.3
29Mar2006 Africa 07:41 12:18 TAM 09:31 80.5
22Jul2009 Asia 00:06 04:29 TAT 02:14 72.1
XIA 01:33 72.8
Table2.BiasandMAEoftheGHIforecastsproducedbyWRF3.6.1andWRF–eclipsefortheperiodinwhichtheobscurationisgreater
◦
thanzeroandthesolarzenithangleislessthan80 .
Duration WRF3.6.1 WRF3.6.1 WRF–eclipse WRF–eclipse
Episode Region Site (min) bias(Wm−2) MAE(Wm−2) bias(Wm−2) MAE(Wm−2)
3Nov1994 S.America FLO 160 438 438 −34 44
11Aug1999 Europe CAR 167 364 364 −42 50
LIN 159 478 480 94 130
PAY 166 580 580 164 170
29Mar2006 Africa TAM 153 348 352 −82 82
22Jul2009 Asia TAT 153 798 798 395 395
XIA 140 493 493 176 176
5.2 ResponseoftheWRF-ARWmodel surfacewindischosensinceitprovidesanindirectandinte-
gratedresponsetotheGHIperturbationsbecauseitincorpo-
ratespressuregradientchangesaswellasvariationsinturbu-
Shortwave schemes have a remarkable role within NWP
lence(i.e.,stability).Thediscussionisfocusedonthesame
models and are more significant in cloudy situations than
BSRNsitesanalyzedinSect.5.1,forconsistency.However,
in cloudless ones due to the approximations assumed in the
the model outcomes are not compared with real measure-
computationoftheradiativetransferequation.Theselection
ments because the temporal resolution of the weather vari-
ofonesolarparameterizationoranotherproducesdifferences
ablesintheBSRNstationsis3-hourlygiventhattheyreport
in the heating rate profile as well as in the surface energy
these data sets to the SYNOP network and, consequently,
balance leading to variations in the other fields due to the
theycannotprovidetherequiredtemporalgranularitytoan-
high nonlinear relationships between the dynamics and the
alyzetheeffectsoftheeclipseovertherealatmosphere.Fur-
physicsofthemodel(Montornèsetal.,2015).
thermore,themodelconfigurationusedintheseexperiments
Including solar eclipses within the mesoscale model is
is not appropriated for a full description of the atmospheric
conceptually the same issue. The shadow of the Moon re-
response as can be found in Founda et al. (2007) and oth-
duces the GHI as viewed in Sect. 5.1 and the heating pro-
ers.Consequently,wepresentareviewofthemeteorological
duced by ozone and water vapor absorption in the strato-
fieldstodemonstratethatthemodelproducesreasonablere-
sphereandtroposphere,respectively.Asaconsequence,the
sultsforthefirst-orderimpact.Moreover,afurtherstudyof
surfaceenergybalanceismodifiedreducingtheavailableen-
the complex nature of the dynamic response to the eclipse-
ergytobetransformedintolatent,sensibleandgroundheat,
inducedperturbationswillbeproposedinfutureworks.
whilethediabatictermintheenergyequationdecreasessig-
Theresponseofthesurfacefluxesisinstantaneousorless
nificantly,producingchangesintheotherfields.
than1minasitisobservedinFig.4andsimilartothatob-
The following analyses are focused on the surface vari-
servedduringatypicalsunsetandsunrise.BeforeMOT(Ta-
ables, in particular, the surface heat fluxes, temperature at
ble1),sensible(SH)andlatentheat(LH)experienceareduc-
2mandwindspeedanddirectionat10m.Surfacefluxesand
tion together with an increase in the ground heat (GH). At
temperature are analyzed because they are the most direct
MOT,thesemagnitudesreachthemaximumdifferencewith
response to the GHI perturbations. On the other hand, the
Atmos.Chem.Phys.,16,5949–5967,2016 www.atmos-chem-phys.net/16/5949/2016/
A.Montornèsetal.:SolareclipsesinWRF-ARWmodel 5957
respect to WRF3.6.1. The range of these deviations varies
1994−11−03 | FLO 1999−08−11 | CAR
from one site and episode to the other, as it is related to 500
thedegreeofobscuration,thetimeofdayandtheyear(i.e.,
250
it is linked to the development of the PBL), land use, soil
properties, and weather conditions (i.e., humidity or cloud 0
presence,amongothers)asindicatedbyEatonetal.(1997).
−250
ThedeparturesinSHbetweenWRF3.6.1andWRF–eclipse
are ∼200Wm−2, following a similar behavior to that re- 04:00 10:00 16:00 22:00 04:00 10:00 16:00 22:00
1999−08−11 | LIN 1999−08−11 | PAY
portedbythesamestudyusingrealmeasurements.InFLO, 500
CAR and LIN, SH reaches slightly negative values around
250
the MOT. LH experiences larger departures than SH, with
differenceslargerthan∼250Wm−2inFLOandCAR.TAM 0
andTATexperienceLHvariationslowerthanSHduetothe )
local meteorological features. The GH shows a significant -2m−250
W
increase reaching near-zero values or even slightly positive ( x 04:00 10:00 16:00 22:00 04:00 10:00 16:00 22:00
ones as a response of the SH decay, as it is highly depen- at flu 500 2006−03−29 | TAM 2009−07−22 | TAT
e
dentonthesoilfeatures.ThelargestGHdeviationsbetween H
250
WRF3.6.1 and WRF–eclipse are produced in TAM because
thissiteislocatedneartheSahara. 0
After the MOT (Table 1), surface fluxes in WRF–eclipse
tend to return to similar values as in WRF3.6.1. At some −250
sites, such as CAR or XIA, SH experiences greater values 04:00 10:00 16:00 22:00 04:00 10:00 16:00 22:00
2009−07−22 | XIA
than WRF3.6.1 once the solar disk is fully visible again. 500
Othersiteswithahighdependenceonthedailypatterns,as
250
atFLOandTAM,showlowerSHvalues.
Inthisdiscussionofthefluxes,PAYisanexception.This
0
site experiences a time lag in the response with respect to
the MOT with positive heat fluxes deviations (Fig. 4). This −250
patternisproducedbecausethegridpointusedfortheanal- 04:00 10:00 16:00 22:00
Time (UTC)
ysescorrespondstoawaterbodyasthissiteislocatedneara
waterarea(i.e.,LakeNeuchâtel). Legend WRF 3.6.1 cloudless WRF-eclipse cloudless
Surface fluxes are important because they provide the
Variable GH LH SH
lowerboundaryconditionforevaluatingtheverticaltransport
parameterized within the PBL schemes. Within the model, Figure4.Sensibleheat(SH),latentheat(LH)andgroundheat(GH)
these physical processes are parameterized in three physi- flux outcomes for each episode and site. Each total solar eclipse
cal packages: the land surface model (LSM), PBL and sur- eventislabeledwiththedate.TheGHinPAYisnotplottedbecause
thenearestpointusedisrepresentedbyawaterbody(i.e.,GHun-
face layer scheme. The LSM approximates those processes
defined).Colorsindicatethecontrolsimulationoutcomes(red)and
occurring at the surface (i.e., surface energy budget, evapo-
thenewimplementation(blue).Thefirstandsecondverticalgray
ration and soil processes, among others), and it returns SH,
solidlinesindicatethetimeofFCTDandLCTD,respectively.The
LH, terrestrial emission and shortwave reflection to the at-
dashedverticalgraylineshowsthetimeofmaximumobscuration.
mospheric model. The PBL scheme parameterizes the ver-
Allresultsareexpressedwith1mintimeresolution.
tical transport of momentum, energy and water vapor be-
tweenthelowerlevelsofthemodelandthefreeatmosphere.
Bothpackagesinteractthroughthesurfacelayerparameter- Variationsinthetemperatureat2mshowadelaywithre-
ization. This physical scheme computes the exchange coef- specttotheGHIandheatfluxes(Fig.5).Themagnitudeand
ficientsandthefrictionvelocityrequiredforcalculatingSH timelagareinagreementtothosereportedduringothersolar
andLHwithintheLSM.Moreover,thesurfacelayerparame- eclipsesusingrealmeasurementssuchasinFernándezetal.
terizationdiagnosesthetemperatureat2mandwindspeedat (1993b)(between10and30min)orFoundaetal.(2007)(be-
10mbasedonthesimilaritytheoryequations(Stull,1988). tween10and15min).FLOshowsthegreatestvariationwith
Therefore,temperatureat2mandwindspeedat10mare −4.4K,12minafterthelowestGHIandSHvalues(Figs.3
two interesting fields for understanding the response of the and 4). CAR, LIN, TAM and TAT experience a similar be-
modelinaneclipseepisodeatfirstorder,withoutconsidering havior to each other. In CAR and LIN, the temperature de-
afullanalysisofthePBL,wouldrequireaspecial,dedicated creases2.9and2.6K,5and3minaftertheMOT(Table1),
studyandwhichisbeyondthescopeofthisone. respectively. TAM shows a reduction of 2.1K, 6min after
themaximumobscuration,whileinTAT,thetemperaturede-
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5958 A.Montornèsetal.:SolareclipsesinWRF-ARWmodel
cantdifferences.CAR,LIN,PAYandTAMarestationsthat
1994−11−03 | FLO 1999−08−11 | CAR
1 experience temperatures around 0.5 and 1K lower than in
0 WRF3.6.1outcomes,withPAYbeingthemostconservative
−1 case due to the lake effect. TAT shows a positive anomaly
−2 between 10:00 and 12:00UTC, falling quickly to near-zero
−3 negative departures. XIA is the site with the highest vari-
−4 ation in the temperature, drifting from positive departures
−5 (∼+0.5K) to negative ones (∼−1K, even ∼−1.5K) dur-
04:00 10:00 16:00 22:00 04:00 10:00 16:00 22:00
ing the successive hours, with a tendency to become more
1999−08−11 | LIN 1999−08−11 | PAY
() K 1 stableattheendoftheday.Theseextremetemperaturevari-
6.1) 0 ationsareaconsequenceofthepatternsdescribedinthesur-
F3.−1 facefluxes.Finally,FLOexperiencespositivedifferencesat
R
W−2 local midday, drifting to near-zero departures at the local
−
e −3 evening. The reason for this positive anomaly is described
s
p
cli−4 bythelocalmeteorologicalconditions.FLOislocatedonthe
e
−
F−5 coast (Fig. 2) and highlyinfluenced by breezes producing a
R
W 04:00 10:00 16:00 22:00 04:00 10:00 16:00 22:00 well-defined wind speed pattern (Fig. 6). The eclipse pro-
es ( 1 2006−03−29 | TAM 2009−07−22 | TAT duces a delay in the wind speed daily maximum leading to
c
eren 0 warmerairatmiddaywithrespecttothesimulationwithout
diff−1 theeclipse.SimilarresultswerereportedinSubrahamanyam
e
ur−2 and Anurose (2011), comparing real measurements for an
at
er−3 eclipse episode with respect to a control day in a region of
p
m
e−4 Indiahighlyinfluencedbythesea–landbreezes.
m t
2 −5 Theresponseofthewindspeedvariesfromonesitetoan-
04:00 10:00 16:00 22:00 04:00 10:00 16:00 22:00
other(Fig.6)linkedtohighnonlinearrelationshipsbetween
2009−07−22 | XIA
1
the model dynamics and physical schemes. The particular
0 variations in wind speed and direction during and after the
−1 eclipsearerelatedtothedegreeofobscurationaswellasthe
−2 localenvironmentandmeteorologicalpatterns,asithasbeen
−3 presentedinotherpreviousstudies(Fernándezetal.,1993b;
−4 Foundaetal.,2007;Wuetal.,2011).
−5 ThetemporalresponseinFLO,CARandLINissimilarto
04:00 10:00 16:00 22:00
Time (UTC) thatobservedforthetemperature(Fig.5).Thesesitesexperi-
enceanabruptreductioninspeed,withnear-zerodeviations
Figure5.Temperaturedifferencesat2mforeachepisodeandsite. somehoursaftertheMOT.CARandLINexperienceamin-
Each total solar eclipse event is labeled with the date. The first imumwindspeed5and3minaftertheMOT,with−1.8and
andsecondverticalgraysolidlinesindicatethetimeofFCTDand −1.6ms−1,respectively.Bothsitesshowwindspeedsabove
LCTD,respectively.Thedashedverticalgraylineshowsthetime
theWRF3.6.1values(lessthan+0.5ms−1)aftertheeclipse
ofmaximumobscuration.Allresultsareexpressedwith1mintime
linking with the pattern observed in SH (Fig. 4). Variations
resolution.
in wind direction (Fig. 7) are negligible both in CAR and
LIN. FLO shows two minima; the first is produced 3min
cays2.2Kwithadelayof4min.Finally,PAYandXIAshow after the MOT and the second minimum ∼4h later, after
the largest delays with similar variations. In the first case, local midday. Both cases show a wind speed reduction of
theminimumvalueisreached1hand16minaftertheMOT ∼1.5ms−1,withthesecondonebeinglessimportant.This
withananomalyof−1.1K.Inthesecondcase,theminimum observed pattern is a direct consequence of the temperature
temperature is shown with a shift of 11min and a variation lag that reduces the sea breeze as it is reflected in wind di-
in−1.2K.Wuetal.(2011)reportedsimilartemperaturede- rection.Between1and2haftertheMOT,winddirectionin
creases during the same solar eclipse over China using the WRF–eclipsechanges,withawesterncomponent(i.e.,from
WRF-CHEMmodule.Theamplitudeofthetemperaturede- land;Fig.2).Duringtheafternoonandsunset,thethermallag
crease in TAM is also in agreement with the WRF simula- produced by the solar eclipse disappears and WRF–eclipse
tionsinGreeceshownbyFoundaetal.(2007).Nevertheless returnstothebaselinedirection.
the local environment and cloudiness determine the actual PAYandTAMshownear-zeropositivevariationsatMOT
observeddifferences. withapositivepeakof+0.5and+0.8ms−1,40and43min
Aftertheeclipse,allsitestendtoreturntosimilarpatterns after the maximum obscuration (Table 1), respectively. Af-
as observed in WRF3.6.1. However, there are some signifi- ter this peak, wind speed shows a negative minimum, more
Atmos.Chem.Phys.,16,5949–5967,2016 www.atmos-chem-phys.net/16/5949/2016/