1 Introduction

Attempts to reproduce the whole magne-tosphere using MHD simulations date back tothe 1980s［1］［2］. With the dawn of the 1990s,advances in computer technology opened away for performing calculations with mini-mum meshes needed to reproduce magnetos-pheric phenomena, and the implementation ofmagnetosphere-ionosphere coupling allows amagnetosphere-ionosphere MHD simulationmodel of practical use［3］［4］. Through the2000s, magnetosphere-ionosphere MHD sim-ulations have evolved into computerized real-time MHD simulations capable of reproducingthe temporarily changing behavior of the mag-netosphere by using solar wind as an initial

value［5］. Because a detailed description of thereal-time MHD simulations developed at theNational Institute of Information and Commu-nications Technology is given in［5］, this paperdescribes the impact of MHD simulations onmagnetospheric physics. It should be notedthat a code for more precise and stable calcu-lations must be developed in order to imple-ment a numerical method of space weatherprediction of practical value. However, itmight be useful to introduce advanced tech-niques used in the field of numerical meteoro-logical prediction that maximize the use oflimited computer resources, as in space weath-er prediction. Therefore, an example of dataassimilation and the implementation of guid-ance are also presented for discussion.

179FUJITA Shigeru

2-3-4 The Global MHD Magnetosphere Simulationand Prospect for the Space Weather Prediction

FUJITA Shigeru

This paper discusses the concept of a magnetosphere-ionosphere compound system intro-duced into magnetospheric physics by self-consistent magnetospheric MHD simulations with theionospheric boundary. It also describes typical magnetospheric phenomena (e.g., sudden com-mencement of magnetism, theta-auroras, substorms) that occur with solar wind changes interms of state transitions occurring in a magnetosphere-ionosphere compound system. Next, thepaper discusses a certain technique used for meteorological purposes (weather prediction) con-sidered useful for future space weather services. To this end, we introduce a preliminary attemptto estimate the optimal values of ionospheric conductivities through data assimilation. The dataassimilation technique based on the present magnetospheric simulation, however, is still unsat-isfactory for space weather prediction, since available numerical models still yield poor phenom-enon reproducibility. Last, the paper discusses to implement the “guidance” scheme used inweather prediction services to space weather. The data created by the simulation from momentto moment are equivalent to objective analysis data in meteorology. Therefore, a guidancescheme equivalent to that used in weather prediction services might be introduced by derivingthe relationships for predicting relevant physical quantities from accumulated objective analysisdata on space weather.

KeywordsMagnetosphere-ionosphere compound system, MHD, Data assimilation, Guidance,Numerical weather prediction

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2 Impact of magnetosphericmodels on magnetosphericphysics

In the past, scientists studying global phe-nomena in the magnetosphere-ionosphere sys-tem would simply estimate an overall pictureof the phenomena using ground-based orsatellite observations, while resorting to MHDor the relevant physical laws where observa-tional data was not available. Since the mag-netosphere would take complex geometriesafter interaction with solar winds, it is difficultto draw a definite conclusion from a combina-tion of ground-based or satellite observationswith human imagination. For example, theexistence of region 1 field-aligned current hadalready been known in the 1970s［6］, but noconclusion had been reached regarding thesource region of the magnetosphere and itspath to the ionosphere. On the other hand, theemergence of numerical magnetospheric sim-ulations capable of producing a realistic repro-duction of global phenomena in the magnetos-phere-ionosphere system has begun to shedclear light on the generation mechanism ofsuch global phenomena. As for the region 1field-aligned current system, simulation analy-ses presented in a document［4］have demon-strated the following scenario; through theinteraction of a cusp characterized byenhanced plasma pressure with a convectionflowing towards the nightside magnetospheredue to reconnection with solar wind magneticfields, a current-generating region appearingon the nightside of the cusp region is formed.The current thus generated is led to the ionos-phere as a field-aligned current through themagnetosphere.

The impact of magnetosphere-ionosphereMHD simulations on magnetospheric physicsis not limited to explaining the phenomenaobserved. Moreover, it extends to the capabili-ty for providing grid-point data to MHD equa-tions under ionospheric boundary conditions,because the artificial effects derived fromnumerical problems are eliminated to theextent possible. This means that the results are

physically self-consistent. The only parame-ters needed to drive this numerical model areplasma data in solar winds. In other words, themodel is capable of autonomous operationwithout the aid of additional observatoryinformation. The resultant spatial 3D time-series data is equivalent to objective analysisdata in terms of meteorology. An analysis ofthat data will help to quantitatively study thephysical processes in the magnetosphere with-in the limits of MHD approximation. (Theobjective analysis will also be mentionedlater.)

Another aspect of the impact of magnetos-phere-ionosphere MHD simulations is theintroduction of a new concept［7］known as a“compound system” into research on magne-tosphere-ionosphere phenomena (see［8］ formore details). MHD simulations provide uswith the states of multiple physical processes(e.g., current and plasma distributions, mag-netic configuration, magnetosphere and ionos-phere convections) being self-consistent withone another. From this perspective, the proce-dure for understanding phenomena that occurin the magnetosphere-ionosphere system as acompound system should not simply entail anunderstanding of “how they occur” but pro-ceed to a state of understanding “why theyought to occur.” In short, the first procedureabove is concerned with the sequence of phys-ical elements and focuses on understandingthe cause and effect process, disregarding theissue of coherency of the whole magnetos-phere-ionosphere system. The latter proceduresuggests that the magnetosphere-ionospheresystem needs to exist so every physical mech-anism comprising that system is a self-consis-tent system.

This concept of the compound system isessential to understanding variations in themagnetosphere-ionosphere system resultingfrom disturbances in solar wind. The suddencommencement (SC) driven by impulses inthe dynamic pressure of solar wind might, forexample, be considered a transition betweentwo states of a compound system that are fit totwo solar wind conditions with different

181FUJITA Shigeru

dynamic pressure. Within this framework, thepreliminary impulse (PI) is a period of fluctua-tion composed primarily of waves generatedupon impact with the magnetosphere system,during which the coupling between the mag-netosphere and ionosphere convections (i.e.,state of connection between electric fields inthe magnetosphere and ionosphere throughmagnetic lines of force) is lost. Conversely,the main impulse (MI) can be considered aperiod of transition to a new state followingrecovery of the connection lost between themagnetosphere and ionosphere convections［9］.Numerical simulations have revealed that inthe period of state transition, the field-align-ment current increases and a transient convec-tion vortex in the magnetosphere is generated.This fact suggests that extra energy is built upin the magnetosphere during state transitionand then consumed in the ionosphere. Increas-es in field-aligned current have also been con-firmed by ground magnetic field observations(for example, see［10］). In addition to varia-tions in the dynamic pressure of solar wind,there are other state transitions caused byinterplanetary magnetic field (IMF) variations.For instance, continuous state transitions willalso occur when IMF is northward as a theta-aurora during changes in the east-west compo-nent of IMF［11］. Other quantities like field-aligned current also show the same behavioras SC. State transitions in a magnetosphere-ionosphere system with a multidimensionaldegree of freedom could cause catastrophicvariations, because the coupling betweenphysical processes fails to keep MHD self-consistent. With the onset of a substorm gen-erated as southward turn of IMF, the failure ofMHD will appear as a reconnection of themagnetic lines of force, thereby demonstratingdiscontinuous state transitions［12］. Suchreconnection causes a high-speed plasma flowto appear in a region of the magnetospheredominated by inertia current. Therefore, thecoupling between the magnetosphere andionosphere convections is lost at this time. Inthe expansion phase following the onset, thecoupling between the magnetosphere and

ionosphere convections recovers as in the MIperiod of SC［13］.

Since the magnetosphere-ionosphere sys-tem described above constitutes a compoundsystem, any one of the self-consistent physicalelements (e.g., current system, plasma distrib-ution, convection or magnetic arrangement)can be taken and discussed out of context.Among these physical elements, the magne-tosphere convection will help promote under-standing of the magnetosphere as a wholebecause it has a direct bearing on behavior ofthe field lines and generation of plasma pres-sure. In other words, “state transitions” mightbe comprehended as “convection transitions”.SC, theta-auroras, and substorms can beunderstood by examining the physical ele-ments derived relative to stationary convectionsystems before and after state transitions, aswell as the transient convection system duringthe transition period.

If the magnetosphere-ionosphere system isregarded as a compound system as discussedabove, one might realize that the meteorologi-cal system constitutes a compound system aswell. A comparison of the two compound sys-tems is interesting. The elements comprisingthe meteorological compound system are con-vection and pressure (temperature), namely,the difference in temperature between thepoles and the equator drives the convection.The convection of the meteorological com-pound system has three cell structures (pole,mid-latitude and equatorial zones), becausethe earth’s rotation prevents the difference intemperature between the poles and the equatorfrom being resolved by direct convectionbetween the two regions. This basic configura-tion corresponds to a single state of the mag-netosphere-ionosphere compound systemassociated with steady solar winds. From analternative perspective, the magnetosphere-ionosphere compound system can characteris-tically assume more states in association withsolar wind conditions than the meteorologicalcompound system. Hence, the state transitionsresulting from solar wind changes describedearlier do not occur in the meteorological

182 Journal of the National Institute of Information and Communications Technology Vol.56 Nos.1-4 2009

compound system. After all, the magnetos-phere-ionosphere compound system and mete-orological compound system differ in terms ofhierarchical structure as shown in Fig. 1. Morespecifically, in the hierarchical structure of themeteorological compound system, a three-cellglobal circulation system, with high and lowpressures, meandering jet streams, is set at topand other synoptic-scale phenomena in itssubstructure. In contrast, the magnetosphere-ionosphere compound system has such sub-structures as ULF waves and structures inher-ent in the stationary magnetosphere convec-tion system as synoptic-scale phenomena.Moreover, multiple states of the compoundsystem associated with various solar windconditions exist as its superstructure. As aresult, compound system state transitionsoccur under varying solar wind conditions.

3 Possibilities and problems ofreal-time simulations

Real-time MHD simulations have beenconducted at the National Institute of Informa-tion and Communications Technology sinceDecember 22, 2003. The world’s first revolu-tionary project in this area uses ACE data asthe initial values of MHD simulations from

moment to moment, and predicts the behaviorof the magnetosphere-ionosphere with a leadtime of about one hour［5］. This project ismeaningful in that it has made MHD simula-tions a practical tool for space weather predic-tion. While numerical models are being rundaily for meteorological weather predictionpurposes, the resultant data is time-series dataon meteorological elements at the grid pointsin a three-dimensional atmosphere. This datarepresents a self-consistent solution to a set ofequations in atmospheric physics, as well as arepository of information not available from amere observational approach that presentsambient conditions consistent with the laws ofphysics.

Such numerical model products (called“objective analysis data” in terms of meteorol-ogy) are publicized by the Japan Meteorologi-cal Agency to researchers. (Past data is updat-ed on the latest numerical models andreleased.) Real-time simulations for spaceweather create precise objective analysis dataon the magnetosphere. It is most important touncover information hidden in the objectiveanalysis data and develop it at a higher levelof refinement to discover something new (datamining). Objective analysis data surveys entailcomparing measured AE index values withcalculated values［14］, comparing observationempirical models on potential distributions ofpolar electric fields with their calculatedvalues［15］, and estimating electron tempera-ture on satellites orbiting in a geostationaryorbit［16］. (This survey implements the guid-ance technique described later.) Such analyti-cal studies should be promoted to discovernew magnetosphere-ionosphere phenomenaand enhance numerical models.

From a practical viewpoint of spaceweather prediction as well as research, it isessential to investigate the relationshipbetween observed values with magnetosphereobjective analysis data as a result of MHDsimulations, by comparing both sets of data, asin correlated analyses. The concept is to iden-tify tendencies in the numerical models as apreparatory step to their practical implementa-

Fig.1 Hierarchical structures of the mag-netosphere-ionosphere compoundsystem and the meteorologicalcompound systemThe magnetosphere-ionosphere compound sys-tem has a number of states according to solarwind conditions under which transitions occur,while the meteorological compound system onlyhas one state.

183FUJITA Shigeru

tion in the guidance scheme discussed later.Real-time simulations in operation involve

certain problems that must be addressed inorder to produce a realistic reproduction ofphenomena as follows:• Upper and lower limits are set for the solar

wind parameters to eliminate extreme solarwind conditions from the scope of calcula-tions for ensuring simulation stability. Incomparing the observed data and calculationresults, it is therefore necessary to ensurethat the solar wind parameters are confinedwithin those limits［5］. Considering the factthat the phenomena of interest are apt tooccur under extreme solar wind conditions,a new real-time simulation code capable ofrunning with added stability needs to bedeveloped.

• No inclination of the magnetic axis is imple-mented. The code must therefore beimproved to allow the magnetic axis toincorporate the effects of inclination fromthe ecliptic plane and meridian plane. Thecode addresses inclination of the magneticaxis on the meridian plane, but such inclina-tion is not factored into the working calcula-tion process. This improvement is essentialto allow for coupling between the thermos-phere-ionosphere model and the magnetos-phere model being developed, because thethermosphere-ionosphere model is con-cerned with daily and seasonal changes.

• Since reflection of the field-aligned currentincident on the ionosphere is not correctlyrepresented, the ionosphere’s electric fieldtends to have a somewhat larger value[Nakata and Yoshikawa, 2009, private com-munication].

• As the propagation of Alfven waves alongthe magnetic field lines is not preciselyreproducible, a spatial dissipation of Alfvenwaves appears during their propagationfrom the ionosphere to the magnetosphere.As for phenomena in which waves play animportant role, comparisons with simulationresults should deserve special notice.

These problems need be resolved to makemagnetosphere objective analysis data more

realistic. The phenomena using MHD simula-tions are limited to those that can be describedin the MHD approximation. This should bekept in mind when comparing the physicalquantities observed on a satellite with theMHD simulation results.

4 Data assimilation - its presentand recommended practice

For numerical models used for Earth Sci-ence, such as the magnetosphere model,atmospheric global circulation models (meteo-rological), and ocean circulation models onceboundary conditions and parameters involvedin the physical laws (e.g., coefficient of vis-cosity, ionospheric conductivity) are assigned,along with initial conditions, the numericalmodel which solves the laws of physics repro-duces the realistic state. Practical numericalmodels, such as those for weather prediction,must use optimal values of such external para-meters, in addition to treating the physicallaws properly. Performing data assimilationhelps achieve these goals.

The data assimilation technique will essen-tially be of no practical value, unless thenumerical model is guaranteed to fully repro-duce the phenomena. From this viewpoint, themagnetosphere MHD model is not yet readyfor full-scale data assimilation aimed at pre-diction, because we do not know the accuracyof the model. It would therefore be meaning-less to apply an advanced data assimilationtechnique called “4-dimensional variationaldata assimilation” to the magnetosphericmodel［17］［18］, whereby observed values areassimilated with the uncertainties of initialvalues from moment to moment to minimizeprediction errors, as practiced in weather pre-diction tasks. Technically, using a data assimi-lation technique should require the iterativerunning of a numerical model. Because avail-able computer capabilities are inadequate forrunning iterative calculations of our magnetos-phere MHD model, the advanced data assimi-lation techniques will not work.

However, if we try to determine relevant

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parameter values by using a data assimilationtechnique to build a numerical model repro-ducing observed values with better accuracy,the data assimilation technique would not bemeaningless (since the validity of results is tobe reviewed separately). The data assimilationtechnique is mentioned in this paper for thepurpose of introducing physical quantities thatmay be subject to data assimilation on themagnetosphere MHD model. We must confessthat much remains to be developed in order toachieve practical use of the data assimilationtechnique.

This paper tries to estimate the optimalvalue of the ionospheric conductivity parame-ter as an example of typical data assimilationon the magnetosphere model. As the MHDmodel generates an ionosphere electric field,an ionosphere current can be obtained fromconductivity and thus ground magnetic fieldchanges can be calculated. Because continu-ous data of the ground magnetic field at multi-ple points are readily available, the observa-tions and numerical model can be easily com-pared in terms of ground magnetic fieldchanges. The current numerical model makesno allowance for inclination of the earth’saxis, and since the location of each geomag-netic observatory and its position in the simu-lation do not agree, there is no way of compar-ing the values observed at each observatorywith the numerical model values. Rather, theAE index that handles information in all longi-tudinal directions by 60 to 70 degrees latitudeas a whole may provide more useful data forassimilation with the simulation.

Because the AE index (estimated by simu-lation) reproduces its observed value withsome degree of accuracy for the data assimila-tion technique, both values are compared. Itshould be noted, however, that the position atwhich solar wind data is imported into thenumerical model shifts from the actual ACEsatellite location to a location near the earth inimplementing numerical simulations; there-fore, a time difference equivalent to this dis-tance exists. The estimated value of the AEindex is thus shifted in the time direction to

estimate the time that maximizes the correla-tion coefficient with the observed value of theAE index. When we use the data collectedduring the ten hours from 0900 hours to 1900hours on July 14, 2006, we find that both theobserved AE index and the AE index estimat-ed by simulation have a high correlation factorof 0.879, provided that the latter is delayed by62 minutes. For now, the data assimilationtechnique for this period will be used to deter-mine ionospheric conductivity.

Detailed procedures for data assimilationcalculations are described below. With themagnetosphere model, the height-integratedconductivity tensors (Σθθ,Σϕϕ,Σθϕ) are definedin relational expressions as:

（1）

（2）

（3）

In these equations, I denotes inclination, andσ0, σ1 andσ2 represent the field-aligned con-ductivity, Pedersen conductivity and Hall con-ductivity, respectively.σ1 andσ2 vary depend-ing on the solar radiation and energy incidentfrom the magnetosphere. According to［19］,such changes are expressed as:

（4）

（5）

a1(ρ, p, T, v,φ), a2(J,φ), a1H(T) and a2H denotethe functions of density (ρ), pressure ( p),temperature (T), current (J), and velocity (v)on the magnetosphere internal boundary,respectively. All are normalized. f (λ) is afunction of cosine (λ) of the solar zenith angle(ϕ).

185FUJITA Shigeru

（6）

（7）

（8）

（9）

Jz in Equation (7) is a vertical component ofcurrent. Once all these preparatory steps arecomplete, the optimal values of (σ0,σoval,σcurr,σsun) are determined by using the data assimi-lation technique. The nudging method of thedata assimilation technique is used to find theset of (σ0,σoval,σcurr,σsun) that minimizes errorbetween the observed value (AEobs) and calcu-lated value (AEcal), starting from an appropri-ate initial value.

（10）

H is called an error function. For now, the fol-lowing equation

（11）

is numerically calculated to determine thedirection in which minimal error function Hexists. Then the optimal value of connectivityis determined by varying the values of (σ0,σoval,σcurr,σsun) in that direction. While fourkinds of AE indices are available (AE, AO,AU and AL), only AE has been chosen as thetarget of data assimilation.

Figure 2 shows the observed values of theAE and AO indices collected for the 10-hourperiod from 0900 hours to 1900 hours on July14, 2006. Figure 3 shows the values of the AEand AO indices estimated by simulation

before the start of data assimilation. (Whilethe AO index is also found in the diagram, it isunfit for data assimilation.) Starting from thestate shown in Fig. 3, the values of (σ0,σoval,σcurr,σsun) are sequentially varied in suchdirection to diminish the error function in themethod described above. Table 1 lists thesteps and values in this process. Figure 4shows the value of the AE index calculatedusing the value of ionospheric conductivityreached after five iterative runs of data assimi-lation. When comparing Fig. 3 and 4, we cansee that the absolute value of the AE index hasneared the observed value (in Fig. 2). Figures 5and 6 show the distributions of Σθθ in effectbefore and after the data assimilation process.The conductivity is found higher in the day-

Fig.2 AE and AO indices (observed val-ues) collected from 0900 hours to1900 hours on July 14, 2006

Fig.3 AE and AO indices calculatedusing ionospheric conductivity ineffect before data assimilationfrom 09:00 to 19:00, July 14, 2006

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time after data assimilation, and is lower in theaurora zone. The value of conductivity derivedhere should depend on the kind of eventadopted. Analyses must further proceed todetermine and average the values of ionos-pheric conductivity that reproduce changes inthe AE index optimally through data assimila-tion using multiple events. If the results arefound to vary significantly, enhancement ofthe numerical model may take precedenceover using data assimilation results to deter-mine an optimal value of ionospheric conduc-tivity. This paper simply introduces an attemptat data assimilation and leaves further analy-ses open as future tasks.

Here, it should be noted that the optimalconductivity value determined by the dataassimilation technique and the actual value do

(in mho) Changes in the factor and error function (H) used to determine step ionospheric conductivity

Table 1 Optimal values of ionospheric conductivity determined using the nudging method

Fig.6 Distributions of ionospheric conduc-tivity (Σθθ) in effect after dataassimilation(in mho) 19:00, July 14, 2006

Fig.5 Distributions of ionospheric conduc-tivity (Σθθ) in effect before dataassimilation(in mho) 19:00, July 14, 2006

Fig.4 AE and AO indices calculatedusing ionospheric conductivity ineffect after data assimilation from 09:00 to 19:00, July 14, 2006

187FUJITA Shigeru

not necessarily agree. This is because thenumerical model does not encompass all phys-ical processes at work, and the mesh intervalsused on the numerical model remain inade-quate for producing a realistic reproduction ofphenomena. In particular, changing the meshsizes would in turn change the optimal valuederived from data assimilation. Thus, the con-ductivity determined by using the data assimi-lation technique might be deemed an artificialvalue intended to reproduce the AE index onthe numerical model in an optimal manner. Inother words, if the observed value of ionos-pheric conductivity is loaded into the currentnumerical model in its present form, whetherthe AE index and ground magnetic fieldchanges are correctly reproducible will beunknown.

5 Numerical model limitationsand implementation of a guid-ance scheme

It is truly important to further develop thenumerical model at a higher level of refine-ment in order to compensate for its undis-putable deficiencies, but there is a techniquethat leverages the capabilities of the existingincompetent numerical model to draw benefi-cial information. It is known that the numeri-cal model used for weather prediction purpos-es does not necessarily deliver appropriateforecasts concerning ground meteorologicalconditions, such as ground surface tempera-ture. In this context, guidance is available forexamining the relationships between otherphysical quantities obtained on the numericalmodel and actually observed values to comeup with predictions in a regressive manner.Regarding space weather, the ring currentintensity and total quantity of radiation beltparticles are essentially not available from theMHD model; however, by accumulating suffi-cient MHD simulation data to allow a compar-ison with actual measurements, predictioncould be made possible by probing into thecorrelations between the quantity of MHD at agiven point and the quantity of radiation belt

particles. The electron temperature on a geo-stationary satellite orbit has been estimatedfrom the pressure derived by real-time magne-tosphere MHD simulations［16］. The pressurederived by MHD simulations is essentiallythat of ions, not electrons. Therefore, thisattempt can be considered an implementationof the guidance scheme.

The method explained above seeks to dothe same as the attempt made to determineionospheric electron density on a neural net byusing solar wind data and the K-index［20］,except that it uses data from a numericalmodel. Regression analyses can be conductedby using multiple regressions, Kalman filters,etc. in addition to the simple least squaremethod. For a more detailed description of theprocedures, refer to “Discussions of WeatherPrediction Guidance”［21］.

Guidance-based weather prediction is aworkaround and not a legitimate way of scien-tific research, because it involves vastamounts of time and cost in developing rele-vant technologies under the constraints ofincomplete available techniques. The properpath to follow should be augmenting the phe-nomenon reproducibility of numerical modelspursuant to the laws of physics.

6 Future challenges

To improve the magnetosphere numericalmodel, it is important to make a detailed checkon real-time simulation results as producedfrom day to day in order to determine theextent to which the results match observations.As a matter of fact, meteorologists at theJapan Meteorological Agency and district/local meteorological observatories have madeday-to-day comparisons of data obtained fromthe meteorological model with actual mea-surements, feeding back the results to refur-bish the numerical model as we see it today.The comparative data collected thus farincludes comparisons with the AE index［14］,polar ionosphere potential［15］, and geostation-ary satellite data［16］. Such data will proveuseful in many ways, including quantitative

188 Journal of the National Institute of Information and Communications Technology Vol.56 Nos.1-4 2009

comparisons with polar ionosphere observa-tion (such as Super DARN) and comparisonsof the times when substorms occur with themodel and actual observations.

The numerical model also has much roomfor further improvement. In addition to allow-ing for inclination of the magnetic axis asmentioned earlier, the following areas ofenhancement are important:• Ionospheric boundary conditions require

further improvement. The higher the ionos-pheric conductivity, the greater the currentflow, thus providing an inappropriate solu-tion under those conditions in case Alfvenconductance of the magnetosphere fallsbelow ionospheric conductivity.

• Two-way connectivity between the magne-tosphere and thermosphere-ionosphere isalso needed. This requirement might haveless significance to the magnetosphere thanthat mentioned above, but the numericalmodel representation of thermosphericeffects in the magnetosphere is meaningfulin geophysical research.

• While solar wind input data is derived fromACE satellite observations, not all observeddata is put to use; in fact, the Bx component(solar-terrestrial direction) of the solar windmagnetic field, and the Vy and Vz compo-nents (east-west and south-north directions,respectively) of solar wind velocity are dis-regarded. Improvements are needed toaccommodate such disregarded factors asinput values to ensure the correct repro-ducibility of magnetospheric variationsresulting from solar wind changes.

• It is important to factor in the behavior ofhigh-energy particles that comprise the ringcurrent into the numerical model, in order toreproduce magnetic storms. Consequently, itis necessary to combine the MHD modeland ring current model. This has alreadybeen implemented in the U.S., but a full-scale coupling model should be worthwhilein Japan as well. The MHD model must besufficiently robust to handle magneticstorms as the object of calculation. This canbe implemented by taking such actions as

varying the mesh geometry or narrowing thetime steps to the extent possible.

• The meteorological numerical modelinvolves a micro process known as the pre-cipitation process. This process is micro-scopic and factored into the numericalmodel as a set of parameters, and also sig-nificant enough to determine not only thegeneration and extinction of clouds, but alsothe behavior of atmospheric global circula-tion as a whole. The magnetosphere modelshould also benefit from more precise han-dling of the magnetic reconnections includ-ed in substorms. Boosting the accuracy ofpredicting the occurrence of substormsshould require the use of more advancedreconnection parameters or coupling withparticle simulations.

7 Conclusions

This paper has discussed the impact thatthe magnetosphere-ionosphere coupling MHDmodel has had on magnetospheric physics as anumerical model. The paper also reviewedwhat kinds of technological developments areneeded to implement a real-time simulationapproach to space weather prediction. Princi-pal findings are summarized as follows:• MHD simulations of the magnetosphere-

ionosphere handled in a self-consistent man-ner have proposed a new concept called the“magnetosphere-ionosphere compound sys-tem”. Magnetospheric phenomena associat-ed with solar wind changes can be explainedin terms of state transitions of the compoundsystem.

• An attempt to estimate ionospheric conduc-tivity by using the data assimilation tech-nique with the AE index has been intro-duced. This method, however, has yet toreach a state of practical usefulness due toincompleteness of the numerical model andthe vast amount of time it takes to performassimilation calculations, but shouldbecome an integral part of future spaceweather prediction.

• The paper also introduced that those physi-

189FUJITA Shigeru

cal quantities that are not reproducible byrunning MHD simulations can be estimatedusing a scheme of guidance. A detailedanalysis of real-time simulation results and athorough probing of the relationshipsbetween calculated and predicted values arerequired to implement such MHD simula-tions.

Acknowledgements

The author is deeply indebted to ProfessorNakamura of Osaka Prefecture University for

his advice on preparing this paper. Thisresearch was conducted with the aid of a com-puter system installed at the National Instituteof Information and Communications Technol-ogy, and by utilizing the mass storage on One-SpaceNet. Some calculations were made usinga computer system installed at the NationalInstitute for Fusion Science. This research wasadministered as part of a joint computer usageresearch project (“Research on Global Behav-ior of the Magnetosphere-Ionosphere Sys-tem”) at the Solar-Terrestrial EnvironmentLaboratory of Nagoya University.

References01 J. Lyon, S. H. Brecht, J. A. Fedder, and P. Palmadesso, “The effects on the earth’s magnetotail from

shocks in the solar wind,” Geophys. Res. Lett., Vol. 7, 721–724, 1980.

02 T. Ogino, “A three-dimensional MHD simulation of the interaction of the solar wind with the Earth’s mag-

netosphere: The generation of field-aligned currents,” J. Geophys. Res., Vol. 91, 6791–6806, 1986.

03 J. A. Fedder, and J. G. Lyon, “The Earth’s magnetosphere is 165Re long: Self-consistent currents, con-

vection, magnetospheric structure, and process for northward interplanetary magnetic field,” J. Geophys.

Res., Vol. 100, 3623–3635, 1995.

04 T. Tanaka, “Generation mechanisms for magnetosphere - ionosphere current systems deduced from a

three-dimensional MHD simulation of the solar wind-magnetosphere-ionosphere coupling processes,”

J. Geophys. Res., Vol. 100, 12057–12074, 1995.

05 M. Den, T. Tanaka, S. Fujita, T. Obara, H. Shimazu, H. Amo, Y. Hayashi, E. Nakano, Y. Seo, K. Suehiro,

H. Takahara, and T. Takei, “Real-time Earth magnetosphere simulator with three-dimensional magneto-

hydrodynamic code,” Space Weather, Vol. 4, S06004, doi: 10.1029/2004SW000100, 2006.

06 K. Iijima and T. Potemra, “The amplitude distribution of field-aligned currents at northern high latitudes

observed by Triad,” J. Geophys. Res., Vol. 81, 2165–2174, 1976.

07 T. Tanaka, “Formation of magnetospheric plasma population regimes coupled with the dynamo process

in the convection system,” J. Geophys. Res., Vol. 108 No. A8, 1315, doi: 10.1029/2002JA009668, 2003.

08 T. Tanaka, “Magnetosphere-Ionosphere Convection as a Compound System,” Space Sci Rev, DOI

10.1007/s11214-007-9168-4, 2007.

09 S. Fujita, T. Tanaka, and T. Motoba, “A numerical simulation of the geomagnetic sudden commence-

ment: 3. A sudden commencement in the magnetosphere-ionosphere compound system,” J. Geophys.

Res., Vol. 110, A11203, doi: 10.1029/2005JA011055, 2005.

10 T. Araki, “A physical model of the geomagnetic sudden commencement. in Solar Wind Sources of Mag-

netospheric Ultra-Low-Frequency Waves,” ed. by M. J. Engebretson, K. Takahashi, and M. Scholer,

American Geophysical Union, Washington, D.C., 183–200, 1994.

11 T. Tanaka, T. Obara, and M. Kunitake, “Formation of the theta aurora by a transient convection during

northward interplanetary magnetic field,” J. Geophys. Res., Vol. 109, A09201, doi: 10.1029/2003JA010271,

2004.

12 T. Tanaka,” The state transition model of the substorm onset,” J. Geophys. Res., Vol. 105, 21081–21096, 2000.

190 Journal of the National Institute of Information and Communications Technology Vol.56 Nos.1-4 2009

13 T. Tanaka, A. Nakamizo, A. Yoshikawa, S. Fujita, H. Shinagawa, H. Shimazu, T. Kikuchi, and K. K. Hashimoto,

“Substorm convection and current system deduced from the global simulation,” J. Geophys. Res., Vol.

115, A05220, doi: 10.1029/2009JA014676, 2010.

14 K. Kitamura, H. Shimazu, S. Fujita, S. Watari, M. Kunitake, H. Shinagawa, and T. Tanaka, “Properties of

AE indices derived from real-time global simulation and their implications for solar wind-magnetosphere

coupling,” J. Geophys. Res., Vol. 113, A03S10, doi: 10.1029/2007JA012514, 2008.

15 M. Kunitake, S. Watari, H. Shinagawa, H. Shimazu, T. Nagatsuma, T. Hori, S. Fujita, and T. Tanaka,

“Application of the magnetospheric model for numerical forecast —Validation using the cross polar cap

potential—,” Special issue of this NICT Journal, 2-2-4, 2009.

16 M. Nakamura, “Prediction of the plasma environment in the geostationary orbit using the magnetos-

phere simulation,” Special issue of this NICT Journal, 2-2-3, 2009.

17 O. Talagrand and P. Courtier, “Variational assimilation of meteorological observations with the adjoint

vorticity equation. I: Theory,” Q. J. R. Meteorol. Soc., Vol. 113, 1311–1328, 1987.

18 P. Courtier and O. Talagrand, “Variational assimilation of meteorological observations with the adjoint

vorticity equation. II: Numerical result,” Q. J. R. Meteorol. Soc., Vol. 113, 1329–1347, 1987.

19 R. M. Robinson, R. R. Vondrak, K. Miller, T. Dabbs, and D. Hardy, “On Calculating Ionospheric Conduc-

tances from the Flux and Energy of Precipitating Electrons,” J. Geophys. Res., Vol. 92, No. A3,

2565–2569, 1987.

20 M. Nakamura, T. Maruyama, and Y. Shidama, “Using a neural network to make operational forecasts of

ionospheric variations and storms at Kokubunji, Japan,” Earth, Planets and Space, Vol. 59, 1231–1239,

2007.

21 Forecast Division, “Manual of the weather forecast guidance,” Bulletin of the forecast technique, Vol. 41,

Japan Meteorological Agency, 1991.

FUJITA Shigeru, Dr. Sci.

Associate Professor, MeteorologicalCollege

Physics of the magnetosphere-ionosphere system