You will be presented with the full text of a science research paper. Please write an abstract for this paper. Your response should include the abstract and no additional text.

Paper text:
the earth s magnetic field is generated by motions of an electrically conducting fluid in the outer core , the bulk being liquid iron .
the processes include magnetic induction and are subsumed under the term ` geodynamo ' .
it is generally accepted that the fluid motions in the outer core , which are most important for maintaining the geodynamo , are driven by convection , i.e. by thermal and compositional buoyancy forces @xcite .
there are in general three ways to study the dynamics of the outer core .
the first builds on theoretical considerations like force balances and thermodynamics ( e.g. * ? ? ?
secondly , it is possible to model the whole system numerically on the basis of the fundamental physical equations . finally , laboratory experiments analogue to the processes proposed for the earth s core can help to determine certain aspects of the dynamics . in this paper ,
we focus on the second approach .
+ an important part of the increase in knowledge about core dynamics in the last two decades came from numerical simulations of the dynamo process . starting from the first successful 3d mhd self - sustained dynamo models of @xcite and @xcite , numerical dynamo simulations have been able to reproduce various features of the geomagnetic field such as field morphology , secular variations and polarity reversals . the problem , however , remains how to apply results from numerical simulations to the earth .
+ a major challenge is the discrepancy between numerical models and the core in terms of the non - dimensional parameters defined in table [ tab : nondim_no ] .
specifically , numerical dynamos have far too slow rotation ( ekman number too large ) , are less turbulent ( rayleigh number too small ) and excessively viscous relative to their electrical conductivity ( magnetic prandtl number too large ) compared to the core .
this gap can not be bridged easily due to the enormous computational power required to resolve all relevant time and length scales .
+ one way of using present - day numerical dynamo simulations to estimate quantities that are relevant to earth s core ( e.g. heat flux , flow velocity , magnetic field strength ) is to extract scaling laws between these quantities and other characteristic parameters from the data . assuming that the relevant processes in the core are the same as in our simulations , we may extrapolate the results to the parameter regime of the core and in that way gain insight into the processes in earth s core .
+ this has been done for various quantities .
important results were the diffusivity - free scalings of heat transport , flow velocity and magnetic field strength @xcite and simple scalings for the magnetic dissipation time @xcite .
the question arises , however , how complex a model needs to be in order to do justice to the data .
+ we address the classical problem of model selection , where a model is defined in terms of a number of parameters . on the one hand ,
the paradigm of occam prefers a model that is less complex over another that is more complex ( when both fit the data equally well ) , generally meaning that the former model contains the fewest parameters of all models .
but what is often not recognised , and is equally important , is that models with fewer parameters can have greater predictive power than more complicated models .
physical theories are not only validated by their fit to existing data , but even more by their performance in predicting new data .
a few words are in order to motivate why this phenomenon is true . + we imagine a noisy dataset with @xmath0 points and fit it with @xmath1 parameters ; we begin by taking @xmath2 to achieve a perfect fit to our data . because of noise
, this model is extremely complex , containing high frequency oscillations ( in the case of a function @xmath3 fitted to points distributed in @xmath4 ) .
imagine now receiving a new datum .
the @xmath0 parameter model will have almost no predictive power for this new datum , since it has fitted all of the noise in the dataset from which it was derived .
indeed , a far simpler model , with @xmath5 will have far greater predictive power .
we use this principle by implementing a procedure called ` leave - one - out cross validation ' , where we systematically omit one of the data points and hold it in reserve as a test point , against which different models can test their predictive power . in this way we evaluate the predictive power of models , and find models based on an optimal number of parameters that have the most predictive power . +
the format of the paper is as follows : in section [ sec : dynamo_dataset ] , we present the database used in our analysis . in section
[ sec : cross_validation ] , we illustrate the method of cross - validation with a toy problem , before going on to apply it to the dynamo problem at hand .
subsequently , we analyse the scaling laws for heat transport , flow velocity and magnetic field strength using diffusivity - free parameters ( section [ sec : diff_free_scal ] ) and traditional non - dimensional numbers ( section [ sec : trad_scal ] ) . section [ sec : mag_dissipation_core ] is concerned with the scaling of magnetic dissipation time as well as the application of the scalings to the core .
in the numerical dynamo simulations used in this study , convection is driven by a fixed superadiabatic temperature contrast @xmath6 between inner and outer boundaries of a rotating spherical shell .
moreover the boussinesq approximation is used , i.e. density variations enter the equations only through a buoyancy term in the momentum equation .
the standard set of equations consists of five equations describing conservation of momentum ( navier - stokes equation ) , magnetic induction , the transport of temperature and the solenoidal nature of the magnetic field @xmath7 and the velocity field @xmath8 ( cf .
eq . [ eqn : ns_eq]-[eqn : solenoidal_u ] ) . + these equations can be non - dimensionalised by introducing four independent control parameters .
their choice is not unique .
we follow @xcite and use the shell thickness @xmath9 of the outer core , the inverse rotation rate @xmath10 , the temperature difference @xmath6 , and the quantity @xmath11 as fundamental scales for length , time , temperature and magnetic field , respectively ; @xmath12 is the outer core radius , @xmath13 the inner core radius , @xmath14 density and @xmath15 magnetic permeability .
this leads to the following set of non - dimensional equations for magnetic field @xmath7 , fluid velocity @xmath8 and temperature @xmath16 : @xmath17 @xmath18 @xmath19 @xmath20 @xmath21 where @xmath22 is the unit vector in the direction of the rotation axis . in these equations
, gravity is assumed to vary proportional to the radius , @xmath23 being the value of gravity at the outer boundary ; volumetric heating is neglected and @xmath24 is the non - hydrostatic pressure .
the four non - dimensional parameters governing equations [ eqn : ns_eq]-[eqn : solenoidal_u ] are defined in table [ tab : nondim_no ] .        only considering models that lie in the ` earth - like triangle ' for magnetic field morphology in figure [ fig : c116_rm_eketa_triangle ] ( criteria of
* ) , the dynamo dataset is reduced from 116 to 61 models .
table [ tab : earthlike_diffless_scalings ] shows the scaling laws that in this case are preferred by loocv under the assumption of equal errors in @xmath25 .
although the dataset is reduced by almost half , the resulting laws only differ in their exponents ( up to @xmath26 ) , but not in the parameters included ( cf .
table [ tab : diffless_scalings ] ) .
christensen , u.  r. & aubert , j. , 2006 .
scaling properties of convection - driven dynamos in rotating spherical shells and application to planetary magnetic fields , _ geophysical journal international _ , * 166*(1 ) , 97114 .
de  koker , n. , steinle - neumann , g. , & vlcek , v. , 2012 .
electrical resistivity and thermal conductivity of liquid fe alloys at high p and t , and heat flux in earth s core , _ p natl acad sci usa _ , * 109*(11 ) , 40704073 .
earth s magnetic field is generated by processes in the electrically conducting , liquid outer core , subsumed under the term ` geodynamo ' . in the last decades , great effort has been put into the numerical simulation of core dynamics following from the magnetohydrodynamic ( mhd ) equations . however , the numerical simulations are far from earth s core in terms of several control parameters . 
 different scaling analyses found simple scaling laws for quantities like heat transport , flow velocity , magnetic field strength and magnetic dissipation time . 
 + we use an extensive dataset of 116 numerical dynamo models compiled by christensen and co - workers to analyse these scalings from a rigorous model selection point of view . our method of choice is leave - one - out cross - validation which rates models according to their predictive abilities . 
 in contrast to earlier results , we find that diffusive processes are not negligible for the flow velocity and magnetic field strength in the numerical dynamos . 
 also the scaling of the magnetic dissipation time turns out to be more complex than previously suggested . assuming that the processes relevant in the numerical models are the same as in earth s core , we use this scaling to estimate an ohmic dissipation of 3 - 8  tw for the core . 
 this appears to be consistent with recent high cmb heat flux scenarios .    2