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We present an analysis of the distribution of H-alpha emission measures forthe warm ionized medium (WIM) of the Galaxy using data from the WisconsinH-Alpha Mapper (WHAM) Northern Sky Survey. Our sample is restricted to Galacticlatitudes |b| > 10. We removed sightlines intersecting nineteen high-latititudeclassical H II regions, leaving only sightlines that sample the diffuse WIM.The distribution of EM sin |b| for the full sample is poorly characterized by asingle normal distribution, but is extraordinarily well fit by a lognormaldistribution, with <log EM sin |b|> = 0.146 +/- 0.001 and standard deviation0.190 +/- 0.001. <log EM sin |b|> drops from 0.260 +/- 0.002 at Galacticlatitude 10<|b|<30 to 0.038 +/- 0.002 at Galactic latitude 60<|b|<90. Thedistribution may widen slightly at low Galactic latitude. We compare theobserved EM distribution function to the predictions of three-dimensionalmagnetohydrodynamic simulations of isothermal turbulence within anon-stratified interstellar medium. We find that the distribution of EM sin |b|is well described by models of mildy supersonic turbulence with a sonic Machnumber of ~1.4-2.4. The distribution is weakly sensitive to the magnetic fieldstrength. The model also successfully predicts the distribution of dispersionmeasures of pulsars and H-alpha line profiles. In the best fitting model, theturbulent WIM occupies a vertical path length of 400-500 pc within the 1.0-1.8kpc scale height of the layer. The WIM gas has a lognormal distribution ofdensities with a most probable electron density n_{pk} = 0.03 cm^{-3}. We alsodiscuss the implications of these results for interpreting the filling factor,the power requirement, and the magnetic field of the WIM.

The Turbulent Warm Ionized Medium: Emission Measure Distribution and MHD Simulations