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A new atmospheric neutrino oscillation tool which utilizes full threeneutrino oscillation probabilities and a full three neutrino treatment of theMSW effect is combined with a standard analysis of the K2K, MINOS, and CHOOZdata to examine the bounds on $\theta_{13}$ implied by existing data, includingthe recent, more finely binned, Super-K atmospheric data. In the region$L/E_\nu\gtrsim 10^4$ km/GeV, we have previously found that the sub-dominantexpansion does not converge and that terms linear in $\theta_{13}$ can besignificant. The current analysis confirms this and leads to the conclusionthat $\theta_{13}$ is bounded from above by the atmospheric data while CHOOZprovides the lower bound. We trace the origin of this result to fully containeddata in the previously mentioned very long baseline region, to a combination ofa quadratic in $\theta_{13}$ term in ${\mathcal P}_{ee}$ and a linear term in${\mathcal P}_{e\mu}$ and their contribution to $R_e$, a broad MSW resonancefor the solar mass-squared difference at 180 MeV, and an increase in$\theta_{12}$ due to this resonant matter effect which alters the sign of thelinear in $\theta_{13}$ term. Assuming CP is conserved in the lepton sector, wefind $\theta_{13}=-0.07^{+0.18}_{-0.11}$, the asymmetry being a reflection ofthe importance of the linear in $\theta_{13}$ terms.

Atmospheric, long baseline, and reactor neutrino data constraints on $\theta_{13}$