Lightning is observed to incept in thundercloud electric fields below the threshold value $E_k$ for discharge initiation. To explain this, the local enhancement of the electric field by hydrometeors is considered. The conditions for the onset of positive corona discharges are studied in air for ellipsoidal geometries. A hydrometeor is simulated as an individual charged conductor in zero ambient field; there is only a field generated by the charge on the hydrometeor surface. By doing so, the feasibility of corona inception from ellipsoidal hydrometeors can be formulated based on the self-sustaining condition of electron avalanches. For representative hydrometeor volumes and typical thundercloud pressure, values between $1.2\,E_k$ and $37\,E_k$ were found for the onset electric field at the tip of the ellipsoid. From simulations the required ambient electric field for corona onset from an uncharged hydrometeor can then be derived. This results in values between $0.07\,E_k$ and $0.8\,E_k$ for semi-axes aspect ratios between 0.01 and 1. The charge required on the hydrometeor surface for corona onset is minimum for semi-axes aspect ratios between 0.04 and 0.07 depending on the considered hydrometeor volume. For the simulated hydrometeors, the values of this onset charge for typical pressures are between 1500\,pC and 3200\,pC. Including a size-correction for comparison to in situ measurement shows agreement with measured precipitation charges. From the results it is concluded that corona onset from ellipsoidal hydrometeors of a realistic volume can be achieved in thundercloud conditions for certain aspect ratios.