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AB STRACTAs the sigma-p co or di nate un der hy dro static ap prox i ma tion can be in ter preted as the mass co or di nate with out the hy dro static ap prox i ma tion, we pro pose a method that up grades a hy dro static model to a nonhydrostatic model with rel a tively less ef fort. The method adds to the prim i tive equa tions the ex tra terms omit ted by the hy dro static ap prox i ma tion and two prog nos tic equa tions for ver ti cal speed w and nonhydrostatic part pres sure p'. With prop erly for mu lated gov ern ing equa tions, at each time step, the dy namic part of the model is first in te grated as that for the orig i nal hy dro static model and then nonhydrostatic con tri bu tions are added as cor rec tions to the hy dro static so lu tions. In ap ply ing phys i cal parameterizations af ter the dy namic part in te gra tion, all phys ics pack ages of the orig i nal hy dro static model can be di rectly used in the nonhydrostatic model, since the up graded nonhydrostatic model shares the same ver ti cal co or di nates with the orig i nal hy dro static model. In this way, the ma jor ity codes of the nonhydrostatic model come from the orig i nal hy dro static model. The ex tra codes are only needed for the cal cu la tion ad di tional to the prim i tive equa tions. In or der to han dle sound waves, we use smaller time steps in the nonhydrostatic part dy namic time in te gra tion with a split-ex plicit scheme for hor i zon tal mo men tum and tem per a ture and a semi-im plicit scheme for w and p'. Sim u la tions of 2-di men sional moun tain waves and den sity flows as so ci ated with a cold bub ble have been used to test the method. The ide al ized case tests dem on strate that the pro posed method re al is ti cally sim u lates the nonhydrostatic ef fects on dif fer ent at mo spheric cir cu la tions that are re vealed in the o ret i cal so lu tions and simulations from other nonhydrostatic models. This method can be used in upgrading any global or mesoscale models from a hydrostatic to nonhydrostatic model. Sci., 20, 727-739, doi: 10.3319/TAO.2008.09.24.01(A) IN TRO DUC TIONThe prim i tive equa tions used as gov ern ing equa tions in at mo spheric hy dro static mod els in clude hy dro static approximation that re places the ver ti cal mo men tum equa tion by the hy dro static bal ance equa tion. The ap prox i ma tion is very ac cu rate when ver ti cal ve loc ity, and hence ver ti cal acce leration, is very small. The hy dro static ap prox i ma tion not only sim pli fies the gov ern ing equa tions but also elim i nates sound waves from the so lu tion to avoid the ne ces sity in handling those fast mov ing waves in time in te gra tion. However, if one needs to sim u late at mo spheric cir cu la tion with strong ver ti cal mo tions, such as thun der storms or hur ricanes, a nonhydrostatic model may be de sired. In this pa per, we de scribe a method that ex tends a hy dro static model to a nonhydrostatic model by add ing the terms and equa tions neglected by the hy dro static ap prox i ma tion to the prim i...