## Method of Calculation of the Convective Seasonal and Yearly Genesis Parameter

Given that the formulation of the Seasonal and Yearly Genesis Parameter (resp. SGP and YGP) of Gray (1968, 1975) is not appropriate for climate change purposes, as indicated in the introduction, Royer et al. (1998) suggested to replace all the thermal contributions by a new thermal potential which can be represented by convective precipitation. This diagnostic is indeed a good integration of the three components of the Gray's YGP thermal potential. It combines the stability of the atmosphere, the humidity of the low levels and SST anomalies, since evaporation is a major contribution to convection. This new formulation of the YGP is able to diagnose the thermal potential with the model components and avoids the dependence to a fixed 26°C SST threshold that the old formulation induced. The dynamical potential is defined as the product of three factors:

• f = 2O sin j is the Coriolis parameter, j is the latitude and O the angular velocity of the Earth, in 10"5 s"1.

• If = (Zr f/ifi) + 5 where Zr is the low level relative vorticity at 950 hPa, in 10-6 s-1.

• IS = (i8V/8Pi + 3)-1 is the inverse of the vertical shear of the horizontal wind (V)

between the pressure (P) levels 950 hPa and 200 hPa, in ms-1/750 hPa.

In CYGP the thermal potential is based on the convective precipitation diagnosed by the models. In order to avoid cyclogenesis being diagnosed over regions of shallow convection, a threshold (PT) has been introduced in the formulation of the thermal potential, i.e. if convective precipitations are less than this amount, the convective potential is set to 0. The choice of the threshold has been made subjectively, in such a way that the spatial repartition of the YGP computed from the ERA40 reanalysis corresponds fairly to global observations. A basic threshold of 3 mm day-1 was fixed for ERA40. Without taking into account the 3 mm day-1 threshold, some near mid-latitude cyclogenesis was artificially diagnosed while the conditions are generally not favorable over these regions. Actually, since ERA40 diagnoses total precipitation, this threshold is useful to remove the areas of weaker non-convective precipitation.

Since the total convective precipitation varies from model to model depending on the convective precipitation scheme, we have attempted to remove this variation by making the convective precipitation threshold (PT) model dependent and proportional to the total oceanic convective precipitation simulated by each model between the latitudes 35°S and 35°N.

Furthermore, in order to make sure that the global count of genesis for the present climate is the same for all the models, a calibration factor p is made model-dependent and chosen so that global TCs computed for the period 1960-99 is the same for all the models and equals 84 TCs per year (as observed, cf. Tsutsui and Kasahara 1996). Using this calibration is a useful feature for normalizing model results for intercomparison, as it avoids that the total level of computed TC genesis be too much dependent on model resolution or specific parameterizations. However this also puts a limitation on the usefulness of the CYGP as a diagnostic tool of model quality. It should be remembered later on that comparisons over a specific area between models are not absolute but only relative to the model global distribution of diagnosed cyclogenesis. In particular, a model tendency to overestimate cyclogenesis over a particular area will be compensated by an underestimate over the other areas to satisfy the constraint put on the total.

The thermal convective potential at each grid-point (i,j), is thus defined as follows:

where k represents the model, PRij(k) the convective precipitation and PT(k) the convective threshold for the model k, and p (k) the calibrating factor.

The TC seasonal genesis potential is then computed for each season as the product of the dynamical potential and the convective potential, and the CYGP is computed as the sum of the seasonal potential over the 4 seasons. 