## Spatial Evaluation of the Temperature Gradient of Evaporation

In order to use the previous analysis to diagnose regions of likely tropical cyclone development, it is necessary to evaluate the gradient, d ln E/dT spatially. This is accomplished by evaluating the gradient of ln E with respect to T, and also the gradient of T with respect to ln E along each direction, and then averaging each over all orientations to obtain the norm, dlnE/dT =±(< dlnE/dT >/<dT/dlnE>)1/2

where < > denotes the integral around the circle. This yields the expression, dlnE/dT = ± { [(@lnE/@x)2+(@lnE/dy)2]/ [(@T/@x)2+(@T/@y)2] }1/2 (5b)

in which d lnE/dT is positive if 3lnE/3x 3T/3x + 3lnE/3y 3T/3y > 0, and is negative if 3lnE/3x 3T/3x + 3lnE/3y 3T/3y < 0, and ox and oy are respectively towards the east and the north. This expression takes account of the full generality of the fields of lnE and T. On substituting (5b) in (4) we can evaluate,

using the expression H = d lnE/ dT — eL/(RT2). The scalar quantity, H, which we will call the hurricane index is a practical index for potential TC development, as is evident from Figs. 1 and 2, which show that the zonal mean annual value of H is negative in the regions of TC development, equatorward of the maximum in lnE, which occurs at T ^26°C. 