4.3 Evaporation of convective precipitation

The CAM 3.0 employs a Sundqvist [169] style evaporation of the convective precipitation as it makes its way to the surface. This scheme relates the rate at which raindrops evaporate to the local large-scale subsaturation, and the rate at which convective rainwater is made available to the subsaturated model layer

$$E_{r_k} = K_E \; (1 - _k) \; {(\hat{R}_{r_k})}^{1/2} .$$ (4.103)

where RH$_k$ is the relative humidity at level $k$, $\hat{R}_{r_k}$ denotes the total rainwater flux at level $k$ (which can be different from the locally diagnosed rainwater flux from the convective parameterization, as will be shown below), the coefficient $K_E$ takes the value 0.2 $\cdot$ 10$^{-5}$ (kg m$^{-2}$ s$^{-1}$)$^{-1/2}$s$^{-1}$, and the variable $E_{r_k}$ has units of s$^{-1}$. The evaporation rate $E_{r_k}$ is used to determine a local change in $q_k$ and $T_k$, associated with an evaporative reduction of $\hat{R}_{r_k}$. Conceptually, the evaporation process is invoked after a vertical profile of $R_{r_k}$ has been evaluated. An evaporation rate is then computed for the uppermost level of the model for which $R_{r_k} \not= 0$ using (4.103), where in this case $R_{r_k} \equiv \; \hat{R}_{r_k}$. This rate is used to evaluate an evaporative reduction in $R_{r_k}$ which is then accumulated with the previously diagnosed rainwater flux in the layer below,

$$\hat{R}_{r_{k+1}} = \hat{R}_{r_k} - \left({{\Delta p_k} \over g}\right) \; E_{r_k} + R_{r_{k+1}} .$$ (4.104)

A local increase in the specific humidity $q_k$ and a local reduction of $T_k$ are also calculated in accordance with the net evaporation

$$q_k = q_k + E_{r_k} \; 2 \Delta t \; ,$$ (4.105)

and

$$T_k = T_k - \left( {L \over c_p} \right) E_{r_k} \; 2 \Delta t \; .$$ (4.106)

The procedure, (4.103)-(4.106), is then successively repeated for each model level in a downward direction where the final convective precipitation rate is that portion of the condensed rainwater in the column to survive the evaporation process

$$P_s = \left( \hat{R}_{r_{K}} - \left({{\Delta p_K} \over g}\right) \; E_{r_K} \right) /\rho_{H_{2}0} .$$ (4.107)

In global annually averaged terms, this evaporation procedure produces a very small reduction in the convective precipitation rate where the evaporated condensate acts to moisten the middle and lower troposphere.