Sensitivity of Offshore Surface Fluxes and Sea Breezes to the Spatial Distribution of Sea-Surface Temperature

Abstract

A series of numerical sensitivity experiments is performed to quantify the impact of sea-surface temperature (SST) distribution on offshore surface fluxes and simulated sea-breeze dynamics. The SST simulations of two mid-latitude sea-breeze events over coastal New England are performed using a spatially-uniform SST, as well as spatially-varying SST datasets of 32- and 1-km horizontal resolutions. Offshore surface heat and buoyancy fluxes vary in response to the SST distribution. Local sea-breeze circulations are relatively insensitive, with minimal differences in vertical structure and propagation speed among the experiments. The largest thermal perturbations are confined to the lowest 10% of the sea-breeze column due to the relatively high stability of the mid-Atlantic marine atmospheric boundary layer (ABL) suppressing vertical mixing, resulting in the depth of the marine layer remaining unchanged. Minimal impacts on the column-averaged virtual potential temperature and sea-breeze depth translates to small changes in sea-breeze propagation speed. This indicates that the use of datasets with a fine-scale SST may not produce more accurate sea-breeze simulations in highly stable marine ABL regimes, though may prove more beneficial in less stable sub-tropical environments.

Appendix

The MYNN surface-layer parametrization of the WRF model uses a bulk-flux algorithm based on the COARE 3.0 algorithm (Fairall et al. 2003) to compute the surface fluxes using a modification implemented by Dr. Joseph Olson. The COARE 3.0 algorithm relies on wind-speed dependent parametrizations of the aerodynamic roughness length

$$\begin{aligned} z_0 =0.11\frac{\nu }{u_*}+\alpha \left( U \right) \frac{u_*^2 }{g}, \end{aligned}$$

(8)

where $\nu$ is the kinematic velocity, $u_*$ is the friction velocity, and $\alpha \left( U \right)$ is the wind-speed dependent Charnock parameter. The wind speed U used in the current version of the MYNN parametrization is given by the value at the lowest grid point, $U_{a}$. Future versions of the code should change the wind speed used in Eq. 8 to the value adjusted to a height of 10 m. As with the COARE 3.0 algorithm, the current version of the MYNN parametrization adds a gustiness component to the mean wind speed computed under convective conditions, which accounts for the unsteady flow causing an appreciable flux in convective conditions not included in the mean wind speed because gusts average to zero (Godfrey and Beljaars 1991; Beljaars 1995). The parametrization is based on the convective velocity scale $w_{*}$, which requires model estimates of the buoyancy flux and the boundary-layer height. The same parametrization is now used over land and water, which removes the old parametrization that created unrealistic values over large air–sea temperature differences.

The first term on the left-hand-side parametrizes the roughness under smooth flow (i.e. light winds), while the second term represents the roughness of the wind waves supporting the surface stress. The roughness length is used to determine the drag coefficient $C_\mathrm{D}$, and thereby the friction velocity as

$$\begin{aligned} u_{*}\equiv \sqrt{\tau /\rho }\approx \sqrt{C_\mathrm{D}}\Delta U=\frac{\kappa }{\ln \left( {\frac{z}{z_{0}}}\right) -\psi _{m}\left( {\frac{z}{L}}\right) }\left[ {U_{a}-U\left( {z_{0}}\right) }\right] , \end{aligned}$$

(9)

where $\tau$ is the momentum flux at the surface or surface stress, $\kappa$ is the von Karman constant (set to 0.4), and z is the height of the lowest grid point. The surface stress should be estimated using a wind speed relative to water (Edson et al. 2013) in which case $U\left( {z_{0}}\right)$ represents the surface current. However, surface currents are not included here, so the friction velocity is computed using the wind speed relative to earth.

Fig. 16

Comparison of the Dyer and Hicks (1970) and COARE 3.0 parametrizations of the stability function for wind shear. Negative values of z / L denote unstable (convective) conditions and positive reflect stably stratified conditions

The function $\psi _{m}\left( {z/L}\right)$ accounts for modulation of the logarithmic wind-speed profile due to atmospheric stability, where L is the Obukhov length. The default parametrization of the stability functions is based on Dyer and Hicks (1970), which differs from the COARE 3.0 parametrization shown in Fig. 16, where the difference is most notable in very stable conditions. The current version in the MYNN parametrization places limits on the value of the Obukhov length as $-10<\,z{/}L\,<\,2$.

The roughness length and friction velocity are then solved iteratively. The thermal and moisture roughness lengths are parametrized as the same function of the roughness Reynolds number $\frac{z_{0}u_{*}}{\nu }$, i.e. $z_{t}=z_{q}=f\left( {\frac{z_{0}u_{*}}{\nu }}\right)$, which are used to calculate the transfer coefficients for heat and moisture for the computation of the sensible and latent heat fluxes in Eqs. 1 and 2, respectively, as

$$\begin{aligned} C_\mathrm{h}=C_{q}=\sqrt{C_\mathrm{D}}\left( {\frac{\kappa }{\ln \left( {\frac{z}{z_{t} }} \right) -\psi _{h}\left( {\frac{z}{L}} \right) }} \right) =\sqrt{C_\mathrm{D} }\left( {\frac{\kappa }{\ln \left( {\frac{z}{z_{q}}} \right) -\psi _{q} \left( {\frac{z}{L}} \right) }} \right) . \end{aligned}$$

(10)

Here, $\psi _{t}$ is a function that parametrizes the effect of stability on the potential-temperature gradient and is assumed equal to the function that accounts for this effect on the mixing ratio (or specific humidity). The fluxes are used to define the Obukhov length as

$$\begin{aligned} L=\frac{\theta _a }{\kappa g}\frac{T_*}{u_*^2 }, \end{aligned}$$

(11)

where $T_{*}\equiv -\left( {\frac{H}{\rho c_\mathrm{p}}}\right) /u_{*}$, and represents the scaling parameter for temperature in Monin–Obukhov similarity theory.

A shortcoming of this definition of the Obukhov length is that it does not account for the contribution of the moisture flux to the buoyancy flux, which is required for the convective velocity scale (which is correctly defined in the MYNN parametrization) and is included by adding the scaling parameter for humidity

$$\begin{aligned} L=\frac{\theta _{a}}{\kappa g}\left( \frac{T_{*} +0.61\theta _{g}q_{*}}{u_{*}^2},\right) \end{aligned}$$

(12)

where $q_{*} \equiv -\left( {\frac{\lambda _{E}}{\rho \lambda }} \right) /u_{*}$ and the buoyancy flux is given by $u_{*} (T_{*} +0.61\theta _{g} q_{*})$ in kinematic units. The moisture flux generally increases the buoyancy over the ocean and can actually overwhelm the temperature stratification, making the surface layer unstable and mixing more efficient. Under conditions of very small surface heat fluxes, the exclusion of the moisture flux tends to incorrectly diagnose the surface layer as being too stable. This shortcoming is an avenue of research that is currently being pursued.

The MYNN parametrization calculates the 2-m temperature and mixing ratio, and the 10-m wind speed as diagnostic variables, which are derived using semi-logarithmic profiles with the same stability functions used for the transfer coefficients. For example, the potential temperature at 2 m is defined as

$$\begin{aligned} \theta \left( 2 \right) =\theta _{g} +\frac{T_{*} }{\upkappa }\left[ {\ln \left( {\frac{2}{z_t}}\right) -\psi _{m} \left( {\frac{2}{L}} \right) } \right] , \end{aligned}$$

(13)

and is combined with the expression for the potential temperature at the first grid point,

$$\begin{aligned} \theta _{a}=\theta _{g}+\frac{T_{*}}{\upkappa }\left[ {\ln \left( {\frac{z}{z_{t}}}\right) -\psi _{m}\left( {\frac{z}{L}} \right) }\right] \end{aligned}$$

(14)

to eliminate the scaling parameter, giving

$$\begin{aligned} \theta \left( 2 \right) =\theta _{g} +\left( {\theta _{a}-\theta _{g}} \right) \frac{\left[ {\ln \left( {\frac{2}{z_t}} \right) -\psi _{h} \left( {\frac{2}{L}} \right) } \right] }{\left[ {\ln \left( {\frac{z}{z_t }} \right) -\psi _{h} \left( {\frac{z}{L}} \right) } \right] }, \end{aligned}$$

(15)

which removes the stability correction in neutral conditions. Similar expressions are used for the 2-m mixing ratio (or specific humidity) and 10-m wind speed as

$$\begin{aligned} q\left( 2 \right) =q_{g} +\left( {q_{a}-q_{g}} \right) \frac{\left[ {\ln \left( {\frac{2}{z_{q}}} \right) -\psi _{q} \left( {\frac{2}{L}} \right) } \right] }{\left[ {\ln \left( {\frac{z}{z_q}} \right) -\psi _q \left( {\frac{z}{L}} \right) } \right] } \end{aligned}$$

(16)

and

$$\begin{aligned} U\left( {10} \right) =U_{g} +\left( {U_{a}-U_{g}} \right) \frac{\left[ {\ln \left( {\frac{10}{z_0 }} \right) -\psi _{m} \left( {\frac{10}{L}} \right) } \right] }{\left[ {\ln \left( {\frac{z}{z_{0}}}\right) -\psi _{m} \left( {\frac{z}{L}} \right) } \right] }, \end{aligned}$$

(17)

respectively, where $U_{g}$ again represents the surface current and is set to zero here.