Ensemble Fog Prediction

Abstract

This chapter is about ensemble fog prediction using numerical models. First, we briefly discuss why we need ensemble prediction. The sensitivity work of fog forecasts to model initial condition and physics are then reviewed. A case study is analyzed to demonstrate how ensemble approach improves over a single-run forecast in both deterministic and probabilistic point of view. The current status of operational ensemble fog forecasting and their performance at NCEP and other agencies are presented. Challenges in model-based fog forecasts are briefly discussed. Finally, ensemble verification method is overviewed as background information to readers.

Appendix: A Balance Theory Based Fog Algorithm for Fog Intensity

The model lowest-level LWC based (Eq. (10.1a)), visibility based or the multi-rule based (Eqs. (10.1a)–(10.1c)) fog-diagnosing schemes can only predict fog occurrence but not intensity. Recently a new fog diagnosis method was developed (Zhou, 2011) based on a balance theory for radiation fog (Zhou & Ferrier, 2008). This theory assumes that a balance among cooling, droplet settling and turbulence must be reached for fog formation and maintenance. From an approximation analysis (singular perturbation method), a critical turbulent exchange coefficient K _c was found for a fog layer

$$ K<{K}_c=1.38\;\Big[\alpha \beta \left( p, T\right) C{}_o\Big]^{1/2}{H}_{sat}^{3/2} $$

(10.15)

K _c is more sensitive to the fog depth (H ^3/2 _sat ) than to the cooling rate (C _o ^1/2) and defines the upper bound of turbulence intensity which a persisting fog can withstand. An initial ground fog usually forms below 10 m near the surface and remains stable for a long time (conditioning) if the surface turbulence does not exceed the critical turbulent exchange coefficient K _c , otherwise the ground fog will dissipate. ${K}_c\sim {H}_{sat}^{3/2}$ means that a deep fog can withstand a much stronger turbulence without being dispersed than a shallow fog. That is why turbulence development is usually observed in a deep fog without dispersing but promoting the fog layer. In other words, turbulence is allowed to exist within a fog layer since it is required for fog further development after it forms but it cannot exceed this critical value. Several factors may cause the turbulence intensity to exceed K _c : (1) a reduction in cooling rate (K _c decreases) due to sunrise, or local clouds, or warm advection; and (2) rising local wind speeds, which increase the surface mechanical turbulence (K increases). On the contrary, an increase in cooling rate or cessation of winds is in favor of persistence of ground fog. The another advantage for this method is that fog LWC can also be estimated (from which fog intensities can be defined)

$$ W\left( z, k\right)={\left[\frac{\beta \left( p, T\right){C}_o{H}_{sat}}{\alpha}\right]}^{1/2}\left[{\left(1-\frac{z}{H_{sat}}\right)}^{1/2}-\frac{2}{1+{e}^{z/\delta}}\right], $$

(10.16)

where δ can be thought as a fog boundary layer (FBL), expressed as

$$ \delta =\frac{K}{2{\left[\alpha \beta \left( p, T\right){C}_o{H}_{sat}\right]}^{1/2}}, $$

(10.17)

Equation (10.16) has one order of accuracy in terms of K, or O(K). In other words, the smaller the K is, the more accurate Eq. (10.16) will be. Since the turbulence intensity in a shallow fog is usually much weaker than that in a dense fog, Eq. (10.16) is more accurate for shallow fog than for deep fog. This analysis was originally made for radiation fog where advection term was excluded. To detect other fog types, particularly marine fog, advection fog etc., advection term can be conveniently added into Eqs. (10.15) and (10.16).

$$ K<{K}_c=1.38\left\{\alpha \right[ A d v+\beta \left( p, T\right) C{}_o\Big]\Big\}{}^{1/2}{H}_{sat}^{3/2} $$

(10.18)

And

$$ W\left( z, k\right)={\left\{\frac{\left[ Adv+\beta \left( p, T\right){C}_o\right]{H}_{sat}}{\alpha}\right\}}^{1/2}\left[{\left(1-\frac{z}{H_{sat}}\right)}^{1/2}-\frac{2}{1+{e}^{z/\delta}}\right] $$

(10.19)

The term inside the first [ ] in Eq. (10.19) is the total liquid water generation rate by both cooling and moisture advection. A positive $A d v\left(-\overrightarrow{V}\cdot \nabla W>0\right)$ means a wet advection from upwind brings more moisture into fog layer, leading to an increase in fog LWC while a negative Adv means a dry advection from upwind brings dry air into fog, leading to a decrease in fog LWC. Equation (10.18) correctly reflects such an impact. If the dry air brought by upwind exceeds the amount of water droplets generated by cooling, the fog layer will disperse at all levels. The following fog LWC diagnostic scheme is designed based on Eq. (10.18) in attempt to deal with various types of fog. Moreover, Eq. (10.19) indicates that a wet advection strengths the critical turbulent exchange coefficient. As a result, fog is more difficult to be dispersed in a wet advection environment, which has been often observed in many long-lasting advection fog events.

Based on Eqs. (10.18) and (10.19), a new fog diagnostic algorithm has been developed and implemented at NCEP in both SREF and NARRE-TL systems. Although objective verification for the new method has not been done yet, subjective evaluation of a few cases have shown improvements over other existing fog algorithm.