A Case Study of the Weather Research and Forecasting Model Applied to the Joint Urban 2003 Tracer Field Experiment. Part 2: Gas Tracer Dispersion

Abstract

The Quick Urban & Industrial Complex (QUIC) atmospheric transport, and dispersion modelling, system was evaluated against the Joint Urban 2003 tracer-gas measurements. This was done using the wind and turbulence fields computed by the Weather Research and Forecasting (WRF) model. We compare the simulated and observed plume transport when using WRF-model-simulated wind fields, and local on-site wind measurements. Degradation of the WRF-model-based plume simulations was cased by errors in the simulated wind direction, and limitations in reproducing the small-scale wind-field variability. We explore two methods for importing turbulence from the WRF model simulations into the QUIC system. The first method uses parametrized turbulence profiles computed from WRF-model-computed boundary-layer similarity parameters; and the second method directly imports turbulent kinetic energy from the WRF model. Using the WRF model’s Mellor-Yamada-Janjic boundary-layer scheme, the parametrized turbulence profiles and the direct import of turbulent kinetic energy were found to overpredict and underpredict the observed turbulence quantities, respectively. Near-source building effects were found to propagate several km downwind. These building effects and the temporal/spatial variations in the observed wind field were often found to have a stronger influence over the lateral and vertical plume spread than the intensity of turbulence. Correcting the WRF model wind directions using a single observational location improved the performance of the WRF-model-based simulations, but using the spatially-varying flow fields generated from multiple observation profiles generally provided the best performance.

Appendix

1.1 Appendix 1.1: Turbulence Derived from WRF Model Surface-Layer Parameters

Due to the diagnostic nature of the QUIC-URB wind solver, only 3D mean wind fields are produced without turbulence quantities. In the absence of further information regarding the turbulence structure in the planetary boundary layer, which is required by the Lagrangian random-walk dispersion model, the turbulence must either be inferred from the mean wind field or parametrized using surface-layer parameters such as $u_*$, 1 / L, and h. By default, the QUIC system uses a combination of parametrized turbulence profiles (in regions that are nominally undisturbed by explicitly resolved building effects), local gradient (in regions near where building flow parametrizations have been applied), and enhanced non-local turbulence schemes (in some building-flow parametrization regions). Williams et al. (2004) has a complete description of the methods employed by the QUIC system to deduce turbulence in and near the building flow parametrizations. The WRF model fields of $u_*$, 1 / L, and h that have been interpolated onto the domain grid of the QUIC system simulation are used as local values within the parametrizations used by the QUIC system’s standard turbulence scheme to yield the 3D spatially-varying turbulence fields required by the Lagrangian random walk dispersion model.

In the surface layer, dimensional analysis combined with empirical observations have confirmed Monin-Obukhov similarity theory, which provides standard relationships between $u_*$, L, and the mean wind speed (Monin and Obukhov 1954; Calder 1966; Stull 1988; Arya 2001). The QUIC system uses parametrizations of the variation of turbulence with vertical position based on surface-layer quantities and h as described in Rodean (1996). For neutral to stable thermal stabilities $(z/L \ge 0)$, the QUIC system uses the following relations for the velocity variances $(\sigma ^2)$ in a local coordinate system rotated such that the u-velocity component is in the local mean wind direction,

$$\begin{aligned} \sigma _u^2= & {} u_*^2 \left( 6.3\left( 1-\frac{z}{h}\right) ^{3/2}\right) , \end{aligned}$$

(10)

$$\begin{aligned} \sigma _v^2= & {} u_*^2 \left( 4.0\left( 1-\frac{z}{h}\right) ^{3/2} \right) , \end{aligned}$$

(11)

$$\begin{aligned} \sigma _w^2= & {} u_*^2 \left( 1.7\left( 1-\frac{z}{h}\right) ^{3/2} \right) . \end{aligned}$$

(12)

For thermally unstable conditions $(z/L < 0)$, another thermal-stability dependent term is added to Eqs. 10–12, which accounts for the generation of turbulence due to buoyancy under thermally unstable conditions, yielding the following relations,

$$\begin{aligned} \sigma _u^2= & {} u_*^2 \left( 6.3\left( 1-\frac{z}{h}\right) ^{3/2}+0.6\left( -\frac{h}{L}\right) ^{2/3}\right) , \end{aligned}$$

(13)

$$\begin{aligned} \sigma _v^2= & {} u_*^2 \left( 4.0\left( 1-\frac{z}{h}\right) ^{3/2}+0.6\left( -\frac{h}{L}\right) ^{2/3}\right) , \end{aligned}$$

(14)

$$\begin{aligned} \sigma _w^2= & {} u_*^2 \left( 1.7\left( 1-\frac{z}{h}\right) ^{3/2}+3.3\left( -\frac{z}{L}\right) ^{2/3} \left( 1-0.8\frac{z}{h}\right) ^{2}\right) . \end{aligned}$$

(15)

1.2 Appendix 1.2: Turbulence Based on WRF Model Turbulent Kinetic Energy Field

In the second method for importing turbulence from the WRF model into the QUIC system, TKE fields are imported directly. As can be seen in the discussion above, the standard turbulence model in QUIC-PLUME is based on $u_*$ instead of e. Unfortunately, the ability to export turbulence data from the WRF model is limited and does not provide a method to separate the 3D interpolated TKE field into the three velocity variance fields. WRF model TKE import scheme where the turbulence is based on the local e value rather than $u_*$. However, the random-walk dispersion model needs the velocity variances rather than e to determine the turbulent diffusion within the plume. The definition of TKE (e) provides a relationship between TKE and the velocity variances but does not indicate the relative magnitudes of the velocity variances,

$$\begin{aligned} e=0.5\left( \sigma _u^2+\sigma _v^2+\sigma _w^2\right) . \end{aligned}$$

(16)

For unstable conditions we can the combine the definition of e with Eqs. 13–15 to yield an equation for e as a function of $u_*$, z, h, and L,

$$\begin{aligned} e=u_*^2 \left( 6.0\left( 1-\frac{z}{h}\right) ^{3/2}+0.6\left( -\frac{h}{L}\right) ^{2/3} +1.65\left( -\frac{z}{L}\right) ^{2/3}\left( 1-0.8\frac{z}{h}\right) ^{2}\right) , \end{aligned}$$

(17)

which can be rearranged to solve for $u_*^2$, which is then substituted back into Eqs. 13–15 to yield $\sigma _u$, $\sigma _v$, and $\sigma _w$ in terms of e,

$$\begin{aligned} \sigma _u^2= & {} e \frac{f_1(z,h,L)}{f_0(z,h,L)}, \end{aligned}$$

(18)

$$\begin{aligned} \sigma _v^2= & {} e \frac{f_2(z,h,L)}{f_0(z,h,L)}, \end{aligned}$$

(19)

$$\begin{aligned} \sigma _w^2= & {} e \frac{f_3(z,h,L)}{f_0(z,h,L)}, \end{aligned}$$

(20)

where $f_0$, $f_1$, $f_2$, and $f_3$ are the functions of z, h, and L within the parentheses on the right-hand side of of Eqs. 17, 13, 14, and 15, respectively. Similar substitutions can be made into Eqs. 10–12 for neutral and stable conditions, which become constant factors for the along-wind, cross-wind, and vertical components based on the standard relationships between $u_*$ and $\sigma$ values of the individual velocity components (Panofsky and Dutton 1984; Roth 2000). For the ratios of $u_*$ and $\sigma$ that the QUIC system uses, the ratios of velocity variances to e are 1.0, 0.67, and 0.28 for the along-wind, cross-wind, and vertical components, respectively.