#### 3.4. Computational Results for the Fishlake Burn Simulation

In the following section selected results of the repeated Latin Hypercube Sampling (rLHS) and the analysis of variance described above are shown. In all computations reported here, the average variance is computed as variance for each simulation day separately, and then averaged over the simulation days.

The vertical level of highest variances in the updraft velocities (1200 m above the ground) have been selected for visualization based on the vertical velocity variance time series plotted in the left panel of

Figure 13. Based on a similar time series of the smoke concentrations and the plume top height estimates form the baseline case (

Figure 6), the analysis level for smoke has been set to 1400 m.

Figure 13b shows the variance of the vertical wind velocity at 1200 m above the terrain, computed from 25 rLHS-sampled simulations. Two well-defined maxima are located outside of the northwestern plot boundary, indicating optimal locations for upper-level vertical velocity measurements. Local variance reaches up to 3

${\mathrm{m}}^{2}/{\mathrm{s}}^{2}$, which corresponds to local deviations in the vertical velocity of about 1.7 m/s between the sampled simulations, which is high enough to be sampled by a Doppler LiDAR, Radar or Sodar. However, the fact that the updraft variances are concentrated over small regions indicate that optimal placement of the measurement devices may play a critical role in constraining model parameters based on the vertical velocity observations.

Figure 14 shows maps of the mean and the normalized variance of the plume top height. The former informs about the expected vertical plume extent which should be taken into account when the plume sampling strategies are considered. The latter shows regions of most pronounced impact of the model parameters on the plume rise. Interestingly, the region directly downwind from the fire, where the plume reaches highest elevations, is not the same as the region of highest plume height average variance. The plume height average variance exhibits high values over two symmetrical regions located on both sides of the plume axis and are pushed much more downwind from the fire compared to the mean plume top height. These results indicate that while the localized vertical smoke sampling (corkscrew path) may be optimal for assessing the maximum plume top height, the sampling region must be significantly extended downwind in order to adequately sample the plume top height variance.

Figure 15a shows the map of the mean smoke concentration at 1400 m, and

Figure 15b is the map of the smoke concentration variance. The mean smoke concentration is intended to inform the measurements where the probability of successful smoke sampling is the highest. The variance on the other hand, shows where the tested model parameters have strongest impact on the smoke concentrations. It is noteworthy that high values of smoke concentrations variances are found over much larger region than the vertical velocity variance shown in

Figure 13b, which suggest that vertical velocity measurements are more suitable for local platforms like ground LiDARs, while the smoke measurements could be performed from airborne platforms covering larger areas.

The rLHS analysis not only informs where the measurement should be taken in order to constrain model parameters, but also allows to find relative contribution of the tested parameters to variances in the variables of interest. We present results of the first-order variance decomposition of vertical velocity at 1200 m, smoke concentration at 1400 m, and the plume top height, attributed to the most important simulation parameters. These spatial plots of the sensitivity indices inform about the relative importance of the tested parameters (such as fuel moisture, heat extinction depth, fire heat flux, etc.) as well as indicate regions of highest impact of these parameters on the variables of interest.

The most critical parameters controlling the vertical velocity, smoke concentration and the plume top height are shown in

Figure 16. The heat flux multiplier contributes to the variance of vertical velocity, smoke concentration and the plume top height up to 50%. Unsurprisingly, the fire heat flux plays the major role in driving the plume rise, which indicates the importance of a detailed fire heat characterization during experimental burns. The second most significant contribution (up to 40%) comes from the heat extinction depth, defining the depth over which the fire heat flux is distributed vertically in the model. The extinction depth seems to have an impact of similar magnitude on the variables of interest like the heat flux multiplier, but its character is different.

Figure 16 suggests that the heat flux multiplier has the opposite effect on the extinction depth. For instance, the vertical velocities are impacted by the heat flux multiplier mostly downwind (northeast) from the fire (see left top panel). The extinction depth, on the other hand, affects mostly vertical velocities upwind from the fire (see right top panel). Similarly, the smoke concentration is impacted by the heat flux in the north-eastern part of the domain, while the extinction depth seems to impact mostly the south-western part. A similar situation can be observed in the bottom panels of

Figure 16, showing the impact of these parameters on the plume top height. Here, the heat flux impact is confined to the very core of the plume, while the extinction depth has the most pronounced impact on the sides of the plume. The differences in these patterns indicate that the placement of the sensor optimal form the perspective of constraining the heat flux may be not optimal for constraining the extinction depth and vice-versa. Also, the patterns of the heat flux contribution seem generally more organized than the ones of the extinction depth. The impact of the extinction depth seems to have non-local character especially when vertical velocity and smoke concentration is considered, spreading across large areas upwind from the fire. That suggests that estimating the extinction depth through the observations of vertical velocities and smoke concentration may be difficult, and may require direct tower-based observations of the vertical attenuation of the fire heat flux.

The analysis presented above focuses on the impact of model parameters on measurable variables like the vertical velocity or the plume height. In that sense, it informs where the signal coming from the changes in the parameters is expected to be highest and consequently, shows locations where measurements should be taken to detect it. As the weather conditions on the burn day cannot be predicated at the moment of experimental planning, the analysis presented in this study has been employed to find most typical historical days for all the burn stations. Five most typical days have been included in this analysis. On the top of the baseline simulation, performed for 09/03/2014, analogous runs have been executed for other 4 typical days listed in

Table 3. These 5 days are treated as an ensemble of most typical scenarios for the Fishlake experimental burn. Shown below are the means and average variances of the variables of interest computed across the simulations performed for these days.

Figure 17 shows maps of mean and variance of the smoke concentration at 1400 m. A pattern can be noticed there, indicating general north-northwest smoke dispersion. The fact that regions of maxima in both mean concentration and the variance can be easily identified, indicates that the typical days are similar to each other in terms of a general flow pattern in the Fishlake region. It should be noted that the wind direction was not a part of burn requirements for this burn site which defined only the wind speed, temperature, and relative humidity. Since typical days show relatively consistent flow pattern, it can be concluded that typical days in terms of the air humidity, wind speed, and moisture are generally associated with south-southwesterly flow.

The maps of the vertical velocity variance and the mean plume top height are shown in

Figure 18. A clear maximum in the updraft fluctuations is evident north-west from the end of the ignition line, as well as a well-defined north-northeasterly plume reaching 3200 m. The statistical analysis of simulations performed for the most typical day such as the one shown in

Figure 17 and

Figure 18, are intended to be used as a guideline in the planning stages of experimental burns when optimal locations of smoke and vertical velocity measurements are being considered.