# Experimental Design of a Prescribed Burn Instrumentation

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Coupled Atmosphere-Fire Simulation

#### 2.2. Statistical Analysis of Typical Burn Dates

#### 2.3. Statistical Optimization of Sensor Placement

#### 2.3.1. Repeated Latin Hypercube Sampling and Sobol Variance Decomposition

- $var\left(Y\right)$ is the total variability of the output Y over the range of the parameters ${X}_{1},\dots ,{X}_{L}$. We take this as the strength of the signal from the sensor.
- $var\left(\right)open="("\; close=")">{Y}_{i}$, called the Variance of the Conditional Expectation (VCE), is an estimate of the variability of the output Y due to the parameter ${X}_{i}$.

## 3. Results

#### 3.1. Determination of Typical Burn Days

#### 3.2. Results from Numerical Experiments

#### 3.2.1. Simulations of Planned Experimental Burns in Fishlake

- reference simulation without fire,
- standard simulation with fire, and
- simulation with fire and doubled heat flux from the fire to the atmosphere.

#### 3.2.2. Simulations of Planned Experimental Burns in North Kaibab

#### 3.2.3. Simulations of Planned Experimental Burns in Fort Stewart

#### 3.3. Sensitivity Study of Sensor Placement

#### 3.3.1. Sampling Setup

- 10 h fuel moisture content, varying from 0.04 to 0.14 water mass/dry fuel mass. 1 h fuel moisture was 10 h fuel moisture minus 0.01, 100 h fuel moisture was 10 h fuel moisture plus 0.01, and live fuel moisture was 0.78. These values were entered as initial moisture values and did not change with time. See [1,19] for a further description of the fuel moisture in WRF-SFIRE.
- Heat extinction depth, varying from 6 m to 50 m. The fire heat flux is entered into WRF boundary layer with exponential decay, rather than all into the bottom layer of cells. The heat is apportioned depending on the height of the cell center above the terrain, with weight 1 at the ground and at the heat extinction depth. This gradual heat insertion is a parameterization for unresolved mixing and radiative heat transfer.
- Heat flux multiplier, varying from 0.5 to 2. The heat flux multiplier was chosen as a measure of the fire effect on the atmosphere; unlike the fuel load, it does not influence the rate of spread.
- Multiplier for the omnidirectional component R in the approximate fire rate of spread (ROS) formula following [34],$$ROS=R+{R}_{W}+{R}_{S}$$
- Multiplier for the wind-induced ROS component ${R}_{W}$
- Multiplier for the slope-induced ROS component ${R}_{S}$
- The simulation day, selected from the “typical” burn days

- The vertical velocity vector component W, interpolated to a given height above the terrain, or to a given altitude above the sea level.
- The smoke intensity (the concentration of WRF tracer
`tr17_1`), interpolated to a given height above the terrain, or to a given altitude above the sea level. - Plume-top height, derived from the smoke concentration.

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

## 4. Conclusions

#### 4.1. Estimation of Typical Days

#### 4.2. Results from Numerical Experiments

#### 4.3. Sensitivity Study of Sensor Placement

- The statistical analysis of runs with carefully sampled parameter sets was shown to provide clear guidelines on placing the measurements in space and time.
- Also, some measurements were found more affected by certain parameters, which can inform what parameters can be indirectly constrained by observations.
- Analyses of the variance in smoke concentration vertical velocity and plume top height from runs executed for different days and with different parameter sets show similar patterns indicating that typical day statistics managed to identify statistically similar days from the standpoint of plume rise and dispersion.
- The variability of the plume at higher altitudes (here, 1000–1400 m above the ground) is concentrated up to couple kilometers downwind from the plot, which suggests that sampling right above the fire, optimal for the fire heat flux measurements, may not be optimal for sampling most active parts of the plume.
- Additional parameters can be considered. The cost of one repetition does not increase with the number of parameters, but more repetitions need to be done for statistical convergence. The variability of the outputs will increase and the added parameters will help model additional uncertainty, which is always present in reality.

#### 4.4. Computing Resources

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Statistics of Weather Data

**Figure A1.**Station data (vertical) vs. month number (horizontal) for station KCWV (Claxton Evans County Airport, 32.19510° N, 81.86960° W 111 ft in Georgia) from 2008 to 2016 with 2 burn windows per year. Points that do and do not meet the burn-requirements (Table 2) are dark and light gray, respectively, and enumerated in the legends and titles, respectively. The abscissa is $t\phantom{\rule{4.44443pt}{0ex}}(mod\phantom{\rule{0.277778em}{0ex}}12)$ for all the years indicated in the title.

**Figure A2.**Station data (vertical) vs. month number (horizontal) for station KLHW (Ft. Stewart, 31.88333° N, 81.56667° W, 46 ft in Georgia) from 2002 to 2016 with 2 burn windows per year. Points that do and do not meet the burn-requirements (Table 2) are dark and light gray, respectively, and enumerated in the legends and titles, respectively. The abscissa is $t\phantom{\rule{4.44443pt}{0ex}}(mod\phantom{\rule{0.277778em}{0ex}}12)$ for all the years indicated in the title.

**Figure A3.**Station data (vertical) vs. month number (horizontal) for station LCSS1 (Savriv, 33.33305° N, 81.591667° W, 275 ft in South Carolina) from 2004 to 2016. Points that do and do not meet the burn-requirements (Table 2) are dark and light gray, respectively, and enumerated in the legends and titles, respectively. The abscissa is $t\phantom{\rule{4.44443pt}{0ex}}(mod\phantom{\rule{0.277778em}{0ex}}12)$ for all the years indicated in the title.

**Figure A4.**Station data (vertical) vs. month number (horizontal) for station QLBA3 (Lindbergh Hill, 36.285556° N, 112.078611° W, 8800 ft in Arizona) for 1999–2016. Points that do and do not meet the burn-requirements (Table 2) are dark and light gray, respectively, and enumerated in the legends and titles, respectively. The abscissa is $t\phantom{\rule{4.44443pt}{0ex}}(mod\phantom{\rule{0.277778em}{0ex}}12)$ for all the years indicated in the title.

**Figure A5.**Station data (vertical) vs. month number (horizontal) for station TT084 (Fishlake D4 Pt #4, 38.960319° N, 111.405983° W, 8523 ft in Utah) for 2012–2016. Points that do and do not meet the burn-requirements (Table 2) are dark and light gray, respectively, and enumerated in the legends and titles, respectively. The abscissa is $t\phantom{\rule{4.44443pt}{0ex}}(mod\phantom{\rule{0.277778em}{0ex}}12)$ for all the years indicated in the title.

**Figure A6.**As in Figure 4 but for station KCVW.

**Figure A7.**As in Figure 4 but for station KLHW.

**Figure A8.**As in Figure 4 but for station LCSS1.

**Figure A9.**As in Figure 4 but for station QLBA3.

**Figure A10.**As in Figure 4 but for station TT084.

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**Figure 1.**Time series of Mahalanobis (standardized) deviation norm $\parallel {\delta}_{t}\parallel $ for each station (6 rows). Points for states that do and do not meet burn requirements are dark and light gray, respectively. For each station, the most typical day in the burn window has the smallest $\parallel {\delta}_{t}\parallel $ and is listed in the title and indicated with a ∇ marker. The abscissa is $t\phantom{\rule{4.44443pt}{0ex}}(mod\phantom{\rule{0.277778em}{0ex}}12)$ for all the years indicated in the plot titles.

**Figure 2.**WRF domain setups for burn simulation: (

**a**) Fishlake; (

**b**) North Kaibab; (

**c**) Fort Stewart, with indication of nearby meteorological stations used to define typical days.

**Figure 3.**Station data (vertical) vs. month number (horizontal) for station FSHU1 (Fish Lake ranger station near Koosharem 10ENE, 38.55167° N, 111.72278° W, 8880 ft in Utah) in years 2001–2016. Points that do and do not meet the burn-requirements (Table 2) are dark and light gray, respectively, and enumerated in the legends and titles, respectively. The abscissa is $t\phantom{\rule{4.44443pt}{0ex}}(mod\phantom{\rule{0.277778em}{0ex}}12)$ for all the years indicated in the title.

**Figure 4.**Scatter plots of FSHU1 pairs of state variables. Black and gray indicate values that are and are not constrained by the burn requirements. The marginal covariance of a pair of variables is depicted by the green ellipse centered at the mean and with axes equal to the deviations in the principal directions. The ellipse projections on the coordinate axes have lengths equaling twice the corresponding marginal standard deviations. Ellipse area decreases with increasing correlation (if tilting up) or decreasing anti-correlation (if tilting down); a circle would indicate zero correlation. Only the values that satisfy the minimum and maximum values for burn requirements in Table 2 are used to compute the covariances, in the considered years regardless of burn season.

**Figure 5.**Latin Hypercube Sampling (LHS). Each of $L=7$ parameters takes the values from its $N=5$ sampling points. The rows are random permutations of the numbers 1 to 5, while the columns are the parameter vectors on which the simulations will be run.

**Figure 6.**Time series of the maximum updraft strength and location from the Fishlake simulation for 09/03/2014. (

**a**) Standard simulation; (

**b**) Simulation with doubled fire heat flux released to the atmosphere.

**Figure 7.**Smoke analysis for the Fishlake burn executed for 09/03/2014. (

**a**) Vertical profile of normalized smoke concentration; (

**b**) Time series of the plume top height.

**Figure 8.**Analysis of the fire-induced winds for the Fishlake simulation executed for 09/03/2014. (

**a**) Time series of the maximum fire-induced horizontal winds and their heights in the baseline case; (

**b**) Same in the double heat case.

**Figure 9.**Smoke analysis for the North Kaibab burn simulation executed for 09/05/2008. (

**a**) Vertical profile of normalized smoke concentrations; (

**b**) Time series of the simulated plume top height.

**Figure 10.**Analysis of the fire-induced wind and updraft for the North Kaibab simulation executed for 09/05/2008. (

**a**) Time series of the maximum fire-induced horizontal winds; (

**b**) TTime series of the maximum fire-induced updraft.

**Figure 11.**Results from numerical simulations for Fort Stewart (02/14/2013) with different ignition procedures. (

**a**) Time series of the simulated maximum fire-induced updraft; (

**b**) Same for plume top height.

**Figure 12.**Analysis of the fire-induced wind and updraft for the Fort Stewart simulation executed for 04/22/2014. (

**a**) Time series of the fire-induced maximum horizontal wind speed; (

**b**) Same for the updraft.

**Figure 13.**(

**a**) The time series of the variance of vertical velocity at different heights above the ground from simulations executed with parameters from the rLHS sampling; (

**b**) Map of the variance of the vertical velocity at 1200 m with the indication of the burn plot (green contour) and the ignition (red line).

**Figure 14.**(

**a**) The mean plume top height; (

**b**) The normalized variance in the plume height. The green contour represents the burning plot boundary and the red line shows the ignition.

**Figure 15.**(

**a**) The mean normalized smoke concentration at 1400 m above the terrain; (

**b**) The normalized smoke concentration average variance at 1400 m above the terrain. The green contour represents the burning plot boundary, the red line shows the ignition.

**Figure 16.**Sensitivity of the vertical velocity at 1200 m (

**top**), smoke concentration at 1400 m (

**middle**), and plume top height (

**bottom**) to the fire heat flux multiplier (

**left**column) and the heat extinction depth (

**right**column).

**Figure 17.**(

**a**) The mean normalized smoke concentration at 1400 m above the ground computed from 5 most typical days; (

**b**) The normalized average variance of the smoke concentration at 1400 m computed from 5 most typical days. Green contour represents burn unit boundaries, red line shows the ignition.

**Figure 18.**(

**a**) The vertical velocity average variance at 1000 m computed from 5 most typical days; (

**b**) The mean plume top height computed from 5 most typical days. Green contour represents burn unit boundaries, white line shows the ignition.

Burn Site | Fishlake | North Kaibab | Fort Stewart |
---|---|---|---|

Meteo forcing | NARR | NARR | NARR |

Number of domains | 5 (realistic) | 5 (realistic) | 5 (realistic) |

Domain sizes(XYZ) | $97\times 97\times 41$ | $97\times 97\times 41$ | $97\times 97\times 41$ |

Model top | 13.2 km | 13.2 km | 13.2 km |

Horizontal resolution | 12 km/4 km/1.33 km/444 m/148 m | 12 km/4 km/1.33 km/444 m/148 m | 12 km/4 km/1.33 km/444 m/148 m |

Vertical resolution | 5.3 m–2233 m | 5.3 m–2233 m | 5.3 m–2233 m |

Fire mesh resolution | 29.6 m | 29.6 m | 29.6 m |

Total number of runs | 7 | 4 | 10 |

Ignition | Helicopter | Point | Straight Line/Point |

Simulation start | 09/03/2014 00:00 UTC | 09/05/2008 00:00 UTC | 04/22/2014 00:00 UTC |

09/11/2016 00:00 UTC | 09/19/2015 00:00 UTC | 04/27/2009 00:00 UTC | |

09/22/2012 00:00 UTC | 09/01/2001 00:00 UTC | 02/27/2013 00:00 UTC | |

09/26/2015 00:00 UTC | 09/02/2011 00:00 UTC | 02/26/2008 00:00 UTC | |

Ignition Time | 15:00 UTC (9:00 local) | 15:00 UTC (9:00 local) | 15:00 UTC (11:00 local) |

Simulation Length | 48 h | 48 h | 48 h |

Fire Output Interval | 5 min | 5 min | 5 min |

Time step (d05) | 0.5 s | 0.5 s | 0.74 s |

1 h fuel moisture | 6.0% | 6.0% | 15.0% |

10 h fuel moisture | 8.0% | 8.0% | 13.0% |

100 h fuel moisture | 9.0% | 9.0% | 13.0% |

1000 h fuel moisture | 12.0% | 12.0% | 18.0% |

**Table 2.**Stations, time windows (mm/dd hh:mm UTC) and value limits for potential burns (burn windows). T—temperature, $\varphi $—relative humidity, s—wind speed.

Station | Burn Season | Min T | Max T | Min $\mathit{\varphi}$ | Max $\mathit{\varphi}$ | Min s | Max s |
---|---|---|---|---|---|---|---|

FSHU1 | 09/01 16:00 UTC–10/31 18:00 UTC | 61 F | 85 F | 16% | 22% | 0 | 15 mph |

KCWV | 02/20 16:00 UTC–02/28 18:00 UTC | 60 | 90 | 30 | 55 | 6 | 20 |

04/15 13:00UTC–04/30 14:00 UTC | 60 | 90 | 30 | 55 | 6 | 20 | |

KLHW | 02/20 16:00 UTC–02/28 18:00 UTC | 60 | 90 | 30 | 55 | 6 | 20 |

04/15 13:00 UTC–04/30 14:00 UTC | 60 | 90 | 30 | 55 | 6 | 20 | |

LCSS1 | 01/01 15:00 UTC–02/01 19:00 UTC | 60 | 90 | 30 | 55 | 6 | 20 |

12/01 15:00 UTC–12/31 19:00 UTC | 60 | 90 | 30 | 55 | 6 | 20 | |

QLBA3 | 09/01 17:00 UTC–10/31 19:00 UTC | 61 | 85 | 16 | 22 | 0 | 15 |

TT084 | 09/01 16:00 UTC–10/31 18:00 UTC | 61 | 85 | 16 | 22 | 0 | 15 |

Burn Site | Fishlake | North Kaibab | Fort Stewart | ||
---|---|---|---|---|---|

Weather Station | FSHU1 | TT084 | QLBA3 | KCWV | KLHW |

Typical days | 09/03/2014 | 09/05/2012 | 09/05/2008 | 04/22/2014 | 04/27/2009 |

09/26/2015 | 09/04/2012 | 09/19/2005 | 02/24/2013 | 02/26/2013 |

Sampling Point | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

10-fuel moisture (kg/kg) | 0.0459 | 0.0613 | 0.0748 | 0.0914 | 0.1219 |

Heat extinction depth (m) | 7.5830 | 12.3531 | 17.3205 | 24.2854 | 39.5620 |

Heat flux multiplier (1) | 0.5827 | 0.8017 | 1.0000 | 1.2473 | 1.7161 |

Multiplier for R (1) | 0.5827 | 0.8017 | 1.0000 | 1.2473 | 1.7161 |

Multiplier for ${R}_{W}$ (1) | 0.5827 | 0.8017 | 1.0000 | 1.2473 | 1.7161 |

Multiplier for ${R}_{S}$ (1) | 0.5827 | 0.8017 | 1.0000 | 1.2473 | 1.7161 |

Simulation day (date) | 09/03/2014 | 09/11/2016 | 09/22/2012 | 09/26/2015 | 09/27/2015 |

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**MDPI and ACS Style**

Kochanski, A.K.; Fournier, A.; Mandel, J.
Experimental Design of a Prescribed Burn Instrumentation. *Atmosphere* **2018**, *9*, 296.
https://doi.org/10.3390/atmos9080296

**AMA Style**

Kochanski AK, Fournier A, Mandel J.
Experimental Design of a Prescribed Burn Instrumentation. *Atmosphere*. 2018; 9(8):296.
https://doi.org/10.3390/atmos9080296

**Chicago/Turabian Style**

Kochanski, Adam K., Aimé Fournier, and Jan Mandel.
2018. "Experimental Design of a Prescribed Burn Instrumentation" *Atmosphere* 9, no. 8: 296.
https://doi.org/10.3390/atmos9080296