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  • View in gallery

    Variation trends of hourly plume rise and meteorological variables, where each panel represents one burn. The x and y axes are hour of the day during a fire and smoke plume rise (m), respectively. The ranges for meteorological variables are between 1 and 5 m s−1 for surface wind speed, 10° and 50°C for fuel temperature, 5% and 15% for fuel moisture, and 600 and 2200 m for PBL height.

  • View in gallery

    Variations of normalized hourly smoke plume rise and meteorological variables: (top) wind, (top middle) fuel temperature, (bottom middle) fuel moisture, and (bottom) PBL height. The minor ticks in the x axis are different hours during a fire. The vertical lines separate various sequence portions.

  • View in gallery

    As in Fig. 2, but for the average sequence.

  • View in gallery

    Scatterplots of the hourly and average observed (x axis) vs simulated smoke plume rise using RxPrise and RxPrise-sfc (y axis). The quantity R2 is the unadjusted squared correlation coefficient.

  • View in gallery

    Hourly smoke plume rise (normalized) from observations and predictions by RxPrise and RxPrise-sfc. The values for the same burn are connected by lines. The three horizontal lines indicate smoke plume heights at the average and plus or minus one-half standard deviation, respectively.

  • View in gallery

    As in Fig. 5, but for the average smoke plume rise.

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A Regression Model for Smoke Plume Rise of Prescribed Fires Using Meteorological Conditions

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  • 1 Center for Forest Disturbance Science, U.S. Department of Agriculture Forest Service, Athens, Georgia
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Abstract

Smoke plume rise is an important factor for smoke transport and air quality impact modeling. This study provides a practical tool for estimating plume rise of prescribed fires. A regression model was developed on the basis of observed smoke plume rise for 20 prescribed fires in the southeastern United States. The independent variables include surface wind, air temperature, fuel moisture, and atmospheric planetary boundary layer (PBL) height. The first three variables were obtained from the Remote Automatic Weather Stations, most of which are installed in locations where they can monitor local fire danger and are easily accessed by fire managers. The PBL height was simulated with the Weather Research and Forecasting Model. The confidence and validation analyses indicate that the regression model is significant at the 95% confidence level and able to predict hourly values and the average smoke plume rise during a burn, respectively. The prediction of the average smoke plume rise shows larger skills. The model also shows improved skills over two extensively used empirical models for the prescribed burn cases examined in this study, suggesting that it may have the potential to improve smoke plume rise and air quality modeling for prescribed burns. The regression model, however, tends to underestimate large plume rise values and overestimate small ones. A suite of alternative regression models was also provided, one of which can be used when no PBL information is available.

Corresponding author address: Yongqiang Liu, Center for Forest Disturbance Science, USDA Forest Service, 320 Green St., Athens, GA 30602. E-mail: yliu@fs.fed.us

Abstract

Smoke plume rise is an important factor for smoke transport and air quality impact modeling. This study provides a practical tool for estimating plume rise of prescribed fires. A regression model was developed on the basis of observed smoke plume rise for 20 prescribed fires in the southeastern United States. The independent variables include surface wind, air temperature, fuel moisture, and atmospheric planetary boundary layer (PBL) height. The first three variables were obtained from the Remote Automatic Weather Stations, most of which are installed in locations where they can monitor local fire danger and are easily accessed by fire managers. The PBL height was simulated with the Weather Research and Forecasting Model. The confidence and validation analyses indicate that the regression model is significant at the 95% confidence level and able to predict hourly values and the average smoke plume rise during a burn, respectively. The prediction of the average smoke plume rise shows larger skills. The model also shows improved skills over two extensively used empirical models for the prescribed burn cases examined in this study, suggesting that it may have the potential to improve smoke plume rise and air quality modeling for prescribed burns. The regression model, however, tends to underestimate large plume rise values and overestimate small ones. A suite of alternative regression models was also provided, one of which can be used when no PBL information is available.

Corresponding author address: Yongqiang Liu, Center for Forest Disturbance Science, USDA Forest Service, 320 Green St., Athens, GA 30602. E-mail: yliu@fs.fed.us

1. Introduction

Prescribed fire (Rx fire) is a forest management tool to reduce the buildup of hazardous fuels and the risk of destructive wildfire. Any fire is ignited by management actions under a predetermined “window” of very specific conditions including winds, temperatures, humidity, and other factors specified in a written and approved burn plan. Rx fire has been widely used. In the southern United States, for example, about 2–3 million ha (6–8 million acres) of forest and agricultural lands are burned by Rx fire each year (Wade et al. 2000). Emissions from Rx fire, however, can impact air quality. Biomass burning is a primary source of ambient particulate matter ≤ 2.5 μm in diameter (PM2.5) in less populated areas in the southeastern United States (Lee et al. 2007). Smoke plumes from two Rx fires in central Georgia led to ground PM2.5 concentrations much higher than the daily U.S. National Ambient Air Quality Standards (Hu et al. 2008; Liu et al. 2009).

Smoke plume rise, also called smoke plume height, is the elevation above the ground of the top of a smoke plume. A typical plume rise is about 1 km for Rx fires and several kilometers for wildfires. Smoke plume rise is an important factor for local and regional air quality modeling. Particles emitted from Rx fires with a higher plume rise are more likely to be transported out of the rural burn site and may affect air quality in downwind remote populated areas. Plume rise is required by many regional air quality models. The Community Multiscale Air Quality (CMAQ) model (Byun and Ching 1999; Byun and Schere 2006), for example, uses the Sparse Matrix Operator Kernel Emissions (SMOKE; Houyoux et al. 2002) modeling system to provide plume rise as part of the initial and boundary conditions for elevated emission sources, including fire emissions.

Various smoke plume rise models have been developed using dynamical (e.g., Latham 1994; Freitas et al. 2007, 2009), empirical (e.g., Briggs 1975; Pouliot et al. 2005), and hybrid (Achtemeier et al. 2011) approaches. One of the differences among various approaches is the degree of complexity. Dynamical models consist of differential equations governing fluxes of mass, momentum, and energy that often require time and space integration. Details of fire behavior and ambient conditions at high spatiotemporal resolutions (e.g., seconds and meters) are needed. Empirical models, on the other hand, are based on field and laboratory measurements using statistical or similarity theory. They usually appear as algebraic expressions that require burn and ambient conditions at a lower time frequency (e.g., 1 h) without spatial resolution. The simplicity of empirical models makes them a more practical tool for forest managers. Empirical models have been included in many fire and air quality management systems such as the Fire Emission Production Simulator (FEPS; Anderson et al. 2004), the Western Regional Air Partnership’s Fire Emission Inventory (Western Regional Air Partnership 2005), and the BlueSky smoke modeling system (Larkin et al. 2009).

Empirical models often use parameters related to fire behavior and atmospheric conditions. The modified Briggs model used in FEPS (Anderson et al. 2004), for example, calculates smoke plume rise using fire heat release, transport wind [averaged wind within the atmospheric planetary boundary layer (PBL)], and atmospheric stability. Heat release is determined by fuel and fire properties including fuel loading, consumption rate, combustion efficiency, buoyant efficiency, and entrainment efficiency. The uncertainty in the related burn properties such as burned area, burn phase (flaming or smoldering) partition, and many empirical parameters is one of the error sources.

On the basis of the statistics of plume rise measurements of Rx fires in the southeastern United States, Liu et al. (2012) proposed a guideline for fire and land managers to estimate smoke plume rise without using any burn and meteorological information. The averaged smoke plume rise over 20 Rx fires, about 1 km, was suggested to be a first-order approximation. A second-order approximation was suggested by making seasonal adjustments, that is, using the average value for spring and fall, decreasing by 0.2 km from the average for winter, and increasing by 0.2 km for summer. The guideline may avoid the uncertainty related to the burn property specification with the empirical models such as the one used in FEPS, but it is unable to describe the variability in smoke plume related to fire behavior and meteorological conditions.

This study was designed to develop an empirical regression model for smoke plume rise of Rx fire, which has a complexity level in between the FEPS approach (Anderson et al. 2004) and the guideline (Liu et al. 2012). Similar to Liu et al. (2012), this study was based on plume rise measurements of Rx fires in the southeastern United States. However, only meteorological conditions, which include both forest understory (a layer between the canopy and forest floor that is made up of small trees, bushes, and large green plants) fuel conditions (temperature and moisture) and weather conditions (wind and PBL height) in this study, were taken into account; a buoyancy factor determined by heat release from burn, which is used in many existing empirical models such as FEPS (Anderson et al. 2004), was not used. The major source for the meteorological conditions was the Remote Automatic Weather Stations (RAWS; http://raws.fam.nwcg.gov/). RAWS is run by the U.S. Forest Service and the U.S. Bureau of Land Management and monitored by the National Interagency Fire Center. There are more than 2000 stations across the United States, most of which are placed in locations where they can monitor fire danger. Thus, the empirical model has the potential to be a practical tool for fire and land managers as well as researchers to obtain smoke plume rise information needed for assessing the air quality impacts of smoke from Rx fires.

The rest of this paper is arranged as follows. The data and methods are described in section 2. The meteorological conditions and relationships with smoke plume rise variations are described in section 3. The models and evaluation are presented in section 4, and the discussion and conclusions are provided in the last two sections.

2. Data and methods

a. Smoke plume rise measurement

The smoke plume rise for 20 Rx fires in the southeastern United States was measured during 2009–11 using a Vaisala, Inc., CL31 ceilometer [a light detection and ranging (lidar) device] with a frequency of 2 s and vertical resolution of 20 m. The results were analyzed in Liu et al. (2012). A summary of the fires is provided in Table 1. Six burns (denoted as F1–F6) occurred at the Fort Benning Army Base (32.33°N, 84.79°W, near Columbus in southwestern Georgia), five (O1–O5) occurred at the Oconee National Forest (33.54°N, 83.46°W, in central Georgia), one (P1) occurred at the Piedmont National Wildlife Refuge (33.15°N, 83.42°W, in central Georgia), and eight (E1–E8) occurred at the Eglin Air Force Base (30.15°N, 86.55°W, near Niceville in northwestern Florida). The burns were typical Rx fires for the southeastern United States, with fuel types of mainly pine understory dead fuels and a few live fuels. The burns had varied sizes (about half of the burns between 500 and about 1000 acres and half over 1000 acres), occurred in three seasons (5 in winter, 13 in spring, and 2 in summer), and applied aerial (11 burns) and ground (9 burns) ignition techniques. Burning lasted between 1 and 6 h, mostly during afternoon hours. Cloudy conditions appeared for a few burn cases.

Table 1.

Prescribed fire information.

Table 1.

b. Meteorological data

The RAWS observation data at four stations were used. The Fort Benning station has the same location as the corresponding burn site. The Brender station is located near the southwestern side of the Piedmont and Oconee burn sites. Two other stations are Naval Live Oaks by the Florida coast and Open Pond at the Florida–Alabama border, about 60 km west and north of the burn site at Eglin, respectively. The averaged meteorological conditions over the two stations were used for Eglin. The automated measurements include solar radiation, wind speed and direction, wind gusts, air temperature, fuel temperature, fuel moisture, relative humidity, dewpoint, wet bulb, and precipitation. Only wind, air temperature, fuel temperature, fuel moisture (10 h), and relative humidity were used in this study.

In addition, the vertical meteorological profiles at the grid points near RAWS simulated with the Weather Research and Forecasting (WRF) Model (Skamarock et al. 2008) were used to estimate PBL height, transport wind, and the stability factor. The WRF domain covered the southeastern United States with a resolution of 4 km and 27 vertical layers. The Yonsei University scheme for PBL processes was selected, which uses a nonlocal K scheme with explicit entrainment layer and parabolic K profile in unstable mixed layer. The PBL height was defined as the geometric height of a model level where potential temperature starts to increase upward. The stability factor used in this study was defined as the difference in air temperature between the model levels near the ground and at the PBL height (multiplying gravity acceleration and divided by temperature).

Figure 1 shows hourly variations of smoke plume rise and meteorological conditions for each of 19 fires (the fire F2 is not shown because it was only 1 h long). The hourly trends of smoke plume rise are classified into increase, decrease, and flat groups (Table 2). For the increase group, hourly smoke plume rise either increases constantly or fluctuates with time but with an overall increasing trend over the burn period.

Fig. 1.
Fig. 1.

Variation trends of hourly plume rise and meteorological variables, where each panel represents one burn. The x and y axes are hour of the day during a fire and smoke plume rise (m), respectively. The ranges for meteorological variables are between 1 and 5 m s−1 for surface wind speed, 10° and 50°C for fuel temperature, 5% and 15% for fuel moisture, and 600 and 2200 m for PBL height.

Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0114.1

Table 2.

Trends of hourly smoke plume rise and meteorological variables. The signs represent increase (/), decrease (\), and flat with or without fluctuation (−).

Table 2.

Three out of the four variables show consistent trends for the increase group. Fuel moisture reduces with time for all 11 burns, PBL height increases or is flat for 10 burns, and surface wind increases or stays steady for 9 burns. Fuel temperature, however, has mixed trends for these burns. Drying fuel or active PBL favors the development of smoke plume, while increasing wind suppresses the development of smoke plume to a larger degree.

Inconsistency is found mainly for two other trend groups. For the five burns in the decrease group, there are no consistent trends in various variables except for fuel temperature, which decreases with time for four burns. For the three burns in the flat group, there are no dominant trends in all variables.

c. Regression model

We here use index notation in the following way: i = 1, …, I is used to represent a specific hour during a burn case, where I is the length of the burn (h); j = 1, …, J is used to represent a burn, where J is the number of total burn cases; l = 1, …, L is used to represent an element in a smoke plume rise sequence, where L is the sum of I (j); m = 1, …, M is used to represent an individual meteorological variable, where M is the number of variables used to build a regression model; n = 1, …, N is used to represent an individual element in a smoke measurement sequence, where N is the number of elements in a smoke plume sequence; and k = 1, …, N is used to represent new sequences created for cross validation.

A multiple linear regression model for smoke plume rise H can be written as
e1
where b0 is the regression intercept, bm are regression coefficients, and Xm are meteorological variables.

d. Validation

Two approaches were used to validate the model performance. The first one included three analyses based on the regression model and the original smoke meteorological data. The first analysis looks at the statistical significance of regression coefficients and model through t test and F test (Blackwell 2008). The critical value is dependent on M, N, and the selected confidence level. A confidence level of 95% was used, meaning that there is a probability of 5 out of 100 cases that a coefficient or regression model would produce a false result. The second analysis is concerned with errors of simulation with the regression model. Smoke plume rise was simulated using the regression model with the observed meteorological variables as inputs, which produced a simulated smoke plume rise sequence Hsimu(n). The differences with the observed sequence Hobs(n) were measured by mean error (ME) and root-mean-square error (RMSE) to understand the systematic and random errors:
e2
e3
The third analysis compares simulated and observed smoke plume rise using scatterplot with N samples.

The other approach was to use a cross-validation technique (Barnett and Preisendorfer 1987) to validate model prediction skills based on new created data subsets and regression models. A technique traditionally used for model validation is to split samples in original dataset into model development and evaluation subsets. There were only 20 burns available for this study and the sample number would be even smaller after the splitting. Thus, this technique was not used for this study; instead, cross validation, a useful tool for evaluation of a model with limited number of samples, was used. The procedure to conduct this validation is as follows:

  1. Create new smoke plume rise subsets for model formation and evaluation. The model formation subset consists of N new sequences with the element (n, k), where k = 1, …, N. The kth new sequence has the same elements as the original sequence Hobs(n) except that the kth element is removed. Thus, the new sequence has (N − 1) elements. The evaluation subset sequence (k) where k = 1, …, N consists of all the removed elements.

  2. Create new meteorological variable subsets for model formation and prediction from the original dataset (n), where n = 1, …, N using the same technique. The model formation subset consists of N new sequences (n, k), where n = 1, …, N − 1 and k = 1, …, N. The prediction subset consists of a sequence (k), where k = 1, …, N.

  3. Build N new regression models: H(k) = using (n, k) and (n, k), where n = 1, …, N − 1 and k = 1, …, N. Note that the coefficients (m = 0, …, M) here are different from the coefficients in Eq. (1).

  4. Use the new models with (k) as inputs to predict smoke plume rise (k), where m = 1, …, M and k = 1, …, N.

  5. The cross validation was conducted in a categorical way. Here (k) (k = 1, …, N) was categorized into the group of positive anomaly if ≥0.5 SDobs (where SDobs is the standard deviation of the observations), negative anomaly if ≤−0.5 SDobs, or normal if otherwise. The same categorization was made for (k). The sequence was assumed to have a binomial distribution. There was a probability of p = ⅓ for (k) and (k) to be in a same group and a probability of q = ⅔ to be in different groups.

  6. The prediction skill of the regression model is S = Nc/N, where Nc is the number of same group occurrence (correct number). Assuming that the binomial distribution could be approximated by normal distribution, a z score (Blackwell 2008) defined as was used to test the statistical significance of the regression model, together with the p score. The z score is a statistical significance indicator that determines whether to reject a null hypothesis, that is, the analyzed pattern (the simulated plume rise falls into a same group of positive anomaly, negative anomaly, or normal as the observed plume rise) is likely randomly generated. For a critical value zcri, which is 1.95 at the 95% confidence level, the hypothesis is rejected if z score > +zcri (z score > 0) or z score < −zcri (z score < 0). A p value (the probability that the null hypothesis has been falsely rejected) smaller than the corresponding significance level (0.05) was used as another criterion.

Note that a total of N new models were developed that produced N predicted smoke plume rise values in the cross-validation procedure.

3. Meteorological conditions

a. Hourly sequence

RAWS observation data were available hourly. WRF simulation outputs at each hour were used accordingly. Hourly smoke plume rise was obtained by averaging the observed values over each of the individual hours during a burn period. Smoke measurement during the first or final hour of a burn period was usually less than 60 min. The average for the hour was not included in the smoke plume rise sequence if the measurement length was less than 25 min. One exception was the first hour for E5, which had a smoke measurement length of about 50 min, but heavy clouds were on top of the smoke layer and therefore the detected heights by the ceilometer were likely those of the clouds rather smoke plume. For this study, I (j) ranged between 1 and 6 for j = 1, …, J, and J = 20 (Table 1). An hourly smoke plume rise sequence Hhour(l) was formed, where l = 1, …, L and L = 58. The corresponding hourly sequence was formed for each of the meteorological variables.

Figure 2 shows variations of hourly smoke plume rise sequence versus each of the four meteorological variable sequences. The sequence elements were normalized by subtracting each element from the sequence average and divided by the standard deviation (SD). The entire smoke plume rise sequence is composed of five portions, including the negative first (F1–F4), third (from late hours of E1 to early hours of E2), and fifth (from late hours of E6 to early hours of E8) portions, and positive second and fourth portions covering the elements in between two adjacent negative portions. There is an exception with the second portion, which has small negative values at a few hours for O1, O3, and O5.

Fig. 2.
Fig. 2.

Variations of normalized hourly smoke plume rise and meteorological variables: (top) wind, (top middle) fuel temperature, (bottom middle) fuel moisture, and (bottom) PBL height. The minor ticks in the x axis are different hours during a fire. The vertical lines separate various sequence portions.

Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0114.1

Wind and fuel moisture vary in an opposite direction to smoke plume rise. Fuel temperature, on the other hand, follows smoke plume rise closely, despite the difference occurring in the third portion where plume rise is negative while temperature is positive, and from the first portion to the first half of the second portion where both have an increasing trend, but temperature remains negative while plume rise has turned to be positive. PBL height also generally follows plume rise except for the first half of the second portion.

The statistics of the hourly sequence are provided in Table 3. Besides the meteorological variables described above, four other variables (air temperature, air relative humidity, transport wind, and stability factor) are also analyzed for comparison. As indicated below, air relative humidity and transport wind have low correlations with smoke plume rise, while surface air temperature and stability have similar relationships with smoke plume rise to fuel temperature and PBL height, respectively.

Table 3.

Statistics of smoke plume rise and meteorological variables. The notations of avg, SD, and r represent average, standard deviation, and correlation coefficient between plume rise and a meteorological variable.

Table 3.

Fuel temperature and surface air temperature have the averages of 30° and 22.4°C and SDs of 8.6° and 7.4°C, respectively. The correlation coefficients with smoke plume rise are 0.434 and 0.464, which are statistically significant (at the 95% confidence level, same hereafter). The critical value is 0.33. Fuel and air temperature are related to sensible heat energy for smoke plume lifting. PBL height and stability factor have the averages of 1320 m and 0.3 m s−2 and SDs of 385 m and 0.1 m s−2, respectively. The correlation coefficients are around 0.40 and are significant. Similar to smoke plume, the development of PBL and status of atmospheric stability depend on sensible heat from the ground. The surface and transport winds have the averages of 3.0 and 5.7 m s−1 and SDs of 0.83 and 2.5 m s−1, respectively. The correlation coefficients of −0.22 for the surface wind and −0.15 for transport wind are insignificant. Winds make the smoke plume move horizontally and therefore reduce the buoyancy in the smoke area for vertical lifting of smoke plume. Fuel moisture and air relative humidity have the averages of 8.69% and 43.2%, and SDs of 2.13% and 13.2%, respectively. Both are negatively correlated to smoke plume rise with a magnitude of 0.53 for fuel moisture (significant), but only 0.02 for relative humidity (insignificant). Evaporation of water within fuels during burning consumes latent heat, which reduces the sensible heat energy used to lift smoke plume.

b. Average sequence

An average sequence of smoke plume rise, Havg(l) (l = 1, …, L, and L = 20 for this study),was formed, where the lth element is the average of Hhour(l) over the hours I (j) for the jth burn. The corresponding average sequence was formed for each of the meteorological variables. The average sequence shows the same feature as the hourly sequence, but the relationships between average meteorological variables and smoke plume rise are closer (Fig. 3). The correlation coefficients have the same signs for each of the meteorological variables between the average and hourly sequence. The magnitude, however, is larger for the average sequence. The coefficients are 0.683 and 0.874 for air and fuel temperature and −0.583 and 0.582 for fuel moisture and PBL height (all significant; the critical value is 0.56), 0.538 for the stability factor (close to the significant level), −0.422 for surface wind, and −0.234 and 0.201 for transport wind and air relative humidity (insignificant).

Fig. 3.
Fig. 3.

As in Fig. 2, but for the average sequence.

Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0114.1

4. Regression models

a. Reference model

The regression model formed using four meteorological variables (surface wind speed, air temperature, fuel moisture, and PBL height), denoted as RxPrise (prescribed fire plume rise), is described here as a reference model. When selecting predictors, those variables that were insignificantly correlated with plume rise were not considered. Air relative humidity was one of such variables. In addition, considering the close relations between surface wind and transport wind, air temperature and fuel temperature, and PBL height and stability factor, transport wind, fuel temperature, and stability factor were not selected in the reference model to avoid multicolinearity. For the same reason, one variable in each pair of variables was not selected if the other was selected in the alternative models described below. It has two forms for hourly and average smoke plume rise prediction, respectively. The regression coefficients are listed in Table 4. The model for hourly smoke plume rise has an intercept b0 of 1111 m, which is 63 m more than the observed average of smoke plume rise. The regression coefficients b1b4 are −64.95, 5.425, −24.64, and 0.153. The corresponding 95% confidence level intervals are (−116.2, −13.7), (−0.62, 11.48), (−45.0, −4.3), and (0.046, 0.26). The p values are 0.0093, 0.0616, 0.0127, and 0.0035, respectively. Three of the four coefficients are statistically significant at the 95% confidence level, while the one for air temperature is close to the level. Thus, all the four variables are important to smoke plume rise modeling.

Table 4.

Regression models RxPrise and RxPrise-Tf. The quantity b0 is the intercept, and b1b4 are regression coefficients for surface wind (Vsfc), air temperature (Ta) or fuel temperature (Tf), fuel moisture (Mf), and PBL height (HPBL). The lower and upper values are 95% confidence intervals of the regression coefficients.

Table 4.

The reference model for average smoke plume rise has an intercept b0 of 885 m. The regression coefficients b1b4 are −82.56, 11.19, −4.06, and 0.133. The corresponding 95% confidence intervals are (−130.3, −34.8), (5.73, 16.7), (−23.3, 15.2), and (0.022, 0.245). The p values are 0.0035, 0.0095, 0.68, and 0.0298, respectively. All coefficients except the one for fuel moisture are statistically significant at the 95% confidence level. This suggests that fuel moisture is not important to smoke plume rise modeling. The average value of a variable can be used if it is not important to the regression model.

b. Alternative models

Five alternative models were formed. RxPrise-Tf is the same as RxPrise except using fuel temperature instead of air temperature. The model is presented in Table 4 as well. The regression coefficients of the model have similar statistical significance to the corresponding coefficients of the reference model, that is, all meeting the criteria for the 95% confidence level except for the average fuel moisture. However, the coefficient for hourly fuel temperature is insignificant at the 95% confidence level.

RxPrise-SF and RxPrise-Vt are the same as RxPrise except using stability factor and transport wind, respectively, instead of PBL height. Their significance properties, presented in Table 5, are very close to those of RxPrise.

Table 5.

As in Table 4, but for RxPrise-SM and RxPrise-Vt and with regression coefficients for surface wind (Vsfc) or transport wind (Vt), air temperature (Ta), and PBL height (HPBL) or stability factor (SF).

Table 5.

RxPrise-sfc and RxPrise-Tf-sfc are the same as RxPrise and RxPrise-Tf, respectively, except only using the three surface variables. The first two regression coefficients are statistically significant at the 95% confidence level (Table 6).

Table 6.

As in Table 4, but for RxPrise-sfc and RxPrise-Tf-sfc.

Table 6.

c. Errors

Simulations with the reference model as well as the alternatives were conducted. The errors were obtained through calculating the differences between the simulated and the observed smoke plume rise. Table 7 shows errors and statistical properties of these models. For hourly modeling, RxPrise has a small systematic error of ME = 4.6 m, which is about 2.5% of the SD value. But it has a large RMSE value of 141 m, which is 75% of the SD value. The squared correlation coefficient is 43% with an adjusted value of 39%, meaning the simulated smoke plume rise explains less than one-half of the observed smoke plume rise variance, though the regression model is significant at the 95% confidence level.

Table 7.

Model errors and statistical significance. Here R2 and are squared regression correlation coefficient and adjusted value by sample numbers.

Table 7.

RxPrise for average smoke plume rise modeling has a systematic error of ME = 9.6 m (about 6% of the SD value) and random error of RMSE = 69 m (about 44% of the SD value). This indicates an increased systematic error but decreased random error in comparison with the hourly plume rise modeling. The squared correlation coefficient is 75% with an adjusted value of 69%, meaning the simulation explains about three-fourths of the observed smoke plume rise variance, which is much improved over the hourly modeling. The regression model for average smoke plume rise is significant at the 95% confidence level.

RxPrise-Tf, RxPrise-SF, and RxPrise-Vt have comparable variance contributions to RxPrise, differing by 1% for hourly modeling and 4% or smaller for average modeling. The contributions from RxPrise-sfc and RxPrise-Tf-sfc, however, are up to 10% for hourly modeling and 7% for average modeling smaller than those from RxPrise. This suggests that the modeling accuracy is increased considerably by using the information on atmospheric PBL. Besides the fact that a regression model will increase the contribution to total variance of the simulated sequence with an additional variable, PBL height is a good indicator for PBL development; after smoke particles are released from fire, the rise of smoke plume largely depends on PBL conditions.

Figure 4 compares the simulated smoke plume rise using RxPrise and RxPrise-sfc with the observed plume rise [the first model validation approach described in section 2d (model validation)]. A model overestimates, exactly estimates, or underestimates an observed plume rise, respectively, if the corresponding point is located above, on, or below the line with a unit slope. For the simulation of hourly plume rise with RxPrise or RxPrise-sfc (Fig 4, top), there are comparable numbers of points located above and below the line. The overestimated values largely offset the underestimated ones, leading to the small modeling systematic error as described above. However, the models tend to underestimate smoke plume rise when the observed smoke plume rise is large and overestimate it when the observed rise is low. This indicates a limitation in the model’s capacity in predicting extreme smoke plume rise. This limitation is more noticeable for RxPrise-sfc. However, because the extremes occur less often in the average sequence, the models have much improved capacity in simulating the average smoke plume rise (Fig 4, bottom) than the hourly rise.

Fig. 4.
Fig. 4.

Scatterplots of the hourly and average observed (x axis) vs simulated smoke plume rise using RxPrise and RxPrise-sfc (y axis). The quantity R2 is the unadjusted squared correlation coefficient.

Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0114.1

The complex control of the meteorological conditions on smoke plume rise could be one reason for the limitation. For example, in the model developed by Briggs (1975) based on laboratory measurements of stack plume, plume rise is proportional to under a stable condition. In comparison with this relation, a linear relation such as RxPrise would predict a slower increase (decrease) in smoke plume rise with decreasing (increasing) wind speed. This would lead to an underestimate (overestimate) of actual large (small) plume rise.

d. Cross validation

Using the second model validation approach described in the data and methods section, smoke plume rise at each of the individual hours and the average over a burn period was “predicted.” Figures 5 and 6 show the hourly and average smoke plume rise predicted using RxPrise and RxPrise-sfc, respectively. As described in the data and methods section, new data subsets were created for model formation and evaluation with the cross-validation procedure. The validation subset had a sample number of L = 58 for the hourly plume rise and L = 20 for the average plume rise sequence. It can be seen that RxPrise is able to produce the observed hourly high plume rise (peak values) during F6, O3–O5, P1, and E5 and the low rise (valley values) during F1, O1, O4, E3, and E7–E8. However, it misses the large values during O2 and E2 and the low values during F3, F4, O1–O2, O5, and E2. The predicted smoke plume rise with RxPrise-sfc has more values falling closer to the normal category. Meanwhile, the predicted average smoke plume rise follows the observed one very well. RxPrise is able to produce the observed high plume rise values for F4–F6, O2–O3, O5, and E4 and the low rise values for F1 and E6. However, it misses the high rise value for F3. In comparison, the prediction with RxPrise-sfc differs more from the measurement for most burns.

Fig. 5.
Fig. 5.

Hourly smoke plume rise (normalized) from observations and predictions by RxPrise and RxPrise-sfc. The values for the same burn are connected by lines. The three horizontal lines indicate smoke plume heights at the average and plus or minus one-half standard deviation, respectively.

Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0114.1

Fig. 6.
Fig. 6.

As in Fig. 5, but for the average smoke plume rise.

Citation: Journal of Applied Meteorology and Climatology 53, 8; 10.1175/JAMC-D-13-0114.1

The cross-validation results for RxPrise are provided in Table 8. The predicted sequence has 20, 18, and 20 elements in the positive anomaly, negative anomaly, and normal groups, respectively. The corresponding numbers for the observed sequence are 16, 19, and 23. The correct number is 33 out of total 58 elements, leading to a prediction skill of 56%. The corresponding z score is 3.81, which is greater than the critical value at the 95% confidence level. The p score is 0.0001, which is smaller than the critical value of 0.05. Thus, the model is statistically significant. The predicted average sequence has 8, 6, and 6 elements in the positive anomaly, negative anomaly, and normal groups, in comparison with the numbers for the observed sequence of 7, 5, and 8. The correct number is 14 out of total 20 elements, leading to a prediction skill of 67%. The corresponding z score is 3.48 and the p value is 0.0005, both of which are significant.

Table 8.

Cross validation for smoke plume rise predictions with RxPrise, RxPrise-sfc, and RxPrise-Tf-sfc. Here G1, G2, and G3 are the numbers of smoke plume rise elements occurring in positive anomaly, negative anomaly, and normal groups; Nc is the correct number; and S is correct percent.

Table 8.

For the prediction of hourly smoke plume rise with RxPrise-sfc, the correct number is only 23 out of 58 elements, leading to a low skill of 40% with a z score of 1.02 and p score of 0.308, both of which are insignificant. For the prediction of average smoke plume rise, the correct number is 10 out of 20 elements, leading to a skill of 50% with a z score of 1.58 and p score of 0.114, both of which are also insignificant. Thus, this alternative model has no statistical skills.

However, things will change if replacing Ta with Tf. The z score and p score for RxPrise-Tf-sfc are 2.69 and 0.007 for hourly plume rise prediction and 3.0 and 0.003 for average plume rise prediction, all are significant at the 95% confidence level.

5. Discussion

  1. A regression model as well as its alternatives with statistical significance has been formulated to provide a practical tool for fire managers to estimate plume rise of prescribed burns. To further understand the value of the regression model, the results from the model were compared with the preliminary results from Daysmoke (Liu et al. 2010) and the FEPS plume rise scheme (the modified Briggs scheme) in simulating the average plume rise sequence of the 20 prescribed burns. The results from the two empirical models will be described in detail in Y.-Q. Liu et al. (2013, unpublished manuscript). The ME and RMSE are −5.6 and 94 m for the regression model, 19 and 281 m for Daysmoke, and 184 and 765 m for the FEPS scheme. Thus, the regression model has much smaller errors for the specific burn cases. The FEPS scheme was found to overestimate plume rise for most burn cases. The reasons are yet to be investigated. One possible reason is that the scheme does not distinguish between wildfires and prescribed fires, but some model parameters may be more appropriate to wildfires than prescribed fires. For example, the heat release rate in the scheme is 8000 Btu lb−1 [1 Btu (British thermal unit) ≃ 1055–1060 J; 1 lb ≃ 0.45 kg], which is about 20% higher than the average value suggested for prescribed burns in the South (Southeastern Forest Experiment Station 1976).

  2. The role of fire behavior, another primary factor often used in empirical smoke plume rise models, could have been indirectly included in the regression models because the meteorological conditions used in this study can impact fire behavior. It is expected that skills of the regression models would be improved by directly incorporating heat release, updraft core number (Liu et al. 2010; Achtemeier et al. 2011), and other important information provided from fire behavior simulation and measurement. Topography is another factor for smoke plume rise. For the prescribed fires conducted in the northwestern United States (H. Harrison and C. Hardy 2002, unpublished manuscript; available online at http://www.atmos.washington.edu/~harrison/reports/plume3.pdf) for example, the burn sites were predominantly located on the lateral slopes of alpine river valleys. The upvalley thermal winds were locally amplified by heat release from the fires. The plumes did not rise solely from thermal buoyancy, but were significantly accelerated by upvalley convergence of horizontal winds.

    The approach of not directly using fire-related factors in the regression model does not mean that these factors are less important for smoke plume rise prediction. They were not used because the primary purpose of the regression model was to provide a practical tool for fire manages. This type of approach has been widely used in statistical weather forecasting. For example, precipitation is determined by dynamic lifting mechanism (vertical velocity), thermal instability, and water vapor supply. Some statistical precipitation forecast models only use the last two factors. This does not mean that the first one is less important; it is not used often because of the difficulty in obtaining a quality value for the factor. This makes the models only using the last two factors a more practical tool for meteorological managers and users.

  3. Empirical smoke plume rise models are easy to use and computation effective. With observed or predicted fire and meteorological conditions, the models are able to provide speedy plume rise information for air quality models (AQM). One of the issues with the models for prescribed burning is the possible low accuracy. For the FEPS scheme, which is one of the two plume rise schemes used by the U.S. Environmental Protection Agency CMAQ model, may sometimes lead to large errors for prescribed burns, as shown above.

Other techniques for plume rise also have both advantages and disadvantages. Dynamic plume rise models are a more complete description of physics and have been used in some AQMs such as “WRF-Chem.” The models, however, usually include many parameters that need to be empirically specified or parameterized. The models themselves need temporal integration and therefore present a speed disadvantage in comparison with empirical models. The complexity and time costs present an issue for fire managers.

Plume rise measurements are needed for model development and evaluation. However, they have a timing issue for AQM. They only provide information while the measurements are being taken, but not at later times, which is also needed by AQM. Satellite measurements have a limited frequency and a specific time when passing over a specific location, and therefore they often miss a large number of prescribed burns, which often have very short burning periods. Also, satellites have difficulty detecting small prescribed burns, especially if they occur in the understory, while ground measurements are too expensive to be installed at every burn site across a region.

Thus, any specific model or technique, including the model developed in this study, could provide more useful plume rise information than other models or techniques for AQM only under certain specific circumstances. The regression model developed in this study is expected to be a practical tool for fire managers and also a useful tool for AQM, with improved skill in plume rise prediction for prescribed burns.

6. Conclusions

A regression model for smoke plume rise has been developed and validated using the observed smoke plume rise of 20 prescribed fires in the southeastern United States, together with observed and simulated meteorological conditions near the burn sites. The model’s ability to predict a plume rise category was statistically significant, although it underestimates large plume rise and overestimates small plume rise. The model can be used to simulate plume rise for individual hours during a prescribed fire or averaged height over the burn period. The model showed more capacity in explaining the observed variance of the average than hourly smoke plume rise. The model skill was found to be improved by adding PBL height information to RAWS variables. If no PBL information is available, an alternative model using surface wind, fuel temperature, and moisture can be used.

The RAWS measurements used in the model are easily obtained by fire and land managers. Thus, the regression model could be a practical tool for them. The regression model also showed improved skill over some existing empirical models for the observed prescribed burn cases. This suggests that it may have the potential for improving air quality modeling. Further evaluation for other regions, however, should be conducted to understand how robust the model’s performance is.

Acknowledgments

The author thanks Sanjeeb Bhoi for conducting WRF simulations, colleagues and field managers for collecting the ceilometer measurements, and four reviewers for their constructive comments and suggestions. This study was supported by the Joint Fire Science Program under Agreement JFSP 081606, JFSP 11172, and NIFC2013-35100-20516. The National Center for Atmospheric Research (NCAR) Command Language (NCL) was used for the regression analysis.

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