RUBY CANYON ENGINEERING ∙ Grand Junction, Colorado 1

Evaluating Possible VAM Emissions Estimation Errors Based 

On Different Sampling Intervals (Quarterly, Monthly, Weekly)

Introduction

Currently, most coal mines reporting ventilation air methane (VAM) emission rates to MSHA are 

reporting using quarterly samples - the minimum required frequency for calculating GHG 

emissions to Subpart FF. The mines can use either their own or MSHA data samples to represent 

the average VAM rate for each quarter, and subsequently the annual emissions for the year. 

However, mine-specific daily and weekly data sets show that significant day-to-day and week-toweek variability can exist. Based on available high-frequency datasets (hourly or weekly) of VAM 

emissions, RCE set out to examine the uncertainty associated with using weekly, monthly, and 

quarterly data sampling based on using a random day selection approach. Based on the analysis, 

RCE determined that there appears to be a significant reduction in the uncertainty of the actual 

VAM rates when going from quarterly to monthly, and from monthly to weekly sampling.

Mine A Data

For Mine A, RCE used daily emission rates from a moderately gassy mine (avg. ~2.5 mmcfd) 

over a one year period. The variation in the methane content was significant. Figure 1 displays 

the VAM flow rate.

Figure 1: Variation in methane rate at Mine A
RUBY CANYON ENGINEERING ∙ June 10, 2015 2

Figure 2 illustrates that the variation of the VAM is mostly attributable to the variation in the 

methane concentration as opposed to the fan volumetric rate, which tends to be nearly constant, 

as the methane content trends very close to the overall VAM emissions rate.

Figure 2: Variation in VAM Rate and methane concentration

Mine B Data

For Mine B shown in Figure 3, RCE had access to the weekly VAM and methane concentration 

data from a very gassy mine (avg. ~10.1 mmcfd). 
RUBY CANYON ENGINEERING ∙ June 10, 2015 3

Figure 3: VAM rate and for Mine B

Mine C Data

For Mine C shown in Figure 4, RCE had access to weekly VAM and methane concentration data 

from moderately gassy mine (avg. ~3.6 mmcfd). 

Figure 4: VAM rate for Mine C
RUBY CANYON ENGINEERING ∙ June 10, 2015 4

Sampling Analysis

Because any real measurement taken to determine the VAM emissions rate occurs on a single 

day (regardless of being a weekly, monthly or quarterly sampling interval), RCE used a random 

number generator to select a day of the week, month or quarter and the corresponding flow or 

methane concentration value in the high frequency data sets. The datasets used for Mine A were 

daily and weekly for Mines B and C. As a result, for Mine A, RCE randomly selected a day of the 

week to represent weekly sampling, a day in the month for monthly sampling and a day in a 

quarter for quarterly sampling. For mines B and C, RCE randomly selected a week of the month 

for monthly sampling and a week of the quarter for quarterly sampling. Every iteration, using the 

random number generator, produces a different result because different time periods (days or 

weeks) are randomly selected within each sampling interval. RCE repeated this method with fifty 

iterations capturing the average VAM rate for each sampling interval over the entire one year data 

set

For Example:

Table 1 shows the results of five iterations of the averaging process for Mine A where the average 

of the daily emissions of 2,520,970 cf/d represents the “actual” methane emissions, and the other 

sampling intervals represent estimates based on the day randomly selected for the sampling.

Table 1: Results of five iterations of the randomly selected days with in a sampling interval, cf/d

Iteration Daily Weekly Monthly Quarterly Delta Wkly Delta Mthly Delta Qtly

1 2,520,970 2,518,376 2,612,805 2,024,167 -2,594 91,835 -496,802

2 2,520,970 2,490,179 2,712,553 2,658,489 -30,790 191,583 137,519

3 2,520,970 2,505,678 2,496,782 2,236,758 -15,292 -24,188 -284,212

4 2,520,970 2,556,666 2,298,133 2,968,794 35,696 -222,837 447,824

5 2,520,970 2,484,333 2,562,171 2,364,823 -36,637 41,201 -156,147

For iteration 1, RCE randomly selected a day to represent the weekly, monthly and quarterly 

average VAM rate measurements within the year. The difference from actual was -2,594, 91,835 

and -496,802 cubic feet per day for weekly, monthly and quarterly random selections respectively. 

Results

Figures 5 and 6 illustrate the variance in data sample measurement for all 50 iterations for Mine 

A. Figure 5 shows the actual values calculated while Figure 6 shows the difference from the actual 

value in terms of percent difference.

Note that the distribution around the actual value (2,520,970 cf/d) in Figure 5 corresponds to the 

zero values line on the x-axis in Figure 6. The results clearly show the deviations associated with 

the quarterly samples are greatest and the weekly samples the smallest. 
RUBY CANYON ENGINEERING ∙ June 10, 2015 5

Figure 5: Deviation from actual VAM rate based on sampling interval for Mine A
RUBY CANYON ENGINEERING ∙ June 10, 2015 6

Figure 6: Deviation from actual expressed as the percent difference for Mine A.

RCE repeated a similar analysis for Mines B and C. For these mines, RCE considered the daily 

average of the VAM emissions based on weekly data to be the “actual” VAM rate or 10,115,000 

cf/d for Mine B and 3,627,000 cf/d for Mine C. Unlike Mine A, RCE did not have hourly/daily 

measurements for Mines B and C. Figures 7 and 8 show the percent difference from actual VAM 

rate for both mines over a 12 month period.
RUBY CANYON ENGINEERING ∙ June 10, 2015 7

Figure 7: Deviation from actual expressed as the percent difference for Mine B.

Figure 8: Deviation from actual expressed as the percent difference for Mine C.
RUBY CANYON ENGINEERING ∙ June 10, 2015 8

RCE conducted a statistical analysis of each mine’s 50 iterations to determine the maximum 

possible error and the uncertainty at one standard deviation. Table 2 shows the lowest and highest 

estimated divergence from the actual value for the three mines. The results show that the possible 

maximum errors (for both low and high ranges) decrease as the sampling frequency increases.

Table 2: Minimum and maximum errors possible based on 50 iterations 

Mine Frequency Actual Value Min Value Max Value % Change Min % Change Max

Mine A

Weekly 2,520,970 2,440,029 2,617,762 -3.2% 3.8%

Monthly 2,520,970 2,269,133 2,790,904 -10.0% 10.7%

Quarterly 2,520,970 1,797,452 3,060,237 -28.7% 21.4%

Mine B Monthly 10,114,965 8,775,116 11,007,874 -13.2% 8.8%

Quarterly 10,114,965 6,751,170 13,667,846 -33.3% 35.1%

Mine C Monthly 3,627,287 3,265,747 3,944,719 -10.0% 8.8%

Quarterly 3,627,287 2,447,102 4,374,362 -32.5% 20.6%

Table 3 shows the average daily VAM emission rate for each mine using either the 4, 12, 52, or 

365 data samples. Table 3 also show the standard deviations for each case. Again, the results 

show that the range of uncertainty decreases as the sampling frequency increases.

Table 3: Average and standard deviation of the 50 iterations

Mine Frequency Average (cf/d CH4) Std Dev (cf/d CH4) Std Dev/Avg

Mine A

Daily (Actual) 2,520,970 0 0.0%

Weekly 2,525,366 40,503 1.6%

Monthly 2,510,417 137,519 5.5%

Quarterly 2,561,020 310,658 12.1%

Mine B

Weekly (Actual) 10,114,965 0 0.0%

Monthly 10,098,118 521,609 5.2%

Quarterly 9,646,562 1,450,069 15.0%

Mine C

Weekly (Actual) 3,627,287 0 0.0%

Monthly 3,601,455 155,361 4.3%

Quarterly 3,539,308 474,720 13.4%
RUBY CANYON ENGINEERING ∙ June 10, 2015 9

Conclusions

Using VAM emissions data recorded daily and weekly from three underground coal mines (one 

with daily sampling and two with weekly sampling), RCE analyzed the average daily VAM 

emissions rate by randomly selecting the sampling day or week during a 12 month reporting 

period. Each case was run for a weekly, monthly, and quarterly sampling frequency over a 12 

month reporting period. 

For Mine A, the results showed that weekly sampling produced a small standard deviation of 1.6% 

compared to daily sampling. For all 3 mines, the results showed the standard deviations increased 

to 4.3-5.2% when sampling frequency decreased from weekly to monthly sampling. Finally, the 

results showed the standard deviations increased to 12.1-13.4% when sampling frequency 

decreased from monthly sampling to quarterly sampling. Due to the day-to-day variability in VAM 

emissions, ranges of maximum possible errors are also greater with decreased sampling 

frequency. Deviations from the actual; value for monthly sampling ranged from 8.8-10.7%, while 

deviations for quarterly sampling ranged from 20.6-35.1%.