v 
variation, which is generally larger, penetrates to greater depths 
than the diurnal wave. These depths vary but are usually of the 
order of tens of centimetres for the diurnal wave and a few metres 
for the annual wave. It was decided that temperature data from 
just below the surface should be gathered for selected fires to 
allow the thermal models to be developed and tested. This was 
made one of the main aims of the field campaign in the Xinjiang 
test areas carried out in August and September of 1995. 
2.2 Field Temperature Measurements 
The first important task was to determine the depth to which the 
diurnal temperature variations penetrated in the test area soil. 
Two of the fires in the Kelazha area were chosen for particular 
study. A portable weather station was then set up about 1 km 
from the nearest fire. The weather station included equipment for 
making soil temperature measurements and we first wanted data 
that were not influenced by the fires. Soil temperatures were 
gathered at depths of 2, 4, 8, 16, 32 and 64 cm for a period of 
about four-and-a-half days. Measurements were made every ten 
minutes and were stored using a data logger. It was observed that 
there was virtually no temperature variation at a depth of 64 cm 
throughout the measurement period and there was only a very 
slight variation at 32 cm. At the shallower depths the temperature 
wave was more significant. This suggested that soil temperature 
measurements made at depths of more than about 30 cm, in a 
similar soil, would be almost unaffected by the diurnal 
temperature variation. It was more important to consider the 
diurnal rather than the annual temperature variation at this stage 
because only the diurnal temperature variation would produce a 
significant change in temperature over the measurement period. 
Measurement grids were marked out at the two coal fires. The 
sites were obviously close to active fires - smoke and sulphurous 
deposits on the ground were clearly visible - and rough surveys of 
surface temperatures had been made with a hand-held radiometer 
to determine the approximate location of the associated thermal 
anomalies. At the first fire, known as fire 141, the grid measured 
30 m by 30 m; at the second fire, fire 143, 15 m by 15 m. 
Temperature measurements at depths of 30 and 50 cm were made 
every 5 m at fire 141 and every 3 m at fire 143. The size of the 
grids was limited by the extent of the areas that had fairly constant 
slope and soil characteristics. The temperature measurements 
were made at two depths so that the temperature gradient at each 
point could be estimated. As discussed above, 30 cm was about 
the minimum depth that the measurements could be made at. It 
would have been preferable to measure at slightly greater depths 
but this was not practical because of the hard ground. 
2.3 Dip Angle Model 
Several authors of coal fire studies (e.g. Mukherjee et al., 1991, 
Bhattacharya and Reddy, 1994) have made use of the equation of 
linear heat flow in a semi-infinite medium (Carslaw and Jaeger, 
1959) for estimating either the depth or temperature of an 
underground fire. Knowing, or estimating one of these quantities 
allowed the other to be calculated. In their study, Saraf et al. 
(Saraf et al., 1995) calculated the depth of a fire by assuming that 
the fire lay directly below the observed surface temperature 
anomaly, measuring the distance of this anomaly to the nearby 
coal outcrop and measuring the dip angle of the coal seam. The 
depth of the coal, and of the fire, followed from simple 
trigonometry. 
For both Kelazha test sites, the distance of the nearest coal 
outcrop to the corner of the test grids was measured and the dip of 
724 
the appropriate coal layer was estimated through general 
observations of the area's geology. (The rocks were well- 
exposed in this semi-desert area.) This allowed an estimate of the 
depth of the coal below each measurement point to be made. 
The equation of linear heat flow really applies to non steady-state 
conditions and requires an estimate of the age of the heat source. 
We assumed, instead, that steady-state heat conditions were 
applicable and made use of our temperature gradient 
measurements. 
The ‘raw’ temperature gradients measured at the two fires were 
corrected for the influence of the solar heat flux using the weather 
station data, to give an estimate of the true vertical heat flux due 
to the fires. Multiplying the temperature gradients by the 
appropriate coal depths and adding them to the observed 
temperatures produced corresponding grids of supposed ‘fire 
temperatures’, directly below each grid point. 
For both fires, the calculated temperatures were far above what 
would be expected for burning coal. Coal burns at temperatures 
of up to around 2000 °C (ARSC, 1989); the calculated 
temperatures were of the order of several thousand degrees. The 
reason for the discrepancy was probably that this model was too 
simple and made too many assumptions. The heat flow was 
assumed to be one-dimensional only, the medium through which 
the heat flowed homogeneous and the coal seam dip constant with 
depth. In addition, many cracks through which hot gases were 
escaping were observed, suggesting that a considerable amount of 
heat was being transferred to the surface by convection rather than 
conduction. The results suggest that this ‘dip angle’ model is not 
a suitable approach to the modelling of these fires. 
2.4 Radial Heat Flow Model 
A more sophisticated approach was developed based on the 
following idea. For one (near) surface temperature measurement, 
there is an infinite range of possible distances to the fire from this 
point and of fire temperatures. However, the grids of temperature 
measurements made in the field constrain the number of possible 
solutions; they are, in fact, boundary, conditions. 
For the case of spherically symmetric heat flow around a point 
heat source, the total heat flow, H, across any surface surrounding 
the heat source is given by 
H = —k4nr’ «T 
(Equation 1) 
dr 
where k is the thermal conductivity, T is the temperature and r is 
the distance from the heat source. This leads to the results (Sears 
et al., 1982) 
— Ankab (T: — T1) 
H (Equation 2) 
b-a 
and 
T=T2-— b(r-a) (- T) (Equation 3) 
r(b-a) 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996 
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