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Heat balance at gravel and pavement surfaces Inuvik
Williams, G. P.
DIVISION OF BUILDING RESEARCH
HEAT BALANCE AT GRAVEL AND PAVEMENT SURFACES
INUVIK
by
G.P. Williams
!'.NALYZEO
Internal Report No. 399 of the
Division of Building Research
OTTAWA September 1972
HEAT BALANCE AT GRAVEL AND PAVEMENT SURFACES
INUVIK
by
G. P. Williams
Ground temperatures have been measured for several years at various depths in the gravel pad on which the Inuvik airport is
constructed. These measurements were undertaken by the Division's
Northern Group to determine the effect of the pad on the permafrost
underlying the gravel. More temperature sensors were installed in
the summer of 1969 when the runways were paved. At that time the
author agreed to make some preliminary calculations of the surface energy balance of the gravel and pavement to assess the effect of
paving on the ground thermal regime. This report records the basic
data used in these calculations. the calculation procedure, and a discussion of the results.
ESTIMATING THE TERMS IN THE HEAT BALANCE EQUATION
Heat transfer to or from a surface can be expressed as a simple heat balance equation:
Q ±Q ±Q ±Q
=
±Qsw £w c e s
where Q
=
net short-wave radiationsw
Q £w
=
net long-wave radiationQ c Q e Q s
= convective heat (sensible) = evaporative heat (latent)
= heat conducted to or from the surface from the
If all the terms on the left-hand side of the equation can be measured or calculated then the heat transferred to or from the soil
can be estimated. The effect on Os' of any change in surface
con-ditions such as paving a gravel surface, can also be evaluated if the various terms in the equation can be calculated with sufficient accuracy. The fundamental basis of the energy balance approach to ground thermal problems is unchallenged; the challenge is the ability to measure or estimate all the quantities needed to exploit the principle.
0sw' the net short-wave radiation term, can be calculated with
good accuracy if solar radiation records are available and the albedo
of the surface is known. The following formula was used in this study:
°
sw = Rsw2
(lOa-a) cal/cm /24 hr.
where R
=
incoming short-wave radiation(cal/cmL./24 hr.>sw
a
=
albedo or per cent of R reflectedsw
The albedo of gravel was assumed to average 11 per cent
over the summer months. The albedo of snow cover on the packed
gravel during the winter was assumed to equal 60 per cent, except
during the melt period when it was assumed to equal 50 per cent. The
albedo of the pavement was assumed to be only slightly higher than that of the gravel; check measurements verified this assumption. Figure 1 shows the two radiometers used for measurements of the
paved runway and gravel shoulder at Inuvik in October 1969. As
albedo varies with weather and the condition of the pavement or gravel further measurements would be useful.
°
tw
was calculated using Swinbank's formula (1). for clearsky long-wave radiation and Budyko's formula (2) for cloudy
condi-tions. The emissivity of the ground surface was assumed equal to
unity. The formula requires that air temperature, surface
tempera-ture and per cent cloud cover be known. The essential parts of the
Q t w (net) Q = -14.7
+
t w (in) clear sky -3-=-J.Q. t
- Q w (in)t
w (out)'\' 4 2 71.7 (J T cal/cm /hr a (1)T
=
Screen Air Temp (0 C)a
cloudy sky
where C = coefficient varies with latitude
N =
%
cloud coverQ = 60 (J T4
t w (out) s
where T
=
Surface Temp (OC)s (J
=
Stefan-Boltzmann Constant ( 2) Q ( )= 14.7+
60 (J T 4 - 71.5 (J T 4 cal/cm2/24hr tw net s a clear sky = 14. 7 - 11. 5 (J T: J if T a = T sI
4 2 (*o
T in cal/cm /rnin) a Q n ( ) = (14. 7 - 11. 5 (J T 4) (1 - C N2) セキ ョセ a cloudy if T=
T a s C = .81 (Budyko (2) )>:< Tables (J T4 by C. J. Shirtliffe and D. G. Stephenson (NRC 5947,
Adjustment if T a ± 240 a T3 a T s T s
>
T
a 2 c al Zcm /hrT
s <T
a+
Q c was calculated using the following simple formula pro-posed by Budyko (2): Q = 14.7 (T c a T ) 1. 2 cal/cm 2 /24 hr s
where T = air temperature (0C)
a
T = surface temperature (OC)
s
This formula assumes that sensible heat flux changes only slightly with changes in wind speed in the moderate to low wind speed regions
and super adiabatic temperature gradients. It agrees reasonably well
with the formula proposed byMichel (3) for wind speeds from 5 to 10 mph.
Qe' the heat loss from evaporation, was ignored in this study. It was assumed that in the summer most of the moisture would either
run off or penetrate the gravel pad. Sublimation from the snow cover
can represent a considerable heat loss over the winter, but in these trial calculations it was neglected.
Qs' the heat transferred into or out of the ground, was obtained by solving the heat balance equation, after the other terms had been calculated.
CALCULATION OF SURFACE HEAT BALANCE FOR GRAVEL
The different components of the heat balance equation were calculated for a gravel surface on a monthly basis from 1959 to 1968, using available weather records from the Inuvik meteorological
station. Tables 1 and 2 show monthly average values of air
tempera-ture, dew point temperatempera-ture, wind speed, solar radiation, relative humidity and mean cloud cover used in the calculations.
-5 ..
The monthly averages of the terms calculated for
sur-face heat balance were averaged for the summer and winter periods. Summer was considered to be from May 1 to September 30; winter
from October 1 to April 30. This averaging was necessary
because the formulae are only suitable for calculating the compo-nents of the heat balance on a long-term basis i. e., for several months or years.
The average surface temperature is required for calcula-tion of OJ, wand 0c and it was necessary to assume values for it
for the summer and winter periods for each year. Several surface
temperatures were assumed for each period and a complete heat balance calculated for each of them, yielding different values for
Os. These calculated values were then compared with Os for the
corresponding period calculated from average measured changes in ground temperature and assumed values for the thermal properties
of the gravel (volumetric heat capacity and latent heat of fusion). The
surface temperatures that gave the most agreement between the values of Os were assumed to be the appropriate ones for the heat balance calculations, and are shown in Tables 3 and 4.
It quickly became evident by this trial and error method that unless reasonably accurate values of surface temperature were available the heat balance method of determining Os would not produce reliable
results. The calculations were continued, however, as it was
con-sidered that it might be of value to establish a calculation procedure and approximate values for the heat balance terms for future analysis.
Table 3 shows the calculated components of summer surface
heat balance. The 9-year average of the components of the surface
heat balance are as follows:
2
o
= +337 cal/cm /24 hr sw °J,w = -181"
"
"
"
o
= -103"
" "
"
co
= -53"
"
"
"
sIn order to obtain this balance it was necessary to assume that the
average surface temperature exceeded the average air temperature by 5. 1°C.
Table 4 shows the calculated components of the winter
sur-face heat balance. The 9-year average of the components of the
surface heat balance were calculated to be:
2
0
=
+42 cal/cm /ZA hr sw°.tw
=
-156"
"
"
0
=
+82"
"
"
c0
=
+32"
"
"
sIt was necessary to assume that the average snow surface
temperature was 4. 2°C colder than the average air temperature.
The assumed average ground air temperature difference for the summer period was compared with differences obtained by
estimat-ing surface temperature from ground temperature profiles. The average
ground temperatur e for each 5 -month summer period was estimated by plotting average ground temperatures at the 2-, 4- and 6-ft depths
and extending the plotted line to the surface. Table 5 shows the
average T a and T s obtained for the periods analyzed. The average
difference HセtI of +3. 4°C obtained by this method compares
reason-ably well with the average difference of +5.1 °e used in the heat balance calculations.
The estimated average surface temperature of the gravel during the 7 -month winter period was obtained by extrapolation of ground temperature profiles (T s 1 ) (the same approach as that used for the
summer period). Another value for surface temperature (T s 11) was
obtained by equating the calculated heat flow from heat balance calcula-tions for each winter period (Os) (Table 4) with the average heat flow
through the snow cover i. e. ,
o
=
ks
(T _ TIl)
s s
D
where k = thermal conductivity of the snow
T s
7
-=
average snow surface temperature during a winterseason used in heat balance calculations
and T 11, the average gravel-snow interface temperature, is
the only Jnknown in the equation. The calculated average surface
temperature (T 11) for a 7 -year leriod was -17.9° C compared with an average valuse of -19. 5°C (T s ) obtained by extending ground temperature profiles (Table 6).
The agreement between average surface temperatures obtained by the two methods is reasonable and suggests the heat balance equa-tions are reasonably representative of surface heat exchange at Inuvi.k. The many uncertainties associated with the calculations, however, make more sophisticated calculations of doubtful value.
COMPARLSON OF HEAT BALANCE FOR GRAVEL PAD AND PAVEMENT
Generally the same method of calculating the components of the heat balance was used to obtain the comparison of heat balance
terms for gravel and paved surfaces shown in Table 7. These
results, prepared for a seminar on the permafrost active layer in 1971 (4), are presented as a basis for discussion, rather than as an accurate comparison of the heat balance for these two surfaces.
No ウゥセゥヲゥ」。ョ」・ can be attached to the calculated difference
of 300 callern Iyear between Q 1 and Q . This is much les s
than the error expected in
qウキセ
the onflterm whose accuracy can beassessed. An error of 1°C in the assumed value of surface
tempera-ture changes the calculated value of Q c or Q.£,w by 2, 000 to 3, 000 cal/cm 2 over a 5-month period.
In making these calculations several points became apparent
that might be of value in future analysis.
(1) There does not appear to be much difference in the amount
of short-wave radiation absorbed in the summer by gravel and paved
surface. More short -wave radiation is absorbed by pavement in
winter because its albedo is low compared with that of compacted
snow over gravel. The difference should be particularly noticeable
during the spring melt period when incoming short-wave radiation
surfaces (+4,700 to +14,000 calories), can be largely offset by differences in heat lost or gained by convection.
(2) The snow cover on the gravel surface is a major factor
in the surface heat balance, not only affecting radiation but also the
rate at which heat can be lost from the ground. Evaporation from a
snow cover over a 7 -rnonth period might be of significance in the total surface heat balance.
(3) The pavement will prevent water from penetrating the
underlying gravel, tending to reduce the moisture content of the soil. This should decrease the amount of latent heat released in freezing and thawing, which suggests that the paved pad will freeze deeper but thaw faster.
(4) Other factors such as the formation of hoar frost under
strong cooling conditions and the effect of roughness of the gravel on the albedo at low sun angles need to be considered in the heat
balance at these two surfaces. Even the direction of the wind
(L e., whether it blows from the cleared forest area directly across
the gravel or first passes over the pavement) may be of significance.
(5) In studies of this kind the need for a method for determining
the surface temperature is most apparent. It is interesting to note that
the relationship between solar radiation and air-surface temperature difference proposed by Gold (5) agrees with the values obtained from
these heat balance calculations for the summer period. Solving for
t:.T, Gold's equation, 19.7 (t:.T) + 237 = Qs w (ca1/cm2/24hr), gives
a value of 5. 1°C for an average Qs w of 337 cal/cm 2/24 hr (Table 3).
CONCLUSION
The components of the surface heat balance equation cannot be calculated accurately enough from available weather records to show how paving the Inuvik airstrip has changed them and thus affected the
ground thermal regime. These preliminary calculations are of
interest, however, because it is considered that they give reasonable estimates of the terms in the heat balance equation for gravel and paved surfaces in an arctic region, information that is almost non-existent at the present time.
-9-ACKNOWLEDGEMENTS
The author gratefully acknowledges the assistance of J. Plunkett in the taking of the field measurements, of R. Armour for his help in analysing the results and of G. H. Johnston for many helpful discussions.
REFERENCES
(1) Swinbank, W. C. Long-Wave Radiation from Clear Skies.
Royal Met. Society Journal, Vol. 89, 1963, p. 339.
(2) Budyko, M.1. The Heat Balance of the Earth Surface.
U. S. Dept. of Commerce Translation by N. A.
Stepanova, 1958.
(3) Michel, B. Winter Regime of Rivers and Lakes. CRREL
Report Ill-Bla, U. S. Corps of Engineers, Hanover,
N. H. April 1971.
(4) Williams, G. P. Surface Heat Exchange and Permafrost.
Proceedings of a Seminar on the Permafrost Active
Layer, 4 and 5 May, 1971, National Research Council
of Canada, Technical Memorandum No. 103.
(5) Gold, L. W. Influence of Surface Conditions on Ground
Temperature. Can. J. Earth Sciences, Vol. 4, 1967,
1959 - 68
1
Monthly Mean Air Temp (0 F)
a Monthly Mean Dew Point Temp 0F
3 Monthly Average ReI. Humidity("!o)
...---
--YEAR JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC
1 -28. 3
-
6. 5 -19. 5 5. 2 2.6.5 47.7 52. 7 44. 5 34.6 14.8 -23.9 -18.4 i959 ;0-
-10 - 3.0 25.0 38.0 43. 0 40. 0 32.0 12.0-
-3-
73 - 68 71 57 64 76 80 78-
--28.4 -12. 5 -14. 0 4. 1 32.. 4 52.9 52.8 49.2 36. 5 17.6 -13. 9 -11. 0 1960-
-15 -16 1 27 41 44 43 33 16 -19 -15-
74 69 73 72 59 65 72 83 85 80 82 -34. 5 -24. 2 -16. 0 I-
1.9 31. 5 51. 2 57.7 49. 3 40.4 18.8 - 7. 1 -12. 6 1961-
-26 -21 I - 8 25 38 45 40 35 16 -12 -18-
70 7'1_..!
71 77 61 66 73 82 86 78 73 -10.5 -11. 1 -16. 0 I 5. 7 26. 8 50.7 56.8 55. 9 36. 0 23.8-
4.5 - 8. 4 1962 -14 -15 -19 I - 1 19 39 46 48 31 23 - 8 -12 74 74 (,1 ! 73 72 66 69 75 82 91 81 80 -22.7 -21. 3 -11. 0 : 14. 5 34. 1 50. 5 56. 7 53. 5 35. 4 16. 5 -13. 2-
9. 3I
1963-
-22 -19 I 10 25 40 45 43 28 14-
13-
65 68...
74 70 68 67 69 74 86-
77 -25. 5 -20.4 -2 ·1.r,I
- 5. 21 28. 7 45. 3 52.8 50.3 35. 2 20. 6-
4.3 -22. 8 1964-
-24 -27 -12 19 34 40 42 30 18 - 8--
725'L..
I
66HS
67 63 75 82 85 '78--28. 2 -3-1. 1 47.2 57. 1 51. 3 37. 3 10.8 O. 5 -17. 4 I 1965 (J. 7
i
11. 6 28. 3 33 46 42 30 3 --
-7 i 5 21 7-
-21-
-
Hjr⦅セ⦅セR
61 67 73 76 76 83 79I
-20. 2 -25. 9 -17·i. 1n
30. 8 51. 1 58. 1 49.2 37.8 12. 6-
9.0 -27. 5 1966-
-
-22 I -11 23 41 46 42 32 9 14 0 --
VGセ⦅ L 68 73 70 67 77 80 83 75 --17.9 -24.5-
9.0 I 10.8 31. 1 48.2 53. 9 48.7 36. 0 14.9-
1.5 -10.6 1967 -22-
-13 I 4 Zl 34 43 40 33 12-
5 -15 73-
78 I:, 71 セ_Lセ 63 68 74 88 86 81 77 -19. 5 -23. 9-
5. ( I 3. 7 :il.2 49. 6 57.9 50. 2 36. 9 20. 7-
8.9 -2.1.9 I 1968 -25 --
8I
- 3 24 37 42 40 31 19 -13 -70-
75 76 74 63 56 70 81 89 75-TABLE 2
MONTHLY AVERAGE WEATHER DATA - lNUVIK
1959 - 68
1 Wind Speed (mph)
2Solar Radiation (cal/sq cm/hr)
3Mean Cloud Cover
YEAR JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC
4. 4 6.2 4. 1
- I
6. 8 8.0 8.2 8. 3 4.8 7.0I
I
5. 7 3. 4 1959 2 3 50 69-
61 70 42 73 76 81I
86 -I
72 1-. 4. 7 6. 5 6. 1 7.5 7.9 8.2 7.5 7.6 6. 4 3. 6 4.5 -1960-
-
-
--
-
-
-
- 64 10 1 57 56 45 47 59 71 73 73 92 75 63 43 4.0 3. 9 5.9 5. 3 8. 1 6. 5 7.3 7.1 7.0 7.0 5. 4 3.9 1961 6 43 158 411 470 575 451 321 135 43 9 0 16 26 69 35 64 53 69 71 73 87 49 65 6.7 4. 9 5.9 7.3 6. 8-
7.6 7.7 7.8 5. 5 5. 0 6.0 1962-
41 181 358 470 472 414 349 - 47 11 0 62 68 43 63 68 73 70 59 75 85 69 72 5. 3 5.2 6.6 7.2 6. 9 8.2 7.4 7.3 6. 9 6. 4 4. 0 5. 1 1963-
50 164 328 536 467 387 284 168 48 10 0 48 48 50 66 58 72 74 72 67 91 65 54 3. 4 3. 2 4. 4 5.7 6. 9 7.4 6.4 6. 1 5. 7 5.8 4.3 7.0 1964 4 42 200 389 526 489 430 290 143 54 10 0 49 62 22 41 57 61 64 72 73 84 70 53 4. 3 3.9 6. 4 7. 1 7.2 7.7 6.9 6. 1 6.9 4. 9 5. 0 3. 3 1965 4 52 172 341 445 520 443 298 160 59 12 0 43 38 59 64 74 61 65 72 70 68 53 56 3. 4 3. 3 6.0 7. 1 7.8 8. 3 7.7 7.3 6. 4 6. 1 4. 1 3.8 1966 5 55 197 - 495-
--
-
-
-
-51 55 48 55 57 71 72 77 75 77 60 50 4.? 3. 8 6. 1 6.1 8. 2 8.1 6. 5 6. 8 6. 4 5. 2 4. 6 3.5 1967 3 41 166 365 409 496 408 301 104 59 11 0 -22-
- 13 4 21 34 43 40 33 12 . -5 -15 4. 3 4. 1 5. 4 5.9 7.9 8.0 8.1 6. 5 5.8 5. 1 1.6 3.9 1968 5 45 187 391 509 582 526 3litO 177 58 10 0 71 61 50 50 65 54· 53 H 66 83 68 45CALCULATED COMPONENTS OF SUMMER SURFACE HEAT BALANCE
Assuming Surface Temperature for Gravel
Assumed HセtI Q {T - T } Q.tw Q Q sw s a c s 1959 55, 248 +5°C -28,272 -15, 453 -11, 523 +6°C -29,802 -19,890 - 5, 556 1960 52,510 +5°C -26, 243 -15, 453 -10,814 +6°C -27,743 -19,890 - 4,877 1961 54,470 +5°C -27,870 -15, 453 -11, 147 +6°C -29, 399 -19,890 - 5, 181 1962 50, 447 +4°C -25,846 -11, 475 -13, 126 +5°C -27, 468 -15, 453 - 7, 526 1963 50,274 +4°C -26,538 -11,475 -12,261 +5°C -28, 129 -15, 453 - 6,692 1964 51, 239 +4°C -28,063 -11,475 -11,701 +5°C -29, 654 -15, 453 - 6, 132 1965 50,855 +4°C -26,547 -11, 475 -12,833 +5°C -28, 138 -15, 453 - 7, 264 1966 53,215 +5°C -29, 391 -15,453 - 8, 731 +6°C -30,982 -19,890 - 2, 343 1967 46,865 +5°C -23, 545 -15, 453 - 7,867 +6°C -25,075 -19,890 - 1,900 51, 500 5. PC -27,700 -15,800 - 8,200 ca1/em2 {+337} ( -181) ( -103) , -53) eal/em /24 h r2
TABLE 4
CALCULATED COMPONENTS OF WINTER SURFACE HEAT BALANCE
Assuming Surface Temperature of Gravel
-Assumed Q !:J.T QJ,w Q Q Q sw (T - T ) e s sAv s a 2 eal/em /24 hr 1959-60 +8,648 _3°C -30,814 + 11, 289 +10,877 _4°C -29, 291 +15,900 + 4, 668 36.5 1960-61 +9, 433 _4°C -35,085 +15,900 + 9,752 _5°C -33, 625 +21,412 + 2,780 29.6 1961-62 +8,914 _4°C -33,096 +15,900 + 8,282 _5°C -31, 613 +21, 412 + I, 287 22.6 1962 -63 +7, 307 _3°C -30, 987 +11,236 +12,444 _4°C -29, 622 +15,900 + 6,415 44.5 1963-64 +9, 594 _4°C -35, 481 +15,900 + 9,912 _5°C -34, 172 +21, 412 + 3, 166 30.8 1964-65 +8,721 _4°C -34,634 +15,900 +10,013 _5°C -33,116 +21, 412 + 2, 983 30.7 1965-66 +9, 565 _4°C -38, 205 +15,900 +12,740 _5°C -36,960 +21, 412 + 5,983 44.0 1966-67 +8, 662 _4°C -32, 409 +15,900 + 7,847 _5°C -30,744 +21, 412 + 670 20. 0 Av 8850 (+42) -33,000 (-156) 17, 400 (+82) 2 + 6,750 eal/em 2 (+32) ea1/em /24 hr
AVERAGE SUMMER AIR AND GROUND SURFACE TEMPERATURES
FOR GRAVEL PAD, INUVIK
1958-1968
I
Summer Period (May-Sept. 5 Month Av)
Year 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 T (Air Temperature) a
5. 1
7. 17.4
7.4
7.8 5.8 6.8 7.8 6.4 7.3 T (Ground Surface s Temperature) (0 C) 12.4 9.2 8. 3 10.3 10.9 11. 6 8. 3 11. 1 9.8 10.0 13. 1 6.T +4.1 +1. 2 +2.9 +3.5 +3.8 +2. 5 +4.3 +2.0 +3.6 +5.8 Average 3.4TABLE 6
COMPARISON OF AVERAGE SURFACE TEMPERATURE OF GRAVEL UNDER SNOW COVER ESTIMATED FROM
SOIL TEMPERATURE PROFILES (T I) WITH TEMPERATURE (Til)
s s
OBTAINED FROM HEAT BALANCE CALCULATIONS
Winter Period (Oct. - April 7 months)
T s (Snow. Av Snow Av Surface
T a Surface) Depth Heat Flow>:c Temp Gravel
Year (0C) °C (cm ) cal/cm 2/24 hr T II T 1 S s 1959-60 -23.0 -26.5 8 36.5 -19.7 -16.6 1960-61 -23.8 -28.3 12 29.6 1961-62 -22.2 -26.7 16 22.6 -13. 2 -21. 2 1962-63 -20.4 -23.9 15 44.5 -11.2 -17.5 1963-64 -24.2 -28. 7 10 30.8 -20.2 -18. 7 1964-65 -22.2 -26.7 8 30.7 -19.9 -23. 0 1965-66 -24. 3 -28.8 8 44.0 -22.0 -21. 9 1966-67 -21. 1 -25.6 8 20.0 -18.8 -18.0 Average -17.9°C -19.5°C
*
As suming steady state conditions, a thermal conductivity of high density snow2 °C
= • 0005 cal cm - sec and Q , heat flow from ground, obtained from heat
cm s
COMPARLSON OF HEAT BALANCE TERMS FOR BARE PAVEMENT
AND SNOW -COVERED GRAVEL, INUVIK
BARE GRAVEL COMPACTED SNOW ANNUAL BALANCE
ON GRAVEL
2 (cal/crn )
(l st May - 30th Sept) (l st Oct - 30th April) ,
.. /
Q +55,300 + 8,600 +63,900
S\V
Net short-wave radiation
Qtw
I
-29, 900 -29. 300 -59. 200Net long-wave radiation
Q Net +25.400 -20,700 + 4, 700 n radiation Q -19, 900 +16.000 - 3.900 c convection Q s l - 5. 500 + 4.700
-
800 ground heat storagePAVED SURFACE ON GRAVEL ANNUAL BALANCE
!
II
(lat May - 30th Sept) (lat Oct - 30th April) (cal/crn ).,2 II
-, Q (net) +56,700 +19,600 +76, 300
,
sw I.
Q t w (net) -29,900 -32, 400 -62, 300,
i
Q +26.800 -12,800 +14,000!
n Q -19.900 + 7,000 -12. 900 c Q s 2 - 6,900 + 5,800 - 1, 100 I \ iFIGURE 1: Short-Wave and Net Radiometers Over Gravel and Paved Surfaces. Inuvik, October 1969.