956 Journal of the Meteorological Society of Japan Vol. 60, No. 4 The Extremely Low Temperature in Hokkaido, Japan during 1976-77 Winter and its Numerical Simulation By Chikara Nakamura* and Choji Magono** epartment of Geophysics, Faculty of Science, Hokkaido D University, Sapporo 060, Japan (Manuscript received 9 September 1981, in revised form 28 April 1982) Abstract In the winter season of 1976-77, the second coldest temperature of -40.8* in Japan was recorded in a basin in Hokkaido island in that season. Three examples of extremely low temperature in Hokkaido were analyzed in mesoscale. As a result it was found that the pattern of horizontal temperature distribution was common to all the cases except cloudy region, although the absolute values were different. Taking into account of cloud amount, altitude and distance from the seashore, the horizontal distribution of extremely low temperature which observed in Hokkaido was well simulated theoretically by calculating the vertical heat transfer near the snow surface. However the simulation for small land basins or narrow valleys was not good. This may be because of unexact estimation of eddy diffusivity which depends on a local wind speed. It was shown that the lower the wind speed the*lower the air temperature immediately near the snow surface, but the temperature at the height of regular screens is the coldest when the wind speed at 9m height is around 1m/s. 1. Introduction During the winter season 1976-77, abnormal meteorological events occurred in East Asia. In Hokkaido, also extremely low temperature was frequently observed during the winter season. The minimum temperature of -40.8* recorded at the Moshiri Basin in the northern region of Hokkaido is the second lowest temperature in Japan. The term *extremely low temperature' means a remarkable cold temperature among daily minimum temperatures or a record low temperature in this paper. The authors undertook to clarify the extremely low temperature in Hokkaido from the meteorological point of view in mesoscale. For the first step they analyzed the horizontal distribution of extremely low temperature and then theoretically simulated the distribution. Ishikawa and Ishida (1973a) studied the heat budget at the surface of snow cover at the Present address: *Nihon Radio Co., Ltd., Tokyo. Hokkaido University. ** Moshiri land basin by measuring the air temperature, wind speed and amount of net radiation. They (1973b and 1977) carried out numerical simulations of the vertical profile of air temperature near the snow surface in the cloudless night at the basin, based on the result of their observation, and succeeded in reproducing the temperature profile. Their calculation method is very useful to simulate the vertical profile of air temperature at a point, but in order to simulate the horizontal distribution of low temperature actually observed, the effect of long wave radiation from the atmosphere, particularly the cloud amount is required to be considered. Therefore in addition to following the method of Isikawa and Ishida (1973b), the present authors used the formulae of the atmospheric radiation given by Kondon (1971), Yamamoto et al. (1973) and Saito (1961) with modifying their formulae. The effects of altitude, topography and sea were also taken into account. This paper will describe the results of analysis and simulation of the distribution of extremelylow-temperature in Hokkaido during the winter season 1976-77 below.
August 1982 C. Nakamura and C. Manogo 957 2. Horizontal distributions of extremely low temperature Fig. 1 shows a topographical map of Hokkaido Island. Mountain chains in the figure roughly indicate regions which rise higher than 500m above sea level. The data of daily minimum temperature were collected from Monthly Meteorological Report in Hokkaido. In making the horizontal distribution map of minimum temperature, the cor- Fig. 1 Topographical map of Hokkaido Island. rection for the altitude was made at a rate of 0.65* per 100m in order to eliminate the effect of altitude. By making this correction, it was able to describe the pattern of extremely low temperature in whole Hokkaido Island, regardless of high mountain areas where no data were available. Case 1*December 29, 1976 For a few days before Dec. 29, 1976, the northwesterly winter monsoon prevailed, having brought the cold air to the Hokkaido Island. The west-high, east-low pressure pattern became weak on the 29th, as seen in Fig. 2a. A long period of cold winter began from the day. The horizontal distribution of minimum temperature at the sea level in the morning is shown in Fig. 3. Compared with Fig. 1, it may be seen that the region of lower temperature is limited to the inland, and that minimum temperature as cold as -25* is restricted to the lower ground areas i.e. basins or valleys. The local weather chart of Hokkaido at 0900 (LST) on Dec. 29 is shown in Fig. 4a. A local orographic anticyclone existed in the center of Hokkaido and that it was fine and calm except the coast of Sea of Japan. The anticyclone seems to have been generated by the cooling of Hokkaido Island in the previous night. Case 2-January 29, 1977 Fig. 2 Surface and 850mb weather maps on days of extremely low temperature.
958 Journal of the Meteorological Society of Japan Vol. 60, No. 4 Fig. 3 Distribution of minimum air temperature (0*) in Hokkaido Island on Dec. 29, 1976. Fig. 5 Same as Fig. 3 except Jan. 29, 1977. Fig. 6 Same as Fig. 3 except Feb. 15, 1977. Fig. 4 Local weather maps at 0900 (LST) on Dec. 29, 1976 and Feb. 15, 1977. In the morning of January 29, 1977 a minimum temperature as cold as -39.6* was observed at Moshiri and extremely low temperatures after an interval of several ten years were also recorded at other regions of Hokkaido. The horizontal distribution of minimum temperature in this morning is shown in Fig. 5. This pattern of minimum temperature is similar to that on December 29, 1976. However the minimum temperature in this morning is about -10* lower than in the previous case. A small cold airmass existed over Hokkaido, as seen in Fig. 2d. An orographic anticyclone was born in the center of Hokkaido and it was calm and fine in whole Hokkaido similarly to the previous case. Case 3-February 15, 1977 A minimum temperature of -40.8* was recorded at the Moshiri basin on February 15, 1977. It may be seen in Fig. 6 that cold regions are limited to the northeast portion of Hokkaido.
August 1982 C. Nakamura and C. Manogo 959 In this point, the horizontal distributoin of minimum temperature is quite different from the two previous cases. The absolute value of minimum temperature, however, was comparable to the previous case. Although the synoptic situation on Feb. 15 was similar to those of the previous cases, as seen in Figs. 2e and 2f, it was very cloudy in the southwestern Hokkaido, and a local anticyclone formed in the northeastern region of Hokkaido, as seen in Fig. 4b. The synoptic and meso-scale conditions described above were common to other extremely cold days. Accordingly it may be said that the extremely low temperature occurred on calm and cloudless days after the atmosphere over Hokkaido Island was replaced by cold air due to the monsoon. This is as generally predicted. In order to get physical understanding of the extreme cooling of Hokkaido, the effect of snow cover is required to be taken in account. The effect will be considered in the next section. 3. Numerical simulation 3.1 Model for numerical calculation 3.1.1 Vertical heat flux The computation conception of our numerical model is shown in Fig. 7. The calculation was made in following two regions, that is, the atmosphere up to 270m height above snow surface and the snow layer down to 1m depth from the snow surface. Lt was assumed that the solar radiation: Is is poured into the 270m height from above. Assuming the horizontal uniformity of air in a small area, the change of air temperature in the atmosphere is presented by the following equation. where *, t, z and KH indicate the potential temperature, time, height above snow surface and eddy diffusivity of air. R shows the radiational cooling rate. The change of temperature in the snow layer is presented by the following equation. where T and K indicate the temperature and thermal diffusivity of the sonw. It is well known that the eddy diffusivity of air is a function of height, stability and wind shear. For simplification in the present calculation, however the diffusivity was assumed to be a function of only height, that is, constant in time, because it was always calm in the night when the extremely low temperature occurred. The value of KH at 21h which was in the paper of Kondo (1971), was practically used as the representative diffusivity for whole Hokkaido in the present paper. As is well known, the atmospheric radiation is affected by the vertical distributions of water vapor. However the absolute value of water vapor is negligibly small in the atmosphere as cold as -30*. Accordingly the effect of water vapor on the radiative transfer was neglected. For the radiational cooling rate, the approximation of Newtonian cooling was adopted, based on the study by Yamamoto et al. (1973) as follows, where T and TS are the air temperature at a height above snow surface and the surface temperature of snow. * is a proportional constant. o is a variable that takes a value of unity when T>TS, and zero when T*TS. The temperature of snow surface: TS was calculated by the following equation of heat balance at the snow surface. Fig. 7 Conception of numerical model. where FN indicates the net radiation flux of both long wave and short wave which are functions
960 Journal of the Meteorological Society of Japan Vol. 60, No. 4 of TS. FH and FS are the sensible heat flux and the conductive heat flux in snow, respectively. FL is the latent heat flux, however, it was neglected in the present calculation. Each term in Eq. (4) is described by the following equations. where IS and IL mean the heat fluxes of incoming solar radiation and incoming long wave radiation, respectively. *s and * indicate albedo of snow surface and Stefan-Boltzmann's constant, *a, Cp and *s are the density and specific heat of air and heat conductivity of snow respectively. The values of factors of snow cover used in the calculation is given in Table 1. Table 1 Values of factors of snow cover Kondo (1971) gave a formula of solar radiation as follows. where J0, d and d are the solar constant, mean and instantaneous distances between the sun and the earth, respectively. *, *, h, * and e are the latitude, solar declination, hour angle, solar zenith angle and vapor pressure (mb) near the ground, although the effect of e is neglected in the present calculation. Because the formula (8) does not include a term which relates to the cloud amount, the present authors empirically modified the formula by adding a factor of cloud amount as shown by the following formula where n is the cloud amount ranging from 0 to 1.0, based on the experience that the incoming solar radiation decreases to one-third when the cloud amount is 1.0. For long wave radiation, Saito (1961) gave the following formula, As Yamamoto et al. suggested, this formula is well applicable to the weather condition of temperature inversion in the lower atmosphere. However Saito's formula is lacked of the term of cloud amount. According to Kondo (1971), about 90% of heat flux which were radiated from the earth surface, return to the earth as downward atmospheric radiation on a cloudy day (n =1.0). The present authors, therefore empirically modified Saito's formula as follows. Because the absolute value of water vapor was negligibly small, e was put to be zero in the present calculation. Thus all the terms in Eq. (4) were formulated, then TS was solved by Newton- Raphson's iterative method, because the equation includes the forth degree of Ts. 3.1.2 Initial and boundary conditions The vertical profile of maximum air temperature on the previous day of an extremely low temperature day, was used as the initial condition for the calculation. The hour angle at a time of maximum air temperature is required in order to start the calculation. This hour angle was taken as an initial time, and maximum surface temperature appeared at this time. TS was obtained from Eqs. (4) and (5). The maximum surface temperature was determined from the data reported in the Monthly Report in Hokkaido. The maximum temperature is very variable according to the place. For simplification, therefore, the calculations were made for two representative initial temperatures, for example 0 and -5* for the case of Dec. 29, 1976, and the results for the selected two initial values were linearly interpolated or extrapolated for other temperatures. The air temperature at 270m height above the ground surface was used as the upper boundary of air layer for the calculation. Practically, the average of air temperatures at 0900 and 2100 at 270m height which measured in Sapporo, Nemuro and Wakkanai (Fig. 1) was adopted as the upper boundary temperature, commonly to all Hokkaido. It was also assumed that the lapse rate at the 270m height was invariable with time. The vertical profile of air temperature between the 270m height and snow surface was determined by a straight line connecting temperatures at the two levels.
August 1982 C. Nakamura and C. Manogo 961 Following Ishikawa and Ishida (1973b), it was assumed that snow temperature at 1m below snow surface was constant with respect to time and that snow temperature increases exponentially as going down from the snow surface to 0* at 1m below. 3.1.3 E*ect of topography As is well known, the air temperature in the coastal region in winter is much higher than that in inland by the effect of warm sea. According to Ookouchi et al, (1978), the effect of sea breeze arrives the inland about 30km from the seashore. So the authors estimated the effect as following empirical formulae. where Tc, Tp and Tw are the minimum air temperature near the coast, the calculated temperature in the inland and the sea surface temperature observed, respectively. x indicates the distance from the coast in kilometers. The formula (10) means that the effect of sea is proportional to a product of the temperature difference and the distance from the coast. The value of proportional constant in (10) was determined as 0.013 by the use of data which were actually observed in a flat coast with simple topography in Hokkaido. The diurnal temperature change reaches, at most, a height of 300m above ground surface in the winter season. And it was considered that the surface temperature inversion is not predominant in steep mountain regions. It was actually confirmed that, in a calm morning, the surface air temperature at a steep mountain slope of 1000m high above sea level was several degrees higher than that at a flat area nearby. Accordingly it was assumed that the temperature inversion occurs only below a height of 270m height above the flat ground, and that the surface air temperature in areas higher than 270m above the flat ground decreases with a lapse rate of 0,65*/l00m. Accordingly the existence of steep mountains was able to be neglected in mapping the isotherm of surface minimum air temperatures. 3.2 Result o* calculation The numerical calculation was carried out from the time of maximum temperature on the previous day to 06:00 in the next morning for three cases described in Section 2.2. The time of 06:00 probably corresponds to the time of minimum temperature. 3.2.1 Horizontal distribution Case 1-December 29, 1976 It was generally cloudless in the night of December 28-29, 1976 in Hokkaido. Therefore the calculation was made under the condition of zero cloud amount, utilizing a maximum temperatuer of -5* at 12:48, 28th at Hoshiri basin (Fig. 1). The result of calculation is shown in Fig. 8. Each curve in the figure indicates the vertical profile of temperature below 100m in 3-hour intervals. It may be seen that air temperature at a height of 100m decreases by several degrees in one night, however the major cooling occurs at layers below a height of about 20m. It is noted that the amount of cooling at the snow surface at one night reaches 25*. A horizontal broken line in the figure shows the height of a screen and the air temperature in the screen is generally called as the surface air temperature. Fig. 9 shows the horizontal distribution of maximum temperature on December 28 as the initial condition for calculation, together with the sea surface temperature observed near the coast. The result of calculation of isotherms of minimum temperature is shown in Fig. 10. Compared with the observed distribution in Fig. 3, it may be said that, as a whole, the agreement Fig. 8 Calculated time change of temperature profile from maximum temperature time on Dec. 28 to 29, 1976.
962 Journal of the Meteorological Society of Japan Vol. 60, No. 4 Fig. 9 Horizontal distribution of maximum air temperature taken as initial condition on Dec. 28, 1976, and sea surface temperature near seashore. Fig. 11 Same as Fig. 10 except Jan. 29, 1977. Fig. 10 Horizontal distribution of calculated temperature at 0600, Dec. 29, 1976. between the calculation and observation is good, however the pattern of calculated isotherms is slightly simpler than that of observed. Case 2-January 30, 1977 It was calm and cloudless in the night of January 29-30, 1977 similarly to the previous case, however the maximum temperature on 29th was about 5* lower than that in the previous case. The result of calculated distribution of minimum temperature is shown in Fig. 11. Comparing the figure with the observed distribution in Fig. 5, it may be seen that these two patterns of isotherms are very similarly to each other, Fig. 12 Horizontal distribution of cloud amount in night of Feb. 14-15 used in calculation. however the calculated pattern is lacked of -35* isotherms. Case 3*February 15, 1977 In the case of February 15, it was cloudy in Hokkaido except its northeastern portion. By the use of a satellite cloud picture and weather chart in the morning on the day, the distribution of cloud amount (0.0-1.0) was determined as shown in Fig. 12. Figures 13a and 13b show the time change of temperature profile on February 14-15 when the cloud amound was 0 and 1.0 respectively. It may be seen that the temperature at the height of screen was lowered by amount of 23* in one night in cloudless regions, but only lowering of several degrees in the cloudy
August 1982 C. Nakamura and C. Manogo 963 Fig. 13a Same as Fig. 8 except Feb. 14 to 15, 1977. Fig. 13 b Same as Fig. 13a except cloud amount of 1.0. Fig. 14 Same as Fig. 10 except Feb. 15, 1977. regions. The calculated pattern of temperature at 06:00 on February 15 is shown in Fig. 14. Comparing this with Fig. 6, it may be said that the agreement of calculated pattern with that of observed minimum temperature in the morning is very good, however isotherms of - 35* which are indicated in the north portion of Hokkaido in Fig. 6, are not seen in Fig. 14. 3.2.2 Response of temperature profile to wind speed It is considered that the eddy diffusivity, KH is a very sensitive parameter of the temperature Fig. 15 Response of the profile of minimum temperature to wind speed. profile, and that the diffusivity is also a function of wind speed. Therefore, the response of temperature profile to wind speed was specially surveyed, as follows. In the present calculation, the value of eddy diffusivity KH was determined by Kondo's method (1971), and it was assumed that KH*/Z was positive, in order to avoid * the instability in computation. The vertical profile of wind speed was temporarily assumed to be described by a logarithmic curve, and to be constant in time. The calculation was made for wind speeds of 0.5, 1.4 and 7.0m/s at 9m
964 Journal of the Meteorological Society of Japan Vol. 60, No. 4 height above the ground surface. Other meteorological parameters are the same as those in January 28-29, 1977. The result of calculation for the profile of temperature at 06:00 is shown in Fig. 15. Following characteristics are noted in the figure. a. In the case of 7m/s wind speed, the minimum temperature, that is, air temperatures at 06:00 are uniformly about -32* in the lowest layer of 15m depth above the snow surface, as indicated by a broken line. The value of -32* at 1.5m height perhaps corresponds to the minimum temperatures in Fig. 5a. b. In the case of 1.4m/s, a cold air accumulates in layers below a height of about 5m as indicated by a solid line, and the minimum temperature at the height of a screen falls down to -39*. The extremely low temperature as cold as reported in the previous part of this paper might observed in such a calm condition. c. In the case of 0.4m/s, cold air locates only in layers immediately near the snow surface, as indicated by a chain line, and the air temperature reaches -43*, however the temperature at the screen height is - 32*. It is noted that the value of the latter temperature is nearly the same as the case of 7m/s. Such a wind condition as calm as 0.4m/s will not actually occur at 9m high in nature. 4. Consideration As seen in Figs. 10, 11 and 14, the calculated distribution of air temperature at 06:00 well describes the pattern of observed minimum temperature in Hokkaido, but it was not able to simulate the extremely low temperature which was locally observed in the inland. About the reason for the failure, following considerations were made. In order to determine the temperature of snow surface which is an important factor of radiative cooling, parameters as many as possible were taken into account in the calculation, and formulae which were used to calculate the vertical heat transfer, are considered to be most reliable at the present time. Accordingly there may be no substantial defects in the calculation method itself. It is also considered that there are no important defects in the determination of boundary condition, that is, the upper boundary at 270m height above snow surface and the lower boundary at 1m depth from the snow surface, because the calculation well simulates both the pattern and absolute value of observed distribution except of the local extremely low temperature. Because the value of maximum temperature taken as an initial condition was very variable from place to place, the calculation was made for only 0, -5, and - 10*, and interpolation or extrapolation was made for other values. This simplification is also not considered as the reason why the local extremely low temperature was not simulated. In general the minimum temperature does not always at 06:00, however the difference between the minimum temperature observed on a day and the calculated temperature at 06:00 in the morning may be negligible, because the time of sunrise is around 06:00 in Hokkaido in the winter. The estimation of the effects of sea and cloud amount is not considered to be inadequate, because the calculated distributions at coastal area and cloud area were well simulated the observed ones. Finally the authors considered that the main reason for the discrepancy between calculation and observation for the extremely low temperature may be in the estimation of eddy diffusivity: KH. As described in 2.1, a value of KH at 21:00 which was determined by Kondo's method, was used as the representative value of eddy diffusivity of whole Hokkaido. As seen in Fig. 15, the wind speed is a very sensitive factor to determine the vertical profile of air temperature, and the eddy diffusivity is a sensible function of wind speed. The diffusivity which used in the present calculation corresponds to about 2m/s wind speed. It is, therefore considered that the representative value of eddy diffusivity are applicable to air in most areas in Hokkaido in the calm night, but is not applicable to areas of particular topography, for example, small land basins or narrow valleys where the wind speed is locally lower than other open areas. It was observed that the surface air was cooled by an amount of 25* in one night on extremely low temperature days. And the rate of cooling was well simulated theoretically, as seen in Figs. 8 and 13a. About this great nocturnal cooling, the following mechanisms are considered. 1) The heat transfer to the snow surface from below was small, because the heat conductivity of dry snow cover is very small. 2) The heat transfer from above, by the atmospheric radiation was negligibly small, because
August 1982 C. Nakamura and C. Manogo 965 the moisture content of air as cold as -30* is very small. As described in Section 3, the extremely low temperature occurred on calm and cloudless days. However such days occur every winter season. Therefore it is considered that the existence of a specially cold airmass over Hokkaido Island is an important factor for occurrence of the record cold temperature in the island. From a result of calculation for the response of vertical profile of air temperature to wind speed, it was confirmed that the lower the wind speed, the lower the air temperature immediately near the snow surface, however it was found that the coldest air temperature will be observed when the wind speed is 1-2m/s, as far as the air temperature at the height of a regular screen (1.5m) concerns. 5. Conclusion Numerical calculation for horizontal distribution of extremely low temperature observed in Hokkaido were made both based on Ishikawa and Ishida's method for calculating the vertical profile of air temperature near the snow surface and by modifying formulae given by Kondo, Yamamoto et al, and Saito. The effects of altitude and sea were also taken into account. As a result of calculation, the pattern of extremely low temperatures observed was well simulated except for small inland basins or narrow valleys. It was concluded that the difference between calculation and observation in the case of basins or valleys was caused by the rough estimation of eddy diffusivity, that is, unexact wind speed in these areas in the calm night. It is hoped that the local distribution of wind speed are taken into account, in order to simulate the horizontal distribution of extremely low temperature more exactly. The response of the vertical profile of air temperature to wind speed was specially calculated. The result of calculation showed that the lower the wind speed, the lower the air temperature immediately near the snow surface, but the air temperature at 1.5m height, that is, at the height of usual screens is the lowest when wind speed is around 1mn/s. Acknowledgments The authors wish to express their best thanks to Dr. N. Ishikawa, Institute of Low Temperature Science, Hokkaido University for his help in the simulating calculation. The calculation was carried out in the Computing Center of Hokkaido University. References Ishikawa, N., 1977: Studies of radiative cooling at land basins in snowy season. Contributions from the Institute of Low Temperature Science, Hokkaido Univ., Ser. A, No. 27, 1-46. and T. Ishida, 1973a: Observations, of radiative cooling at basins in midwinter and snow-melting season. J. Meteor. Soc. Japan, 51, 197-203., and, 1973b: Numerical prediction of heat balance over dry and wet snow cover under conditions of nocturnal radiative cooling. Low Temperature Science, Ser. A, No. 31, 107-116 (in Japanese). Kondo, J., 1971: Effect of radiative heat transfer on profiles of wind, temperature and water vapor in the atmospheric boundary layer. J. Meteor. Soc. Japan, 49, 75-94. Ookouchi, M., M. Uryu and R. Sawada, 1978: A numerical study of the effects of a mountain on the land and sea breezes. J. Meteor. Soc. Japan, 56, 368-386. Saito, T., 1961. Empirical formula of the atmospheric radiation. J. Meteor. Res., 13, 206-215. Yamamoto, G., A. Shimanuki, M. Aida and N. Yasuda, 1973: Diurnal variation of wind and temperature fields in the Ekman layer. J. Meteor. Soc. Japan, 51, 377-387.
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