J. Jpn. Soc. Soil Phys.
౔৕ͷ෺ཧੑ

No. 124, p.35 ∼ 42 (2013)஍ද໘ۙ๣Ͱͷ஍த೤ྲྀྔͷଌఆʹ͓͚ΔԹ౓ޯ഑๏ͱ೤ྲྀ൘๏ͷൺֱ͓Αͼஷ೤ͷӨ‫ڹ‬ླ໦৳࣏ 1 · ൧௩‫ ࢠܓ‬2,3 · ౉ᬒจ༤ 1 · ౡా୔඙ 1 · ߴ‫ڮ‬ɹ‫ ޛ‬1Comparison between temperature gradient and heat ﬂux plate methods and effect of heat storage
for determination of soil heat ﬂux at near soil surface
Shinji SUZUKI 1 , Keiko IIDUKA2,3 , Fumio WATANABE1 , Sawahiko SHIMADA1 and Satoru TAKAHASHI1

Abstract: The soil heat ﬂux is an important componentof heat exchange across the ground surface and is an essential input component used to help quantify evapotranspiration ratio based on the heat budget. Consequently, it
is useful to understand the characteristics of soil heat ﬂux
measurement methods. One objective of the current study
was to compare the temperature gradient method with theheat ﬂux plate method at a depth of 0.02 m. A second objective was to assess the effect of heat storage in the soil
surface layer (0.02 m thickness) under different soil waterconditions. Further, the effect of the Philip’s correction on
the measurement of the heat ﬂux plate method was also assessed. The results indicate that the soil heat ﬂux measured
by the heat ﬂux plate method was almost identical withthe heat ﬂux measured by the temperature gradient method
when the soil thermal conductivity was approximately halfof the conductivity of the heat ﬂux plate (i.e., wet condition). In contrast, the heat ﬂux plate method overestimatedthe absolute value of the soil heat ﬂux with a constant ratio when the soil thermal conductivity was approximately
1/10 of the conductivity of the heat ﬂux plate (i.e., dry condition). In addition, the practical effect of the Philip’s correction was not observed. Further, the heat storage in thesurface layer showed a diurnal variation with a range comparable to the variation of the soil heat ﬂux at a depth of
0.02 m, whereas the net daily heat storage was quite small.
Key Words : measuring methods of soil heat ﬂux, thermal
conductivity, soil surface temperature, heat budget, evaporation from soil surfaceʹ͔ܽͤͳ͍ɽͦͷͨΊ஍த೤ྲྀྔ͸ɼϘʔΤϯൺ๏΍ϖϯϚϯ๏ͳͲɼ೤ऩࢧΛ΋ͱʹͯ͠ৠൃࢄྔΛଌఆ ·ਪఆ͢Δ৔߹Ͱ΋ॏཁͳߏ੒ཁૉͱͳ͍ͬͯΔɽ஍த೤ྲྀྔͷଌఆํ๏ʹ͸ɼԹ౓ੵ෼๏΍೤ྲྀ൘๏ͳͲ͕͋Δ
͕ʢԬా, 1983; ޿ాΒ, 2001ʣɼ͜ͷ͏ͪ೤ྲྀ൘๏͸ɼ೤ྲྀ൘ͱσʔλϩΨʔ͕͋Ε͹ൺֱత؆ศʹଌఆͰ͖ΔͨΊʹ޿͘༻͍ΒΕ͍ͯΔɽ೤ྲྀ൘๏͸ɼҎԼͷࣜͰද͢

Fourier ͷ๏ଇʹ‫͍ͯͮج‬஍த೤ྲྀྔΛଌఆ͢Δ΋ͷͰ͋Δɽ

G = −λdTdZ(1)͜͜ʹɼG ͸஍த೤ྲྀྔʢW m−2 ʣͰԼ޲͖͕ਖ਼ɼλ͸೤ྲྀ൘ͷ೤఻ಋ཰ʢW m−1 K−1 ʣɼdT /dZ ͸Թ౓ޯ഑ʢ◦ C m−1 ·ͨ͸ K m−1 ʣͰɼ೤ྲྀ൘ͷදཪͷԹ౓ࠩʢ◦ CʣΛ೤ྲྀ൘ͷް͞ʢmʣͰআͨ͠΋ͷʹ૬౰͢Δɽ࣮ࡍʹ͸ɼ೤ྲྀ൘දཪͷԹ౓ࠩʹΑͬͯ೤ిଯʢ೤ిରΛ௚ྻʹෳ਺ճ࿈݁ͨ͠΋ͷʣʹੜ͡Δ‫ʹྗిى‬ɼϝʔΧʔʹΑͬͯఆΊΒΕͨ‫਺܎ࢉ׵‬Λ৐͡Δ͜ͱʹΑͬͯ೤ྲྀྔ
͕ࢉग़͞ΕΔɽ·ͨ೤ྲྀ൘͸ɼ์ࣹΛආ͚ΔͨΊɼ͓ΑͼηϯαʔΛ‫ݻ‬ఆͯ͠౔৕ͱີணͤ͞Δඞཁੑ͔Βɼ౔৕தʹຒઃ͞ΕΔɽҰํͰ೤ऩࢧ‫؍‬ଌͷ࣮‫ʹॻݧ‬͸ɼԹ౓ޯ഑๏͕঺հ͞Ε͍ͯΔʢSauer and Horton, 2005ʣɽ
Թ౓ޯ഑๏΋ Fourier ͷ๏ଇʢʢ1ʣࣜʣʹ‫͕ͮ͘ج‬ɼ͜ͷ৔߹ɼλ ͸Թ౓ޯ഑ͷத৺ਂ͞ʹ͓͚Δ౔৕ͷ೤఻ಋ཰ʢW m−1 K−1 ʣɼz ͸ਂ͞ʢmʣɼT ͸஍Թʢ◦ CʣͰ͋Δɽ

1. ͸͡Ίʹ
஍த೤ྲྀྔ͸ɼ཮໘Λ‫ڥ‬քͱͨ͠೤ަ‫׵‬ͷղੳ΍ධՁ͜ͷΑ͏ʹԹ౓ޯ഑๏Ͱ͸ɼԹ౓ޯ഑ͱ೤఻ಋ཰͕‫ٻ‬ΊΒΕΕ͹ɼ஍த೤ྲྀྔΛ‫ٻ‬ΊΔ͜ͱ͕Ͱ͖Δɽ
೤ྲྀ൘๏ͷ໰୊఺ͱͯ͠ɼ
ʢaʣ೤ྲྀ൘͕౔৕ͱ͸ҟͳΔ෺࣭Ͱߏ੒͞Ε͍ͯΔ͜ͱ͔Βɼ౔৕ͱ೤ྲྀ൘ͷ೤఻ಋ

1 Department of Bioproduction and Environment Engineering, Faculty ofRegional Environment Science, Tokyo University of Agriculture. 1-1-1
Sakuragaoka Setagaya, Tokyo 156-8502, Japan. Corresponding authorɿླ໦৳࣏ɼ౦‫ژ‬೶‫ۀ‬େֶ஍Ҭ‫ڥ؀‬Պֶ෦ੜ࢈‫ֶ޻ڥ؀‬Պ
2 Department of Agricultural Engineering, Graduate School of Tokyo
University of Agriculture. 1-1-1 Sakuragaoka Setagaya, Tokyo 156-8502,
Japan.
3 Present address: Shigeru Co.,Ltd. 330 Yuracho, Ota 373-0036, Japan
2013 ೥ 2 ݄ 3 ೔डߘɹ 2013 ೥ 6 ݄ 13 ೔डཧ཰͕ҟͳΔ৔߹ʹɼ೤ྲྀ൘ͱͦͷपғͷ౔৕ͷͦΕͧΕΛ௨ա͢Δ೤ྲྀʹҧ͍͕ੜ͡Δ‫ݒ‬೦͕͋Δ͜ͱɼʢbʣ೤ྲྀ൘͕౔৕தͷӷঢ়ਫ͓Αͼਫৠ‫ؾ‬ͷҠಈΛ੍‫͢ݶ‬ΔՄ
ೳੑ͕͋Δ͜ͱɼ
ʢcʣ͞Βʹɼ೤ྲྀ൘ͱ౔৕ͷ઀৮ͷෆ۩߹͕݁ՌʹӨ‫ڹ‬Λ‫ͱ͜͢΅ٴ‬ɼ͕‫͛ڍ‬ΒΕΔʢSauer and36౔৕ͷ෺ཧੑɹୈ 124 ߸ɹ (2013)

Horton, 2005ʣɽҰํԹ౓ޯ഑๏Ͱ͸ɼʢdʣ౔৕ͷ೤఻ಋ཰ͷਖ਼֬ͳ஋ΛಘΔ͜ͱ͕೉͍͠ͱ͞Ε͍ͯΔʢSauerand Horton, 2005ʣɽ͜ͷ͏ͪʢaʣʹ͍ͭͯ͸ɼPhilip ͷิਖ਼ʢPhilip, 1961ʣ͕͠͹͠͹༻͍ΒΕΔʢHarazono etal., 1998; van Loon et al., 1998; Sauer and Horton, 2005;
Frey et al., 2011ʣɽ͜Ε͸ɼ౔৕ͱ೤ྲྀ൘ͷ೤఻ಋ཰ɼ͓

ଌఆʹ஫ҙΛ෷͍ɼҎԼͷ 3 ͭΛ໨తͱͨ͠ɽ͢ͳΘͪɼ
ʢiʣ஍ද໘ۙ๣ʹ͓͍ͯ೤ྲྀ൘๏ͱԹ౓ޯ഑๏Λൺֱͯ͠ɼ྆ऀͷಛ௃Λ໌Β͔ʹ͢Δ͜ͱɼʢiiʣ·ͨͦͷࡍɼ೤ྲྀ൘๏Ͱ͸্‫ه‬ʢaʣͷӨ‫͍ۛͯͭʹڹ‬ຯ͢Δඞཁੑ͔ΒɼPhilip ͷิਖ਼ͷӨ‫ݕ͍ͯͭʹڹ‬౼͢Δ͜ͱɼ
ʢiiiʣ͞
Βʹද૚ͷஷ೤ͷӨ‫ݕ͍ͯͭʹڹ‬౼͢Δ͜ͱɼͰ͋Δɽ

Αͼ೤ྲྀ൘ͷ‫ܗ‬ঢ়ʹԠͯ͡ɼ೤ྲྀ൘Ͱଌఆ͞Εͨ஋Λิͳ͓౔৕ͷ೤఻ಋ཰΍ମੵ೤༰ྔ͸ɼਫ෼ྔʹΑͬͯมਖ਼͢Δ΋ͷͰ͋Δɽʢbʣ͸ɼ೤ྲྀ൘ͷ্Լʹɼ೤ྲྀ൘ͷप

Խ͢Δ͜ͱ͔Βɼຊ‫͚͓ʹڀݚ‬Δൺֱ΍‫ݕ‬౼͸ҟͳΔ౔ғͱ͸ҟͳΔ౔৕ਫ෼ྔͷ͕ࠩੜ͡Δ‫ݪ‬ҼͱͳΔ͜ͱʹ৕ਫ෼ྔͷ΋ͱͰߦͬͨɽ

Ճ͑ɼ೤ྲྀ൘͕ਫৠ‫ؾ‬ͷҠಈΛःஅͨ͠৔߹ɼ೤ྲྀ൘͸

2. ࢼྉ͓Αͼํ๏જ೤༌ૹΛ‫ܭ‬ଌ͢Δ͜ͱ͕Ͱ͖ͳ͍ͱ͍͏΋ͷͰ͋Δɽ
೤ྲྀ൘๏ͱԹ౓ޯ഑๏͸ͱ΋ʹɼ্‫ه‬ͷଌఆ্ͷཧ༝

2.1 ‫؍‬ଌ஍఺ʹΑΓɼ౔৕தͷ͋Δਂ͞ʹ͓͚Δ೤ྲྀྔΛଌఆ͢Δɽຊ‫͚͓ʹڀݚ‬Δ‫؍‬ଌ͸ɼ౦‫ژ‬೶‫ۀ‬େֶੈా୩ΩϟϯύͦͷͨΊ஍ද໘ʹ͓͚Δ೤ྲྀྔΛ஌ΔͨΊʹ͸ɼ೤ྲྀ൘εͷੜ࢈‫ֶ޻ڥ؀‬Պࢼ‫ݧ‬ะ৔ʢN 35◦ 38’ 33”ɼE 139◦ 38’๏΍Թ౓ޯ഑๏Ͱ஍த೤ྲྀྔΛଌఆͨ͠ਂ͞ΑΓ΋্૚ʹஷཹ͞ΕΔ೤ྔ͕Ճຯ͞Εͳ͚Ε͹ͳΒͳ͍ɽ͜ͷՃຯ͞ΕΔ೤ྔΛԹ౓ੵ෼๏ʹΑͬͯࢉग़͠ɼ஍ද໘ʹ
͓͚Δ஍த೤ྲྀྔΛ‫ٻ‬ΊΔํ๏͸ɼ૊Έ߹Θͤ๏ͱ‫ݺ‬͹Ε͍ͯΔʢԬా, 1983; ޿ాΒ, 2001; Sauer and Horton,2005ʣɽͦͷࡍɼ೤ྲྀ൘๏΍Թ౓ޯ഑๏ʹΑͬͯ஍த೤
ྲྀྔΛܾఆ͢Δਂ͞ʹ͍ͭͯ͸ٞ࿦͕ଟ͍ɽSauer andHortonʢ2005ʣ͸ɼ೤ྲྀ൘Λ 0.05 m Ҏਂʹຒઃ͢Δ͜ͱʹΑΓɼʢbʣͷӨ‫ڹ‬Λগͳ͘͢Δ͜ͱ͕Ͱ͖ɼ·ͨʢdʣͷཧ༝ʹΑΓɼԹ౓ޯ഑๏͸ਂ͞ 0.20 m ҎਂͰଌఆ͢
Δ΂͖Ͱ͋Δͱ͍ͯ͠Δɽ͞Βʹɼ஍ද໘Ͱ͸஍Թͷৼ෯͕େ͖͍͜ͱʹՃ͑ɼஅଓతʹ೔ӄ͕Ͱ͖ͯ೔ࣹ͕
ःΒΕΔ৔߹͕͋Γɼ஍ද໘΁ͷೖࣹͷมԽʹΑͬͯ஍ද໘Թ౓͕େ͖͘มԽ͢Δ͜ͱ͔ΒʢHeusinkveld et al.,2004ʣɼ஍ද໘ۙ๣Ͱ೤ྲྀྔΛଌఆͨ͠৔߹ʹ͸ɼଌ‫ث‬ͷԠ౴͕ଌఆʹӨ‫ڹ‬Λ‫ݒ͕ͱ͜͢΅ٴ‬೦͞ΕΔɽҰํͰɼ஍Թͷৼ෯͸ਂ͘ͳΔʹͭΕͯ‫ݮ‬ਰ͢Δʢਂ͍ҐஔͰͷԹ౓ޯ഑͕ඇৗʹখ͘͞ͳΔʣ͜ͱ͔Βɼਂ͕͞ਂ͘ͳ
Δͱɼ೤ྲྀ൘๏΍Թ౓ޯ഑๏Ͱͷଌఆ͕ࠔ೉ʹͳΔ౳ͷ‫ݒ‬೦΋͋ΔʢHeusinkveld et al., 2004ʣɽͦͷͨΊ࣮ࡍͷใࠂྫͰ΋ɼਂ͘ͳΔʹͭΕͯԹ౓ޯ഑๏ʹΑΔ஍த೤ྲྀྔͷଌఆਫ਼౓͕޲্ͨ͠ͱ͢ΔҰํͰʢKimball et al.,1976ʣɼ೤ྲྀ൘๏΍Թ౓ޯ഑๏ʹ͓͍ͯͦΕͧΕɼਂ͞
0.02 m ΑΓઙ͍ҐஔͰͷଌఆ͕ྑ޷Ͱ͋ͬͨͱ͍͏΋ͷ΋͋ΔʢHeusinkveld et al., 2004; Evett et al., 2012ʣɽ

4”ɼAlt 47 mʣʹͯɼΨϥεԹࣨʹઃஔ͞ΕͨϥΠγϝʔλʔʢॎ · ԣͦΕͧΕ 1.0 mɼਂ͞ 0.8 mʣͰߦͬͨɽϥΠγϝʔλʔʹ͸ 2008 ೥ʹɼ5 mm ;Δ͍Λ௨աͨ͠‫׊‬৭௿஍౔ʢ೪౔ɿγϧτɿ࠭ͷ࣭ྔൺ = 27ɿ35ɿ38ʣΛɼ‫ס‬૩ີ౓͕ 0.91 Mg m−3 ͱͳΔΑ͏ʹॆరͨ͠ɽ2010೥Ҏ߱ɼຊ‫ڀݚ‬Λ࢝ΊΔ·Ͱ͸ɼϥΠγϝʔλʔʹՃਫ͓ͯ͠Βͣɼ౔৕͕ඇৗʹ‫ס‬૩ʢମੵ‫ؚ‬ਫ཰໿ 0.03 m3

m−3 ʣ͍ͯͨ͠ɽҎ߱ɼ͜ͷਫ෼ঢ়ଶΛ‫ס‬૩ঢ়ଶͱ͢Δɽଌ‫ث‬ͷઃஔલʹɼଌ‫౔͕ث‬৕ʹີண͠΍͘͢ͳΔΑ͏ɼϥΠγϝʔλʔͷද૚ 0.05 m ͷ౔৕Λ 2 mm ;Δ͍Λ௨աͤ͞ɼϥΠγϝʔλʔͷ΄΅தԝͰҎԼͷଌఆΛߦͬͨɽ

2.2 Թ౓ޯ഑ͱ஍த೤ྲྀྔͷଌఆਂ͞ͷܾఆԹ౓ޯ഑๏Ͱ͸ɼԹ౓ޯ഑ʢdT /dZ ʣΛਖ਼֬ʹ‫ٻ‬ΊΔ͜ͱ͕ॏཁͱͳΔɽdT /dZ ͷࢉग़͸ɼҟͳΔਂ͞Ͱଌఆ
ͨ͠஍ԹͷࠩΛਂ͞ͷࠩͰআͯ͠‫ٻ‬ΊΔํ๏͕ҰൠతͰ
͋ΔɽCobos and Bakerʢ2003ʣ͸ɼ೤఻ಋ཰Λ‫ٻ‬Ίͨਂ
͞ʢ0.10 mʣͷ্Լ 6 mm Ͱ dT /dZ Λಘͨ৔߹ͱɼ্Լ

12 mm Ͱಘͨ৔߹Λൺֱͨ͠ͱ͜Ζɼ྆ऀͷҧ͍͸΄ͱΜͲͳ͔ͬͨͱड़΂͍ͯΔɽ·ͨ஍ԹͷԖ௚෼෍Λ‫ۂ‬ઢʢͨͱ͑͹ਂ͞Λಠཱม਺ͱͨ͠ 2 ࣍ؔ਺ͳͲʣͰۙࣅ
͠ɼਂ͞Ͱඍ෼͢Δ͜ͱʹΑͬͯ dT /dZ ΛಘΔ৔߹΋͋ΔʢSauer et al., 2003; Sauer and Horton, 2005ʣɽຊ‫ݚ‬೤ྲྀ൘๏΍Թ౓ޯ഑๏ʹΑΔଌఆ͕஍ද໘ۙ๣ͰՄೳ
Ͱ͋Ε͹ɼ૊߹ͤ๏ʹΑͬͯ஍த೤ྲྀྔΛमਖ਼͢Δࡍʹɼ㼀㼔㼑㼞㼙㼕㼟㼠㼛㼞ஷ೤ྔͷ‫ʹࢉܭ‬ඞཁͳύϥϝʔλʔʢਂ͞͝ͱͷ஍Թͱ౔৕ͷ‫ס‬૩ີ౓͓Αͼମੵ‫ؚ‬ਫ཰ʣͷ਺Λ‫ݮ‬Β͢͜ͱ͕
Ͱ͖Δɽ͔͠͠ɼ೤ྲྀ൘๏ͱԹ౓ޯ഑๏ͷൺֱΛ໺֎ͷಉҰͷਂ͞Ͱߦͬͨใࠂ͸͍͔ͭ͘ͳ͞Ε͍ͯΔ΋ͷͷʢCobos and Baker, 2003; Sauer et al., 2003; Ochsner et al.,2006ʣɼͦΕΒ͸্‫ه‬ͷཧ༝ʹΑΓ 0.06 m ҎਂΛର৅ͱ͓ͯ͠Γɼͱ͘ʹԹ౓ޯ഑๏ͷ஍ද໘ۙ๣Ͱͷ࣮༻ੑʹ㻾㼍㼐㼕㼍㼠㼕㼛㼚㻌㼟㼔㼕㼑㼘㼐͍ͭͯͷٞ࿦͸े෼Ͱ͸ͳ͔ͬͨɽ஍த೤ྲྀྔ͸ɼ཮໘ʹ͓͚Δ೤ऩࢧͷఆྔԽʹඞཁͳଌఆ߲໨Ͱ͋ΔͨΊɼଌఆํ๏͝ͱͷಛੑΛ஌Δ͜ͱ͸ॏཁͰ͋Δɽͦ͜Ͱຊ
‫Ͱڀݚ‬͸ɼଌ‫౔ͱث‬৕ͷ઀৮͓Αͼ஍ද໘ʹ͓͚ΔԹ౓

Photo. 1 ౔৕ද໘ʹઃஔͨ͠αʔϛελʔԹ౓‫ࣹ์ͱܭ‬আ͚ɽ
Radiation shield covering on a thermistor placed at soil surface.

࿦จɿ஍ද໘ۙ๣Ͱͷ஍த೤ྲྀྔͷଌఆʹ͓͚ΔԹ౓ޯ഑๏ͱ೤ྲྀ൘๏ͷൺֱ͓Αͼஷ೤ͷӨ‫ڹ‬37஍த೤ྲྀྔΛ‫ ͯ͠ࢉܭ‬G g0.02 ͱͨ͠ɽ Gg0.02 ͱ G g0.02
Λൺֱ͢Δ͜ͱʹΑͬͯɼ஍ද໘Թ౓ͷଌఆํ๏ͷଥ౰ੑʹ͍ͭͯ‫ݕ‬౼ͨ͠ɽGg0.02 ͱ G g0.02 ͷൺֱ͸ɼ์ࣹԹ౓‫ʹܭ‬Αͬͯ஍ද໘Թ౓Λଌఆ͠ɼ͔ͭ dT /dZ ܾఆͷ৚݅Λຬͨͨ࣌͠ࠁʹ͓͚Δ஍த೤ྲྀྔͷൺֱͱͳΔɽ

2.5 ೤ྲྀ൘๏ʹΑΔଌఆ
ਂ͞ 0.02 m ʹ೤ྲྀ൘ʢHFT-1.1, Radiation Energy Bal-ance Systems, Inc.ʣΛຒઃ͠ɼ10 ෼ִؒͰग़ྗిѹΛσʔλϩΨʔʢU12-014, Onset Computer Co.ʣʹ‫ه‬࿥͠
ͨɽU12-014 ͸೤ిର༻ʹ։ൃ͞ΕͨσʔλϩΨʔͰ͋ΔͨΊɼU12-014 ʹిѹ͕ೖྗ͞ΕΔͱɼଌఆ஋͸Թ౓ͱͯ͠ϩΨʔʹ‫ه‬࿥͞ΕΔ͕ɼͦͷ஋Λ 5 ࣍ࣜͰిѹʹม‫͢׵‬Δ͜ͱʹΑΓɼ೤ྲྀ൘͔Βग़ྗ͞ΕΔඍऑͳిѹ
Fig. 1 2011 ೥ 7 ݄ 13 ೔ 17:40 (a) ͓Αͼ 2011 ೥ 7 ݄ 18 ೔
5:30 (b) ʹ͓͚Δ஍ԹͷԖ௚෼෍ɽr2 ͸ܾఆ܎਺Λࣔ͢ɽ
Soil temperature proﬁles observed at 17:40 on 13 July, 2011 (a)and at 5:30 on 18 July, 2011 (b). r2 is the coefﬁcient of determination.

Λਫ਼౓Α͘ଌఆ͢Δ͜ͱ͕Ͱ͖Δʢླ໦Β, 2011ʣ
ɽHFT-

1.1 ͸ԁ൫ঢ়Ͱɼ௚‫͕ͦ͞ްͱܘ‬ΕͧΕ 38, 3.9 mmɼ೤఻ಋ཰͸ 1.0 W m−1 K−1 Ͱ͋ΔʢRadiation and Energy
Balance Systems, 2004ʣɽҎ߱ɼ೤ྲྀ൘ʹͯଌఆͨ͠஍த
೤ྲྀྔΛ Gp0.02 ͱ͠ɼdT /dZ Λ࠾༻ͨ࣌͠ࠁͷ Gg0.02‫Ͱڀ‬͸ɼϥΠγϝʔλʔͷ஍ද໘͔Βਂ͞ 0.04 m ·Ͱɼͱൺֱͨ͠ɽͳ͓࢖༻ͨ͠೤ྲྀ൘͸ɼࣄલʹಉ͡‫ࣜܗ‬ͷ

0.01 m ִؒͰαʔϛελʔԹ౓‫ܭ‬ʢTR-0106, T& DʣΛਫฏํ޲ʹઃஔ͠ɼ2011 ೥ 7 ݄ 8 ೔͔Β 8 ݄ 25 ೔ʹ͔͚ͯɼ஍ԹΛσʔλϩΨʔʢTR-71Ui, T& Dʣʹ 10 ෼ؒ੡඼Ͳ͏͠Ͱൺֱ͠ɼ੡඼ؒͰࠩҟ͕ͳ͍͜ͱΛ֬ೝ͠
ͨɽ·ͨ Gg0.02 ͱ Gp0.02 ͷൺֱʹ͓͚Δ Gg0.02 ͷ‫ࢉܭ‬ʹ͍ͭͯɼλs ͸ɼ஍த೤ྲྀྔ΍஍Թʹൺ΂ͯ࣌ؒʹΑΔ

ִͰ‫ه‬࿥ͨ͠ɽ஍ද໘ʹઃஔͨ͠Թ౓‫ܭ‬͸ɼ‫ײ‬෦ͷ൒෼มԽ͕গͳ͍ͨΊɼλs Λଌఆ೔͝ͱʹ 1 ೔ͷதͰҰఆͱ͕౔৕ʹຒΊࠐ·ΕΔΑ͏ʹ͠ɼ೔ࣹΛආ͚ΔͨΊʹׂͨ͠ɽΓസΛ͔ͿͤͨʢPhoto. 1ʣɽ஍ԹͷԖ௚෼෍Λௐ΂ͨͱ

2.6 Philip ͷิਖ਼͜ΖɼFig. 1ʢaʣʹࣔ͢Α͏ʹɼਂ͞ʹରͯ͠஍ԹΛ௚

Philipʢ1961ʣ͸ɼԁ൫ঢ়ͷ೤ྲྀ൘ʹର͢Δิਖ਼܎਺Λઢۙࣅͨ͠ࡍͷܾఆ܎਺ʢr2 ʣ͕খ͘͞ɼઢ‫ܗ‬ੑͷ௿͍৔߹͕‫؍‬ଌ͞ΕͨҰํͰɼFig. 1ʢbʣʹࣔ͢Α͏ʹɼr2͕େ͖͘ɼઢ‫ܗ‬ੑ͕ඇৗʹߴ͘ͳΔ৔߹͕‫ݟ‬ΒΕͨɽͦ͜Ͱɼ౔৕ͷ೤఻ಋ཰Λ‫ٻ‬ΊΔਂ͞Λ 0.02 m ͱ͠ɼ஍ද
໘͔Βਂ͞ 0.04 m ·Ͱͷ஍ԹΛਂ͞ͷؔ਺ͱͯ͠௚ઢ

ҎԼͷΑ͏ʹఏҊͨ͠ɽ

  

Gc
λs
h
× 1−
= 1 − 1.92
Gm
d
λm

(2)

͜͜ʹɼ Gc ɼGm ɼhɼd ɼλm ͸ͦΕͧΕɼิਖ਼‫ޙ‬ͷ஍ۙࣅͨ͠ࡍɼ r2 ͕ 0.990 Λ௒͑Δ࣌ࠁͷ dT /dZ ʢۙࣅத೤ྲྀྔʢW m−2 ʣɼ೤ྲྀ൘ʹΑΓଌఆ͞Εͨิਖ਼લͷ௚ઢͷ܏͖ʣΛ࠾༻͢Δ͜ͱͱͨ͠ɽ͜ͷ͜ͱ͔Βɼ೤஍த೤ྲྀྔʢຊ‫Ͱڀݚ‬͸ Gp0.02 ʣɼ೤ྲྀ൘ͷް͞ʢmmʣɼྲྀ൘ͷຒઃਂ͞΋ 0.02 m ͱͨ͠ɽ೤ྲྀ൘ͷ௚‫ܘ‬ʢmmʣɼ೤ྲྀ൘ͷ೤఻ಋ཰ʢW m−1 K−1 ʣ

2.3 ϥΠγϝʔλʔ্Ͱͷ೤఻ಋ཰ͷଌఆͱ஍ද໘Թ
౓ͷ֬ೝγϯάϧχʔυϧ೤ಛੑ‫ܭ‬ʢKD2, Decagon devices,Ͱ͋Δɽʢ2ʣࣜʹΑͬͯ Gp0.02 Λิਖ਼͠ɼͦͷӨ‫ͭʹڹ‬͍ͯ‫ݕ‬౼ͨ͠ɽ

2.7 ‫ס‬૩ີ౓͓Αͼମੵ‫ؚ‬ਫ཰ͷଌఆϥΠγϝʔλʔ্Ͱͷ λs ͓Αͼ์ࣹԹ౓‫ʹܭ‬ΑΔ஍

Inc.ʣͷϓϩʔϒʢ௚‫ ܘ‬1.27 mmɼ௕͞ 60 mmʣΛਂ͞
0.02 m ʹਫฏʹຒઃͨ͠ɽ஍ද໘ʹग़ͨ͠ϓϩʔϒͷίද໘Թ౓ͷଌఆʹͱ΋ͳͬͯɼଌ‫ث‬Λઃஔͯ͋͠Δ෇ۙ

ωΫλʔ෦෼͸ϓϥενοΫ༰‫ث‬ͷதʹೖΕ͓͖ͯɼଌ

Ͱɼ஍ද໘͔Βਂ͞ 0.02 m ͷෆ᎟ཚ౔৕ͱɼਂ͞ 0.01

ఆ࣌ʹ೤ಛੑ‫ܭ‬ຊମΛϓϩʔϒʹ઀ଓͯ͠ɼଌఆ೔͝ͱ

∼ 0.03 m ͷෆ᎟ཚ౔৕ΛɼεςϯϨε੡ԁ౵༰‫ث‬ʢ௚‫ܘ‬
50 mmɼߴ͞ 25 mmʣΛ༻͍ͯ࠾औͨ͠ɽ஍ද໘͔Βਂ
͞ 0.02 m ͷෆ᎟ཚ౔৕͸ɼ༰‫ث‬Λ஍ද໘͔Βਂ͞ 0.02
m ·ͰԖ௚ʹૠೖ͢Δ͜ͱʹΑͬͯɼ·ͨਂ͞ 0.01 ∼0.03 m ͷෆ᎟ཚ౔৕͸ɼද૚ͷ౔৕Λް͞ 0.01 m औΓআ͖ɼ༰‫ث‬Λਂ͞ 0.03 m ·ͰԖ௚ʹૠೖͯ͠࠾औͨ͠ɽ
࠾औͨ͠౔৕ࢼྉ͸࣮‫ؼͪ࣋ʹࣨݧ‬Γɼ105 ◦ C Ͱ 24 ࣌ؒ‫ס‬૩ͤ͞ɼ‫ס‬૩ີ౓ʢρd , Mg m−3 ʣͱମੵ‫ؚ‬ਫ཰ʢθ ,m3 m−3 ʣΛଌఆͨ͠ɽෆ᎟ཚ౔৕ͷ࠾औ‫਺ݸ‬͸ɼλs ͱ์ࣹԹ౓‫Ͱܭ‬஍ද໘Թ౓Λଌఆͨ͠೔͝ͱʹ 1 ‫Ͱͭͣݸ‬͋Δɽ஍ද໘͔Βਂ͞ 0.02 m ͷ ρd ͱ θ ͸ද૚ͷஷ೤ྔͷࢉग़ʹ༻͍ɼਂ͞ 0.01 ∼ 0.03 m ͷ θ ͸ λs ͷධՁʹ༻

ʹ 1 ∼ 2 ճɼ౔৕ͷ೤఻ಋ཰Λଌఆ͠ɼ͜ΕΛ λs ͱͨ͠ɽ·ͨ λs ͷଌఆʹซͤɼαʔϛελʔԹ౓‫ʹܭ‬ΑΔ஍
Թଌఆͱಉ࣌͡ࠁʹɼଌ‫ث‬Λઃஔͯ͋͠Δ෇ۙͷ౔৕໘ʹ͓͍ͯɼ໿ 0.15 m ͷߴ͔͞Βɼ์ࣹԹ౓‫ܭ‬ʢTHI-300,
λείδϟύϯʣΛ༻͍ͯ஍ද໘Թ౓Λଌఆͨ͠ɽ์ࣹ
Թ౓‫Ͱܭ‬ͷ஍ද໘Թ౓ͷଌఆ͸ɼ5 ඵִؒͰ 3 ճ‫܁‬Γฦ͠ɼͦͷฏ‫ۉ‬஋Λղੳʹ༻͍ͨɽ

2.4 Թ౓ޯ഑๏ʹΑΔ஍த೤ྲྀྔͷࢉग़্ड़ͷ௨Γ‫ٻ‬Ίͨ dT /dZ ͱ λs Λʢ1ʣࣜʹ୅ೖͯ͠஍த೤ྲྀྔΛ‫ٻ‬ΊɼGg0.02 ͱͨ͠ɽҰํͰɼ஍ද໘Թ౓
ʹ์ࣹԹ౓‫Ͱܭ‬ଌఆͨ͠Թ౓Λ༻͍ͯԹ౓ޯ഑Λ‫ٻ‬Ίɼ౔৕ͷ෺ཧੑɹୈ 124 ߸ɹ (2013)38

Table 1 ‫ס‬૩͓Αͼ࣪५ঢ়ଶͷͦΕͧΕͰ‫ه‬࿥͞Εͨ஍Թɽ
Soil temperatures recorded under dry and wet condition, respectively.
Temperature (◦ C)
Depth (m)

0
0.02
0.04

Dry*

΍ද૚ͷஷ೤ྔʢΔGʣͷධՁ͸ɼஅଓతͳ਺೔ؒͷσʔλΛ༻͍ͯߦͬͨɽ͜Ε͸ɼλs ΍ ρd ɼθ ͷଌఆ͕ࣗಈ‫؍‬

Wet*ଌͰ͸ͳ͘ɼචऀΒ͕ϥΠγϝʔλʔ্ͰߦͳͬͨͨΊ

max

min

max

min

46.9
43.7
40.6

27.8
28.8
29.7

15.2
13.2
13.5

2.1
3.6
4.8

Ͱ͋Δɽ

2.10 ೤఻ಋ཰ͷ‫ূݕ‬͞ΒʹɼϥΠγϝʔλʔʹॆరͨ͠౔৕ͱಉ͡౔৕Λ࣮‫ͯʹ಺ࣨݧ‬෩‫ޙס‬ɼ2 mm ;Δ͍Λ௨աͤ͞ɼ୤ΠΦϯ∗ Approximate volumetric water content at a depth of 0.02 m for the dry

and wet condition was 0.03 and 0.27 m3 m−3 , respectively.

ਫͷఴՃɼ͋Δ͍͸࿍‫ס‬૩ʹΑͬͯਫ෼ྔΛௐઅ͠ɼϥΠγϝʔλʔʹॆర͞Εͨঢ়ଶͱಉ͡ ρdʢ0.91 Mg m−3 ʣʹͳΔΑ͏ʹɼ௚‫ ܘ‬50 mmɼߴ͞ 75 mm ͷεςϯϨε

͍ͨɽ੡ԁ౵༰‫ॆʹث‬రͨ͠ɽ࡞੒ͨ͠‫ࢼڙ‬ମ͸ɼৠൃΛ๷͙

2.8 ද૚ͷஷ೤ྔͷࢉग़ͨΊʹ༰‫୺্ث‬ΛϓϥενοΫϑΟϧϜͰີด͠ɼ20 ◦ C஍ද໘ʹ͓͚Δ஍த೤ྲྀྔʢG∗ , W m−2 ʣ͸ɼG∗ = ΔG + Gͷ࣮‫ ͍͓ͯʹ಺ࣨݧ‬24 ࣌ؒҎ্੩ஔͨ͠‫ޙ‬ɼγϯάϧ(3)

ͱද͞ΕΔɽΔG ͸Թ౓ޯ഑๏΍೤ྲྀ൘๏Ͱ஍த೤ྲྀྔ
Λଌఆͨ͠ਂ͞ʢຊ‫Ͱڀݚ‬͸ 0.02 mʣΑΓ্૚ͷஷ೤ྔʢW m−2 ʣͰ͋Γɼ

ΔG = CΔzͷଌఆ͸ɼ֤ଌ‫ث‬Λઃஔ͔ͯ͠Β 2 ೔‫ʹޙ‬։࢝ͨ͠ɽͳ
͓‫ס‬૩ঢ়ଶɼ࣪५ঢ়ଶͱ΋ʹɼ Gg0.02 ͱ Gp0.02 ͷൺֱ

ΔT
Δt

(4)

Ͱ‫ٻ‬ΊΒΕΔɽ͜͜ʹɼC ͸౔৕ͷମੵ೤༰ྔʢJ m−3

K−1 ʣɼΔz ͸૚ͷް͞ʢ0.02 mʣɼΔT /Δt ͸஍Թͷ‫࣌ܦ‬มԽ཰ʢ◦ C s−1 ·ͨ͸ K s−1 ʣͰ͋ΔɽC ͸ҎԼͷࣜʹΑͬͯ‫ٻ‬ΊΒΕΔɽC = Csρd +Cwρw θ(5)χʔυϧ೤ಛੑ‫ܭ‬Λ༻͍ͯ λs Λଌఆͨ͠ɽ‫ࢼڙ‬ମ͸ λsͷଌఆ‫ޙ‬ɼ࿍‫ס‬૩ͤͯ͞ θ Λ‫ٻ‬Ίͨɽଌఆ͞Εͨ λs Λɼθ ͱͷؔ܎ͱͯ͠੔ཧͨ͠ɽ
ͱ͜ΖͰɼϥΠγϝʔλʔͷ஍Թͷ࠷େ஋ͱ࠷খ஋͸

Table 1 ʹࣔ͢஋ͱͳΓɼϥΠγϝʔλʔ্Ͱ λs Λଌఆͨ͠ਂ͞ 0.02 m ͷ஍Թ͸ɼ‫ס‬૩ঢ়ଶͰ͸ 40 ◦ C Λ௒͑ɼ࣪५ঢ়ଶͰ͸ 5 ◦ C ΛԼճͬͨɽ౔৕ʹ͓͍ͯɼʢ1ʣࣜͷ λ ʢ͢ͳΘͪ λs ʣ͸ɼ‫ʹີݫ‬͸જ೤༌ૹ΋‫ؚ‬Ή‫͔ݟ‬͚ͷ೤఻ಋ཰Ͱ͋Δʢ‫࡚ٶ‬Β, 2005ʣɽ౔৕தͷ೤఻ୡʹ
͓͚Δજ೤༌ૹͷ‫د‬༩͸ɼԹ౓ʹΑͬͯมԽ͢ΔͨΊɼ

λs ͸Թ౓ґଘੑΛࣔ͠ɼஶ͘͠‫ס‬૩ͨ࠭͠Λআ͖ɼҰൠʹԹ౓ͷ্ঢͱͱ΋ʹ λs ͕େ͖͘ͳΔʢHiraiwa andKasubuchi, 2000; Sakaguchi et al., 2007ʣɽͦ͜Ͱɼλs ͷԹ౓ґଘੑ͕஍த೤ྲྀྔʹ‫͢΅ٴ‬Ө‫ڹ‬Λௐ΂ΔͨΊɼ‫ס‬͜͜ʹɼCs ͱ Cw ͸౔৕ͷ‫ݻ‬૬ͱӷ૬ͷఆѹൺ೤ͰɼͦΕͧΕ 837ɼ4,186 J kg−1 K−1 ͱͨ͠ʢ޿ాΒ, 2001ʣ
ɽρw ͸ਫͷີ౓ʢ1,000 kg m−3 ʣͰ͋ΔɽϥΠγϝʔλʔΑΓ࠾औͨ͠ෆ᎟ཚ౔৕ʢ஍ද ∼ ਂ͞ 0.02 mʣͷ ρd ͱθ Λʢ5ʣࣜʹ୅ೖ͠ʢͨͩ͠ ρd ͷ୯ҐΛ kg m−3 ͱ͢ΔʣɼC Λ‫ٻ‬ΊͨɽΔT ͸ɼ͋Δ࣌ࠁ j ʹ͓͍ͯɼͦͷલ‫ޙ‬ʢ࣌ࠁ j − 1 ͱ j + 1ʣͷ஍ද໘ͱਂ͞ 0.02 m ͷԹ౓
j−1
j+1
j−1
j+1
ʢT0 ɼT0 ɼT0.02 ɼT0.02 ʣ͔Βɼ
ΔT =

j+1
j−1
T0j+1 + T0.02
T j−1 + T0.02
− 0
2
2

(6)

Ͱ‫ٻ‬ΊͨɽͦͷͨΊɼΔt ͸ 20 minʢ= 1,200 sʣͱͨ͠ɽΔG ͕ਖ਼ͷ৔߹͸ɼ஍Թͷ্ঢʹͱ΋ͳ͏೤ͷஷཹΛද͠ɼෛͷ৔߹͸ɼ஍Թͷ௿Լʹͱ΋ͳ͏์೤Λද͢ɽ஍த೤ྲྀྔʹ‫ ͢΅ٴ‬ΔG ͷӨ‫ݕ͍ͯͭʹڹ‬౼ͨ͠ɽ

2.9 ҟͳΔ౔৕ਫ෼ྔʹ͓͚Δଌఆ
2012 ೥ 11 ݄ 4 ೔͔ΒɼϥΠγϝʔλʔʹ 100 mm ͷਫಓਫΛ 10 ೔ʹ෼͚ͯՃ͑ɼϥΠγϝʔλʔද໘ΛϏχʔϧγʔτͰ෴ͬͯ 2 िؒ੩ஔ͠ɼ࣪५ͳঢ়ଶʢද૚
ͷମੵ‫ؚ‬ਫ཰໿ 0.27 m3 m−3 ʣͱ͠ɼ2012 ೥ 11 ݄ 30 ೔
∼ 12 ݄ 18 ೔ʹ্‫ه‬ͷଌఆΛ‫܁‬Γฦͨ͠ɽҎ߱ɼ͜ͷঢ়ଶΛ࣪५ঢ়ଶͱ͢Δɽ‫ס‬૩ঢ়ଶɼ࣪५ঢ়ଶͱ΋ʹɼҰ࿈

Fig. 2 Fourier ͷ๏ଇͰ‫ٻ‬Ίͨ஍த೤ྲྀྔʹ͓͚Δ஍ද໘Թ౓
ΛαʔϛελʔԹ౓‫Ͱܭ‬ଌఆͨ͠৔߹ʢGg0.02 ʣͱ์ࣹԹ౓‫ܭ‬Ͱଌఆͨ͠৔߹ʢG g0.02 ʣͷൺֱɽr2 ͓Αͼ RMSE ͸ͦΕͧΕܾఆ܎਺ͱฏํฏ‫ۉ‬ೋ৐‫ࠩޡ‬Λࣔ͢ɽComparison of soil heat ﬂux calculated by the Fourier’s law using
surface temperature measured by thermistor (Gg0.02 ) with that
calculated using surface temperature measured by radiation thermometer (G g0.02 ). r2 and RMSE represent the coefﬁcient of determination and root mean square error, respectively.

࿦จɿ஍ද໘ۙ๣Ͱͷ஍த೤ྲྀྔͷଌఆʹ͓͚ΔԹ౓ޯ഑๏ͱ೤ྲྀ൘๏ͷൺֱ͓Αͼஷ೤ͷӨ‫ڹ‬39

ʢGg0.02 ʣͱɼ์ࣹԹ౓‫ʹܭ‬Αͬͯଌఆͨ͠஋Λ༻͍ͯ‫ٻ‬Ίͨ΋ͷʢG g0.02 ʣ͸ɼ−30 ∼ 51 W m−2 ʹ෼෍ͭͭ͠
͓͓ΉͶҰக͠ɼ྆ऀͷܾఆ܎਺ʢr2 ʣ͓Αͼฏํฏ‫ۉ‬ೋ৐‫ࠩޡ‬ʢRMSEʣ͸ͦΕͧΕɼ0.963 ͱ 3.6 W m−2 Ͱ͋ͬͨʢFig. 2ʣɽ͜ͷ RMSE ͷ஋͸ɼ‫ޙ‬ड़͢Δ Gg0.02
ͱ Gp0.02 ͷൺֱʹ͓͚Δ‫΅΄ͱࠩޡ‬ಉ౳ɼ͋Δ͍͸ͦΕҎԼͰ͋ͬͨͨΊɼԹ౓ޯ഑๏ʹΑΔ஍த೤ྲྀྔͷࢉग़ʹ͓͍ͯɼαʔϛελʔԹ౓‫Ͱܭ‬ଌఆͨ͠஍ද໘Թ౓Λ
༻͍Δ͜ͱʹ໰୊͸ͳ͔ͬͨ΋ͷͱߟ͑ΒΕΔɽ

3.2 ೤఻ಋ཰ଌఆͷଥ౰ੑ
Fig. 3 ʹࣔ͢Α͏ʹɼ‫ס‬૩ঢ়ଶͰ͸ɼମੵ‫ؚ‬ਫ཰ʢθ ʣ

Fig. 3 ମੵ‫ؚ‬ਫ཰ͷؔ܎Ͱදͨ͠౔৕ͷ೤఻ಋ཰ɽ
Soil thermal conductivity as a function of volumetric soil watercontent.

͸ 0.02 ∼ 0.03 m3 m−3 ͱ‫ۃ‬Ίͯ௿͍஋Ͱ͋ΓɼϥΠγϝʔλʔ্Ͱଌఆ͞Εͨ λs ͸ 0.09 ∼ 0.10 W m−1 K−1Ͱ͋ͬͨɽ͜Εʹର࣪͠५ঢ়ଶͰ͸ɼθ ͕ 0.25 ∼ 0.29

m3 m−3 Ͱ͋ΓɼϥΠγϝʔλʔ্Ͱଌఆ͞Εͨ λs ͸
0.42 ∼ 0.48 W m−1 K−1 Ͱ͋ͬͨɽϥΠγϝʔλʔ্Ͱͷ λs ͷଌఆ஋͸ɼ࣮‫Ͱ಺ࣨݧ‬ଌఆͨ͠஋ͱ͓͓ΉͶҰக
ͨ͠ʢFig. 3ʣɽ࣮‫Ͱ಺ࣨݧ‬ଌఆͨ͠ 41 ͓Αͼ 4 ◦ C ʹ͓͚Δ λs ͸ɼ‫ס‬૩ঢ়ଶͰ͸ϥΠγϝʔλʔ্Ͱଌఆ͞Εͨλs ΑΓ΋Θ͔ͣʹେ͖ͳ஋ɼ࣪५ঢ়ଶͰ͸Θ͔ͣʹখ͞ͳ஋ͱͳ͕ͬͨɼͦͷࠩ͸ඇৗʹখ͔ͬͨ͞ʢ໿ 0.03 W
m−1 K−1 ʣɽ͜ͷ͜ͱ͔ΒɼϥΠγϝʔλʔ্Ͱͷ λs ͷଌఆʹ͓͍ͯɼ೤ಛੑ‫ܭ‬ͷϓϩʔϒͱ౔৕ͱͷ઀৮ͷෆ۩߹౳ͷ໰୊͸ͳ͔ͬͨͱߟ͑ΒΕΔɽ

3.3 ೤ྲྀ൘๏ͱԹ౓ޯ഑๏ͷൺֱ‫ס‬૩ঢ়ଶͰͷ஍த೤ྲྀྔ͸ɼ−16 ∼ +43 W m−2 ͷؒΛਪҠ͠ʢFig. 4ʣɼԹ౓ޯ഑๏ʹΑΔଌఆ஋ʢGg0.02 ʣʹର͢Δ೤ྲྀ൘๏ʹΑΔଌఆ஋ʢGp0.02 ʣͷ r2 ͱ RMSE ͸ͦΕͧΕɼ0.997 ͓Αͼ 15.4 W m−2 Ͱ͕͋ͬͨʢTable
Fig. 4 ‫ס‬૩ঢ়ଶʹ͓͚ΔԹ౓ޯ഑๏ʢGg0.02 ʣͱ೤ྲྀ൘๏
ʢGp0.02 ʣͰ‫ٻ‬Ίͨ஍த೤ྲྀྔͷൺֱɽനൈ͖ͱృΓͭͿ͠͸ͦΕͧΕ Philip ͷิਖ਼͋Γɼແ͠Λࣔ͠ɼθ ͸ਂ͞ 0.02 m ʹ͓͚Δ͓Αͦͷମੵ‫ؚ‬ਫ཰Λࣔ͢ɽܾఆ܎਺ʢr2 ʣ͓Αͼฏํฏ‫ۉ‬ೋ৐‫ࠩޡ‬ʢRMSEʣ͸ Table 2 ʹࣔ͢ɽComparison between soil heat ﬂux measured by the temperature
gradient method (Gg0.02 ) and that measured by the heat ﬂux plate
method (Gp0.02 ) with (open) and without (closed) Philip’s correction under dry condition. θ denotes approximate volumetricwater content at a depth of 0.02 m. Coefﬁcient of determination(r2 ) and root mean square error (RMSE) are shown in Table 2.

૩ঢ়ଶɼ͓Αͼ࣪५ঢ়ଶͰͷϥΠγϝʔλʔͷ θ ʢਂ͞

0.01 ∼ 0.03 mʣʹ΄΅౳͍͠‫ࢼڙ‬ମΛ༻ҙ͠ɼ߃Թνϟϯόʔ಺ʹͯͦΕͧΕ 41 ͓Αͼ 4 ◦ C ʹԹ౓Λઃఆ͠ɼλs Λଌఆͨ͠ɽ
͜ΕΒͷ࣮‫Ͱ಺ࣨݧ‬ͷ λs ͷଌఆͰ͸ɼ1 ͭͷ θ ʹରͯ͠‫ࢼڙ‬ମΛ 1 ͭ༻ҙ͠ɼ֤‫ࢼڙ‬ମʹର͠ɼλs Λ 15 ෼͓͖ʹ 3 ∼ 5 ճଌఆͯ͠ɼͦͷฏ‫ۉ‬஋Λ‫ٻ‬Ίͨɽ

3. ݁Ռ͓Αͼߟ࡯
3.1 ஍ද໘Թ౓ଌఆͷଥ౰ੑ
ʢ1ʣࣜͰ‫ٻ‬ΊͨԹ౓ޯ഑๏ʹΑΔ஍த೤ྲྀྔʹ͍ͭ

2ʣɼ܏͖͕΄΅ 3 ͱͳΓʢਤࣔ͸͍ͯ͠ͳ͍ʣɼԹ౓ޯ഑
๏ʹରͯ͠೤ྲྀ൘๏͸ɼ஍த೤ྲྀྔ͕ਖ਼ʢԼ޲͖ʣͷ࣌͸աେධՁ͠ɼ஍த೤ྲྀྔ͕ෛʢ্޲͖ʣͷ࣌͸աখධՁͨ͠ɽͭ·Γɼ೤ྲྀ൘๏͸஍த೤ྲྀྔͷઈର஋ΛҰఆͷׂ߹ͰաେධՁͨ͠ɽSauer et al.ʢ2003ʣ΍ Ochsner
et al.ʢ2006ʣ͸ɼຊ‫ͱڀݚ‬ಉ͡‫ࣜܗ‬ͷ೤ྲྀ൘Λ࢖ͬͯԹ౓ޯ഑๏ͱൺֱͨ݁͠Ռɼ೤ྲྀ൘๏͸Թ౓ޯ഑๏ʹൺ΂ɼ஍த೤ྲྀྔͷઈର஋ΛҰఆͷׂ߹ͰաখධՁͨ͠ͱใࠂ

Table 2 ‫ס‬૩ɼ࣪५ঢ়ଶͷͦΕͧΕʹ͓͚ΔԹ౓ޯ഑๏ͱ೤
ɼ͓ྲྀ൘๏ͷؒͷܾఆ܎਺ʢr2 ʣͱฏํฏ‫ۉ‬ೋ৐‫ࠩޡ‬ʢRMSEʣΑͼ Philip ͷิਖ਼͕ଌఆ๏ͷਫ਼౓ʹ‫͢΅ٴ‬Ө‫ڹ‬ɽ
Coefﬁcient of determination (r2 ) and root mean square error(RMSE) between soil heat ﬂux measured by the temperature gradient method and that by the heat ﬂux plate method under dry andwet condition, respectively. The effect of Philip’s correction on
the accuracy of measurement is also shown.

correction

r2

Dry*
RMSE
(W m−2 )

r2

Wet*
RMSE
(W m−2 )

No
Yes

0.997
0.997

15.4
11.0

0.983
0.982

2.1
3.4

Philip’sͯɼ஍ද໘ͷԹ౓ʹɼׂΓസΛऔΓ෇͚ͨαʔϛελʔ∗ Approximate volumetric water content at a depth of 0.02 m for the dryԹ౓‫Ͱܭ‬ଌఆͨ͠஋Λ༻͍ͯԹ౓ޯ഑Λࢉग़ͨ͠΋ͷand wet condition was 0.03 and 0.27 m3 m−3 , respectively.

౔৕ͷ෺ཧੑɹୈ 124 ߸ɹ (2013)40

൘ͱ౔৕ͷ઀৮ͷෆ۩߹Λ‫͛ڍ‬ɼOchsner et al.ʢ2006ʣ㻤㻜͸ɼ೤ྲྀ൘͕જ೤༌ૹͷ‫د‬༩Λ‫ܭ‬ଌͰ͖ͳ͔ͬͨ͜ͱΛ㻳㼜 㻜㻚㻜㻞 㻔㼃㻌㼙 㻙 㻞㻕㻢㻜‫͍ͯ͛ڍ‬Δɽຊ‫Ͱڀݚ‬͸ Fig. 3 ΑΓɼϥΠγϝʔλʔ্Ͱͷ λs ͷଌఆʹ໰୊͸ͳ͔ͬͨͱߟ͑ΒΕΔɽਤࣔ͸㻝㻦㻝㻌㻸㼕㼚㼑

㻠㻜͍ͯ͠ͳ͍͕ɼԾʹʢ1ʣࣜʹ 40 ◦ C Ͱଌఆ͞Εͨ λs Λ༻͍ͯ΋ɼ Gg0.02 ͸΄ͱΜͲมԽ͠ͳ͍ɽ೤ྲྀ൘ͷઃ㻞㻜ஔͷࡍʹ΋ɼ౔৕ͱͷ઀৮͕ྑ͘ͳΔΑ͏ʹ஫ҙΛ෷ͬͨɽ೤ྲྀ൘͕஍த೤ྲྀྔͷઈର஋ΛҰఆͷׂ߹Ͱաେධ

㻜Ձͨ͠ͱ͍͏ࣄ࣮͔Βɼજ೤༌ૹʹؔ͢Δ໰୊Ͱ͸ͳ͍㻙㻞㻜ͱߟ͑ΒΕΔɽҰํͰɼ౔৕͕ඇৗʹ‫ס‬૩͍ͯͨͨ͠Ί䃗㻩㻌㻜㻚㻞㻣㻌㼙 㻟㼙㻙㻟

㻙㻠㻜
㻙㻠㻜

㻙㻞㻜

㻜

㻞㻜

㻠㻜

㻢㻜

ʹ λs ͕খ͘͞ɼ೤ྲྀ൘ͷ೤఻ಋ཰ʢλm ʣͷ໿ 1/10 ͷ஋㻤㻜㻳㼓 㻜㻚㻜㻞 㻔㼃㻌㼙㻙㻞 㻕

Fig. 5 ࣪५ঢ়ଶʹ͓͚ΔԹ౓ޯ഑๏ʢGg0.02 ʣͱ೤ྲྀ൘๏
ʢGp0.02 ʣͰ‫ٻ‬Ίͨ஍த೤ྲྀྔͷൺֱɽനൈ͖ͱృΓͭͿ͠͸ͦΕͧΕ Philip ͷิਖ਼͋Γɼແ͠Λࣔ͠ɼθ ͸ਂ͞ 0.02 m ʹ͓͚Δ͓Αͦͷମੵ‫ؚ‬ਫ཰Λࣔ͢ɽܾఆ܎਺ʢr2 ʣ͓Αͼฏํฏ‫ۉ‬ೋ৐‫ࠩޡ‬ʢRMSEʣ͸ Table 2 ʹࣔ͢ɽComparison between soil heat ﬂux measured by the temperature
gradient method (Gg0.02 ) and that measured by the heat ﬂux plate
method (Gp0.02 ) with (open) and without (closed) Philip’s correction under wet condition. θ denotes approximate volumetricwater content at a depth of 0.02 m. Coefﬁcient of determination(r2 ) and root mean square error (RMSE) are shown in Table 2.

Ͱ͋ͬͨɽͦͷͨΊɼपғͷ౔৕ΑΓ΋೤఻ಋ཰ͷେ͖͍೤ྲྀ൘ʹଟ͘ͷ೤͕ྲྀΕͨ΋ͷͱߟ͑ΒΕΔɽ
࣪५ঢ়ଶͰ͸ɼ Gg0.02 ͱ Gp0.02 ͕ɼ−34 ∼ 78 W m−2ͷؒΛਪҠ͠ʢFig. 5ʣɼ−20 W m−2 ҎԼ͓Αͼ 20 W

m−2 Ҏ্Ͱ͸ɼ೤ྲྀ൘๏͕஍த೤ྲྀྔΛաେධՁ͢Δ܏
޲͕͋ͬͨ΋ͷͷ͓͓ΉͶҰக͠ɼr2 ͱ RMSE ͸ͦΕͧΕ 0.983 ͓Αͼ 2.1 W m−2 ͱɼ‫ס‬૩ঢ়ଶͰͷ৔߹ʹൺ΂ͯ‫͕ࠩޡ‬ඇৗʹখ͘͞ͳͬͨʢTable 2ʣɽ࣪५ঢ়ଶͰ
͸ɼλs ͕૿Ճ͠ λm ͷ໿ 1/2 ͱͳͬͨ͜ͱ͔ΒʢFig. 3ʣɼ೤ྲྀ൘๏͕஍த೤ྲྀྔΛաେධՁ͢Δ܏޲͕ऑ·Γɼ‫ס‬૩ঢ়ଶʹൺ΂ɼ Gg0.02 ͱ Gp0.02 ؒͷ‫ݮ͕ࠩޡ‬গͨ͠΋ͷͱߟ͑ΒΕΔɽ

㻴㼑㼍㼠㻌㼟㼠㼛㼞㼍㼓㼑㻌㻔㼃㻌㼙 㻙㻞 㻕

3.4 Philip ͷิਖ਼ͷӨ‫ڹ‬㻞㻜䃗 㻩㻌㻜㻚㻜㻟㻌 㼙 㻟 㼙㻙㻟

㻝㻜
㻜
㻙㻝㻜
㻔㼍㻕 㻭㼡㼓 㻞㻡㻘㻌㻞㻜㻝㻝㻙㻞㻜㻴㼑㼍㼠㻌㼟㼠㼛㼞㼍㼓㼑㻌㻔㼃㻌㼙 㻙㻞 㻕

㻜㻦㻜㻜

㻠㻦㻜㻜

㻤㻦㻜㻜 㻝㻞㻦㻜㻜 㻝㻢㻦㻜㻜 㻞㻜㻦㻜㻜㼀㼕㼙㼑䃗 㻩㻌㻜㻚㻞㻣㻌㼙 㻟 㼙 㻙㻟㻤㻜ิਖ਼ʹΑΔਫ਼౓ͷվળ͸‫ݦ‬ஶͰ͸ͳ͔ͬͨɽ·ͨ࣪५ঢ়ଶͰ͸ɼPhilip ͷิਖ਼ͷ݁Ռɼr2 ͸‫ס‬૩ঢ়ଶͷ৔߹ͱಉ༷ʹ΄ͱΜͲมԽ͠ͳ͔ͬͨ΋ͷͷɼRMSE ͕ 1.6 ഒͱͳͬͨʢTable 2ʣɽ͜Ε͸ิਖ਼ʹΑͬͯɼ஍த೤ྲྀྔͷෛͷ஋ʹ͓͚ΔԹ౓ޯ഑๏ͱͷဃ཭͕ਐΜͩͨΊͱߟ͑㻠㻜ΒΕΔʢFig. 5ʣɽ

㻜Harazono et al.ʢ1998ʣ͸ɼPhilip ͷิਖ਼ʹΑͬͯɼ೔

㻙㻠㻜
㻙㻤㻜

Philip ͷิਖ਼܎਺ʢʢ2ʣࣜʣ͸ɼ‫ס‬૩ঢ়ଶͰ͸໿ 0.82ɼ
࣪५ঢ়ଶͰ͸໿ 0.89 ͱͳͬͨɽͦͷ݁Ռɼ‫ס‬૩ঢ়ଶͰ͸ Gg0.02 ͱ Gp0.02 ͷؒͷ r2 ͸΄ͱΜͲมԽ͠ͳ͔ͬ
ͨ΋ͷͷɼิਖ਼Λ͠ͳ͔ͬͨ৔߹ʹൺ΂ͯ RMSE ͕ 4.4
W m−2 ‫ݮ‬গͨ͠ʢTable 2ʣɽ͔͠͠ Gg0.02 Λਅͷ஋ͱԾఆͨ͠৔߹ɼґવͱͯ͠ิਖ਼‫ޙ‬ͷ RMSE ͸ิਖ਼લ‫ޙ‬ͷ
RMSE ͷࠩʢ4.4 W m−2 ʣͷ 2.5 ഒ΋େ͖͘ɼPhilip ͷ㻔㼎㻕 㻰㼑㼏㻌㻝㻝㻘㻌㻞㻜㻝㻞
㻜㻦㻜㻜

㻠㻦㻜㻜

㻤㻦㻜㻜 㻝㻞㻦㻜㻜 㻝㻢㻦㻜㻜 㻞㻜㻦㻜㻜㼀㼕㼙㼑

ද૚ 0.02 m ͷஷ೤ྔͷ೔มԽɽ(a)ɼ(b) ͸ͦΕͧΕ‫ס‬૩ɼ࣪५ঢ়ଶΛࣔ͠ɼθ ͸ਂ͞ 0.02 m ʹ͓͚Δ͓Αͦͷମੵ‫ؚ‬ਫ཰Λࣔ͢ɽ

Fig. 6தͷ஍த೤ྲྀྔ͕ 50 ∼ 60 % ૿Ճͨ͠ʢิਖ਼܎਺͕ 1.5∼ 1.6 Ͱ͋ͬͨʣͱड़΂͍ͯΔɽ·ͨ Frey et al.ʢ2011ʣ͸ɼิਖ਼܎਺͕ 0.5 ∼ 0.7 Ͱ͋ͬͨͨΊɼิਖ਼͸ॏཁͰ͋Δͱड़΂͍ͯΔɽPhilip ͷิਖ਼܎਺͸ɼʢ2ʣࣜʹࣔ͢Α͏ʹɼ౔৕ͱ೤ྲྀ൘ͷ೤఻ಋ཰ɼ͓Αͼ೤ྲྀ൘ͷ‫ܗ‬ঢ়ʹΑܾͬͯ·Δ͕ɼຊ‫Ͱڀݚ‬͸ɼ‫ס‬૩ঢ়ଶͰ͸ิਖ਼܎਺͕

0.82 ͱେ͖͔ͬͨͨΊɼ·ͨ࣪५ঢ়ଶͰ͸ิਖ਼ʹΑͬͯ‫͕ࠩޡ‬େ͖͘ͳͬͨ͜ͱ͔ΒɼPhilip ͷิਖ਼ͷ࣮༻্ͷDiurnal changes of heat storage in surface layer (0.02 m thickness) under dry (a) and wet (b) conditions. θ denotes approximate
volumetric water content at a depth of 0.02 m.

ޮՌ͸ೝΊΒΕͳ͔ͬͨɽ

͓ͯ͠Γɼຊ‫ڀݚ‬͸͜ΕΒͱ͸ରরతͳ݁Ռͱͳͬͨɽஷ೤ྔʢΔGʣͷ೔มԽʹ͍ͭͯɼ‫ס‬૩ঢ়ଶͰ͸ 2011
೥ 8 ݄ 25 ೔ɼ࣪५ঢ়ଶͰ͸ 2012 ೥ 12 ݄ 11 ೔ͷྫΛ

Sauer et al.ʢ2003ʣ͸ɼ೤ྲྀ൘๏ͷաখධՁͷ‫ݪ‬Ҽͱͯ͠ɼ೤ྲྀ൘ͷதԝ෦ͱ֎ԑ෦ʹੜ͡Δ೤ྲྀͷҧ͍΍೤ྲྀ

3.5 ද૚ͷஷ೤ͷӨ‫ڹ‬

Fig. 6ʢaʣʢbʣʹࣔ͢ɽ‫ס‬૩ঢ়ଶͰ͸ɼΔG ͕ −12 ∼ 17
−2
W m ͰਪҠ͠ɼ5:30 ∼ 14:30 ·Ͱ͸ਖ਼ͷ஋ɼ14:30 Ҏ࿦จɿ஍ද໘ۙ๣Ͱͷ஍த೤ྲྀྔͷଌఆʹ͓͚ΔԹ౓ޯ഑๏ͱ೤ྲྀ൘๏ͷൺֱ͓Αͼஷ೤ͷӨ‫ڹ‬
Table 3 ‫ס‬૩ɼ࣪५ঢ়ଶͷͦΕͧΕʹ͓͚Δද૚ 0.02 m ͷஷ೤ྔͷ೔ੵࢉྔɽ
Daily heat storage in surface layer (0.02 m thickness) under dry
and wet condition, respectively.
Heat storage (kJ m−2 )
Dry*
Wet*
Mean
Standard deviation

24.7
21.6

12.3
52.0

∗ Approximate volumetric water content at a depth of 0.02 m for the dry

and wet condition was 0.03 and 0.27 m3 m−3 , respectively.

41஫ҙ͕ඞཁͰ͋Δ΋ͷͷɼ஍ද໘ۙ๣Ͱ΋࢖༻Ͱ͖Δ͜
ͱ͕֬ೝͰ͖ͨɽ࣮༻తʹ͸ɼ೤ྲྀ൘ͷ‫ޮͯ͠ͱ༻ূݕ‬Ռ͕͋Δ΋ͷͱߟ͑ΒΕΔɽ·ͨɼ೤ྲྀ൘๏ʹΑΔ஍த
೤ྲྀྔͷଌఆʹ͓͍ͯɼPhilip ͷิਖ਼ͷ࣮༻తͳޮՌ͸ೝΊΒΕͳ͔ͬͨɽ͞Βʹɼද૚ 0.02 m ͷஷ೤ྔ͸ɼ1೔ͷதͰ͸ਂ͞ 0.02 m ʹ͓͚Δ஍த೤ྲྀྔͱಉఔ౓ͷมԽΛ͕ࣔͨ͠ɼ1 ೔ͷੵࢉͰ͸‫ۃ‬Ίͯখ͔ͬͨ͞ɽ͜
Ε͸ɼஷ೤ͱ์೤ʹΑͬͯਖ਼ຯͷஷ೤ྔ͕૬ࡴ͞ΕΔͨ
ΊͰ͋Δɽ

ँࣙ
߱ʹෛͷ஋Λࣔͨ͠ɽ࣪५ঢ়ଶͰ͸ɼΔG ͷਪҠ͕ −62∼ 89 W m−2 ͱɼ‫ס‬૩ঢ়ଶͷ৔߹ʹൺ΂ͯ޿͘ͳΓɼ஍த೤ྲྀྔͷมԽ෯ʢFig. 5ʣʹඖఢ͢Δ΄ͲͷมԽ෯ͱͳͬ
ͨɽ·ͨ 6:30 ∼ 13:30 ·Ͱ͸ਖ਼ͷ஋ɼ13:30 Ҏ߱ʹෛͷ஋Λࣔͨ͠ɽΔG ͷ೔มԽ͸ɼ‫ס‬૩ঢ়ଶͱ࣪५ঢ়ଶͷͦΕͧΕʹ͓͍ͯɼ‫؍‬ଌ‫ؒظ‬தɼಉ༷ͷ܏޲Λࣔͨ͠ɽ࣪
५ঢ়ଶͰ͸ɼ‫ס‬૩ঢ়ଶʹൺ΂ɼ஍ԹͷมԽ෯͕খ͔ͬ͞

ຊ‫ڀݚ‬ͷ਱ߦʹ͋ͨͬͯ͸ɼ౦‫ژ‬೶‫ۀ‬େֶ஍Ҭ‫ڥ؀‬Պֶ෦ੜ࢈‫ֶ޻ڥ؀‬Պ஍ਫ޻ֶ‫ࣨڀݚ‬ઐ߈ੜͷ‫ྗڠ‬Λ௖͍ͨɽ·ͨ๺ւಓ೶‫ڀݚۀ‬ηϯλʔͷኍా஌ྑത࢜ɼ͓Αͼ Cranﬁeld University ͷ Robert W. Simmons ത࢜ΑΓɼ‫ʹߘݪ‬ରͯ͠‫و‬ॏͳॿ‫ݴ‬Λࣀͬͨɽ‫ँͯ͠ه‬ҙΛද͠·͢ɽͨʹ΋͔͔ΘΒͣʢTable 1ʣɼΔG ͷมԽ෯͕େ͖͘ͳͬ

Ҿ༻จ‫ݙ‬

ͨͷ͸ʢFig. 6ʣɼਫͷఆѹൺ೤ʢCW ʣ͕౔৕ͷଞͷߏ੒ཁૉʹൺ΂ͯେ͖͍͜ͱ͔Βɼ࣪५ঢ়ଶʹ͓͚Δ౔৕ͷ

Cobos, D.R. and Baker, J.M. (2003): In situ measurement of soilମੵ೤༰ྔʢCʣ͕‫ס‬૩ঢ়ଶΑΓ΋େ͖͘ͳͬͨͨΊͱ

heat ﬂux with the gradient method. Vadose Zone Journal, 2:ߟ͑ΒΕΔɽ

589–594.

͜ͷΑ͏ʹɼΔG ͸ 1 ೔ͷதͰେ͖͘มԽ͢ΔͨΊɼ

Evett, S.R., Agam, N., Kustas, W.P., Colaizzi, P.D. and Schwartz,

Mayocchi and Bristowʢ1995ʣ΍޿ాΒʢ2001ʣ͕ࢦఠ͠
͍ͯΔ௨Γɼ1 ೔ະຬͷִ࣌ؒؒͰ஍ද໘ʹ͓͚Δ஍த

conductivity and heat ﬂux: Comparison to soil heat ﬂux plates.

೤ྲྀྔͷมԽΛৄࡉʹௐ΂Δ৔߹͸ɼ೤ྲྀ൘΍Թ౓ޯ഑๏Ͱ‫ٻ‬Ίͨ஍த೤ྲྀྔʹ ΔG ΛՃ͑Δඞཁ͕͋ΔɽҰํͰɼΔG Λ 1 ೔Ͱੵࢉ͠ɼ‫؍‬ଌ‫ؒظ‬Λ௨ͯ͠ฏ‫͢ۉ‬Δͱɼ

‫ס‬૩ঢ়ଶͰ͸ 24.7 ± 21.6 kJ m−2 ɼ࣪५ঢ়ଶͰ͸ 12.3 ±52.0 kJ m−2 ͱͳͬͨʢTable 3ʣɽ1 ೔ੵࢉͷ ΔG ͸ɼ஍ද໘Թ౓ʹΑΔ஍த೤ྲྀྔͷଌఆ‫ࠩޡ‬ʢFig. 2ʣ΍ɼԹ౓ޯ഑๏ͱ೤ྲྀ൘๏ͷؒͷ‫ࠩޡ‬ʢTable 2ʣΛ 1 ೔Ͱੵࢉͨ͠৔߹ͱൺֱ͢Δͱɼ1/10 ҎԼͱ‫ۃ‬Ίͯখ͍͞ɻ͜Ε͸ɼਖ਼ෛʹมԽ͢Δ ΔG ͕ɼ1 ೔Λ௨ͯ͠૬ࡴ͞ΕͨͨΊͰ͋Δɽ͜ͷ͜ͱ͔Βɼ‫ق‬અมಈ΍௕‫ظ‬มಈͷධՁͷΑ͏ʹɼ஍த೤ྲྀྔΛ 1 ೔ੵࢉͰ༻͍ΔΑ͏ͳ৔߹͸ɼ஍ද໘͔Βް͞ 0.02 m ͷ ΔG ͸஍த೤ྲྀྔʹ΄ͱΜͲӨ‫ڹ‬Λ‫͑ߟͱ͍ͳ͞΅ٴ‬ΒΕΔɽ

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ཁࢫ஍த೤ྲྀྔ͸ɼ཮໘ʹ͓͚Δ೤ަ‫׵‬ͷॏཁͳߏ੒ཁૉͰ͋Γɼ೤ऩࢧΛ΋ͱʹͨ͠ৠൃࢄྔͷఆྔԽʹඞཁͰ͋ΔɻͦͷͨΊɼଌఆํ๏ͷಛੑΛ஌Δ͜ͱ͸༗ӹͰ͋Δɽຊ‫Ͱڀݚ‬͸ɼҟͳΔ౔৕ਫ෼ͷ΋ͱɼ
ʢiʣਂ͞ 0.02 m ʹ͓͍ͯԹ౓ޯ഑๏ͱ೤ྲྀ൘๏Λൺֱ͢Δ͜ͱɼ
ʢiiʣͦͷࡍɼ೤ྲྀ൘๏ʹ͓͍ͯ Philipͷิਖ਼ͷӨ‫ݕ͍ͯͭʹڹ‬౼͢Δ͜ͱɼ
ʢiiiʣ͞Βʹද૚ʢް͞ 0.02 mʣͷஷ೤ͷӨ‫ݕ͍ͯͭʹڹ‬౼͢Δ͜
ͱɼΛ໨తͱͨ͠ɽͦͷ݁Ռɼ౔৕ͷ೤఻ಋ཰͕೤ྲྀ൘ͷ೤఻ಋ཰ͷ໿ 1/2 ͷ৔߹ʢ࣪५ঢ়ଶʣͰ͸ɼԹ౓ޯ഑๏ͱ೤ྲྀ൘๏͸ඇৗʹΑ͘Ұக͕ͨ͠ɼ౔৕ͷ೤఻ಋ཰͕೤ྲྀ൘ͷ೤఻ಋ཰ͷ໿ 1/10 ͷ৔߹ʢ‫ס‬૩ঢ়ଶʣͰ͸ɼ೤ྲྀ൘๏͸஍த೤ྲྀྔͷઈର஋ΛҰఆͷׂ߹ͰաେධՁͨ͠ɽ·ͨ Philip ͷิਖ਼ͷ࣮༻తͳޮՌ͸ೝΊΒΕͳ͔ͬͨɽ͞Βʹද૚ͷஷ೤ྔ͸ɼ1 ೔ͷதͰ͸ਂ͞ 0.02 m ʹ͓͚Δ஍த೤ྲྀྔͱಉఔ౓ͷมԽΛ͕ࣔͨ͠ɼ1 ೔ͷੵࢉͰ͸‫ۃ‬Ίͯখ͔ͬͨ͞ɽ
Ωʔϫʔυɿ஍த೤ྲྀྔଌఆ๏ɼ೤఻ಋ཰ɼ஍ද໘Թ౓ɼ೤ऩࢧɼ౔৕໘ৠൃ