4.4 Diffusion coefficient
The diffusion coefficient was obtained using both
approaches based on surface roughness using formulae
for the logarithmic law of wind velocity and heat
transfer. The former was suggested by Kondo and
Yamasawa (1983).
4.4.1 Roughness estimation: Surface roughness
is calculated using relationships between wind velocity
at an isobaric surface of 800 - 900 mb and that at the
ground meteorological monitoring station in the
procedure suggested by Kondo and Yamasawa (1983).
First, the geostropheric wind speed is calculated using
the following equation
G = V900 - TH E nun (14)
where G, V800, and V900 is geostrophic wind speed and wind speed
at isobaric surfaces of 800 and 900 mb, respectively.
Then, the G values from wind data at
aerometeorological stations were interpolated to make it
correspond with the points of the ground meteorological
monitoring stations (Automated Meteorological Data
Aquisition System). :
U*/G can be converted to Vz/G in the following
deformed formula for the logarithmic law of wind
velocity;
Vz =-U* 1. VA PP
G Tx In 7) (15)
where Vz: Daily average of wind speed at a ground
meteorological station, G: geostrophic wind speed at an
isobaric surface of 800 - 900 mb, U*: surface friction
velocity, k: Karman's constant, Z0: roughness, Z:
altitude of wind gauge (Z=Z-d). Here, in this study,
zero-plane displacement (d) is also assumed as zero in
the same way as for Kondo and Yamazawa (1983).
Surface roughness is given in the following equation;
[2
ES ent (Kondo and Yamasawa, 1983) (16)
1
In-G- -A-Incgs (E. B?
Cg
where G: geostrophic wind speed at an isobaric surface
of 800 - 900 mb, Cg: U*/ G, f: 2 o sin ¢ (Coriolis
factor) f: latitude, A: 1.5, B: 4, U*: surface friction
velocity, k: Karman's constant, Z0: roughness.
4.4.2 Estimation of diffusion coefficient:
Substitution of roughness (Z0) into equation (Eq.15)
gives the surface friction velocity (U*).
Then, we can obtain the diffusion coefficient (K) by
substituting the surface friction velocity (U*) into the
following equation:
K= Ut n Zu as (17)
where K: diffusion coefficient, U*: surface friction
velocity, k: Karman's constant, Z: altitude of wind
gauge.
Then the diffusion coefficients obtained from the
meteorological monitoring stations were interpolated to
coincide to each NOAA image pixel in the same way as
for shortwave radiation. The value on both sides of the
mapping frame was obligatorily given by the values of
the diffusion coefficient at the nearest monitoring points
(Fig.15).
Fig. 15 Distribution of diffusion coefficient
in and around Hokkaido Island, Japan
(Oct. 17,1990).
4.5 Determination of gradient of the
saturated vapor pressure curve
For the last parameter of the thermal inertia model, it is
necessary to determine the inclination of the saturated
vapor pressure model/curve based on the relationships
between temperature and saturated vapor pressure. The
gradient of the tangent to the curve was obtained as a
differential coefficient at an average value of air and
surface temperatures.
5. THERMAL INERTIA
Parameters such as downward/ upward shortwave and
long wave radiation, daily amplitude of both surface and
air temperatures and net radiation, relative wetness of
soil surface and diffusion coefficient were derived from
the above heat balance analyses using meteorological
and NOAA AVHRR data obtained at noon and in the
early morning (here, nighttime data were used instead of
those for early morning). It is then, possible to
compute the thermal inertia in each NOAA AVHRR
image pixel by substituting these parameters into the
thermal inertia model (Eq.1).
6. CONCLUSIONS
In this study, the author constructed a prototype database
of attributes and sample data from ground
meteorological and hydrological monitoring stations.
By feeding the other data such as information from
aerometeorological and ground meteorological stations
into this database, and integrating it with geographical
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996
