2.3 Air temperature and surface temperature
Near the ground surface, F¯(t,z) + F- (t,z) = F¯ (t,0), exp (-5/3k_inf r(z)dz) 1 and S(t,z)= S(t,0) exp (k_viss(z)dz) S(t,o). Using these Equations, we can obtain the model as follows:

Parameters
	phase(hour)	cgrglg (J2s-1K-2m-4)	b	W (ms-1)	Albedo	emissivity
Concrete	1.5	3.6x106	0	2	0.306	1.
Asphalt	1.5	1.0x106	0	2	0.255	1.
Soil	1.5	0.39x106	0.1	2	0.239	1.
Grass	0.5	0.39x106	0.1	2	0.289	1.
Tree	0.5	0.0	0.5	2	0.345	1.

Table 1: Parameters used for a model calculation.

	Expected values		Fitting results
	A	b	a	b
concrete	1	-0.287	0.935 ±0.012	-0.276 ±0.013
asphalt	1	-0.315	0.959 ±0.016	-0.224 ±0.017
soil	1	-0.324	1.00 ±0.025	-0.280 ±0.025
grass	1	-0.296	1.105 ±0.033	-0.373 ±0.033
tree	1	-0.264	0.840 ±0.033	-0.028 ±0.030

Table 2: Expected values of a and b fitting results.

3. Data analysis for ground measurement data
Applying the model to the ground measurement data, we measured surface temperature, air temperature humidity and wind velocity on some types of ground objects on a fine day (no cloud). Data wee taken on concrete, asphalt, soil, grass and trees every hour for 24 hours on August 28 1997, January 10 1998 (Shiono, 1998), and March 2 1998. In addition to temporal measurement, data have been taken using a logger since August 1998 for concrete. The quantity of the solar irradiance was provided by Nara Meterological station.

The energy distribution for each radiation as a function of time is shown in Figure 2. Sensible heat flux latent heat flux and conductive heat flux are calculated using the formula described in Appendix. The phase difference d between solar radiation (or conductive heat in the ground) and surface temperature was assumed to be 1.5 hours for concrete, asphalt and soil and as a half hour for grass and a tree. The wind efficiency bis assumed to be 0.1 for soil and grass, and to be 0.5 for a tree. The wind velocity for sensible heat transfer is assumed to be 2 ms-1. One hour delay of the conductive heat phase is used especially for soil. The parameters used for the model Calculation are summarized in Table 1. The coefficients a and b are determined by the least-squared fit using daytime data. Expected values of a and be are summarized in Table 2.


Figure 2: Energy distribution of solar irradiacne, energy emitted from air and surface, sensible heat and conductive heat, and the least-squares fitting results for concrete, asphalt, soil, grass and a tree.
2. The results of fitting the data to a straight line are shown in Figure 2. Data is plotted with rhomus and the fitted results are shown with the dotted line. The results of the data measured for concrete, asphalt, soil, grass and trees on August 28 1997 are summarized in Table 2. For concrete, asphalt, soil and grass, the values of a and b of fitted results almost agree with the expected values within experimental errors. For soil and grass, the value of b is changed by the value of evaporation efficiency. For trees, the value b evaluated from the data are different from expected value. We measured the air temperature and the leaf temperature inside the canopy of the tree. This situation was different from the definitions of air and surface temperature in the model.

From these results, the model works well only for concrete, asphalt, soil and grass at ground level. For grass and soil, we have to introduce a new factor to estimate the evaporation efficiency. For the tree, we have to improve our measurement of temperature to satisfy the parameters of the model.

4. Satellite data Analysis
We used remote sensing data ovserved by a Thematic Mapper ™ sensor on board the LANDSAT satellite. The measured energy by TM sensor is affected by the atmosphere, which itself acts as an emitter. We recalibrated TM data using the relationship between the temperature measured at ground level and that measured by the TM sensor using the assumption of the atmospheric conditions being almost the same. The surface temperatures on the ground were measured at Tanabe Bay and on the roof of Nara Women’s University in Japan. Figure 3 shows the results of the relationship. X-axis shows the brightness temperature of the TM sensor (EOC, 1990) and Y-axis that of the ground measurement. For converting the surface temperature on the ground to the brightness temperature, the numerical values of emissivity 0.98 and 0.94 were used for water (Tanabe bay) and concrete (rooftop), respectively. Rhombi show the data points and the dotted line the results fitted to a straight line. The brightness temperature of TM data is recalibrated using the following relationship.


Figure 3 : Brightness temperature of TM data and that of the ground measurement data.


Using the relationship of Equation (4), the surface temperature of TM data measured on Aug. 2020 1995 is evaluated. Using the surface temperature measured by TM sensor, air temperature, and solar radiation measured by AMeDAS (Automated Meteorological Data Acquisition System), and the model, the maximum of sensible heat flux, conductive heat flux, latent heat flux in the day are estimated as shown in Figure 4 for non-vegetation area. Fore estimating the energy flux for vegetation area, we should improve the model of radiation balance.


Figure 4 :(a) Sensible heat flux, (b) Conductive heat flux and (c) Latent heat flux on Aug. 20 1995, in Kansai area in Japan.
5. Conclusion
We have developed a model of radiation balance near ground level to estimate air temperature using surface temperature. To apply the model to data, we measured air temperature, humidity and wind velocity on concrete, asphalt, soil, grass and trees every hour 24 hours.

We applied the model to the ground measurement data. The model works well only for concrete, asphalt, soil and grass. We have to introduce new ideas for determination of evaporation efficiency and to improve measurements of air temperature and surface temperature for trees satisfy the parameters of the model.

Using the model for non-vegetation area, we estimated the maximum latent, conductive and sensitive and sensitive heat flux in the day. For estimating the energy flux, we should improve the model for vegetation area.

Acknowledgement
This work was supported by Grant-in-A 10780326 for Encouragement of Young Scientist, Japan Society for the Promotion of Science. The LANDSAT/TM and MSS data were provided by the Earth Observation Satellite Company (EOSAT) and National Space Development Agency (NASDA) in Japan. AMeDAS data was provided by Nara Branch, Japan Weather Association. The water temperature data measured at Tanable Bay was provided by Fisheries laboratory of Kinki University in Japan.

Reference
EARTH OBSERVATION CENTER, NATIONAL SPACE DEVELOPMENT AGENCY OF JAPAN, 1990, LANDSAT-5 data user’s HandBook (Remote Sensing Technology Center of Japan)

HOUGHTON, T.JOHN, 1996, The Physics of atmospheres, Cambridge University Press KAHLE, B. ANNE, 1977 A Simple thermal model of the erath’s surface for geologic mapping by remote sensing J. of Geophysical Research, Vol 82, No. 11,1673-1680.