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Evaluation of the Diurnal Warming of Sea Surface Temperature Using Satellite-Derived Marine Meteorol


Journal of Oceanography, Vol. 58, pp. 805 to 814, 2002

Evaluation of the Diurnal Warming of Sea Surface Temperature Using Satellite-Derived Marine Meteorological Data
Y OSHIMI KAWAI* and HIROSHI KAWAMURA
Center for Atmospheric and Oceanic Studies, Graduate School of Science, Tohoku University, Aoba-ku, Sendai 980-8578, Japan (Received 14 September 2001; in revised form 1 March 2002; accepted 9 March 2002)

In order to produce a high-quality sea surface temperature (SST) data set, the daily amplitude of SST (?SST) should be accurately known. The purpose of this study was to evaluate the diurnal variation of sea surface temperature in a simple manner. The authors first simulated ?SST with a one-dimensional numerical model using buoyobserved meteorological data and satellite-derived solar radiation data. When insolation is strong, the model-simulated 1-m-depth ?SST becomes much smaller than the in situ value as wind speed decreases. By forcibly mixing the sea surface layer, the model ?SST becomes closer to the in situ value. It can be considered that part of this difference is due to the turbulence induced by the buoy hull. Then, on the assumption that the model results were reliable, the authors derived a regression equation to evaluate ?SST at the skin and 1-m depth from daily mean wind speed (U) and daily peak solar radiation (PS). ?SST is approximately proportional to In(U) and (PS)2, and the skin ?SST estimated by the equation is not inconsistent with in situ observation results reported in past studies. The authors prepared maps of PS and U using only satellite data, and demonstrated the ?SST evaluation over a wide area. The result showed that some wide patchy areas where the skin ?SST exceeds 3.0 K can appear in the tropics and the mid-latitudes in summer.

Keywords: ? Sea surface temperature, ? satellite observation, ? diurnal warming, ? solar radiation, ? wind speed, ? numerical model.

1. Introduction An operational, higher-resolution sea surface temperature (SST) product is required by several groups, including the Global Ocean Data Assimilation Experiment (GODAE) and numerical weather prediction. This product should have a spatial resolution near or better than 10 km, temporal resolution of 24 hours or less, and should include proper account of skin temperature effects (http: //www.bom.gov.au/bmrc/ocean/GODAE/2ndIGST/ IGST_Report.html). In making such a high-resolution SST product, one of important problems is how to deal with the diurnal variation of SST (Smith, 2001). Many researchers have indicated that the amplitude of the SST diurnal variation (?SST) caused by solar heating sometimes goes up to 3 K or more under calm and clear conditions (e.g., Stramma et al., 1986; Price et al., 1987; Yokoyama et al., 1995; Fairall et al., 1996b). If satellite* Corresponding author. E-mail: kawai@ocean.caos.tohoku. ac.jp
Copyright ? The Oceanographic Society of Japan.

derived SSTs are simply averaged to make a daily SST map without considering the diurnal variation, unnatural patches or streaks may appear because of the warming. Our purpose in this study is to develop a method to evaluate ?SST from satellite-derived data only. For example, Price et al. (1987) proposed an empirical equation to evaluate the SST amplitude using wind stress and air-sea heat flux data observed with a moored buoy in the Sargasso Sea. Webster et al. (1996) produced another type of equation that consists of daily peak solar radiation, daily mean wind speed and precipitation rate. Since it is difficult to obtain daily air-sea heat flux accurately from satellite data only, we use an empirical equation similar to that of Webster et al. (1996). We first describe the data and a numerical model used in this paper (Section 2), and simulate the diurnal variation of SST using buoy data and satellite-derived hourly solar radiation data by the simple numerical model (Section 3). A regression equation to evaluate the daily SST amplitude is then produced from the model results (Section 4). The model ?SST is better for the purpose than the in situ data, which may include warming or cooling

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caused by advection. In this study, the temperature variation owing to advection is not taken into consideration. Finally, we demonstrate the ?SST evaluation in practice using satellite-derived wind speed and solar radiation data by the regression equation (Section 5). 2. Data and Procedure 2.1 Solar radiation data Tanahashi et al. (2000, 2001) have developed a method to evaluate solar radiation at the earth’s surface from Geostationary Meteorological Satellite/Visible Infrared Spin Scan Radiometer (GMS/VISSR) data. This sensor observes the earth every hour from about thirty minutes after the hour, in the observation area 60°N–60°S and 80°E–160°W. The spatial resolution of the visible channel is 1.25 km at nadir, and that of the infrared channel is 5.0 km at nadir. Tanahashi et al.’s estimated solar radiation image has a spatial resolution of 0.01° and a time resolution of one hour. This study used the solar radiation product produced from GMS/VISSR data by Tanahashi et al. 2.2 Buoy data We used the global drifting-buoy data set distributed by the Marine Environmental Data Service (MEDS) in Canada. MEDS acquires, processes, quality controls and archives drifting buoy messages reporting continuously over the global telecommunications system (GTS). The data of the TRITON (Triangle Trans-Ocean buoy Network) and TAO (Tropical Atmosphere Ocean) buoys moored in the equatorial area are included in the data set. We also used the data of the moored buoys managed by Japan Meteorological Agency (JMA), which were not included in the MEDS data set. This study used the data during Jan. 1998 to Dec. 1999. We selected the buoy data that included at least air temperature and wind speed besides sea surface temperature, and made a daily time series for each buoy if there are more than four observations in the daytime per day. A corresponding time series of solar radiation derived from GMS/VISSR data was matched up with the daily buoy time series. The solar radiation was averaged in a bin of

0.40° × 0.40° the center of which was a daily mean position of a drifting buoy. In the case of the JMA buoys, the size of the bin was 0.10° × 0.10°. If the daily time series of solar radiation was incomplete (an observation of VISSR had failed, or the beginning or end of the time series was greater than 150 W/m2), this data set was excluded. Since there solar radiation product contains only data during 06–19 LST (Japan Standard Time), equatorial buoy data far from the meridian of 135°E could not be matched up with the solar radiation data. Most of the selected data were those of the TOGA (Tropical Ocean and Global Atmosphere)-style drifting buoys and the JMA ones, and some of the TRITON buoy data were included. Information about these buoys and their sensors is listed in Table 1. The values of solar radiation, air temperature, humidity and wind speed between observations were calculated by linear interpolation. If there was no observation at 0000 or 2400 LST, the data at the nearest time of the day were substituted. If humidity data were not included, relative humidity was assumed to be a constant value of 75.0% in a model simulation. Using these meteorological data we simulated the diurnal variation of temperature in the sea surface layer by the numerical model. 2.3 Model simulation In order to simulate the diurnal variation of temperature in the vicinity of the sea surface we used the KondoSasano-Ishii (KSI) model, which is a simple one-dimensional numerical one described in Kawai and Kawamura (2000). The skin temperature was computed separately using the Fairall et al. (1996b) parametric skin model. The calculation of air-sea heat and momentum fluxes was improved in this study. Fairall et al. (1996a)’s method was adopted here to compute heat and momentum turbulence transfer at the sea surface. Integration was initiated from 0000 LST. The initial values of current speed and eddy diffusion coefficients were set to zero. The initial profile of salinity was assumed to be vertically homogeneous, and set to 34.0 psu. That of seawater temperature was given as follows: the vertical temperature gradient is 0.1 K/50 m in 0~50-m depth, and 1-m-depth temperature is set to the buoy-ob-

Table 1. Positions of buoy sensors and size of buoy hulls.
TOGA-style buoy Type Height of anemometer Depth of SST sensor Length of buoy Maximum diameter of buoy Drifting 1.5 m (1.0 m or 0.5 m for several buoys) 1.0 m 3.2–3.7 m About 0.7 m TRITON Moored 3.5 m 1.5 m 5.53 m 2.4 m JMA buoy Moored 7.5 m 1.0 m 9.0 m 10.0 m

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served value at 0000 LST. The bottom depth was set to 50.0 m, and it was assumed that momentum and sensible heat flux are zero at the bottom. The SST diurnal variation is small when the wind is strong. Hence, we did a model simulation only for the case that daily mean wind speed is equal to or less than 10.0 ms–1. The total number of data points used for the model simulations was 1718. Figure 1 shows the positions of the data used. 3. Reliability of Simulated SST Diurnal Warming We define ?SST as the difference between the maximum after 0900 LST and the minimum before 0900 LST. Figure 2 shows the relation between buoy-observed ?SST and model-simulated values. The model-simulated temperature at the same depth as the corresponding buoy SST sensor was compared with the buoy SST (Table 1). Wind speeds measured with the buoy sensors at various heights above the sea surface were converted to the equivalent neutral wind speeds at a height of 10 m:
U (10 m ) = u* In(10 / z0 ) k

ences between them are within ±0.5 K. (Note that the scales of the axes in Fig. 2(b) are different from those in Fig. 2(a).) However, all the model ?SSTs are smaller than the in situ ones in the case of buoy ?SST ≥ 1.5 K. This difference could be caused by the platform effect described by Kawai and Kawamura (2000). When conditions are clear and wind speed is very low, a vertical temperature gradient develops in the vicinity of the sea surface in the daytime. If there is a large vertical temperature gradient above 1-m depth, it suppresses heat transfer

[

],

(1)

where u* is the friction velocity, z 0 is the surface roughness length, k is the von Kármán constant (0.4). u* and z 0 can be computed by iteration (Fairall et al., 1996a). Averaged U(10m) during 09–15 LST is used, and U refers the time-averaged U(10m) hereafter. In the case of buoy ?SST < 1.5 K, the model ?SSTs agree well with the in situ ones, and most of the differ-

Fig. 1. Positions of buoy observations used for the model simulations. Solid circles represent drifting buoys and TRITION buoys, and asterisks represent JMA buoys.

Fig. 2. Relation between buoy-observed ?SST and model-simulated value (both in Kelvin). (a) Drifting buoys (open circles) and TRITON buoys (plus signs), (b) JMA buoys.
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Fig. 3. Relation between ?SST (K) and wind speeds averaged during 09–15 LST (ms –1). Only the data of PS (Peak Solar radiation) ≥ 800 Wm –2 are plotted. (a) Buoy-observed values, (b) model results (1-m-depth temperature).

from the sea surface to 1-m depth. Hence, it becomes more difficult to increase the 1-m-depth temperature as wind speed decreases under clear conditions. On the other hand, the buoy-observed 1-m-depth temperature increases monotonously as wind speed decreases (Fig. 3(a)). This may be because the hull of a buoy disturbs the temperature field and breaks a large vertical gradient around the buoy. The model ?SST does not increase when U becomes less than about 2.5 ms –1 (Fig. 3(b)). We then added artificial mixing to the sea surface layer in the model simulation. Figures 4 and 5 show the cases when the minimum of the eddy diffusion coefficients were set to 1.0 × 10–5 m2s –1 (weak mixing) and 8.0 × 10–5 m2s–1 (strong mixing) above 1-m depth, respectively. The eddy diffusion coefficients could not be less than the minimum value in the model. If the artificial mixing is added, the model ?SST becomes closer to the in situ values in the case of buoy ?SST ≥ 1.5
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Fig. 4. As Fig. 2, except for setting the minimum eddy diffusion coefficients of 1.0 × 10–5 m2s–1 above 1-m depth in the model simulation.

K. When the strong mixing was forcibly added in the simulations of the drifting-buoy data, some of the model ?SST values became too large compared with the in situ values. The minimum value of 8.0 × 10–5 m2s –1 is too large for the drifting buoys. In the case of the JMA-buoy data, the model ?SSTs with the strong mixing agree with the in situ values better than those with the weak mixing. However, the model ?SSTs are still smaller than the in situ values when the latter are over 2.0 K. In order to examine whether these in situ data were affected by advection of heat, we calculated the possible

Fig. 6. Relation between buoy-observed ?SST and possible maximum ?SST (both in Kelvin). Open circles represent JMA-buoy data and asterisks represent drifting-buoy data.

Fig. 5. As Fig. 2, except for setting the minimum eddy diffusion coefficients of 8.0 × 10 –5 m 2s–1 above 1-m depth in the model simulation.

maximum ?SST (?SSTmax) at 1-m depth defined by the following formula:

?SSTmax =

1 cρ

∫t (S ? Q)dt,
tm
0

(2 )

where c is the specific heat of seawater at constant pressure, ρ is the density of seawater, S is the solar radiation absorbed between the sea surface and 1-m depth, Q is the net heat flux at the sea surface, which is the sum of the

sensible and latent heat fluxes and the net longwave radiation (upward is positive). The time when S is equal to Q in the morning is specified by t0, and tm is the time when SST reaches its peak. Q was calculated in the model, and S was here assumed to be 61% of the radiation at the sea surface. ?SST is expected to be ?SSTmax if there is no advection of heat, no heat exchange at 1-m depth, and temperature is completely constant above 1-m depth. ?SST never exceeds ?SST max to the extent that heat advection can be neglected. Figure 6 shows the relation between the buoy ?SST and ?SSTmax. Almost all of the ?SST over 2.0 K are nearly equal to or greater than ?SSTmax, which means that those in situ data should be affected by heat advection. Furthermore, most of the data clearly affected by heat advection are the JMA-buoy data. Murakami and Kawamura (2001) used wavelet analysis to investigate relations between SST and heat flux including solar radiation at the sea surface based on JMA-buoy data. They pointed out that the heat flux changes SST in the daily cycle, and heat advection sometimes becomes effective on the change of SST in longer-term periods. The shift of Kuroshio recirculation or the polar front causes such heat advection in the marginal seas around Japan, where the JMA buoys were moored. SST in a coastal area is easily affected by heat advection. It is very difficult to estimate the SST warming due to advection of heat in a time scale of one day. We neglect this warming by using the model-simulated ?SST. Although there is still slight uncertainty under weak wind
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conditions, we can almost rely on the results of the model simulations. The model-simulated temperatures are considered as the true ones hereafter, and are used to construct a simple regression equation to evaluate ?SST from wind speed and solar radiation only. 4. Empirical Estimation of SST Diurnal Warming Figure 7 shows the relation between the daily amplitude of the skin temperature (skin ?SST) and U in the case of PS ≥ 800 Wm–2, where PS is the daily peak solar radiation. Although the skin ?SST is about 1 K at most when U is about 5.0 ms–1, it increases abruptly as U decreases. The skin ?SST has a linear relation with In(U). The relation between the skin ?SST and daily peak solar radiation is shown in Fig. 8. It also rapidly becomes larger as PS increases. A linear function of (PS)2 can approximate this relation. We therefore propose the following form of a regression equation relating ?SST to PS and U:
?SST = a( PS)2 + b[In(U )] + c( PS)2 [In(U )] + d .

(3)

a wide region. The coefficients in Eq. (3) were determined by a least squares fit with the restriction that ?SST must be equal to or less than zero when PS = 0. If the right hand of Eq. (3) is negative, ?SST is evaluated to be zero. The coefficients are listed in Table 2. Following Webster et al. (1996), we also determined difference coefficients for U > 2.5 ms–1 and U ≤ 2.5 ms–1. This threshold value comes from Fig. 3 in Section 3. The regression equation is shown as a surface in Fig. 9. If U is less than 0.5 ms–1, we regarded this U as 0.5 ms–1 in determining the coefficients because an anemometer attached to a buoy cannot accurately measure extremely low wind speed. The results of our model simulations show that the skin ?SST can be up to more than 6 K when it is almost windless, and daily maximum solar radiation is greater than 950 Wm–2. This maximum ?SST is much larger than that given in Webster et al. (1996). However, our model results do not contradict past observation results. Stramma et al. (1986) reported an example of day-night SST difference of more than 4.0 K in the Sargasso Sea using satellite data (their figure 5).

This form was determined with reference to Webster et al. (1996)’s regression equation:
?SST = a( PS) + b( P) + c[In(U )] + d ( PS)[In(U )] + e(U ) + f ,
Table 2. Regression coefficients for skin ?SST.
U > 2.5 ms – 1 a b c d 3.0494 × 10 – 6 –2.8258 × 10 – 2 –1.1987 × 10 – 6 –2.5893 × 10 – 2 U ≤ 2.5 ms – 1 5.0109 × 10 – 6 2.2063 × 10 – 1 –3.3394 × 10 – 6 –2.0216 × 10 – 1

( 4)

where a, b, c, d, e and f are regression coefficients, and P is the daily average precipitation rate. We do not use P here because it is difficult to obtain precipitation data over

Fig. 7. Relation between skin ?SST (K) and wind speeds averaged during 09–15 LST (ms –1). Only the data of PS ≥ 800 Wm –2 are plotted.
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Fig. 8. Relation between skin ?SST (K) and daily peak solar radiation (Wm–2). Only the data of U ≤ 2.5 ms–1 are plotted.

Yokoyama et al. (1995) observed the temperature at about 2-cm depth in Mutsu Bay at the northern end of Honsyu Island, Japan. According to their data, the SST amplitude on 7 July 1992 was up to 5.2 K. We also determined the regression coefficients for the 1-m-depth ?SST in the same manner. Satellite SST is usually derived by using 1-m-depth SST observed with drifting buoys as the ground truth. Hence, the 1-m-depth ?SST is also worth evaluating. The ?SSTs simulated with the forcible mixing are necessary to determine the coefficients because these ?SSTs are closer to the in situ val-

ues than those with no artificial mixing. According to Figs. 4 and 5, the platform effect of the drifting buoys will be weaker than that of the JMA buoys since the drifting buoys are much smaller than the moored ones (Table 1). The regression coefficients were determined using the model ?SSTs simulated with the weak artificial mixing (eddy diffusion coefficients of 1.0 × 10–5 m2s–1, Fig. 4), which gives better agreement between the model ?SSTs of the drifting buoys and the in situ ones. The relation between this model ?SST and wind speed is shown in Fig. 10. The ?SST simply increases as wind speed decreases, even when the wind is very weak (see Fig. 3(b)). These coefficients for 1-m-depth ?SST are listed in Table 3, and the regression equation is shown in Fig. 11. The ?SST evaluated by the regression equation is about 2.0 K at most. This is similar to Price et al. (1987)’s result, but the regression results are a little smaller than the Price et al.’s one because Price et al. used buoy-observed 0.6-m-depth temperatures as SST, not 1-m-depth values. The ?SST evaluated by Webster et al. (1996) is close to our 1-m-depth ?SST rather than our skin ?SST. 5. Application of the Regression Equation We have evaluated ?SST in practice from satellitederived solar radiation and wind speed through the regression equation. We can draw daily peak solar radia-

Fig. 9. Surface plot of skin ?SST (K) by the regression equation.

Table 3. Regression coefficients for 1-m-depth ?SST.
U > 2.5 ms – 1 a b c d 2.4069 × 10 – 6 7.5810 × 10 – 2 –9.2014 × 10 – 7 –1.8838 × 10 – 1 U ≤ 2.5 ms – 1 1.8265 × 10 – 6 –6.6016 × 10 – 2 –2.8672 × 10 – 7 –5.8428 × 10 – 2

Fig. 10. Relation between 1-m-depth ?SST (K) simulated with the weak forcible mixing (the minimum eddy diffusion coefficients are 1.0 × 10–5 m 2s–1) and wind speeds averaged during 09–15 LST (ms –1). Only the data of PS ≥ 800 Wm–2 are plotted.

Fig. 11. As Fig. 9 except for 1-m-depth ?SST (K).
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tion maps from the GMS solar radiation data set described in Section 2. Daily mean wind speed maps are drawn from the following satellite data. 5.1 Satellite wind speed data Wind speed can be measured from space with a microwave radiometer or a scatterometer. The Special Sensor Microwave Imager (SSM/I) is flown by the Defense Meteorological Satellite Program (DMSP). The SSM/I sensors were available on three or four polar orbiting satellites in 1999 and 2000: DMSP F-11, F-13, F-14 and F15. The local times for the ascending equatorial crossing of the F-11, F-13, F-14 and F-15 satellites are approximately 0730, 0530, 0830 and 0930, respectively. A detailed description of the SSM/I and the algorithms to derive wind speed can be found in Wentz (1997). Another microwave radiometer onboard the Tropical Rainfall Measuring Mission (TRMM) satellite is available to measure wind speed (Wentz and Meissner, 2000). This radiometer, the TRMM Microwave Imager (TMI), is wellcalibrated and similar to the SSM/I. Observation by the TMI covers a global region extending from 40°S to 40°N. Since the orbit of the TRMM satellite is not sun-synchronous, the local time of the observation changes for any given earth location. SeaWinds is a microwave scatterometer onboard the QuikSCAT (QSCAT) satellite. The QSCAT satellite flies in a sun-synchronous orbit with the local equator crossing time at the ascending node of 0600±30 minutes (JPL/PO.DAAC, 2001a, b). Wind speed data are derived from SSM/I and TMI data by Remote Sensing Systems. QSCAT/SeaWinds wind data products are produced by the National Aeronautics and Space Administration (NASA) Scatterometer

Projects, and distributed by NASA/Physical Oceanography Distributed Active Archive Center (PO.DAAC). These data are available on their web sites. The spatial resolution of all the data is 0.25° and the reference level of the wind speed is 10 m. In this study we used the level 3 product of the SeaWinds wind speed, and simply averaged all the above-mentioned wind speed data for each day. 5.2 Regression coefficients and ?SST maps The regression coefficients in Eq. (3) were determined using the wind speed averaged only during 09–15 LST (Tables 2 and 3). However, in order to make daily mean maps that completely cover the area from 60°N to 60°S and from 80°E to 160°W, we had to collect the satellite-derived wind speed data throughout a whole day. Therefore, a new set of regression coefficients was determined in this section using the daily mean wind speed instead of the daytime-mean wind speed. The regression coefficients for the skin ?SST and the 1-m-depth value are shown in Tables 4 and 5, respectively. The correlation coefficients are lower than those when the daytimemean wind speed is used (Table 6). This means that the wind speed at the time when insolation is strong is more important in evaluating ?SST. Furthermore, it is expected that the accuracy of the evaluation declines as ?SST increases since fewer data points are used for the regression. Figures 12 and 13 show the maps of daily peak solar radiation and mean wind speed on 27 July 1999, respectively. Both data sets were averaged in each 0.25° × 0.25° bin. The skin and 1-m-depth ?SSTs evaluated from these data are shown in Fig. 14. The spatial resolution of ?SST

Table 4. As Table 2, except that U is a daily mean.
U > 2.5 ms – 1 a b c d 3.2708 × 10 – 6 –7.9982 × 10 – 2 –1.3329 × 10 – 6 7.3287 × 10 – 2 U ≤ 2.5 ms – 1 5.6814 × 10 – 6 4.0052 × 10 – 1 –3.9637 × 10 – 6 –3.6700 × 10 – 1

Table 5. As Table 3, except that U is a daily mean.
U > 2.5 ms – 1 a b c d 2.3989 × 10 – 6 5.7289 × 10 – 2 –9.2463 × 10 – 7 –1.4236 × 10 – 1 U ≤ 2.5 ms – 1 1.9361 × 10 – 6 1.4576 × 10 – 2 –4.1966 × 10 – 7 –1.0322 × 10 – 1

Table 6. Statistics of ?SST evaluated by the regression equation.
Wind speed Daytime mean Depth Skin 1-m-depth Skin 1-m-depth Correlation coefficient 0.919 0.938 0.854 0.920 Root mean square error (K) 0.27 0.13 0.35 0.14

Daily mean

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is also 0.25°. Areas with large ?SST almost correspond to weak-wind areas. We can see patches of the skin ?SST of more than 3.0 K in the tropics and the mid-latitudes of the northern hemisphere. The skin ?SSTs at the centers of the patches are up to 4.0–5.0 K, and the 1-m-depth ?SSTs in these patch areas are about 1.5 K. (Note that the evaluated skin ?SST has an RMS error of 0.35 K.) 6. Conclusions Our purpose in this study was to evaluate the SST diurnal variation in a simple manner. We first simulated

?SST with a one-dimensional model using buoy-observed meteorological data and solar radiation produced from GMS/VISSR data by Tanahashi et al. (2001). The modelsimulated ?SST agrees well with the in situ value when the latter is less than 1.5 K. On the other hand, in cases when the in situ ?SST is over 1.5 K, the former is smaller than the latter, and the difference between them becomes larger as the in situ ?SST increases. It can be inferred that the platform effect described by Kawai and Kawamura (2000) causes the large difference when a large temperature gradient develops near the sea surface under clear and calm conditions. By adding artificial mixing in the sea surface layer the model ?SST becomes closer to the in situ value.

Fig. 12. Daily peak solar radiation (Wm–2) on 27 July 1999 produced from GMS/VISSR data.

Fig. 13. Daily mean wind speed (ms –1) on 27 July 1999 produced from QSCAT/SeaWinds, TMI and SSM/I data.

Fig. 14. Map of ?SST (K) on 27 July 1999 evaluated from daily peak solar radiation and daily mean wind speed by the regression equation. (a) Skin, (b) 1-m-depth.
Evaluation of the Diurnal Warming of SST 813

Since we could be certain that the model results are reliable, we then derived a regression equation to evaluate ?SST from U and PS only. Our regression equation is similar to that of Webster et al. (1996). However, the term describing daily mean precipitation rate was not included in our equation, and (PS)2 is used instead of PS. ?SST is approximately proportional to In(U) and (PS)2. Although the skin ?SST evaluated by our equation is much greater than that found by Webster et al. (1996), our greater skin ?SST is not inconsistent with the observation results published by other researchers. We determined another set of the regression coefficients for the 1-m-depth ?SST since the reference depth of satellite-derived SST is usually 1 m. The regression equation was used in practice to obtain ?SST distribution over a wide area. We made daily maps of peak solar radiation, and daily mean wind speed by simply averaging SSM/I, TMI and SeaWinds wind speed data. The result showed that some wide patchy areas where the skin ?SST exceeds 3.0 K can appear in the tropics and the mid-latitudes in summer. Acknowledgements The moored buoy data around Japan used in this study were collected by the Japan Meteorological Agency, and are distributed by the Japan Meteorological Business Support Center. The global drifting buoy data set is produced and distributed by the Marine Environmental Data Service in Canada. We would like to acknowledge Etienne Charpentier of the Data Buoy Co-operation Panel (DBCP), Meteorological Service of NZ Ltd., the Bureau of Meteorology in Australia, Environment Canada and the Naval Oceanographic Office in the United States for providing us with information about drifting buoys. The SSM/ I and TMI wind data are produced by Remote Sensing Systems and sponsored in part by NASA’s Earth Science Information Partnerships (ESIP): a federation of information sites for Earth science; and by the NOAA/NASA Pathfinder Program for early EOS products; principal investigator: Frank Wentz. The QSCAT/SeaWinds wind data products are produced by the National Aeronautics and Space Administration (NASA) Scatterometer Projects, and are distributed by NASA/Physical Oceanography Distributed Active Archive Center (PO.DAAC). We would like to acknowledge Syuichi Tanahashi for providing us with solar radiation data derived from GMS/ VISSR. The present study is supported by ADEOS-I and ADEOS-II projects of the National Space Development Agency of Japan.

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