We investigate microwave radiation from the ocean surface to observe changes in microwave radiation for various air-sea temperature differences by using data of the Special Sensor Microwave/Imager 19 GHz and the TRMM Microwave Imager 19 and 10 GHz. To this end, we developed a method of removing the atmospheric effect. Under strong winds exceeding 7m/s, atmospheric-effect-removed temperatures of both vertical and horizontal polarizations increase, and the ratio of the V/H increase in stable condition is less than that in neutral or unstable conditions. Furthermore, in neutral or unstable conditions, the ratio of the V/H increasing at 10GHz is larger than that at 19GHz.
 The ocean surface is comparatively more uniform than the land surface. As a result, its microwave properties may be described by fewer parameters than those of the land surface. At a fixed incidence angle, the microwave radiation from the specular ocean surface is theoretically expressed in Fresnel format, and can be described by frequency, sea surface temperature (SST) and sea surface salinity [Klein and Swift, 1977; Swift, 1980]. When an ocean surface wind is blowing, the surface becomes roughened. Many field experiments have been conducted to investigate the microwave radiation from the roughened ocean surface [Hollinger, 1971; Webster et al., 1976]. Microwave radiation from a roughened surface is not omnidirectional, and anisotropic features depending on the wind direction are remarkable [Wentz, 1992].
 An additional parameter possibly needed to describe the microwave radiation of the ocean surface may be the difference between the air temperature and SST (AS-dif). Few studies of AS-dif effects on microwave radiation have been made. In the global ocean, AS-dif is almost zero or slightly negative (i.e., the air temperature is lower than SST). However, in some regions and in special seasons, AS-dif becomes positive, such as in the Arabian Sea in summer, or the ocean in high latitudes of the northern hemisphere in spring or summer. In those regions, microwave radiation from the ocean's surface might change, since drag coefficients related to surface roughness are reported to change with conditions of AS-dif [Kondo, 1975].
 Data used for studying the change of microwave radiation due to AS-dif are from the Special Sensor Microwave/Imager (SSM/I) aboard the U.S. Defense Meteorological Satellite Program (DMDP). SSM/I is a seven-channel microwave radiometer operating at frequencies from 19.3 to 85.0 GHz [Hollinger et al., 1989, 1991]. The TRMM Microwave Imager (TMI) data are also used, in particular in the Arabian Sea. The TMI sensor is similar to SSM/I, but has an additional frequency (10GHz). TMI is installed on the Tropical Rainfall Measuring Mission (TRMM) [Kummerow et al., 2000].
 In section 2, we will describe a new method of removing the atmospheric effects. In section 3, we study AS-dif effects on the SSM/I 19 GHz by using colocated data set made from SSM/I and buoy. Section 4 investigates AS-dif effects on the TMI 19 and 10 GHz in the Arabian Sea by using the air temperature analyzed from the weather forecast model. Section 5 will present summaries.
2. Method of Removing the Atmospheric Effects
 To study AS-dif effects on the ocean microwave radiation, we should remove atmospheric effects produced by water vapor, cloud liquid water, and oxygen. In a range of frequencies from 10 to 37 GHz, absorption and radiation by water vapor are strongest at frequencies around 22.235 GHz. Absorption and radiation by either cloud liquid water or oxygen become stronger at higher frequencies [Liebe, 1985]. This paper will study the AS-dif effect at frequencies of the SSM/I 19 GHz and TMI 19 and 10 GHz. The SSM/I 22.235 and 37 GHz could remove atmospheric effects on the SSM/I 19 GHz, and also the TMI 21.3 and 37 GHz could remove the atmospheric effects on the TMI 19 and 10 GHz.
Figure 1 shows the atmospheric effect on the TMI 10 GHz vertical polarization data (hereafter 10V); the vertical axis is TMI 21V, and the horizontal axis is TMI 37V. By specifying 21V and 37V, a corresponding atmospheric effect (hereafter A_effect) on 10V is read-out. A_effect is defined by equation (1).
Here, T_top is the calculated theoretical brightness temperature of satellite height, and T_surface is the brightness temperature (microwave radiation) of the specular ocean surface without the atmospheric effect.
 The microwave radiative transfer model gives T_top, and a detailed description of the model used here is found in [Shibata, 1994]. The model uses the Japanese radio sonde observations of all sites during four seasons. The total accumulated water vapor ranges from 3 to 75 Kg/m**2. The cloud liquid water is added to sonde observations with an interval of 0.01 Kg/m**2 up to 1.2 Kg/m**2, except for sonde observations under clear weather conditions. The complex dielectric constant used in calculating the ocean brightness temperature in the radiative transfer model is based on a comparatively older reference [Klein and Swift, 1977], but adjustments of the brightness temperature are made to match the model to the SSM/I observations (e.g., for 37V, values of −4.2, −2.5, −1.0, and −0.5 K are added to the model at SST of 0, 10, 20, and 30°C). More recent references of the complex dielectric constant are available [Cruz-Pol and Ruf, 2000; Ellison et al., 1998; Guillou et al., 1998].
Figure 1 is translated to a table to read-in 21V /37V and read-out A_effect of 10V. Effects on the vertical (V) and horizontal (H) polarizations are read-out by different tables. Figure 1 shows a case of 20°C SST, and similar tables are prepared with 5°C intervals of SST from 0 to 35°C. Rainy cases can be eliminated by removing observations with A_effect larger than a specified value (exceeding the range region in Figure 1). The radiative transfer model adopted here is based on cloud liquid water over the ocean, so the current method of the atmospheric correction cannot be applied for the clouds containing the ice crystal or over land.
 Error of the current method can be estimated from this figure. It is seen that a 1K increase of 37V induces a 0.2K increase in the atmospheric effect on 10V, and that an increase of 21V does not largely affect the atmospheric effect. Similarly, a 1K increase of either 37V or 21V induces an atmospheric effect of 0.7 K on 19V, although the corresponding figure is not shown here. If the noise temperature of 37V due to the sensor is assumed as 0.5 K, the error in the atmospheric effect on 10V is estimated as 0.1 K. Figure 1 shows an average value for 10V. At each grid point of (37V, 21V) in Figure 1, 10V has several temperatures due to different atmospheric vertical profiles and different liquid water. For 10V, standard deviations (sd) from the averaged value for each grid range from 0.1 to 0.3K; for 19V, they range from 0.3 to 0.4K. This sd adds another removal error of the current method.
3. SSM/I and Buoy Colocated Data
 We study the AS-dif effect on the SSM/I 19 GHz by using a colocated data set produced from the SSM/I and buoy data. The Earth Observation Research Center (EORC) of the National Space Development Agency of Japan (NASDA) produced this colocated data set. The SSM/I data used here were from the sensor aboard DMSP Flight-11. Buoy data were from the NOAA National Data Buoy Center (NDBC) and the Tropical Atmospheric Ocean project (TAO) buoys. The period of colocated data is 3.5 years, from July 1992 to December 1995. The buoy wind speed is corrected at a 10-meter height. The collocated data set contains SSM/I, buoy air temperature, SST, surface wind, and other parameters. This data set contains three observations of buoy wind, i.e., time difference of the SSM/I and buoy observation is the smallest, the second, and the third. This study omits those cases with a difference of wind speed among the three observations exceeding 1.5m/s.
 The atmospheric effect is calculated by the method described in section 2, and rainy cases are omitted. By subtracting the atmospheric effect from the SSM/I 19GHz data, we can see how the ocean wind affects the brightness temperature of 19GHz as shown in Figure 2. The upper panel of Figure 2 shows 19V, and the lower panel shows 19H at SSTs ranging from 10 to 20°C. The vertical axis of each panel is the brightness temperature, and the horizontal axis is the buoy wind speed. The brightness temperature of the 19V channel does not change significantly for wind speeds below 7m/s, and it increases by 0.4K/(m/s) above that point. The brightness temperature of the 19H channel increases almost monotonically by 1.1K/(m/s). Those features are similar to those reported earlier [Hollinger, 1971; Webster et al., 1976; Rosenkranz, 1992].
Figure 3 shows the wind effect on the 19GHz data under different AS-dif conditions; the vertical axis is 19V, and the horizontal axis is 19H. SST ranges from 0 to 10°C in Figure 3a, from 10 to 20°C in Figure 3b, and from 20 to 30°C in Figure 3c. The upper panel in each figure corresponds to a stable condition in which the air temperature exceeds the SST (i.e., it is set as being larger than 1.0°C), the middle panel corresponds to a neutral condition in which the air temperature is nearly equal to SST (i.e., it is set as being the absolute value of AS-dif less than 0.5°C), and the lower panel corresponds to an unstable condition in which the air temperature is less than SST (i.e., it is set as being less than −1.0°C).
Figure 3 shows that the number of neutral and unstable conditions is much larger than the number of stable condition. For all SST ranges and under both neutral and unstable conditions, the 19V temperature does not change below a point of 19H increasing by 8K, and it increases above that point. As seen in Figure 2, the 19V temperature does not change for a wind speed below 7 m/s. The wind speed corresponding to the 8K-point is 7 m/s. Both V and H temperatures increase above this point with an increase ratio of about 0.37 (=V/H).
 This feature is not clearly seen under stable condition. The main reason may be that the observed number is small. However, even though it is a small number, it seems that the V and H temperatures do not increase significantly above the 8K-point, especially below SSTs of 20°C. Another feature seen under stable conditions is that the V temperature increases by about 0.5 below the 8K-point. The mechanism of the 0.5 K temperature increase is not understood now.
4. TMI 19 and 10 GHz in the Arabian Sea
 TMI aboard TRMM has an additional frequency of 10 GHz compared to SSM/I [Kummerow et al., 2000]. TRMM was launched in November 1997, and the TMI data have been available since December 1997. At 10GHz, the brightness temperature of the ocean surface is sensitive to SST; its sensitivity for vertical polarization is about 0.5K/°C for SST exceeding 10°C. Observations by NASDA's Airborne Microwave Radiometer (AMR) in the Pacific Ocean have confirmed this dependence on SST. Based on the AMR results, EORC began retrieving SST from TMI after the TMI data became available [Shibata et al., 1999]. The atmospheric effect at 10GHz is weaker than that at 19GHz, but the wind effect is of similar order. The wind effect must be removed when retrieving SST. In the EORC algorithm, SST is converted from 10V after the atmospheric correction described in section 2 is made, and the wind effect on 10V is removed by subtracting an increment of temperature, Tinc, estimated by equation (2).
Here, TH is the brightness temperature of 10H with the atmospheric correction made, TSH is a specified threshold, and R is a constant.
 R is assumed to be 0.63 in the global ocean. The EORC SST retrieval algorithm works well [Shibata et al., 1999], but not in the Arabian Sea in summer. Figure 4a illustrates the difference between SST from the EORC TMI SST and the SST from the Reynolds SST [Reynolds and Smith, 1994]. It shows an average value of difference for August 1–10, 1998, and a negative value of 3–4K is found in the Arabian Sea.
 A smaller value of R would reduce this error. As seen in Figure 3, the V/H increase ratio under stable conditions is smaller than the ratios for neutral or unstable conditions. Figure 4b shows an average value of differences between the air temperature and the Reynolds SST for August 1–10, 1998. The air temperature is adopted from the weather forecast model operated by the Japan Meteorological Agency (JMA), which is called as the Global Analysis (GANAL). A positive value of 0.5–2K is found in the Arabian Sea, Pacific equatorial region, and some other regions. The negative value of the SST difference in the Arabian Sea shown in Figure 4a corresponds well to the positive value of AS-dif in the same region shown in Figure 4b. The SST bias in early August in the Arabian Sea can be seen on other days in summer, but it disappears in other seasons.
 To study the relationships in the Arabian Sea further, it may be valuable to consider the TMI data in individual cases. In the Arabian Sea, the monsoon wind is dominant. A southwest wind blows from mid-April to mid-October, and a northeast wind blows from mid-October to mid-April. In this paper, three months, January, February, and August 1998, are selected for studies. The SST in the Arabian Sea is almost constant at around 26°C in these three months.
 The TRMM orbit is not Sun-synchronous, and local observation time changes from 0 to 24 hours in about 46 days. The TRMM satellite orientation changes from forward to backward, and backward to forward again in this period. Therefore, TMI may be looking forward or backward when the satellite changes orientation.
Figure 5a depicts the AS-dif and wind in the Arabian Sea on August 4, 1998. The air temperature and wind are taken from GANAL at the TRMM passage time. The AS-dif is positive almost throughout the Arabian Sea. A steady southwest wind blows in this season. The TMI swath is overlaid on the GANAL wind map and is lightly shaded. In early August, TMI was looking forward, and TRMM flew from the southwest to the northeast in this figure. Therefore, TMI was looking downwind (i.e., the sensor looking in the wind direction). In early August, there are several examples showing positive AS-dif; Figure 5a is a typical one.
Figure 5b shows a similar situation on August 19, 1998. A positive AS-dif is found south of Socotra Island (12°N, 54°E). A steady southwest wind is also blowing. In mid August, TRMM was looking backward. TMI is thus looking upwind.
 The positive AS-dif in the Arabian Sea is dominant in summer and disappears in other seasons. Figure 5c presents an example of the neutral condition on February 6, 1998. AS-dif is almost zero in the Arabian Sea, and a northeast wind is blowing. At that time, TMI was looking downwind. Figure 5d shows an example of the unstable condition on January 21, 1998, and TMI is looking upwind.
Figures 6a–6d depict the brightness temperature of the TMI 19GHz in the Arabian Sea corresponding to each day described in Figures 5a–5d. The TMI data are selected from definite areas under corresponding AS-dif conditions. The wind speed ranges from 10 to 13m/s in Figure 6a, from 11 to 12 m/s in Figure 6b, from 4 to 11m/s in Figure 6c, and from 7 to 10m/s in Figure 6d. TMI version 4 is used in this study. A positive bias of the brightness temperature due to calibration error in the TMI data has been reported with versions less than the 4th [Wentz et al., 2001]. In the SSM/I 19GHz in Figure 3c, 19V takes a value of 168K for the weak wind speed. In Figure 6c, it is 171 K, and a positive bias of about 3 K is confirmed.
 Among the four cases in Figure 6, the case on February 6 (Figure 6c) shows results similar to those under neutral or unstable conditions in Figure 3, in which two different responses to the ocean wind are found. In this case, the wind speed ranges from 4 to 11m/s. In other cases, only parts of the strong wind with increasing V and H temperatures are found. The ratio of the V/H increase for stable conditions is less than that for neutral or unstable conditions. This is the same as found in Figure 3.
Figure 7 shows the TMI 10GHz data under the same conditions as 19GHz data in Figure 6. Almost the same features are found in 10GHz data. The 19 and 10 GHz data differ as follows. (1) Under neutral or unstable conditions, the ratio of the V/H increase at 10GHz exceeds that at 19GHz. (2) Under stable conditions, the ratio of the V/H increase in the downwind case (Figures 6a and 7a) is less than that in the upwind case (Figures 6b and 7b). (3) The length of the weak wind part at 10GHz is shorter than that at 19GHz. Days of the four cases in Figures 6 and 7 are typical ones; similar features are found on other days corresponding to each condition.
Table 1 shows the ratios of the V/H increase at 19 and 10GHz on the four dates. The V/H increase is approximated as linear from a specified start point. At 19GHz in Figure 6, the starting point is (19H, 19V)=(87K, 171K). At 10GHz, it is (10H, 10V)=(84K, 166K). Ratios of the TMI 19GHz data in the Arabian Sea for neutral or unstable conditions are about 0.5, and they are slightly larger than that obtained with the SSM/I buoy data set (0.39). Causes of the difference are not clear.
Table 1. Ratio of V/H Temperature Increase at 19 and 10 GHz in the Arabian Sea
Stable Downwind (Aug. 4, 1998)
Stable Upwind (Aug.19, 1998)
Neutral Downwind (Feb. 6, 1998)
Unstable Upwind (Jan. 21, 1998)
Figure 7 and Table 1 demonstrate that the negative error of SST in the Arabian Sea shown in Figure 4a is due to two natural conditions: the positive AS-dif and strong wind. As shown in equation (2), the wind correction is made when 10H data exceed the specified value, corresponding to a wind speed of 7m/s. The V/H increase ratio is assumed constant in the global ocean, but a smaller ratio should be applied in the Arabian Sea satisfying those two conditions. In Figure 4b, it is seen that AS-dif is also positive in the Pacific equatorial regions. In those regions, the wind speed is less than 7m/s, and no wind correction is made.
5. Summaries and Discussions
 We investigate microwave radiation from the ocean surface to observe changes of microwave radiation for various air-sea temperature differences, by using data of the SSM/I 19 GHz and the TMI 19 and 10 GHz. To this end, we developed a method of removing the atmospheric effect contained in those data by using data of higher frequencies such as 22 and 37GHz. Modified V and H temperatures after atmospheric corrections made indicate how the ocean wind affects the brightness temperature of the ocean surface. For weak winds (below 7m/s), the V temperature does not change, but the H temperature increases; for strong winds, both V and H temperatures increase.
 Under strong wind, the ratios of V/H increase under stable conditions differ from the ratios under other (neutral or unstable) conditions. The ratio under stable conditions is less than those under neutral or unstable conditions. Furthermore, those ratios differ with frequency (in this paper, only 19 and 10GHz are checked). Another feature of SSM/I data under stable conditions is that the 19V temperature increases by about 0.5K for weak winds of less than 7m/s, although this has not been definitely confirmed.
 Under strong wind, whitecaps and foam are formed on the ocean surface, and strongly affect microwave radiation. For strong wind, the V and H temperature increases described above are due to whitecaps and foam. Differing ratios of the V/H increase between the stable and other conditions indicate that the effects of whitecaps and foam may change under those conditions. The mechanism inducing such differences is not clear, and understanding the mechanism will be left to future work.
 A practical problem with different ratios of the V/H increase is posed in the SST retrieval algorithm. In the EORC SST algorithm, SST is retrieved from the 10V data. For strong winds exceeding 7m/s, the brightness temperature of 10V increases. It is necessary to cancel the wind effect by using 10H, which is more sensitive to the ocean wind. We assume that the ratio of the V/H increase is constant in the global ocean. This assumption is generally applicable, but not in the Arabian Sea in summer, where it is necessary to modify the ratio by using the information about the air-sea temperature difference. Similar modifications will be necessary in other regions where the air-sea temperature is positive and strong wind blows.
 This work was supported by the Earth Observation Research Center of the National Space Development Agency of Japan to prompt algorithm developments for the Advanced Microwave Scanning Radiometer aboard Advanced Observation Satellite-II.