Download Air Temperature at Ocean Surface Derived from Surface

Journal of Oceanography
Vol. 51, pp. 619 to 634. 1995
Air Temperature at Ocean Surface
Derived from Surface-Level Humidity
MASAHISA KUBOTA* and AKIRA SHIKAUCHI**
School of Marine Science and Technology, Shimizu, Shizuoka 424, Japan
(Received 8 December 1994; in revised form 18 April 1995; accepted 20 April 1995)
A new method deriving surface air temperature from specific humidity is proposed. Surface atmospheric pressure and relative humidity in addition to specific
humidity are necessary in order to derive surface air temperature. Assuming
effects of variation of atmospheric pressure and relative humidity are small,
climatological values are used for those values. Derived surface air temperature is
compared with in situ surface air temperature. A cross-correlation coefficient is
high and the rms error is small. However, the agreement between them varies
spatially. The errors are largest in the eastern equatorial region and highlatitudes. The former may be caused by a large sampling error and remarkable
interannual variation related to ENSO phenomena. On the other hand, the latter
may be related to sensitivity of saturated vapor curve to air temperature. Sensible
heat fluxes are estimated by using derived surface air temperature and compared
with that by in situ data. For the whole North Pacific, a cross-correlation coefficient, a mean error and an rms difference are 0.89 W m–2, 0.58 W m–2 and 8.03 W
m–2, respectively.
1. Introduction
Momentum flux transfer between atmosphere and ocean is a main driving force for ocean
circulation, while heat transfer between them is important for atmospheric circulation. Global
estimates of heat transfer is crucial for understanding the mechanism of climatic variability in a
combined system consisting of atmosphere and ocean. The knowledge of global estimates of the
surface heat flux requires many physical parameters in the atmospheric and ocean boundaries for
the global scale. However; it is not easy to estimate global surface heat fluxes using in situ ocean
observation data. Since our interests focus on the heat budget in a global scale in most cases, the
sparsity and inhomogeneity of in situ can be a big problem. Using satellite data is only the way
to overcome the problem.
There are some problems to estimate turbulent heat fluxes because we need to obtain and
combine several physical parameters. This is different from the case of momentum flux which
can be obtained from one remote sensor such as a microwave scatterometer. Moreover, it is
difficult to obtain every necessary physical parameters from satellite data at present. Using a
fairly comprehensive bulk formula (e.g., Liu et al., 1979) we need wind speed (v), sea surface
temperature (Ts), air temperature (Ta), saturation specific humidity (Qs) and specific humidity
(Qa) at sea surface. Since Qs is calculated using Ts which can be easily obtained from an infrared
*Present affiliation: Center System Research, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153,
Japan.
**Present affiliation: Sanyo Techno Marine, Inc., Nihonbashi Horidome-cho, Chuo-ku, Tokyo 103, Japan.
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M. Kubota and A. Shikauchi
remote sensor such as NOAA/AVHRR, an estimate of Qs is possible using satellite data. On the
other hand, it is not so easy to directly obtain Qa using satellite data. Liu (1986) derived a statistical relation between monthly mean Qa and precipitable water (V) using 17 years of radiosonde
reports from 46 midocean meteorological stations. The statistical relation was evaluated by Hsu
and Blanchard (1989) using measurements during 13 field experiments distributed over the
global ocean. The results indicated that the relation could be used with monthly mean and also
instantaneous soundings. Therefore, not only Qs but also Qa can be calculated by satellite data
alone. Our final problem is to calculate Ta. Generally, Ta can be obtained from a microwave
sounder such as NOAA/High Resolution Infrared Sounder (HIRS). However, there are very few
studies evaluating NOAA/HIRS estimating Ta because of the sparse spatial resolution and the
accuracy. Therefore, it is important to develop a technique to calculate Ta using satellite data in
order to obtain sensible heat flux. Thadathil et al. (1993) derived a statistical relation to get
surface level air-temperature from satellite observations of precipitable water. However, it is not
clear whether the relation is applicable for a global extent or not because the statistical relation
is based on regional observation and is not evaluated by independent observational data in the
study.
It is the main objective of the present study to develop a technique to estimate Ta. In the present
study, the possibility to obtain Ta from satellite data alone will be examined. The data and the
method will be described in Section 2. In Section 3, validation of the estimated Ta will be done
by comparing to observed Ta. Sensible heat flux obtained by using the estimated Ta will be
presented and compared with that by observed data in Section 4. Simple sensitivity analysis
concerning the estimated Ta and sensible heat flux is carried out in Section 5. The conclusion will
be given in Section 6.
2. Data and Method
Sea surface temperature (Ts), surface air temperature (Ta), scalar wind (W), atmospheric
pressure (P), relative humidity (R) and specific humidity (Qa) in Monthly Summaries Trimmed
Groups (MSTG) from COADS Release 1 (Slutz et al., 1985) are used in the present study.
Although data are available beginning in 1854, data during 1970–1979 alone are chosen here
because the number of the data was higher in this period (Woodruff et al., 1987). Temporal and
spatial resolutions are monthly and 2° × 2°, respectively.
Ta is derived from Qa, which is given by applying the Liu (1986)’s statistical relation to
precipitable water, in the following way (e.g., Blanc, 1985; Iwasaka and Hanawa, 1990). First,
vapor pressure (ea) can be calculated from Qa by
ea = PQa / ( 0.622 + Qa ).
(1)
On the other hand, Ta is given from ea and R by the following equation.
Ta = −273.2 − 5419.285 / ( ln ea − ln R − ln 6.11 − 19.836).
(2 )
Therefore, Ta can be calculated in principle by P, Qa and R. Specific humidity (Qa) can be derived
from precipitable water data observed by a microwave radiometer by using the statistical
formulae by Liu (1986). However, because P and R cannot be directly observed by a satellite, Ta
cannot be calculated by satellite data alone. Therefore, it is a critical issue to determine surface
Air Temperature at Ocean Surface Derived from Surface-Level Humidity
621
pressure and relative humidity. It should be noted that an effect of P on ea is not so large compared
with that of Qa because of relatively small fluctuation of P in space and time. Moreover, lnR
seems to be much smaller than lnea, ln6.11 and 19.836. Therefore, we may calculate exact surface
air temperature even by using climatological mean values for both P and R. Also, it should be
noted that precipitable water can be estimated from satellite data with an accuracy of about 0.2
g cm–2 which is comparable to the accuracy achieved from radiosonde profiles (Abbot and
Chelton, 1991). More than 20 bulk formula with different transfer coefficients are proposed to
estimate turbulent flux. Blanc (1985) estimated turbulent flux by using ten published bulk
transfer coefficient schemes with more than 2600 sets of shipboard observations. He showed that
the scheme-to scheme differences results in a typical maximum variation of 70% for an average
sensible heat flux determination of ±25 W m–2. The bulk transfer coefficient scheme proposed
by Kondo (1975) is used in the present study. The scheme is based on roughness Reynolds
number observations combined with the Owen-Thomson (1963) theory of heat and mass transfer
above a rough solid surface.
3. Validation of Derived Surface Air Temperature
First, derived surface air temperature (Ta′) is compared with observed surface air temperature (Ta) for 10-year average values. Here, monthly Ta′ is derived from monthly Qa, P and
R, and then the monthly Ta′ data are averaged for the 10 years. Figure 1 shows a scatter diagram
between derived values and observed values. The correlation coefficient is quite high, 0.996.
Also, the rms error is small, 0.83°C. This result indicates that Ta averaged over a long time period
can be estimated with enough accuracy if we can obtain data of Qa, P and R. Figure 1 also shows
that the rms error is larger in a low-temperature region from 0°C to 10°C where Ta′ is larger
Fig. 1. Comparison of the observed surface air temperature (Ta) and derived surface air temperature (Ta′)
for the 10-years mean value.
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M. Kubota and A. Shikauchi
than Ta.
Next, applying of the present method to climatological monthly mean values is investigated.
Climatological monthly mean Ta′ data are derived from each monthly derived Ta′ by using each
monthly P, Qa and R for the period of 1970–1979. Figure 2 shows scatter diagrams between Ta
and Ta′ for January, April, July and October. We can easily find the high correlation values and
the small rms error as shown in Table 1. It should be noted that the values for boreal winter are
not as good as that for other seasons. This feature is consistent with results from the scatter
diagrams, which shows that the differences between both values are large in the low-temperature
region. Above-mentioned results indicate that derivation of the 10-year averaged and the
climatological monthly mean Ta is successful using Qa, P and R observed at the same time.
However, it should be noted that we must actually use climatological values for P and R because
we cannot obtain those values from satellite data. Therefore, it is necessary to validate the derived
Ta by comparing with observed Ta.
We calculate monthly Ta by using (a) monthly-mean data, (b) climatological monthly-mean
Fig. 2. Same as in Fig. 1 except for the climatological monthly mean values. (a) January, (b) April,
(c) July, and (d) October.
Air Temperature at Ocean Surface Derived from Surface-Level Humidity
623
Fig. 3. Maps of correlation coefficients between (a) Ta and Ta′ or (b) Ta and Ta″. Contour interval is 0.05.
The shaded region indicates the correlation coefficient larger than 0.95. A hanning filter is applied two
times to correlation coefficients.
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M. Kubota and A. Shikauchi
data for P and R, and compare the obtained values with observed Ta. For convenience, Ta derived
by using original P and R data is represented by Ta′, while that using climatological mean data
for P and R is denoted by Ta″. Maps of correlation coefficients and rms errors are given in Figs.
3 and 4, respectively. The correlation coefficients between Ta and Ta′ are remarkable high and
larger than 0.95 in most areas except marginal seas northwest of the North Pacific and the
Fig. 4. Same as Fig. 3, except for rms errors. Contour interval is 0.1. The shaded region indicates the rms
error larger than 1.5°C.
Air Temperature at Ocean Surface Derived from Surface-Level Humidity
625
Table 1. Correlation coefficients and rms errors between climatological monthly mean Ta and derived Ta.
Derived Ta is obtained from monthly mean values of P, Qa and R.
Rms error (°C) Correlation coefficient
January
April
July
October
Average
1.17
0.61
0.49
0.66
0.83
0.9928
0.9980
0.9974
0.9967
0.9960
Fig. 5. A density map of ocean observations of W(Ts-Ta) in 1979.
equatorial areas. Also rms errors are quite low and less than 0.4°C in most areas in the case of
using original data. On the other hand, the correlation coefficients between Ta and Ta″ calculated
by using climatological monthly mean values for P and R are larger than 0.95 for the North
Pacific, and not so high and so variable for the tropical region. This low correlation coefficient
in the tropical region may be associated with the large sampling error because data density in the
tropical region is quite low. A density map for W(Ts-Ta) data in 1979 is given in Fig. 5 as an
example. The total observation number is larger than 250 in the northern North Pacific, while that
is less than 50 in the equatorial Pacific except coastal regions and along ocean routes. The effect
of the sampling error in the tropical region is notable not only in Fig. 3, but also in Fig. 4(b). The
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M. Kubota and A. Shikauchi
contour strongly overlie the main ocean routes such as from Panama to Australia.
Next, we investigate time variability of a spatial correlation and rms difference obtained by
averaging in the analyzed region, i.e. North Pacific (Fig. 6). The correlation coefficients between
Ta and Ta′ are quite high, larger than 0.995 and the rms differences are quite small, about 0.5
degree. Additionally, the correlation coefficients between Ta and Ta″ are still high, between 0.985
and 0.995 and the rms differences are small, 1.0 degree. These values appear to give enough
accuracy for estimating heat fluxes. Also, it should be noted that seasonal variations of
correlations between Ta and Ta′ of being high in winter and low in summer are remarkable. Such
seasonal variability is not so clear in the rms differences. The correlation value is strongly
dependent on the spatial variability in Ta and Ta′. Therefore, the remarkable seasonal variation
may be caused by the large contrast of surface air temperature in winter between high and low
latitudes.
Fig. 6. Time variation of (a) spatial correlation coefficients and (b) rms differences. 䊊 indicates a value
between Ta and Ta′. + indicates a value between Ta and Ta″.
Air Temperature at Ocean Surface Derived from Surface-Level Humidity
627
4. Sensible Heat Flux
In the previous section, derived surface air temperatures were compared with observed
surface air temperature. Since one purpose of deriving surface air temperature is to estimate
sensible heat flux by using the surface air temperature, it is necessary to validate the obtained
sensible heat flux. Sensible heat fluxes are calculated by using three kinds of surface air
temperature, and compared with each other. Moreover, the comparison is carried out for four
regions: region A (20°S–20°N); region B (20°N–50°N); region C (50°N–80°N); and the whole
region (20°S–80°N).
In the first case, sensible heat flux calculated by using original Ta is compared with that by
surface air temperature derived from original P, Qa and R data, i.e. Ta′. The results are given in
Table 2. The data number in regions A and B are comparable, while the data number in region
C is extremely small. This result indicates accuracy of the present method of deriving surface air
temperature by P, Qa and R. For the whole North Pacific, the correlation coefficient is 0.89 and
a mean error is 0.58 W m–2 and a rms difference is 8.03 W m–2. Though the rms difference seems
to be larger than most value of sensible heat flux, the smallness of the mean error may be
encouraging for applying the present method to calculate global sensible heat flux. In the
equatorial region, a mean error is the largest and an rms difference is the smallest. The small rms
difference may be due to small variability there.
Second, sensible heat flux calculated by using Ta″ is compared with that by using Ta′. Table
3 presents comparison results, which indicate an error about sensible heat flux derived by using
Ta″. In this case, a mean error is remarkably small in all regions. However, correlation
coefficients for the equatorial region is small compared with other regions. This is due to the
climatological value not being so useful because variability in the equatorial region has a
remarkable bi-modal character depending on ENSO phenomena. Moreover, it should be noted
Table 2. A comparison between the sensible heat flux by original data and that by using surface air
temperature derived from original P and R.
Region
Data number
Corre. coeff.
Mean diff. (W m–2 )
Rms diff. (W m –2 )
20°S–20°N
182328
0.95
2.23
3.74
20°N–50°N 50°N–80°N 20°S–80°N
36966
0.87
–1.46
11.36
4308
0.93
–1.39
14.45
321429
0.89
0.58
8.03
Table 3. A comparison between the sensible heat flux by using derived surface air temperature from
climatological P and R data and from original P and R data.
Region
Data number
Corre. coeff.
Mean diff. (W m–2 )
Rms diff. (W m –2 )
20°S–20°N
182328
0.66
0.22
9.02
20°N–50°N 50°N–80°N 20°S–80°N
136966
0.91
0.17
9.99
2135
0.94
0.12
13.91
321429
0.86
0.16
9.36
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M. Kubota and A. Shikauchi
that a climatological value is not reliable because there are very few data in the equatorial region
as shown in Fig. 5.
Finally, sensible heat flux calculated by using Ta is compared with that by Ta. This result
shown in Table 4 includes both errors caused by derived surface air temperature by P, Qa and R
and by using climatological values for P and R. Still, mean error for the whole region is small,
0.79 W m–2. The mean error for the equatorial region is positive, while mean errors for the midand high-latitudes are negative. It is concluded that these errors are caused by the deriving method
because the same features are found in Table 2. On the other hand, the rms error increases with
the latitude and that for the high-latitude region is considerably large, 23.04 W m–2. This large
value may be in part due to the smallness of the data number there. However, it is considered that
Table 4. A comparison between the sensible heat flux by using original data and surface air temperature
derived from climatological P and R.
Region
Data number
Corre. coeff.
Mean diff. (W m–2 )
Rms diff. (W m –2 )
20°S–20°N
182328
0.63
2.45
9.68
20°N–50°N 50°N–80°N 20°S–80°N
136966
0.80
–1.31
14.96
2135
0.86
–1.80
23.04
321429
0.76
0.79
12.22
Fig. 7. Relationship of the slope of the saturated vapor pressure curve as a function of temperature.
Air Temperature at Ocean Surface Derived from Surface-Level Humidity
629
there is a more essential problem for deriving air surface temperature in the high-latitudes.
Shikauchi (1994) pointed out that the accuracy of deriving temperature is quite sensitive in the
low-temperature region because of the characteristics of the saturated vapor pressure curve.
Figure 7 shows the relationship of the slope of the saturated vapor pressure curve as a function
of temperature. We can easily understand that the sensitivity increases as the temperature
increases. This means the accuracy of the predicted air-temperature is worse for the lowtemperature region. This may be the cause of the large rms error for the high-latitude region.
5. Sensitivity Analysis
In the previous section we obtained encouraging results, especially for the overall region.
However, several problems still exist in the results, for example, the large rms errors for the highlatitude region and the low correlation coefficient for the equatorial region.Therefore, simple
sensitivity analysis is carried out.
Results shown in Table 3 are reflected by the effectiveness of using climatological monthly
mean values for P and R. Therefore, it is important to evaluate the sensitivity of derived air
surface temperature to P and R. Substituting equation (1) into (2) we can obtain a relation of P,
Qa, R and Ta. The partial derivatives of Ta about P and R are calculated from the obtained equation.
The results give the magnitude of the partial derivative about R to be about 100 times as large as
that of P. However, what is important is not only the partial derivatives but the deviations, which
are given by
∆Ta =
∂ Ta
∂T
∆P + a ∆R.
∂P
∂R
(3)
It may be expected that ∆P and ∆R are strongly regional dependent. Figure 8 shows a map of the
partial derivative of Ta about R and the deviation which is defined as the partial derivative of Ta
about R times standard deviation of R at each grid point. The partial derivative of Ta about R is
large in the mid-latitude region and small in the high-latitudes and the eastern tropical region. It
is interesting that the maximum value can be found in the eastern subtropics northeast of the
Hawaii Islands. Kubota (1994) pointed out this region to be related to strong Ekman convergence
associated with the Subtropical High. On the other hand, distribution of the deviation is quite
different from that of the partial derivative. The deviation is extremely large in the equatorial
upwelling region and shows a complicated feature, while that in the mid- and high-latitude
regions is flat except along the coast. The large value in the tropical region may be due to large
variability of R depending on the seasonal and interannual El Nino phenomena (Giese and Cayan,
1993). The large sensitivity of derived Ta to R explains the large mean error and the low correlation coefficient for the equatorial region shown in Table 4.
The sensitivity of the calculated sensible heat flux to the derived surface air temperature
given by ∆Qh/Ta is also important. Maps of the partial derivative of Qh about Ta and the deviation
defined as the partial derivative by a standard deviation of Ta at each grid point are shown in Fig.
9. Figure 8(a) suggests that the partial derivative of the Qh about Ta is relatively large in the high
latitudes. However, the distribution of the deviation shown in Fig. 9(b) is similar to that for the
Ta about R. The deviation is large in the eastern tropical region in this case. This is also due to
the sea surface temperature in the tropical region drastically changes corresponding to the El
Nino phenomena. This is clarified by the distribution of standard deviations of Ta shown in
Fig. 10.
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M. Kubota and A. Shikauchi
Fig. 8. A map of (a) the partial derivative of Ta about R and (b) the deviation of Ta defined as the partial
differential of Ta times a standard deviation of R. Contour interval is (a) 0.05°C and (b) 0.9°C.
Air Temperature at Ocean Surface Derived from Surface-Level Humidity
631
Fig. 9. A map of (a) the partial derivative of Qh about Ta and (b) the deviation of Ta defined as the partial
differential of Qh times a standard deviation of Ta. Contour interval is (a) 0.2 W m–2 °C–1 and (b) 20
W m–2.
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M. Kubota and A. Shikauchi
Fig. 10. A map of the standard deviation of Ta. Unit is °C. Contour interval is 1.0°C.
The above results show that the estimate of the sensible heat flux in the eastern equatorial
Pacific by using the present method is highly sensitive by the large variability for Ta and R related
to the El Nino phenomena. On the other hand, the sensitivity results cannot explain the large rms
differences in the high latitude regions shown in Table 4. Probably this may be related to the
characteristics of the saturated vapor pressure curve pointed out in Shikauchi (1994). Variation
of water vapor pressure is less sensitive to temperature variation in the low-temperature region
as mentioned before. This suggests the inaccuracy of derivation of low air-temperature by the
present method.
6. Conclusions
In the present study a new method to obtain the air temperature above the ocean from surfacelevel humidity is proposed. The method is based on the saturated vapor pressure curve. In order
to estimate sensible heat flux, surface atmospheric pressure and relative humidity are necessary
in addition to air temperature. Since, unfortunately these data cannot be obtained from satellite,
climatological values are used for these data. The effectiveness of the present method was
verified by using COADS including various ocean observation data such as P, Ts, Ta, Qa and R.
Here, monthly averaged data, i.e. MSTG from COADS Release 1 are used because Liu’s
statistical relation between Qa and V is applicable for time scales greater than two weeks (Liu et
al., 1991). Shikauchi (1994) examined the validity of sensible heat flux obtained by the method
in the present study for time scale varying from one day to one month and found that reliability
of the estimated sensible heat flux is high for the averaging-period of more than 10 days. Surface
air temperature can be derived by the present method even if climatological values for P and R
are used. The temporal correlation coefficients between derived and observed surface air
temperatures are larger than 0.95 for the North Pacific. However, these are not so high for the
tropical region depending on the large sampling error. On the other hand, the spatial correlation
coefficient are between 0.985 and 0.995 and the rms differences are about 1°C. These values are
Air Temperature at Ocean Surface Derived from Surface-Level Humidity
633
encouraging. Remarkable seasonal variability can be found in time variation of the spatial
correlation coefficients, while it is not the case for time variation of the rms difference.
Moreover, sensible heat flux estimated by using the derived surface air temperature is
validated. For the whole North Pacific the cross-correlation coefficient is 0.89 and a mean error
is 0.58 W m–2 and an rms difference is 8.03 W m–2. It should be noted that sensible heat flux
estimated by the ocean observation data is not always accurate. Weare (1989) estimated the
uncertainties in calculation of the heat fluxes at the surface of the tropical and subtropical oceans
based upon the bulk formulae and archived marine weather reports. He concluded that the total
uncertainty for individual observations of the sensible heat fluxes are 12 W m–2. Therefore, the
rms difference shown in the present study may be comparable with the total uncertainty. Also,
the smallness of a mean error appears to be important for estimating global sensible heat flux.
Finally, the sensitivity of the derived air temperature to P and R and that of the derived
sensible heat flux to Ta are examined. As expected, the sensitivity of the derived air temperature
to R is much larger than that of P. The large sensitivity in the high-latitudes may be closely related
to the characteristics of the saturated vapor pressure curve for low-temperatures. On the other
hand, the large sensitivity in the eastern equatorial region may be associated with the large
variability of R there depending on the seasonal and interannual El Nino phenomena.
A new technique to estimate global sensible heat flux by using satellite data is developed.The
results show that validity of the present method varies depending on season and region. The use
of satellite data and bulk formulae are considered to be critical in order to estimate global heat
flux. However, the validity of estimating heat flux should be investigated. Kubota and Shikauchi
(1994) compared latent and sensible heat fluxes resulted from satellite data with those estimated
by in situ data. The agreement between them remarkably varies dependent on analyzed regions.
Therefore, considering characteristics of the method and the data, several kinds of data and
methods should be complementally used to obtain accurate heat fluxes.
Acknowledgements
We are grateful to Mrs. Akio Kaneda, Hisashi Takahashi and Shoichi Mitsumori for their
assistance.
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