Yuei-An Liou and Chuang-: Lun Chang
Center for space and Remote Sensing Research
And Institute of Space Sciences
National Central University
Taipei [email protected]
A ground-based water vapor radiometer (WVR) operating at 23.8 and 31.4 GHz was utilized to observe water vapor and temperature profiles at the Taipei weather station from March 18 to 25, 1998. The profiles were inferred from WVR observed brightness temperatures of the sky through a statistical regression method whose coefficients are derived based on radiosonde soundings collected at the same site every March starting from the year 1998 to 1997. The regression method is evaluated through a self-consistent test by comparing its observation of water vapor and temperature profiles with those observed by radiosonde observations (ground truth). While the weighted root mean square error (RMSE) between the retrievals and ground truth is somewhat large about 1.5 g/m3 for the water vapor, the RMSE decreases exponentially with altitude. In contrast, the RMSE for the temperature is on the range of 2.2 to 3 K. to improve the retrieval accuracy, surface observations of temperature, water vapor density, and pressure are used as constraints. We found the RMSE for both water vapor and temperature retrievals are significantly near the surface. Essentially, zero RMSEs are acquired at the surface for both variables.
With the constraints of surface meteorological measurements, the regression scheme is applied to derive water vapor and temperature profiles. Two extreme cases are chosen for the current study, one with an atmosphere of monotonically decreasing water vapor and temperature profile and the other with a non-monotonically decreasing (inversion) profile. While WVR does not capture a low-elevation inversion (high-frequency signals) in both temperature the profiles for the latter case, it does perform well in determining the profiles for the former case.
Atmospheric water vapor and temperature profiles dominate the energy balance of the atmosphere. Their distributions are therefore important to better initialize and constrain numerical weather predictions models. The most typical way to measure the atmospheric profiles is by radiosonde soundings, which suffers from the cost of the advices and their limiting use to certain areas of land. Microwave radiometry represents an alternatives way to measure the profiles for all-weather conditions. This radiometric approach relies on the fact that the absorption lines of water vapor and oxygen locate in the microwave region (Solheim et al., 1998).
In this paper, we present observations of atmospheric profiles by a dual-channel, ground-based radiometric approach from a field campaign conducted at the Taipei weather station from March 18 to 25, 1998. this study is improved upon our previous study demonstrating measurements of total water vapor by the same data set (Liou, 1998). This paper is began with Radiative transfer that briefly addresses the fundamentals of radiometric sensing technique. The retrieval scheme and the 2-channel measurements of atmosphere profiles are subsequently presented.
Atmosphere profiles dominate microwave emissions of the atmosphere so that they can be retrieved from radiometric measurements. Atmospheric emissions are characterized by the Radiative transfer described as (Ulaby et, al., 1981).
where r is the position function, m, i, is the optical depth, Np and J is the source function, W/m2-sr. Eq. (1) can be explained by the Kirchhoff’s law, which states that under conditions of local thermodynamic equilibrium, thermal emission must be equal to absorption. For upward -looking radiometry, its solution can be written as
and Ke is the extinction coefficient of the atmosphere. In the microwave region, Eq. (2) by the Rayleigh-Jeans law can be rewritten as
where Tbg is the brightness temperature observed by radiometer, K, Tbe represents cosmic brightness temperature (2.7 K), and Ta is the temperature of the atmospheric K. note that the extinction coefficients in Eq. (3) has been replaced by Ka in Eq. (4) because absorptions in liquid water cloud regions exceeds scattering by at least two orders of magnitude (Janssen, 1993).
Equation (4) states that atmospheric variables dominate brightness temperature through their influence on the absorption coefficient. In turn, the variables can be retrieved from the observed brightness temperatures through regression retrieval scheme.
Multiple Regression Retrieval Scheme
To derive multiple regression coefficients, 10-years radiosonde soundings collected at the Taipei weather station, Central Weather Bureau (CWB), every March from the year 1998 to 1997 were used. The use of monthly climatological data is intended to reduce the influence of seasonal variation on the inversions of atmospheric variables. Atmospheric brightness temperatures are determined by using Eq. (4) whose water vapor, liquid water and oxygen absorption characteristics are characterized by the Liebe model (Liebe and Layton, 1987). The amount of cloud liquid water is derived with an adiabatic assumption when relative humidity is higher than 98% (Liou, 1998).
Since water vapor and temperature are of two key parameters to determine the absorption characteristics of the atmosphere, their profiles can be determined by the radiometric observations of the atmosphere. That is,
For self-consistency, the regression coefficients obtained from the 10-year radiosonde data are used to infer atmospheric profiles from brightness temperatures at the two frequencies of interest. The retrievals are compared with those measured by radiosonde soundings (ground truth). Fig.1 shows climatological profiles of (a) water vapor density and (b) temperature, and RMSE’s in (c) water vapor density (d) temperature between retrievals and ground truth based on radiosonde data collected every march from the year 1998 to 1997. The weighted RMSE’s appear large, 1.50 g/m3 for water vapor density, and 2.9 K for temperature. Absolute values of the variables are used ad the weights to compute the weighted RMSE’s is greatly influenced by the mismatching near the surface. Hence, surface meteorological measurements are incorporated constraints to improve the retrievals. Eq. (5) can then be written as
To represents surface temperature, K
Po is surface pressure, mb
VDo is surface water vapor density, g/m3.
Figure 2 shows RMSE’s between WVR observations with constraints of surface meteorology and radiodonde measurements for (a) water vapor density, and (b) temperature. A comparison between Fig. 1 and Fig. 2 demonstrates that surface meteorology constraints have improved the retrievals. The improvement appear more significant near surface, essentially zero RMSEs for both variables. The corresponding weighted RMSEs are reduced to 0.83 g/m3 for water vapor density, and to 1.62 K for temperature.
Observed Atmospheric Profiles from Radiosondes and WVR
Two extreme atmospheric profiles are chosen for the current study to examine the performance of the 2-channel WVR approach’s capability in measuring atmospheric profiles. One of them has an atmosphere with monotonically decreasing water vapor and temperature profiles and the other with an inversion profile.
Figure 3 compares WVR and radiosonde observed (a) water vapor density and (b) temperature profiles collected at 03/19/1998 OOUTZ when water vapor density and temperature monotonically decreases with altitude. The differences between WVR and radiosonde observations in water vapor density and temperature are given in Fig. 3 (c) and (d), respectively. Generally, speaking, WVR reasonably captures variations of atmospheric profiles without extra information of surface meteorology. Nevertheless, its observations tend to worsen closed to the surface, by deviating from radiosonde observations by 3 g.m3 for water vapor density and by 2 to 5 K for temperature. With surface meteorological measurements, the retrievals are much improved near the surface for both water vapor density and temperature although they are somewhat enlarged a little bit near 3 km height for the water vapor density.
Figure 4 shows WVR and radiosonde observed (a ) water vapor density and (b) temperature profiles collected at 03/19/1998 12UTZ when inversion in water vapor density and temperature occur at low elevation. The differences between WVR and radiosonde observations in water vapor density and temperature are given in Fig. 4 (c) and (d), respectively. Similar to the precious case (Fig. 3), WVR indeed captures the general trend of the variations in the atmospheric profiles without surface meteorology. However, Fig. 4(a) and (c) indicate that a 2-channel WVR approach can not resolve fast-varying water vapor density profile. Moreover, the 2-channel approach is not able to improve its retrieval of water vapor density in the regions of fast-varying profile even though the near-surface profile is improved with more magnificent because the inversion in temperature is relatively weak compared to that in water vapor density.
We investigate the use of a ground-based WVR operating at 23.8 and 31.4 GHz in measuring water vapor and temperature profiles. Field data of WVR, radiosonde, and surface meteorological observations at the Taipei weather station were collected from March 18 to 25, 1998. The WVR observations are used to infer water vapor and temperature profiles with and without surface meteorological measurements as constraints. Two extreme atmospheric profiles are chosen for the study, one with an atmosphere of monotonically decreasing water vapor and temperature profiles and the other with a non-monotonically decreasing profile. We show that the 2-channel WVR approach captures the general trend of atmospheric variations in water vapor and temperature except that it does not resolve the high-frequency signals in the region of inversion due to the limited number of WVR channels. In addition, the WVR observations can be significantly improved near the surface if the surface meteorological measurements are incorporated in the retrieving process.
Acknowledgements: The authors appreciate much the National Space Program Office grant NSC87-NSPO(A)-PC-FA07-05. They also thank Radiometrics Corporation fir the loan of WVR and CWB for providing a space to conduct the WVR experiment.
- Janssen, M.A., 1993: An introduction to the passive microwave remote sensing of atmospheres. In: Atmospheric Remote Sensing by Microwave Radiometry, M.A. Janssen (ed) John Wiley & Sons. Inc., New York, NY, U.S.A.
- Liebe, H.J., and D. H. Layton, 1987: Millimeter-wave Properties of the Atmospheric. National Telecommunication and Information Administration, Boulder, CO, USA, 470pp.
- Liou, Y, A., 1998: Observed spatial variation in perceptible water vapor by a ground-based, dual-channel radiometer. 19th Asian Conference on Remote Sensing, Manila, Nov. 16-20.
- Solheim, F., J.R. Godwin, E.R. Westwater, Y. Han, S.J. Keihm, K. Marsh, and R. Ware, 1998: Radiometric profiling of temperature, water vapor and cloud liquid water using various inversion methods. Radio Sci., 33, 393-404.
- Ulaby, F. T., R.K. Moore, and A.K. Fung., 1981: Microwave Remote Sensing: Active and Passive, Vol. 1, Artehc House Inc., Norwood.