Latitudinal and Scan-dependent Biases of Microwave Humidity Sounder Measurements and Their Dependences on Cloud Ice Water Path

In recent decades, satellite data assimilation and numerical weather prediction (NWP) have become two of the most important scientific and technological achievements in meteorology. Meteorological satellite data assimilation can generate more accurate initial fields, which can improve model forecasts and the outputs of NWP models (Xue, 2009). At present, most global operational data assimilation systems are geared towards using observations made under clear-sky conditions. Clouds, precipitation particle sizes, and the wavelength of electromagnetic radiation may affect the absorption and scattering of radiation in cloudy skies. The use of satellite remote sensing data affected by clouds and precipitation without properly correcting cloud-dependent biases can lead to a significant decrease in the quality of the forecast field (Errico et al., 2007). Therefore, quality control of satellite data must be carried out before satellite data assimilation.

The elimination and assimilation of satellite remote sensing data from cloudy areas has become an active area in the field of satellite data assimilation in recent years. (Seto et al., 2005) proposed rain/no rain classification methods using simulated TMI and precipitation radar data to calculate monthly clear-sky brightness temperatures with a 1^°× 1^° spatial resolution as a background reference, then used 85 and 22 GHz channels to distinguish precipitation. (Roebeling and Holleman, 2009) used cloud microphysical parameters retrieved from the Spinning Enhanced Visible and Infrared Imager to detect precipitation and estimate the precipitation rate. (Geer et al., 2010) used the 22- and 37-GHz channels to calculate the amount of liquid water in clouds above a certain threshold to determine whether each satellite observation field contained clouds. An algorithm for retrieving the cloud liquid water path (LWP) using measurements from the 23.8- and 31.4-GHz Advanced Microwave Sounding Unit-A (AMSU-A) window channels so that clear-sky measurements over oceans could be identified was examined (Weng and Grody, 1994; Weng et al., 1997). All these methods, however, are only applicable to data from microwave sensors.

Microwave imagers and microwave sounders both have channels that are sensitive to clouds and precipitation and can eliminate cloudy data using their own detection channels. However, the Microwave Humidity Sounder (MHS) lacks a low-frequency detecting channel because it is operated alongside AMSU-A, so MHS is unable to identify liquid clouds, but it can detect ice clouds well using the ice water path (IWP) algorithm developed by (Weng and Grody, 2000) and (Weng et al., 2003). The MHS measurements have a high resolution (∼17 km at nadir) and five channels at high frequencies. Scattering from cloud particles dominates in the high-frequency MHS channels. Compared with measurements made under clear-sky conditions, MHS measurements are lower in the presence of clouds and decrease even more if precipitation or ice particles are present. Note that absorption and scattering of hydrometeors and ice particles are neglected in the simulations done in this study. Simulated brightness temperatures (B) and observed brightness temperatures (O) will thus have large differences where there are clouds. Whether the observation field has ice clouds will be determined by the difference between O and B (O-B). The O-B values are useful to identify ice clouds when assimilating clear-sky MHS observations into numerical models. Examining the relationship between O-B and IWP will help improve the efficiency of the operational assimilation procedure and is the focus of this study.

Observation and background field errors are assumed unbiased and follow a Gaussian distribution in data assimilation. Biases in satellite data may have a negative influence on assimilation results and may reduce the accuracy of NWP models (Dee, 2005; Auligné et al., 2007). So, biases in O-B need to be estimated and revised before exploring the relationship between O-B and the bias predictor IWP. These biases generally include calibration errors, radiative transfer model errors, and errors in the background field (Li and Zou, 2017). Taking into account the influences of clouds, surface emissivity, and Antarctic and Arctic sea ice, we consider only data from 60^°N to 60^°S over oceans. The Community Radiative Transfer Model (CRTM), version 2.2.4, developed by the Joint Center for Satellite Data Assimilation, is selected as the simulation model (Han et al., 2006, Han et al., 2007; Chen et al., 2008, Chen et al., 2010). Reanalysis data from the European Center for Medium-Range Weather Forecasts (ECMWF) are used as background fields to the CRTM, which are composed of vertical profiles of atmospheric temperature and humidity at 37 vertical levels from the Earth's surface to the model top (1 hPa), surface pressure, surface skin temperature, 2-m dewpoint temperature, 2-m temperature, and 10-m wind speed and wind direction.

This paper is organized as follows: A brief introduction to MHS channel characteristics and the CRTM are provided in the next section. Section 3 describes the scan-angle and latitudinal bias characteristics of all MHS channels. The relationship between O-B and IWP, and the influence of LWP on this relationship is examined in section 4. Section 5 gives a summary and discussion.

The AMSU-B has been onboard the National Oceanic and Atmospheric Administration (NOAA) series of satellites (NOAA-15, -16, and -17) since 1998. The MHS developed by EUMETSAT, onboard the NOAA-18 and -19 satellites and the MetOp-A and MetOp-B satellites, is the successor to the AMSU-B. The NOAA-18 satellite was launched on 20 May 2005 into an orbit at an altitude of 854 km. Its local equatorial crossing time is about 1400, making it an afternoon satellite. Since the launch of the NOAA-18 satellite, the MHS has officially become a part of the Advanced Television and Infrared Observation Satellite Operational Sounder package. Currently, the Advanced TIROS Operational Vertical Sounder consists of the High Resolution Infrared Radiation Sounder, AMSU-A, and MHS for retrieving temperature, humidity, and ozone soundings in all weather conditions, and is generating products from the NOAA-19, Metop-A, and Metop-B satellites. This instrument package provides information on temperature and humidity profiles, total ozone, clouds, and radiation, on a global scale, to the operational user community. The NOAA-19, MetOp-A, and MetOp-B satellites were launched on 6 February 2009, 19 October 2006, and 17 September 2012, respectively. The NOAA-19 satellite is an afternoon-configured satellite and the MetOp-A/B satellites are both morning-configured satellites. Each of these four polar-orbiting satellites provides near-global coverage twice daily (Qin and Zou, 2016).

The MHS is a cross-track-scanning, self-calibrating, five-channel microwave radiometer whose center frequencies are 89.0 GHz (channel 1), 157.0 GHz (channel 2), 183.31±1.0 GHz (channel 3), 183.31±3.0 GHz (channel 4), and 190.31 GHz (channel 5). Table 1 shows the main parameters of these MHS channels. This sounder has an instantaneous field of view (FOV) of 1.1^° at half power point, providing a nominal spatial resolution at a nadir of 17 km. The antenna provides cross-track scan coverage of ±49.5^° from nadir with a total of 90 earth-viewing angles per scan line. Each FOV needs 8/3 s to scan. Figure 1 shows the weighting functions at nadir of the five MHS channels calculated using the CRTM for American standard atmosphere. MHS channels 1 and 2 are semi-transparent window channels that are affected by ice clouds and the Earth's surface emissions. These two channels are also used for retrieving IWP (Weng and Grody, 2000; Weng et al., 2003). Channels 3, 4, and 5 can be used to obtain information about humidity in the troposphere. Channel 5 has the highest central frequency among the three sounding channels and is most sensitive to scattering from thin clouds (Qin and Zou, 2016).

Figure 1.  Weighting functions at nadir of NOAA-18 MHS channels 1-5 for an American standard atmosphere.

Over the past decade, MHS data have been assimilated in operational and research data assimilation and forecast systems. For example, the ECMWF uses a four-dimensional variational system to assimilate a wide range of satellite data, including satellite infrared and microwave radiances (Thépaut, 2003). Compared with infrared humidity sensors (Zou et al., 2013), microwave radiation can penetrate through non-precipitating clouds and carries rich atmospheric humidity information within the clouds. The assimilation of microwave humidity sounder data is of great significance for climate change research and improving quantitative precipitation forecasts.

The CRTM can be used for the rapid calculation and simulation of satellite radiances, covering microwave, infrared, and visible frequency regions. The first version of the CRTM was released in 2004 and has undergone improvements since then. The version employed in this study is v2.2.4 (Han et al., 2007; Weng, 2007). The background field data used in the simulations are from ERA-Interim at 0000 UTC, 0600 UTC, 1200 UTC and 1800 UTC, respectively, i.e., vertical profiles of atmospheric temperature and humidity, surface pressure, surface skin temperature, 2-m dewpoint temperature, 2-m temperature, and 10-m wind speed and wind direction, with a horizontal resolution of 0.75^°× 0.75^°. The model level top of the ERA-Interim data is at 1 hPa. This dataset covers the globe and is constantly updated in real time. All the simulations of brightness temperature in this research were carried out under the assumption of clear-sky conditions.

The total content of liquid water in the atmospheric column per unit area is called the LWP. AMSU-A 23.8-, 31.4-, and 50.3-GHz channels are used to retrieve LWP. The IWP represents the total amount of ice particles in the atmospheric column per unit area and is obtained from measurements in the MHS window channels. Note that the IWP data are retrieved from MHS brightness temperature observations in window channels at frequencies higher than 85 GHz, whose wavelengths are much larger than ice particles. The ice particle is assumed spherical in the Mie theory (Mie, 1908) that is used for the retrieval. Therefore, the MHS-derived IWP retrievals used in this study are different from those of other instruments, such as MODIS and CloudSat IWP retrieval products (Jiang et al., 2012).

The IWP and LWP (over ocean) values used in this paper are from the NOAA Comprehensive Large Array-data Stewardship System IWP and Cloud Liquid Water products (Weng and Grody, 2000; Weng et al., 2003). The spatiotemporal resolutions of the IWP and LWP data are the same as those of the MHS and AMSU-A, respectively.

MHS radiation is simulated by the CRTM under the assumption of a clear sky. As the first step, data not affected by clouds are extracted from all observations. Clouds can be roughly divided into water-phase clouds and ice-phase clouds. Since the MHS cannot identify liquid clouds because it lacks low-frequency channels, 23.8- and 31.4-GHz data from AMSU-A, which is also onboard NOAA-18, are used to retrieve the LWP over oceans to identify whether the ocean observations are clear-sky observations. MHS and AMSU-A data must first be matched in time and space so that both LWP and IWP datasets have the same spatiotemporal resolutions.

The AMSU-A and MHS onboard NOAA-18 have the same number of orbits in a day. One AMSU-A scan line is 8 s, and that of MHS is 8/3 s; the time between successive orbits is 100 min. Collocation of the data is done by finding the nearest MHS FOV to the center of an AMSU-A FOV. Figure 2 shows an example of matched data. One AMSU-A FOV covers nine MHS FOVs, which is related to the difference between the beam widths and azimuth angles of the two instruments. Figure 2a shows a complete AMSU-A scan line with 30 FOVs. Figures 2b and c show the first 15 FOVs and the last 15 FOVs, respectively, of the scan line in Fig. 2a. Matched data are shown in blue. Only those MHS data points over oceans where the MHS-retrieved IWP and the matched AMSU-A-retrieved LWP are both less than 0.01 kg m^-2 are used for the analysis of MHS bias characteristics.

Figure 2.  (a) AMSU-A (red ellipses) and MHS (black ellipses) FOVs along an AMSU-A scan line. Blue ellipses show the matched data, i.e., MHS data closest to the center of the AMSU-A FOVs. The scanning direction is from east to west. (b) AMSU-A FOVs 1-15 and MHS FOVs 1-45, and (c) AMSU-A FOVs 16-30 and MHS FOVs 46-90. The color convention in (b) and (c) is the same as that in (a). Data are from the descending part of the orbit.

Observations and model simulations entering an assimilation system should be unbiased, so bias correction should be carried out during quality control. Biases are generally caused by instrument calibration errors, radiative transfer model errors, and systematic errors in the background field. The relationship between observations (O), simulations (B), observational errors (μ_o) and simulation errors (μ_b) can be simply expressed as (Weng et al., 2012): \begin{equation} (O-\mu_{\rm o})-(B-\mu_{\rm b})=(O-B)-(\mu_{\rm o}+\mu_{\rm b}) . \ \ (1)\end{equation} According to Eq. (1), the sum μ_o+μ_b can reflect the errors both in observations and simulations. Taking the average of the right-hand-side in Eq. (1) over many samples, we conclude that the differences between observations and simulations over a long period can be used to estimate the total errors. To avoid the influences of clouds, surface emissivity, Antarctic and Arctic sea ice, and the NOAA-18 orbital drift period, data from 60^°N to 60^°S over oceans are considered. Given that satellite instruments are geographically dependent and that the optical path of the cross-track detector changes with scan angle, MHS biases will reflect latitudinal and scan-angle characteristics.

Figure 3a shows the scanning track of the NOAA-18 MHS at nadir of its descending orbit from 20 June to 7 July 2014, and we can clearly see the periodic orbital drift of NOAA-18 in Fig. 3b. To avoid the influence of orbital drift, we use the 18 days of data from 20 June to 7 July 2014 to calculate the MHS biases. Mean O-B values for different scan angles are calculated using 18 days of data from which O-B biases μ(α) as a function of scan angle are obtained: \begin{equation} \mu(\alpha_i)=\overline{O(\alpha_i)-B(\alpha_i)} , \ \ (2)\end{equation} where α_i is the scan angle for FOV i. There are 90 different FOVs along each scan line. The bias of each FOV subtracts the nadir bias, i.e., the bias of the mean of FOVs 45 and 46. Because of the cross-track scanning, the observation at nadir is closest to the real state of the atmosphere.

Figure 3.  The scanning track at nadir using NOAA-18 MHS descending-orbit data from 20 June to 7 July 2014. Panel (b) is a close-up look at an area southwest of South Africa.

To obtain O-B biases varying with latitude, mean O-B values at nadir within every 5^° latitudinal band are calculated: \begin{equation} \mu(\varphi_j)=\overline{O(\varphi_j)-B(\varphi_j)} , \ \ (3)\end{equation} where φ_j represents different latitude bands and j=(1,…,24) represents every 5^°-latitude band.

Figure 4 shows the scan-angle dependence of O-B biases for MHS channel 3. The distribution of the number of matched MHS data points is not uniform. MHS data volumes of the 3× i-1(i=1,2,…,30) fields are greater than the others because the AMSU-A beam width is three times that of the MHS and closer to nadir. Due to differences in the MHS data volumes for different scan angles, the statistical results from fields with a large quantity of data are more reliable. A five-point smoothing algorithm is used when calculating the means and standard deviations of O-B. Figure 5 shows the latitudinal dependence of O-B biases calculated within 5^°-latitude bands for MHS channel 3. The largest amount of data appears between the equator and 30^°N, which may be related to the omnipresent water clouds in the Southern Hemisphere. The variance of O-B is greater when there is less data in a latitudinal band.

Figure 4.  Scan-angle dependence of O-B biases for MHS channel 3 using clear-sky (i.e., IWP <0.01 kg m^-2 and LWP <0.01 kg m^-2) oceanic data points between 60^°S and 60^°N from 20 June to 7 July 2014. The solid green line and vertical green lines represent the means and standard deviations of O-B, respectively, and black dots show the O-B value (left ordinate). The yellow-shaded area gives the data count at different beam positions (right ordinate).

Figure 5.  Latitudinal dependence of O-B biases calculated within 5^°-latitude bands for MHS channel 3 using clear-sky (i.e., IWP <0.01 kg m^-2 and LWP <0.01 kg m^-2) oceanic nadir data points between 60^°S and 60^°N from 20 June to 7 July 2014. The solid green line and vertical green lines represent the means and standard deviations of O-B, respectively, and black dots show the O-B values (left ordinate). The red curve shows the amount of data in each latitudinal band (right ordinate).

Figure 6a shows the mean O-B of MHS channels 1-5 as a function of scan angle. Negative values are seen for the window channels. In particular, the O-B values of channel 2 are all negative. O-B values are all positive for the non-window channels. On the same scan line, the mean O-B of the first 45 FOVs is always greater than that of the last 45 FOVs. This asymmetry may be due to either the error in encoding the antenna pointing angle or to the polarization misalignment in the radiometer receiver (Weng et al., 2003). The antenna `seeing' the space craft in its side lobes and different items on the side of MHS may also cause an asymmetry. Figure 6b shows the standard deviations of MHS channels 1-5 O-B as a function of scan angle. The standard deviations show some small changes as the scan angle changes, and the standard deviations of the window channels are higher than those of the non-window channels. The lower the detection height of the non-window channels, the smaller the standard deviation and the more stable the MHS data. Figure 7a shows the mean O-B of MHS channels 1-5 as a function of latitudinal band. The mean O-B of channels 1 and 2 reach their minimum near 50^°S and then increase as the latitude increases into the Northern Hemisphere. The mean O-B in non-window channels does not show as much change as the latitude increases into the Northern Hemisphere, and the higher the detection height, the greater the change. Note that the mean biases of all five channels are positive. Figure 7b shows the standard deviations of MHS channels 1-5 O-B as a function of latitudinal band. The standard deviations of channels 1, 2, and 5 range from 0.5-6.5 K and show a maximum value near 20^°N and a minimum value near 47.5^°N. The standard deviations of channels 3 and 4 gradually increase from south to north, with greater increases seen in channel 3.

Figure 6.  Scan-angle dependence of (a) O-B biases and (b) standard deviations for MHS channels 1-5 using clear-sky (i.e., IWP <0.01 kg m^-2 and LWP <0.01 kg m^-2) oceanic data points between 60^°S and 60^°N from 20 June to 7 July 2014.

Figure 7.  Latitudinal dependence of (a) O-B biases and (b) standard deviations calculated within 5^°-latitude bands for MHS channels 1-5 using clear-sky (i.e., IWP <0.01 kg m^-2 and LWP <0.01 kg m^-2) oceanic nadir data points from 60^°S to 60^°N from 20 June to 7 July 2014.

Equation (4) is used to calculate a new O-B with scan-angle and latitudinal errors removed: \begin{equation} (O-B)_{\rm after}=(O-B)_{\rm before}-\mu(\alpha)-\mu(\varphi) . \ \ (4)\end{equation}

Data from 8 July 2014 are used to illustrate the relationship between this modified O-B and IWP. Figure 8 shows the spatial distributions of bias-corrected O-B over oceans between 60^°N and 60^°S on 8 July 2014 for the five MHS channels. In general, the bias-corrected O-B values are all close to zero over oceans under clear-sky conditions. Figure 9 shows the distribution of liquid-phase clouds over oceans between 60^°N and 60^°S on 8 July 2014 using LWP retrieved from NOAA-18 AMSU-A observations. Figure 10 shows the distribution of ice clouds over oceans between 60^°N and 60^°S on 8 July 2014 using IWP retrieved from NOAA-18 MHS observations. Comparing Figs. 8, 9b, and 10b, the O-B values of all channels are negative where there are ice clouds.

Figure 8.  Spatial distributions of NOAA-18 MHS channels 1-5 bias-corrected O-B over oceans under clear-sky conditions [panels (a-e), respectively] from descending nodes between 60^°S and 60^°N on 8 July 2014.

Figure 8.  (Continued)

Figure 9.  Geographical distribution of NOAA-18 AMSU-A LWP (units: kg m^-2) over oceans from (a) ascending nodes and (b) descending nodes between 60^°S and 60^°N on 8 July 2014.

Figure 10.  Geographical distribution of NOAA-18 MHS IWP (units: kg m^-2) over oceans from (a) ascending nodes and (b) descending nodes between 60^°S and 60^°N on 8 July 2014.

Figure 11 shows scatterplots of bias-corrected O-B for MHS channels 1-5 as a function of MHS-retrieved IWP over oceans between 60^°N and 60^°S on 8 July 2014. Due to the effect of ice scattering on MHS brightness temperature observations, the bias-corrected O-B fields have negative biases with increasing magnitudes as IWP increases. Such a variation of negative O-B biases with IWP becomes more significant when the LWP values are large.

Figure 11.  Scatterplots of bias-corrected O-B for MHS channels 1-5 as a function of IWP (units: kg m^-2) over oceans from ascending and descending nodes between 60^°S and 60^°N on 8 July 2014. The different colors represent different ranges of LWP (units: kg m^-2).

Figure 12 shows the means and standard deviations of MHS O-B before and after the bias correction as a function of IWP. Mean values of O-B for all channels decrease after the bias correction has been performed (Fig. 12a). Channel 1 has the weakest response to this relationship and channel 2 the strongest. For the three high-level sounding channels (channels 3-5), the negative biases decrease rapidly with increasing IWP. As IWP increases, the standard deviations of the O-B of window channels 1 and 2 before and after bias correction also increase (Fig. 12b). However, a decrease in the O-B standard deviations of window channels 1 and 2 is seen when IWP exceeds 0.5 kg m^-2, due to small data samples. For the other channels, O-B stabilizes as the height of the detection increases because surface emissivity and clouds have less effect on microwave channels. Figure 13 shows the means and standard deviations of MHS O-B after the bias correction as a function of IWP on 8 July of each year from 2011 to 2017. The latitudinal and scan-angle biases used in Fig. 13 are calculated using data from 20 June to 7 July of each year. In general, the trends in each year are consistent (Fig. 13a). When the IWP is greater than 1.0 kg m^-2, trends vary greatly from year to year for the same channel (Fig. 13b). This is related to the lesser amount of data associated with large IWP values. For the window channels, the difference between years is also large when the IWP is less than 0.1 kg m^-2, because of the interference from surface emissivity and IWP retrieval errors associated with such small IWP values.

Figure 12.  The (a) means and (b) standard deviations of MHS channels 1-5 (black, purple, blue, red, and green lines, respectively) O-B before (dashed lines) and after (solid lines) the bias correction is done as functions of IWP between 60^°S and 60^°N on 8 July 2014. The gray shaded area represents the amount of data (right ordinate; counting interval: 0.01 kg m^-2).

Figure 13.  The (a) means and (b) standard deviations of MHS channels 1-5 (black, purple, blue, red, and green lines, respectively) O-B after bias correction as a function of IWP between 60^°S and 60^°N on 8 July of the years 2011-2017. In each color group representing the different channels, the years (solid curve for years 2011, 2013, 2015, 2017; dashed curve for 2012, 2014, 2016) go from light-colored (starting at 2011) to dark-colored (ending at 2017). The gray shaded area represents the amount of data (right ordinate; counting interval: 0.01 kg m^-2).

This paper examines the relationship between MHS-derived O-B and IWP, and the impact of AMSU-A-derived LWP on it, based on summertime data from 2011-2017. First, MHS brightness temperatures are simulated using CRTM v2.2.4, with ERA-Interim background fields as inputs to the model. A clear sky is assumed. Since the instruments are on the same NOAA-18 satellite, MHS and AMSU-A data are then matched so that clear-sky data can be identified for use in the MHS bias correction. The scan-angle and latitudinal dependences of MHS channels 1-5 O-B are examined next, and biases are then removed from the original set of MHS O-B. Finally, variations in the bias-corrected O-B as a function IWP and the influence of LWP on it are analyzed. The results can be summarized as follows:

(1) Scan-angle deviations of the MHS window channel O-B biases range from -1.7 K to 1.0 K, with channel 1 showing the largest deviations. The scan-angle deviations of the first 45 FOVs are always greater than those of the last 45 FOVs on the same scan line. Negative values are seen for the window channels. In particular, the O-B values of channel 2 are all negative. O-B values are all positive for the non-window channels. The range of fluctuations increases as the height of the detection altitude increases. The latitudinal deviations of O-B are positive for all MHS channels. The latitudinal-band deviations of the MHS window channels shows a significant minimum around 50^°S, and the latitudinal-band deviations of the non-window channels increase as the detection altitude increases. The standard deviations of channels 1, 2, and 5 range from 0.5-6.5 K and show a maximum value near 20^°N and a minimum value near 47.5^°N. The standard deviations of channels 3 and 4 gradually increase from south to north, with greater increases seen in channel 3.

(2) In general, the bias-corrected O-B values are all close to zero over oceans under clear-sky conditions. Bias-corrected O-B values and IWP agree well, with O-B decreasing as IWP increases, for the non-window channels. The higher the detection height, the less obvious is this trend. The response of window channels to the relationship is not clear.

This study uses summertime data to calculate MHS biases and CRTM-simulated brightness temperatures. There may be some discrepancies between biases in different seasons. Different radiation transmission modes will also affect the statistics. The MHS IWP retrieval products may have biases (Jiang et al., 2012). In future work, these issues will be addressed and further studies on the application of MHS cloud-dependent bias corrections in meteorological satellite data assimilation and the improvement of the accuracy of model predictions will be pursued.