5.1. Measurements for MWHS on Board FY-3A Meteorological Satellite
 This paper uses brightness temperatures of FY-3A satellite-based MWHS observations from 1 June 2008 to 31 May 2009 distributed at latitude from 78.5° to 82.5° and longitude from 10° to 60° where station 20046 and 01004 matched and the surface types are land. The brightness temperature observations are shown inFigure 8, located at 78.92°N latitude and 11.93°E longitude. The five colors indicate brightness temperatures in different channels. From Figure 8, one can easily see that the brightness temperatures in the channel of 182.31 GHz are most stable in the whole year. Brightness temperatures in each channel reflect the cumulative water vapor contribution at different altitudes. In order to simulate brightness temperature values at the same time every day, we use radiosonde information including temperature profiles, humidity profiles and pressure profiles, wind speed, and other information. Figure 9 shows the surface water vapor density values of the whole year from June 2008 to May the next year.
 The brightness temperature input variables in five channels are critical in the ANN retrieval model. The retrievals benefit their sensitivity and accuracy, therefore, the observation values in water vapor channels and window channels from FY-3A MWHS are shown inFigure 10 with a range of 0°–20°E latitude and 60°–90°N longitude.
Figure 10. The brightness temperature observations in five channels from FY-3A MWHS (time 20090901_0742). The range is within 0–20°E and 60–90°N.
Download figure to PowerPoint
 It is demonstrated that the brightness temperature values in the Arctic region are generally much more stable (approximately located at 250–280K) than midlatitude and tropical regions above the same surface type. The reason is due to the lower temperature and relatively larger water vapor density with less variance compared to midlatitude and tropical regions.
5.2. Data Processing and Simulation
 The paper uses three data sets, including training, test, and validation data sets from two stations. One is 01004, with latitude 78.92°N and longitude 11.93°E, and the other is 20046, with latitude 82.61°N and longitude 58.05°E. Then we selected radiosonde profiles from these stations at 12:00 UT during 1 year (from 1 June 2008 to 31 May 2009). For the radiosonde data sets, they provide the profiles of temperature, mixer ratio of water vapor, pressure, height and relative humidity. Exclude the radiosonde data which the height less than 15 km, and use cloud-judge function (if relative humidity is larger than 95%, then we assume it is cloudy) to exclude the data sets in cloudy sky. Here, we received a total of 361 data, and exclude 3% rainy data and incomplete data and 23% cloudy data. Then these remaining profiles are processed at discrete levels every 200 m up to 15 km. Although the number of independent measurements is only 50 levels output, this sampling ensures the retrieval profiles can accurately represented on the fixed levels.
 The brightness temperature values from five channels are read form MWHS level 1 data. Here, the surface temperature, surface pressure and relative humidity are also directly connected. The radiosonde data sets include various climate facets of the variability in clear-sky Arctic region and are numerous enough to be split into training, test and validation sets. Notice that training data sets must be representative for all the test and validation sets. In the training process, surface information (surface temperature, pressure and emissivity) and brightness temperatures in five channels are linearly normalized as input values with the range of [0, 1]. Similarly, water vapor density profiles are normalized as output values. The Gaussian noises are added in the surface temperature, pressure and observed brightness temperatures, which are 0.5 K, 0.3 kPa and 0.5 K, respectively. This extends the training data sets slightly and reduces the sensitivity of the network to noise in the data and can represent all the errors affecting the observations.
5.3. Retrievals and Analysis
 Typical results for all seasons are shown in Figures 11 and 12. Figure 11 shows the comparison between water vapor density retrievals from ANN model and from radiosonde data sets. Each single dot represents water vapor density in one layer. Here “23” and “215” mean the number of test data and training data. There is a good linear relationship which indicates that the water vapor density retrievals are well agreement with the profiles from radiosonde observations. Figure 12 shows bias and RMS in percentage of the water vapor density between water vapor density retrievals from ANN model and from radiosonde data sets. It has the same specification with single point and test box. The largest bias error appeared at the altitude of ∼1.5–2 km. It has higher accuracy at higher altitude. But in Figure 12 (right), the relative water vapor RMS is higher in high latitude. This is because its value is relative to the signal, and in higher layers, the water vapor content is much lower than the layers near the surface.
Figure 11. Comparison between relative humidity retrievals using ANN and relative humidity from radiosonde data sets.
Download figure to PowerPoint
Figure 12. (left and right) Relative humidity RMS error between relative humidity retrievals using ANN and relative humidity from radiosonde data sets.
Download figure to PowerPoint
 To explain the accuracy of water vapor density retrievals explicitly, Figure 13 shows one profile comparison and bias of water vapor density profile between retrievals using ANN method and from radiosonde data sets in randomly 1 day at a certain time. Here the date is at 12:00 UT on 29 November 2008; the surface temperature is 267.05 K, the total water vapor is 6.103 kg/m2, and the surface pressure is 98.16 kPa.
 The RMS error is considered to be the criteria to judge the retrievals deviated from parameters from radiosonde data. It can be expressed as
where zrad and zretr are the radiosonde observation and water vapor density retrievals, respectively, and N is the total number of comparisons.
 Relative RMS can be expressed as
 Here, V is integrated water vapor content and can be calculated as
where q is specific humidity, p is pressure, ρ is liquid water vapor density, g is acceleration of gravity, and p0 is surface pressure.
 Figures 14 and 15 are mean RMS error for discrete altitudes and for different data. In Figure 14, it apparently can be seen that in higher altitudes, FY-3A MWHS can retrieve water vapor density values with smaller bias and root-mean-square error; this means that in higher altitudes, MWHS retrievals are in good agreement with the values from radiosonde observations and vice versa in the lower altitudes. This is the system characteristic of satellite microwave humidity sounder. Also in different seasons, the RMS error values are varied as the season changes.Figure 15 shows water vapor density RMS of the period 1 June 2008 to 31 May 2009 in station 01004; several days were selected in each month. In the later days of spring and earlier days of summer, the RMS is larger than other days in the whole year.
 As far as we know, the wavelet function-based BP neural network has not been used in the water vapor density retrievals. This paper presents a Mexican hat function-based BP neural network which plays an important role in retrieval research.Figure 16shows the comparison and BIAS and RMS of water vapor density retrievals with respect to radiosonde data sets. It shows that all the above methods can retrieve humidity profiles with high accuracy. Based on the character of satellite-borne MWHS, these methods have better retrievals in higher altitude than in lower altitude of troposphere, while the BP neural network with the Mexican hat method has relatively better retrievals than the BPANN method, especially in the layers from 3 km up to 10 km.
 Besides analyzing the RMS error in different atmospheric altitude, it also analyzes the variation among the whole year from 1 June 2008 to 31 May 2009. A sample was collected every 10 days throughout the year, a total of 36 data sets were chosen, and the root-mean-square errors in different seasons are shown inTable 2.
Table 2. The Root-Mean-Square Error in Different Seasons in Testing Area
|Mean Temperature (K)||256.0281||257.3486||254.3049||249.9409|
|Mean Pressure (kPa)||99.1502||98.2049||99.0866||98.5673|
|Mean Water Vapor Density (g/m3)||1.1802||1.2293||1.0039||0.5991|
|Mean RMS (g/m3)||0.1341||0.1011||0.1043||0.1202|
|Mean RMS (%)||13.7079||12.0239||13.4273||11.7503|
 From Table 2, we can easily see that at station 20046, in summer, the RMS error is the largest one; it means that in summer, the water vapor density profile retrievals are the least accurate. In winter, the RMS error is smallest, and the water vapor profiles in winter can achieve the best agreement with them from radiosonde observations. In spring, the RMS error of retrievals is larger than in autumn. In the last row, the retrievals are expressed as a percentage, not an absolute number. It demonstrates that, compared to integrated water vapor content, in winter it has the smallest relative RMS (11.75%) and in spring it has the largest relative RMS (13.70%). Compared to surface mean water vapor density, in winter the mean water vapor density is 0.5991 g/m3 with a RMS of ∼0.1202 g/m3 that is about 20%. In the other seasons the mean percentage RMS error is about 10%.
 To demonstrate the performance of this algorithm outside of the region, the algorithm used in this paper has been applied to locations that do not have radiosonde soundings. For a reliable comparison, we selected another site in the Arctic around the radiosonde station (01004) where the climate situations are mostly within training data sets to validate the algorithm (without retraining the neural network). Through this experiment, we can assess how well it will perform on other regions and judge the impact of these retrievals. The validation results are shown in Table 3. Because there are only a few radiosonde stations in the Arctic region, the authors used brightness temperature values for five channels in different locations, like latitude 78°N–82°N and longitude 12°E–50°E, and retrieved the water vapor density profiles. Compared with profiles from other instruments, the RMS is less than 0.3 g/m3 and relative RMS (compared to integrated water vapor content) is about 21%, which are acceptable.
Table 3. The Root-Mean-Square Error in Different Seasons in Validating Area
|Station: 78°N to 82°N 12°E to 50°E||Spring||Summer||Autumn||Winter|
|Mean Temperature (K)||264.2842||277.7597||269.3013||261.9129|
|Mean Pressure (kPa)||101.1343||101.2170||100.4361||100.3406|
|Mean Water Vapor Density (g/m3)||2.0194||5.6938||2.6404||1.7771|
|Mean RMS (g/m3)||0.1435||0.2603||0.1972||0.1373|
|Mean RMS (%)||18.97||20.98||17.43||15.92|