For FY-3C/MWHTS measurements, the bias can be put into two categories: scan bias, which changes with the scan angle of the instruments, and air-mass bias, which tends to vary with the air mass and surface characteristics of the Earth. In our study, the bias correction scheme is a two-step process: scan correction and air-mass correction. The bias correction can be carried out by either adjusting the satellite measurements or the simulations [
21]. In general, the satellite measurements are adjusted, in order to avoid bias correction at each iteration in the physical retrieval procedure.
3.2.2. Air-Mass Correction
Bias in the radiative transfer model, because of errors in the physics or spectroscopy, or from imprecise modeling of the atmospheric process, is related to the atmospheric state sounding by the satellite. Removing this bias in physical terms is difficult, in generally, predicting it using a statistical method with bias predictors is preferred. In order to identify the air mass, which can provide a good representation of the atmospheric state, MWHTS observation bias/temperature and bias/humidity correlations, which can be used to study which combinations of atmospheric variables could be taken as bias predictors, are calculated at each pressure level using the statistical analysis dataset compiled in
Section 3.1. These correlations are shown in
Figure 4. For temperature, it can be seen that there is a correlation between MWHTS brightness temperature bias and the layer 1000–200 hPa, 200–50 hPa and 20–1 hPa for Channels 2–5 and Channels 11–14, but the correlation for Channels 6–10 is very weak. The humidity correlations are displayed for most of the channels in the layer 1000–100 hPa, shown as
Figure 4b. In addition, there is a high correlation between the surface temperature and Channel 4. However, it is surprising that, for bias/temperature correlations, the temperature sounding Channels 6–9 show little correlation; for bias/humidity correlations, the humidity sounding channels show weaker correlation than most of the temperature sounding channels; and window Channels 1 and 10, which sense the surface, do not show high correlation with the surface. It is important to realize that we are talking about the bias, not the brightness temperatures themselves. It is not necessary to follow the weight functions shown in
Figure 1, that is if a channel senses a given atmosphere layer, the bias will depend on this layer. However, the bias may be caused by another layer, because of correlations present in different layers [
25].
As a result of this correlation analysis, we can find that a certain correlation exists between the bias and air mass, but it is not significant, especially in Channels 6–9 for bias/temperature. In order to represent the relationship between the bias and air mass, we consider two kinds of statistical regression methods: linear regression methods and nonlinear regression methods. For the linear regression methods, we select the multiple linear regression model, which is widely used in the bias correction in the operational physical retrieval system and the radiances’ assimilation system. For the nonlinear regression methods, in recent years, many regression models have been introduced to the field of atmosphere remote sensing, such as artificial neural networks, kernel-based regression, particle swarm optimization, support vector machine, and so on. Considering the computational cost, the nonlinear mapping ability and the nonlinear problem solved in our study, we select the neural networks. Therefore, we develop two correction methods: air-mass LRC and NNC, representing the linear and nonlinear relationship between MWHTS observation bias and air mass, respectively.
• LRC method:
Assuming a linear relationship between the brightness temperature bias and the air mass, the LRC method uses a set of bias predictors to predict the bias through the following equation [
25]:
where
is the index of channel,
is the bias predictors and
and
are the coefficients, which are computed by carrying out a least-squares fit on the data samples containing the brightness temperature bias and air mass.
For the bias predictors
, after some testing, the best combination of predictors for the MWHTS would be: 1000–200 hPa thickness, 200–50 hPa thickness, 20–1 hPa thickness, surface skin temperature and column water vapor. In our study,
is constructed using the temperature profiles, humidity profiles and surface skin temperature in the statistical analysis dataset compiled in
Section 3.1.
and the corresponding differences of observations and simulations are used to calculate the coefficients
and
in this linear regression algorithm.
• NNC method:
In recent years, neural networks have been widely used in the retrieval of atmospheric geophysical parameters using remote sensing data, as NNs can be used to learn and compute functions for which the analytical relationships between inputs and outputs are complex (e.g., highly nonlinear) [
11]. In our study, we focus on BP NNs, which are based on the error back propagation learning algorithm proposed by Rumelhart et al. in 1986, due to their strongly nonlinear mapping ability [
41]. Following the vast majority of publications on applying NNs to the atmospheric remote sensing and considering the nonlinear problem of this work, we choose a three-layer networks. The schematic diagram of the three-layer BP NNs containing one hidden layer is shown in
Figure 5. The input layer in which no computation is carried out has
L nodes representing the length of the input vector
. Then, each node is connected to all
M nodes of the hidden layer. Each node in the hidden layer performs a nonlinear computation and is connected to each node of the output layer. The output vector
containing
N values is generated by a weighted sum over all of the output vector
of the hidden layer. Readers interested in additional details on initialization, training, optimization and other advanced topics can refer to [
41,
42].
In our study, the differences of observations and simulations in the statistical analysis dataset in
Section 3.1 are taken as the output vector of the pairs input/output vector, and the corresponding temperature profiles, humidity profiles and skin temperatures are taken as the input vector of the pairs input/output vector (i.e., bias predictors); thus, the length
L of the input vector
is 74, and the length
N of the output vector
is 15 in the BP NNs. The steepest descent method is selected in the training phase. Based on many tests, the hidden layer with 30 hidden nodes was found to be best in our study. The connection weights and bias are determined through the training using 90% of the pairs input/output vector; the other 10% of pairs are used for validation and stopping the training.
Finally, based on the above analysis, we can get the corrected brightness temperatures:
where
is the corrected brightness temperatures in channel
j and
is the brightness temperatures without bias correction. In order to evaluate the effects of corrected brightness temperatures on the retrieval accuracy of atmospheric temperature and humidity profiles, we will build a physical retrieval system based on one-dimensional variational algorithm for MWHTS measurements.