Deep Retrieval Architecture of Temperature and Humidity Profiles from Ground-Based Infrared Hyperspectral Spectrometer

Abstract

Temperature and humidity profiles in the atmospheric boundary layer are essential for climate studies. The ground-based infrared hyperspectral spectrometer has the advantage of measuring radiances emitted from the atmosphere at a high temporal and moderate vertical resolution. In this article, the retrieval of temperature and humidity profiles from ground-based infrared hyperspectral observations is exploited. Although existing inversion algorithms based on physical models or statistical learning have made some progress, they still suffer from high computational complexity or poor performance. Motivated by the strength of the deep learning, we present a deep retrieval architecture (DReA) by skillfully designing a light-weight one-dimensional convolution neural network (CNN) to retrieve the temperature and humidity profiles. Experiments were conducted using atmospheric emitted radiance interferometer (AERI) and radiosonde data to demonstrate the superiority of the proposed DReA. The validation of the DReA with the radiosonde, using 802 profiles with 37 layers below 3 km, presents an excellent retrieval ability with a root mean square error (RMSE) of 0.87 K for the temperature and 1.06 g/kg for the water vapor mixing ratio. Furthermore, a thorough comparison with commonly used inversion methods such as the traditional back propagation (BP) and the eigenvector (EV) regression method, shows that our proposed DReA method obtains a leading solution in retrieving temperature and humidity profiles.

1. Introduction

Thermodynamic profiles in the atmospheric boundary layer are particularly valuable for a range of atmospheric research and operational needs, e.g., the climate monitoring, weather nowcasts and forecasts, the initialization of numerical weather prediction (NWP) models, and others [1,2]. For example, the vertical distribution of temperature and humidity changes drastically over the diurnal cycle and the passage of climate features such as frontal boundaries can lead to very rapid changes in the thermodynamic structure of the atmospheric boundary layer [3,4]. Thus, the precise and continuous acquisition of atmospheric thermodynamic profiles plays a crucial role in improving the accuracy of operational applications and situational awareness.

In general, the conventional radiosonde can directly achieve highly representative and trustworthy thermodynamic profiles [5,6], but at the price of low temporal resolution (routinely once or twice per day) [7], which is inappropriate for capturing the diurnal evolution of the atmospheric condition in the whole process. One alternative that could surmount this deficiency is the use of the ground-based remote sensing technology due to its high temporal and moderate vertical resolution [8] compared to radiosonde sounding. The ground-based infrared hyperspectral spectrometer, one type of passive remote sensing radiometer, can measure high spectral resolution radiances that are naturally emitted by the atmosphere at selected band channels. Furthermore, the atmospheric temperature and humidity profiles can be retrieved via the obtained atmospheric radiances.

In this paper, we explore the problem of the inversion of the atmospheric temperature and humidity profiles leveraging the ground-based infrared hyperspectral spectrometer observations. Existing mainstream retrieval methods can be roughly divided into two main categories as follows:

• Physical inversion methods apply the physical characteristics of atmospheric radiation transfer and the iterative optimization strategy. One representative method, named AERIprof [9,10,11], is based upon an onion-peeling technique. AERIprof performs with greater efficiency because it only needs to compute the diagonal of the Jacobian matrix. However, the main drawback of the algorithm is that it heavily relies on the accuracy of the statistical first guess. To surmount the problem, another paradigm based on the optimal estimation [12], i.e., AERIoe [13,14], applies a Gauss–Newton optimal estimation scheme to retrieve thermodynamic profiles.
• Statistical inversion methods [15] construct the regression equation defined by the atmospheric parameters and the radiometer measurements from the spectral channels. The eigenvector (EV) regression method [16], as one popular statistical inversion method, establishes the linear regression relationship between the atmospheric observations and the corresponding radiometer data via the least squares to obtain the inversion results. The BP neural network algorithm [17] can realize the nonlinear projection from the input observations to the output retrieval profiles. Compared with the EV regression method, it is more inclined to portray the physical essence of atmospheric temperature and humidity profile retrievals.

Despite pioneering works’ efficacy for the retrieval of the atmospheric temperature and humidity profiles, their performance may still be constrained by some bottlenecks. For example, many physical inversion methods introduce iterative optimization solutions which bring the computational complexity to a certain extent. In addition, the type of method is extremely dependent upon the initial value of the profiles. Inaccurate initial values can lead to the deterioration of the retrieval results.

Although the statistical inversion model represented by BP has made some progress in computational efficiency, its performance has not been greatly improved due to the limited representation ability of the BP network.

To tackle the aforementioned drawbacks, a deep neural network model is constructed to retrieve the atmospheric temperature and humidity profiles. As it is known, deep learning has achieved great success in various meteorological studies [18], including in weather forecasting [19,20,21], particular matters estimation [22,23,24,25], precipitation prediction [26,27] and environmental parameter retrieval [28,29,30]. Given the shortcomings of the existing inversion methods, and inspired by the superiority of CNN, e.g., powerful feature representativeness, the elimination of the need for feature engineering and the learned model generalization [31,32], we present a novel deep retrieval architecture (DReA) via delicately constructing a light-weight one-dimensional CNN for the retrieval of the temperature and humidity profiles. There are two main advantages of using 1D CNN compared with other classical machine learning methods. The first one is that 1D CNN can automatically learn and extract high nonlinear features from the raw data. This is in contrast to classical machine learning methods, such as support vector machines (SVMs) or random forests, which require handcrafted feature engineering and may not capture all the high-level features in the data. Another advantage of 1D CNN is that it can learn in an end-to-end fashion. However, the learning process of the traditional machine learning methods includes two stages. In summary, the key theoretical advantage of using 1D CNN over other classical machine learning methods is their ability to automatically learn and extract high-level features from the raw data in an end-to-end way.

The DReA is stacked by several one-dimensional convolution layers, downsampling layers, nonlinear layers and fully connected (FC) layers, which can sufficiently excavate the nonlinear relations between the atmospheric profile and the atmospheric radiation. The atmospheric emitted radiance interferometer (AERI), a well-calibrated ground-based infrared instrument, and the radiosonde observations are exploited to demonstrate the superiority of the proposed DReA. More significantly, we present for the first time the use of one-dimensional convolutional neural networks for the retrieval of atmospheric profiles from ground-based infrared hyperspectral spectrometer data. The validation of DReA with the radiosonde, using 802 profiles with 37 layers below 3 km, shows an excellent inversion capability. The root mean square error (RMSE) of the temperature was 0.87 K, and the water vapor mixing ratio was 1.06 g/kg. The contributions of our work can be summarized as follows:

(1)

We propose a novel deep learning framework named DReA for the retrieval of atmospheric profiles from ground-based infrared hyperspectral spectrometer observations.

(2)

The proposed DReA is constructed using 1D CNN, which is highlighted and can fully exploit the high nonlinear relation between the observations and the atmospheric profiles.

(3)

Comprehensive experiments are conducted to demonstrate that the proposed method outperforms the existing statistic methods. Furthermore, we present some case studies which verify that the proposed method can still efficiently retrieve the atmospheric profiles even when there are cold and warm frontal passages.

2. Data Sources

This study analyzes the proposed retrieval algorithm using observations from the atmospheric emitted radiance interferometer (AERI) and the radiosonde deployed in the South Great Plain (SGP) site [33]. We apply the AERI data under clear-sky conditions from 2006 to 2017 to retrieve the atmospheric temperature and humidity profiles. These radiosonde data serve as the truth profile for the AERI retrieval.

2.1. AERI Data

The AERI, a ground-based passive interferometer, was specifically designed and fabricated by the University of Wisconsin [34] for the Department of Energy’s Atmospheric Radiation Measurement (ARM) program [35,36]. AERI can measure downwelling atmospheric emitted radiances from the wavelengths of 3.3–18.2 $\mathsf{\mu }$m (520–3000 cm${}^{-1}$) at a spectral resolution of better than 1 cm${}^{-1}$ [37], which has been widely applied to the retrieval of temperature and humidity profiles in the atmospheric boundary layer [13,38]. The AERI is a multi-channel ground-based passive instrument, including 311 water vapor absorption channels and 244 carbon dioxide channels, as shown in Figure 1, which are used for the retrieval of humidity and temperature profiles, respectively [39].

2.2. Radiosonde Data

Currently, the radiosonde is often regarded as the ground truth of the atmospheric temperature and humidity profiles. The radiosonde can observe many meteorological elements, e.g., the geopotential height, temperature, dew point temperature and wind direction by sounding balloons four times per day. We use the radiosonde data of a specific synoptic time from upper-air stations in SGP to validate the performance of the retrieved profiles from AERI. The radiosondes used in this study include RS92-KL (beginning 17:30 UTC 9 February 2005–8 February 2010), RS41-SGP (from 8 February 2010 to 13 November 2017), and RS92-SGPD (from 13 November 2017 to present), all manufactured by Vaisala [40].

2.3. Retrieval Methodology

In this section, we firstly give the retrieval problem formulation, then introduce the key components of the CNN to facilitate the understanding of the proposed model. Finally, we provide a detailed introduction of DReA, including the forward propagation and the training processes of DReA.

2.4. The Retrieval Problem Formulation

We are provided with the AERI observations $\mathbf{Y}={\left\{{\mathbf{y}}_i\right\}}_{i=1}^N$ and the corresponding state values $\mathbf{X}={\left\{{\mathbf{x}}_i\right\}}_{i=1}^N$ from the radiosonde, where ${\mathbf{y}}_i$ means the value observed at a certain time, and ${\mathbf{x}}_i$ is the state vector measured by the radiosonde at the corresponding time. It should be noted that we apply the same one notation $\mathbf{X}$ to denote the temperature value ${\mathbf{X}}^t$ or humidity value ${\mathbf{X}}^q$ for simplicity in the following discussion. N is the total number of data obtained. Here, to be simple, we use the same notation ${\mathbf{x}}_i$ to define an arbitrary temperature value ${\mathbf{x}}_i^t={\left[t_1,t_2,...,t_m\right]}^T$ or a humidity vector ${\mathbf{x}}_i^q={\left[q_1,q_2,...,q_m\right]}^T$ in the algorithm description, where $t_j$ and $q_j$ denote the temperature and water vapor mixing ratio in the jth vertical bin, respectively, and m represents the total number of vertical bins. Furthermore, T means the transpose operation. Ultimately, we desire to obtain the optimal state value $\widehat{\mathbf{X}}$ applying the AERI observation $\mathbf{Y}$ and the thermodynamic profile $\mathbf{X}$ from the radiosonde.

2.4.1. One-Dimensional Convolutional Layer

The convolutional layer is used to extract features from data samples and is the core part of a convolutional neural network. The parameters of the convolutional layer include the convolutional kernel (filter), step length (stride), and boundary padding (padding), which determine the size of the output feature map of the convolutional layer. In general, the one-dimensional convolution operation is defined as follows:

$$o_{iq}^l=\sum _j\sum _{p\in r_q}{z}_{jp}^{l-1}\times {\omega }_{ijp}^l+b_i^l$$

(1)

where $o_{iq}^l$ denotes the $i^{th}$ convolved feature in the q position at the $l^{th}$ layer. $z_{jp}^{l-1}$ means the feature in the p position on the $j^{th}$ feature map of the ${(l-1)}^{th}$ layer. ${\omega }_{ijp}^l$ refers to the connected weight value in the p position from the $i^{th}$ to the $j^{th}$ feature map. $b_i^l$ denotes the bias value at the $l^{th}$ layer. $r_q$ denote the convolution neighborhood with index q.

2.4.2. One-Dimensional Max Pooling Layer

The primary characteristic of the pooling layer is to perform secondary feature extraction by downsampling the feature map from the previous convolutional layer, which can remove redundant information and simplifies the network complexity. The 1D max pooling layer accomplishes feature reduction by only keeping the maximum value of the feature map in a patch with a given pool size. The one-dimensional max pooling is defined as follows:

$$o_{ip}^l=\underset{\forall q\in r_p}{max}{z}_{iq}^{l-1}$$

(2)

where $o_{ip}^l$ refers to the obtained $i^{th}$ pooling feature in the p position at the $l^{th}$ layer by downsampling $z_{iq}^{l-1}$. $r_p$ represents the pooling region partitioned by the index p.

2.4.3. FC Layer

The FC layer maps the feature space calculated from the previous layer (convolution, pooling, etc.) to the label space by rearranging the extracted feature maps into feature vectors. The operation of FC layer is given as:

$$o_i^l=\sum _j{z}_j^{l-1}\times {\omega }_{ij}^l+b_i^l$$

(3)

where $o_i^l$ is the $i^{th}$ FC layer output feature at the $l^{th}$ layer. ${\omega }_{ij}^l$ refers to the connected weight value from features $i^{th}$ to $j^{th}$.

2.4.4. ReLU

The introduction of the activation function is the basis for a neural network to approximate any nonlinear function. The ReLU activation function can be selected to solve the problem of gradient disappearance in DNN and can accelerate the convergence of the algorithm. The operation of ReLU is taken by:

$$ReLU\left(z\right)=max(0,z)$$

(4)

2.4.5. BN Layer

The BN can accelerate CNN training by normalizing layer inputs [41], which is defined as follows:

$$\overline{z_i}=\frac{z_i-E\left(Z\right)}{Var\left(Z\right)}$$

(5)

where Z = ${\left\{z_i\right\}}_{i=1}^N$, $E\left(Z\right)$ is the mean of the Z and $Var\left(z\right)$ is the variance over the Z.

2.5. Deep Retrieval Architecture (DReA)

Inspired by the strong representation of CNN, we propose a novel deep retrieval architecture (DReA) shown in Figure 2. The proposed DReA can promote the inversion of the thermodynamic profile by constructing the complicated projection from the AERI observation to the radiosonde data. DReA consists of two modules: one feature extraction module to mine the nonlinear between the AERI observation and the radiosonde value, and one regression module to accomplish the retrieval task. The feature extraction module is built by technically stacking several one-dimensional convolutions, batch normalization, one-dimensional max pooling, and ReLU layers, alternately. The regression module, similarly to BP neural network, is fabricated by some FC and ReLU layers. From a technical perspective, the proposed DReA regards the radiosonde data as the supervisory signal to mine its underlying relationship with AERI observations.

2.5.1. The Forward Propagation of DReA

Formally, our proposed DReA can be formulated as follows: the feature extraction module of DReA is represented as $G_{\theta }$ with its trainable parameters $\theta$, and the regression module of DReA is denoted as $H_{\varphi }$ with parameters $\varphi$. $G_{\theta }$ consists of the one-dimensional convolutional, BN, pooling, and ReLU layers. $H_{\varphi }$ consists of the FC and ReLU layers. As defined in Section 2.4, we are given N AERI observation samples $\mathbf{Y}={\left\{{\mathbf{y}}_i\right\}}_{i=1}^N$, and the corresponding N radiosonde values $\mathbf{X}={\left\{{\mathbf{x}}_i\right\}}_{i=1}^N$. An input observation ${\mathbf{y}}_i$ undergoes the feature extraction module $G_{\theta }$ to generate the feature:

$${\mathbf{f}}_i=G_{\theta }\left({\mathbf{y}}_i\right)$$

(6)

The generated feature ${\mathbf{f}}_i$ is delivered to the regression module $G_{\varphi }$, and obtains the retrieval value defined as follows:

$${\widehat{\mathbf{x}}}_i=H_{\varphi }\left({\mathbf{f}}_i\right)$$

(7)

where ${\widehat{\mathbf{x}}}_i$ represents the retrieval value using the observation ${\mathbf{y}}_i$, and we define all retrieval values as ${\widehat{\mathbf{X}}}_i={\left\{{\widehat{\mathbf{x}}}_i\right\}}_{i=1}^N$ using the observations $\mathbf{Y}={\left\{{\mathbf{y}}_i\right\}}_{i=1}^N$.

Generally speaking, the proposed DReA can be parameterized using $G_{\theta }\circ H_{\varphi }$, so the forward process can be defined as:

$${\widehat{\mathbf{x}}}_i=G_{\theta }\circ H_{\varphi }\left({\mathbf{y}}_i\right)$$

(8)

2.5.2. The Training of DReA

The forward phase is performed by utilizing the AERI observations to obtain the retrieval value. In the training process, on the basis of the profile inferred by DReA, the radiosonde data are employed as the supervised signal which teaches the DReA to invert more correct values via optimizing the DReA parameters. The objective function of DReA optimization can be define as follows:

$$L(\mathbf{\theta },\mathbf{\varphi })=\frac{1}{V}\frac{1}{N}\sum _{i=1}^N{∥{\mathbf{x}}_i-{\widehat{\mathbf{x}}}_i∥}^2$$

(9)

where $L(\mathbf{\theta },\mathbf{\varphi })$ denotes the learning function which is applied to optimize the parameters $\mathbf{\theta }$ and $\mathbf{\varphi }$. The notation V represents the length of vector ${\mathbf{x}}_i$.

Furthermore, interpretatively, there are two different DReA models for the retrieval of the temperature and humidity profiles, respectively. The main difference lies in some adjustments of the model structure. For the retrieval of the temperature profile, the objective function is written as:

$$L({\mathbf{\theta }}^t,{\mathbf{\varphi }}^t)=\frac{1}{V}\frac{1}{N}\sum _{i=1}^N{∥{\mathbf{x}}_i^t-{\widehat{\mathbf{x}}}_i^t∥}^2$$

(10)

where ${\mathbf{\theta }}^t$ and ${\mathbf{\varphi }}^t$ denote the parameters of the temperature retrieval models. ${\widehat{\mathbf{x}}}_i^t$ is the retrieval value of the temperature profile using the corresponding observation ${\mathbf{y}}_i^t$. Similarly, the objective function of the humidity retrieval can be defined as:

$$L({\mathbf{\theta }}^q,{\mathbf{\varphi }}^q)=\frac{1}{V}\frac{1}{N}\sum _{i=1}^N{∥{\mathbf{x}}_i^q-{\widehat{\mathbf{x}}}_i^q∥}^2$$

(11)

In the model learning procedure, the objective function is minimized to propagate the gradient and further update the model parameters.

3. Experiments

3.1. Network Setting

For the retrieval of the atmospheric temperature, the input to the DReA comprises 555 channels (constituted of 244 temperature sensitive channels and 311 water vapor sensitive channels) of data measured by the AERI instrument, considering that the water vapor absorption channels contain the vertical distribution information of temperature [42]. The feature extraction module of the proposed DReA has four 1D convolution layers: Conv1 (200 channels, 5 filters), Conv2 (400 channels, 5 filters), Conv3 (500 channels, 5 filters), Conv4 (550 channels, 5 filters). There are successively BN, ReLU, and 1D max pooling layers behind each convolution layer. Needless to say, the pool size is 2 and its stride is 2. The regression module of the proposed DReA includes two FC layers: FC1 (1000 neurons) and FC2 (37 neurons). The FC1 layer is followed by ReLU and Dropout. The FC2 is also the output layer. The detailed structure and its parameters are depicted in Figure 3a.

However, it should be noted that the CNN channel has a different meaning from the temperature and water vapor channels. The CNN channel denotes the feature transformation, while the channels of temperature and water vapor denotes the wave band.

For the retrieval of the atmospheric humidity, the input to the proposed DReA is 311 channels of data measured by the AERI instrument. The feature extraction module of DReA has four 1D convolution layers: Conv1 (100 channels, 5 filters), Conv2 (150 channels, 5 filters), Conv3 (200 channels, 5 filters), Conv4 (250 channels, 5 filters). In addition to the first convolution layer which is followed by BN, ReLU, and 1D max pooling layers, there are successively BN and ReLU layers behind each one. Furthermore, the pool size is 2 and its stride is 2. The regression module of the proposed DReA includes two FC layers: FC1 (1000 neurons) and FC2 (37 neurons). The FC1 layer is followed by ReLU and Dropout. There is a ReLU layer behind FC2 to obtain the non-negative value. The framework of the humidity retrieval is depicted in Figure 3b.

3.2. Implementation Details

3.2.1. Data Preprocessing

The sounding data and AERI radiation data from 2006 to 2017 were refined and matched according to the following criteria:

(1)

Quality control [43]: AERI radiation spectra may contain outliers in the measuring process, so some spectral features with obvious outliers, e.g., negative radiation and smoothed spectra, were removed for obtaining a good quality.

(2)

Cloud mask: the presence of clouds can significantly impact the observed AERI radiation, so the laser cloud altimeter and the AERI radiation data themselves were used for cloud detection to select clear sky samples.

(3)

Temporal matching: the measurement data obtained from each observation instrument were matched in time, and the time of the sounding was used as the guide to select AERI data with the closest time for comparison.

We choose to retrieve the profile below 3km, and each profile contains 37 layers. The vertical resolution is nonlinear, which is described as follows: from 10 m to 20 m below 0.1 km, with a total of eight layers, and from 20 m to 120 m between 0.1 km and 1 km, with a total of 19 layers, and from 120 m to 210 m between 1 km and 2 km, with a total of six layers, and from 210 m to 300 m between 2 km and 3 km, with a total of four layers.

First, we eliminated some abnormal data from the obtained AERI observations to ensure the quality of the data. Secondly, the clear-sky sample data need to be selected because the amount of information of data collected under cloudy, rainy, and other uncertain conditions is insufficient for the inversion. Limited by the radiosonde observation data, we obtained 8153 clear-sky samples from 2006 to 2017 checked by those specific rules to assure the data quality, covering different profile samples. The collected AERI and radiosonde data from 2006 to 2016 were used in the training process and the data from 2017 were applied for the test. Thus, there were 7351 samples for the training dataset and 802 samples for the test dataset.

3.2.2. Network Training Details

We implemented all the experiments using Pytorch [44]. The DReA was trained using the Adam [45] optimizer with a learning rate of 0.0001 and a betas of (0.9, 0.999). The learning rate annealing strategy was adopted as: ${\eta }_p={\eta }_0{(1+\alpha p)}^{-\beta }$, where p meant the training progress changed from 0 to the maximum number of iterations, and $\alpha =0.001$, $\beta =0.75$. ${\eta }_0$ is the initial learning rate, i.e., 0.0001.

3.3. Comparison Methods

To verify the effectiveness of CNN in the inversion studies, we compare the proposed DReA with state-of-the-art statistic inversion methods, two of which are related to the focus of our work: (1) Eigenvector (EV) regression method is a reversible linear transformation in which some components in the transformation space have low variance and carry almost no adequate information [46]. These components can be discarded from the perspective of mean square meaningful optimality [47]. Therefore, the EV regression method can effectively extract information and compress the data dimension, which is especially suitable for processing hyperspectral data [48]. In practice, the EV regression method performs well in the statistical inversion of atmospheric parameters [49]. (2) The BP neural network imitates the behavior of animal neural networks without mathematical modeling and is capable of performing the parallel processing of large amounts of data with a fast computing speed [50]. The BP learning process can be started by specifying the input and output samples based on the pre-screened local historical data [51]. After reaching a certain number of iterations or error accuracy, the best BP model is obtained and can be used to invert the temperature and humidity profiles.

The EV regression and BP methods are conducted in Matlab R2021a. For the proposed DReA, we performed experiments for 200 epochs in a deep learning environment, i.e., the Ubuntu operating system, Nvidia Geforce RTX 3080Ti, pytorch 1.13.1.

3.4. Evaluation Criteria

We evaluate the retrieval profiles by considering the radiosonde instrument as the gold standard to examine the model performance in terms of both the regression fit and the inversion accuracy. The applied evaluation criteria are the root mean square error (RMSE) and the mean absolute error (MAE) [52] which are defined as follows:

$$RMSE=\sqrt{\frac{1}{m}\sum _{i=1}^m{({\widehat{x}}_i-x_i)}^2}$$

(12)

$$MAE=\frac{1}{m}\sum _{i=1}^m|{\widehat{x}}_i-x_i|$$

(13)

where m means the total number of samples. ${\widehat{x}}_i$ is the model prediction result, and $x_i$ is ground truth data.

3.5. Results and Analysis

3.5.1. Validation of DReA

To evaluate the performance of the DReA, we take all 802 SGP-sounding instrument profiles described as valid values. Figure 4 shows the linear description between the retrieval results of the temperature and the radiosonde measurements and Figure 5 shows the linear description between the retrieval results of the water vapor mixture ratio and the radiosonde measurements, where the scatter plots of the 37-layer vertical atmospheric profiles are presented, and the compared data include data below 3 km, with a total of 29,674 data points. Among them, the DReA model has a correlation coefficient of 0.95 for the water vapor mixing ratio and 0.99 for the temperature, which is the highest among the three methods and the closest to the actual sounding value. Then, the BP and EV regression methods follow closely. In general, for the temperature and water vapor mixing ratio inversion profiles, the fit between the sounding instrument observations and the results of the three inversion models is relatively satisfactory. Most of the inversion results are uniformly distributed around the fit line. The inversion values are more obviously linearly correlated with the actual values, which are statistically robust and consistent.

3.5.2. Comparison Experiments

As we know, the RMSE and MAE are smaller, which means that the performance of the inversion model is better.

Table 1. The retrieval error on the test dataset (802 samples). The bold numbers denote the best results.

Methods		RMSE	MAE
Temperature (K)	EV regression	1.18	0.76
	BP	1.14	0.86
	DReA	0.87	0.60
Humidity mixing radio (g/kg)	EV regression	1.41	1.09
	BP	1.11	0.80
	DReA	1.06	0.74

shows the RMSE and MAE between the radiosonde data and the retrieval result from the test dataset. From Table 1, for the retrieval of the temperature profile, we can find that the RMSE of the DReA model is 0.87 K, and the MAE is 0.60 K, which is greatly superior to BP. For the retrieval of humidity, the RMSE of the DReA model is 1.06 g/kg, and the MAE is 0.74 g/kg. It can be more intuitively found that the DReA has obtained a smaller RMSE and MAE than the other two methods, both in terms of temperature and water vapor mixing ratio, indicating that 1D CNN has a tremendous learning capability in retrieval studies.

To demonstrate the efficiency of the proposed method. We further compare the time consumption for the three methods, as shown in

Table 2. The time consumption of the retrieval methods.

	Train Time (Temperature)	Test Time (Temperature)	Train Time (Humidity)	Test Time (Humidity)
EV regression	0.002420 s	0.000932 s	0.001964 s	0.001617 s
BP	55.53 s	0.008 s	45.16 s	0.003 s
Our method	251.19 s	1.54 s	71.65 s	1.57 s

. From Table 2, we can find that, in the training stage, our proposed method has more time than the other methods, but the costing time is also acceptable. In the test stage, the time consumption is just approximately 1.5 s, which is very efficient. In practical application, the performance and cost time of the test phase are more concerned.

3.5.3. Bias Variation with Height

Figure 6 and Figure 7 show the thermodynamic profile retrieval bias with the height of the various techniques including the EV regression, the BP, and the DReA. Red dots represent the mean of the deviations and the blue dots near the red dots represent the median. The numbers indicated by the blue horizontal dashed line are outliers. The left and right boundaries of the solid blue horizontal line contain data from the first quartile to the third quartile. The vertical black line represents the 0 vertical line.

Figure 6 shows the temperature bias for the three methods. The blue shadows show a bias range of $\pm 1$ K. Most DReA-based temperature bias is within $\pm 1$ K below 3 km, and the blue horizontal dashed line is shorter than other methods, indicating that DReA achieves high accuracy for retrieving temperature profiles. At heights between 0 and 1.5 km, the length of the blue horizontal dashed line for the DReA method is shorter than for the other methods (Figure 6a–c), showing that the bias of the derived temperature is more concentrated near the mean and median. For the fluctuation trend up to a height of 3 km, the mean temperature bias obtained by DReA is positive.

In Figure 7, the blue shadows show the humidity profile retrieval bias for the three methods. The bias range of the water vapor mixing ratio is within $\pm 0.5$ g/kg below 3 km. This indicates that DReA achieves a high accuracy for retrieving humidity profiles near the surface. Below 3 km, the bias and median for all three methods are within $\pm 0.5$ g/kg, indicating that all three methods are effective for moisture contours. The bias is usually closer to the median below 1.5 km but drastically deviates above 1.5 km. The interquartile range of the DReA is almost always within $\pm 0.5$ g/kg for all methods and is overwhelmingly minimal at each altitude. In further analysis, the bias and median of the eigenvalue regression are too discrete, and the bias and median of BP are too oscillatory up to 1.5 km—while only the bias and median of DReA are not discrete and oscillatory.

To further compare the retrieval error of all three methods, the RMSE and bias for each layer are depicted as shown in Figure 8. From Figure 8, we can find that the bias of the proposed DReA is very close to 0, which means that our method performs more robustly in retrieving the atmospheric profiles. Although the RMSE curve of BP is approaching ours, the bias curve of BP is poor, especially for the retrieval of a water vapor mixing ratio.

3.5.4. Case Studies

In order to better illustrate the efficiency of the proposed DReA, we perform some case studies including single-day analysis, cold frontal passages, and warm-air advection.

Single Day Analysis

Figure 9 and Figure 10 show the comparison plot of the thermodynamic profiles for a particular day (29 January 2017), referring to the true value data from the radiosonde. It is obvious that the atmospheric temperature profile of the proposed DReA is much closer to the true value among these three methods.

Specifically, Figure 9a–c show the temperature profiles of different methods at two moments (11:30 UTC and 23:30 UTC). The solid and dashed lines represent the value from the radiosonde and AERI inversion, respectively. Compared to the EV regression method, DReA shows only a tiny difference with the radiosonde data at the bottom layer. At 11:30 UTC and 23:30 UTC, between the heights of 2000 m and 3000 m, the EV regression method clearly deviates from the radiosonde data, and is not as good as our method. At altitudes below 1000 m, the temperature profiles from our method are much closer to the true values than those from the BP method. Overall, from one-day cases, we observe that the deviation of DReA is less than the deviation of the two other methods. Furthermore, the change in temperature throughout the day is well presented. This demonstrates that DReA has the superior ability to capture temperature changes over a day.

Similarly to Figure 9, Figure 10a–c show the water vapor mixing ratio profiles at two moments for different methods. Obviously, at 11:30 UTC and 23:30 UTC, DReA is more exact than the EV regression and BP, especially under the height of 1000 m and at an altitude above 2500 m. We find that the EV regression method is smooth but too far away from the true value of the radiosonde. The BP method is closer to the true value but excessively oscillating. Comparatively, our proposed DReA can improve the tendency of the water vapor mixing ratio, which confirms the ability of the DReA method to retrieve the water vapor mixing ratio vertical structure over a day.

Overall, from Figure 9 and Figure 10, we can find there is imperfect fit between the retrieval curve and the real curve. The reason for this is that the effective information contained in the infrared high-spectral data at this particular height is significantly weakened, either globally or locally, resulting in discrepancies between the trends of retrieval profiles and the actual temperature and water vapor mixing ratio profiles. However, compared the other methods, the our retrieval results are slightly better. To better estimate the real differences between the methods, we further plot error bars about the retrieval result in the single day as shown in Figure 11. We can find that the overall trend of the error bar is consistent with the corresponding time of Figure 9 and Figure 10. At 23:30, the retrieval error of our DReA is especially small, which demonstrates that the proposed method can deal with the changes of a certain day.

Cold Frontal Passages

A cold front occurs when a cold air mass moves towards a warmer air mass. Cold fronts can lead to dramatic changes in the weather [53]. The rapid temperature and water vapor transition during the cold frontal passages can contribute to the development of severe weather. According to the criteria, Figure 12 shows the example of a cold frontal passage at the SGP site on 15 November 2017. Figure 12a presents the vceil [54] time–height cross-section for one cold frontal passage event. Figure 12b depicts the interpolated sounding time–height cross-section of the temperature (top) and mixing ratio (bottom) using the analysis data. Figure 12c shows the period of the time–height cross-section of the temperature (top) and mixing ratio (bottom) from the DReA inversion value. From the vceil plot (Figure 12a), we can find that there are clouds below 2000 m at the time of 0:00 UTC to 14:00 UTC. Since we invert the results under clear skies, the time–height cross-section during the cloud time period are blocked in gray (Figure 12b,c), and not analyzed. Comparing with the interpolated sounding, we can find the DReA performs satisfactorily under clear sky conditions (from 14:00 UTC to 24:00 UTC).

Examples of the thermodynamic atmospheric profiles during the cold front passage event from each method are given in Figure 13. Figure 12a,b indicate a cold frontal passage at approximately 12:00 UTC. We choose two moments before and after the cold front transit to analyze the retrieval performance of DReA. Figure 13a,b shows temperature profiles at 11:30 and 23:30 UTC, and Figure 13c,d show the mixing ratio profiles at 11:30 and 23:30 UTC. After the cold front, the temperature and water vapor mixing ratio will obviously drop, and the results of Figure 13 fully verify this point. The comparative analysis demonstrates DReA retrievals and compares more favorably with concurrent radiosonde profiles during the cold front passage event. It is worth mentioning that the nocturnal inversion intensities on the event are excellently captured by DReA. The experimental findings prove that DReA has the ability to handle the inversion for the cold front passage event. In order to more intuitively analyze the errors of various inversion algorithms, Figure 14 presents the error bar at a cold frontal passage. The error changes in different layers are the same as Figure 12 and Figure 13, showing that the proposed method can retrieve the profiles at a cold frontal passage, especially between the heights of 2000 m and 3000 m.

Warm-Air Advection

When a warm front crosses the border, the warm air mass takes the place of the former cold air mass, so the temperature and water vapor mixing ratio rise. According to this, an individual example of warm-air advection events is selected for analysis as shown in Figure 15. Figure 15a shows the vceil time–height cross-section for a warm-air advection event on 25 May 2017. Figure 15b presents the interpolated sounding time–height cross-section of the temperature (top) and mixing ratio (bottom) during the period. Figure 15c presents the period time–height cross-section of temperature (top) and mixing ratio (bottom) during the period. From Figure 15a, we find there are clouds mainly concentrated above 4000 m after 12:00 UTC. We therefore grayed out the contours after 12:00 UTC in (b) and (c). Results based on the unmarked gray fraction demonstrates that the temperature and mixing ratio trends can be broadly inverted by DReA.

Figure 16a,b show the temperature profiles, and Figure 16c,d show the mixing ratio profiles before and after the warm-air advection event (11:30 UTC and 23:30 UTC). After the event, the ground temperature and mixing ratios increase from 280 K to 300 K and from 5 g/kg to 10 g/kg, respectively, and our proposed DReA effectively indicate the point. Additionally, the comparison of inversion results with other methods in Figure 16, the retrieved temperature and humidity profiles are in better agreement with the radiosonde, which further demonstrates the proposed DReA, which still performs well in the warm-air advection event. We also give the error bar at a warm frontal passage as shown in Figure 17. It is not difficult to find that, after a warm frontal passage, the temperature and water vapor mixing ratio retrieval error of DReA is relatively low, which means that the proposed method is capable of capturing sharp weather changes.

4. Conclusions

In this paper, we developed a novel retrieval approach, i.e., a deep retrieval architecture (DReA), for the inversion of atmospheric temperature and humidity profiles from the ground-based infrared hyperspectral spectrometer. The proposed DReA is designed using CNN, including two modules, namely the feature extraction module and regression module, to achieve the high-level features of infrared hyperspectral observations and construct persuasive nonlinear projections from the input observations to the true profile values. Comprehensive retrieval experiments on atmospheric emitted radiance interferometer (AERI) observations were conducted, applying the radiosonde data as the gold standard. The results demonstrate that DReA substantially outperforms the representative EV regression and BP methods for the retrieval of the ground-based infrared hyperspectral data. Case studies further verify the efficiency of one-dimensional CNN in the retrieval of atmospheric thermodynamic profiles.

Despite the effectiveness of the DReA, there are still some aspects that can be further improved. Firstly, the proposed DReA is a totally data-driven method by mining the relationship between the AERI observations and radiosonde data via the deep neural network, without relying on knowledge of physics. In future studies, a novel hybrid approach [55,56] for the retrieval of thermodynamic profiles will be developed by integrating a physics-based model, e.g., a line-by-line radiative transfer model (LBLRTM) [57] with the data-driven algorithm, i.e., the deep neural network. Secondly, the work mainly focuses on a clear-sky scenario which is a strict constraint. We will further discuss the retrieval of atmospheric profiles under cloudy conditions [58] in the following research. Finally, in this study, the inversion is conducted only using the infrared hyperspectral spectrometer. As we know, multiple sensors can provide more abundant information and benefit each other [4]. Inspired by this, the research on the inversion of temperature and humidity profiles in combination with the ground-based microwave radiometer and infrared hyperspectral spectrometer will be carried out in a data-driven manner.