# Improvements in atmospheric water vapor content retrievals over open oceans from satellite passive microwave radiometers

Elizaveta V. Zabolotskikh, Bertrand Chapron

► To cite this version:

Elizaveta V. Zabolotskikh, Bertrand Chapron. Improvements in atmospheric water vapor content retrievals over open oceans from satellite passive microwave radiometers. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2017, 10 (7), pp.3125-3133. 10.1109/JS-TARS.2017.2671920. [https://doi.org/10.1109/JS-TARS.2017.2671920](https://doi.org/10.1109/JS-TARS.2017.2671920).

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# Improvements in Atmospheric Water Vapor Content Retrievals Over Open Oceans From Satellite Passive Microwave Radiometers

Elizaveta V. Zabolotskikh and Bertrand Chapron

**Abstract**—The study is dedicated to the development of an improved algorithm for integrated water vapor content (WVC) retrieval from the advanced microwave sounding radiometer 2 (AMSR2) measurement data over open ocean areas. The algorithm is based on physical modeling of the brightness temperature (BT) of the upwelling radiation of the atmosphere – ocean system. The BT inversion is carried out with neural networks (NNs), trained on an ensemble of BTs, calculated using the dataset of the atmospheric and oceanic parameters. The improvement in the WVC retrieval algorithm as compared to previously developed one is associated, first, with the usage of the new ocean emissivity empirical model and, second, with the exclusion of the vertically polarized BT from NNs inputs. The new model was incorporated into the BT geo-physical model and a new set of NNs coefficients was obtained for WVC algorithm. Though the results of the numerical experiment demonstrate higher retrieval accuracy for the old version of the NN model, real-valued validation with global positioning system (GPS) WVC shows better performance of the new NN model with the excluded vertically polarized AMSR2 BT from the NNs algo-rithm inputs. The advantages of the new algorithm are the most remarkable under conditions of high winds. This is confirmed by the validation based on the database of GPS WVC measurements under extreme winds. The improved WVC retrieval algorithm is mostly beneficial for the studies of extreme weather events such as polar lows, extratropical and tropical cyclones, associated with high winds.

**Index Terms**—Algorithms, atmosphere, geophysical measure- ments, passive microwave remote sensing, oceans.

## I. INTRODUCTION

WATER vapor is one of the major greenhouse gases. Atmospheric water in its vapor and liquid states is a key parameter in the global hydrological cycle, a component of climate change and ocean-atmosphere energy exchange studies [1]. Its changes in the Arctic are poorly described due to the lack of direct observations and large sea ice cover over which atmospheric water retrievals are either complicated or impossible [2]. Radiosonde (r/s) atmospheric total water vapor content

(WVC) measurements are considered as the most accurate since they provide precise moisture data at various pressure levels [3]. However, r/s method is expensive and can only be used at meteorological stations. Therefore, r/s data are mostly used for validation purposes of other WVC products. The other method, competing with r/s in high accuracy, uses observations from ground-based global positioning system (GPS) networks [4]. WVC estimation based on GPS measurements is possible for the atmosphere over any surfaces [4]. One of the greatest advantages of the GPS WVC data is their high temporal resolution. Besides, GPS WVC values are instrumentally independent and may be even used for r/s WVC correction [5]. Still only satellite remote sensing measurements can provide spatial WVC mapping at global and regular scale. And only satellite WVC estimates are available over remote ocean areas.

Satellite WVC retrieval techniques can be conventionally divided into three major groups dependently on the spectral range and the physics of measurements. The first group covers visible [6], [7] and near IR methods [8]–[10]. These methods are based on the measurements of the solar radiation reflected by land surface in the visible and near-infrared spectral regions over cloudless areas. This technique is limited by daytime and requires for an instrument to have at least one channel in a water absorption band. Another group of methods, also applicable in cloudless conditions, uses measurements of thermal IR radiation in two split-window channels [11]–[13]. Split window channels are affected by the surface, the mean air temperature, and additionally by the atmospheric absorption, which is mainly caused by the water vapor in this spectral region. These methods are independent on the day light but do not work in cloudy atmospheres. The performance of the visible, near IR and thermal IR methods is strongly influenced by the aerosols [9], [13].

Regular long-term observations of water vapor over the open sea water are provided by satellite passive microwave instruments. Both atmospheric WVC and total cloud liquid water content (CLW) have been successfully retrieved from such satellite passive microwave instruments, as the Scanning Multichannel Microwave Radiometer on board the Nimbus 7, the Special Sensor Microwave/Imager and the Special Sensor Microwave Imager and Sounder on board the DMSP series satellites, the WindSat radiometer, the Microwave Instrument onboard the Tropical Rain Measurement Mission satellite and the series of the Advanced Microwave Sounding Radiometers (AMSR, AMSR-E and AMSR2). Many algorithms for WVC and CLW

Manuscript received June 16, 2016; revised January 26, 2017; accepted February 16, 2017. This work was supported by the Russian Science Foundation through the Project 16-17-00122.

E. V. Zabolotskikh is with the Satellite Oceanography Laboratory, Russian State Hydrometeorological University, 195196 St. Petersburg, Russia (e-mail: liza@rshu.ru).

B. Chapron is with the Institut Francais de Recherche et d'Exploitation de la MER, 29280 Plouzane, France (e-mail: bchapron@ifremer.fr).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSTARS.2017.2671920
retrievals from microwave radiometer data have been developed for nonprecipitating atmospheres during the last decades [14]–[17]. Still most of them have large errors under significantly changing environmental conditions, especially under high CLW (>0.5 kg/ m²) or high wind speed (>15 m/ s) conditions.

In this study, we suggest an improvement to a previously developed algorithm [18] for WVC retrieval from the AMSR2 measurement data. The algorithm is based on the numerical experiment, consisting of physical modeling of the brightness temperature (BT) of the atmosphere–ocean system and the following neural network (NN) inversion to retrieve WVC. The algorithm improvement is due to the latest elaboration of the ocean emissivity empirical model [19] and the exclusion of a vertically polarized BT from the algorithm inputs. Incorporation of the new ocean emissivity parameterization, valid for high wind conditions, allowed accounting more accurately for the ocean contribution to the BT of the upwelling radiation of the atmosphere–ocean system. This resulted into higher accuracy estimation of WVC for the areas of high winds (>15 m/ s), which is especially important for high wind studies.

Validation of the new algorithm is carried out using GPS WVC data. During the validation, WVC values were retrieved both with NN with four BT inputs and with NN with an excluded vertically polarized BT input. To estimate quantitatively the algorithm improvements under high wind conditions, the new algorithm was compared with an old one [18] specifically for GPS and r/s WVC measurements in tropical cyclones (TCs) and polar lows (PLs). We also compared the results of the new algorithm application with the two operational WVC products—the Remote Sensing Systems (RSS) WVC and the WVC product, produced by the GCOM-W1 data providing service of the Japan Aerospace Exploration Agency (JAXA) for high wind events.

Two examples of extreme weather events, associated with high winds— a PL, and a TC—are shown to demonstrate the application of the new WVC algorithm for high wind event studies.

## II. ALGORITHM

### A. Physical Modeling

Physical modeling of the atmosphere–ocean system BTs is a traditional way of retrieval algorithm development based on a closed scheme of the numerical experiment. During the forward problem solution, the atmospheric and oceanic parameters are considered to be known. They are used to calculate BTs, exploring microwave radiation transfer modeling (RTM). During the inverse problem solution, some inversion operators are used to retrieve one or another geophysical parameter from the simulated BTs. Comparison of the parameters known in advance before the forward problem solution with the parameters retrieved after the inverse problem solution allows calculating the theoretical retrieval error.

In this study, we restricted the RTM by the approximation of the “pure absorption,” neglecting microwave radiation scattering on rain drops and ice particles. Such an approximation for the frequencies of K and Ka bands is always justified for clear atmospheres and almost always, for cloudy atmospheres, since

the cloud drop radii rare exceed 20 μ [20]. When restricting consideration by nonprecipitating conditions, we need only the parameterization of the atmospheric absorption and the ocean emission to fully describe and calculate the BT of the upwelling microwave radiation [21]. In the microwave range of frequencies below 100 GHz, the atmospheric absorption is defined by the three components: oxygen, water vapor, and cloud liquid water. Thus, for the nonscattering one-dimensional approximation, the atmospheric absorption and the atmospheric parts of the total upwelling brightness are the functions of the vertical profiles of air pressure, temperature, humidity, and CLW. To estimate these functions, we used [22] for molecular oxygen and [23] for water vapor absorption spectra. The choice of water vapor absorption model is crucial in the RTM if the final objective of the study is the WVC retrieval algorithm development. The model, described in [23], was chosen since it had been proven to be the most accurate for the considered frequencies [24]. The ocean radiation depends on the ocean emissivity at horizontal and vertical polarization. Under calm sea conditions, it is a function of frequency, incidence angle, sea surface temperature (SST) and sea surface salinity (SSS). The wind influenced component of the emissivity is a function of sea surface wind speed (SWS) and wind direction. The dependence of the ocean microwave radiation on such parameters as SST, SSS, and wind direction is weak at K and Ka bands relatively to SWS. In this study, we used the model of SSS and SST dependence of the dielectric permittivity of the sea water, described in [25], and did not take into account the wind direction microwave signal. The error of the last assumption depends on SWS and polarization and does not exceed 2K. The empirical parameterization of the ocean emission SWS dependency has undergone significant changes during the last several years. In our previous AMSR2 algorithms, we used the empirically parameterized ocean emissivity model [26] in forward modeling to calculate the BTs for the retrieval algorithm development. In that model, an abrupt increase of both horizontally and vertically polarized emissivity, starting from some threshold SWS is implied. Still this model is valid only up to SWS = 18 m/ s. In the new algorithm, we used recently developed empirical model for the ocean emissivity, valid for higher wind conditions [19]. It is also featured by an abrupt increase of both horizontally and vertically polarized emissivities starting at SWS is approximately 12 m/ s but the values of δBT/δSWS are different as compared to [26]. This model for the wind induced emissivity is an empirical parameterization derived from a high-quality dataset of consolidated ocean observations [19]. According to this model, the wind induced emissivity can be presented as a sum of the roughness signal and the foam signal: ε = α · (1 − f) + β · f. Here, α is a coefficient, responsible for wind induced roughness and its influence on emission, β is a coefficient responsible for all kinds of the foam, and f is the fraction of the ocean covered by the foam. The foam fraction is mainly a function of wind speed, whereas α and β are the functions of frequency, SST, SSS, incidence angle, SWS, and polarization. This model was already successfully used in SWS algorithm development. Its main advantages manifested themselves in the range of high winds with SWS greater than 15 m/ s [27].
<table><caption>TABLE I
RADIOSONDE OBSERVATION SITES USED IN THE BT NUMERICAL CALCULATIONS</caption><thead><tr><th rowspan="2"></th><th colspan="2">Station</th><th rowspan="2">h over<br>sea<br>level, m</th><th rowspan="2">Longitude</th><th rowspan="2">Latitude°</th><th rowspan="2">Maximum<br>WVC,<br>kg/m<sup>2</sup></th></tr><tr><th>Number</th><th>Name</th></tr></thead><tbody><tr><td>1</td><td>01028</td><td>Bjornoya</td><td>20</td><td>19.00</td><td>74.50</td><td>27</td></tr><tr><td>2</td><td>01001</td><td>Jan Mayen</td><td>9</td><td>-8.66</td><td>70.93</td><td>23</td></tr><tr><td>3</td><td>01400</td><td>Ekofisk</td><td>29</td><td>3.21</td><td>56.53</td><td>29</td></tr><tr><td>4</td><td>70414</td><td>Shemya Afb</td><td>31</td><td>174.10</td><td>52.71</td><td>40</td></tr><tr><td>5</td><td>70308</td><td>St. Paul</td><td>6</td><td>-170.22</td><td>57.16</td><td>32</td></tr><tr><td>6</td><td>91165</td><td>Lihue</td><td>30</td><td>-159.34</td><td>21.99</td><td>47</td></tr><tr><td>7</td><td>91285</td><td>Hilo</td><td>12</td><td>-155.05</td><td>19.72</td><td>45</td></tr><tr><td>8</td><td>47945</td><td>Minamidaitojima</td><td>20</td><td>131.23</td><td>25.83</td><td>69</td></tr><tr><td>9</td><td>91765</td><td>Pago Pago</td><td>5</td><td>-170.71</td><td>-14.33</td><td>56</td></tr><tr><td>10</td><td>47971</td><td>Chichijima</td><td>8</td><td>142.18</td><td>27.08</td><td>60</td></tr><tr><td>11</td><td>47991</td><td>Minamitorishima</td><td>9</td><td>153.96</td><td>24.30</td><td>77</td></tr><tr><td>12</td><td>91376</td><td>Majuro</td><td>4</td><td>171.29</td><td>7.07</td><td>67</td></tr><tr><td>13</td><td>91334</td><td>Truk</td><td>5</td><td>151.84</td><td>7.46</td><td>73</td></tr></tbody></table>

## B. Data for Numerical Calculation

For the algorithm development, we created the database of WVC values and corresponding simulated AMSR2 BTs. Radiosounding meteorological data with atmospheric pressure, humidity, and temperature measurement data, complemented with SST and SWS data and model profiles of CLW, were used for BT numerical calculations. The r/s data from the small island stations from Wyoming University, containing more than 40 atmospheric pressure level measurements from the Earth surface up to relative humidity of about 10%, were selected. These data supplied the meteorological parameter profiles for the BT calculations and total WVC values. The r/s station locations and some of their parameters are presented in the Table I. Each atmospheric set of meteorological parameter profiles was complemented with the MODIS SST data and the World Ocean Atlas SSS data. Then, artificial SWS values, varying in the range of 0–60 m/s, were randomly added to the dataset. Cloud liquid water modeling was fulfilled in accordance with the method, based on the statistical data on clouds at different atmospheric heights.

The upper and lower boundaries of clouds were estimated using the analysis of relative humidity profiles. Uniform cloud liquid water ($w$) profiles were used for the clouds with the thickness less than 1 km with typical $w$ values of 0.05–0.10 $g/m^3$. For the clouds with the thicknesses greater than 1 km, the $w$ profiles were described by a triangle function. The details of the method are described in [28].

In all, 15 000 radiosounding, SWS, SST, and SSS data were used for calculations. The range of the parameter variability covered the whole band of their natural variability: SWS—0–60 m/s, CLW—0–2 kg/m$^2$, WVC—0.5–77 kg/m$^2$, SST—-1.8–31° C.

## C. Neural Networks

After the BT calculations normally distributed radiometric noise with $\Delta T = 0.7$ K, equivalent temperature [29] was added to the resulted BT values. The array of the calculated BTs

and corresponding WVC values was randomly divided into two datasets. The first dataset (DS1) was used to train NN-based algorithms, the second dataset (DS2) was used to test the trained algorithms. Each dataset consisted of approximately 7500 data on WVC and BTs. The values of WVC, calculated with r/s humidity profile integration, were considered as the ground-truth WVC. The root mean square differences between the ground-truth WVC values and the WVC values, retrieved with the trained NN algorithms from the modeled BT values, were treated as the algorithm theoretical retrieval errors.

A multilayer perceptron (MLP) NN architecture was used to develop the inverse algorithms. The MLP with back-propagation learning algorithm is one of the most widely used NN models. It is shown in [30] that any continuous function can be approximated by an MLP with a single hidden layer of processing neurons. In this study, MLP backpropagation NNs with a single hidden layer of neurons were used to retrieve WVC. It is discussed in [31] that various researchers usually need to conduct many experimental trials before they can finalize the NN configuration. We complicated the NN configuration increasing the number of neurons in the hidden layer and calculating the retrieval errors using DS1 ($\sigma_{tr}$) and DS2 ($\sigma_{ts}$). This complication led to the steady decrease of $\sigma_{tr}$. At some number of hidden neurons, $\sigma_{tr}$ continued to decrease but $\sigma_{ts}$ started to increase. This meant NNs overtraining and the loss of the generalization capabilities. This number of hidden neurons was considered to be the optimal choice for the retrieval algorithm.

The choice of the BTs to be used in the retrieval algorithms should be driven by the BT sensitivity to WVC. The sensitivity of AMSR2 channel measurements to water vapor is the greatest at 23.8 GHz—the frequency near a water vapor absorption line at 22.235 GHz. Beside large sensitivity to WVC, the BT at 23.8 GHz is also very sensitive to liquid water and surface wind. So, at least two more BT inputs should be used in a retrieval algorithm beside a single BT at 23.8 GHz [32]. Addition of more BT inputs to the retrieval algorithm may be beneficial through taking into account the other atmospheric and oceanic parameters with weaker influencing on BT. But in the case of too low BT sensitivity (lower than radiometric noise of measurements), this may just incorporate additional noise into retrievals. It was shown in [33], that the vertically polarized BTs at 18.7 and 36.5 GHz are excessive in the WVC retrievals. Their additions to NN inputs did not lead to the decrease in the retrieval error.

In this study, two NNs were trained and tested. The first one (NN1) is identical to the one, described in [33] for AMSR-E WVC retrievals. It uses four AMSR2 BT inputs—horizontally polarized BT at 18.7 GHz, vertically and horizontally polarized BT at 23.8 GHz, and horizontally polarized BT at 36.5 GHz (referred to as T18H, T23V, T23H, and T36H correspondingly). The second NN (NN2) uses only three AMSR2 inputs—T18H, T23H, and T36H. Both NN optimal schemes are presented in Fig. 1. The optimal neuron number equals 5 for NN1 and 7 for NN2.

The difference between the two NNs is not only the number of BT inputs. It is essential that the NN1 explores both vertically and horizontally polarized measurements, while in the NN2 we removed the vertically polarized BT at 23.8 GHz from the BT
<figure><img src="image_2.png" /><figcaption>Fig. 1. NN algorithms for atmospheric WVC retrievals from the AMSR2 measurement data: (a) NN1, used in the previous version of the algorithm [18] and (b) NN2, used in the new version of the algorithm.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. Scatter plots of the retrieved versus ground-truth WVC values: (a) old AMSR2 WVC retrieval algorithm (NN1, four brightness temperature inputs); and (b) new AMSR2 WVC retrieval algorithm (NN2, three BT inputs, only horizontally polarized channels).</figcaption></figure>

inputs. Such a simplification was done for the following reasons. First, published data on the wind induced ocean emissivity at high winds at the vertical polarization show large inconsistencies [26]. The second consideration is associated with the absence of the wind direction dependence in the empirical emissivity model. The horizontally polarized wind direction signal has nearly the same spectral and polarization signature as wind speed and is not separable from the last. The vertically polarized wind direction signal is unique [15]. When we model BT without taking it into account, this signal starts to be a source of the BT errors. Thus, the inclusion of improperly modeled BTs into a retrieval algorithm would inevitably lead to the error increase. This is substantiated in the validation section.

### III. NUMERICAL MODELING RESULTS

Both NN1 and NN2 algorithms were trained with the dataset DS1 and tested with the dataset DS2. The scatter plots of retrieved versus ground-truth WVC values are presented in Fig. 2. Fig. 2(a) shows the performance of the NN1 AMSR2 WVC retrieval algorithm (four BT inputs, including the vertically polarized BT). Fig. 2(b) shows the performance of the NN2 AMSR2 WVC retrieval algorithm (three BT inputs, only horizontally polarized channels). The NN1 retrieval error $\sigma_{NN1} = 1.1$ kg/m$^2$, the NN2 retrieval error $\sigma_{NN2} = 1.4$ kg/m$^2$.

So, the NN1 inversion function performs 25% better than the NN2. This result is consistent with the general idea of the informational content of passive microwave multichannel measurements. Microwave radiation of the atmosphere-ocean system is

a nonlinear function of many atmospheric and oceanic parameters. A parameter dependency may be too weak for retrieving this parameter, but at the same time it may be large enough to produce significant errors if ignored in physical modeling [15]. So, the BT modeling should take into account all BT parameter dependencies. And an ideal retrieval scheme needs to have as many input BT channel measurements as there are geophysical parameters affecting these measurements.

To retrieve WVC, we need to have at least three input BTs to account for the most influencing parameters – SWS, WVC, and CLW. The fourth BT, sensitive both to WVC and less influencing parameters should be beneficial because when we have only three input BTs there is not enough input information to discriminate between all the parameter impacts. This is confirmed by the theoretical results, illustrated by Fig. 2.

So we have obtained a predictive result when testing the new algorithm with the modeled dataset DS2. Nevertheless, this result relates only to the general ability of NNs to reproduce excellently nonlinear functions of multiple variables. In fact, the outperformance of NN1 as compared to NN2 only confirms two facts: first, that there are more than three geophysical parameters influencing the BT in K and Ka bands, and second, NN algorithms are suitable for approximation of multiparameter functions. It makes no difference how well we defined the RTM. This result does not relate to the adequateness of the AMSR2 BT model. In other words, we can only suppose that if the BT model is valid, the NN1 performs better than the NN2.

### IV. VALIDATION

The numerical modeling results should be checked with independent WVC measurements. Only independent verification can provide the actual algorithm errors and allow making conclusion about the adequate algorithm performance. Thus, both the NN1 and the NN2 algorithms, trained on the simulated data set, were then validated by means of their application to the AMSR2 Level 1R BT data and comparison of the retrieved WVC values with GPS WVC data.

GPS WVC measurements are considered to be an excellent source of quasi-ground-truth WVC data to validate satellite WVC retrievals [5]. The great advantage of GPS WVC measurements is their high temporal resolution ensuring availability of precise time collocation important for the comparison of different estimates of such variable parameter as WVC. In general, GPS WVC estimation accuracies are comparable with those of r/s or even higher, and sometimes even used to calibrate and correct r/s measurements [5]. GPS signals are delayed in the lower atmosphere by dry air, water vapor, and hydrometeors. The effects generated by hydrometeors are relatively small, so, if the data on surface pressure are available, the water vapor, integrated along each GPS signal path, can be retrieved from the signal delay [34]. This factor along with permanently growing GPS regional networks [35], [36] makes GPS WVC data very attractive to validate remote sensing WVC retrieval methods. Many studies have shown that WVC can be determined with an accuracy better than 2 kg/m$^2$ using GPS observations [35], [37]. WVC can be estimated from zenith phase delay
<table><caption>TABLE II
GPS STATIONS USED TO VALIDATE THE WVC RETRIEVAL ALGORITHM</caption><thead><tr><th rowspan="2">Station</th><th rowspan="2">h over sea level, m</th><th colspan="2">GPS</th><th colspan="2">AMSR2</th><th rowspan="2">d, m</th></tr><tr><th>Longitude</th><th>Latitude °</th><th>Longitude</th><th>Latitude</th></tr></thead><tbody><tr><td>1</td><td>ASPA</td><td>22</td><td>-170.72</td><td>-14.33</td><td>-170.62</td><td>-14.407</td><td>20</td></tr><tr><td>2</td><td>CNMR</td><td>10.33</td><td>145.74</td><td>15.23</td><td>145.98</td><td>15.09</td><td>30</td></tr><tr><td>3</td><td>COCO</td><td>3.72</td><td>96.83</td><td>-12.19</td><td>96.694</td><td>-12.38</td><td>26</td></tr><tr><td>4</td><td>DGAR</td><td>9.53</td><td>72.37</td><td>-7.27</td><td>72.202</td><td>-7.28</td><td>19</td></tr><tr><td>5</td><td>FUNC</td><td>29.55</td><td>-16.91</td><td>32.65</td><td>-16.855</td><td>32.39</td><td>29</td></tr><tr><td>6</td><td>GLPS</td><td>5.43</td><td>-90.30</td><td>-0.74</td><td>-89.97</td><td>-0.58</td><td>42</td></tr><tr><td>7</td><td>SA40</td><td>10.72</td><td>166.916</td><td>-0.52</td><td>166.94</td><td>-0.72</td><td>23</td></tr><tr><td>8</td><td>SA42</td><td>8.96</td><td>147.43</td><td>-2.06</td><td>147.54</td><td>-1.8</td><td>32</td></tr><tr><td>9</td><td>SG27</td><td>8.47</td><td>-156.61</td><td>71.32</td><td>-156.78</td><td>71.71</td><td>44</td></tr></tbody></table>

(ZPD) induced in GPS using so-called global mapping functions (GMF) – the expressions for the calculating the ratios of the slant path delays to ZPD. GMF inaccuracies are associated with the hypothesis of azimuthally homogeneous atmosphere [38] and satellite position. These inaccuracies grow at low elevation angles [39].

In this study, we used Suominet GPS data on WVC from nine GPS stations [34]. In SuomiNet GPS, the signal delays are calculated using the GMF in the form of a cosecant of the satellite elevation angle [38]. The accuracy of the GPS-derived WVC is affected by the elevation-angle-dependent errors [40]. These errors are latitude dependent because the sites at high latitudes have a higher percentage of the low-elevation observations [41]. Most of the GPS sites used in this study are tropical except SG27 with the latitude of 71.7N. So the elevation-angle-dependent errors in their WVC estimates are low.

The AMSR2 measurements were collocated with the GPS measurements in time and space for comparison. To avoid land influence on AMSR2 retrievals, the measurements over the ocean close to the stations were used instead of the measurements over stations in a distance not exceeding 50 km (for most of the stations – not exceeding 30 km). The locations of these measurement pixels are given in Table II and are shown in Fig. 3, where the AMSR2 WVC fields retrieved over the GPS stations are shown. White circles indicate the locations of the GPS stations; black circles indicate the locations of the points for comparison. WVC values over the selected GPS stations cover almost the whole range of the WVC variability. WVC fields in Fig. 3 show the absence of land contamination for the black circles.

The criteria of the spatial and temporal collocation are: the difference in space $d_{\text{AMSR2}} < 25$ km, the difference in time $t_{\text{AMSR2}} < 30$ min. We found about 6000 match-ups for the period of August 2012–August 2015. Both NN1 and NN2 algorithms were applied to the AMSR2 Level 1R BTs. Before the algorithm application the following constant additions were summed with the AMSR2 BTs: $\Delta T_{18H} = 0.3$ K, $\Delta T_{23H} = 0.9$ K, $\Delta T_{23V} = 0.7$ K, $\Delta T_{36H} = -3.8$ K to adjust for the differences between the simulated and measured BTs [24].

The scatter plots of the AMSR2 retrieved WVC versus the GPS WVC are presented in Fig. 4, where black diamonds show the performance of the NN1 algorithm, and black circles show the performance of the NN2 algorithm. Both algorithms provide

<figure><img src="image_4.png" /><figcaption>Fig. 3. WVC fields retrieved over the GPS stations with the AMSR2 NN1 algorithm. White circles indicate the locations of the GPS stations, black circles indicate the locations of the AMSR2 pixels used for WVC retrieval.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4. Scatter plots of the AMSR2 retrieved versus GPS WVC values: black diamonds for the NN1 retrieved WVC; white circles for the NN2 retrieved WVC.</figcaption></figure>

the results highly correlated with the GPS WVC, both are a little bit biased: 0.5 kg/m² for the NN1 retrievals and 0.6 kg/m² for the NN2 retrievals. The retrieval error of the NN1 algorithm is $\sigma_{\text{NN1}} = 2.5$ kg/m² and the retrieval error of the NN2 algorithm is $\sigma_{\text{NN2}} = 1.8$ kg/m². This result is contrary to the numerical modeling results, for which the NN1 algorithm outperforms the NN2 algorithm. Such a contradiction is due to inappropriate modeling of the vertically polarized wind induced ocean emissivity. NN approach is a powerful learning technique for solving nonlinear remote sensing inverse problems [42]. When tested on the synthetic dataset of the same origin as used
<figure><img src="image_6.png" /><figcaption>Fig. 5. (a) AMSR2 SWS, (b) AMSR2 WVC fields on January 29, 2016 at approximately 12:15 UTC. SWS is retrieved with the algorithm [18], WVC is retrieved with the NN2 algorithm, developed in this study.</figcaption></figure>

for training, the NN1 with more BT inputs performs 25% better than the NN2. But when applied to the AMSR2 measurement data, the NN2 algorithm with excluded T23V input performs 33% better. If we had had a correct wind induced emissivity model, the validation results would have been identical to the numerical modeling results. In our case, we see that the inclusion of T23V as an additional NN input does not help to resolve the multiparameter BT dependence. Instead, it serves as a source of additional noise when the WVC retrieval algorithm is applied to real AMSR2 measurement data. Since at high winds the ambiguities in the ocean emission modeling are the greatest, we checked the algorithm performance separately for SWS >15 m/s.

Both the NN1 and the NN2 WVC retrieval algorithms were applied to the AMSR2 BTs in extreme weather events to estimate quantitatively their performance under high wind conditions and compare it with the performance of the two available operational WVC products. The first product is the RSS AMSR2 daily WVC product consisting of daily averaging descending and ascending paths on a regular grid [43]. Such data did not allow comparing with the swath AMSR2 data in polar regions but the part of the data relating to the TCs were compared. The second product is the JAXA WVC swath Level 2 product on the same grid as the AMSR2 Level 1R BTs. When considering hurricane winds (SWS >33 m/s), we also used the Best Track data on maximum winds and radii of storm and hurricane winds to compare with the SWS retrieved from the AMSR2 with a method described in [44].

The Best Track data are the results of the postseason reanalysis of the TC positions and intensities from all available data [45]. Below we illustrate the NN2 algorithm application in two extreme events: a PL and a TC cases.

Fig. 5 shows the fields of the SWS and WVC, retrieved on January, 29 2016 at approximately 12:15 UTC. WVC is retrieved with the NN2 algorithm, developed in this study. Quasi-synchronous r/s measurements at the stations Jan Mayen and Torshavn, taken at a distance of 50 km to avoid land contamination, were taken at 12:00 UTC. $WVC_{r/s}$ at Jan Mayen is 5.1 kg/m² at SWS ~ 9 m/s. The AMSR2 retrieved WVC was 5.5 kg/m² for the NN1 and almost the same—5.3 kg/m² for the NN2. The station Torshavn at the same time was on the way of the PL manifesting itself in the WVC vortex with

<figure><img src="image_7.png" /><figcaption>Fig. 6. (a) AMSR2 SWS, (b) AMSR2 WVC fields on July 9, 2016 at approximately 3:30 UTC. SWS is retrieved with the algorithm [18], WVC is retrieved with the NN2 algorithm, developed in this study.</figcaption></figure>

high WVC values of 16–18 kg/m² and wind speeds exceeding 30 m/s. At 12:00 UTC SWS values around the station were about 20 m/s. WVC retrieved with the NN1 algorithm was as low as 4 kg/m², whereas WVC retrieved with the NN2 algorithm was 11.5 kg/m², which is in much higher correspondence with an in situ WVC at Torshavn, $WVC_{r/s}$ approximately 9.8 kg/m². The JAXA WVC was not available close to r/s site but at some distance from the site it was about 12.5 kg/m².

Accurate comparisons should take into account the possibility of atmospheric fronts, passing between the AMSR2 and r/s measurement times. Such fronts may change significantly the atmosphere over the station. But it is obvious, that WVC value of 4 kg/m², retrieved with the NN1 algorithm, was too low and cannot be explained by the atmospheric front: the time difference in the satellite and r/s measurements was as low as 15 min.

The next example shown in Fig. 6 relates to a super typhoon Nangka. On July 9, the Joint Typhoon Warning Center estimated the 10-min peak wind as 50 m/s, which is in a good correspondence with the AMSR2 winds [see Fig. 6(a)], imaged at approximately 3:30 UTC. According to the Best Track data relating to the radii of hurricane winds, the winds over the CNMR GPS station were about 33 m/s. AMSR2 SWS in the vicinity of the station showed 32 m/s. Quasi-synchronous WVC estimated by the CNMR GPS on July 9, 2016 at approximately 3:15 UTC equaled to 64 kg/m². AMSR2 retrieved WVC was approximately 55.5 kg/m² for the NN1 algorithm and approximately 62.8 kg/m² for the NN2 algorithm.

Neither the JAXA nor the RSS WVC was available over the CNMR site to be used for comparison. The fields of these alternative WVC products close to CNMR site showed the values of about 68–70 kg/m². Both examples demonstrate the outperformance of the NN2 algorithm as compared to the NN1 algorithm under conditions of high winds (>15 m/s) in PLs and TCs.

To estimate quantitatively the joint effect of these developments at high winds, we collected the database of the collocated GPS and r/s WVC data and the AMSR2 retrieved WVC values
<figure><img src="image_8.png" /><figcaption>Fig. 7. (a) Scatter plots of the AMSR2 retrieved versus ground-truth WVC values from the GPS and r/s stations for high wind events with SWS > 15 m/s: diamonds for the NN1 retrieved WVC; circles for the NN2 retrieved WVC.</figcaption></figure>

for the conditions of extreme winds (ground-truth data). This database included 53 match-up measurement data for the TCs and PLs of 2012–2016. For the TCs GPS WVC measurements from the CNMR and CRO1 stations were used. The ground-truth data for the PLs were represented by the r/s WVC measurements at Jan Mayen, Bjørnøy, and Torshavn r/s stations in the Arctic Ocean. All match-ups were analyzed jointly with SWS, retrieved from the AMSR2 [44].

The resulting scatter plot of the retrieved from AMSR2 WVC from the ground-truth WVC is shown in Fig. 7(a). Fig. 7(b) illustrates the AMSR2 retrieved WVC deviation from the ground-truth WVC dependently on SWS. Though there are still not enough match-up data to support the statistical generalization of the results, these 53 cases show unambiguously that the NN1 algorithm significantly underestimates WVC under high wind conditions. The retrieval error of the NN1 algorithm ($\sigma_{NN1} = 4.0 \text{ kg/m}^2$) is almost twice higher than the retrieval error of the NN2 algorithm ($\sigma_{NN2} = 2.3 \text{ kg/m}^2$). It can also be seen that WVC underestimation with the NN1 algorithm grows with SWS [see Fig. 7(b)]. The mean difference between the AMSR2 retrieved WVC versus ground-truth WVC is $0.6 \text{ kg/m}^2$ for the NN2 and $-1.6 \text{ kg/m}^2$ for the NN1 algorithm.

We also downloaded the RSS AMSR2 daily WVC product and the JAXA WVC swath Level 2 WVC products for all these high wind events. Only 40 measurements of WVC in the TCs could be used for the comparison with the RSS product since it contains daily averaged descending and ascending data which cannot be matched to the GPS or r/s WVC measurements. These 40 not masked RSS WVC measurements under conditions of SWS > 15 m/s yielded $\sigma_{RSS} = 3.5 \text{ kg/m}^2$. The error of the NN2 algorithm, calculated with the same data (40 GPS measurements), proved to be 2.5 m/s, approximately 33% lower. The JAXA WVC values were compared both with the GPS WVC and with the r/s WVC for 47 WVC not masked measurements. The error of the standard JAXA WVC Level 2 product for the conditions of SWS > 15 m/s proved to be 5.1 kg/m², whereas the error of the NN2 algorithm, calculated with the same 47 data, was 2.4 kg/m², twice lower.

V. CONCLUSION

The new algorithm for WVC retrieval from AMSR2 measurement data, based on the results of the BT modeling and the NN technique for solving the inverse problem, is suggested in this paper. Two NNs – an NN1 with four AMSR2 BT inputs (T18H, T23V, T23H, and T36H) and an NN2 with three BT inputs (T18H, T23H, and T36H) – were trained on the simulated dataset DS1 of the BTs and WVC values. These NNs were then tested first on the simulated dataset DS2 and then on the AMSR2 measurements over the GPS sites. The results of the validation with the GPS WVC measurements for the whole range of the atmospheric and oceanic conditions indicate a 33% improvement of the NN2 algorithm ($\sigma_{NN2} = 1.8 \text{ kg/m}^2$) as compared to the NN1 algorithm for WVC retrieval from AMSR2 data ($\sigma_{NN1} = 2.5 \text{ kg/m}^2$). This improvement is achieved by the exclusion of the vertically polarized BT at 23.8 GHz from the NNs algorithm inputs. Though the results of the numerical experiment showed better results for the NN1 algorithm with more BT inputs, independent validation with GPS WVC data showed the converse results: the NN2 algorithm with the excluded vertically polarized BT outperformed the NN1 algorithm. The general validation was carried out for all conditions including the whole range of SWS values from 1 up to 38 m/s.

Though there are a lot of methods for WVC retrievals from satellite passive microwave instruments, we suppose that the appearance of a new one providing accurate results under a wide range of environmental conditions, including high winds, is not unreasonable. The methods for WVC retrievals over oceans from satellite passive microwave scanners claim the accuracies from 1 kg/m² (see the RSS publications, e.g., [15], [46]) to 3.5 kg/m² [17]. These accuracies are greatly dependent on the datasets which are used for their estimation [47]. Thus, the comparison of any retrieval method accuracies makes sense only if they are calculated with the same dataset of match-up satellite and ground-truth data. The main result of the presented study is the AMSR2 WVC retrieval algorithm with the high accuracy under extreme wind conditions. This accuracy is due to the new wind induced ocean emissivity parameterization, valid
for high wind conditions and implemented into the BT geo-
physical model. To substantiate this main achievement of the
study, the retrieval error of the new NN2 WVC algorithm was
calculated specifically for high wind events. In total, 53 cases
of the high wind events over the r/s or GPS stations constituted
the base for this specific validation relating to the performance
under conditions of high winds (>15 m/s). We found that the
old NN1 algorithm significantly underestimated WVC under
high wind conditions, and this underestimation deepened with
wind speed. The retrieval error of the NN1 algorithm, calculated
at high wind conditions, is 4.0 kg/m², which is almost twice
higher than the retrieval error of the newly developed NN2 algo-
rithm. To emphasize the importance of the new AMSR2 WVC
retrieval algorithm and underline its innovative character, we
checked the RSS AMSR2 daily WVC product and the JAXA
WVC swath product in relation to the same datasets for which
the NN2 algorithm was applied. It was found that the NN2 algo-
rithm performed 33% better than the RSS AMSR2 operational
algorithm and twice better than the JAXA operational algorithm
for SWS >15 m/s.

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<figure><img src="image_9.png" /></figure>

**Elizaveta V. Zabolotskikh** was born in Leningrad, Russia, in 1967. She received the B.S. and M.S. degrees in semiconductor physics from Leningrad Polytechnical Institute, Leningrad, in 1990, the Ph.D. degree in physics and mathematics from St. Petersburg State University, St. Petersburg, Russia, in 2002, the Doctor of Science degree in oceanology from the Russian State Hydrometeorological University (RSHU), St. Petersburg, in 2016.

From 1993 up to 1997, she was employed as an Engineer in the A.F. Ioffe Physical and Technical Institute, Russian Academy of Sciences, Moskva, Russia. From 1997 to 2012, she was at the Scientific Foundation "Nansen Environmental and Remote Sensing Centre", St. Petersburg, as a Senior Scientist. She is currently a Senior Scientist at the Satellite Oceanography Laboratory, RSHU. Her research interests include satellite passive microwave measurement modeling and calibration, simulation of the radiation transfer in the atmosphere-ocean system, data processing, geophysical parameter retrieval algorithm development, high wind event studies, and multisensor data analysis.

<figure><img src="image_10.png" /></figure>

**Bertrand Chapron** was born in Paris, France, in 1962. He received the B.Eng. degree from the Institut National Polytechnique de Grenoble, Grenoble, France, in 1984 and the Doctorat National (Ph.D.) degree in fluid mechanics from the University of Aix-Marseille II, Marseille, France, in 1988.

He spent three years as a Postdoctoral Research Associate at the NASA/GSFC/Wallops Flight Facility, Wallops Island, VA, USA. He is currently the Head of the Spatial Oceanography group at IFREMER, Plouzané, France. He is also responsible of the CERSAT. He is the Coinvestigator or Principal Investigator in several ESA, NASA, and CNES projects. He has experience in applied mathematics, physical oceanography, electromagnetic waves theory, and its application to ocean remote sensing.