Improving thermodynamic profile retrievals from microwave 1 radiometers by including Radio Acoustic Sounding System ( RASS ) 2 observations

Abstract. Thermodynamic profiles are often retrieved from the multi-wavelength
brightness temperature observations made by microwave radiometers (MWRs)
using regression methods (linear, quadratic approaches), artificial
intelligence (neural networks), or physical iterative methods. Regression
and neural network methods are tuned to mean conditions derived from a
climatological dataset of thermodynamic profiles collected nearby. In
contrast, physical iterative retrievals use a radiative transfer model
starting from a climatologically reasonable profile of temperature and water
vapor, with the model running iteratively until the derived brightness
temperatures match those observed by the MWR within a specified uncertainty. In this study, a physical iterative approach is used to retrieve temperature
and humidity profiles from data collected during XPIA (eXperimental
Planetary boundary layer Instrument Assessment), a field campaign held from
March to May 2015 at NOAA's Boulder Atmospheric Observatory (BAO) facility.
During the campaign, several passive and active remote sensing instruments
as well as in situ platforms were deployed and evaluated to determine their
suitability for the verification and validation of meteorological processes.
Among the deployed remote sensing instruments were a multi-channel MWR as
well as two radio acoustic sounding systems (RASSs) associated with 915
and 449 MHz wind profiling radars. In this study the physical iterative approach is tested with different
observational inputs: first using data from surface sensors and the MWR in
different configurations and then including data from the RASS in the
retrieval with the MWR data. These temperature retrievals are assessed
against co-located radiosonde profiles. Results show that the combination of the MWR and RASS observations in the retrieval allows for a more accurate characterization of low-level temperature inversions and that these retrieved temperature profiles match the radiosonde observations better than
the temperature profiles retrieved from only the MWR in the layer between
the surface and 3 km above ground level (a.g.l.). Specifically, in this layer
of the atmosphere, both root mean square errors and standard deviations of
the difference between radiosonde and retrievals that combine MWR and RASS
are improved by mostly 10 %–20 % compared to the configuration that does not
include RASS observations. Pearson correlation coefficients are also
improved. A comparison of the temperature physical retrievals to the
manufacturer-provided neural network retrievals is provided in Appendix A.


use radiance data from microwave radiometers, infrared spectrometers, and other 294 observations as input. The microwave radiative transfer model, MonoRTM (Clough et al., 2005), 295 serves as the forward model, which is fully functional for the microwave region and was 296 intensively evaluated previously on MWR measurements (Payne et al. 2008;. 297 We start with the state vector X a = [T, Q, LWP] T , where superscript T denotes transpose, 298 and vectors and matrices are shown in bold. T (K) and Q (g kg -1 ) are temperature and water 299 vapor mixing ratio profiles at 55 vertical levels from the surface up to 17 km, with the distance 300 between the levels increasing geometrically with height. LWP is the liquid water path in (g m -2 ) 301 that measures the integrated content of liquid water in the entire vertical column above the 302 MWR, and is a scalar. For this study, X a has dimensions equal to 111 x 1 (two vectors T and Q 303 with 55 levels each, and LWP). The retrieval framework of Turner and Blumberg (2019) is used, 304 but only using MWR data (no spectral infrared). Here, we demonstrate the 305 15 extensionaugmentation of the retrieval to include RASS profiles of Tv, and the resulting impact 306 this has on the retrieved temperature profiles and information content. 307 The observation vector Y includes temperature and water vapor mixing ratio measured 308 at the surface in-situ, and spectral Tb measured by the MWR. The MonoRTM model F is used as 309 the forward model from the current state vector X, and is then compared to the observation 310 vector Y, iterating until the difference between F(X) and Y is small within a specified uncertainty 311 (Eq 1).
Note that the 2-m surface-level observations of temperature and water vapor mixing 325 ratio (T sfc and Q sfc , respectively) are included as part of the observation vector Y, and thus the 326 uncertainties (0.5 K for temperature and less than 0.4 g kg -1 for mixing ratio) in these 327 observations are included in S ε . 328 The mean state vector of the climatological estimates, or a "prior" vector X a , is a key 329 component in the optimal estimation framework and it is the first guess of the state vector X, 330 X 1 in Eq. (1). It provides a constraint on the ill-posed inversion problem. The prior is calculated 331 independently for each month of the year from climatological sounding profiles (using 10 years 332 of data) in the Denver area. The covariance matrix, S a , of the "prior" vector includes not only 333 temperature or water vapor variances but also the covariances between them. Using around 334 3,000 radiosondes launched by the NWS in Denver, each radiosonde profile is interpolated to 335 the vertical levels used in the retrieval, after which the covariance of temperature and 336 17 temperature, temperature and humidity, and humidity and humidity is computed for different 337 levels. LWP is arbitrarily assigned in X a , with large values chosen for its uncertainty in S a , so that 338 it does not impact (constrain) the retrieval. 339 Four configurations are chosen for the observational vector Y (Y 1 , Y 2 , Y 3 , and Y 4 ). In each 340 of these, the surface observations are obtained by the 2-m BAO in-situ measurements of 341 temperature and humidity. The MWR provides Tb measurements from 22 channels from the 342 zenith scan for the zenith only configuration (Y 1 ), while when using the zenith plus oblique Tb 343 inputs (Y 2 , Y 3 , and Y 4 ) the same 22 channels were used from the zenith scans together with only 344 the four opaque channels (56.66, 57.288, 57.964 and 58.8 GHz) from the oblique scans. Using 345 additional measurements from the co-located radar systems with RASS, the observational 346 vector is further expanded with either RASS 915 (Y 3 ) or RASS 449 (Y 4 ) virtual temperature 347 observations. The covariance matrix of the observed data, S ε , depends on the chosen Y i as seen 348 in the matrix S εi (with i = 1:4) descriptions, with increasing dimensions from Y 1 to Y 2 and 349 additional increasing dimensions to Y 3 or Y 4 through the multi-level measurements of the RASS 350 (Turner and Blumberg, 2019  The uncertainty in the MWR Tb observations was set to the standard deviation from a 356 detrended time-series analysis for each channel during cloud-free periods. The method to 357 detect those cloud-free periods is described in detail in Section 3.2. The derived uncertainties 358 ranged from 0.3 K to 0.4 K in the 22 to 30 GHz channels, and 0.4 to 0.8 K in the 52 to 60 GHz 359 channels. We assumed that there was no correlated error between the different MWR 360

channels. 361
For the RASS, co-located RASS and radiosonde profiles were compared and the standard 362 deviation of the differences in Tv were determined as a function of the radar's signal-to-noise 363 ratio (SNR). This relationship resulted in uncertainties that ranged from 0.8 K at high SNR values 364 to 1.5 K at low SNR values. Again, we assumed that there was no correlated error between 365 different RASS heights. Following these assumptions, the covariance matrix S ε is diagonal. 366 The Jacobian matrix, K, is computed using finite differences by perturbing the elements 367 of X and rerunning the forward model. It has dimensions m x 111, where m is the length of the 368 vector Y i , therefore its dimension increases correspondingly with the inclusion of more 369 observational data. K makes the "connection" between the state vector and the observational 370 19 data and should be calculated at every iteration. 371 372 3.2 Bias-correction of MWR observations using radiosondes or climatology 373 Observational errors propagate through retrieval into the derived profiles (i.e. the bias 374 of the observed data will contribute to a bias in the retrievals). For that, retrieval uncertainties 375 in Eq. (1) from Y = Y 1 or Y 2 derive only from uncertainties in surface and MWR data, while 376 retrieval uncertainties from Y = Y 3 or Y 4 come from uncertainties in the surface, MWR, and RASS 377

measurements. 378
The bias of the retrieval depends on both the absolute accuracy of the forward model 379 and on any observational systematic offset, of which the systematic error in the MWR 380 observations could potentially be reduced through application of an MWR Tb bias-correction 381 procedure. In this study, two different approaches were used for the bias-correction: the first is 382 based on a comparison to the radiosondes, while the second uses climatological profiles. The 383 first method could be used for a field campaign where occasional co-located radiosonde 384 launches are taken, while the second would be used for deployments without any supporting 385 radiosonde observations. 386 For both approaches, the first step is to identify clear-sky periods during which the bias 387 can be estimated (to eliminate uncertainties associated with cloudsto reduce the degrees of 388 freedom associated with clouds) and subsequently the bias can be removed from the observed 389 days. This method identified spectral calibration errors in the MWR observations that could not 417 be explained by physically realistic atmospheric profiles. This bias-correction technique, which 418 accounts for those unphysical spectral calibration features, will be referred to as 'TROPoe BC'. 419 The biases from the two bias-correction schemes are within the uncertainties of each 432 other for most of the channels except at the higher frequencies in the V-band. Biases in the 433 most opaque channels are significantly affected by the accuracy of the boundary layer 434 temperature profiles. When TROPoe BC is used, a monthly average prior temperature profile is 435 used in the PR, and thus differences between this prior profile and the actual temperature 436 23 profile can result in a spectral bias in the more opaque MWR channels. On the contrary, the 437 radiosonde BC uses a direct measurement of the temperature profile (from the radiosonde), 438 and thus is more accurate. It is also important to note that, in both approaches, the biases in 439 the opaque channels for zenith and for oblique scans (for radiosonde BC these are red and blue, 440 respectively; and for the TROPoe BC these are black and green, respectively) are very similar to 441 each other. This supports the assumption that the true bias is nearly independent of the scene, 442 or that the sensitivity to the scene (e.g., zenith or off-zenith) is small. 443 The bias-correction methods were applied by removing the corresponding calculated 444 biases from the MWR Tb observations before the retrievals were performed. Later in Section 4, 445 differences in the retrieved temperature profiles will be shown when using the two bias-446 correction approaches. These differences will be more evident in the temperature profiles 447 exhibiting near-ground temperature inversions. 448 However, the final goal of this study is not to assess the sensitivity to different bias-449 correction approaches but to verify that the inclusion of RASS observations does improve 450 retrieved temperature profiles, independently of the bias-correction method used. 451 452

Analysis of physical retrieval characteristics 453
The retrieved profiles of the four different PR configurations presented in Table 1  Converted to a correlation matrix, it is possible to visualize these dependencies, as presented in 545 MWRzo Sop (Fig. 3c). To understand the level-to-level correlations among the 4 different retrieval 558 configurations in Table 1, the Sop matrices were averaged over all radiosonde events, and 559 converted to correlation matrices (Fig. 4). A clearly visible narrowing of the spread around the 560 main diagonal and correlation reduction in the off-diagonal elements result by adding 561 additional observations, from MWR zenith only (Fig. 4a), to MWR zenith-oblique (Fig. 4b), to 562 the larger impact obtained by the usage of the RASS 915 (Fig. 4c), concluding with the RASS 449 563 MWRzo449 retrievals is because that configuration has more observational information 567 compared to the other retrieval configurations. 568 Other statistically important features to analyze in the PRs, besides their uncertainty, 569 are the vertical resolution already introduced in the example of Fig. 3b, and the degree of 570 freedom for signal (DFS). These two features, derived from the Akernels of each PR 571 30 configuration, averaged over all radiosonde events, are shown in Fig 4f and 4g. The vertical 572 resolution (Fig. 4f) shows the width of the atmosphere layer used for each retrieval height, 573 computed as the full-width half-maximum value of the averaging kernel. The cumulative DFS 574 profile (Fig. 4g) is a measure of the number of independent pieces of information in the 575 observations below the specified height. For example, at the 1 km AGL level the vertical 576 resolution of MWRzo449 is 0.5 km (i.e. information is from +/-0.5 km around the retrieval 577 height is considered in the retrieval), while all other retrievals use the information from more 578 than +/-1.5 km. Also, the DFS, as a cumulative measure, shows an increase in pieces of 579 presented in Fig. 1. As expected, the radiosonde BC method yielded a retrieved profile closer to 628 the radiosonde temperature profile than when using TROPoe BC, for which the inversion in the 629 temperature profile close to the surface is too accentuated (particularly the black, purple, and 630 cyan lines, all of which used oblique scan data). 631 The relative statistical behavior (Pearson correlation, RMSE, and bias) of the PRs for 632 both temperature and mixing ratio against radiosondes is shown in Figure 6, using both bias-633 correction approaches. PRs obtained after applying the radiosonde BC (Fig. 6a) present overall 634 34 smaller RMSE and bias (the latter almost equal to zero up to 3 km AGL) and slightly higher 635 correlations compared to the statistics of the PRs obtained after applying the TROPoe BC (Fig.  636   6b). This could be expected since for the comparison in Fig. 6a a subset of the radiosondes was  637 already used for the Tb bias correction. Also, the different retrievals show a narrower 638 distribution for the panels in Fig. 6a. Nevertheless, the results obtained when applying either 639 bias-correction methods (in Fig. 6a, b)  other in relation to moisture, because the Tv observations from the RASS are dominated by the 649 ambient temperature (not moisture), and thus have little impact on the water vapor retrievals. 650 35 We found that the AQKernels are almost identical for all four PR configurations (not shown). 651 Detailed statistical evaluation of the PRs mixing ratio profiles are presented in Fig, 7, also  652 averaged over all radiosonde events, and show very similar correlations, RMSEs, and biases for 653 all PRs, implying that the impact of including RASS observations in the retrieval is minimal on 654 this variable. Finally, it is noted that Fig. 7 shows the mixing ratio of the data from TROPoe BC. 655 The radiosonde BC mixing ratio results are almost identical. PRs using the TROPoe BC (Fig. 8b) compared to the PRs using the radiosonde BC (Fig. 8a). Three  Table 2 includes the same data as in Figure 8 but  The results presented in Table 2     To remove any observational systematic error in the MWR Tb observations, two bias-769 correction procedures were tested. The first one takes advantage of the many radiosondes 770 launched during XPIA, and the second one uses climatological profiles. As expected, the 771 radiosonde bias-correction method gives retrieved profiles closer to the radiosonde 772 temperature profiles than when using the climatological based method. Nevertheless, our 773 results show that regardless of the bias-correction method used, the inclusion of the 774 observations from the active RASS instruments in the PR approach improves the accuracy of the 775 temperature profiles by around 10-20% compared to the PR configuration using only surface 776 observations and MWR observed brightness temperature from the zenith scan. Of the PRs 777 configurations tested, generally better statistical agreement is found with the radiosonde 778 observations when the RASS 449 is used together with the surface observations and brightness 779 temperature from the zenith and averaged oblique MWR observations. 780 The AKernel and the posterior covariance matrices for temperature are used to derive 781 the one-sigma uncertainty, vertical resolution, and cumulative degree of freedom as a function 782 of height for the different PRs, and the level-to-level correlated uncertainty of the retrievals. 783 Results show that the inclusion of the active instruments improves all of the above-mentioned 784 43 variables in the 0-3km layer, including at heights between 2-3km that are above the maximum 785 RASS height. Thus, the positive impact of the RASS observations extends into the atmosphere 786 above the height of measurements themselves. 787 Furthermore, 15 cases when temperature profiles from the radiosonde observations 788 were the furthest away from the mean climatological average were selected, and the statistical 789 comparison was reproduced over this subset of cases. These are the cases usually the most 790 difficult to retrieve and the most important to forecast; therefore, it is essential to improve the 791 retrievals in these situations. Even for this subset of selected cases the inclusion of active 792 sensor observations in the PRs is found to be beneficial. 793 Finally, the impact of the inclusion of RASS measurements on the retrieved humidity 794 profiles was considered, but the inclusion of RASS observations did not produce significantly 795 better results, compared to the configurations that do not include them. This was not a surprise 796 as RASS measures virtual temperature, effectively adding very little extra information to the 797 water vapor retrieval. In this case a better option would be to consider adding other active 798 remote sensors such as water vapor differential absorption lidars (DIALs) to the PRs. Turner and 799 Löhnert (2021) showed that including the partial profile of water vapor observed by the DIAL 800 substantially increases the information content in the combined water vapor retrievals. 801 Consequently, to improve both temperature and humidity retrievals a synergy between MWR, 802 RASS, and DIAL systems would likely be necessary. 803