New satellite constellations to provide high-resolution atmospheric observations from microwave (MW) sounders operating in low-Earth orbit are now coming online and are providing operationally useful data. The first of these missions, the NASA Time-Resolved Observations of Precipitation structure and storm Intensity with a Constellation of Smallsats (TROPICS) Earth Venture (EVI-3) mission, was successfully launched into orbit on May 7 and 25, 2023 (Eastern Daylight Time, two CubeSats in each of the two launches). TROPICS is now providing nearly all-weather observations of 3-D temperature and humidity, as well as cloud ice and precipitation horizontal structure, at high temporal resolution to conduct high-value science investigations of tropical cyclones (TCs). TROPICS is providing rapid-refresh MW measurements (median refresh rate of better than 60 min early in the mission with four functional CubeSats, and now approximately 70–90 min with three functional CubeSats) over the tropics that can be used to observe the thermodynamics of the troposphere and precipitation structure for storm systems at the mesoscale and synoptic scale over the entire storm lifecycle. Hundreds of high-resolution images of TCs have been captured thus far by the TROPICS mission, revealing the detailed structure of the eyewall and surrounding rain bands. The new 205-GHz channel in particular (together with a traditional channel near 92 GHz) is providing new information on the inner storm structure, and, coupled with the relatively frequent revisit and low downlink latency, is already informing TC analysis at operational centers. Here, we present an overview of the TROPICS mission after two years of successful science operations with a focus on the suite of geophysical (Level 2) products (atmospheric vertical temperature and moisture profiles, instantaneous surface rain rate, and TC intensity) and the science investigations that have been enabled by these new measurements.

The four NASA TROPICS Earth Venture (EVI-3) CubeSat constellation satellites were successfully launched into orbit on May 8 and May 26, 2023 (NZST) – two satellites were deployed in each launch. TROPICS is now providing nearly all-weather observations of 3-D temperature and humidity, as well as cloud ice and precipitation horizontal structure, at a median refresh rate of approximately 60 minutes to conduct high-value science investigations of tropical cyclones. TROPICS provides microwave measurements in twelve channels spanning 90-205 GHz over the tropics that can be used to observe the thermodynamics of the troposphere and precipitation structure for storm systems at the mesoscale and synoptic scale over the entire storm lifecycle. Hundreds of high-resolution images of tropical cyclones have been captured thus far by the TROPICS mission, revealing detailed structure of the eyewall and surrounding rain bands. The new 205-GHz channel in particular (together with a traditional channel near 91.65 GHz) is providing new information on the inner storm structure, and, coupled with the relatively frequent revisit and low downlink latency, is informing tropical cyclone analysis at operational centers. In this paper, the radiance and geophysical performance of Pathfinder and the constellation satellites is presented, showing that the mission is on track to meet its baseline requirements.

In this paper, the key models, assumptions, and statistical characterizations/uncertainties are examined to better understand how to evaluate hyper-spectral sampling (HSS) and "multi-angle-sampling (MAS) systems and interpret results that are commonly presented in the contemporary literature. The analysis presented is based on a set of thousands of representative, global atmospheric profiles over a variety of surfaces. These profiles are used with a line-by-line radiative transfer model to calculate the at-sensor radiance for a variety of viewing angles, spectral response functions, channelization schemes, and noise assumptions. A neural-network-based retrieval scheme [Blackwell, 2005] similar to one that is used for AIRS/AMSU on Aqua and for TROPICS near-real-time processing is used to retrieve the profiles. Errors are characterized by bias, RMS uncertainty, averaging kernel width, and retrieved profile error correlation width for a variety of sensor configurations to explore HSS and MAS performance. Neural network jacobians [Blackwell, 2012] facilitate the direct calculation of these metrics in some cases.

We have developed and implemented a near-real-time retrieval algorithm to estimate temperature and water vapor vertical profiles from TROPICS [1] L1b brightness temperature observations. A neural network approach, with heritage in our past work [2] in the operational Atmospheric Infrared Sounder science products [3], was selected due to fast execution time, overall accuracy, and robustness to a wide variety of meteorological conditions. Here, we describe our methodology, present initial performance results on the TROPICS Pathfinder mission on test data sets, and describe our ongoing efforts to validate the algorithm.

Currently, the planetary boundary layer (PBL) is challenging to assess in PBL remote sensing retrievals from space. To address this, we have developed a new 3D deep neural network (DNN) which enhances detail and reduces noise in 3D granules of temperature and humidity retrieved from hyperspectral infrared and microwave sounders. We show that this approach improves accuracy and detail including key features such as capping inversions at the top of the PBL over land, resulting in improved accuracy in estimations of PBL height.

The Microsized Microwave Atmospheric Satellite (MicroMAS-2A) is a 3U CubeSat that was launched in January 2018 as a technology demonstration for future microwave sounding constellation missions, such as the NASA Time-Resolved Observations of Precipitation structure and storm Intensity with a Constellation of Smallsats (TROPICS) mission now in development. MicroMAS-2A has a miniaturized 1U ten-channel passive microwave radiometer with channels near 90, 118, 183, and 206 GHz for moisture and temperature profiling and precipitation imaging [4]. MicroMAS-2A provided the first CubeSat atmospheric vertical sounding data from orbit, and to date it is the only CubeSat to provide temperature and moisture sounding and surface imaging. In this article, we analyze six segments of data collected from MicroMAS-2A in April 2018 and compare them to ERA5 reanalysis fields coupled with the Community Radiative Transfer Model (CRTM). This initial assessment of CubeSat radiometric accuracy shows biases relative to ERA5 with magnitudes ranging from 0.4 to 2.2 K (with standard deviations ranging from 0.7 to 1.2 K) for the four mid-tropospheric temperature channels and biases of 2.2 and 2.8 K (standard deviations 1.8 and 2.6 K) for the two lower tropospheric water vapor channels.

In recent years, CubeSats have emerged as a platform of intense interest for a wide range of applications, including remote sensing. Of specific interest in this paper are data processing challenges associated with the MIT's Microwave Atmospheric Satellite (MicroMAS). Due to the motion of MicroMAS and the geometry of the data acquisition process, measurements are not collected on a regular grid of spatial locations as required by most applications. Thus, a fundamental problem in processing these data is that of interpolation. The problem is further complicated by the fact that MicroMAS collects data from several frequencies at a single location. A baseline algorithm that can be used to solve this multi-frequency scattered data interpolation problem is to fit data from each frequency via independent Gaussian Process (GP) and apply standard GP regression to estimate unknown data on the regular grid for each frequency separately. However, this approach ignores the correlation between frequencies. From the covariance structure in the aforementioned Independent Multiple output GP Regression (IMGPR) algorithm, we proposed a Correlated Multiple output GP Regression (CMGPR) algorithm which replaces a set of delta vectors with parameterized weight vectors learned from the dataset. To test the effectiveness of our proposed algorithms, we use NOAA's ATMS temperature data. According to the experimental results, the CMGPR algorithm performs better than the IMGPR.

With the recent development of CubeSats, several ultracompact, low cost, and rapidly deployable satellites have been developed for earth observation missions. Because of the geometry of the acquisition process, measurements are irregularly sampled, whereas in meteorological applications, data are preferred on a regular grid. This problem is further complicated by the fact that, due to CubeSats' compact sizes and constraints, such as limited power, errors occur in geolocation calibration, resulting in positional errors. In this letter, we analyze how the commonly used triangulation-based linear data interpolation scheme behaves under probabilistic models for the positional errors. The derived distribution of interpolation error caused by positional error is intractable even under a Gaussian distribution for positional errors. To address this problem, we developed an analytical closed-form solution to the first two moments of the interpolation error. Using models for positional errors motivated by our prior work, experimental results show that, compared with the first-order linear model, the second-order one provides a better approximation in terms of the mean and variance, which is very close to that is obtained using more computationally intensive Monte Carlo simulations. This model also allows for the closed-form calculation of mean squared interpolation error, which can be of use in the context of system design where the impact of positional errors on remote sensing products must be considered.

With their greatly reduced sizes, low development cost and rapid construction times, CubeSats have emerged as a platform of intense interest for a wide range of applications, including remote sensing. However, due to their compact form factor, performance tradeoffs relative to larger existing platforms have been encountered. Of specific interest in this paper are data processing challenges associated with the Micro-MAS platform. In meteorological applications, the radiometer samples are preferred on a regularly spaced grid for generating subsequent scientific products such as vertical temperature and water vapor profiles, or fusing with other gridded datasets. However, in reality, MicroMAS radiometer samples are not regularly spaced, and are expected to have geolocation errors comparable in magnitude to the beam-width [10]. In this work, we present a joint maximum a posteriori (MAP) estimation approach to determine both sample locations as well as brightness temperature on a regular spatial grid given irregularly sampled data corrupted by noise and uncertainty in sample locations. The performance of this approach is tested on Advanced Technology Microwave Sounder (ATMS) data which demonstrates significant improvement both qualitatively and quantitatively compared with traditional estimation methods.

We present a new high-fidelity method of calibrating a cross-track scanning microwave radiometer using Global Positioning System (GPS) radio occultation (GPSRO) measurements. The radiometer and GPSRO receiver periodically observe the same volume of atmosphere near the Earth's limb, and these overlapping measurements are used to calibrate the radiometer. Performance analyses show that absolute calibration accuracy better than 0.25 K is achievable for temperature sounding channels in the 50-60-GHz band for a total-power radiometer using a weakly coupled noise diode for frequent calibration and proximal GPSRO measurements for infrequent (approximately daily) calibration. The method requires GPSRO penetration depth only down to the stratosphere, thus permitting the use of a relatively small GPS antenna. Furthermore, only coarse spacecraft angular knowledge (approximately one degree rms) is required for the technique, as more precise angular knowledge can be retrieved directly from the combined radiometer and GPSRO data, assuming that the radiometer angular sampling is uniform. These features make the technique particularly well suited for implementation on a low-cost CubeSat hosting both radiometer and GPSRO receiver systems on the same spacecraft. We describe a validation platform for this calibration method, the Microwave Radiometer Technology Acceleration (MiRaTA) CubeSat, currently in development for the National Aeronautics and Space Administration (NASA) Earth Science Technology Office. MiRaTA will fly a multiband radiometer and the Compact TEC/Atmosphere GPS Sensor in 2015.

We introduce a new technique for absolute “through-theantenna” calibration of cross-track-scanning passive microwave radiometers viewing earth from a low-earth orbit. This method offers significant advantages, in that neither internal calibration targets nor noise diodes are needed to calibrate the radiometer. The algorithm does require periodic updates of the atmospheric state, which can be readily provided by GPS radio occultation observations, for example. An iterative algorithm retrieves the radiometer gain given a sequence of observations of the earth's limb. The algorithm uses a parameterized radiative transfer model of a spherically-stratified atmosphere. The algorithm works best for opaque temperature sounding channels. This method, when used on idealized radiometer measurements (impulse response functions in frequency and space), yields calibration accuracies similar to those that could be obtained with ideal internal calibration targets. This analysis is based on global Monte Carlo simulations using the NOAA88b profile set. An analysis will also be presented showing how calibration performance degrades as the radiometer characteristics deviate from the ideal case. Among the factors considered are: 1) antenna pattern, 2) spectral passband, 3) pointing errors, 4) atmospheric state variability, 5) the number of limb observations required, and 6) sensitivity to sensor noise.

A variety of new imaging modalities, such as optical diffusion tomography, require the inversion of a forward problem that is modeled by the solution to a three-dimensional partial differential equation. For these applications, image reconstruction is particularly difficult because the forward problem is both nonlinear and computationally expensive to evaluate. In this paper, we propose a general framework for nonlinear multigrid inversion that is applicable to a wide variety of inverse problems. The multigrid inversion algorithm results from the application of recursive multigrid techniques to the solution of optimization problems arising from inverse problems. The method works by dynamically adjusting the cost functionals at different scales so that they are consistent with, and ultimately reduce, the finest scale cost functional. In this way, the multigrid inversion algorithm efficiently computes the solution to the desired fine-scale inversion problem. Importantly, the new algorithm can greatly reduce computation because both the forward and inverse problems are more coarsely discretized at lower resolutions. An application of our method to Bayesian optical diffusion tomography with a generalized Gaussian Markov random-field image prior model shows the potential for very large computational savings. Numerical data also indicates robust convergence with a range of initialization conditions for this nonconvex optimization problem.

In this paper, we propose a general framework for nonlinear multigrid inversion applicable to any inverse problem in which the forward model can be naturally represented at differing resolutions. In multigrid inversion, the problem is adjusted to be solved at each resolution by using the solutions at both finer and coarser resolutions. To do this, we formulate a consistent set of coarse scale cost functionals to ultimately reduce the finest scale one. At each resolution, both the forward model and inverse problems are discretized at the lower resolution; thus reducing computation. Our simulation results for the application of optical diffusion tomography indicate the potential for fast and robust convergence.