Inverse problems for regularization matrices

Discrete ill-posed problems are difficult to solve, because their solution is very sensitive to errors in the data and to round-off errors introduced during the solution process. Tikhonov regularization replaces the given discrete ill-posed problem by a nearby penalized least-squares problem whose solution is less sensitive to perturbations. The penalization term is defined by a regularization matrix, whose choice may affect the quality of the computed solution significantly. We describe several inverse matrix problems whose solution yields regularization matrices adapted to the desired solution. Numerical examples illustrate the performance of the regularization matrices determined

Characterization of Mesoscale Waves in the Jupiter NEB by Jupiter InfraRed Auroral Mapper on board Juno

In 2017, the Jupiter InfraRed Auroral Mapper (JIRAM), on board the NASA-ASI Juno mission, observed a wide longitude region (50° W–80° E in System III) that was perturbed by a wave pattern centered at 15° N in the Jupiter’s North Equatorial Belt (NEB). We analyzed JIRAM data acquired on 2017 July 10 using the M-channel and on 2017 February 2 with the spectrometer. The two observations occurred at different times and at slightly different latitudes. The waves appear as clouds blocking the deeper thermal emission. The wave crests are oriented north–south, and the typical wave packet contains 10 crests and 10 troughs. We used Fourier analysis to rigorously determine the wavenumbers associated with the observed patterns at a confidence level of 90%. Wavelet analysis was also used to constrain the spatial localization of the largest energies involved in the process and determine the wavelengths carrying the major contribution. We found wavelengths ranging from 1400 to 1900 km, and generally decreasing toward the west. Where possible, we also computed a vertical location of the cloud pressure levels from the inversion of the spectral radiances measured by the JIRAM spectrometer. The waves were detected at pressure levels consistent with the NH3 as well as NH4SH clouds. Phase velocities could not be determined with sufficient confidence to discriminate whether the alternating crests and troughs are a propagating wave or a manifestation of a fluid dynamical instabilit

On the spatial distribution of minor species in Jupiter's troposphere as inferred from Juno JIRAM data

The spatial distribution of water, ammonia, phosphine, germane, and arsine in the Jupiter's troposphere has been inferred from the Jovian Infrared Auroral Mapper (JIRAM) Juno data. Measurements allow us to retrieve the vertically averaged concentration of gases between ~3 and 5 bars from infrared‐bright spectra. Results were used to create latitudinal profiles. The water vapor relative humidity varies with latitude from <1% to over 15%. At intermediate latitudes (30–70°) the water vapor maxima are associated with the location of cyclonic belts, as inferred from mean zonal wind profiles (Porco et al., 2003). The high‐latitude regions (beyond 60°) are drier in the north (mean relative humidity around 2–3%) than the south, where humidity reaches 15% around the pole. The ammonia volume mixing ratio varies from 1 × 10−4 to 4 × 10−4. A marked minimum exists around 10°N, while data suggest an increase over the equator. The high‐latitude regions are different in the two hemispheres, with a gradual increase in the south and more constant values with latitude in the north. The phosphine volume mixing ratio varies from 4 × 10−7 to 10 × 10−7. A marked minimum exists in the North Equatorial Belt. For latitudes poleward 30°S and 30°N, the northern hemisphere appears richer in phosphine, with a decrease toward the pole, while the opposite is observed in the south. JIRAM data indicate an increase of germane volume mixing ratio from 2 × 10−10 to 8 × 10−10 from both poles to 15°S, with a depletion centered around the equator. Arsine presents the opposite trend, with maximum values of 6 × 10−10 at the two poles and minima below 1 × 10−10 around 20°S

On the spatial distribution of minor species in Jupiter's troposphere as inferred from Juno JIRAM data

The spatial distribution of water, ammonia, phosphine, germane, and arsine in the Jupiter's troposphere has been inferred from the Jovian Infrared Auroral Mapper (JIRAM) Juno data. Measurements allow us to retrieve the vertically averaged concentration of gases between ~3 and 5 bars from infrared‐bright spectra. Results were used to create latitudinal profiles. The water vapor relative humidity varies with latitude from <1% to over 15%. At intermediate latitudes (30–70°) the water vapor maxima are associated with the location of cyclonic belts, as inferred from mean zonal wind profiles (Porco et al., 2003). The high‐latitude regions (beyond 60°) are drier in the north (mean relative humidity around 2–3%) than the south, where humidity reaches 15% around the pole. The ammonia volume mixing ratio varies from 1 × 10−4 to 4 × 10−4. A marked minimum exists around 10°N, while data suggest an increase over the equator. The high‐latitude regions are different in the two hemispheres, with a gradual increase in the south and more constant values with latitude in the north. The phosphine volume mixing ratio varies from 4 × 10−7 to 10 × 10−7. A marked minimum exists in the North Equatorial Belt. For latitudes poleward 30°S and 30°N, the northern hemisphere appears richer in phosphine, with a decrease toward the pole, while the opposite is observed in the south. JIRAM data indicate an increase of germane volume mixing ratio from 2 × 10−10 to 8 × 10−10 from both poles to 15°S, with a depletion centered around the equator. Arsine presents the opposite trend, with maximum values of 6 × 10−10 at the two poles and minima below 1 × 10−10 around 20°S

On the clouds and ammonia in Jupiter’s upper troposphere from Juno JIRAM reflectivity observations

We analyse spectra measured by the Jovian Infrared Auroral Mapper (JIRAM, a payload element of the NASA Juno mission) in the 3150–4910 cm−1 (2.0–3.2 μm) range during the perijiove passage of 2016 August. Despite modelling uncertainties, the quality and the relative uniformity of the data set allow us to determine several parameters characterizing the Jupiter’s upper troposphere in the latitude range of 35°S–30°N. Ammonia relative humidity at 500 millibars varies between 5 per cent to supersaturation beyond 100 per cent for about 3 per cent of the processed spectra. Ammonia appears depleted over belts and relatively enhanced over zones. Local variations of ammonia, arguably associated with local dynamics, are found to occur in several locations on the planet (Oval BA, South Equatorial Belt). Cloud altitude, defined as the level where aerosol opacity reaches unit value at 3650 cm−1 (2.74 μm), is maximum over the Great Red Spot (>20 km above the 1 bar level) and the zones (15 km), while it decreases over the belts and towards higher latitudes. The aerosol opacity scale height suggests more compact clouds over zones and more diffuse clouds over belts. The integrated opacity of clouds above the 1.3-bar pressure level is found to be minimum in regions where thermal emission of the deeper atmosphere is maximum. The opacity of tropospheric haze above the 200-mbar level also increases over zones. Our results are consistent with a Hadley-type circulation scheme previously proposed in literature for belts and zones, with clear hemisphere asymmetries in cloud and haze