During most volcanic eruptions and many periods of volcanic unrest, detectable quantities of sulfur dioxide (

In this study, we detail a probabilistic enhancement of an infrared

We highlight analyses of several recent significant eruptions, including the 22 June 2019 eruption of Raikoke volcano, in the Kuril Islands; the mid-December 2016 eruption of Bogoslof volcano, in the Aleutian Islands; and the 26 June 2018 eruption of Sierra Negra volcano, in the Galapagos Islands. This retrieval method is currently being implemented in the VOLcanic Cloud Analysis Toolkit (VOLCAT), where it will be used to generate additional cloud object properties for real-time detection, probabilistic characterization, and tracking of volcanic clouds in support of aviation safety.

During most volcanic eruptions and many periods of volcanic unrest, detectable quantities of sulfur dioxide (

Globally, measurements of

In this study, we detail a probabilistic enhancement of the infrared

Both CrIS instruments are currently operating in full spectral resolution mode (FSR), providing MWIR spectra at 0.625 cm

Flowchart showing the probabilistic framework for Monte Carlo height and VCD, yielding a PDF for the height, which is not generally Gaussian and may be heavily skewed, and a Gaussian distribution of conditional VCD

The NOAA Unique CrIS/ATMS Processing System (NUCAPS) already includes a retrieval of

In this study we analyze several recent significant eruptions, including the 22 June 2019 eruption of Raikoke volcano, in the Kuril Islands; the mid-December 2016 eruption of Bogoslof volcano, in the Aleutian Islands; and the 26 June 2018 eruption of Sierra Negra volcano, in the Galapagos Islands. This retrieval method is currently being implemented in the VOLcanic Cloud Analysis Toolkit (VOLCAT,

As a preliminary we discuss several methods which we describe here as “classical”. In fact these methods are relatively recent; however, they do not make full use of the probability spaces that we will exploit here. Previous analyses of the height and distribution of volcanic

Summary of Recent Infrared

The infrared trace gas methods of

For a 1 km thick box profile layer, the concentration of anomalous

In the present study, we pre-compute a limited database of Jacobians for 1 km thick

Following

For simplicity, throughout the remainder of this work we refer to this type of height retrieval with a function notation:

Throughout, we make a distinction between our method being probabilistic and other methods being deterministic; however, we note here that the classical methods are all based on the optimal estimation (a Bayesian method) of

Instead of calculating the mean and covariance of the climatological background as in a traditional trace gas retrieval, we treat the background (

In this framework, the

Implicitly,

This study aims to estimate the probability distribution of

Although we could directly estimate the height PDF from sampling the many different backgrounds, we treat our retrieval as an update on the

We impose a Gaussian prior with mean and variance given by the

The likelihood function is constructed directly by retrieving the height due to the real spectrum

Although slower than retrieving the layer height (

Although this method is used primarily for detection (using

Because the estimated VCD depends strongly on the layer height, we refer to an estimate of total VCD where the layer is given as a specified height as a “conditional VCD”. In this framework, the VCD estimates of

Although we do not know the true vertical profile of

Here, we give approximation formulae for the mean and variance partial VCD. The derivation of these formulae is detailed in Appendix

The variance can also be calculated from the statistics of the conditional VCD expectation:

The covariance between the partial VCDs for two altitudes (

In this system, we retrieve probabilistic

For strong

In addressing this issue, we adopt the second approach. The specialized Jacobian must be dominated by channels with approximately linear forward model responses (Fig.

One complication here is the fact that the channels with the most linear response are also those which are least sensitive to

At every stage of the retrieval, the background state of the volcanic

In constructing the background spectrum channel-wise marginal PDFs (histograms) and covariance matrix, periods with little or no

SNPP CrIS mean

This leaves a database of more than

For each season–latitude–longitude bin, we construct a representative sample of 10 000 possible background spectra that conform to the set of channel-wise marginal distributions and the covariance matrix relevant to that bin. Although our database is large enough to construct this sample for each bin, we generate these possible spectra via another method because it is preferable (from a mathematical standpoint) that the samples represent only what is known statistically about the spectra. That is a subtle point, but because the channel marginal distributions are represented as histograms (with finite range), generating synthetic background spectra very slightly damps the possible variance contained in a set of real measured spectra and limits the possibility of two key issues: (i) that real but anomalous or erroneous background spectra will be used and (ii) that real spectra with

Since the channel-wise marginal distributions are generally non-Gaussian (e.g., Fig.

NOAA-20 CrIS has very similar radiometric characteristics as SNPP, except that NOAA-20 FOV 7 noise is within specification and is therefore considered in this study (JPSS CrIS SDR Team,

At approximately 18:00 UTC on 21 June 2019 (04:00 LT), Raikoke volcano in the Kuril Islands erupted for the first time since 1924 (

NOAA-20 CrIS mean total VCD

Time evolution (top to bottom) of the Raikoke

In the 2016–2017 eruptive period at Bogoslof volcano, 70 explosive events were identified

Initial (classical)

Of particular importance in this small cloud made up of only a few (17) FOVs, SNPP CrIS FOV 7 is significantly nosier (above specification) than that of other FOVs

Because the probabilistic framework allows the calculation of a mean partial VCD, we may derive a formula for the mean or expected concentration profile by similar means as those for Eq. (

On 26 June 2018, after a period of elevated seismicity, the onset of a major eruption at Sierra Negra was signaled by volcanic tremor at 19:40 UTC, producing an ash and

Time evolution (top to bottom) of the 27 June 2018 Sierra Negra

Although a deep analysis of the differences between the present method and others is beyond the scope of the present work, here we highlight a brief representative comparison of our

Representative comparison between TROPOMI, IASI, and CrIS

As mentioned above, CrIS is a very similar instrument to IASI (both Fourier transform Michelson interferometers). The relevant instrument differences are that IASI (aboard EUMETSAT satellites METOP-A/B, 21:30 LTAN) covers both the

Comparison between TROPOMI and CrIS

TROPOMI is a UV spectrometer operating aboard the TROPOMI the Copernicus Sentinel-5 Precursor (S5P) satellite, which orbits only 3.5 min behind SNPP CrIS

Representative example comparison of CALIOP lidar backscatter

The last source of comparison data is 532 nm backscattered lidar measurements from the CALIOP overpass of the Raikoke cloud between 14:32 and 14:36 UTC on 25 June 2019 (Fig.

As mentioned above, our strongest total VCD measurement from the Raikoke cloud was

A more detailed view of the comparison between CrIS VCDs and TROPOMI conditional VCDs at 15 km altitude is shown for two regions of the Raikoke cloud in Fig.

The main focus and strength of our approach is the ability to generate physics-based PDFs for the height. Because our retrieval is based on the operational algorithm in use for IASI, our retrieved heights are very similar to those from IASI, although there are key differences readily apparent in Fig.

Although not shown here,

Because we retrieve a PDF on each CrIS FOV rather than a single estimate, we can compare the PDFs directly to data from a CALIOP overpass of the cloud. Here we show an example comparison from Raikoke; however, a full comparison for every overpass of the Raikoke cloud is the subject of future work. For the first several days after the eruption, there was still significant ash suspended in the dispersing cloud, leading to the appearance of several highly attenuating layers in CALIOP data between 10–15 km (Fig.

Overall, there is good agreement between the CrIS

In the strictest sense, such PDFs can only be attributed to the presence of similar statistical features in the background. Specifically, if the background spectrum probability space is dominated by two sets of meteorological conditions (for example, one mode representing deep convective cloud radiances and another for cloud-free radiances), then multiple populations of the Monte Carlo height samples may accumulate, leading to a multimodal height PDF.

Relaxing this strict interpretation, there is some evidence that these bimodal PDFs may represent the presence of

By retrieving PDFs for height and partial VCD it is possible to enhance time series analysis of

To estimate the mass of an

From Fig.

Despite this early underestimation and the fact that the

New probabilistic enhancement of existing hyperspectral IR

This technique is capable of resolving larger VCD values than would be anticipated for a linearized approach due to two factors: (i) the use of the height PDF increases the retrieved total VCD compared with a single height estimate and (ii) the use of a specialized channel subset retrieval that improves the linear approximation when the signal is certain to be dominated by

Preliminary comparisons suggest that this method generally compares well with other measurements of

As a logical extension of the probabilistic framework, this technique enables the characterization of

The algorithms presented here are currently being integrated into VOLCAT, where they will be used for operational

The general problem of sampling a correlated random vector (

This is accomplished by solving

For the purpose of generating the correlated random background spectrum in the present study, we make several modifications to the classical method of

Because each of the correlations matching inverse problems requires multiple rounds of numerical integration of Eq. (

The estimated radial limit of integration

Although each channel pair inverse problem can be solved separately by Newton's method or other algorithms, we solve all of the problems jointly, restating the problem as a gradient and descent minimization of the total square correlation error

As in the text,

The mean partial VCD is calculated as the expectation

Because the algebraic form of the variance is

Since the dummy variable

Similarly, for the covariance between partial VCD at two altitudes

Of particular importance is that these formulae may be used to calculate the expectation and variance values of the partial VCD between two altitudes.
The expected value is

To smooth the changes between retrievals in adjacent background cells, we use a bilinear interpolation of the background spectra. For a general quantity (

The following CrIS channels are used in this work and are identified by their wavenumber value (cm

1300.0, 1300.625, 1301.25, 1301.875, 1302.5, 1303.125, 1303.75, 1304.375, 1305., 1305.625, 1306.25, 1306.875, 1307.5, 1308.125, 1308.75, 1309.375, 1310., 1310.625, 1311.25, 1311.875, 1312.5, 1313.125, 1313.75, 1314.375, 1315., 1315.625, 1316.25, 1316.875, 1317.5, 1318.125, 1318.75, 1319.375, 1320., 1320.625, 1321.25, 1321.875, 1322.5, 1323.125, 1323.75, 1324.375, 1325., 1325.625, 1326.25, 1326.875, 1327.5, 1328.125, 1328.75, 1329.375, 1330., 1330.625, 1331.25, 1331.875, 1332.5, 1333.125, 1333.75, 1334.375, 1335., 1335.625, 1336.25, 1336.875, 1337.5, 1338.125, 1338.75, 1339.375, 1340., 1340.625, 1341.25, 1341.875, 1342.5, 1343.125, 1343.75, 1344.375, 1345., 1345.625, 1346.25, 1346.875, 1347.5, 1348.125, 1348.75, 1349.375, 1350., 1350.625, 1351.25, 1351.875, 1352.5, 1353.125, 1353.75, 1354.375, 1355., 1355.625, 1356.25, 1356.875, 1357.5, 1358.125, 1358.75, 1359.375, 1360., 1360.625, 1361.25, 1361.875, 1362.5, 1363.125, 1363.75, 1364.375, 1365., 1365.625, 1366.25, 1366.875, 1367.5, 1368.125, 1368.75, 1369.375, 1370., 1370.625, 1371.25, 1371.875, 1372.5, 1373.125, 1373.75, 1374.375, 1375., 1375.625, 1376.25, 1376.875, 1377.5, 1378.125, 1378.75, 1379.375, 1380., 1380.625, 1381.25, 1381.875, 1382.5, 1383.125, 1383.75, 1384.375, 1385., 1385.625, 1386.25, 1386.875, 1387.5, 1388.125, 1388.75, 1389.375, 1390., 1390.625, 1391.25, 1391.875, 1392.5, 1393.125, 1393.75, 1394.375, 1395., 1395.625, 1396.25, 1396.875, 1397.5, 1398.125, 1398.75, 1399.375, 1400., 1400.625, 1401.25, 1401.875, 1402.5, 1403.125, 1403.75, 1404.375, 1405., 1405.625, 1406.25, 1406.875, 1407.5, 1408.125, 1408.75, 1409.375, 1410.0

1300., 1300.625, 1301.25, 1301.875, 1302.5, 1303.125, 1303.75, 1304.375, 1305., 1305.625, 1306.25, 1306.875, 1307.5, 1308.125, 1308.75, 1309.375, 1310., 1310.625, 1311.25, 1311.875, 1312.5, 1313.125, 1313.75, 1314.375, 1315., 1315.625, 1316.25, 1316.875, 1317.5, 1318.125, 1318.75, 1319.375, 1320., 1320.625, 1321.25, 1321.875, 1322.5, 1323.125, 1323.75, 1324.375, 1325., 1325.625, 1326.25, 1326.875, 1327.5, 1328.125, 1328.75, 1329.375, 1330., 1330.625, 1331.25, 1331.875, 1332.5, 1362.5, 1363.125, 1363.75, 1387.5, 1388.125, 1388.75, 1389.375, 1390., 1390.625, 1391.25, 1391.875, 1392.5, 1393.125, 1393.75, 1394.375, 1395., 1395.625, 1396.25, 1396.875, 1397.5, 1398.125, 1398.75, 1399.375, 1400., 1400.625, 1401.25, 1401.875, 1402.5, 1403.125, 1403.75, 1404.375, 1405., 1405.625, 1406.25, 1406.875, 1407.5, 1408.125, 1408.75, 1409.375, 1410.

In general, the total cloud mass can be calculated by integrating the total VCD

We treat the above time series of PDFs of

To make this calculation in practice, a finite difference formula is needed for

With random processes for the mass and mass rate of change calculated we can calculate the decay rate coefficient as a function of these two random processes:

Calculating the PDF for the instantaneous

Notably, the distributions are not Gaussian either the decay rate coefficient or the

The Level-1B CrIS data utilized in this study are available from the Goddard Earth Sciences Data and Information Services Center (GES-DISC,

DMH and MJP conceived of the main concepts. DMH developed the mathematical framework and details for the probabilistic retrieval. DMH developed the code used to construct the background spectra and perform the retrieval. MJP performed all radiative transfer modeling. MJP and DMH analyzed the sensitivity of the Jacobians and developed the specialized retrieval for strong loading. DMH and MJP both tested and tuned the retrieval as well as interpreted and discussed the results. DMH and MJP wrote the manuscript.

The authors declare that they have no conflict of interest.

The views, opinions, and findings contained in this report are those of the authors and should not be construed as an official National Oceanic and Atmospheric Administration or U.S. Government position, policy, or decision.

The authors wish to thank Lieven Clarisse for sharing the data used to construct the

This research has been supported by the National Oceanographic and Atmospheric Administration JPSS Proving Ground and Risk Reduction (PGRR) Program (grant no. NA15NES4320001).

This paper was edited by Thomas von Clarmann and reviewed by two anonymous referees.