Keywords

1 Introduction

The injection of large amounts of fine and coarse ash and rock fragments and corrosive gases into the troposphere and lower stratosphere is usually followed by a long lasting ashfall which can cause a variety of damages (Wilson, 1972). When volcanic ash accumulates on buildings, its weight can cause roofs to collapse. Because wet ash conducts electricity, it can cause short circuits and failure of electronic components, especially high-voltage circuits and transformers. Eruption clouds and ash fall commonly interrupt or prevent telephone and radio communications in several ways, including physical damage to equipment and frequent lightning due to electrically charged ash particles. Even more important, volcanic ash clouds are an increasing hazard to aviation safety because of growing air traffic volumes that use more efficient and susceptible jet engines (Miller and Casadevall, 2000). Several hundreds of commercial aircrafts have unexpectedly encountered volcanic ash in flight and at airports in the past 15 years. Tens of these encounters caused in-flight loss of jet engine power, which nearly resulted in the crash of the airplane. A range of damages may occur to airplanes that fly through an eruption cloud depending on the concentration of volcanic ash and gas aerosols in the cloud, the length of time the aircraft actually spends in the cloud, and the actions taken by the pilots to exit the cloud itself (Maki and Doviak, 2001). Fine ash can also be a health hazard as aerodynamically fine particles will be taken into the lungs during breathing.

Real-time and areal monitoring of a volcano eruption, in terms of its intensity and dynamics, is not always possible by conventional visual inspections, especially during worse visibility periods which are quite common during eruption activity. Remote sensing techniques both from ground and from space represent unique tools to be exploited (Rose and Schneider, 1996; Rose et al., 2000; Wen and Rose, 1994). Microwave weather radars can gather three-dimensional information of atmospheric scattering volumes up several hundreds of kilometers, in all weather conditions, at a fairly high spatial resolution (less than a kilometer) and with a repetition cycle of few minutes (Harris and Rose, 1983; Rose et al., 1995; Maki and Doviak, 2001; Lacasse et al., 2004; Marzano et al., 2006a, b). Ground-based radar systems represent one of the best methods for determining the height and volume of volcanic eruption clouds. Single-polarization Doppler radars can measure horizontally polarized power echo and Doppler shift from which ash content and radial velocity can be, in principle, extracted.

In this work, in order to quantitatively evaluate the ash retrieval by weather radars, a prototype algorithm for volcanic ash radar retrieval (VARR) is formulated and discussed. Starting from measured single-polarization reflectivity, the estimation method has been based on two cascade steps: (i) a classification of eruption regime and volcanic ash category and (ii) estimation of ash concentration and fall rate. Finally, the VARR algorithm is applied to C-band radar data available during the eruption of the Grímsvötn volcano in Iceland during November 2004, discussing the obtained results.

2 Volcanic Ash Radar Retrieval

The retrieval of ash concentration C a and fall rate R a from measured radar reflectivity Z Hm is a typical remote sensing inverse problem. As an inverse problem, it exhibits properties of non-uniqueness and instability of the solution. In order to circumvent this difficulty, the inverse problem can be stated as an estimation problem in a probabilistic framework. A crucial role in this approach is played by the a priori information which consists of all knowledge about the geophysical solution, possibly translated as constraints within the inverse problem. In our context this means to construct an effective model of ash cloud microphysics for remote sensing purposes.

The microwave weather radar response is mainly controlled by the atmospheric particle size distribution (PSD) within the range volume bin. In case of ash cloud formation processes within a humid environment, we may suppose to have two distinct phenomena within an observed range volume: (i) coexistence of ash particle and hydrometeors without mixing processes and (ii) aggregation of ash particles with hydrometeors to form a new mixed-phase particle.

2.1 Microwave Model

There is a fairly large consensus about the capability to model PSD through either a normalized Gamma or Weibull distribution (Marzano et al., 2006a). In case of a multi-mode size distribution, it is always possible to suppose more than one analytical PSD characterized different mean sizes and total number of particles. In this work, the size distribution N p (r) of an ensemble of particles p has been modeled by factorizing its analytical expression as follows:

$$N_{\textrm{p}} (r) = N_{{\textrm{tp}}} F_{\textrm{p}} (r),$$
((1))

where r is the particle radius and N tp the total particle number. The generalized Gamma function F p in Eq. (1) can be interpreted as the probability to find a particle within a radius bin and is given by,

$$F_{\textrm{p}} (r) = \frac{1}{{\Gamma (v_{\textrm{p}} )}}\left( {\frac{r}{{r_{{\textrm{cp}}} }}} \right)^{v_{\textrm{p}} - 1} \frac{1}{{r_{{\textrm{cp}}} }}\exp \left( { - \frac{r}{{r_{{\textrm{cp}}} }}} \right),$$
((2))

where ν p is the PSD skewness parameter, r cp is the PSD characteristic radius, and Γ is the complete Gamma function. The particle total number N tp of particles, having a mixing ratio q p and a density ρ p, is expressed by

$$N_{{\textrm{tp}}} = \left( {\frac{{q_{\textrm{p}} }}{{r_{{\textrm{cp}}}^3 }}\frac{3}{{4\pi \rho _{\textrm{p}} }}\frac{{\Gamma (v_{\textrm{p}} )}}{{\Gamma (v_{\textrm{p}} + 3)}}} \right).$$
((3))

Microwave scattering from ash particles and from cloud water and ice droplets satisfies the Rayleigh approximation. Under this condition, the radar reflectivity factor at horizontal polarization Z Hp due to an ensemble of particles p is expressed as the sixth moment of PSD as follows:

$$Z_{{\textrm{Hp}}} = \eta _{{\textrm{Hp}}} \frac{{\lambda ^4 }}{{\pi ^5 |K_{\textrm{p}} |^2 }} = \int\limits_0^\infty {r^6 N_{\textrm{p}} (r)dr =\, } N_{{\textrm{tp}}} r_{{\textrm{cp}}}^6 \frac{{\Gamma (\nu + 6)}}{{\Gamma (\nu )}},$$
((4))

where η Hp is the radar volumetric reflectivity, λ the wavelength, and K p the dielectric factor of the particle ensemble. The last term of Eq. (4) is obtained by substituting the analytical Gamma PSD given in Eq. (1). The advantage of using a generalized gamma function is that it can be obtained an analytical solution for any PSD moments.

2.2 Retrieval Algorithm

In the case of Plinian and sub-Plinian volcanic eruptions, we can exploit both experimental and modeling results to characterize ash particles (Marzano et al., 2006b). We have defined three classes (or modes) of ash sizes: fine ash, coarse ash, and lapilli. As a synthesis of available volcanic information, within each class we have supposed a Gaussian random distribution for: (i) D n with average value m D n equal to 0.01, 0.1, and 1 mm for fine, coarse, and lapilli ash and a standard deviation \(\sigma _{D_n } = 0.2m_{D_n }\) and (ii) C a with mean value m C a equal to 0.1, 1, and 5 g/m3 for light, moderate, and intense concentration regimes and a standard deviation \(\sigma _{c_a } = 0.5m_{c_a }\). In total we have a number N c = 9 of classes: fine ash, coarse ash, and lapilli each of them in low, moderate and intense concentration. By exploiting the previous microphysical model of pure ash, the physically based volcanic ash radar retrieval (VARR) algorithm can be structured as follows: (i) detection of the ash class from the measured reflectivity Z Hm within each range bin by using a Bayesian identification technique and (ii) retrieval of the ash amount and fall rate from the measured Z Hm by applying a polynomial regression method.

For what concerns the classification step, its aim is related to the possibility to automatically discriminate between ash categories which were defined as fine, coarse, and lapilli sizes. In the overall retrieval scheme, classification may represent a first qualitative output before performing parameter estimation. Maximum a posteriori probability (MAP) criterion can be used to carry out cloud classification in a model-based supervised context. Using the Bayes theorem, if c is the ash class, then the conditional probability density function (PDF) of a class c given a measurement Z Hm reduces to (Marzano et al., 2006b)

$$\hat c = {\textrm{Mode}}\left[ {p(c\left| {Z_{{\textrm{Hm}}} } \right.)} \right],$$
((5))

where Mode is the modal value of the posterior PDF \(p(c|Z_{{\textrm{Hm}}} )\). Assuming a Gaussian probability framework to describe \(p(c|Z_{{\textrm{Hm}}} )\)and exploiting the Bayes theorem, computing Eq. (5) means to know the reflectivity mean m Z (also called class centroid) and standard deviation σ Z of Z Hm for each ash class c. The prior PDF can be used to subjectively weight each class as a function of other available information (such as coincident satellite and/or in situ data).

Once an ash class is detected, then an estimate of ash concentration and fall rate is possible. A way to approach the quantitative retrieval problem is to adopt a statistical parametric model to describe the relation P–Z Hm where P stands for either C a or R a. Assuming a power-law model, we can write the estimated quantity for each class c as (Marzano et al., 2006b)

$$\left\{ \begin{array}{l} \hat C_{\textrm{a}} ^{(c)} = \alpha \left[ {Z_{{\textrm{H}} _{\textrm{m}}} } \right]^\beta \\[6pt] \hat R_{\textrm{a}} ^{(c)} = \gamma \left[ {Z_{{\textrm{H}} _{\textrm{m}}} } \right]^\delta \\ \end{array} \right.,$$
((6))

where c = 1:N c and the “hat” indicates estimated quantity.

3 Case Study

An eruption started in Grímsvötn in the evening of November 1, 2004 and was observed by a C-band weather radar located in Keflavik, Iceland. The aim of this section is to show an application of VARR to experimental data, but the complete analysis of the volcanic eruption is beyond the scopes of this work. The Keflavik weather radar is an Ericsson C-band radar without a Doppler capability (Vogfjörd et al., 2005). It is located about 3 km north of the Keflavik international airport at 47 m above sea level in southwest Iceland. Its main operational characteristics are: transmitted peak power of 245.2 kW, antenna beam-width of 0.9°, pulse duration of 2.15 μm, pulse repetition frequency of 250 Hz, and antenna gain of 44.9 dB. The radar system at Keflavik is remotely operated by the Icelandic Meteorological Office (IMO) in Reykjavik and it has been recently updated. Currently, scanned images are routinely acquired every 20 min for normal weather monitoring and every 5 min during volcanic eruptions. The lowest detectable height by weather radar is a function of the elevation angle of the radar beam, the distance of the target from the radar and the earth’s curvature. Using the Keflavik radar characteristics, this relation can be used to infer the lower and upper radar detection limits above the Grímsvötn volcano.

3.1 Grímsvötn Volcano Eruption

Iceland seismic structure is of relevant importance for Icelandic volcanic plume evolution. On the morning of November 1, a jökulhlaup tremor was observed on the seismic records at the Grímsfjall station. In the early morning of Nov. 1, an earthquake swarm began beneath Grímsvötn and at 20:10 earthquake magnitudes increased and the swarm intensified. An eruption warning was sent to the Civil Defense at 20:10, November 1. During the next 2 h about 160 earthquakes were recorded with magnitudes up to 2.8. Volcanic tremor was first observed and after an earthquake with a magnitude of 2.7 occurred at 21:50. The frequency of the tremor energy was concentrated around 1 Hz. The intensity of the tremor increased in the next hours. The volcanic tremor was continuous throughout the night. An increase in power between 04:00 and 05:00 h on November 2, 2004 was observed.

Radar volume scans were continuously acquired and data have been made available from 23:00 on November 1, 2004 till 06:00 on November 2, 2004 every half an hour (Vogfjörd et al., 2005). Reflectivity data were radially averaged to 2 km. From the available radar imagery it was observed that the eruption plume increased in size around 04:00. Figure II.4.1 shows the plan-position indicator (PPI) radar image at 0.5° elevation angle of the measured reflectivity field at the same time. The image is zoomed, for clarity, around the volcano vent placed at a location around 255 km on x and 42 km on y.

Fig. II.4.1
figure 1

Plan-position indicator (PPI) at 0.5° elevation of the measured horizontally polarized reflectivity at 04:00 UTM during the Grímsvötn volcano eruption on November 2, 2004. The triangle indicates the volcano vent

Full size image

The signal of volcanic cloud is quite evident from both PPI and RHI signatures with values up to 35 dBZ. Notice that the height of this signature avoids any misinterpretation as a rain cloud radar echo, whereas the minimum detectable reflectivity factor (MDZ) of the Keflavik radar at 260 km is about –5 dBZ. At the time of observation after about 5 h from the first radar ash echo, the volcanic plume has been already advected toward northwest and the reflectivity maximum contour results to be slightly misplaced with respect to the volcano vent (indicated by a triangle). The extension of the ash cloud area is about 1,000 km2 with an average wind velocity of about 10 km/h.

3.2 Results

The measured reflectivity images can be then inverted to retrieve the ash concentration and ashfall rate by applying the VARR technique. If the VARR classification algorithm is applied, from radar PPI data, we can detect the class index displayed in Fig. II.4.2. The code of the ash classes is listed in the caption of the figure itself. We note that the reflectivity peak is associated to a light concentration of lapilli which corresponds to an average reflectivity of 34 dBZ. Surrounding this area and closer to the volcano vent, we note the presence of an intense concentration of coarse ash whose average reflectivity is about 21 dBZ. Around this high-reflectivity plume along the northwest direction, there is a dispersion of moderate and light concentration of coarse corresponding to an average reflectivity of 14 and 4 dBZ, respectively. Fine ash is only weakly detected at the border of the PPI sector. This ash areal distribution is quite realistic as the eruption has started few hours before and there is an experimental evidence that lapilli can be suspended in air for some hours after the explosion. A sorting of ash particles is also typical during the evolution of the erupted volcanic cloud. Unfortunately, we do not have any chance to verify these results within the ash plume.

Fig. II.4.2
figure 2

Plan-position indicator (PPI) at 0.5° elevation of the estimated class index c, derived from the PPI scan shown in Fig. II.4.1 by applying the VARR classification algorithm. Classes are enumerated as 3 = (intense concentration of fine ash), 4 = (light concentration of coarse ash), 5 = (moderate concentration of coarse ash), 6 = (Intense concentration of coarse ash), 7 = (light concentration of lapilli). The triangle indicates the volcano vent

Full size image

Figure II.4.3 shows the results in terms of estimated ash concentration C a, obtained by applying the VARR technique given in Eq. (13) to the measured reflectivity PPI data. Values of C a up 6 g·m−3 and of C a up 31 kg·h−1·m−2 are noted. It is worth underlining that the C a estimated pattern does not resemble the measured Z H PPI pattern in the sense that we would have expected the larger concentration in correspondence of higher reflectivity values. This difference may be explained by looking at Fig. II.4.1 taking into account the estimated ash class pattern of Fig. II.4.2. In fact, higher values of radar reflectivity are associated to a low concentration of lapilli. This means that, in order to give a comparable radar reflectivity, the concentration of coarse ash must be much larger than that of lapilli.

Fig. II.4.3
figure 3

Plan-position indicator (PPI) at 0.5° elevation of the estimated ash concentration C a [expressed in dB or 10 Log10(g m−3)], derived from the PPI scan shown in Fig. II.4.1 by applying the VARR algorithm. The triangle indicates the volcano vent

Full size image

4 Concluding Remarks

The potential of using ground-based weather radar systems for volcanic ash cloud detection and quantitative retrieval has been evaluated. The relationship between radar reflectivity factor, ash concentration, and ashfall rate has been statistically derived for various eruption regimes and ash sizes by applying a radar reflectivity microphysical model previously developed. A prototype algorithm for volcanic ash radar retrieval (VARR) has been proposed and applied. Starting from measured single-polarization reflectivity, the inversion technique to retrieve ash concentration and fall rate has been based on two cascade steps: (i) a classification of eruption regime and volcanic ash category and (ii) estimation of ash concentration and fall rate.

An application of the VARR technique has been finally shown taking into consideration the eruption f the Grímsvötn volcano in Iceland on November 2004. Volume scan data from a Doppler C-band radar, located at 260 km from the volcano vent, have been processed by means of VARR. Examples of the achievable VARR products have been discussed.