. Data insertion in volcanic ash cloud forecasting. Annals of Geophysics, 57.

During the eruption of Eyjafjallajökull in April and May 2010, the London Volcanic Ash Advisory Centre demonstrated the importance of infrared (IR) satellite imagery for monitoring volcanic ash and validating the Met Office operational model, NAME. This model is used to forecast ash dispersion and forms much of the basis of the advice given to civil aviation. NAME requires a source term describing the properties of the eruption plume at the volcanic source. Elements of the source term are often highly uncertain and significant effort has therefore been invested into the use of satellite observations of ash clouds to constrain them. This paper presents a data insertion method, where satellite observations of downwind ash clouds are used to create effective ‘virtual sources’ far from the vent. Uncertainty in the model output is known to increase over the duration of a model run, as inaccuracies in the source term, meteorological data and the parameterizations of the modelled processes accumulate. This new technique, where the dispersion model (DM) is ‘reinitialized’ part­way through a run, could go some way to addressing this.


I. INTRODUCTION
atellite imagery is an important tool for detecting and monitoring volcanic ash clouds.IR satellite sensors are used for imaging ash day and night and performing retrievals of the physical properties of ash clouds [e.g.Wen and Rose, 1994;Francis et al., 2012;Pavolonis et al., 2013].We present a novel method to combine IR observations and dispersion modelling for volcanic ash forecasting, and give a brief overview of some of the current methods.Here, the term eruption plume is used to describe a column of ash erupting from the volcano vent.Ash which has been passively transported by wind is described as downwind or distal.
When using volcanic ash DMs such as the Numerical Atmosphericdispersion Modelling Environment (NAME) [Jones et al., 2007], many of the eruption source parameters (ESP) contributing to the source term (e.g.eruption plume height, mass emission rate) need to be estimated, often with high uncertainty, which can cause large uncertainties in model output [Devenish et al., 2012a].Furthermore, errors in the simulated ash cloud location in space and time can result from uncertainties in the driving meteorology [Eckhardt et al., 2008], which have been shown to cause cumulative uncertainties in model output [Dacre et al., 2011] and can lead to errors in calculated ash column loading (ACL).

S
Operationally, some of the effects of ESP uncertainty are addressed through validation of model output against remotely sensed and insitu observations prior to a forecast being issued [Webster et al., 2012].Millington et al. [2012] developed a method to enable likewith like comparison of IR satellite imagery and DM output using the fast radiative transfer model RTTOV to simulate images from the Spinning Enhanced Visible/Infrared Imager (SEVIRI) sensor onboard the Meteosat Second Generation satellite.Data assimilation (DA) is used to estimate the true state of a system where both model output and observations are uncertain.This can then be used as an initial state from which to produce a forecast for some later time.DA in this field has been approached a number of ways.Denlinger et al. [2012] presented a Bayesian method to forecast uncertainty in ash dispersion.A genetic algorithm variational approach is presented by Schmehl et al. [2011] to minimize differences between modelled and observed ash concentrations.Inversion modelling is a DA method that has been used to estimate optimized ESPs, for both volcanic ash [e.g.Stohl et al., 2011;Kristiansen et al., 2012] and SO 2 [e.g.Eckhardt et al., 2008;Flemming and Inness, 2013;Boichu et al., 2014], using later observations to reduce ESP uncertainty and hence improve DM predictions.The above methods have been shown to improve ESP estimation; however, even if the source term is known perfectly, uncertainties in model output can still increase with run time.A simple method is presented here using satellite observations to initialize DM simulations at a series of timesteps.This may halt the propagation of some uncertainty via sequential updates of the simulations instead of ESP correction, and requires little to no prior knowledge of the eruption source term.

II. METHODS
The viability of using retrievals from IR satellite observations of downwind ash clouds to initialize NAME dispersion and sequentially update NAME output (data insertion) is examined.No uncertainty analysis has yet been undertaken; this is an initial investigation which assumes negligible uncertainty in both the model and observations (see section IV for a short discussion).We use ACL and ash cloud height (ACH) estimates from the 1314 May 2010 Eyjafjallajökull ash cloud retrieved from the SEVIRI sensor following the 1Dvariational (1DVar) method of Francis et al. [2012], and meteorological data from the global version of the Met Office Unified Model (MetUM).1d) shows a large patch of ash over Greenland which is not visible in 1c) nor in 1b).It is possible to make out a pink area in that region in 1a) which may be ash; there is a negative brightness temperature (BT) difference in this region of the image (BT at 10.8 µm wavelength BT at 12.0 µm wavelength) [not shown] which could indicate the presence of ash, but it is not clearly distinguishable from background values.Fig. 13c) in Johnson et al. [2012] shows lidar and CAS derived ash concentration profiles for 14 May at 59.6°N 7.0°W.The ash layer has a peak concentration at ~800 µg m 3 and is ~2 km thick extending from ~57 km altitude.Fig. 2 shows "best guess" and data insertion (1 & 2 km) modelled profiles for the same location at 1315 UTC using both PSDs in Table 1, and a shaded region showing the approximate extent of the observed ash layer shown in Johnson et al. [2012].All of the modelled peak concentrations are in reasonable agreement with the measurement derived profiles, with those from the data insertion runs slightly higher.These layers are also ~2 km below the measured altitude (at a concentration of 200 µg m 3 ), possibly reflecting an underestimation of heights in the 1DVar retrieval.However, the thickness of these layers is 23 km and therefore in better agreement than the "best guess" source term estimate, which is ~4 km.
Figure 2: Ash concentration profiles for 1315 UTC 14 May at 59.6°N 7.0°W.The solid line is the "best guess" NAME source term estimate.Other lines are the data insertion (DI) method assuming 1 and 2 km thick ash layers using the measured distal (M) and operational (O) PSDs shown in Table 1.The line "DI 1 km PSD(M)" is from Fig. 1d).The filled box shows the approximate observed concentration profile from Fig. 13c) in Johnson et al. [2012].

IV. DISCUSSION
By assuming that the ash forms a single 12 km thick layer distributed normally in the vertical, potential multilayered ash clouds are ignored.Also, ash particles with sizes outside the SEVIRI detection range and ash obscured by overlying meteorological cloud for long time periods may not be included in the 'virtual source'.Therefore the data insertion method may produce less conservative forecasts than where the ash is initialized at the eruption plume.However, the vertical depth and distribution of the ash layer can be updated according to observations from satellitebased lidar (e.g.CALIOP) or research flights when they become available.These observations could also be used to validate the 1DVar height estimates, which correspond to the height of radiative emission and therefore may be below the top of the ash cloud for a sparse cloud [Francis et al., 2012].
Evaluation of both model and observation accuracy is challenging as neither constitute the "truth"; the model is not a true representation of reality and in cases of disagreement it is therefore unclear which is correct.A more sophisticated implementation of this scheme could address this by implementing weights that account for the model and observation uncertainties specific to each model and observation location.For historical events, epistemic uncertainties could be informed using other available data, but in an operational setting when a DM must be run in nearreal time, these may be unknown or poorly constrained.Uncertainties can be provided by the 1DVar scheme, however accurate and reliable model uncertainties are more difficult to calculate.There is ongoing work in the dispersion modelling community to better characterize and quantify both model and observational uncertainty and future work will focus on including these.
In this paper a novel approach using the Met Office NAME DM and a 1DVar IR satellite retrieval algorithm is suggested.A data insertion method is shown, using retrievals of downwind ash clouds within NAME as a snapshot from which to reinitialize ash dispersion instead of using the eruption source term.An example shows good agreement with ash position and column loading from satellite imagery, and layer thickness and peak concentrations agree reasonably with aircraft measurements, however layer altitude estimates are too low.A more sophisticated sequential update assimilation scheme should allow known uncertainties in the model and observations to be well characterized and tracked throughout to provide a forecast indicating uncertainty.
[Rose et al., 1995]ed operationally in NAME and distal PSD based on Table1fromDacre et al. [2013],derived from FAAM observations on 14 May 2010.Both the operational PSD and one based on the distal PSD from Table1inDacre et al. [2013]derived from FAAM measurements, which is more representative of the SEVIRI detection thresholds, are used for the simulations.A timeseries of simulations are then combined to produce a forecast.The presence of water in the atmosphere as clouds can obscure ash by overlying it, by ash particles becoming coated in ice, or where an ash cloud has a high water content[Rose et al., 1995], so by combining a series of model runs initialized using the observations, it is more likely that features obscured by atmospheric water in one image are captured in others and evolved with time in the dispersion model.
Table1:III.RESULTS Fig. 1a) shows a SEVIRI 'DustRGB' false color composite image at 1315 UTC on 14 May 2010 where ash shows as a pink streak extending northwest from Scotland toward Iceland and as a yellow region west of Iceland [Devenish et al., 2012b], b) is a NAME simulation for that time using a source term based on the Met Office's "best guess" of the plume height, calculated eruption rate and the operational PSD in Table 1 [Webster et al., 2012], and c) is retrieved ACL.The data insertion forecast d) is a combination of the greatest ACL values (for each grid cell) of four NAME simulations ending at 1315 UTC 14 May, initialized using retrievals from 2115 UTC 13 May, 0115, 0515 & 0915 UTC 14 May, assuming 1 km layer thickness and normal vertical distribution at the time of insertion.Both the "best guess" and data insertion simulations are in good agreement with the ash position in 1a & c), however 1b) shows lower ACL over the northeast and north of Iceland and much higher values west of Iceland than either the retrieval or data insertion simulation.Fig.