In this study, we investigate a strategy to accelerate the data assimilation (DA) algorithm. Based on evaluations of the computational time, the analysis step of the assimilation turns out to be the most expensive part. After a study of the characteristics of the ensemble ash state, we propose a mask-state algorithm which records the sparsity information of the full ensemble state matrix and transforms the full matrix into a relatively small one. This will reduce the computational cost in the analysis step. Experimental results show the mask-state algorithm significantly speeds up the analysis step. Subsequently, the total amount of computing time for volcanic ash DA is reduced to an acceptable level. The mask-state algorithm is generic and thus can be embedded in any ensemble-based DA framework. Moreover, ensemble-based DA with the mask-state algorithm is promising and flexible, because it implements exactly the standard DA without any approximation and it realizes the satisfying performance without any change in the full model.@en

Remote sensing, as a powerful tool for monitoring atmospheric phenomena, has been playing an increasingly important role in inverse modeling. Remote sensing instruments measure quantities that often combine several state variables as one. This creates very strong correlations between the state variables that share the same observation variable. This may cause numerical problems resulting in a low convergence rate or inaccurate estimates in gradient-based variational assimilation if improper error statistics are used. In this paper, two criteria or scoring rules are proposed to quantify the numerical robustness of assimilating a specific set of remote sensing observations and to quantify the reliability of the estimates of the parameters. The criteria are derived by analyzing how the correlations are created via shared observation data and how they may influence the process of variational data assimilation. Experimental tests are conducted and show a good level of agreement with theory. The results illustrate the capability of the criteria to indicate the reliability of the assimilation process. Both criteria can be used with observing system simulation experiments (OSSEs) and in combination with other verification scores.@en

Using data assimilation (DA) to improve model forecast accuracy is a powerful approach that requires available observations. Infrared satellite measurements of volcanic ash mass loadings are often used as input observations for the assimilation scheme. However, because these primary satellite-retrieved data are often two-dimensional (2-D) and the ash plume is usually vertically located in a narrow band, directly assimilating the 2-D ash mass loadings in a three-dimensional (3-D) volcanic ash model (with an integral observational operator) can usually introduce large artificial/spurious vertical correlations.

In this study, we look at an approach to avoid the artificial vertical correlations by not involving the integral operator. By integrating available data of ash mass loadings and cloud top heights, as well as data-based assumptions on thickness, we propose a satellite observational operator (SOO) that translates satellite-retrieved 2-D volcanic ash mass loadings to 3-D concentrations. The 3-D SOO makes the analysis step of assimilation comparable in the 3-D model space.

Ensemble-based DA is used to assimilate the extracted measurements of ash concentrations. The results show that satellite DA with SOO can improve the estimate of volcanic ash state and the forecast. Comparison with both satellite-retrieved data and aircraft in situ measurements shows that the effective duration of the improved volcanic ash forecasts for the distal part of the Eyjafjallajökull volcano is about 6 h.@en

The 2010 Eyjafjallajökull volcano eruption had serious consequences to civil aviation. This has initiated a lot of research on volcanic ash forecasting in recent years. For forecasting the volcanic ash transport after eruption onset, a volcanic ash transport and diffusion model (VATDM) needs to be run with Eruption Source Parameters (ESPs) such as plume height and mass eruption rate as input, and with data assimilation techniques to continuously improve the forecast. Reliable and accurate ash measurements are crucial for providing successful ash clouds advices. In the first phase of this research work, simulated aircraft-based volcanic ash measurements, will be assimilated into a transport model to identify the potential benefit of this kind of observations in an assimilation system. The results show that assimilating aircraft-based measurements can improve the state of ash clouds, and can provide an improved forecast. We also show that for an advice on the aeroplane flying level, aircraft-based measurements should preferably be taken at this level. Furthermore it is shown that in order to make an acceptable advice for aviation decision makers, accurate knowledge about uncertainties of ESPs and measurements is of great importance. The forecast accuracy of distal volcanic ash clouds is important for providing valid aviation advice during volcanic ash eruptions. However, because the distal part of a volcanic ash plume is far from the volcano, the influence of eruption information on this part becomes rather indirect and uncertain, resulting in inaccurate volcanic ash forecasts in these distal areas. In this thesis, we use real-life aircraft in situ observations, measured in the North-West part of Germany during the 2010 Eyjafjallajökull eruption, in an ensemble-based data assimilation system to investigate the potential improvement on the forecast accuracy with regard to the distal volcanic ash plume. We show that the error of the analyzed volcanic ash state can be significantly reduced by assimilating real-life in situ measurements. After assimilation, it is shown that the model-based aviation advice for Germany, the Netherlands and Luxembourg can be improved. We suggest that with suitable aircrafts measuring once per day across the distal volcanic ash plume, the description and prediction of volcanic ash clouds in these areas can be improved significantly. Among the data assimilation approaches, the ensemble Kalman filter (EnKF) is a well-known and popular method. A proper covariance localization strategy in the analysis step of EnKF is essential for reducing spurious covariances caused by the finite ensemble size, as shown for this application for assimilation of aircraft in situ measurements. After analyzing the characteristics of the physical forecast error covariances, we present a two-way tracking approach to define the localization matrix for covariance localization. The result shows that the Two-way-tracking Localized EnKF (TL-EnKF) effectively maintains the correctly specified physical covariances and largely reduces the spurious ones. The computational cost of TL-EnKF is also evaluated and is shown to be advantageous for both serial and parallel implementations. Compared to the commonly used distance-based covariance localization, the two-way tracking approach is shown to be more suitable. In addition, the covariance inflation approach is verified as an additional improvement to TL-EnKF to achieve more accurate results. A timely prediction requires that the computations of the data assimilation system can be performed quickly (at least than the Wall-clock). We therefore investigate strategies for accelerating the data assimilation algorithm. Based on evaluations of the computational time, the analysis step of the assimilation turns out to be the most expensive part. After a study on the characteristics of the ensemble ash state, we propose a mask-state algorithm which records the sparsity information of the full ensemble state matrix and transforms the full matrix into a relatively small one. This will reduce the computational cost in the analysis step. Experimental results show the mask-state algorithm significantly speeds up the analysis step. Subsequently, the total amount of computing time for volcanic ash data assimilation is reduced to an acceptable level. The mask-state algorithm is generic and thus can be embedded in any ensemble-based data assimilation framework. Moreover, ensemble-based data assimilation with the mask-state algorithm is promising and flexible, because it implements exactly the standard data assimilation without any approximation and it realizes the satisfying performance without any change of the full model. Infrared satellite measurements of volcanic ash mass loadings are often used as input observations for the assimilation scheme. However, these satellite-retrieved data are often two-dimensional (2D), and cannot easily be combined with a three-dimensional (3D) volcanic ash model to improve the volcanic ash state. By integrating available data including ash mass loadings, cloud top heights and thickness information, we propose a satellite observational operator (SOO) that translates satellite-retrieved 2D volcanic ash mass loadings to 3D concentrations at the top layer of the ash cloud. Ensemble-based data assimilation is used to assimilate the extracted measurements of ash concentrations. The results show that satellite data assimilation can force the volcanic ash state to match the satellite observations, and that it improves the forecast of the ash state. Comparison with highly accurate aircraft in situ measurements shows that the effective duration of the improved volcanic ash forecasts is about a half day.@en

In this paper, we reconstruct the vertical profile of volcanic ash emissions by assimilating satellite data and ground-based observations using a modified trajectory-based 4D-Var (Trj4DVar) approach. In our previous work, we found that the lack of vertical resolution in satellite ash column data can result in a poor estimation of the injection layer where the ash is emitted into the atmosphere. The injection layer is crucial for the forecast of volcanic ash clouds. To improve estimation, Trj4DVar was implemented, and it has shown increased performance in twin experiments using synthetic observations. However, there are some cases with real satellite data where Trj4DVar has difficulty in obtaining an accurate estimation of the injection layer. To remedy this, we propose a modification of Trj4DVar, test it with synthetic twin experiments, and evaluate real data performance. The results show that the modified Trj4DVar is able to accurately estimate the injection height (location of the maximal emission rate) by incorporating the plume height (top of the ash plume) and mass eruption rate data obtained from ground-based observations near the source into the assimilation system. This will produce more accurate emission estimations and more reliable forecasts of volcanic ash clouds. Also provided are two strategies on the preprocessing and proper use of satellite data.@en

The forecast accuracy of distal volcanic ash clouds is important for providing valid aviation advice during volcanic ash eruption. However, because the distal part of volcanic ash plume is far from the volcano, the influence of eruption information on this part becomes rather indirect and uncertain, resulting in inaccurate volcanic ash forecasts in these distal areas. In our approach, we use real-life aircraft in situ observations, measured in the northwestern part of Germany during the 2010 Eyjafjallajokull eruption, in an ensemble-based data assimilation system combined with a volcanic ash transport model to investigate the potential improvement on the forecast accuracy with regard to the distal volcanic ash plume. We show that the error of the analyzed volcanic ash state can be significantly reduced through assimilating real-life in situ measurements. After a continuous assimilation, it is shown that the aviation advice for Germany, the Netherlands and Luxembourg can be significantly improved. We suggest that with suitable aircrafts measuring once per day across the distal volcanic ash plume, the description and prediction of volcanic ash clouds in these areas can be greatly improved.@en

Since the 2010 Eyjafjallajökull volcano eruption caused a big problem to aviation and economy, improvement on volcanic ash forecast has been put onto the research agenda. Satellite-based measurements are considered as the most common and cheapest type of volcanic ash observations. However, due to its intrinsic functionality, satelliteretrived two-dimensional data can not be easily and directly combined with a three-dimensional volcanic ash model to improve volcanic ash forecasts continuously. Here we propose a satellite observational operator to transfer 2D volcanic ash mass loadings to 3D concentrations. The uncertainties of reconstructed 3D ash concentrations are also quantified. Sequential data assimilation is used to continuously assimilate the reconstructed volcanic ash concentrations. The results are evaluated in a multiobservational network including satellite-based measurements and aircraft in-situ measurements. Here we show for long-time assimilating satellite-based measurements, Ensemble Squre Root Filter (EnSR), as a common sequential data assimilation technique, is more efficient than Ensemble Kalman Filter (EnKF) because the ensemble size required for EnSR is considerable less than the ensemble size of EnKF for a comparable assimilation performance. Moreover, the forecast after assimilation is validated to be accurate and valid within 15 hours. @en

Wildfires are one of the major environmental issue in the Mediterranean area. Prescribed burning (PB) is increasingly used in Europe as a practice to reduce fire risk, through dead fine fuel reduction. Several studies have focused on fire effects on vegetation and soil microbial community, but very few on ecosystem processes involved in water cycle. This study aims to estimate interception by the litter and fermentation layer and the successive evaporation flux in laboratory conditions, using a water balance and 2H and 18O isotopes mass balance calculation, in order to assess PB effects on the hydrology and ecosystem in pine plantations. PB was carried out in spring 2014 in three pine plantations of Southern Italy, dominated by Pinus halepensis (Cilento, Vallo di Diano e Alburni National Park, CVDANP), P. pinaster (Vesuvio National Park, VNP) and P. pinea (Castel Volturno Nature Reserve, CVNR). A dataset concerning the effects of PB on vegetation structure, floristic composition, microbial biomass and activity in the fermentation layer and 5-cm of soil beneath is available for the same stands. In each plantation, two cores of litter and fermentation layer were sampled in a burned area and in a near unburned area (control), respectively, with a collector to extract an “undisturbed” core. Then, each core was transferred in a lysimeter installed in the Water Lab of Delft University of Technology. In total, three lysimeters were set up and each experiment was carried out in duplicate. The laboratory had constant temperature, and both temperature and relative humidity were recorded every 15 minutes. To simulate rainfall, 1 litre of tap water was sprinkled uniformly on the lysimeter with a plant spray (equivalent to 32 mm of rain). The precipitation was sprinkled every 3 days for a period of two months. Soil moisture and temperature were measured during the experiment every 15 minutes in the top and bottom of the litter and fermentation layer. Interception water was collected for isotope analysis from every layer with Rhizon soil moisture samplers by applying a vacuum with 5 ml syringes. Samples were collected two times per day (in the morning and in the evening) and at two different depths for each layer ( 4 cm and 7 cm in litter layer and 10 and 15 cm in fermentation layer) until 2 days after rain simulation. Water samples were analysed with laser spectrometry using the liquid water isotope analyser (LGR-LWIA). The influence of different litter layers and PB on interception and litter layer evaporation was assessed. Then, the evaporation flux measured using the lysimeter was compared with the calculated evaporation flux using the isotopes mass balance. Generally, the preliminary results indicate a slight increase in evaporation flux in burned areas compared to the controls, in P. pinea and P. pinaster stands. By contrast, in P. halepensis stand, a significant decrease in evaporation flux was detected in prescribed burned plot. The isotope mass balance method to measure litter evaporation is promising and could be used in future, in-situ, measurements of evaporation from the litter layer. @en

The 2010 Eyjafjallajökull volcano eruption had serious consequences to civil aviation. This has initiated a lot of research on volcanic ash forecast in recent years. Ensemble-based data assimilation uses the observation data to improve the parameter and state estimation and subsequently the volcanic ash forecast accuracy. Due to the computational complexity of ensemble-based algorithms and the large scale of real-life applications, application of these methods usually introduces a large computational cost, particularly in the analysis step of assimilation processes. Because the other time-consuming part in the single CPU case, the forecast step, can be efficiently and easily parallelized. In this study, we focus on speeding up of the analysis step. For volcanic ash assimilation of aircraft-based measurements, the most time-consuming part in the analysis step has been shown to be the computation of the Kalman gain matrix. After a careful study on the characteristics of ensemble ash states, we propose a model-reduced Kalman gain (MR-Gain) approach which transforms the ensemble state matrix into a low-rank matrix by a multiplication with an index matrix which recorded the sparsity information of the ensemble state matrix, and thus the computational cost of all the ensemble-related matrix multiplications are reduced. After the computation of Kalman gain, using the previously recorded state index, the full analyzed ensemble states are reconstructed. The result shows the MR-Gain approach is exact, which can be used to replace the original full matrix with a much low computation cost. Computer experiments show that the computing time for the analysis step with the new approach is a factor of ten times faster than the conventional analysis step. The result also shows that with the accelerated analysis step in volcanic ash assimilation system, the total amount of computing time for volcanic ash forecast can be significantly reduced by up to a factor of 5. @en