Volcanic eruptions release a large amount of volcanic ash, which can pose hazard to human and animal health, land transportation, and aviation safety. Volcanic Ash Transport and Dispersion (VATD) models are critical tools to provide advisory information and timely volcanic ash forecasts. Due to the complexity and the uncertainty of many dynamic processes involved in the volcanic ash distribution, even the most advanced VATDs today are not capable to reproduce the reality accurately. It is necessary to integrate available observations in the models for more accurate predictions by employing data assimilation techniques.In addition to a valid VATD, ash emissions, usually used as input so the model, are crucial for the forecasts of the locations and shapes of the ash cloud. In general, the eruption source parameters for the construction of the emission are poorly known, which include Plume Height (PH), Mass Eruption Rate (MER) and vertical distribution of the emission rate. Even when PH can be obtained from ground-based observations in some cases, the emission source computed from this PH and a MER empirically related to this PH remains highly uncertain. Not to mention the volcanoes which are unmonitored or hardly accessible, the PH can merely be retrieved from satellite data with a large uncertainty and temporal insufficiency. Fortunately, satellite instruments are able to observe the movement of an ash cloud with a global coverage. Therefore, this thesis focuses on the estimation of the volcanic ash emissions by assimilating Ash Mass Loadings (AMLs) retrieved from satellite data to improve the accuracy of forecasts. Among all available data assimilation approaches, Four Dimensional Variational assimilation (4D-Var) approach was chosen as a suitable one. 4D-Var seeks an optimal set of parameters, including model states, initial conditions and systematic parameters, by minimizing a cost function which combines the model simulations and observations over a period according to their statistic properties. 4D-Var with a standard form of the cost function is tested in a twin experiment framework, where synthetic observations of ash columns computed from model simulated 3D ash concentrations are used. The results show that Standard 4DVar (Std4DVar) is unable to reconstruct the vertical profile of the emission. The injection layer containing the maximal amount of emission rate cannot be accurately determined. This failure is attributed to the fact that AML data lacks vertical resolution. Using the AMLs, it is difficult to reconstruct the volcanic ash emission presented in forms of an eruption column.To deal with this problem, a Trajectory-based 4D-Var (Trj4DVar) approach is proposed. Trj4DVar reformulates the cost function in a regression type which computes the total difference between observed ash columns and a linear combination of simulated trajectories coupled with a priori emission knowledge. The results of twin experiments show that, for most cases, Trj4DVar is capable of estimating the input emission column when a large assimilation window (> 6 hours) is used. The twin experiments is repeated where different values of noise are given in the synthetic observations or perturbations are used in the meteorologic data. The outcomes show that there is still a small possibility that Trj4DVar fails to determine the injection height accurately. Being disturbed by the weather condition (light and cloud, etc) at that moment, satellite instrument can be hampered to observe the ash cloud, which may increase the possibility of failure for the use of Trj4DVar. To remedy this, Trj4DVar is modified to incorporate observations of PH and MER in addition to satellite AMLs. The modified Trj4DVar is shown to be able accurately estimate the injection height based on the results of twin experiments.When it comes to using real-life field data, the situation is more complicated. The detection of volcanic ash can be disturbed by the weather condition such as water vapor. This will result in observations of undetected or wrongly-detected ash. Besides, many sensors ,such as UV and visible sensors, have limited temporal coverage which can only observe during daylight. In order to find effective method in dealing with the temporal and sometimes spatial insufficiency of the data, investigations are carried out on how to use the data properly to benefit more and produce a reasonable estimate. A prepossessing procedure and guidance on the proper use of satellite data are presented.Finally, a deeper analysis is given on the failure of using Std4DVar in this application. It is found that using Std4DVar to assimilate remote sensing data can be tricky. Remote sensing measures quantities that combine several state variables. This creates Sensor-Induced Correlations between the state variables which share the same observation variable and may be physically unrelated. This may cause numerical problems resulting in a low convergence rate or inaccurate estimates of parameters using gradient-based variational assimilation if an erroneous or improper specification of error statistics is adopted. These problems are usually ignored when a reasonable result is obtained, or are avoided by reducing the 3D model to a 2D model. However, it results in significantly unreliable and misguiding estimates for the application in this thesis. Two criteria are proposed to quantify the negative effects of the SICs, which give indications of the effectiveness of the assimilation process and the forecast quality. They are simple to implement and very practical for the use of remote sensing data. They are tested in the twin experiments. The results show that they are able to give evaluation on the design and configuration of the assimilation system with remote sensing data.