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Malini K – Validation of Kriging

Malini K received her Master of Science in Computer Science and Engineering (CSE). Her research work was supervised by Prof. K S Rajan. Here’s a summary of her research work on Validation of Kriging to Understand ‘Volcanic Eruption Event Temperature Profiles’ To Improve Gradients in Numerical Weather Prediction Models:

When volcanoes erupt explosively, the ash gets airborne and reaches till stratosphere vertically, and then spreads laterally to synoptic scales due to wind. Detecting the presence of ash in the atmosphere accurately is a challenge. Although several remote, in-situ, and near-sensing techniques exist, due to the variety and complexity of the physical and chemical properties of ash, that get ejected, even within between spells of the eruption of a given volcanic event, it is hard to distinguish it from other aerosols such as desert sand, ice clouds, etc. The false positives in the detection render these solutions unreliable and inconsistent. As a result, weather parameters are explored as an alternative strategy to predict the presence of ash. In specific, the temperature variable is identified as the proxy variable to study the spatial distribution of ash in the atmosphere. There are several beneficial reasons to study temperature because the values do not vary randomly, low-cost equipment suffice to gather the data, the diurnal variations can be accounted for easily, the ability to convert scales from negative to positive metrics for numerical calculations does not vary significantly with ash type, etc. For this research, the eruption of the Icelandic volcano, Eyjafjallajokull is chosen, due to the severe negative impact it created on the economy across Europe in April and May 2010. World Meteorological Organisation (WMO) and International Civil Aviation Authority (ICAO) together have created Volcanic Ash Advisory Center (VAAC) to model the concentration and simulate the transportation of ash to inform the hazards of ash fall to various stakeholders across the world. The London VAAC used a VAFTDM known as Numerical Atmospheric-dispersion Modelling Environment (NAME) to model the ash spread. This theoretical model had several limitations, chief of them being related to the accuracy of the Numerical Weather Prediction (NWP) models that were supported for ash modelling. The UK Met Office dealing with the NWP associated with the NAME model supported and offered multiple models such as Unified Model (UM), ECMWF, and a few others to predict the weather variables. Since each VAAC uses its own NWP model that varies spatially and temporally, a benchmarking exercise was conducted to compare the VAFTD models. The benchmarking allowed the use of either NCEP or ECMWF NWP. For this research, NCEP NWP was chosen for analysis since x out of 12 VAFTD models used this NWP. On analysis, it was observed that NCEP NWP had large grid sizes and therefore small-scale spatial variations were not effectively captured, especially in the vertical extent, even across years. So, we chose to analyse the interpolation model used in the generation of gridded outputs for NCEP since there were limitations observed in using the Ensemble Kalman Filter (EnKF) technique. In this context, the suitability of regression-based interpolation methods was considered to model the NCEP values better. A sample of flight-based ash temperature data from the 2010 Eyjafjallajokull eruption was taken for case study. Initially, a linear regression technique was employed. Since the outputs of the Multiple Linear Regression (MLR) method were not observed to be highly accurate in modelling the missing day’s temperature using 3 out of 4 day’s samples, a non-linear regression method, based on geostatistics, known as Kriging was chosen. Kriging, originally developed for ore mining problems, was cross applied to an atmospheric problem in this research. The advantage of using Kriging is that it generates prediction surfaces. In addition, when compared against deterministic methods such as IDW, Kriging can produce error estimates too. Initially, the Simple Kriging (SK) method was applied to generate profiles. Since the nature of the dataset was highly clustered and heteroskedastic, a better kriging method was required to model the variations better. A stochastic variant of kriging called Empirical Bayesian Kriging (implemented in ArcGIS version 10.3) was chosen to account for the non-stationary random field. Again, the effect of using an intrinsic random function (non-transitive) in generating and fitting the semivariograms over the use of a transitive function-based approach (by making transformations) was compared. The former is denoted as EBK while the latter is referred to as EBKT. The non-linear kriging-based interpolation estimates were observed to be significantly better than the traditional MLR method when compared against the NCEP NWP estimates. In addition, a detailed error analysis was performed to compare the 3 kriging methods. The EBK method outperformed SK and EBKT in both point estimates and block grade averages. The EBK prediction surfaces were then overlaid on NCEP NWP rasters, in the area of interest, to generate risk maps. The aviation domain was chosen as a case study to apply this methodology. Using the risk map generated, Go/No-Go Zones were identified to mark the presence of airborne ash to ensure safe routes for the operation of aircrafts.

 

June 2023