Post-Depositional Movement of Methanesulphonic Acid at Law Dome, Antarctica, and the Influence of Accumulation Rate

A series of ice cores from sites with different snow-accumulation rates across Law Dome, East Antarctica, was investigated for methanesulphonic acid (MSA) movement. The precipitation at these sites (up to 35 km apart) is influenced by the same air masses, the principal difference being the accumulation rate. At the low-accumulation-rate W20k site (0.17 in ice equivalent), MSA was completely relocated from the summer to winter layer. Moderate movement was observed at the intermediate-accumulation-rate site (0.7 in ice equivalent), Dome Summit South (DSS), while there was no evidence of movement at the high-accumulation-rate DE08 site (1.4 in ice equivalent). The main DSS record of MSA covered the epoch AD 1727-2000 and was used to investigate temporal post-depositional changes. Co-deposition of MSA and sea-salt ions was observed of the surface layers, outside of the main summer MSA peak, which complicates interpretation of these peaks as evidence of movement in deeper layers. A seasonal study of the 273 year DSS record revealed MSA migration predominantly from summer into autumn (in the up-core direction), but this migration was suppressed during the Tambora (1815) and unknown (1809) volcanic eruption period, and enhanced during an epoch (1770-1800) with high summer nitrate levels. A complex interaction between the gradients in nss-sulphate, nitrate and sea salts (which are influenced by accumulation rate) is believed to control the rate and extent of movement of MSA.

(Table 1) Snow accumulation in the McMurdo Dry Valleys

Snowfall was measured at 11 sites in the McMurdo Dry Valleys to determine its magnitude, its temporal changes, and spatial patterns. Annual values ranged from 3 to 50 mm water equivalent with the highest values nearest the coast and decreasing inland. A particularly strong spatial gradient exists in Taylor Valley, probably resulting from local uplift conditions at the coastal margin and valley topography that limits migration inland. More snow occurs in winter near the coast, whereas inland no seasonal pattern is discernable. This may be due, again, to local uplift conditions, which are common in winter. We find no influence of the distance to the sea ice edge. Katabatic winds play an important role in transporting snow to the valley bottoms and essentially double the precipitation. That much of the snow accumulation sublimates prior to making a hydrologic contribution underscores the notion that the McMurdo Dry Valleys are indeed an extreme polar desert.

Accumulation and climate at Peyto Glacier, Canada

The eight-year record of mass balance of Peyto Glacier is correlated to meteorological data measured near the glacier and at Lake Louise 30 km to the south. The period investigated includes the llighest and lowest accumulations for the past 40 years. The primar'y controls of net annual balance are seen to be the depth of the 'winter sno,y pack and the temperature record during the summer. Extensive summer snowfalls in the ablation area can slow down melt rates very considerably and affect the net annual balance positively. The variable nature of winter accumulation and its influence on snowline retreat and ice melt is illustrated by three years' data.

Characteristics of the Vernagtferner mass balance for the period from 1964 to 2014

The main characteristics of the Vernagtferner mass balance are sumarized in the table below. The mass balance years from 1964/65 to 2003/2004 are listed. The table includes the total area of the glacier (basis for the calculations), the equilibrium line altitude (ELA), percentage of the accumulation area in relation to the total area (AAR) and the specific net mass balance in mm w.e. (water equivalent) per year. It becomes clear that, after a rather minor growth period in the mid 1970's, the glacier continually lost mass since the beginning of the 1980's. Besides that, a clear increase of mass balance years with extreme mass losses could be observed in the last decade. The "glacier-friendly" summer with a well-balanced mass balance in 1999 could only interrupt the series of years with extreme mass losses, but this means no change in the trend. The minor mass loss in 1999 was caused by a winter snow cover above average, which prevented the glacier from becoming snow free over large areas and thus resulted in a lower ice melt. Although real summer conditions in 2000 were mainly restricted to August and produced a snow free area only slightly larger than in 1999, there have been further ice losses. This trend of negative mass balance continued also in the years 2001 and 2002. Nevertheless, the losses are moderate because a smaller part of the glacier became ice free until autumn (appr. 50 %). The summer 2003 caused a loss of ice in a dimension never seen since the beginning of the scientific investigations. This resulted from a combination of different factors: after only a moderate winter snowcover the glacier became snow free very early. For the first time the ablation area spanned over the entire glacier (blue fields in the mass balance tables!). Only one short snowfall event interrupted the ablation period, which lasted twice as long as in the years of large losses in the 1990's. The extreme mass loss in 2003 will also influence the mass balance in the following year 2004. The graphical representation of the elevation distribution of the specific mass balance together with the absolute mass balance can be found individually for each year by choosing one of the mass balance values from the table. These diagrams also include the area-height-distribution of the glacier and the ablation area. A tabular version of the numeric values in dependence of the elevation, provided separately for the accumulation area, the ablation area and the total glacier, can be found in colums "Persistent Identifier". The tables include the results for three different parts of the glacier and for the total glacier.

Tab. 1: Mass changes and balances 1982/83 for stakes on the Inland Ice at Päkitsup ilordlia north-east of Jakobshavn

In connection with hydropower investigations in West Greenland mass balance measurements have been carried out 1982/83 on the Inland lce at Päkitsup ilordlia north-east of Jakobshavn. The mass balance was measured at seven stakes drilled into the ice at altitudinal intervals of 200 metres from 300 m to 1500 m a.s.l. The measurements show that mass balance conditions in the Jakobshavn area must have been abnormally positive for the 1982/83 hydrological year.

Table 1: Basic mass-balance, Peyto Glacier, 1967/1974

The eight-year record of mass balance of Peyto Glacier is correlated to meteorological data measured near the glacier and at Lake Louise 30 km to the south. The period investigated includes the llighest and lowest accumulations for the past 40 years. The primar'y controls of net annual balance are seen to be the depth of the 'winter sno,y pack and the temperature record during the summer. Extensive summer snowfalls in the ablation area can slow down melt rates very considerably and affect the net annual balance positively. The variable nature of winter accumulation and its influence on snowline retreat and ice melt is illustrated by three years' data.

Table 2: Firn temperature, ram resistance, mass balance and submergence velo city measurements on Colle Gnifetti

Distributional patterns of glaciological parameters at the Colle Gnifetti core drilling site are described and their interrelationships are brietly discussed. Observations within a stake network established in 1980 furnish information about snow accumulation (short term balance), submergence velocity of ice tlow (long term balance), ram hardness (melt layer stratigraphy), and firn temperature. In addition, a numerical model was used to estimate local variations of available radiant energy. Melt layer formation is considerably more intensive on the south facing parts of the firn saddie where incoming radiation is high. These melt layers seem to effectively protect some of the fallen snow from wind erosion. As a result, balance ist up to one order of magnitude larger on south facing slopes. Heat applied to the surface is therefore positively correlated with balance, whereas the relation between solar radiation and firn temperature is less dear. Distributional patterns of submergence velocity confirm that the observed spatial variability of surface balance is representative for longer time periods and greatly intluences the time scale and the stratigraphy of firn and ice cores from Colle Gnifetti.

Glacier mass balance measurements on Fourcade and Polar Club glacier, King George Island

The east coast of the AP is highly influenced by cold and dry air masses stemming from the adjacent Weddell Sea. By the contrary, the west coast jointly with the South Shetland Islands are directly exposed to the humid and relatively warm air masses from the South Pacific Ocean carried by the strong and persistent westerly winds. Systematic glaciological field studies are very scarce on both sides of the AP, among them can be mentioned a mass-balance program performed continuously since summer 1998/99 by the Instituto Antártico Argentino (IAA) on Vega Island, James Ross Archipelago, on the northeastern flank of the AP. Another continuous plurianual glaciological research has been initiated in 2010 jointly by the University of Bonn and the IAA at the Fourcade Glacier on King George Island (KGI) within the framework of the ESF project IMCOAST (FK 03F0617B). Two transects of mass balance stakes were installed from the top of the Warszawa Ice Dome down to the border of the glaciers Fourcade and Polar Club, to serve for calibration and validation of modeling efforts. The stakes were measured at the beginning and end of each summer field campaign in November 2010, February - March 2011, January - March 2012, and especially during the austral winter 2012 up to March 2013 every 10 to 14 days depending on weather conditions. During the austral winter 2013 and until June 2014 the measurements were conducted every 20 to 30 days, weather permitting. Snow density was measured as well in every field trip from June 2012 until June 2104, establishing a rather homogeneous value along the different parts of the glacier. Snow density in late summer, rho_s is usually higher than the one in late winter, rho_w. Seasonal average values were calculated for the area covered by the mass balance stakes, being rho_s= 471 Kg/m**3 and rho_w = 363 Kg/m**3.

Volume changes of Jacobshavn Isbrae between 1985, 1997 and 2007

Following three decades of relative stability, Jakobshavn Isbrae, West Greenland, underwent dramatic thinning, retreat and speed-up starting in 1998. To assess the amount of ice loss, we analyzed 1985 aerial photos and derived a 40 m grid digital elevation model (DEM). We also obtained a 2007 40 m grid SPOT DEM covering the same region. Comparison of the two DEMs over an area of ~4000 km**2 revealed a total ice loss of 160 ± 4 km**3, with 107 ± 0.2 km**3 in grounded regions (0.27 mm eustatic sea-level rise) and 53 ± 4 km**3 from the disintegration of the floating tongue. Comparison of the DEMs with 1997 NASA Airborne Topographic Mapper data indicates that this ice loss essentially occurred after 1997, with +0.7 ± 5.6 km**3 between 1985 and 1997 and -160 ± 7 km**3 between 1997 and 2007. The latter is equivalent to an average specific mass balance of -3.7 ± 0.2 m/a over the study area. Previously reported thickening of the main glacier during the early 1990s was accompanied by similar-magnitude thinning outside the areas of fast flow, indicating that the land-based ice continued reacting to longer-term climate forcing.

Surface mass balance along the K-transect in West Greenland

A 21-year record is presented of surface mass balance measurements along the K-transect. The series covers the period 1990-2011. Data are available at 8 sites along a transect over an altitude range of 390 - 1850 m at approximately 67° N in West Greenland. The surface mass balance gradient is on average 3.8 x 10**-3 m w.e./m, and the mean equilibrium line altitude is 1553 m a.s.l. Only the lower 3 sites within 10 km of the margin experience a significant increasing trend in the ablation over the entire period.

Methodologies for Collision Risk Computation = Metodologías para Cálculo de Riesgo de Colisión

Esta tesis aborda metodologías para el cálculo de riesgo de colisión de satélites. La minimización del riesgo de colisión se debe abordar desde dos puntos de vista distintos. Desde el punto de vista operacional, es necesario filtrar los objetos que pueden presentar un encuentro entre todos los objetos que comparten el espacio con un satélite operacional. Puesto que las órbitas, del objeto operacional y del objeto envuelto en la colisión, no se conocen perfectamente, la geometría del encuentro y el riesgo de colisión deben ser evaluados. De acuerdo con dicha geometría o riesgo, una maniobra evasiva puede ser necesaria para evitar la colisión. Dichas maniobras implican un consumo de combustible que impacta en la capacidad de mantenimiento orbital y por tanto de la visa útil del satélite. Por tanto, el combustible necesario a lo largo de la vida útil de un satélite debe ser estimado en fase de diseño de la misión para una correcta definición de su vida útil, especialmente para satélites orbitando en regímenes orbitales muy poblados. Los dos aspectos, diseño de misión y aspectos operacionales en relación con el riesgo de colisión están abordados en esta tesis y se resumen en la Figura 3. En relación con los aspectos relacionados con el diseño de misión (parte inferior de la figura), es necesario evaluar estadísticamente las características de de la población espacial y las teorías que permiten calcular el número medio de eventos encontrados por una misión y su capacidad de reducir riesgo de colisión. Estos dos aspectos definen los procedimientos más apropiados para reducir el riesgo de colisión en fase operacional. Este aspecto es abordado, comenzando por la teoría descrita en [Sánchez-Ortiz, 2006]T.14 e implementada por el autor de esta tesis en la herramienta ARES [Sánchez-Ortiz, 2004b]T.15 proporcionada por ESA para la evaluación de estrategias de evitación de colisión. Esta teoría es extendida en esta tesis para considerar las características de los datos orbitales disponibles en las fases operacionales de un satélite (sección 4.3.3). Además, esta teoría se ha extendido para considerar riesgo máximo de colisión cuando la incertidumbre de las órbitas de objetos catalogados no es conocida (como se da el caso para los TLE), y en el caso de querer sólo considerar riesgo de colisión catastrófico (sección 4.3.2.3). Dichas mejoras se han incluido en la nueva versión de ARES [Domínguez-González and Sánchez-Ortiz, 2012b]T.12 puesta a disposición a través de [SDUP,2014]R.60. En fase operacional, los catálogos que proporcionan datos orbitales de los objetos espaciales, son procesados rutinariamente, para identificar posibles encuentros que se analizan en base a algoritmos de cálculo de riesgo de colisión para proponer maniobras de evasión. Actualmente existe una única fuente de datos públicos, el catálogo TLE (de sus siglas en inglés, Two Line Elements). Además, el Joint Space Operation Center (JSpOC) Americano proporciona mensajes con alertas de colisión (CSM) cuando el sistema de vigilancia americano identifica un posible encuentro. En función de los datos usados en fase operacional (TLE o CSM), la estrategia de evitación puede ser diferente debido a las características de dicha información. Es preciso conocer las principales características de los datos disponibles (respecto a la precisión de los datos orbitales) para estimar los posibles eventos de colisión encontrados por un satélite a lo largo de su vida útil. En caso de los TLE, cuya precisión orbital no es proporcionada, la información de precisión orbital derivada de un análisis estadístico se puede usar también en el proceso operacional así como en el diseño de la misión. En caso de utilizar CSM como base de las operaciones de evitación de colisiones, se conoce la precisión orbital de los dos objetos involucrados. Estas características se han analizado en detalle, evaluando estadísticamente las características de ambos tipos de datos. Una vez concluido dicho análisis, se ha analizado el impacto de utilizar TLE o CSM en las operaciones del satélite (sección 5.1). Este análisis se ha publicado en una revista especializada [Sánchez-Ortiz, 2015b]T.3. En dicho análisis, se proporcionan recomendaciones para distintas misiones (tamaño del satélite y régimen orbital) en relación con las estrategias de evitación de colisión para reducir el riesgo de colisión de manera significativa. Por ejemplo, en el caso de un satélite en órbita heliosíncrona en régimen orbital LEO, el valor típico del ACPL que se usa de manera extendida es 10-4. Este valor no es adecuado cuando los esquemas de evitación de colisión se realizan sobre datos TLE. En este caso, la capacidad de reducción de riesgo es prácticamente nula (debido a las grandes incertidumbres de los datos TLE) incluso para tiempos cortos de predicción. Para conseguir una reducción significativa del riesgo, sería necesario usar un ACPL en torno a 10-6 o inferior, produciendo unas 10 alarmas al año por satélite (considerando predicciones a un día) o 100 alarmas al año (con predicciones a tres días). Por tanto, la principal conclusión es la falta de idoneidad de los datos TLE para el cálculo de eventos de colisión. Al contrario, usando los datos CSM, debido a su mejor precisión orbital, se puede obtener una reducción significativa del riesgo con ACPL en torno a 10-4 (considerando 3 días de predicción). Incluso 5 días de predicción pueden ser considerados con ACPL en torno a 10-5. Incluso tiempos de predicción más largos se pueden usar (7 días) con reducción del 90% del riesgo y unas 5 alarmas al año (en caso de predicciones de 5 días, el número de maniobras se mantiene en unas 2 al año). La dinámica en GEO es diferente al caso LEO y hace que el crecimiento de las incertidumbres orbitales con el tiempo de propagación sea menor. Por el contrario, las incertidumbres derivadas de la determinación orbital son peores que en LEO por las diferencias en las capacidades de observación de uno y otro régimen orbital. Además, se debe considerar que los tiempos de predicción considerados para LEO pueden no ser apropiados para el caso de un satélite GEO (puesto que tiene un periodo orbital mayor). En este caso usando datos TLE, una reducción significativa del riesgo sólo se consigue con valores pequeños de ACPL, produciendo una alarma por año cuando los eventos de colisión se predicen a un día vista (tiempo muy corto para implementar maniobras de evitación de colisión).Valores más adecuados de ACPL se encuentran entre 5•10-8 y 10-7, muy por debajo de los valores usados en las operaciones actuales de la mayoría de las misiones GEO (de nuevo, no se recomienda en este régimen orbital basar las estrategias de evitación de colisión en TLE). Los datos CSM permiten una reducción de riesgo apropiada con ACPL entre 10-5 y 10-4 con tiempos de predicción cortos y medios (10-5 se recomienda para predicciones a 5 o 7 días). El número de maniobras realizadas sería una en 10 años de misión. Se debe notar que estos cálculos están realizados para un satélite de unos 2 metros de radio. En el futuro, otros sistemas de vigilancia espacial (como el programa SSA de la ESA), proporcionarán catálogos adicionales de objetos espaciales con el objetivo de reducir el riesgo de colisión de los satélites. Para definir dichos sistemas de vigilancia, es necesario identificar las prestaciones del catalogo en función de la reducción de riesgo que se pretende conseguir. Las características del catálogo que afectan principalmente a dicha capacidad son la cobertura (número de objetos incluidos en el catalogo, limitado principalmente por el tamaño mínimo de los objetos en función de las limitaciones de los sensores utilizados) y la precisión de los datos orbitales (derivada de las prestaciones de los sensores en relación con la precisión de las medidas y la capacidad de re-observación de los objetos). El resultado de dicho análisis (sección 5.2) se ha publicado en una revista especializada [Sánchez-Ortiz, 2015a]T.2. Este análisis no estaba inicialmente previsto durante la tesis, y permite mostrar como la teoría descrita en esta tesis, inicialmente definida para facilitar el diseño de misiones (parte superior de la figura 1) se ha extendido y se puede aplicar para otros propósitos como el dimensionado de un sistema de vigilancia espacial (parte inferior de la figura 1). La principal diferencia de los dos análisis se basa en considerar las capacidades de catalogación (precisión y tamaño de objetos observados) como una variable a modificar en el caso de un diseño de un sistema de vigilancia), siendo fijas en el caso de un diseño de misión. En el caso de las salidas generadas en el análisis, todos los aspectos calculados en un análisis estadístico de riesgo de colisión son importantes para diseño de misión (con el objetivo de calcular la estrategia de evitación y la cantidad de combustible a utilizar), mientras que en el caso de un diseño de un sistema de vigilancia, los aspectos más importantes son el número de maniobras y falsas alarmas (fiabilidad del sistema) y la capacidad de reducción de riesgo (efectividad del sistema). Adicionalmente, un sistema de vigilancia espacial debe ser caracterizado por su capacidad de evitar colisiones catastróficas (evitando así in incremento dramático de la población de basura espacial), mientras que el diseño de una misión debe considerar todo tipo de encuentros, puesto que un operador está interesado en evitar tanto las colisiones catastróficas como las letales. Del análisis de las prestaciones (tamaño de objetos a catalogar y precisión orbital) requeridas a un sistema de vigilancia espacial se concluye que ambos aspectos han de ser fijados de manera diferente para los distintos regímenes orbitales. En el caso de LEO se hace necesario observar objetos de hasta 5cm de radio, mientras que en GEO se rebaja este requisito hasta los 100 cm para cubrir las colisiones catastróficas. La razón principal para esta diferencia viene de las diferentes velocidades relativas entre los objetos en ambos regímenes orbitales. En relación con la precisión orbital, ésta ha de ser muy buena en LEO para poder reducir el número de falsas alarmas, mientras que en regímenes orbitales más altos se pueden considerar precisiones medias. En relación con los aspectos operaciones de la determinación de riesgo de colisión, existen varios algoritmos de cálculo de riesgo entre dos objetos espaciales. La Figura 2 proporciona un resumen de los casos en cuanto a algoritmos de cálculo de riesgo de colisión y como se abordan en esta tesis. Normalmente se consideran objetos esféricos para simplificar el cálculo de riesgo (caso A). Este caso está ampliamente abordado en la literatura y no se analiza en detalle en esta tesis. Un caso de ejemplo se proporciona en la sección 4.2. Considerar la forma real de los objetos (caso B) permite calcular el riesgo de una manera más precisa. Un nuevo algoritmo es definido en esta tesis para calcular el riesgo de colisión cuando al menos uno de los objetos se considera complejo (sección 4.4.2). Dicho algoritmo permite calcular el riesgo de colisión para objetos formados por un conjunto de cajas, y se ha presentado en varias conferencias internacionales. Para evaluar las prestaciones de dicho algoritmo, sus resultados se han comparado con un análisis de Monte Carlo que se ha definido para considerar colisiones entre cajas de manera adecuada (sección 4.1.2.3), pues la búsqueda de colisiones simples aplicables para objetos esféricos no es aplicable a este caso. Este análisis de Monte Carlo se considera la verdad a la hora de calcular los resultados del algoritmos, dicha comparativa se presenta en la sección 4.4.4. En el caso de satélites que no se pueden considerar esféricos, el uso de un modelo de la geometría del satélite permite descartar eventos que no son colisiones reales o estimar con mayor precisión el riesgo asociado a un evento. El uso de estos algoritmos con geometrías complejas es más relevante para objetos de dimensiones grandes debido a las prestaciones de precisión orbital actuales. En el futuro, si los sistemas de vigilancia mejoran y las órbitas son conocidas con mayor precisión, la importancia de considerar la geometría real de los satélites será cada vez más relevante. La sección 5.4 presenta un ejemplo para un sistema de grandes dimensiones (satélite con un tether). Adicionalmente, si los dos objetos involucrados en la colisión tienen velocidad relativa baja (y geometría simple, Caso C en la Figura 2), la mayor parte de los algoritmos no son aplicables requiriendo implementaciones dedicadas para este caso particular. En esta tesis, uno de estos algoritmos presentado en la literatura [Patera, 2001]R.26 se ha analizado para determinar su idoneidad en distintos tipos de eventos (sección 4.5). La evaluación frete a un análisis de Monte Carlo se proporciona en la sección 4.5.2. Tras este análisis, se ha considerado adecuado para abordar las colisiones de baja velocidad. En particular, se ha concluido que el uso de algoritmos dedicados para baja velocidad son necesarios en función del tamaño del volumen de colisión proyectado en el plano de encuentro (B-plane) y del tamaño de la incertidumbre asociada al vector posición entre los dos objetos. Para incertidumbres grandes, estos algoritmos se hacen más necesarios pues la duración del intervalo en que los elipsoides de error de los dos objetos pueden intersecar es mayor. Dicho algoritmo se ha probado integrando el algoritmo de colisión para objetos con geometrías complejas. El resultado de dicho análisis muestra que este algoritmo puede ser extendido fácilmente para considerar diferentes tipos de algoritmos de cálculo de riesgo de colisión (sección 4.5.3). Ambos algoritmos, junto con el método Monte Carlo para geometrías complejas, se han implementado en la herramienta operacional de la ESA CORAM, que es utilizada para evaluar el riesgo de colisión en las actividades rutinarias de los satélites operados por ESA [Sánchez-Ortiz, 2013a]T.11. Este hecho muestra el interés y relevancia de los algoritmos desarrollados para la mejora de las operaciones de los satélites. Dichos algoritmos han sido presentados en varias conferencias internacionales [Sánchez-Ortiz, 2013b]T.9, [Pulido, 2014]T.7,[Grande-Olalla, 2013]T.10, [Pulido, 2014]T.5, [Sánchez-Ortiz, 2015c]T.1. ABSTRACT This document addresses methodologies for computation of the collision risk of a satellite. Two different approaches need to be considered for collision risk minimisation. On an operational basis, it is needed to perform a sieve of possible objects approaching the satellite, among all objects sharing the space with an operational satellite. As the orbits of both, satellite and the eventual collider, are not perfectly known but only estimated, the miss-encounter geometry and the actual risk of collision shall be evaluated. In the basis of the encounter geometry or the risk, an eventual manoeuvre may be required to avoid the conjunction. Those manoeuvres will be associated to a reduction in the fuel for the mission orbit maintenance, and thus, may reduce the satellite operational lifetime. Thus, avoidance manoeuvre fuel budget shall be estimated, at mission design phase, for a better estimation of mission lifetime, especially for those satellites orbiting in very populated orbital regimes. These two aspects, mission design and operational collision risk aspects, are summarised in Figure 3, and covered along this thesis. Bottom part of the figure identifies the aspects to be consider for the mission design phase (statistical characterisation of the space object population data and theory computing the mean number of events and risk reduction capability) which will define the most appropriate collision avoidance approach at mission operational phase. This part is covered in this work by starting from the theory described in [Sánchez-Ortiz, 2006]T.14 and implemented by this author in ARES tool [Sánchez-Ortiz, 2004b]T.15 provided by ESA for evaluation of collision avoidance approaches. This methodology has been now extended to account for the particular features of the available data sets in operational environment (section 4.3.3). Additionally, the formulation has been extended to allow evaluating risk computation approached when orbital uncertainty is not available (like the TLE case) and when only catastrophic collisions are subject to study (section 4.3.2.3). These improvements to the theory have been included in the new version of ESA ARES tool [Domínguez-González and Sánchez-Ortiz, 2012b]T.12 and available through [SDUP,2014]R.60. At the operation phase, the real catalogue data will be processed on a routine basis, with adequate collision risk computation algorithms to propose conjunction avoidance manoeuvre optimised for every event. The optimisation of manoeuvres in an operational basis is not approached along this document. Currently, American Two Line Element (TLE) catalogue is the only public source of data providing orbits of objects in space to identify eventual conjunction events. Additionally, Conjunction Summary Message (CSM) is provided by Joint Space Operation Center (JSpOC) when the American system identifies a possible collision among satellites and debris. Depending on the data used for collision avoidance evaluation, the conjunction avoidance approach may be different. The main features of currently available data need to be analysed (in regards to accuracy) in order to perform estimation of eventual encounters to be found along the mission lifetime. In the case of TLE, as these data is not provided with accuracy information, operational collision avoidance may be also based on statistical accuracy information as the one used in the mission design approach. This is not the case for CSM data, which includes the state vector and orbital accuracy of the two involved objects. This aspect has been analysed in detail and is depicted in the document, evaluating in statistical way the characteristics of both data sets in regards to the main aspects related to collision avoidance. Once the analysis of data set was completed, investigations on the impact of those features in the most convenient avoidance approaches have been addressed (section 5.1). This analysis is published in a peer-reviewed journal [Sánchez-Ortiz, 2015b]T.3. The analysis provides recommendations for different mission types (satellite size and orbital regime) in regards to the most appropriate collision avoidance approach for relevant risk reduction. The risk reduction capability is very much dependent on the accuracy of the catalogue utilized to identify eventual collisions. Approaches based on CSM data are recommended against the TLE based approach. Some approaches based on the maximum risk associated to envisaged encounters are demonstrated to report a very large number of events, which makes the approach not suitable for operational activities. Accepted Collision Probability Levels are recommended for the definition of the avoidance strategies for different mission types. For example for the case of a LEO satellite in the Sun-synchronous regime, the typically used ACPL value of 10-4 is not a suitable value for collision avoidance schemes based on TLE data. In this case the risk reduction capacity is almost null (due to the large uncertainties associated to TLE data sets, even for short time-to-event values). For significant reduction of risk when using TLE data, ACPL on the order of 10-6 (or lower) seems to be required, producing about 10 warnings per year and mission (if one-day ahead events are considered) or 100 warnings per year (for three-days ahead estimations). Thus, the main conclusion from these results is the lack of feasibility of TLE for a proper collision avoidance approach. On the contrary, for CSM data, and due to the better accuracy of the orbital information when compared with TLE, ACPL on the order of 10-4 allows to significantly reduce the risk. This is true for events estimated up to 3 days ahead. Even 5 days ahead events can be considered, but ACPL values down to 10-5 should be considered in such case. Even larger prediction times can be considered (7 days) for risk reduction about 90%, at the cost of larger number of warnings up to 5 events per year, when 5 days prediction allows to keep the manoeuvre rate in 2 manoeuvres per year. Dynamics of the GEO orbits is different to that in LEO, impacting on a lower increase of orbits uncertainty along time. On the contrary, uncertainties at short prediction times at this orbital regime are larger than those at LEO due to the differences in observation capabilities. Additionally, it has to be accounted that short prediction times feasible at LEO may not be appropriate for a GEO mission due to the orbital period being much larger at this regime. In the case of TLE data sets, significant reduction of risk is only achieved for small ACPL values, producing about a warning event per year if warnings are raised one day in advance to the event (too short for any reaction to be considered). Suitable ACPL values would lay in between 5•10-8 and 10-7, well below the normal values used in current operations for most of the GEO missions (TLE-based strategies for collision avoidance at this regime are not recommended). On the contrary, CSM data allows a good reduction of risk with ACPL in between 10-5 and 10-4 for short and medium prediction times. 10-5 is recommended for prediction times of five or seven days. The number of events raised for a suitable warning time of seven days would be about one in a 10-year mission. It must be noted, that these results are associated to a 2 m radius spacecraft, impact of the satellite size are also analysed within the thesis. In the future, other Space Situational Awareness Systems (SSA, ESA program) may provide additional catalogues of objects in space with the aim of reducing the risk. It is needed to investigate which are the required performances of those catalogues for allowing such risk reduction. The main performance aspects are coverage (objects included in the catalogue, mainly limited by a minimum object size derived from sensor performances) and the accuracy of the orbital data to accurately evaluate the conjunctions (derived from sensor performance in regards to object observation frequency and accuracy). The results of these investigations (section 5.2) are published in a peer-reviewed journal [Sánchez-Ortiz, 2015a]T.2. This aspect was not initially foreseen as objective of the thesis, but it shows how the theory described in the thesis, initially defined for mission design in regards to avoidance manoeuvre fuel allocation (upper part of figure 1), is extended and serves for additional purposes as dimensioning a Space Surveillance and Tracking (SST) system (bottom part of figure below). The main difference between the two approaches is the consideration of the catalogue features as part of the theory which are not modified (for the satellite mission design case) instead of being an input for the analysis (in the case of the SST design). In regards to the outputs, all the features computed by the statistical conjunction analysis are of importance for mission design (with the objective of proper global avoidance strategy definition and fuel allocation), whereas for the case of SST design, the most relevant aspects are the manoeuvre and false alarm rates (defining a reliable system) and the Risk Reduction capability (driving the effectiveness of the system). In regards to the methodology for computing the risk, the SST system shall be driven by the capacity of providing the means to avoid catastrophic conjunction events (avoiding the dramatic increase of the population), whereas the satellite mission design should consider all type of encounters, as the operator is interested on avoiding both lethal and catastrophic collisions. From the analysis of the SST features (object coverage and orbital uncertainty) for a reliable system, it is concluded that those two characteristics are to be imposed differently for the different orbital regimes, as the population level is different depending on the orbit type. Coverage values range from 5 cm for very populated LEO regime up to 100 cm in the case of GEO region. The difference on this requirement derives mainly from the relative velocity of the encounters at those regimes. Regarding the orbital knowledge of the catalogues, very accurate information is required for objects in the LEO region in order to limit the number of false alarms, whereas intermediate orbital accuracy can be considered for higher orbital regimes. In regards to the operational collision avoidance approaches, several collision risk algorithms are used for evaluation of collision risk of two pair of objects. Figure 2 provides a summary of the different collision risk algorithm cases and indicates how they are covered along this document. The typical case with high relative velocity is well covered in literature for the case of spherical objects (case A), with a large number of available algorithms, that are not analysed in detailed in this work. Only a sample case is provided in section 4.2. If complex geometries are considered (Case B), a more realistic risk evaluation can be computed. New approach for the evaluation of risk in the case of complex geometries is presented in this thesis (section 4.4.2), and it has been presented in several international conferences. The developed algorithm allows evaluating the risk for complex objects formed by a set of boxes. A dedicated Monte Carlo method has also been described (section 4.1.2.3) and implemented to allow the evaluation of the actual collisions among a large number of simulation shots. This Monte Carlo runs are considered the truth for comparison of the algorithm results (section 4.4.4). For spacecrafts that cannot be considered as spheres, the consideration of the real geometry of the objects may allow to discard events which are not real conjunctions, or estimate with larger reliability the risk associated to the event. This is of particular importance for the case of large spacecrafts as the uncertainty in positions of actual catalogues does not reach small values to make a difference for the case of objects below meter size. As the tracking systems improve and the orbits of catalogued objects are known more precisely, the importance of considering actual shapes of the objects will become more relevant. The particular case of a very large system (as a tethered satellite) is analysed in section 5.4. Additionally, if the two colliding objects have low relative velocity (and simple geometries, case C in figure above), the most common collision risk algorithms fail and adequate theories need to be applied. In this document, a low relative velocity algorithm presented in the literature [Patera, 2001]R.26 is described and evaluated (section 4.5). Evaluation through comparison with Monte Carlo approach is provided in section 4.5.2. The main conclusion of this analysis is the suitability of this algorithm for the most common encounter characteristics, and thus it is selected as adequate for collision risk estimation. Its performances are evaluated in order to characterise when it can be safely used for a large variety of encounter characteristics. In particular, it is found that the need of using dedicated algorithms depend on both the size of collision volume in the B-plane and the miss-distance uncertainty. For large uncertainties, the need of such algorithms is more relevant since for small uncertainties the encounter duration where the covariance ellipsoids intersect is smaller. Additionally, its application for the case of complex satellite geometries is assessed (case D in figure above) by integrating the developed algorithm in this thesis with Patera’s formulation for low relative velocity encounters. The results of this analysis show that the algorithm can be easily extended for collision risk estimation process suitable for complex geometry objects (section 4.5.3). The two algorithms, together with the Monte Carlo method, have been implemented in the operational tool CORAM for ESA which is used for the evaluation of collision risk of ESA operated missions, [Sánchez-Ortiz, 2013a]T.11. This fact shows the interest and relevance of the developed algorithms for improvement of satellite operations. The algorithms have been presented in several international conferences, [Sánchez-Ortiz, 2013b]T.9, [Pulido, 2014]T.7,[Grande-Olalla, 2013]T.10, [Pulido, 2014]T.5, [Sánchez-Ortiz, 2015c]T.1.