Andreev's Theorem on hyperbolic polyhedra

In 1970, E. M. Andreev published a classification of all three-dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, $C$, Andreev's Theorem provides five classes of linear inequalities, depending on $C$, for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing $C$ with the assigned dihedral angles. Andreev's Theorem also shows that the resulting polyhedron is unique, up to hyperbolic isometry. Andreev's Theorem is both an interesting statement about the geometry of hyperbolic 3-dimensional space, as well as a fundamental tool used in the proof for Thurston's Hyperbolization Theorem for 3-dimensional Haken manifolds. It is also remarkable to what level the proof of Andreev's Theorem resembles (in a simpler way) the proof of Thurston. We correct a fundamental error in Andreev's proof of existence and also provide a readable new proof of the other parts of the proof of Andreev's Theorem, because Andreev's paper has the reputation of being ``unreadable''.Comment: To appear les Annales de l'Institut Fourier. 47 pages and many figures. Revision includes significant modification to section 4, making it shorter and more rigorous. Many new references include

A Peak Wind Probability Forecast Tool for Kennedy Space Center and Cape Canaveral Air Force Station

This conference abstract describes the development of a peak wind forecast tool to assist forecasters in determining the probability of violating launch commit criteria (LCC) at Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS) in east-central Florida. The peak winds are an important forecast element for both the Space Shuttle and Expendable Launch Vehicle (ELV) programs. The LCC define specific peak wind thresholds for each launch operation that cannot be exceeded in order to ensure the safety of the vehicle. The 45th Weather Squadron (45 WS) has found that peak winds are a challenging parameter to forecast, particularly in the cool season months of October through April. Based on the importance of forecasting peak winds, the 45 WS tasked the Applied Meteorology Unit (AMU) to develop a short-range peak-wind forecast tool to assist in forecasting LCC violatioas.The tool will include climatologies of the 5-minute mean end peak winds by month, hour, and direction, and probability distributions of the peak winds as a function of the 5-minute mean wind speeds

Update to the Lightning Probability Forecast Equations at Kennedy Space Center/Cape Canaveral Air Force Station, Florida

This conference presentation describes the improvement of a set of lightning probability forecast equations that are used by the 45th Weather Squadron forecasters for their daily 1100 UTC (0700 EDT) weather briefing during the warm season months of May- September. This information is used for general scheduling of operations at Cape Canaveral Air Force Station and Kennedy Space Center. Forecasters at the Spaceflight Meteorology Group also make thunderstorm forecasts during Shuttle flight operations. Five modifications were made by the Applied Meteorology Unit: increased the period of record from 15 to 17 years, changed the method of calculating the flow regime of the day, calculated a new optimal layer relative humidity, used a new smoothing technique for the daily climatology, and used a new valid area. The test results indicated that the modified equations showed and increase in skill over the current equations, good reliability, and an ability to distinguish between lightning and non-lightning days

Modifications to the Objective Lightning Probability Forecast Tool at Kennedy Space Center/Cape Canaveral Air Force Station, Florida

The 45th Weather Squadron (45 WS) at Cape Canaveral Air Force Station (CCAFS) includes the probability of lightning occurrence in their 24-Hour and Weekly Planning Forecasts, briefed at 0700 EDT for daily operations planning on Kennedy Space Center (KSC) and CCAFS. This forecast is based on subjective analyses of model and observational data and output from an objective tool developed by the Applied Meteorology Unit (AMU). This tool was developed over two phases (Lambert and Wheeler 2005, Lambert 2007). It consists of five equations, one for each warm season month (May-Sep), that calculate the probability of lightning occurrence for the day and a graphical user interface (GUI) to display the output. The Phase I and II equations outperformed previous operational tools by a total of 56%. Based on this success, the 45 WS tasked the AMU with Phase III to improve the tool further

Developing a Peak Wind Probability Forecast Tool for Kennedy Space Center and Cape Canaveral Air Force Station

This conference presentation describes the development of a peak wind forecast tool to assist forecasters in determining the probability of violating launch commit criteria (LCC) at Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS) in east-central Florida. The peak winds are an important forecast element for both the Space Shuttle and Expendable Launch Vehicle (ELV) programs. The LCC define specific peak wind thresholds for each launch operation that cannot be exceeded in order to ensure the safety of the vehicle. The 45th Weather Squadron (45 WS) has found that peak winds are a challenging parameter to forecast, particularly in the cool season months of October through April. Based on the importance of forecasting peak winds, the 45 WS tasked the Applied Meteorology Unit (AMU) to develop a short-range peak-wind forecast tool to assist in forecasting LCC violations. The tool will include climatologies of the 5-minute mean and peak winds by month, hour, and direction, and probability distributions of the peak winds as a function of the 5-minute mean wind speeds

Update to the Objective Lightning Probability Forecast Tool in use at Cape Canaveral Air Force Station, Florida

This conference poster describes the improvement of a set of lightning probability forecast equations that are used by the 45th Weather Squadron forecasters for their daily 1100 UTC (0700 EDT) weather briefing during the warm season months of May-September. This information is used for general scheduling of operations at Cape Canaveral Air Force Station and Kennedy Space Center. Forecasters at the Spaceflight Meteorology Group also make thunderstorm forecasts during Shuttle flight operations. Five modifications were made by the Applied Meteorology Unit: increased the period of record from 15 to 17 years, changed the method of calculating the flow regime of the day, calculated a new optimal layer relative humidity, used a new smoothing technique for the daily climatology, and used a new valid area. The test results indicated that the modified equations showed and increase in skill over the current equations, good reliability and an ability to distinguish between lightning and non-lightning days

Update to the Objective Lightning Probability Forecast Tool in Use at Cape Canaveral Air Force Station, Florida

This conference presentation describes the improvement of a set of lightning probability forecast equations that are used by the 45th Weather Squadron forecasters for their daily 1100 UTC (0700 EDT) weather briefing during the warm season months of May-September. This information is used for general scheduling of operations at Cape Canaveral Air Force Station and Kennedy Space Center. Forecasters at the Spaceflight Meteorology Group also make thunderstorm forecasts during Shuttle flight operations. Five modifications were made by the Applied Meteorology Unit: increased the period of record from 15 to 17 years, changed the method of calculating the flow regime of the day, calculated a new optimal layer relative humidity, used a new smoothing technique for the daily climatology, and used a new valid area. The test results indicated that the modified equaitions showed and increase in skill over the current equations, good reliability, and an ability to distinguish between lightning and non-lightning days

Developing a Peak Wind Probability Forecast Tool for Kennedy Space Center and Cape Canaveral Air Force Station

No abstract availabl

A Sounding-based Severe Weather Tool to Support Daily Operations at Kennedy Space Center and Cape Canaveral Air Force Station

People and property at Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS) are at risk when severe weather occurs. Strong winds, hail and tornadoes can injure individuals and cause costly damage to structures if not properly protected. NASA's Launch Services Program and Ground Systems Development and Operations Program and other KSC programs use the daily and weekly severe weather forecasts issued by the 45th Weather Squadron (45 WS) to determine if they need to limit an activity such as working on gantries, or protect property such as a vehicle on a pad. The 45 WS requested the Applied Meteorology Unit (AMU) develop a warm season (May-September) severe weather tool for use in the Meteorological Interactive Data Display System (MIDDS) based on the late morning, 1500 UTC (1100 local time), CCAFS (XMR) sounding. The 45 WS frequently makes decisions to issue a severe weather watch and other severe weather warning support products to NASA and the 45th Space Wing in the late morning, after the 1500 UTC sounding. The results of this work indicate that certain stability indices based on the late morning XMR soundings can depict differences between days with reported severe weather and days with no reported severe weather. The AMU determined a frequency of reported severe weather for the stability indices and implemented an operational tool in MIDDS

Objective Lightning Forecasting at Kennedy Space Center and Cape Canaveral Air Force Station using Cloud-to-Ground Lightning Surveillance System Data

The 45th Weather Squadron (45 WS) at Cape Canaveral Air-Force Station (CCAFS)ln Florida issues a probability of lightning occurrence in their daily 24-hour and weekly planning forecasts. This information is used for general planning of operations at CCAFS and Kennedy Space Center (KSC). These facilities are located in east-central Florida at the east end of a corridor known as 'Lightning Alley', an indication that lightning has a large impact on space-lift operations. Much of the current lightning probability forecast is based on a subjective analysis of model and observational data and an objective forecast tool developed over 30 years ago. The 45 WS requested that a new lightning probability forecast tool based on statistical analysis of more recent historical warm season (May-September) data be developed in order to increase the objectivity of the daily thunderstorm probability forecast. The resulting tool is a set of statistical lightning forecast equations, one for each month of the warm season, that provide a lightning occurrence probability for the day by 1100 UTC (0700 EDT) during the warm season