Master thesis in meteorology, oceanography and climate, 30 hp. Case study of CAT over the North Atlantic Ocean. Kristoffer Molarin

Transcription

1 Master thesis in meteorology, oceanography and climate, 30 hp Case study of CAT over the North Atlantic Ocean Kristoffer Molarin Supervisors: Tomas Mårtensson and Gunilla Svensson Department of Meteorology Stockholm university May 28, 2013

2 Abstract This study investigates 32 clear-air turbulence (CAT) reports from 2011 over the North Atlantic Ocean using two widely known turbulence indices, TI1 and TI2, developed by Ellrod and Knapp in A turbulence index is based on fields from a numerical weather prediction model and express the probability of encountering CAT. The CAT reports were measured by commercial aircraft at cruise altitude (around m), and the indices were calculated with two different model resolutions (0.225 and horizontal grid spacing) using data from the Integrated Forecast System (IFS) at the European Center for Medium- Range Weather Forecasts (ECMWF). The results in this study show that both TI1 and TI2 had a correct CAT forecast for the same event in 22 of the cases, and only six observations were not predicted by either index. Also, in 17 of the 32 cases, TI1 and TI2 had a correct CAT forecast using both resolutions. The jet stream connected to a strong vertical wind shear was responsible for triggering the majority of the CAT cases. TI1 and TI2 therefore show to be two good turbulence indices for these cases. Four cases, over southern Greenland (one case), west of Ireland (one case) and Newfoundland (two cases), were more thoroughly investigated. CAT was predicted by both indices using both resolutions in all four cases. It could be confirmed by using satellite images, analysis maps and soundings that there was a high probability that CAT was present at the time of all four observations, indicating that the CAT forecasts were all correct. The indices also obtained overall a good result regarding the 24 hour forecast prior to these four observations, and overall a fairly good result for the 48 hour forecast.

3 Contents 1 Introduction 3 2 Theory Theory of turbulence Properties and causes of clear-air turbulence Different types of instability Dynamic instability/inertial instability Static instability Shear instability Kelvin-Helmholtz instability Identifying clear-air turbulence using satellite images Ellrod and Knapp s turbulence indices Deformation Turbulence index 1 and Calculation from numerical model data of clear-air turbulence Data Turbulence reporting systems The International Civil Aviation Organisation categories of turbulence Maximum Derived Equivalent Vertical Gust velocity Aircraft Meteorological Data Relay Model data Thresholds for the turbulence indices Results Summary of the results Case studies of four turbulence events Southern Greenland West of Ireland Newfoundland Discussion 29 7 Conclusions and summary 32 2

4 1 Introduction 1 INTRODUCTION Turbulence is a phenomena which is mainly associated with the planetary boundary layer, where the turbulence arises due to contact with the Earth s surface. Turbulence may however also occur on higher altitudes, undisturbed by the surface. There are many definitions of what clear-air turbulence (CAT) is. In this report CAT is defined as non-convective turbulence in cloud free areas in the troposphere outside the planetary boundary layer. Mountain-wave turbulence is also not included in this definition. CAT is mostly created through shear instability in areas with strong wind shear, where the wind speed changes significantly over a distance. The jet stream is often associated with CAT, since vertical and horizontal wind shear are connected to the jet stream. CAT has been known since World War two, when fighter jets flew in CAT areas. Today CAT is of importance regarding safety onboard aircraft. CAT is often only a nuisance, but it can cause structural damage to aircraft, human injuries and even fatalities. Therefore a CAT forecast is desirable (Ellrod and Knapp, 1992; Dutton and Panofsky, 1970; Wallace and Hobbs, 2006). CAT is a micro-scale phenomena and usually exists for a short time period (Overeem, 2002). As of today, most CAT forecasts are based on macro-scale phenomena, and this is the main reason why today s CAT forecasts are not very reliable. Improvements are needed for discovering areas of risks regarding aviation safety, but CAT has not been thoroughly investigated, and the mechanics behind turbulence are still being studied. There have been a number of studies trying to pinpoint the parameters which can best indicate areas with the presence of CAT (e.g. Sharman et al. (2011)). CAT observations are reported through instrumented aircraft reports, such as Aircraft Meteorological Data Relay (AMDAR). The intensity of the turbulence, flight level and position are included in these reports. The intensity is divided into no, light, moderate and severe turbulence and depends on how much of the aircraft s altitude, position and speed that is changed due to the turbulence. These three parameters will change very little when the turbulence intensity is low, compared to severe turbulence, when the aircraft s position changes considerably. The size of the aircraft plays a big role since different sizes will experience different intensity levels. When forecasting turbulence an index is used. These CAT indices are based on numerical model output and may provide a good CAT forecast, but these indices are not always correct (Turner and Bysouth, 1999). Examples of CAT indices are turbulence index 1 and 2, TI1 and TI2, (Ellrod and Knapp, 1992), Brown index (Brown, 1973) and Dutton index (Dutton, 1980). Usually, a CAT warning is given after it has been reported by pilots. This study is triggered by the project REsearch on a CRusier Enabled Air Transport Environment (RECREATE). The project is funded through the Seventh Framework Programme of the European Commission, and there are several different European countries working on this project, including Sweden and the Swedish Defence Research Agency (FOI). The main purpose of this RECREATE project is to reduce the use of fuel and carbon dioxide emissions for civil aircraft by introducing air-to-air refueling on long haul flights. Pilots always use weather charts before take-off to plan the route. The route plan depends on expected winds and forecasted weather, whereas this determines the amount of fuel the aircraft needs at take-off and thus affect the take-off weight. If the aircraft departs with 3

5 1 INTRODUCTION less fuel than needed to arrive at its destination, it will need even less fuel during take-off, since the fuel itself weighs a lot. The required fuel will be provided during the air-to-air refueling. Three possible regions where this process may be possible for transatlantic flights are over southern Greenland, west of Ireland and Newfoundland. However, if there is too much turbulence during the air-to-air refueling process, it is difficult and dangerous to perform it. Therefore it is necessary to know in advance if turbulence will be present during this operation. This is the meteorological part of the RECREATE project (Mårtensson et al., 2011). In this report a number of CAT cases are studied over the North Atlantic Ocean. AMDAR reports for the whole year of 2011 are compared with model data from the European Centre for Medium-Range Weather Forecasts (ECMWF). This study aims to answer the following questions: 1. How well does TI1 and TI2 predict CAT? 2. What triggers CAT to occur? 3. Are the CAT forecasts different using a fine and a coarse resolution in the model? 4. Studying four specific cases more thoroughly, can it be confirmed using external material (such as soundings, satellite images and analysis charts) that CAT occurred, and could CAT be predicted 24 and 48 hours prior to the observation? 4

6 2 THEORY 2 Theory 2.1 Theory of turbulence Turbulence can be proposed as irregular swirls of motion, eddies, and these eddies will eventually dissipate due to friction (Stull, 1988). Turbulence can also be created by larger scale atmospheric motions, which also can be influenced by the turbulence (Lester, 1994). Reynolds averaging can be used in order to describe turbulence through statistical measures, and making it possible to model turbulence. Reynolds averaging implies that a variable is described as the sum of a mean value and a perturbation. In the case of turbulence, the wind is divided into a mean wind and a perturbation part according to Stull (1988) (see Figure 1): u = ū + u (1) where the mean part ū represents the mean horizontal wind and the perturbation part u is the wave effect, or turbulence effect, superimposed on the mean wind. Figure 1: The wind may be split into a mean part (a) and a perturbation part (b) (Stull, 1988). Large vertical gradients in temperature and wind-velocity fields are especially responsible for turbulence in the atmosphere. There are a few atmospheric processes (which may strengthen or weaken one another) that causes these large gradients. One process is a wind velocity profile in the planetary boundary layer which is caused by the friction of the airflow at Earth s surface. There is also uneven heating of Earth s surface, which leads to differences in thermal convection. Another process is condensation and crystallization in cloud-forming processes which causes release of heat and leads to differences in temperature. A large vertical gradient may also be caused by convergence and interaction of different air masses near fronts (this can also occur in the upper atmosphere) that results in large horizontal differences in wind velocity and temperature, and by air that is modified when flowing over mountains, creating waves on the lee side (Vinnichenko et al., 1980). 5

7 2.2 Properties and causes of clear-air turbulence 2 THEORY 2.2 Properties and causes of clear-air turbulence The dimensions of CAT are km horizontally along the wind direction and across the wind flow km (Meteorological Office College, 1997). The vertical dimensions are normally m, but may also be 25 m or 4500 m. The lifetime of CAT is roughly between half an hour and a whole day (Overeem, 2002). CAT is mainly located in the upper troposphere and lower stratosphere in the atmosphere (the highest probability of encountering CAT is between 10 and 15 km according to Lester (1994)) and often occurs in a strongly stable region (Pao and Goldburg, 1969). Regarding aircraft, they are influenced by turbulence when the vertical airflow varies on horizontal length scales about the length of the aircraft s size, thus 100 m (Sharman et al., 2006). There are two widely accepted mechanisms that cause CAT: firstly from a mountain barrier standing waves at the lee side, mountain waves (not included in this study), and secondly Kelvin-Helmholtz (KH) instability, which occurs in thin stable layers with strong vertical wind shear. These two mechanisms are strongest during the winter months when wind speed and horizontal temperature gradients are largest (Hopkins, 1977). The primary cause of CAT is believed to be KH instability, and there are some theoretical studies and empirical measurements that connect CAT with KH instabilities. Another theory is that this instability only is the triggering mechanism (Hopkins, 1977; Keller, 1990; Lester, 1994). CAT can also be created due to strong shear waves which are a result from strong winds coming across the tops of thunderstorm clouds. According to Lester (1994), CAT may also be produced by increasing vertical wind shear through internal gravity waves generated by boundary layer convection, mountains, thunderstorms and jet streaks. The jet stream is an example of a large-scale phenomena which produce shear layers around hundreds of kilometers in length, and have a lifespan of a day or more. These vertically sheared stable layers are the reason why a CAT area can develop roughly tens of kilometers in length or more, and also explain why CAT can last longer than half an hour while being a micro-scale phenomena (Lester, 1994). CAT exists in connection to the jet stream on the side with the lowest temperatures, the underside of the jet stream and in the area between the tropopause and the jet stream where the wind shear is large. Around 60% of CAT observations are reported near the jet stream (Overeem, 2002). CAT is also produced around the tropopause due to dynamic instability, which is associated with tropopause folding. The latter is defined as stratospheric air that is transported into the troposphere at upper-level fronts (Shapiro, 1980). CAT can also be caused near the tropopause by layers of wind shear that are connected with strong temperature inversions (Wingrove et al., 1989). CAT can also exist on the warm side just above an upper-level front where the atmosphere is stable. The necessary condition for KH instability will be favoured when the temperature gradient increases (frontogenesis) since the vertical wind shear also will increase then according to the thermal wind equation. The temperature gradient may increase due to deformation (Overeem, 2002). 6

8 2.3 Different types of instability 2 THEORY 2.3 Different types of instability Turbulence arises in order to reduce instability in the atmosphere, which may have different origins. There are various sorts of turbulence which occurs during different conditions in the atmosphere Dynamic instability/inertial instability If perturbations that occurs in a flow are amplified instead of being reduced, the flow is said to be dynamical unstable. A flow can be dynamical stable in relation to small perturbations, but unstable regarding perturbations with larger amplitudes (Ayra, 2001). The rotation usually stabilizes an air parcel from horizontal movements, which is similar to a statically stable atmosphere with respect to vertical movements (Holton, 2004) Static instability The vertical temperature profile decides if the atmosphere is static stable or unstable. If an air parcel is removed from its equilibrium position and the air parcel then experiences a negative buoyancy that forces the air parcel back to its equilibrium position, the atmosphere is said to be statically stable. If the air parcel instead would experience a positive buoyancy the atmosphere is in static instability (Ayra, 2001). The static stability can be expressed with the Brunt-Väisälä frequency, N, with one layer of air: N 2 = g θ v θ v z where g is the gravity constant and θ v is the virtual potential temperature. For N 2 > 0, the atmosphere is statically stable and the air parcel oscillates around its equilibrium point. When N 2 = 0, no accelerating force exists and the parcel will be in neutral equilibrium, while N 2 < 0 means that the displacement of the air parcel will increase with time (Holton, 2004) Shear instability Shear instability is a result when adjacent air layers move with different wind speeds. Shear instability can occur both in the horizontal and vertical direction. One special case of vertical shear instability is KH instability. One condition for horizontal shear instability is that there should be a local maximum in the shear vorticity s vertical component. This maximum is also an inflection point in the horizontal wind profile (horizontal shear instability is sometimes also called inflection point instability), since the horizontal second derivative changes sign here. This mainly happens at the cyclonic shear part of the jet stream (Brown, 1972; Woetmann Nielsen and Petersen, 2012) Kelvin-Helmholtz instability KH instability occurs at the interface between two layers of a fluid in a flow, where the layers have different densities and wind speeds, but are stable stratified. The energy source of KH instability is the mechanical energy produced by the vertical wind shear. If there is no turbulence, an initiating process is needed to create the (2) 7

9 2.4 Identifying clear-air turbulence using satellite images 2 THEORY motions that will get the energy from the velocity shears to produce turbulence. A large static stability can prevent the onset of KH instability unless the vertical wind shear is large enough. A condition for KH instability is that the Richardson number, Ri, should be less than the critical value Ri c = The Richardson number is defined as: where S = V z Ri = g θ v θ v z V z is the vertical wind shear. 2 = N 2 S 2 (3) Small waves takes form on the interface which tends to grow when Ri reaches the critical value and evolves into turbulence. KH instability is a mechanism for the development of CAT, and Ri is used to localize areas with CAT. Thus, a low Ri does not necessarily mean that CAT is localized in that region. There may also be uncertainties with the calculation of Ri (Ellrod and Knapp, 1992; Ayra, 2001; Wallace and Hobbs, 2006; Woetmann Nielsen and Petersen, 2012) KH instability can be seen in the atmosphere through the shape of clouds. They look like breaking ocean waves, or seen from satellite images as billow clouds. An example of KH instability in the atmosphere is seen in Figure 2, where the instability is seen in the tops of the cirrus clouds. Figure 2: Photo showing Kelvin-Helmholtz instability in the tops of cirrus clouds. Figure source: Robinson (2011). 2.4 Identifying clear-air turbulence using satellite images Occasionally satellite images give a useful idea where CAT is present. Signatures in visible, water vapour and infrared are present for a large part of CAT outbursts. The pattern of CAT (mostly seen in visible and infrared imagery) are transverse cirrus cloud banding, directed perpendicular to the wind direction. The equator ward side of the subtropical jet is often an area where the transverse clouds can be found, which indicate large horizontal and vertical wind shears (Ellrod, 2000). Billows are also another wave cloud that can reveal the presence of CAT, and they may indicate that KH instability is present. Billows are regularly spaced and 8

10 2.4 Identifying clear-air turbulence using satellite images 2 THEORY narrow patterns in cirrus or mid-level clouds, which also are oriented perpendicular to the wind direction. Transverse bands differs from billows by being more irregular with larger spacing and width (Ellrod, 1989). Darkening of water vapour images in time usually also indicate that turbulence occurs. Figure 3 shows an example of transverse bands and billows which may indicate the presence of CAT. While these are some examples of how turbulence may be seen with satellite images, Knox (2001) notes that detecting CAT with remote sensing is very difficult. Figure 3: Visible image from the GOES-east satellite, showing transverse bands and billows. Figure source: Ellrod (1989). 9

11 3 ELLROD AND KNAPP S TURBULENCE INDICES 3 Ellrod and Knapp s turbulence indices Many different CAT indices exist today (see e.g. Paul and Joshi (2013)), and two of them are used in this report. A CAT index is based on fields from a numerical weather prediction model and express the probability of encountering CAT (Dutton, 1980). Two of the most established indices have been developed by Ellrod and Knapp (1992). They presented a method to forecast CAT which is based on the production of two kinematic terms: vertical wind shear and deformation. 3.1 Deformation Deformation can be described as: kinematic property of the flow that tends to transform an original circle of fluid into an elongated elliptical shape (Mancuso and Endlich, 1966). Deformation is an important mechanism in producing or destroying horizontal temperature gradients, and hence upper-level frontal zones. Deformation is a feature of a flow, and may be found in troughs and the exit area of the jet stream. Deformation is the sum of both horizontal shear and horizontal stretching, where deformation by horizontal shearing is defined by: D sh = v x + u y Deformation by horizontal shear can affect a fluid parcel in two ways: either it tends to shrink along the horizontal direction perpendicular to the shear vector, or, due to shear vorticity, to rotate the parcel and deforming it by stretching parallel to the shear vector (along the x-axis in Figure 4a). Horizontal stretching on the other hand is defined as: D st = u x v y Horizontal stretching will concentrate the isotherms along the axis of dilation (the x-axis in Figure 4b) due to advection of the temperature field. This is only possible if the initial temperature field has a finite gradient along the y-axis in Figure 4b, the axis of contraction. The horizontal temperature gradient can be increased due to these two forms of deformation. The total deformation is then defined as: (4) (5) D = (D st 2 + D sh 2 ) 1/2 (6) If the horizontal temperature gradients are increased, the deformation strengthens upper-level frontal zones, and thereby increasing the chance of CAT occurrence (Ellrod and Knapp, 1992; Holton, 2004; Mancuso and Endlich, 1966; Reap, 1996). 10

12 3.2 Turbulence index 1 and 23 ELLROD AND KNAPP S TURBULENCE INDICES Figure 4: Illustration of horizontal shearing deformation (figure a) and horizontal stretching deformation (figure b). C and W indicate cold and warm air respectively. Figure source: Holton (2004) 3.2 Turbulence index 1 and 2 The two turbulence indices introduced by Ellrod and Knapp (1992) has its origin in the thermal wind relationship (equations (7) and (8)) and in the frontogenesis equation (equation (9)): T y = ft g T x = ft g U g z V g z (7) (8) F = 1 2 hθ (Dcos(2β) + C) (9) where T is the temperature, f is the Coriolis parameter and U g and V g is the u- and v-component of the geostrophic wind, F is the frontogenesis (when the temperature gradient increases and fronts are created), h θ is the magnitude of the horizontal gradient of potential temperature, β is the angle from the axis of dilation to the isotherms of potential temperature and C is the convergence: ( u C = x + v ) (10) y The geostrophic wind is asumed to be equal to the horizontal wind, wheras the magnitude of the horizontal temperature gradient may then be written as: ( f 2 T 2 g 2 h T = ( ( T x ( ( Ug ) 2 + z ) 2 ( ) ) T = y ( ) )) Vg = ft z g V z (11) If frontogenesis occurs on a constant pressure surface, equation (11) can be inserted in equation (9), which only can be done if the following assumption is made (Ellrod and Knapp, 1992; Mancuso and Endlich, 1966): 11

13 h θ = h T (12) (Overeem, 2002) notes that making this assumption is questionable. Ellrod and Knapp (1992) makes further the assumption that cos(2β) = 1, so the frontogenesis will be maximized, and again this assumption is questionable since an overestimation of CAT may then be obtained (Overeem, 2002). These assumptions applied to equation (9) results in: F T = 1 ft 2 g (D + C) V (13) z where F T is the intensity of frontogenesis on a constant pressure surface. The product of vertical wind shear and deformation gives the highest correlation (Mancuso and Endlich, 1966), whereas Ellrod and Knapp (1992) simplified equation (13) by assuming that the product of f and T is constant (which is doubtful since the indices should be independent regarding the geographical position) and leave out the constant 0.5 and the convergence. This yields turbulence index 1, TI1: T I1 = D V (14) z Usually the convergence is much smaller than the deformation, but can sometimes be important. Therefore, Ellrod and Knapp (1992) also introduced the second turbulence index (Overeem, 2002): T I2 = (D + C) V (15) z 3.3 Calculation from numerical model data of clear-air turbulence By using the u- and v-component of the wind on one pressure level from a numerical weather prediction model, the deformation and convergence (in equations (14) and (15)) may be calculated on constant pressure surfaces. The infinitesimal differences are approximated with the differences between grid points. Calculating for example u x in point u(x,y,z) is approximated by using the grid point values of the u-component in point u(x+1,y,z) and u(x-1,y,z): u(x, y, z) u(x + 1, y, z) u(x 1, y, z) = (16) x 2n where n is the distance in the x-direction between two grid points. In similar manner are the other terms calculated in the deformation and convergence formula. The vertical wind shear in equations (14) and (15) over a layer for a grid point is approximated by: ( (utop ) (x, y) u bottom (x, y) 2 ( ) ) vtop (x, y) v bottom (x, y) (17) z z where u top and v top are the u- and v-component of wind speed at the top of the layer, u bottom and v bottom are the u- and v-component of wind speed at the bottom of the layer and z is the height difference between the top and the bottom of the layer. 12

14 4 DATA 4 Data 4.1 Turbulence reporting systems Below are two widely different turbulence reports that are used in instrumented aircraft reports The International Civil Aviation Organisation categories of turbulence The International Civil Aviation Organisation (ICAO) categories of turbulence divides a peak value of the deviation from normal vertical acceleration (1g) into four categories. Table 1 illustrates the different categories, where higher turbulence values indicates a higher turbulence intensity level (World Meteorological Organization, 2003). This deviation accounts for every sort of turbulence. Only moderate and severe turbulence (see Figure 5 for symbols) are shown in significant weather charts (SIGWX). Such a chart is shown in figure 6. They present the most important meteorological phenomena that are relevant for air traffic, such as CAT, jet stream, clouds, frontal system, tropopause height, tropical cyclone, sandstorm and volcanoes. This forecast was made on May 25th 2013 at 06 UTC over North America, North Atlantic, Europe, western Asia and Northern Africa, and is valid for May 26th 06 UTC at flight level (shown as e.g. FL320 in the figure, which corresponds to feet, roughly 9754 meter) (World Area Forecast Centres, 2004). There are five CAT areas, as shown in the box in the lower part of the figure, which are illustrated with closed dashed lines. Both moderate and severe turbulence is forecasted, and all five turbulence areas are connected to a jet stream. Peak value from normal acceleration Description of turbulence Intensity 0 < 0.15g None g < 0.5g Light 1 0.5g < 1.0g Moderate 2 1.0g Severe 3 Table 1: The ICAO categories of turbulence used in AMDARs. This measurement technique does however not take into account the aircraft weight, thus if a small aircraft flies through a CAT area and experiences moderate or severe turbulence, a larger aircraft would probably report no or light turbulence if it would enter the same area. Since the weight of different aircraft types differs considerably, the acceleration varies under the same force (World Meteorological Organization, 2003). Figure 5: The left symbol indicate moderate turbulence (turbulence intensity 2) and the right symbol indicate severe turbulence (turbulence intensity 3). 13

15 4.1 Turbulence reporting systems 4 DATA Figure 6: Significant weather chart (SIGWX) made on May 25th 2013 at 06 UTC, valid for May 26th 06 UTC. The forecast indicate important information for air traffic: CAT, jet streams, clouds, frontal system, tropopause height, tropical cyclone, sandstorm and volcanoes. The five CAT areas (closed dashed lines) are all connected to the jet stream. The forecast is for flight level (between and feet, roughly between and meter). Courtesy of WAFC SIGWX (2013) Maximum Derived Equivalent Vertical Gust velocity Derived Equivalent Vertical Gust (DEVG) is independent regarding aircraft type and is not an actual velocity, but derived from the measured vertical acceleration. Since this turbulence reporting system is aircraft independent, i.e. the properties of the aircraft (e.g. weight) are taken into account, turbulence reports from different aircraft types are comparable. DEVG values are reported in tenths of ms 1, and this reporting system is a very sensitive technique. The DEVG can be calculated as: DEV G = 20Am n (18) V where A is an aircraft specific parameter that varies with flight conditions, m is the total weight of the aircraft (in metric tonnes), n is the modulus of the peak 14

16 4.2 Aircraft Meteorological Data Relay 4 DATA acceleration deviation from 1.0g and V is the calibrated air speed at the time of the occurrence of the acceleration peak (Vinnichenko et al., 1980). 4.2 Aircraft Meteorological Data Relay The turbulence observations were obtained through instrumented aircraft reports. Initiated by the World Meteorological Organization (WMO), Aircraft Meteorological Data Relay (AMDAR) is a program that reports meteorological data from the whole globe using commercial aircraft. AMDAR reports contain temperature, pressure, altitude, geographical position, wind speed and direction and vertical velocity as meteorological parameters. Some aircraft can also measure density, and may also be equipped with an advanced global positioning system (GPS) that can provide position and wind vector information with great precision (World Meteorological Organization, 2003). The AMDAR data was obtained for the whole year of 2011 from the United Kingdom s Meteorological Office (MetOffice). The parameters included were time, geographical position (both horizontally and vertically), air temperature outside of the aircraft, phase of flight (all 32 cases occurred during a routine observation at cruise altitude) and the wind speed and direction. The area of interest is the North Atlantic, so the AMDAR data ranges between 40 N and 70 N and 60 W and 10 W. The turbulence reporting system that have been used in the AMDAR data in this report are the ICAO categories of turbulence. On average around AMDAR reports per day were obtained with around with an entry for turbulence reporting reports were obtained, and nearly all of these observations reported no turbulence (turbulence intensity 0, see Table 1). There were only 32 reports that observed turbulence, where all these reports contained a turbulence degree 1. The frequency between turbulence reports on a given flight is approximately 7-10 minutes. An aircraft has a velocity of ca 900 km/h at cruise altitude (around m), so the aircraft has travelled km between every observation. It may seem very low that only 32 reports observed turbulence, but actually it is fairly reasonable. According to the AMDAR Technical Specification (2000), turbulence is measured during 10 seconds with a recommended sampling rate of 8 Hz. Thus, assuming a typical 7 hour cruise phase for a transatlantic flight, the AMDAR equipment is active for about 7 minutes (assuming 10 minutes intervals between observation), which corresponds to about 2.9% of the cruise time. Another study (Sharman et al., 2006) suggest that aircraft encounter turbulence about 3% of the time on cruise altitude. This means a probability of 0,0875% (0,03 0,029) that any AMDAR observation will detect turbulence. Using this probability (0,0875%) on the number of valid observations in the dataset for this study (226159), it would suggest that there would have been 198 turbulence reports for 2011, whereas 32 were obtained. 15

17 4.3 Model data 4 DATA 4.3 Model data The model data was provided by ECMWF. Data from the Integrated Forecast System (IFS) was used. IFS Cycle 36r4 (introduced November 9th 2010), 37r2 (introduced May 18th 2011) and 37r3 (introduced November 15th 2011) were operational during 2011 (ECMWF, 2012). The analysis data was available every sixth hour (0000, 0600, 1200 and 1800 UTC) while the forecast data was made every 12th hour (0000 and 1200 UTC). The analysis serves to be the best fit to observations and are the best gridded estimate of the state of the atmosphere. The forecasts are based on the 0000/1200 UTC analysis and are made globally ten days forward in time. Model levels were used as height coordinates, and the operational model has 91 model levels, with the top at 0.01 hpa. Other height levels that can be used in the operational model are surface (fields that represent the meteorology at the surface), pressure levels (which are interpolated by the model from its model levels) and isentropic levels (which are either potential temperature or potential vorticity). Two horizontal resolutions were used: a fine resolution of x0.225 and a coarse resolution of x1.125 (MARS User Guide, 2013). One longitudinal grid spacing of and corresponds for all latitudes to 25 and 125 km. One latitudinal grid spacing of corresponds to 22 km at 40 N and 9 km at 70 N, while corresponds to 96 km at 40 N and 43 km at 70 N. 4.4 Thresholds for the turbulence indices A correct CAT forecast in this study is said when CAT was predicted as much as 1 away from the observation site in both the latitudinal and longitudinal direction. This area has been chosen since the aircraft has then flown roughly in one of the largest horizontal model resolution s grid boxes. Regarding the vertical direction, it is determined that CAT was predicted correctly if turbulence existed as much as the aircraft s length away from the observation, thus roughly 100 m. In order to distinguish when turbulence occurred, a threshold was determined for each index. The threshold for TI1 was set to s 2 and TI s 2. These thresholds were determined by comparing all 32 turbulence reports and thereby estimating when and where turbulence occurred, and by comparing to the thresholds set up by Overeem (2002) for TI1 and TI2. 16

18 5 RESULTS 5 Results 5.1 Summary of the results Figure 7 shows a schematic picture of where all the 32 turbulence reports occurred. The red boxes illustrates the areas in Figure 8, 12 and 14, and the arrows indicate four cases which are thoroughly investigated later in the report. Observations where only TI1/TI2 had a correct CAT forecast are represented with symbols of the colour cyan/blue, while symbols with a red colour represents observations where no index predicted that CAT would occur. All the other colours (black, green and magenta) represents the observations when both indices had a correct CAT forecast (Figure 7 is summarized among other things in Table 2). More than half of the turbulence events were reported in November and December alone. It is noticeable that most of the observations (22 of 32) were made between 50 and 60 N, and only three turbulence events occurred over Greenland. Also, there seems to be a large amount of observations over or just outside of Newfoundland. All observations occurred between and m above sea level. Table 2 shows the obtained results for the two turbulence indices as well as the two different resolutions. For the majority of all cases (22 of the total 32) the two individual indices had a correct forecast of CAT, while there were two cases when each one of the indices had a more accurate forecast than the other. Six turbulence events were not foreseen by either indices. Regarding the resolution, there were 17 cases (more than 50%) when the simulation with both resolutions had a correct CAT forecast. In five cases the fine resolution had a correct forecast of CAT while the coarse resolution was incorrect, but there were also four cases when the opposite occurred. Since the indices did not predict a correct CAT forecast for six cases, there are also six cases when none of the resolution had a forecast of CAT. Table 3 shows the different mechanisms that triggered the different turbulence observations. Studying the output from the model from a subjective view, it can be concluded that in eight cases, the jet stream connected to a strong vertical wind shear were the triggering mechanism, while in seven cases the jet stream together with a large horizontal temperature gradient, the tropopause height and a strong vertical wind shear caused the turbulence. Six observations were caused by the jet stream and the tropopause height, while the jet stream itself caused five turbulence events. The jet stream and a large horizontal temperature gradient caused three events. A large horizontal temperature gradient was responsible for one report, as was the tropopause height and a combination of the jet stream, a large horizontal temperature gradient and a strong vertical wind shear. 17

19 5.1 Summary of the results 5 RESULTS Figure 7: Geographical location of where the 32 turbulence observations occurred according to the AMDAR data. The symbols with cyan/blue colour represents observations where only TI1/TI2 predicted CAT, while the the cases when no turbulence was reported are represented with red colour. All the other colours (black, green and magenta) represents the observations when both indices had a correct CAT forecast. The red boxes illustrates the same area shown in Figure 8, 12 and 14, and the arrows show the location of the four cases which are studied more closely later in the report. TI1 correct TI2 correct TI1 and TI2 correct No index correct Correct fine resolution Correct coarse resolution Both resolutions correct No resolution correct Table 2: Table containing the results regarding the accuracy of the two indices TI1 and TI2 (see equations (14) and (15)) as well as the two resolutions. 18

20 5.2 Case studies of four turbulence events 5 RESULTS CAT caused by: Number of cases Jet stream connected to a strong vertical wind shear 13 Jet stream connected to a strong vertical wind shear, a large horizontal temperature gradient and the tropopause height 7 Jet stream connected to a strong vertical wind shear, and the tropopause height 7 Jet stream and a large horizontal temperature gradient 3 A strong vertical wind shear and the tropopause height 1 Tropopause height 1 Table 3: The table shows the results of the number of observations of different mechanisms that triggered the turbulence. 5.2 Case studies of four turbulence events Three possible regions has been suggested in the RECREATE project where aircraft refueling air-to-air may be possible (Mårtensson et al., 2011). These regions are southern Greenland, west of Ireland and Newfoundland, whereas four specific cases (one over southern Greenland, one over west of Ireland and two over Newfoundland) have been chosen and thoroughly studied. Precisely these four cases for each region has been chosen (there were also other turbulence reports in these three regions) because they were closest to when the latest forecast was made Southern Greenland The turbulence over southern Greenland was reported on February 19th 2011 at UTC at N, W, while the latest analysis was made the same day at 12 UTC. The observed turbulence was triggered by a strong vertical wind shear and the tropopause height, and occurred at m above mean sea level (AMSL). Figure 8 shows the latest analysis for TI1 and TI2 (where the black dot illustrates the location of the turbulence event) where everything below the thresholds (white surface in Figure 8) are said to be no turbulence. The altitude for this figure is AMSL, the closest model level to the height at which the observation occurred. The result is that both indices predicted that CAT existed where the turbulence was reported. There also seems to be somewhat of a similarity between all the figures. The fine resolution results obtains higher values of TI1 and TI2 than the coarse resolution. Figure 9 shows the latitudinal and longitudinal cross section for Figure 8a) and b), where it can be observed that there is a similarity between TI1 and TI2. Studying the three different terms in the indices definition (see equations (14) and (15)), it could be determined that the vertical wind shear was the significant term. Figure 10 shows a sounding from southern Greenland (61.08 N, W) at 12 UTC (the red line visualizes the height of the aircraft). The sounding indicates that there were no clouds present where the turbulence was reported, which is verified from satellite images (not included), and the diagram verifies that the aircraft flew at the tropopause height. There was no jet stream near the observed turbulence (the measured wind speed from the AMDAR data was 18 m/s), but there was a low pressure system south of Greenland visible up to at least 300hPa. This low pressure 19

21 5.2 Case studies of four turbulence events 5 RESULTS system created winds that were north-easterly up to the point of observation, which can be seen if the wind in the right side part of Figure 10 is studied. It is also seen from the wind profile that there existed a large vertical wind shear around the same height as where the CAT was observed. Figure 8: The analysis for February 19th 2011 at 12 UTC. Figures a) and b) shows model result for TI1 and TI2 using the fine resolution, and figures c) and d) shows TI1 and TI2 for the coarse resolution. The black dot illustrates where the turbulence event occurred, and the lines in Figure a) and b) represents cross sections shown in Figure 9. The altitude for the model result is m above mean sea level (AMSL), while the observation occurred at AMSL. In order to investigate how well the forecasts 24 and 48 hours prior to the turbulence event were, the analysis that was made closest to the reported turbulence in time was used as the true state of the atmosphere and compared to the 24 and 48 hour forecasts. Figure 11 shows the forecast made on 18th February at 12 UTC, thus 24 hours prior to the turbulence event. Comparing this forecast to the analysis 20

22 5.2 Case studies of four turbulence events 5 RESULTS in Figure 8, it can be determined that CAT was well predicted 24 hours in advance. Figure 11 illustrates that TI1 in the fine and coarse resolution bear somewhat of a resemblance to TI1 in Figure 8, and vice versa for TI2. The same result was obtained when comparing Figure 9 to the 24 hour forecast (figure not included). Regarding the 48 hour forecast, no turbulence was predicted for either indices in both resolutions in the horizontal or vertical plane (figures not included). Table 4 shows the summarized results for all four cases regarding the 24 and 48 hour forecast. Figure 9: Figure a) and b) shows the latitudinal cross section for the north-south line in Figure 8a) and b) respectively, and Figure c) and d) shows the longitudinal cross section for the east-west line in Figure 8a) and b). The black dot illustrates where the turbulence event occurred. 21

23 5.2 Case studies of four turbulence events 5 RESULTS Figure 10: Sounding over southern Greenland (61 N, 45 W) on February 19th 2011 at 12 UTC (courtesy of University of Wyoming (2011a)). The red line shows at which height the aircraft was flying. 22

24 5.2 Case studies of four turbulence events 5 RESULTS Figure 11: All four figures are the forecast made on 18th February 2011 at 12 UTC, thus the 24 hour forecast for Figure 8. The figures are otherwise the same as in Figure 8. Correct +24 hour CAT forecast Correct +48 hour CAT forecast Southern Greenland Yes No West of Ireland Yes Yes Newfoundland Yes (only TI1) Yes Table 4: The summarized results for the 24 and 48 hour forecasts prior to the four turbulence events (both resolutions are included). 23

25 5.2 Case studies of four turbulence events 5 RESULTS West of Ireland The reported turbulence over western Ireland occurred on October 5th 2011 at UTC, and the latest analysis was made the same day at 1200 UTC. The turbulence occurred at AMSL at 51.9 N, W and was triggered by the jet stream connected to a strong vertical wind shear. The observed wind speed was 53.5 m/s and came from west north-west. Figure 12 shows the latest analysis made for TI1 and TI2 using both the fine and coarse resolution. The indices using both resolutions predicted CAT to be in the vicinity where the turbulence occurred. The figure also shows that TI1 and TI2 are similar to each other for each resolution. It is interesting when studying the different terms individually in the indices definition. It turns out that the deformation and convergence term are more significant than the vertical wind shear regarding the line of CAT that crosses through the middle of Ireland in Figure 12a) and b), while the vertical wind shear is more significant for the line of CAT that is located in the northern parts of Ireland. For the coarse resolution, Figure 12c) and d), it is only the vertical wind shear that is significant. Billow clouds may have been present at the time of the observation, as the visible satellite image from October 5th 2011 at 17 UTC shows in Figure 13a). Figure 13b) provides the analysis chart on October 6th 2011 at 00 UTC, which shows two cold fronts (and a weakening cold front) located east of Ireland moving eastward. Comparing this surface analysis chart with the surface analysis map for October 5th 12 UTC (not included), it can be estimated that the two cold fronts were located around the site where the turbulence occurred when the report was made. The 24 and 48 hour forecast for both indices and resolutions performed a good prediction for CAT both horizontally and vertically, see Table 4. However, TI1 and TI2 in both the 24 and 48 hour forecast did not have the exact same form as the October 5th analysis had (figures not included). 24

26 5.2 Case studies of four turbulence events 5 RESULTS Figure 12: As figure 8, but for October 5th 2011 at 12 UTC. The altitude for the model result is m above mean sea level (AMSL), while the observation occurred at AMSL. 25

27 5.2 Case studies of four turbulence events 5 RESULTS Figure 13: Figure a) shows a visible satellite image over western Europe (courtesy of EU- METSAT/Met Office (2011)) on October 5th 2011 at 17 UTC. The arrow illustrates where the turbulence occurred. Figure b) provides the surface analysis chart over western Europe on October 6th 2011 at 00 UTC (courtesy of Met Office (2011)) Newfoundland There were two turbulence events that were reported over Newfoundland on November 24th 2011, at 2.49 UTC (at N, 57.9 W on an altitude of AMSL) and 3.03 UTC (at N, W on an altitude of AMSL). The latest analysis was made at 00 UTC the same day. Both turbulence events were caused by the jet stream connected to a strong vertical wind shear, and the tropopause height. The observed wind speed was 72 m/s and came from west. Figure 14 shows that both indices predicted CAT to be at or around the observation using both resolutions. It can also be seen from the figure that TI1 in both resolutions are similar to each other, and vice versa for TI2. The vertical wind shear was the significant term in the indices definition. Figure 15a) provides an infrared satellite image over eastern North America on November 24th 2011 at 00 UTC (where the blue square illustrates the same area as in Figure 14). It may seem from the cloud structure that a front is present along the east coast of United States of America (USA) and southern Canada, which is confirmed in the surface analysis map in 15b), which is from the same time as the satellite image. Figure b) shows that it is a cold front with the associated warm front a little south of Newfoundland s coast, and the low pressure center is located just outside of Nova Scotia coast s. The satellite image in figure a) indicates that the upper-level front may be at the same site as the observation. The sounding (from 00 UTC at N, W) in Figure c) shows that there are no clouds at the same height as the observations, and that the turbulence events occurred at the tropopause height. It is also recognized in Figure c) that it probably existed a significant vertical wind shear at the same height as the observations, due to the rapid change in wind speed (from 75 to 46 ms 1 ) for a very short distance. 26

28 5.2 Case studies of four turbulence events 5 RESULTS Regarding the 24 hour forecast made on November 23th at 00 UTC, only TI1 predicted that CAT would exist around the same area as the two observations, which was obtained using both resolutions. However, CAT was forecasted with both indices and resolutions in the 48 hour forecast, see Table 4 (figures not included). Figure 14: As figure 8 and 12, but for November 24th 2011 at 00 UTC. The altitude for the model result is m above mean sea level (AMSL), while the observations occurred at and AMSL. 27

29 5.2 Case studies of four turbulence events 5 RESULTS Figure 15: Figure a) shows satellite image (infrared 11 µm) over eastern North America for November 24th 2011 at 00 UTC (courtesy of GOES NH (2011)). The blue square illustrates the same area as in Figure 14. Figure b) shows a surface analysis map over eastern North America for November 24th 2011 at 00 UTC (courtesy of Weather Prediction Center (2011)). Figure c) shows a sounding over Newfoundland (47.31 N, W) at 00 UTC (courtesy of University of Wyoming (2011b)). The red line shows at which height the aircraft was flying. 28

30 6 DISCUSSION 6 Discussion First and foremost, it is important to remember that the forecast results are not from the exact same time as when the turbulence was reported. Also, it is reported if any aircraft experience turbulence, and so that area can be avoided by other aircraft. It should also be noted that these 32 turbulence observations were all categorized as light (turbulence category 1). However, since aircraft that fly between Europe and North America are large and heavy and the turbulence reporting system that was used does not account for weight, there has to exist stronger turbulence in order for the aircraft to experience moderate or severe turbulence. Moreover, since flying through a CAT area can be dangerous to both aircraft and humans, the pilots choose to avoid areas where CAT may encounter, and thus no observations can be made. Regarding the indices, they have a tendency to predict CAT where it does not exist any, rather than the other way around, and thus have a high false alarm rate (Overeem, 2002). This is mainly due to the approximation cos(2β) = 1, where again β is the angle from the axis of dilation to the isotherms of potential temperature, and thus the frontogenesis will be maximized. Taking the statements above in consideration, the results can be analyzed. Figure 7 illustrates that the turbulence events are not reported south of 48 N, whereas the explanation is simply that aircraft fly a more northern route between Europe and North America due to the great circle distance. Regarding the high amount of observations over Newfoundland, that is the most common geographical position where aircraft fly during transatlantic flights. Therefore, aircraft pass the jet stream at this location, leading to a higher probability of encountering turbulence at this specific region. Most of the observations were reported during wintertime, which seems logical since the wind speed and horizontal temperatures gradients are largest then. It should be noted that the turbulence reporting system measures every sort of turbulence. However, since there are only a few observations over mountain areas (Greenland and Ireland), and one of these cases are shown below to be CAT, it can be concluded that most of the reports are CAT. Table 2 shows that both indices are more or less equally good at forecasting CAT, and that only a small number of events were not predicted. That in itself is a very good result since it is usually difficult to make a good CAT forecast. What is even more interesting are the results when comparing the two different resolutions in Table 2. The majority of the turbulence events were forecasted with both the fine and the coarse resolution runs. There were also four cases when the coarse resolution run predicted CAT and the fine resolution did not. The reason for this could be that the turbulence was triggered by large-scale phenomena that could have been the major contribution for triggering the turbulence, which the coarse resolution run easier can recognize. It is interesting and important from a computational point of view that the coarse resolution run were in most cases equally good as the fine resolution run. From Table 3 it is obvious that the jet stream connected to a vertical wind shear plays a big role when it comes to creating turbulence. It is therefore no coincidence that both turbulence indices predicted CAT in most cases since these two phenomena contributed to almost all of the turbulence events and are accounted for in the indices definition. 29