Teddie L. Keller

Factors affecting the detection of trends: Statistical considerations and applications to environmental data

Detection of long-term, linear trends is affected by a number of factors, including the size of trend to be detected, the time span of available data, and the magnitude of variability and autocorrelation of the noise in the data. The number of years of data necessary to detect a trend is strongly dependent on, and increases with, the magnitude of variance (σN2) and autocorrelation coefficient (ϕ) of the noise. For a typical range of values of σN2 and ϕ the number of years of data needed to detect a trend of 5%/decade can vary from ∼10 to >20 years, implying that in choosing sites to detect trends some locations are likely to be more efficient and cost-effective than others. Additionally, some environmental variables allow for an earlier detection of trends than other variables because of their low variability and autocorrelation. The detection of trends can be confounded when sudden changes occur in the data, such as when an instrument is changed or a volcano erupts. Sudden level shifts in data sets, whether due to artificial sources, such as changes in instrumentation or site location, or natural sources, such as volcanic eruptions or local changes to the environment, can strongly impact the number of years necessary to detect a given trend, increasing the number of years by as much as 50% or more. This paper provides formulae for estimating the number of years necessary to detect trends, along with the estimates of the impact of interventions on trend detection. The uncertainty associated with these estimates is also explored. The results presented are relevant for a variety of practical decisions in managing a monitoring station, such as whether to move an instrument, change monitoring protocols in the middle of a long-term monitoring program, or try to reduce uncertainty in the measurements by improved calibration techniques. The results are also useful for establishing reasonable expectations for trend detection and can be helpful in selecting sites and environmental variables for the detection of trends. An important implication of these results is that it will take several decades of high-quality data to detect the trends likely to occur in nature.

Detecting the recovery of total column ozone

International agreements for the limitation of ozone-depleting substances have already resulted in decreases in concentrations of some of these chemicals in the troposphere. Full compliance and understanding of all factors contributing to ozone depletion are still uncertain; however, reasonable expectations are for a gradual recovery of the ozone layer over the next 50 years. Because of the complexity of the processes involved in ozone depletion, it is crucial to detect not just a decrease in ozone-depleting substances but also a recovery in the ozone layer. The recovery is likely to be detected in some areas sooner than others because of natural variability in ozone concentrations. On the basis of both the magnitude and autocorrelation of the noise from Nimbus 7 Total Ozone Mapping Spectrometer ozone measurements, estimates of the time required to detect a fixed trend in ozone at various locations around the world are presented. Predictions from the Goddard Space Flight Center (GSFC) two-dimensional chemical model are used to estimate the time required to detect predicted trends in different areas of the world. The analysis is based on our current understanding of ozone chemistry, full compliance with the Montreal Protocol and its amendments, and no intervening factors, such as major volcanic eruptions or enhanced stratospheric cooling. The results indicate that recovery of total column ozone is likely to be detected earliest in the Southern Hemisphere near New Zealand, southern Africa, and southern South America and that the range of time expected to detect recovery for most regions of the world is between 15 and 45 years. Should the recovery be slower than predicted by the GSFC model, owing, for instance, to the effect of greenhouse gas emissions, or should measurement sites be perturbed, even longer times would be needed for detection.

Observations, Simulations, and Analysis of Nonstationary Trapped Lee Waves

Abstract Although considerable understanding of mountain waves has been gained with the aid of the steady-state assumption, it is clear that mountain waves evolve over time. Group velocity arguments indicate that this evolution can occur in less than 1 h. This study uses observations of trapped lee waves to measure the rate at which their horizontal wavelengths change, including a detailed analysis of two events in which such changes are clearly documented. In one case, Doppler lidar observations show a steady increase in horizontal wavelength of 6% h−1 over 4 h and clearly illustrates the relationship between the wave clouds and wave motions. In a second case, visible satellite imagery reveals an increase in wavelength of 14% h−1, which is related to temporal changes in vertical air motions measured by wind profilers within the wave field. Hourly vertical profiles of wind and virtual temperature measured by radio acoustic sounding systems (RASS) and wind profilers reveal important changes in the wave env...

Implications of the Hydrostatic Assumption on Atmospheric Gravity Waves

Abstract The validity of the hydrostatic approximation is examined for use in predicting the dynamics of topographically generated atmospheric gravity waves (lee waves) propagating in an atmosphere with realistic wind shear. To isolate nonhydrostatic effects, linear, analytic solutions derived both with and without the hydrostatic assumption are compared. The atmospheric profiles of wind and stability are chosen both to render the governing equations analytically tractable and be representative of typical atmospheric conditions. Two atmospheric models are considered: 1) a troposphere-only model in which the wind increases linearly with height and the stability is constant and 2) a troposphere-stratosphere model, which retains the important effect of the vertical wind shear in the troposphere and adds the essential feature of a stability jump at the tropopause. The nonhydrostatic trapping effect of wind shear on gravity wave modes is clearly illustrated in the troposphere-only atmospheric model. In the tro...

Terrain-Induced Turbulence over Lantau Island: 7 June 1994 Tropical Storm Russ Case Study

Abstract Numerical simulations of terrain-induced turbulence associated with airflow over Lantau Island of Hong Kong are presented. Lantau is a relatively small island with three narrow peaks rising to between 700 and 950 m above mean sea level. This research was undertaken as part of a project to better understand and predict the nature of turbulence and shear at the new airport site on the island of Chek Lap Kok, which is located to the lee of Lantau. Intensive ground and aerial observations were taken from May through June 1994, during the Lantau Experiment (LANTEX). This paper focuses on flow associated with the passage of Tropical Storm Russ on 7 June 1994, during which severe turbulence was observed. The nature of the environmental and topographic forcing on 7 June 1994 resulted in the turbulence and shear being dominated by the combination of topographic effects and surface friction. High-resolution numerical simulations, initialized using local sounding data, were performed using the Clark model. ...

Analysis and simulations of a troposphere-stratosphere gravity wave model. I

Abstract An analytical model is presented that accommodates nonhydrostatic shearing stratified flow over an obstacle, and that can be modified to include a superposed stratosphere with constant wind and higher stability. A simulation code is used in parallel with the analytic calculations to demonstrate a methodology for determining the wavelength and magnitude of gravity wave energy reflected, and that transmitted, by the tropopause.

Deep-Tropospheric Gravity Waves Created by Leeside Cold Fronts

Abstract The water vapor channel of the Geostationary Operational Environmental Satellite GOES-8 reveals narrow (30 km wide), elongated (500–1000 km) bands that propagate southward on the eastern side of the Rocky Mountains from Colorado to Texas. Two events in which surface and wind profiler observations show that these bands are associated with leeside cold fronts are documented in detail, and several other cases are summarized. The wind profilers observe vertical motions exceeding 1 m s−1 in narrow plumes at the leading edge of the fronts, in broader zones in the upper troposphere, and in the lower stratosphere. These cause vertical displacements of up to 1 km and are responsible for the signature in water vapor images. The bands occur when the Rocky Mountains block either arctic leeside cold fronts coming from the north or northeast or Pacific cold fronts coming from the northwest. The blocking changes the frontal orientation and disrupts geostrophic thermal wind balance near the terrain-modified fron...

Incompressible and Anelastic Flow Simulations on Numerically Generated Grids

Abstract In the numerical simulation of incompressible and anelastic flows, it is necessary to solve an elliptic equation at each time step. When the boundaries of such flows are nonrectangular, it may be advantageous to solve the equations on a new, numerically generated coordinate grid, in which the property or orthogonality has been preserved. Flow equations in general curvilinear coordinate maintaining the conservative form are given for both anelastic models using the momentum equations, and for incompressible modern using the vorticity equation. The general problem of grid-generation in two dimensions is presented, and a quasi-conformal transformation technique is discussed in detail. Some examples of grids generated by this technique are exhibited. Three examples of the flow of a stratified fluid over obstacles are presented, in which the grid-generation permits some new results to be obtained.

Evaluations of Upper-Level Turbulence Diagnostics Performance Using the Graphical Turbulence Guidance (GTG) System and Pilot Reports (PIREPs) over East Asia

AbstractThe forecast skill of upper-level turbulence diagnostics is evaluated using available turbulence observations [viz., pilot reports (PIREPs)] over East Asia. The six years (2003–08) of PIREPs used in this study include null, light, and moderate-or-greater intensity categories. The turbulence diagnostics used are a subset of indices in the Graphical Turbulence Guidance (GTG) system. To investigate the optimal performance of the component GTG diagnostics and GTG combinations over East Asia, various statistical evaluations and sensitivity tests are performed. To examine the dependency of the GTG system on the operational numerical weather prediction (NWP) model, the GTG system is applied to both the Regional Data Assimilation and Prediction System (RDAPS) analysis data and Global Forecasting System (GFS) analysis and forecast data with 30-km and 0.3125° (T382) horizontal grid spacings. The dependency of the temporal variation in the PIREP and GFS data and the forecast lead time of the GFS-based GTG co...

Lee waves Associated with a commercial jetliner accident at Denver International Airport

AbstractAt 1818 mountain standard time 20 December 2008, a Boeing 737 jetliner encountered significant crosswinds while accelerating for takeoff at the Denver International Airport (DIA), ran off the side of the runway, and burst into flames. Passengers and crew were able to evacuate quickly, and, although there were injuries, there were no fatalities. Winds around the time of the accident were predominantly from the west, with substantial spatial and temporal speed variability across the airport property. Embedded in this mostly westerly flow were intermittent gusts that created strong crosswinds for the north–south runways. According to the report from the National Transportation Safety Board, it was one of these strong gusts that initiated the events that led to the runway excursion and subsequent crash of the aircraft. Numerous aircraft reported significant mountain-wave activity and turbulence over Colorado on the day of the accident. To determine whether wave activity may have contributed to the str...