Lagrangian Models. Anne Douglass Code 613.3 Atmospheric Chemistry and Dynamics Branch NASA Goddard Space Flight Center . Type 1 Requires specific knowledge of air parcel origin Solar history Temperature history Valid for 5-7 days (some cases a few days longer) . Type 2
Code 613.3 Atmospheric Chemistry and Dynamics Branch
NASA Goddard Space Flight Center
Requires specific knowledge of air parcel origin
Valid for 5-7 days (some cases a few days longer)
Study “overall transport properties”
Requires large numbers of parcels and statistical analysis of their behaviorLagrangian Models
Web of Science Search
1994 - present
Journal of Geophysical Research Atmospheres
Geophysical Research Letters
“trajectory” - title, key word, abstract - ~500 publications
Two main types of applications
There are different approaches to solving the trajectory equation:
Stohl A., Computation, Accuracy and Applications of Trajectories - A Review and Bibliography, Atmospheric Environment, 32, 947-966, 1998.
Assume you can come up with a solution to initialization issues for constituents that change on time scales of the integration e.g., NOx/Noy
Use the trajectories to account for solar history
overhead O3 column
Keep some sense of how errors related to mixing or position errors in the trajectories can impact results.
APPLICATION 1 - Use back trajectories + photochemical model to interpret stratospheric aircraft observations
NASA’s ER-2 was deployed for the Photochemistry of Ozone Loss in the Arctic Region in Summer (POLARIS) mission flown during the summer of 1997 to measure radicals responsible for the summer photochemical destruction of ozone.
One key aspect of this decline is the concentration of nitrogen radicals, and their abundance relative to the reservoir HNO3.
Pierson, J. M. et al., Influence of air mass histories on radical species during the Photochemistry of Ozone Loss in the Arctic Region in Summer (POLARIS) mission, J. Geophys. Res., 105, 15,185-15,199, 2000.
Parcel Theta (K)
High latitude summer is nearly continuously in sunlight, but back trajectories show that late April air parcels intercepted by the ER-2 have different solar history.
The outliers (from the late April flight shown on the previous slide) join the main group when the solar history is accounted for using back trajectories.
Subsequent laboratory measurements of the rates for
NO2 + OH + M HNO3 + M
OH + HNO3 NO3 + H2O
greatly reduce the model - measurement disparity.
April 26 points are outliers
NOx/NOy was initialized in for both calculations using observations at the flight track. The steady state calculation produces higher NOx/NOy because periods of darkness and latitudinal variation of solar zenith angle are not accounted for.
This calculation assumes no mixing.
Although 10 days is a long time for a backward trajectory, the solar history is likely to have smaller errors than the exact location, and this is the main source of error for the steady-state comparison.
(and trajectories are more serene in a summer circulation . . .)
If you start forward trajectories from a regular grid (no matter how dense), the result (no matter how long the calculations) is an irregular distribution of endpoints.
If you start from a regular grid and go backwards, the endpoints are similarly irregular.
The application called Reverse Domain Fill (RDF) starts backward trajectories from a dense regular grid, and produces a distribution of endpoints.
Take observations that you have and interpolate to this distribution.
Wave breaking features are better resolved
PV is higher
Smoothed RDF not the same as analyzed PV
5o box car smoothed
Gridded ISAMS RDF from Jan 10 RDF from Jan 9
RDFs for Jan 11 are calculated using back trajectories from an equal area grid. Back trajectories are 1 to 7 days duration. Each day’s data from the terminus of the back trajectory is projected to the equal area grid. Filamentary structures appear as the back trajectory duration lengthens.
Sutton et al., High Resolution Stratospheric Tracer Fields Estimated from Satellite Observations Using Lagrangian Trajectory Calculations, JAS 1994.
RDF from Jan 5 RDF from Jan 4
The left panel RDF for January 7 projects gridded ISAMS data from January 2. The center panel RDF for the same day) projects the along-track data from January 2. The right hand panel is the along-track data (Jan. 2).
The main features are the same in (a) and (b) (disregarding the missing data), showing that the winds play the predominant role in producing the RDF structure, not fine structure from the along-track observations.
In January/February this year a DC-8 mission took place out of Pease New Hampshire (Polar Aura Validation Experiment PAVE).
One of the instruments on the DC-8 is an ozone lidar AROTEL.
The DC-8 flight track nearly coincided with the Aura track for the Microwave Limb Sounder.
The GSFC Chemistry and Transport Model used winds and temperatures from Goddard’s Global Modeling and Assimilation Office meteorological fields to simulate ozone (and other constituents). GMAO assimilated fields are 1 lat x 1.25 long horizontal resolution.
The CTM is usually run at 2 lat x 2.5 long to meet computing constraints.
MLS (upper left) and AROTAL (lower left) show a sharp vortex edge.
CTM edges are sharper at 1x1.25 (upper right) than at 2x2.5 (lower right), but not nearly as sharp as observed.
2 x 2.5
A few days later, MLS and AROTAL show a structure (a filament) that is also apparent in the 1x1.25 CTM but only vaguely hinted at in the 2x2.5 CTM.
At 2 x 2.5 the grid point model “overmixes”. Does this matter to O3 evolution (or to a global predictive model?)
2 x 2.5
The RDFs show that the GMAO winds contain the information to produce a filament that looks like the observed filament.
At the same time, the RDFs show more and more structure as the “mixing free” calculation goes back farther and farther in time. This gives a sense of the importance of mixing processes in the stratosphere - there is *too much* structure in the RDF for the longest back trajectories.
How, when, where do parcels mix?
Can models simulate mixing on appropriate temporal and spatial scales?
D = diffusion coefficient
Radius of interaction
The CLaMS model was constructed to take advantage of the high spatial resolution afforded by the RDF approach, and at the same time to simulate mixing processes that also play a role in constituent distributions.
McKenna et al., A new Chemical Lagrangian Model of the Stratosphere (CLaMS) 1. Formulation of advection and mixing, J. Geophys. Res., 107, 2002.
Start with a uniform grid - think of a grid point as enclosed by a circle
After some time the circle is distorted into an ellipse.
The Lyapunov exponent is the mean logarithmic expansion rate of the principal axes
The Lyapunov exponent varies (e.g., small at transport barriers, larger in the surf zone). The CLaMS algorithm “mixes” when the Lyapunov exponent exceeds a critical value.
t = 12 hours
“low resolution” r0 ≈ 200 km (7000 grid points)
“pure” advection (no mixing)
c = ∞
c = 1.2 days-1
c = 0.6 days-1
CLaMS low resolution simulation (r0 ≈ 200 km)
CLaMS high resolution simulation r0 ≈ 60 km
Isentropic advection using Prather’s numerical transport scheme
CLaMS produces structure in this simulation of ozone change for winter 1999/2000 at 450K. Ozone loss is sensitive to chlorine deactivation (ClO + NO2 + M ClONO2 + M) and denitrification, both of which are sensitive to excess mixing.
In some cases, maintaining the separation of air masses and structure is important to the photochemical processes.
Importance of this sort of structure to the global scale is less clear and a present topic of investigation.
Massive numbers of trajectories give insight into the overall transport properties of meteorological fields (whether from a data assimilation system or a general circulation model).
These trajectory calculations clearly show the problems with the meteorological data sets.
Both diabatic and kinematic trajectories for UKMO and FVDAS show that the air in the central tropics comes from middle latitude - this level of horizontal mixing is not support by aircraft or satellite observations.
It is important that using the heating rates to specify the vertical transport does not solve the problem. Although either of these simulations will behave more physically at polar latitudes when the vertical transport is specified by the heating rates, there are issues with mixing and mass balance that affect the simulations and affect comparisons of simulated and observed constituent fields.
The trajectory approach is an important tool in process study land. Trajectories
The trajectory approach has some issues/limitations:
The trajectory approach will serve the user best if s/he understands the limitations and avoids the pitfalls of the “black box”.