Global Synoptic Dynamic Model (GSDM)
This quasi-phase space diagram plots standardized anomalies of global relative atmospheric angular momentum (AAM) on the x-axis and of the time tendency of global relative AAM on the y-axis. The anomalies are based on a 1968-96 climatology and are standardized using 5-day average data from 1968-2006 since a 5-day running mean is applied to daily data. The 5-day average standard deviation for global AAM is 1.2x1025 kg m2 s-1 and for the global tendency is 1.4x1019 kg m2 s-2. The global tendency is estimated from the global AAM time series using a 4th order (5-point) finite difference scheme. The scheme while highly accurate has problems when 5 points are not available, like at the end of the record, i.e., the most recent data. As a result, there will be changes in the last 4 points plotted when new data are added. In the future, the time tendency for the last points will be estimated from the torques. The global budget of AAM is fairly well balanced and using the torques will help minimize the changes seen currently.
The diagram defines one component of the Global Synoptic Dynamic Model (GSDM) described in Weickmann and Berry (2007; WB07). We name it the global wind oscillation (GWO). Another component is defined by the MJO and there is a link to its phase space plot on the webpage. The plotting routine for the GWO was provided courtesy of Matt Wheeler. In WB07, four stages of the GSDM were defined. For the GWO these have been replaced by eight phases (1-8), which are broadly similar to the eight phases of the Madden-Julian Oscillation (Wheeler and Hendon, 2004). See below for discussion of the relationship between the MJO and GWO. For legacy purposes and as a reminder: Current Phase 1 was Stage 4, Phase 3 was Stage 1, Phase 5 was Stage 2 and Phase 7 was Stage 3.
The clockwise rotation of the trajectory depicts an atmospheric mode that is termed the global wind oscillation (GWO). The GWO tracks changes in global AAM, which are forced by surface torques – predominantly the mountain torque, the frictional torque and the coriolis torque. Some general relationships are: a) the mountain torque dominates the other torques and is positive in Phase 5 and negative in Phase 1, b) the frictional torque tends to damp the global AAM anomaly and thus is positive in ~Phase 3 and negative in ~Phase 7 and c) the frictional torque leads the mountain torque. The MJO also produces signals in the global torques and global AAM as its convection signal propagates eastward in the tropics. However, most of the variability in the GWO is independent of the MJO. A paper in preparation will compare the GWO and the MJO.
The four primary phases of the GWO are described below, along with generally cold season (November-March) probable weather impacts for the USA. The GWO recurrence interval, or the time to make a circuit, ranges from a broad 15-80 days. Phases 7 and 3 project strongly on El Nino and La Nina circulation states, respectively. Phases 1 and 5 are transitional.
Phase 3 (La-Nina like) – the global relative AAM anomaly is negative. The negative anomaly is primarily due to easterly upper level wind anomalies that extend from the Eastern Hemisphere tropics to the Western Hemisphere mid-latitudes. A retracted Pacific Ocean jet stream is a key feature in the total field. Troughs are probable across the western USA with a ridge over the southeast. High impact weather is favored across the Plains and the Pacific Northwest.
Phase 5 – the global relative AAM tendency is positive. This means that negative AAM is being removed from the atmosphere by surface friction and mountains. At the same time, westerly wind anomalies are intensifying in equatorial regions of the Western Hemisphere. Fast, zonally oriented Rossby wave dispersion events in both hemispheres are a coherent feature of this phase and Phase 1. A cold regime is probable across the central USA.
Phase 7 (El-Nino like) – the global relative AAM anomaly is positive. Westerly wind anomalies move into the Eastern Hemisphere, broaden in latitudinal extent and link up with deep westerly flow anomalies over the mid-latitude Western Hemisphere. An extended Pacific Ocean jet stream and southward shifted storm track is observed, favoring high impact weather events along the USA west coast.
Phase 1 – the global relative AAM tendency is negative. Positive (westerly) AAM anomalies are being removed by surface friction in the Western Hemisphere mid-latitudes and through mountain torques across the Northern Hemisphere topography. The next phase of the oscillation (if it continues) is represented by easterly wind anomalies intensifying over equatorial regions of the Western Hemisphere. This phase has enhanced subtropical jets and closed lows in the subtropics favoring rainfall events over the southwestern USA.
When the Madden-Julian Oscillation (MJO) is active, it can contribute to trajectories in the GWO phase-space. But the dominant GWO process is a friction-mountain torque index cycle that describes the atmosphere’s adjustment to large or clustered mountain torque events. These two slow modes can interact and possibly excite one another. The friction-mountain torque index cycle includes teleconnection patterns like the PNA and the NAO. These patterns have equivalent barotropic structures and exchange large amounts of angular momentum with the ocean-earth through their surface wind anomalies.
The global AAM can only be changed by the action of global torques. However, we use the GWO as an index of zonal mean and regional changes in the circulation. This brings in other physical processes like momentum fluxes and Rossby wave dispersion. The global, zonal and regional relationships will be described in a paper in preparation. As an example, subseasonal zonal AAM changes are dominated by zonal mean momentum fluxes. As a result there is a difference between the latitude band where a torque generates an AAM anomaly, the band where the anomaly appears in the atmosphere and the latitude band where it is removed. The flux convergence of AAM is also the dominant forcing for the poleward movement of zonal AAM anomalies, which is a well-known MJO signal. Torques can be generated as a response to the meridional propagation of AAM anomalies. The poleward movement is produced by the phasing of fluxes due to the zonal mean mass circulations and those due to mid-latitude synoptic and other eddies. Wave breaking is a regional phenomenon that contributes to meridional movements in zonal mean AAM anomalies.