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Jason M. Cordeira Graduate Student Webpage

  

2009

Deptartment of Earth and Atmospheric Science
University at Albany - SUNY / ES 318 / cordeira"at"atmos.albany.edu

  
Northern Hemisphere (NH) ZONAL Available Potential Energy (APE):

 
Forecast NH APE products:
Updated daily at 1800 UTC from 1200 UTC data:

I am currently experiencing technical issues with the APE forecasts (as well as the analyses). I apologize if you are a regular guest of this page, but I will not be able to fix this problem immediately. Please be patient as I work to fix this issue and make a better energetics page. Thank You.
      
1 to 7 (8 to 16) day forecast generated from 1.0- (2.5-) degree GFS.
Shading represents standardized anomaly (0 to 1, 1 to 2, 2 to 3, etc).
Click here to see a comparison between yesterday's and today's APE forecast.

Archive NH ZONAL APE Products:
(1) "The APE Tape" - Daily time series of NH ZONAL APE from 1950-2008: Click Here

(2) Yearly Archive of mean + standardized anomaly NH Z APE:
1950 1951 1952 1953 1954 1955 1956 1957 1958 1959
1960 1961 1962 1963 1964 1965 1966 1967 1968 1969
1970 1971 1972 1973 1974 1975 1976 1977 1978 1979
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Details: Daily averaged Z APE values with shaded standardized anomaly: Grey: +/- 0 to 1 std dev.; Light red or light blue: +/- 1 to 2 std dev.; Dark red or dark blue: greater than 2 std dev.)

(3) Yearly Archive of standardized NH Z APE anomaly:
1950 1951 1952 1953 1954 1955 1956 1957 1958 1959
1960 1961 1962 1963 1964 1965 1966 1967 1968 1969
1970 1971 1972 1973 1974 1975 1976 1977 1978 1979
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Details: Daily averaged standardized Z APE anomaly.

(4) Yearly Archive of 2-day d(NH Z APE)/dt:
1950 1951 1952 1953 1954 1955 1956 1957 1958 1959
1960 1961 1962 1963 1964 1965 1966 1967 1968 1969
1970 1971 1972 1973 1974 1975 1976 1977 1978 1979
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Details: d(Z APE)/dt calculated as a finite difference --> (APE@day+1 - APE@day-1)/2 days.

(5) Yearly Archive of 4-day d(NH Z APE)/dt:
1950 1951 1952 1953 1954 1955 1956 1957 1958 1959
1960 1961 1962 1963 1964 1965 1966 1967 1968 1969
1970 1971 1972 1973 1974 1975 1976 1977 1978 1979
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Details: d(Z APE)/dt calculated as a finite difference --> (APE@day+2 - APE@day-2)/4 days.

(6) Ranked Z APE Data: - Available through email
Jan - Dec 1950-2008 [ranked by magnitude of -d(Z APE)]
Sep - Nov 1950-2008 [ranked by magnitude of -d(Z APE)]
Dec - Feb 1950-2008 [ranked by magnitude of -d(Z APE)]

Details: Here d(Z APE)/dt is calculated as the difference between the maximum and minimum APE values over a 14-day period. The period of the collapse is determined as the time between these maximum and minimum values. The date listed in the text file is the onset of the collapse if d(Z APE) is negative (e.g. at the top of the file) or the onset of Z APE generation if d(Z APE) is positive (e.g. at the bottom of the file).

Brief Explanation:
Available potential energy (APE) represents a fundamental quantity that can be used to gauge the effect of transient baroclinic eddies upon the planetary circulation (Wintels and Gyakum 2000). Margules (1903) first described APE as the portion of the atmosphere's potential and internal energy that can be converted to kinetic energy and was first calculated by Lorenz (1955). Peixoto and Oort (1992) demonstrated that synoptic-scale eddies are responsible for a majority of the baroclinic energy converions during the winter. The APE tendency equation (see Dutton and Johnson, 1967) is also of interest, but is not discussed further (yet) here. The reader is referred to the aforementioned literature for more information.

Calculation and Climatology Details:
1. Datasets

The APE calculations utilized the following four datasets:
(i) 2.5-degree NCEP-NCAR Reanalysis
(ii) 1.0-degree NCEP-GFS Analyses
(iii) 0.5-degree NCEP-GFS Analyses
(iv) 2.5-degree NCEP-GFS Analyses

Dataset (i) was used for the yearly climatology plots from 1950-2007.
Dataset (iii) was used for 2008 as it is the highest resolution dataset we have archived for the year. Dataset (1) would have been preferred for continuity; however, our archive is currently incomplete for that year.
Dataset (ii) is currently in use for 2009. This dataset is being used in conjunction with Dataset (iv) to generate APE forecasts to 16 days.

An analysis of APE values during periods of overlap within datasets is presented to show continuity between the 2.5-degree and 0.5-degree NCEP datasets. It is assumed the 1.0-degree dataset would lie between the two curves below. Vertical levels were held constant:


Correlation between curves: 0.979 | R-squared value between curves: 0.959

2. Calculation procedure:

APE values were calculated by evaluating a form of the approximate expression for APE derived by Lorenz (1955) on an isobaric surface using the potential temperature given by Eq. 4.16 in Wiin-Nielsen and Chen (1993):



Here, theta is the potential temperature, the dotted over-bar denotes layer averages, and the solid over-bar denotes hemispheric averages. Lower-case Kappa represents the quantity [Rd/Cp]. The domain over which the APE was calculated was 20.0-85.0N (for all longitudes). This approximate expression has proven to be sufficient for the purpose of assessing planetry-scale integrals of APE, even though it tends to overestimate APE values in the lowest layer (Siegmund, 1994).

Note that (1.1) uses a surface (lid) pressure of 1000 hPa (100 hPa) and therefore does not take into account APE contributions from below (above) 1000 hPa (100 hPa). Pressure levels (and bounded layers) were limited to those in the NCEP-NCAR Reanalysis [Dataset (1)]: 1000, 925, 850, 700, 600, 500, 400, 300, 200, and 100 hPa.

All APE values were calculated using GEMPAK 4 x daily grids, however, are presented as daily averages [(00Z + 06Z + 12Z + 18Z) / 4]. This applies to all presented materials, except for 2009 values. Since 2009 updates in real-time once per day, and due to the time-intensive nature of the calculation, only the 12 UTC values are plotted.

3. Climatology

Climatological values of APE were catalogued by averaging the 4 x daily values as outlined above from 1 January through 31 December for each calendar year from 1950-2007. 2008 was not included in calculating climatological values due to the change in dataset. The climatological mean-daily values were calculated by averaging all data for each Julian day (e.g. the climatological value for 1 January was calculated by averaging 1 Jan 1950, 1 Jan 1951, 1 Jan 1952... 1 Jan 2007). From these values, the standard deviation was also calculated. No smoothing of these data were done.

Note that the climatological value may not always represent the yearly signal of the APE time series. Although the climatology represents an average of the 58-years of data, it tends to be too high in the 1950s and perhaps too low in later years.
References:
Dutton, J. A. and Johnson, D. R. 1967: The theory of available potential energy and a variational approach to atmospheric energetics. Adv. in Geophys., 12 (Academic Press), pp. 333-436.

Lorenz, E. N., 1955: Available potential energy and teh maintenance of the general circulation. Tellus, 7, 157-167.

Margules, M., 1903: Uber die energie der sturme. Jahrb. Zentralanst. Meteor., 1-26 (Translation by C. Abbe (1910) in Smithsonian Institute Miscellaneous Collection 51, 553-595.

Peixoto, J. P. and A. H. Oort, 1992: Physics of climate. American Institute of Physics, 520 pp.

Siegmund, P. 1994: The generation of available potential energy, according to Lorenz's exact and approximate equations. Tellus, 46A, 566-582.

Winn-Nielsen, A. and T.-C. Chen, 1993: Fundamentals of Atmospheric Energetics, (Oxford University Press), 376 pp.

Wintels, W., and J. R. Gyakum, 2000: Synoptic climatology of Northern Hemisphere available potential energy collapses. Tellus, 52A, 347-364.

Acknowledgements:
The compilation of these time series would not have been possible without the generosity of Eyad Atallah who shared the APE calculation program.