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values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
values represent the algebraic averageof a large number of individual values, some positiveand some negative.Professor Beers fails to distinguish between neglecting a term as small in comparison with larger termsand neglecting it in comparison with other terms of thesame order of magnitude. Consider equation (3) frommy paper:idp awdt az-_ 4- - = - div V.The approximate magnitude of the three terms islo+, and sec-', respectively. Therefore,(l/p)dp/dt may be neglected without doing violenceto the
with I.At least 63 (75) per cent of the time, term I is 10 (4)times larger than term 11, or more. These statisticswere based upon 236 comparisons of terms I and 11.These comparisons were made from ten consecutive1500 GCT 500-mb maps beginning with 13 February1953. From each map, these comparisons were madefrom a geographical grid of 48 points equally spacedover the United States. In these comparisons, thefields of wind and pressure were analyzed independently; their functions I and I1 in (5) were
with I.At least 63 (75) per cent of the time, term I is 10 (4)times larger than term 11, or more. These statisticswere based upon 236 comparisons of terms I and 11.These comparisons were made from ten consecutive1500 GCT 500-mb maps beginning with 13 February1953. From each map, these comparisons were madefrom a geographical grid of 48 points equally spacedover the United States. In these comparisons, thefields of wind and pressure were analyzed independently; their functions I and I1 in (5) were
. Sea-level weather map; 1830 GCT 25 December 1950.JUNE 1953ERNEST M. RAMPEYFIG. 3. 850-mb chart; 1500 GCT 25 December 1950.culation at sea level, 850 and 700 mb, but not at500 mb. 500 mb.chosen for type I is 700 mb, while that for type I1 isThus, lows which appear on the sea-level map, butwhich are not closed at 850 mb, are not included.5. Type I : Evaluation of temperature advectionSimilarly, lows which are closed at 500 mb and higherhave been excluded from this investigation.As will be shown
. Sea-level weather map; 1830 GCT 25 December 1950.JUNE 1953ERNEST M. RAMPEYFIG. 3. 850-mb chart; 1500 GCT 25 December 1950.culation at sea level, 850 and 700 mb, but not at500 mb. 500 mb.chosen for type I is 700 mb, while that for type I1 isThus, lows which appear on the sea-level map, butwhich are not closed at 850 mb, are not included.5. Type I : Evaluation of temperature advectionSimilarly, lows which are closed at 500 mb and higherhave been excluded from this investigation.As will be shown
NMC level. III data werein general available twice a day at 0000 and 1200 GMT,and were used for comparison together with the level IIIdata (map) of ANMRC (Australian Numerical Meteorology Research Centre) in Melbourne.564 JOURNAl. OF THE ATMOSPHERIC SCIENCES VO~.UME339 SEP 197400 GMTSURFACEFro. lc. FIo. 1. Examples of data maps for 00 GMT=t=3 h, 9 September 1'974. (a) 200 mb map includes the data in the layer
NMC level. III data werein general available twice a day at 0000 and 1200 GMT,and were used for comparison together with the level IIIdata (map) of ANMRC (Australian Numerical Meteorology Research Centre) in Melbourne.564 JOURNAl. OF THE ATMOSPHERIC SCIENCES VO~.UME339 SEP 197400 GMTSURFACEFro. lc. FIo. 1. Examples of data maps for 00 GMT=t=3 h, 9 September 1'974. (a) 200 mb map includes the data in the layer
for stratiform instability and convectively coupled waves. J. Atmos. Sci , 58 , 1567 – 1584 . Majda , A. J. , B. Khouider , G. N. Kiladis , K. H. Straub , and M. G. Shefter , 2004 : A model for convectively coupled tropical waves: Nonlinearity, rotation, and comparison with observations. J. Atmos. Sci , 61 , 2188 – 2205 . Mapes , B. E. , 1998 : The large-scale part of tropical mesoscale convective system circulations: A linear vertical spectral band model. J. Meteor
for stratiform instability and convectively coupled waves. J. Atmos. Sci , 58 , 1567 – 1584 . Majda , A. J. , B. Khouider , G. N. Kiladis , K. H. Straub , and M. G. Shefter , 2004 : A model for convectively coupled tropical waves: Nonlinearity, rotation, and comparison with observations. J. Atmos. Sci , 61 , 2188 – 2205 . Mapes , B. E. , 1998 : The large-scale part of tropical mesoscale convective system circulations: A linear vertical spectral band model. J. Meteor
thelines on a transparent overlay, shown in fig. 2, wasplaced on a point where the smoothed value was tobe computed. The line b-d was always oriented northsouth. The smoothed value obtained was equal to(a+l.+c+d+e)/S, and the distance (f) was equal to25 deg lat. A comparison of a smoothed map with anunsmoothed map showed about what would be ex= 1 Xsec-I, 8 X 23 Xsurface of non-divergence might be located from thetwelve cross sections. It resulted that a surface of leastdivergence could be located at
thelines on a transparent overlay, shown in fig. 2, wasplaced on a point where the smoothed value was tobe computed. The line b-d was always oriented northsouth. The smoothed value obtained was equal to(a+l.+c+d+e)/S, and the distance (f) was equal to25 deg lat. A comparison of a smoothed map with anunsmoothed map showed about what would be ex= 1 Xsec-I, 8 X 23 Xsurface of non-divergence might be located from thetwelve cross sections. It resulted that a surface of leastdivergence could be located at
change ofabout 0.1C in 12 hr at these latitudes. As may be seen later, thisis smaller than R2At. For the purpose of this study, equation (12)is sufficient.2 74 JOURNAL OF METEOROLOGY VoLixI?: 16FIG. 1. Positions of an air particle and of an isobaric surface at two different times.a finite interval of timei.e., AAt, may be evaluatedfrom data on isobaric maps.In fig. 1, surfaces p(tl) and P(t2) represent thehypothetical positions of an isobaric surface at timestl and t2, respectively. B(x2, y
change ofabout 0.1C in 12 hr at these latitudes. As may be seen later, thisis smaller than R2At. For the purpose of this study, equation (12)is sufficient.2 74 JOURNAL OF METEOROLOGY VoLixI?: 16FIG. 1. Positions of an air particle and of an isobaric surface at two different times.a finite interval of timei.e., AAt, may be evaluatedfrom data on isobaric maps.In fig. 1, surfaces p(tl) and P(t2) represent thehypothetical positions of an isobaric surface at timestl and t2, respectively. B(x2, y
