Atmospheric Rossby Waves Fall 12: Analysis of Northern and Southern hpa Height Fields and Zonal Wind Speed Samuel Schreier, Sarah Stewart, Ashley Christensen, and Tristan Morath Department of Atmospheric and Geological Sciences, Iowa State University, Ames, IA ABSTRACT This study uses hpa heights in both hemispheres as well at zonal winds from 3-1hPa to analyze large scale synoptic waves. Data was collected from August 29, 12 to November 7, 12 and included wave number, speed, amplitude and zonal wind speed. The wave and zonal wind data was plotted graphically and analyzed against Rossby Wave Theory. In general, observations did agree with the theory. Reasons for this agreement could include analysis procedures, the very short study period of three months, and human error in data collection and analysis. 1. Introduction Large-scale atmospheric waves are an essential part of the Earth s weather. These waves are responsible for movements of warm, cold air, precipitation and even the generation of convective systems such as thunderstorms. Large-scale wave movements have minimum and maximum amplitudes, which are known as troughs and ridges. These troughs and ridges are tracked by forecasters, and when applied with quasigeostrophic theory, can be a powerful forecasting tool. Examples of this application are finding areas of upward motion from positive vorticity advection and temperature advections. Troughs will advect positive vorticity near their exit region, which will form a low pressure system ahead of the trough, creating upward motion and often resulting in precipitation. This illustrates that wave predictability can be used to forecast and analyze weather. Waves in both hemispheres will change corresponding to seasonal changes. Typically the strongest waves are seen in the winter, meaning amplitudes typically grow while the wave numbers decrease. Spring and summer tend to see weaker waves, meaning there will be smaller amplitudes and more wave numbers. The goal for this study is to analyze observed wave and zonal wind data and compare that to Rossby Wave Theory. Expected results should show large wave numbers correlate with lower amplitudes and faster wave motion. 2. Data Data collection was important to be able to complete a proper waves analysis. From the Iowa Weather Products page, observations were taken daily of the Northern and Southern Hemisphere wave patterns and a cross section of the zonal wind pattern from August 29, 12 to November 11, 12. Data collected daily includes position of the defined target contour with respect to the degree latitude line on the hectopascal (hpa) map, wave number, amplitude, wave motion, and zonal wind. Target contours for each of the hemispheres include 558 meters (m) in the Northern Hemisphere and 528 meters (m) in the Southern Hemisphere. All data was recorded on a spreadsheet.
(a) Waves Several parameters are examined at the hpa map at the Northern and Southern poles. First is the wave number which is obtained by counting the number of crossings that the target contour makes across the degree latitude line and divide by 2. k = N / 2 Where k is the wavenumber and N is the number of target contour crossings (558m in the North and 528m in the South) to the target latitude ( ). This parameter indicates a notable magnitude of the wave(s) and gives a representation of how active the waves are for that time period. It is important to note that waves that do not exceed the latitude line are excluded as notable waves. Therefore, our data is limited to large scale wave motions. The second parameter obtained is the amplitude of each individual wave (both positive and negative) found using the target latitude and the height contours. To understand the waves amplitude we calculate the maximum height (Z_max) and minimum height (Z_min) of each wave and then calculate the average over all the waves. Average Z_max = (Zmax_1 + Zmax_2 + + Zmax_n)/n Average Z_min = (Zmin_1 + Zmin_2 + + Zmin_n)/n To obtain amplitude for the waves of a given hemisphere on a given day, you subtract the Average Z_min from the Average Z_max and divide by 2: Amplitude = (Z_max Z_min)/2 Amplitude gives a good indication of the size and intensity of the waves. However, it is important to again recognize that smaller waves that do not extend beyond the line are not accounted for in the amplitude. Therefore, we would expect an amplitude representative of the whole atmosphere to be lower than what is indicated in this study. The third parameter is to obtain the motion of the wave on a given day. To compute the speed (C), it is best to find where a target contour intersects the target longitude one day and evaluate from the previous day to obtain the change in the wave s position. To calculate the exact motion, the following equation is helpful. C = [lon(day+1) - lon(day-1)] /2 2
(b) Zonal Wind It is important to take observations in the vertical profile to get an understanding of how the winds are behaving at present and how they are changing in time. For this analysis, several observations are made. The first observation made is the maximum zonal wind speed for both the Northern and Southern Hemisphere and the latitude(s) at which it is observed. The second observation is the zonal wind speed at hpa at degrees latitude in both hemispheres. The third is the maximum zonal wind speed between 3 and 1 hpa at degrees latitude. All of these observations are taken daily along with the waves analysis. 3. Methods (a) hpa Charts When collecting data from the hpa charts, generalizations were made. For example, on numerous occasions it was impossible to distinguish the relationship between the hpa contour and the degree North or South latitude line. The map s resolution on the PALS Weather Data Viewer made it impossible to tell whether the hpa line crossed the degree line or not. In such circumstances, the line was assumed to have crossed. By doing this, the data may have a tendency to show more waves than actually occurred by the given definition. These estimations were used to keep the data consistent, and considered valid because the error associated with the estimations occurred only a few times. When calculating the amplitude, similar assumptions were made when documenting the average maximum and average minimum amplitudes. It was sometimes impossible to tell precisely what magnitude to use, as the contour would again overlay the degree latitude line. The lower value was assumed if it was a maximum. Results will then reflect the movement of large scale waves. If it was a minimum, the lower height value was recorded. In borderline cases like these, verifiable evidence that the contour did indeed cross our threshold degree line was required in order to raise or lower our magnitudes accordingly. (b) Zonal Wind Throughout the wave documentation and calculation processes, many steps were taken to improve accuracy and precision in the analysis. When the zonal wind values were documented, degrees North and South latitude was estimated, respectively. This can lead to errors in estimation of the magnitude of the zonal wind at degrees. Locations of mountains and other geographical features that were distinguishable on the map were used to further improve our estimation of degrees North and South. (c) Other Methods There were times when large pronounced waves crossed far beyond the degree latitude line. These waves contained small protrusions, related to secondary cold fronts at the surface, resulting in a second crossing of the degree line. These secondary crossings were not applied in the calculations, as they were clearly 3
Zonal Wind Speed (m/s) associated with the main wave feature. This only happened on a few occasions, but still resulted in a lower number of waves than was defined. The above assumptions were necessary, as the goal of the project is to understand the motion of waves on the synoptic scale. As stated above, several different assumptions were made while documenting and analyzing the PALS Weather data. The assumptions made were justifiable with the intent of better understanding the processes driving the motion of waves on the synoptic scale. Ultimately, the analysis will result in a depiction more representative of the real relationship between the jet stream and large scale wave features evident in hpa height maps. 4. Results and Analysis (a) Zonal wind The zonal wind speed is a good indicator of the wave speed and direction of propagation. Negative and positive speeds on the zonal wind maps describe two different directions of the wind. Where positive winds indicate westerly winds, easterly winds are denoted by negative numbers. 9 8 7 hpa Zonal Wind Speeds vs. Date y = -.228x + 9463 R² =.188 SH 6 4 3 y =.182x - 7486 R² =.183 NH 8/29/12 9/5/12 9/12/12 9/19/12 9/26/12 /3/12 //12 /17/12 /24/12 /31/12 11/7/12 Date NH U SH U NH trendline SH trendline Figure 1 The zonal wind in the Northern and Southern hemispheres differ in relative magnitude. Southern hemisphere zonal winds were mostly greater than those in the Northern hemisphere, until about a month after the official change of seasons (September 21). Once the seasonal transition was established, zonal winds in both hemispheres tended to be of similar magnitude. The magnitude of the zonal wind for the Southern hemisphere decreased from late August to early November, whereas the Northern hemisphere zonal wind magnitudes increased (to a lesser degree) over the same period. Northern hemisphere average mb zonal wind speed at 4
Ampltidue in m U in m/s o latitude was 13.7 m/s whereas the average mb zonal wind speed at o latitude was 26.57 m/s. The differences in speed may be explained by the differential of landmass between the two hemispheres. The magnitude is lower in the Northern hemisphere at this latitude due to the mountainous terrain and expansive landmasses, both of which exert frictional effects on the atmosphere. Conversely, the oceans in the Southern Hemisphere cover nearly all of the latitude area. Frictional effects on the wind at mb are significantly less than those in the Northern Hemisphere due to less frictional dissipation, and therefore zonal wind speeds are greater. Range for maximum wind speed at mb NH: m/s to 6m/s, and SH: 3m/s to 8m/s. The higher range in the southern hemisphere is likely due to smaller frictional dissipation than that of the Northern hemisphere. This explains the low values of the coefficients of determination, represented by R 2 in the figure. The low R 2 values are prominent for the southern hemisphere. Intuitively, the Northern Hemisphere would tend to have less variability in the winds due to the presence of extensive landmass exerting the frictional effect to slow down the winds. The opposing nature of friction is stronger for stronger winds, and weaker for slower winds, therefore bringing the range values closer together in the Northern Hemisphere. Since there are less frictional effects in the Southern Hemisphere, due to the extensive oceanic composition, the faster winds (at the top of the range) remain faster than the slower winds (at the bottom of the range.) The slopes of the amplitude and hpa zonal wind are both positive in the Northern Hemisphere (Figure 2). Amplitudes increase over the period, having a small positive slope compared to that of the hpa zonal wind trend, which slopes positively to a greater degree. In the Southern Hemisphere, both the amplitude and hpa zonal wind have a negative trend (Figure 3). As in the Northern Hemisphere, the Southern Hemisphere magnitude of change in amplitude is small compared to the change in hpa zonal wind. 2 225 175 1 125 Northern Hemisphere Amplitude vs. hpa Zonal Wind y =.236x - 9567. R² =.24 NH Amplitude 7 6 4 3 75 25 y =.182x - 7486. R² =.183 U NH 8/29/12 9/5/12 9/12/12 9/19/12 9/26/12 /3/12 //12 /17/12 /24/12 /31/12 11/7/12 Date NH Amplitude U NH Linear (NH Amplitude) Linear (U NH) Figure 2 5
Amplitude (m) hpa Zonal Wind Speed (m/s) The overall change of the Northern Hemisphere wave amplitude is positively correlated with the change in hpa zonal winds over the period. Though the maxima and minima seem to be opposing through most of the graph, there is an overall increase in the magnitude of both parameters. The most apparent feature being when the wave amplitude is large (small), the zonal wind tends to be small (large). This opposing relationship here is due to frictional effects. When zonal winds are large, frictional forces become stronger, and therefore decrease the amplitude of the wave. With the transition from summer to late autumn, the zonal winds and amplitudes become larger due to the expansion of lower heights into higher latitudes, contributing to larger magnitudes of wave minima, and hence to the amplitudes. The Southern Hemisphere amplitude and hpa zonal wind decreased during the period. With the seasonal transition from winter to spring, colder air began to recess toward the South Pole. This caused amplitude measurements taken from o latitude using the contour 528m to become smaller over the period. Southern Hemisphere Amplitude vs. Zonal Wind Speed 3 3 2 1 y = -.124x + 5318. R² =.5 Amplitude SH 9 8 7 6 4 3 y = -.228x + 9463 R² =.188 U SH 8/29/12 9/5/12 9/12/12 9/19/12 9/26/12 /3/12 //12 /17/12 /24/12 /31/12 11/7/12 Date Amplitude SH (m) U SH Amplitude SH U SH Figure 3 The change in wave amplitude is positively correlated with the hpa zonal wind change over the period. Though the maxima and minima are opposing through most of the graph, there is an overall decrease in the magnitude of both parameters. The most apparent feature is that, generally, when the wave amplitude is 6
Amplitude (m) large (small), the zonal winds tend to be small (large). This opposing relationship is similar to that of the Northern Hemisphere, except when zonal winds are large in the Southern Hemisphere, frictional forces are not as prominent. The ocean surface which covers most of the southern hemisphere interferes with the reliability of comparing zonal wind strengths, being comparatively weak in the Northern Hemisphere due to landmass, high terrain, and hence frictional effects. The magnitude of change in the hpa zonal wind therefore is greater than that of the Northern Hemisphere. The seasonal change that occurred during the period is opposite in the Southern Hemisphere to that in the Northern Hemisphere; therefore the trend in the wave amplitude will be opposite as well, as shown in Figure 6. (b) Wave amplitude Wave amplitude varies over a temporal scale and generally increases with time in the Northern Hemisphere. However, the amplitude tends to decrease over time in the Southern Hemisphere. (Figure 4 and Figure 5). The amplitude increase (Northern Hemisphere) is due to the season change, from warm summer temperatures to cool autumn temperatures; this corresponds to wave numbers generally increasing during the time period (Figure 7). As the wave number increases (decreases), the amplitude generally increases (decreases). In the case of the Southern Hemisphere, the amplitude decreases over time, corresponding to a wave number decrease (Figure 8).This is correlated with the seasonal change from winter to spring in the Southern Hemisphere. 3 NH Amplitude vs. Date 2 y =.236x - 9567. R² =.24 1 NH Amplitude Linear (NH Amplitude) 8/29/12 9/5/12 9/12/12 9/19/12 9/26/12 /3/12 //12 /17/12 /24/12 /31/12 11/7/12 Date Figure 4 7
Amplitude (m) 3 3 2 SH Amplitude vs. Date y = -.124x + 5318. R² =.5 1 SH Amplitude Linear (SH Amplitude) 8/29/12 9/5/12 9/12/12 9/19/12 9/26/12 /3/12 //12 /17/12 /24/12 /31/12 11/7/12 Date Figure 5 The difference between Northern and Southern amplitude trends over the period are shown below (figure 8). The opposite signs of trend line slopes between hemispheres are prominent. The difference in amplitude magnitude between each hemisphere decreases over the period, corresponding to more similar amplitudes at the end of the period. 8
Amplitude (m) NH and SH Amplitude vs. Date 3 3 y = -.124x + 5318. R² =.5 2 1 NH Amplitude (m) SH Amplitude (m) Linear (NH Amplitude (m)) y =.236x - 9567. R² =.24 Linear (SH Amplitude (m)) 8/29/12 9/5/12 9/12/12 9/19/12 9/26/12 /3/12 //12 /17/12 /24/12 /31/12 11/7/12 Date Figure 6 Though the slopes of each trendline are shown to be opposite in sign, they also differ in absolute value by nearly a factor of two. During the period, the amplitude maxima in the Southern hemisphere seemed to correspond relatively well to the occurrence of the minima in the Northern hemisphere. This correlation tends to become less prominent as the amplitude of the waves in the northern hemisphere become larger here. The average amplitude over the period for the Northern Hemisphere was 161.6m whereas the Southern Hemisphere average amplitude was still higher, having a value of 188.4. Differences in the average amplitude over the change of season for both the Southern and Northern Hemispheres are shown in Figures 6a and 6b, respectively. 9
3 SH Amplitude Winter 2 1 8/29/12 8/31/12 9/2/12 9/4/12 9/6/12 9/8/12 9//12 9/12/12 9/14/12 9/16/12 9/18/12 9//12 SH amp winter Average Linear (SH amp winter) y = -.3656x + 15229 3 SH Amplitude Spring 3 2 1 9/21/12 9/25/12 9/29/12 /3/12 /7/12 /11/12 /15/12 /19/12 /23/12 /27/12 /31/12 11/4/12 SH amp Spring Average Linear (SH amp Spring) y = -1.857x + 449 Figure 6a
3 NH Amplitude Summer 2 1 8/29/12 8/31/12 9/2/12 9/4/12 9/6/12 9/8/12 9//12 9/12/12 9/14/12 9/16/12 9/18/12 9//12 NH amp Summer Average Linear (NH amp Summer) y =.158x - 492.31 3 NH Amplitude Autumn 2 1 9/21/12 9/25/12 9/29/12 /3/12 /7/12 /11/12 /15/12 /19/12 /23/12 /27/12 /31/12 11/4/12 NH amp Autumn Average Linear (NH amp Autumn) y =.4846x - 1981 Figure 6b 11
Wavenumber (c) Wavenumber The wavenumber tends to vary with time in both the Southern and Northern Hemispheres. The Northern Hemisphere NH wavenumber vs. date is shown to have a positive trend, indicating more waves toward the end of the period than at the beginning. This increase in wave number has to do with the fact that transitioning from Summer to Autumn in the Northern Hemisphere will cool the atmosphere, and waves of low heights can extend further our from the North Pole, crossing the o latitude circle, and therefore being denotes as waves in this analysis. Beginning with a typical wavenumber between one and two, the wavenumber had increased to be between 4 and 5 by the end of the period. The Northern Hemisphere wavenumber ranges between and 5, meaning that there were no waves to be recorded, and therefore the data should be disregarded on those days. The average wavenumber for the Northern Hemisphere was 3.17; the Southern Hemisphere average was higher, at 3.7. Therefore, the southern hemisphere tended to have more waves than in the northern hemisphere on average over the period, despite the downward trend in wavenumber. The turning point when similar wave numbers appear in both hemispheres takes place in October. This provides significant implications; since the changing of seasons is gradual, then so should be the transition between the numbers of waves produced during that period. In the Southern Hemisphere, the slope of the trend line is much less prominent than that of the Northern Hemisphere. The small decrease in wavenumber in the Southern Hemisphere may be correlated with the fact that the Southern Hemisphere is dominated by ocean, rather than land, which influences the magnitudes of frictional effects and surface heating. The transition in the Northern Hemisphere is much sharper than that of the Southern Hemisphere. Land surfaces heat and cool more rapidly than ocean surfaces, and tend to cause fluctuations in the Northern Hemisphere wave patterns to be more prominent. 6. NH Wavenumber vs. Date 5. 4. 3. 2. 1.. y =.394x - 1621 R² =.3624 8/29/12 9/5/12 9/12/12 9/19/12 9/26/12 /3/12 //12 /17/12 /24/12 /31/12 11/7/12 NH Wave Number Date Linear (NH Wave Number) Figure 7 12
Wavenumber SH Wavenumber vs. Date 7 6 5 4 3 2 1 y = -.5x + 8.11 R² =.98 8/29/12 9/5/12 9/12/12 9/19/12 9/26/12 /3/12 //12 /17/12 /24/12 /31/12 11/7/12 Date SH Wavenumber Linear (SH Wavenumber) Linear (SH Wavenumber) Figure 8 The amplitude dependence on wave number is shown to be more prominent in the Southern Hemisphere than the Northern Hemispheres. Both hemispheres show a decreasing amplitude as the wave number increases (Figure 9 and Figure ). This agrees with the Rossby Wave Theory. More short waves are generally present as the wave number increases, so the average amplitude of the waves will decrease. Having the same amount of energy distributed over a larger number of waves causes each wave to receive a lesser amount of this energy. Short waves have smaller amplitudes than long waves because energy must be conserved. Thus, the amplitude of the waves must decrease. Because the coefficient of determination is small in the Northern Hemisphere, at.23, while it is.153 in the Southern Hemisphere, the significance of the correlation is better seen in the Southern Hemisphere (figure 9). The low coefficient of determination in the Northern Hemisphere may be due to zero being plotted for a wave number. This point also has a value of zero for the amplitude. Therefore, including outliers may cause something to look statistically significant, when it truly isn t, or the opposite. The slope of the trend line in figure is significantly smaller in magnitude, and gives rise to the general trend possibly being misread in comparison to the southern hemisphere data. 13
Amplitude (m) Amplitude (m) 3 Wavenumber SH vs. Amplitude 3 2 1 y = -13.688x + 239.15 R² =.1538 1 2 3 4 5 6 7 Wavenumber Figure 9 3 Wavenumber NH vs. Amplitude 2 1 y = -3.29x + 172.7 R² =.23 1 2 3 4 5 6 Wavenumber Figure 14
Wave Motion degrees/day (d) Wave motion Wave motion, calculated in degrees per day, are seen to correlate with the wavenumber in both the Northern and Southern Hemispheres. The wave motion tended to be faster in the Northern Hemisphere when wavenumbers were low, as shown in Figure 11. This disagrees with the Rossby Wave Theory, though error in concluding that wave motion decreases with increasing wavenumber could be significant, due a point having a wavenumber of zero. Though short waves have a larger wave number than long waves and travel faster than long waves, this graph shows that wave motion tends to be fastest for waves with smaller wavenumbers, at least in the Northern Hemisphere. The slope of the trendline appearing in the Southern Hemisphere case has opposite sign and smaller magnitude. This indicates a positive relationship between wavenumber and wave motion, namely, wave speed increases as wave number increases (Figure 12). This does not agree with the Rossby Wave Theory. As the wave number increases, the wave motion should also increase. The distinction between the two hemispheres may be explained by taking multiple sources of error, such as human error in the wave motion calculations. Also to be considered should be the difference in the surfaces over which the waves traveled. The Southern Hemisphere is much closer to an ideal frictionless surface than the rugged terrain of the Northern Hemisphere. Retrograding waves, waves remaining stationary, or waves which disappeared due to deamplification could have been neglected from the dataset, though they were not ignored. Therefore, this wave motion data may not have been an attractive representation of theory, but does represent what actually occurred over the domain. The Rossby Wave Theory tends to be difficult to reconstruct through observational data; this theory is valid for barotropic flow, though waves characteristic of the real atmosphere rarely or may never have the same density throughout their depth. Therefore, it can be inferred from analysis that the barotropic assumption required by Rossby Wave Theory may not be valid for the real atmosphere. 25 Wave Motion vs. Wavenumber NH 15 5 1 2 3 4 5 6 Wave Motion vs. Wave Number NH Wavenumber Linear (Wave Motion vs. Wave Number NH) y = -.783x + 14.128 R² =.13 15
Wave Motion degrees/day Figure 11 35 Wave Motion vs. Wavenumber SH 3 25 15 5 1 2 3 4 5 6 7 Wavenumber Wave Motion vs. Wavenumber SH Linear (Wave Motion vs. Wavenumber SH) y =.4839x + 16.74 R² =.7 Figure 12 The wave motion also displays a dependence on the hpa zonal winds. The Northern Hemisphere (Figure 13) shows indication of a positive relationship between the the hpa zonal winds and wave motion. The relationship is barely positive, with a slope of.14 and an R 2 value of.1. The graph shows that wave motion can increase with higher hpa zonal wind speeds, but not necessarily concretely. Retrograde motion is accounted for in the figures, therefore showing less than ideal correlations between hpa zonal wind speed and wave motion. The Southern Hemisphere (figure 14) shows a positive correlation between these parameters as well. For positive values of hpa zonal flow, as the hpa wind increases, wave motion increases. The Southern Hemisphere displayed the positive correlation better than the Northern Hemisphere, because the coefficient of determination is.8 compared to.1 in the Northern Hemisphere. Rossby Wave Theory states that waves propagate westward if no zonal flow is present. The zonal flow must reach approximately 3 m/s in order for waves to begin moving east depending on the wavelength. According to Rossby Wave Theory, as the hpa zonal flow moving eastward increases, the wave should propagate faster toward the east. For both hemispheres, as the hpa zonal flow increases, the wave motion toward the east increases, but not to the extent which theory suggests. The linear fit is not strong for both the Northern and Southern Hemispheres, but the general trend over the domain agrees with Rossby Wave Theory. 16
hpa Zonal Wind m/s hpa Zonal Wind m/s 7 hpa Zonal wind vs Wave motion Northern Hemisphere 6 4 3 2 4 6 8 12 14 16 18 Wave Motion m/s Zonal wind vs Wave motion Linear (Zonal wind vs Wave motion) y =.141x + 32.98 R² =.15 Figure 13 9 hpa Zonal Wind vs. Wave Motion Southern Hemisphere 8 7 6 4 3 5 15 25 3 Wave Motion m/s SH Zonal Wind vs. Wave Motion Linear (SH Zonal Wind vs. Wave Motion) y =.1986x + 47.765 R² =.82 Figure 14 The wave motion was believed to also have a dependence on the upper-level 1-3 hpa zonal wind(uupper). Both the Northern (Figure 15) and Southern (Figure 16) Hemispheres show correlation coefficients of zero between these parameters. As the 1-3 hpa wind increases, wave motion remains steady overall, though the slope is slightly positive for both Hemispheres. This neither agrees nor disagrees with the Rossby Wave Theory, as the correlations between parameters over the domains are approximately zero. The 17
NH 1-3hpa Zonal Wind m/s discrepancy may be due to the way wave motion was calculated, or from assuming a non-realistic barotropic atmosphere The positive slopes show agreement with Rossby Wave Theory, although the correlation coefficient being zero does not confirm Rossby Wave Theory. 6 NH Uupper vs. Wave Motion 4 y =.422x + 19.733 R² =.1 3 2 4 6 8 12 14 16 18 Wave Motion m/s NH wave motion vs. 1-3hpa zonal wind Linear (NH wave motion vs. 1-3hpa zonal wind) Figure 15 18
Zonal wind speeds (m/s) SH!-3hPa Zonal Wind 8 SH Uupper vs Wave Motion 7 6 4 3 y =.53x + 4.5 R² =. 5 15 25 3 Wave Motion m/s SH Uupper vs Wave Motion Linear (SH Uupper vs Wave Motion) Figure 16 (e) Thermal wind The thermal wind relationship states that whenever there is a horizontal temperature gradient, there will always be a change in the geostropic wind with height. Therefore, higher winds will be located at lower pressure levels. The observational procedure used in this study supports the thermal wind relationship for both the Northern and Southern Hemispheres. The wind speed for the 1-3hPa level is almost always greater than for the hpa level as shown, in figures 17 and 18, below. 8 7 6 4 3 Southern Hemisphere Zonal Wind vs. Date 8/29/12 9/5/12 9/12/12 9/19/12 9/26/12 /3/12 //12 /17/12 /24/12 /31/12 11/7/12 Date U Uupper Figure 17 19
Zonal Wind Speed (m/s) 6 Northern Hemisphere Zonal Wind vs. Date 4 3 8/29/12 9/5/12 9/12/12 9/19/12 9/26/12 /3/12 //12 /17/12 /24/12 /31/12 11/7/12 Date U Uupper 5. Conclusion Figure 18 The goals of this study were to analyze synoptic wave and zonal wind data and compare observations in order to see if that data agreed with Rossby Wave Theory. In general, the results of this study were, for the most part, in agreement with Rossby Wave Theory. There were a few instances where the data did not agree with the theory, but those discrepancies can be attributed to human error in wave data documentation and a short period of observation. This study shows promise that the Rossby Wave Theory is a reliable forecasting tool, but further research should be done using a longer observation period and perhaps computerized wave tracking.