94 10.3 Differences for GRACE A and GRACE B
Figure 10.8: Comparison of twang patterns in ACC1A of GRACE A (left column) and GRACE B (right column) for two scenarios. Upper row: scenario for February/ March of 2007 at LT hour between 1 and 2;
lower row: scenario for April/ May of 2007 at LT hour between 5 and 6.
11. Temporal and spatial behavior of twang parameters 95
types may be holding a majority. For those patterns, where a majority of a type can be clearly detected, it is notable that for GRACE A this type is the opposed type as to the one forming the corresponding pattern for GRACE B.
As the patterns for GRACE A and GRACE B are, apart from the number of twangs and the mixture of types for GRACE A, quite similar, a geographical or geographically associated influence onto the spacecraft is evident. A reason for the reversed type of twang for one satellite compared to the other might be found in the fact that the leading satellite is yawed by 180 degrees in order to establish the inter-satellite ranging system, KBR. This means that the cause for twangs found within the ACC1A data of GRACE has to be found in external sources as prime reason. Further elaboration can be found in part V of this thesis.
11 Temporal and spatial behavior of twang parameters
In this chapter the temporal and spatial behavior of the previously introduced twang parameters shall be described by means of observations. We will not draw further conclusions based on these observations in this chapter. However, many of these observations will be regarded when stating our hypothesis in part V of this thesis. This is necessary as no obervation for itself can give clear evidence for the hypothesis, but they need to be considered summed up.
11.1 Amplitude
In chapter 8.3.2 on page 71 we discussed how the average daily amplitude is behaving over time.
This discussion was only addressing the daily behavior and does not reflect the geographical distribution. As we deduced a possibleβprime cycle influence, we now will address the question whether the general amplitudea, as introduced in equation (8.3) (p. 67), is correlated to the geolocation. In figure 11.1 we display the amplitudes of positive twangs of GRACE B detected in January and February of the year 2008 between LT 12h and 00h. A clear distinction of amplitudes per band is visible. For this scenario there appear to be two main ranges for amplitudes. The most Northern pattern as well as a pattern that starts at approximate latitude 40° S stretching south, have an amplitude ranging from 2·10−7 to 7·10−7 m/s2. The other patterns, located in between the just mentioned patterns, running approximately horizontal at approximately 20°N and 20° S latitude, come with an amplitude ranging from 1·10−6 to 1.6·10−6 m/s2. We chose to display this scenario as a distinction in the amplitudes is very clear in this case, and close to no twangs can be found covering the amplitudes from 7−10·10−7 m/s2. This is a clear indicator for the fact, that not only the distribution of twangs but also their amplitudes are strongly depending on the geographical location of the GRACE satellite.
The next logical step is to address the question whether there is any specific reason for this behavior of the amplitudes of the twangs. In order to examine this issue we chose to display every twang with its corresponding amplitudeawith respect to the day of year of 2008 and to the argument of latitude. The argument of latitude is described in section 10.2.
In figure 11.2 this scenario is displayed for positive and negative twangs. We decided to separate these two types, as we found earlier in section 9 that the orientation of twangs is also often subject to be limited to certain latitudes. On the right side the negative twangs are shown, and the positive twangs on the left side. Again it is clearly visible that the amplitude is correlated to specific latitudes throughout the time. This is more clear for the negative twangs than for the positive twangs. In case of the negative twangs, the band formed by twangs that follow a certain range of latitudes appears to be restricted to a very limited range of amplitudes. Also,
96 11.1 Amplitude
Figure 11.1: Mean amplitude (asymmetry neglected) for each positive twang of ACC1A GRACE B data of January and February 2008 between LT hour 12 and 00.
those patterns that run across a broader bandwidth of latitudes, such as the one visible in the argument of latitude starting at 50° and decaying at approximately 130° from day of year 0 to approximately 200, appear to be very limited to a certain amplitude. This behavior is less obvious in case of the positive twangs. The horizontal patterns of twangs are less strictly correlated to a specific amplitude. Yet, also for the positive twangs dependencies of amplitude values with respect to the latitude are visible. Here, the majority of twangs have an amplitude ranging from approximately 0.9·10−7 m/s2 to 1.3·10−7 m/s2. The negative twangs appear to have two sets of patterns, where one set is ranging from low 0.6·10−7 m/s2 to approximately 0.85·10−7 m/s2 and are the blue patterns visible in the left image. Another range for the negative twangs is from approximately 1−1.4·10−7 m/s2. These two ranges are a lot more separated from each other than the ranges visible for the patterns formed by positive twangs.
Also, in both images we have clusters of twangs in patterns that suddenly have a rather big amplitude. For both types this is the case between day of year 150 to 300 (approximate values) and is especially visible between argument of latitudes 250° to 350°. Especially in the case of the positive twangs this high amplitude starts to appear rather suddenly with respect to the amplitude of the surrounding twangs of the same pattern and those which are located near the described area.
An interesting phenomenon visible for the scenario displayed of the negative twangs can be found around day of year 250 at latitudes 0° to 100°. There are two horizontal bands which start occurring a few days prior to DOY 250 and remain existing towards the end of the year 2008.
However, the pattern visible at approximately 250 DOY that runs rather vertically dissects these two bands. The two bands appear to have a slightly but notable larger amplitude after this event than before.
Also for the along-track axis a strong correlation between the magnitude of the amplitude of the twang and the geographical location of the satellite at the time of the occurrence of the twang can be found. In figure 11.3 we present three images, where the left and the center image are displaying the twangs in the along-track component. The left image is showing the positive twangs in the along-track axis, and the center image the negative twangs. Note, that we are separating into these two types now according to along-track appearance and not by means of the
11.1 Amplitude 97
Figure 11.2: Mean amplitude (asymmetry neglected) for positive (left image) and negative twangs (right image) in the radial component of ACC1A data of GRACE B. The x-axis represents the day of year (DOY) of 2008 and the y-axis is the argument of latitude.
Figure 11.3: Mean amplitude (asymmetry neglected) for positive (left image) and negative twangs (center image) in the along-track component and positive twangs in the cross-track component (right image) of ACC1A data of GRACE B. The x-axis represents the day of year (DOY) of 2008 and the y-axis is the argument of latitude.
radial component. For positive twangs it is notable that twangs forming the oval shape pattern in the center of the picture have a relatively high amplitude of more than 10·10−9 m/s2. This also applies to the other areas, where the nadir surface of the satellite is lit by direct sunlight (cf.
section 12.2). This strict correlation to those areas is not detectable for the negative twangs, where other correlations are dominating the image, such as the rather horizontal band slightly above degree 300°. In both figures also other areas and patterns are limited in their range of amplitude.
The very right image of figure 11.3 is an example for the geographical appearance for the amplitude of the twangs in the cross-track axis of the ACC1A data. In contrast to the radial and along-track data of the same dataset, no clear correlation to the geographical location can be detected. Throughout the whole year 2008 the amplitude appears to be rather non-systematic with respect to the geographical occurrence of the twang in this axis. Only vague correlations can be observed, as for example, twangs with a higher amplitude appear to have a majority in the oval shaped pattern in the center of the image. This phenomenon is surprising as for the other two axes a very clear and distinct correlation could be detected and the natural