Quantification of Cloud and Inversion Properties Utilizing the GPS Radio Occultation Technique

Transcription

1 Quantification of Cloud and Inversion Properties Utilizing the GPS Radio Occultation Technique Clark Evans Florida State University Department of Meteorology June 8, 2004

2 Abstract In this paper, Global Positioning System (GPS) radio occultations (ROs) are analyzed through regions of clouds to quantify properties of clouds and test the accuracy of the RO technique. Dry and moist occultation data from the aforementioned GPS satellites over the Americas and the Atlantic Ocean during May 2002 are obtained and filtered into ten categories based upon occultation latitude and GOES-8 satellite imagery analyses of clouds in the region. Comparisons of mean profiles and standard deviations from the mean for all data sets, fractional differences from the mean for the dry data sets and features observed in the moist data sets are performed. It is shown that there are noticeable impacts in data from bending angle, refractivity, temperature and vapor pressure retrievals owing to unique properties of clouds as sensed by the GPS RO technique. These impacts are the result primarily of the inherently different properties associated with each of the major cloud types of cirrus, convective, cumulus and stratus. These retrievals also serve to highlight the lack of variation found in the height of the tropopause in the tropics and the greater spread in the height of the tropopause in the midlatitudes. It is also shown that inversion layers can be analyzed with a high degree of precision when taking into account cloud categorizations. In analyzing for inversions in vapor pressure data, it is shown that there are possible disagreements between moist temperature and humidity data; this is likely due in part to a combination of the methods used to the calculation of both sets of variables and the inherent error in moist temperature retrievals. From these findings, a method to improve upon the retrieval of temperature and vapor pressure data through regions of clouds is proposed utilizing the Clausius-Clapeyron relationship. 1

3 1. Introduction The RO technique holds great promise in understanding many atmospheric features, ranging from the evolution of short-term synoptic-scale features throughout the troposphere to the variation of long-term atmospheric climate signals. Two ongoing Global Positioning System (GPS) radio occultation (RO) proof-of-concept experiments, the CHAMP [CHAllenging Minisatellite Payload; e.g. Wickert et al. (2001)] and SAC-C [Satélite de Aplicaciones Cientificas-C; e.g. Hajj et al. (2004)] missions, currently provide a vast array of meteorological data through space-based observations of the atmosphere. It has been previously shown [such as in Wickert et al (2001) and Gerding and Weisheimer (2003)] that the data obtained from these satellites provides accurate and useful meteorological data, allowing for improved numerical weather prediction and climate studies. In this work, impacts of moisture on bending angle, refractivity, temperature and water vapor measurements associated with each of the major cloud types are analyzed using GPS occultation data obtained from CHAMP and SAC-C. Ideas for future studies in the field aimed at further understanding of atmospheric properties and features as well as at improving the occultation retrieval techniques themselves are demonstrated. A description of the RO technique is presented by Kursinski et al. (1997) and is only briefly summarized from their work here. A GPS satellite, as it rises or sets with respect to the receiving satellite, can measure atmospheric properties through the transmission of a signal through the earth s atmosphere. As it traverses the atmosphere, the signal is bent according to Snell s law by refraction processes due to stratification. The amount that the signal is bent is given by bending angle α, the distance between the occulting ray and the center of the earth as defined by the local curvature radius r t or impact parameter a. In the general case, it is not possible to retrieve the variation in the index of refraction directly from this data; however, 2

4 assuming spherical symmetry and a radial direction to the gradient of the index of refraction, an Abel inversion (utilizing integration) can be used to obtained the variation in the index of refraction n. With data for n, values for refractivity N, pressure p, temperature T and water vapor pressure P w can be found as a function of atmospheric bending angle (Kursinski et al. 1997): N p T 6 5 W = ( n 1) 10 = x10, (1) 2 P T where p = pressure (hpa), T = temperature (K) and P w = vapor pressure (hpa). In this equation, the known orbits of a pair of GPS satellites are used in a double differencing scheme to eliminate p the ionospheric path delay in the occultation signal. The first term, 77.60, is the dry T refractivity term and dominates below 60-90km. The second term, the moist term, plays an important role near the surface where water vapor content is non-negligible. Values of dry temperature and pressure are obtained from (1) either utilizing the equation of state and assuming a hydrostatic atmosphere or by utilizing an iterative process to obtain both independently of each other. Water vapor measurements are generally obtained utilizing ancillary data such as large-scale temperature analyses; however, improved methods have been developed or are in development. Moist temperature data is obtained from the dry temperature data, corrected where necessary in the lower atmosphere by ancillary moisture data (UCAR 2004b). Uncertainty in the measurements in a dry atmosphere is of small magnitude, while uncertainty in moist refractivity data is around 1% in the moist case. Further research by Hajj et al. (2004) and Kursinski et al. (1995, 1997) show that temperature retrieved from GPS measurements are of high accuracy and are consistent with data from other sources such as radiosondes and weather forecasts to within <1 K in a dry atmosphere 3

5 and to within 1-2 K in a moist atmosphere. Measurements are thus assumed to be accurate enough to distinguish fine features in the atmosphere. Details about completed cloud analyses are presented below in section two. Analysis design is presented in section three, while results are presented in section four. Ideas for expanding upon these results with an improved retrieval method within a saturated atmosphere are presented in section five. A summary and conclusion of the main ideas presented in this work are presented in section six, followed by acknowledgements and references. 2. Cloud and Satellite Imagery Categorizations Before any analyses of the occultation data can be performed, the data needs to be separated based upon an analysis of cloud imagery in the vicinity of each occultation perigee point into defined latitude bands and cloud categories. This is necessary as not all clouds have the same properties nor do they have the same impacts on signals that are transmitted through them, such as GPS occultation signals. Furthermore, clouds in the tropics have different properties than those in the midlatitudes, owing to inherent differences in the atmosphere in these regions such as mean troposphere depths, freezing level and mean water vapor content in the lower atmosphere. 2.1 Defining the region of analysis The defined time period of consideration is May 2002, owing to ample data availability during this time frame. Visible and infrared satellite imagery from the GOES-8 satellite are selected for analysis; this satellite imagery is available at three-hour intervals (starting at 0Z each day) during this month. Above 60 S and 60 N, the imagery quality becomes degraded due to impacts of the curvature of the earth. Therefore, occultations taken north of 60 N and south of 60 S are eliminated. Due to the sheer number of occultations available and the necessity of vast 4

6 amounts of imagery for the categorizations of these profiles, the viewable range is limited to the approximate optimal viewable range of the GOES-8 satellite. With the GOES-8 satellite centered over 75 W, this optimal range was taken to be between 30 W and 100 W, covering much of the Atlantic Ocean and parts of North and South America. From an original total of 6497 occultations considered from CHAMP and SAC-C during the month of May 2002, as depicted in Figure 1, a new total of 940 occultations remain. As noted above, the atmosphere exhibits different properties in the tropics and midlatitudes. Therefore, the region is further split into midlatitude and tropical regions, defined as between 60 S and 30 S and 30 N and 60 N for the midlatitudes and between 30 S and 30 N for the tropics. Five cloud categories are established within each region based upon the predominant cloud types commonly observed cirrus, convective (i.e. cumulonimbus), cumulus (i.e. as a result of diurnal heating over land) and stratus clouds; with regions of no clouds being the fifth category resulting in ten categories for analysis. The perigee latitude and longitude of each occultation is obtained to facilitate the task of organizing the occultations by cloud type. While occultations from CHAMP and SAC-C have been shown to have horizontal resolutions of about 200km (Kursinski et al. 1995), utilizing the perigee points for categorization is sufficient to gain an understanding of characteristics of an occultation passing through different regions of clouds. Occultations are divided into bins centered ±90 minutes on the times of the obtained satellite imagery (e.g. for imagery at 0300Z, occultations between 0130Z and 0430Z are considered) for comparison with the satellite imagery. Both infrared and visible imagery are obtained as both the relative depth and height of clouds can be detected as opposed to just the relative heights from the cloud top temperatures in infrared imagery alone. 5

7 2.2 Cloud categorization procedure and examples Utilizing a subjective process based upon the known features of clouds on satellite imagery, the regions around each occultation are analyzed for any present cloud types utilizing infrared and, where available, visible satellite imagery. In the cirrus cloud categorization depicted in Figure 2, note the bright depiction on the infrared image at right but the very faint depiction on the visible image at left, characterizing a high altitude cloud with cold cloud tops but very low thickness such as cirrus clouds. These qualities are used in the other cloud analyses of cirrus clouds. In all, 53 RO profiles are identified as passing through cirrus clouds in the midlatitudes and tropics. Furthermore, in the convective cloud occultation example depicted in Figure 3, note the bright depiction on the infrared image and a very bright depiction on the visible image, characteristics of a cloud mass with cold cloud tops and high thicknesses, such as convective clouds. A total of 190 profiles are categorized in the midlatitude and tropical convective categories. In the cumulus occultation example depicted in Figure 4, note the faint but non-negligible depiction on the infrared image and the corresponding faint depiction on the visible image. On both, the clouds in the region have a very spotty nature; these facts are all consistent with cumulus clouds, particularly those formed as a result of diabatic heating during the daytime. A total of 271 occultations are categorized as passing through cumulus clouds in the midlatitudes and tropics. Finally, in the stratus occultation example highlighted in Figure 5, note the dull depiction on the infrared image corresponding to a somewhat uniform and bright depiction on the visible image, characteristic of a cloud mass with relatively warm cloud tops but uniform thickness, such as stratus clouds. These are much more prevalent in the midlatitudes than in the tropics, with 188 total occultations in both regions during May

8 Occultations analyzed as passing through relatively ambiguous types of clouds those passing through cloud types such as stratocumulus that combine features of multiple cloud types (such as stratocumulus) or those that are analyzed as passing through multiple types of clouds are discarded from the analysis. In total, 792 occultations were categorized within one of the ten occultation categories previously defined, as categorized in Table 1 and depicted in Figure 6. The number of occultations per height level is presented in Figure Analysis Design Three analyses are designed to quantify features that appear in each of the categories. The first experiment analyzes means and standard deviations from the ten RO categories for each of the five primary variables obtained from the atmospheric RO profiles (e.g. temperature with moisture effects neglected T dry, refractivity N, bending angleα, temperature with moisture effects T wet and vapor pressure V p ). This is done both in comparison to each other and in separate analyses for unique atmospheric features detected in these profiles. The second analysis expands upon the first by analyzing the fractional differences from the overall mean profile within the tropics and midlatitudes for each of the three dry occultation variables (T dry, N and α ) in an attempt to better quantify features present in these profiles. The third analysis analyzes individual profiles of the two wet occultation variables (V p and T wet ) to test the hypothesis that cloud and associated inversion layers can be accurately detected utilizing the GPS RO technique. A relationship between vapor pressure and moist temperature data is verified as a part of the final analysis. 7

9 3.1 Analysis of mean profiles and their standard deviations In an attempt to gain insight from the averages and variations amongst all of the profiles in each occultation category for all of the available atmospheric variables bending angle, refractivity, vapor pressure and wet and dry temperature mean and standard deviation profiles are created for each of the ten occultation categories. Data from each dry occultation file are available on an irregular height interval below 40.0 km. The average interval is about every km. Data from each moist occultation file are available on a regular height interval of 0.1 km. In order to account for the differences in the two intervals, data from the dry occultation files are interpolated utilizing a simple averaging procedure to intervals of 0.1 km. In this binning procedure, all points within ± 0.05 km of the desired height interval (40.0km, 39.9km 0.0km) are gathered and a simple average sum of all points divided by the number of points in the interval is taken and assigned to the desired height level. The mean and standard deviation profiles are plotted and analyzed with respect to each other and with respect to the collection of profiles within each category. Results from this analysis are presented in section Analysis of fractional differences from the mean profile under dry conditions Extending the previous analysis, mean profiles for all cloud-categorized occultations are created, separately for the midlatitudes and the tropics. Only the dry variables bending angle, refractivity and dry temperature are considered for this study, as moisture data are occasionally lacking for a given dry atmospheric profile. With the mean profiles calculated, the fractional differences from the mean for each of the ten cloud occultation categories mean profiles are then calculated. This is done to gain insight into where the greatest fractional differences lie from the mean profile in terms of differences in the meteorological variables with respect to profiles in 8

10 similar latitudinal bands. As before, these differences are plotted for each of the three variables and analyzed with respect to the deviation from zero, or the mean profile. Results from this analysis are presented in section Analysis of individual water vapor and temperature profiles In an attempt to distinguish both cloud and inversion layers through the atmospheric column as well as any impacts these cloud layers may have on the occultation profiles, a subset of thirty occultations, three within each of the ten occultation categories, is randomly selected from the set of cloud-categorized occultations. Plots of vapor pressure and, where desired for further analysis, wet temperature are created for each of these thirty profiles utilizing nonaveraged and non-interpolated data at a vertical resolution of 0.1km from the occultation files. In the atmosphere, clouds are present generally where temperature decreases with height at or near the saturated adiabatic lapse rateγ s. Utilizing the solved form of the Clausius- Clapeyron equation assuming sufficiently warm temperatures ( -30 C) for condensation processes to be dominant within clouds, e lv lv = eso exp[ ], (2) R T R s + v where e s is the saturation vapor pressure, e so an empirically-derived saturation vapor pressure at a temperature of 0 C ( K) and equal to 6.11 hpa, l v the latent heat of vaporization, R v the moist air gas constant, T the desired temperature and T o the reference temperature ( K), it can be shown that in a saturated atmosphere, e s is an exponentially decaying function of inverse temperature and thus a function that decays exponentially to near-zero with increasing height. In vt 0 9

11 isothermal or inversion layers, where the temperature increases or is nearly constant with height, values of e s should similarly increase or remain approximately constant with height. Utilizing these profiles in conjunction with this information, inversion layers should be identifiable in the atmosphere. Profiles from each of the ten cloud occultation categories are analyzed for such layers as well as for any anomalous findings in the profiles that may result in incomplete data analyses. Examples of these profiles and results from this analysis are presented in section Results 4.1 Analysis of mean and standard deviation profiles Mean and standard deviation profiles are created for each of the five variables under consideration bending angle, dry refractivity, dry temperature, moist temperature and vapor pressure utilizing the procedure outlined in section 3a. Separate plots are created and analyzed for the tropics and midlatitudes owing to different atmospheric properties, particularly in the spring and fall months respectively in the northern and southern hemispheres found in these regions. Features from each of the five variable categories are highlighted below. Analysis of bending angle data through each of the cloud categories in both latitude bands reveals several interesting features. There is little distinction between the mean profiles (Figure 8, top panels) for any of the cloud categories in either the tropics or the midlatitudes, except for a small positive bias in mean bending angle through convective clouds between 5 km and 8 km in the tropics. In the midlatitudes, however, there is a significant bulge at an altitude of about 13 km (Figure 8, bottom panels). This is due to seasonal and synoptic variations in the vertical location of the tropopause throughout the midlatitudes owing to the transition in typical weather patterns as a result of the global change in seasons in both hemispheres. 10

12 Standard deviation profiles show little variation from each other, much like the mean profiles, and overall deviations from the mean are approximately one order of magnitude less than the values of the bending angles themselves: 0.03 radians in the mean versus radians in the standard deviation. In the tropics, there are deviations less than radians above 8 km. At that point, there is greater deviation until about 3km when the profiles begin to diverge. This is likely a result of a decreasing number of data points in the tropical categories at low altitudes, as exhibited in Figure 7. In the midlatitudes, overall standard deviations are approximately equal to those in the tropics throughout the vertical, except as previously mentioned near 13 km owing to variations in the tropopause. However, the midlatitude cirrus category exhibits a higher than average standard deviation beginning at about 6 km and continuing down to the surface, most likely due to the relatively low number of profiles in this category. As previously noted and in general, these variations are primarily a function of typical seasonal and synoptic atmospheric variation. Similar results to those seen in the bending angle data are shown in the refractivity data. In the mean profiles (Figure 9, top panels), there is little deviation in the actual refractivity values through each of the occultation categories in both the midlatitudes and the tropics. Standard deviation data (lower panels), however, exhibit some interesting features. The tropopause is evident in both the tropics and midlatitudes, with deviations of about 2 N-units in the tropics near 15 km and deviations of about 5 N-units in the midlatitudes near 12 km. Standard deviation values are small relative to the actual values of refractivity, about 5% of the size of the actual refractivity values. There is a slightly greater spread in the low levels with the tropical categories than with the midlatitude categories, owing to increased moisture at the low levels. Other than a 11

13 slightly larger standard deviation with the midlatitude cirrus category, there is little difference between the cloud types, especially in the tropics. Some features present in bending angle and refractivity analyses also appear in dry temperature retrievals. The depiction of the tropopause is even sharper in the tropics with the dry temperature retrieval; the variations in the height of the tropopause in the midlatitudes are clearer, however, serving to qualitatively verify the previous findings. In the tropics, there is again little deviation between the standard deviation profiles (Figure 10, bottom left) for each of the cloud categories, while the region of the tropopause is denoted by a maximum deviation. Differences between the cloud categories appear upon further inspection. It is known that the dry temperature retrieval has a cold bias in the lowest few kilometers above the surface (above T = 250 K) due to moisture, per Kursinski et al. (1995). For instance, convective clouds, the thickest and oftentimes the highest of all cloud types considered in this study, exhibit a strong cold bias in both the tropics below 10 km and the midlatitudes below 7 km (Figure 10, upper panels). Clear-air and stratus categories exhibit the smallest cold biases, owing to a lack of clouds above the lowest few kilometers above the surface. In the standard deviation profiles, two qualities are of particular interest. In the tropics, there are very high deviation values for all of the cloud categories near the surface. This is likely due to enhanced moisture content inherent to the tropical latitudes along with fewer data points in each category at these levels. In the midlatitudes (Figure 10, lower right), along with diffuse variations near the tropopause, the cirrus and cumulus categories exhibit higher deviations in the lowest 5 km above the surface. Cirrus clouds are typically found in the most moisture-laden, warmest regions on the globe; thus, there should be greater deviation between those midlatitude occultations near 30 N and 30 S and those at higher latitudes, both in terms of cloud-based and 12

14 surface-based moisture. Cumulus clouds may be found at a wide range of altitudes, particularly in the midlatitudes, and thus deviations are higher than normal throughout much of the lower atmosphere. Owing to the manners in which they are derived, there should be little distinction between the dry and moist temperature retrievals above the lowest 5-10 km above the surface, something highlighted upon a comparison of Figures 10 and 11. Noteworthy is the range in deviations between the tropical (3-20 C) and midlatitude (6-11 C) standard deviations as well as the high deviations at high altitudes, as seen in the dry data. Temperature retrievals through particular cloud types in both the midlatitudes and tropics (Figure 11, upper panels) exhibit the warmest temperatures in the cirrus and clear-air categories and the coolest temperatures in the convective and stratus categories. This makes physical sense, as clear-air regions offer the greatest amount of daytime heating and cirrus cloud regions are often found in the warmest regions of the globe, while stratus and convective clouds portend low amounts of insolation and are occasionally found in regions of reduced temperature. Thus, the corrections applied to the dry temperature data bring about more accurate results in terms of the temperatures expected through particular types of clouds. It is in the vapor pressure data, as derived from the reanalysis temperature data, in which impacts due to cloud properties are greatest. This is due to the fact that vapor pressure increases through regions of clouds. Figure 12 presents the mean (upper panels) and standard deviation (lower panels) profiles for this vapor pressure data below 15 km; values above this height are negligible due to low moisture content resulting in low vapor pressure values. For the same reason, impacts of the tropopause are not evident in this data. 13

15 The convective and cirrus categories have the highest mean values of vapor pressure at any given height level, especially above the lowest few kilometers from the surface. Since these clouds are typically found at higher heights, higher vapor pressures should be found at these levels, as seen here. The clear-air and stratus categories depict the lowest values of vapor pressure throughout the column due to relatively small overall impacts of moisture and clouds throughout the atmospheric column. The same general trend is repeated in the standard deviation profiles. Data from the cloud categories in both the tropics and midlatitudes have greater standard deviations in the height ranges in which they are typically found in the atmospheric column due to variations between clouds. Two clear examples of this are shown in the convective category between 6 km and 9 km as well as in the stratus and clear-air categories near the surface, where the greatest impacts of moisture and moisture gradients are exhibited. 4.2 Analysis of fractional differences from the mean for dry state variables Obtaining a mean profile for both the tropical and midlatitude categories provides a simple means of comparing how each categorical profile compares to the other four profiles in each region through the differences between them and the mean profile. In the figures presented for the midlatitudes and the tropics, fractional differences for each of the three dry state variables bending angle, refractivity and dry temperature from the overall mean profile (e.g. T T total dry T total dry cat dry ) are presented. Values greater than zero in the bending angle and refractivity panels reflect where the mean overall profile has a greater value at that particular height than the cloudcategorized mean profile (a negative bias). Subsequently, values less than zero reflect where the cloud-categorized mean profile has a greater value at that particular height than the mean overall profile in that latitude band (a positive bias). In the temperature panels, values less than zero 14

16 represent positive biases with negative values of temperature due to the majority of temperatures being less than zero, resulting in a sign change in the actual fractional differences. Variations in heights of the tropopause are again evident throughout the midlatitudes for each of the five cloud categories, as shown in the spread of fractional differences in each of the three variables (Figure 13) between heights of 11 km and 16 km. These impacts are most prevalent with the cirrus cloud category near 13 km, with large fractional differences from the mean profile in both bending angle and refractivity, yet extend through to each category on a smaller scale. Due to increased water vapor content, the greatest impacts on refractivity, bending angle and dry temperature should be seen in the deeper, moister cloud types owing to contributions to refractivity from water vapor in equation (1); this is verified by Kursinski et al. (1997), where it is noted that the positive biases in bending angle and refractivity due to water vapor are primarily a function of effects due to the large permanent dipole moment of water vapor and observed in these profiles with the convective cloud categories. Similarly, with fewer impacts due to moisture in regions lacking clouds, there should be smaller differences in profiles of bending angle and refractivity for the clear-air categories (especially above the surface), features observed in Figure 13. Differences in dry temperature retrievals are well correlated to the differences in bending angle and refractivity for each of the five categories in terms of relative magnitude; this is as expected from equation (1). Cold biases are exhibited in the difference profiles within the convective and stratus categories, while warm biases are exhibited in the difference profiles within the cirrus, clear-air and cumulus categories. Near and slightly above the tropopause at about 11km, however, there is a distinct cold bias with the cirrus cloud categories. This is 15

17 representative of these clouds due to their relatively high altitudes, typically near the tropopause. Finally, a greater spread in each set of data at high altitudes in the midlatitudes is exhibited above 20 km. This is explained primarily as a function of stratospheric variations associated with midlatitude weather systems and circulations. Due to the uniform nature to the height of the tropopause throughout the tropics, little difference in the profiles is shown above 10 km, or below the typical tropical tropopause (Figure 14). Thus, the aforementioned stratospheric variation is not exhibited in the tropics, a result of the more homogenous nature of the stratosphere in these latitudes. Results for all three state variables reflect those seen in the midlatitudes, particularly the biases exhibited in the convective cloud categorical mean profile. Some of the strongest negative biases in bending angle and refractivity (and thus the strongest warm biases in dry temperature) are reflected in the clear-air categorical mean profile, as in the midlatitudes. On the whole, these differences are slightly larger for each cloud category in the tropics than those exhibited for the corresponding cloud category in the midlatitudes in the lower atmosphere. Two key distinctions are made between the tropics and the midlatitudes. The first is that a strong negative (warm) bias in the stratus categories appears within the stratus profiles in the tropics where there is none in the midlatitudes. This is more along the lines of what is expected with low, relatively thin clouds in the atmosphere relatively small bending and a warm bias above the surface in dry temperature retrieval along the lines of the previously noted impacts of water vapor on the retrievals of each of these variables. Figure 7 shows that nearly five times as many profiles are present (particularly in the lowest few kilometers above the surface) in the tropical stratus category than in the midlatitude stratus category, introducing small sample size 16

18 biases into the latter group and giving more credence to the results from the tropical categorizations. The second key distinction is a minimization of much of the biases exhibited with the cirrus cloud category in the midlatitudes. A slight cold bias is still shown between 10 km and 14 km in the tropical cirrus differences, but this bias is smaller in magnitude than in the midlatitudes. The greatest impacts from cirrus clouds are still reflected closer to the surface (near increased regions of moisture not entirely due to clouds), but there is no longer a distinct bias with respect to the other categories near the tropopause in either the bending angle or refractivity data. On a whole, however, cloud impacts in both the midlatitudes and tropics, as reflected in the GPS data, are well observed. This serves as a means of verification of the RO technique in regions of high moisture, suggesting the data to be reasonably accurate and that properties of clouds can be accurately determined through an analysis of differences of a particular profile from the mean overall profile within each latitudinal band. 4.3 Moist profile examples To better correlate features relating to the moist variables of wet temperature and vapor pressure, individual profiles are analyzed for inversion layers and cloud impacts on the retrievals of these quantities. An inversion layer is defined as a height range in which temperature increases with height, while an isothermal layer is one in which the temperature remains constant with height. Similarly, vapor pressure values in isothermal layers and frontal inversions should remain constant or increase with height and saturation vapor pressure values should increase or remain constant with height for all types of inversions and isothermal layers. With this information, particular types of inversions can be analyzed for in the occultation data profiles. Occultations passing through thicker clouds or those that appear in entirely saturated 17

19 atmospheres, such as convective and stratus cloud regions, should have fewer inversions, while those profiles passing through clear regions or regions where clouds are located high in the atmosphere should have greater numbers of occultations featuring inversion layers. This is primarily a function of the weather systems typically associated with each type of clouds. An analysis of the thirty selected profiles shows this to be the case. Eight profiles in total display inversion layers, while fifteen do not. An additional seven profiles are ambiguous in nature, often ending above the lowest 4-5km above the surface. Of the eight profiles that reflect inversion layers, three are present in the cirrus occultation groups, two each in the clear-air and cumulus groups, and one in the stratus groups. Of those that did not, one is in the clear-air groups, six are in the convective groups, and four each are present in the cumulus and stratus categories. The majority of ambiguous profiles are found in the clear-air and cirrus occultation categories. From the eight profiles that reflect inversion layers, four are chosen to highlight these findings. Two additional profiles, one that does not highlight an inversion layer and another with ambiguous findings, are selected to complete a representative sample. Basic information about each of these six occultations is presented in Table 2. The non-inversion profiles are shown in Figure 15, while the inversion profiles are depicted in Figures 16 and 17. In the left panels are plots of vapor pressure while in the right panels are plots of moist temperature, allowing for an effective analysis of each variable with respect to each other in visible inversion layers. In each of the Figures, only the region between 2 km and 8 km is shown, as this is the region of greatest interest with respect to cloud and inversion features in the atmosphere. Figure 15 depicts examples of an ambiguous profile (Cirrus2) and a profile lacking inversion layers (Convective). The ambiguous profile is denoted as such due to a high ending altitude 6.14 km and the lack of any identifiable structures in the lower atmosphere that lend 18

20 themselves to analysis. The convective profile is denoted as having no inversion impacts as the profile of vapor pressure decreases at a nearly constant exponential rate with height. This profile is representative of all six convective category profiles as well as representative of an entirely moist atmosphere in which there are no intervening inversion layers. Furthermore, a fair correlation between moist temperature and vapor pressure is observed with this example, i.e. there are no regions in which an inversion is noted in the moist temperature profile. Figure 16 depicts two profiles Cirrus1 and Cumulus - containing layers in which vapor pressure is constant with height at some point above the end of the occultation. Note the nearconstant values of vapor pressure (right panel) between 3.75 km and 5 km with Cirrus1 and between 3.75 km and 7.25 km with Cumulus. A similar response is expected in the moist temperature analysis; however, temperature values are not constant with height and, in fact, decrease with height at a greater rate (-22 C decrease with Cumulus and -6 C through the inversion layer in Cirrus1) through these layers than at any other point in the analysis. Similarly, steeper gradients in the vapor pressure curves are highlighted by near-vertical curves in the temperature profiles, suggesting that these impacts are not limited to the height altitudes in which inversions are present. This may indicate a poor quality of the moisture information supplied to the T wet retrievals. Figure 17 depicts two profiles Clear and Stratus with inversions at the end of the profile. Inversions in the vapor pressure data are observed between 4 km and 5.25 km in Clear and between 2.75 km and 4.75 km in Stratus. The corresponding moist temperature profiles are depicted in the left panel of the figure. Once again, we see results that suggest that temperature is decreasing with height within these regions at a rate greater than any observed within the lower atmosphere, with temperature decreases of about 12 C over the inversion in Clear and 11 C over 19

21 the inversion in Stratus. These six examples show that the RO vapor pressure data can accurately sense inversion layers in regions in which they are most commonly found (and similarly not sense inversion layers in regions in which they should not be found) based upon cloud analyses. Poor correlation is shown between the vapor pressure and moist temperature profiles in regions in which inversions are present. While some of this poor correlation may be a result of an inability to distinguish particular types of inversions (e.g. frontal versus subsidence) from vapor pressure data alone (resulting in diminished confidence in the analysis due to vertical variations of vapor pressure), preliminary results suggest that there is a misfit between the corrections applied to the dry temperature retrievals to obtain moist temperature and vapor pressure profiles derived from the GPS occultations and moist reanalysis data. This misfit is likely a result of poor corrections applied to the dry temperature data, errors that arise with interpolation of the reanalysis data of the moisture variables, and may not be limited just to inversion layers. In an attempt to achieve greater accuracy in the moist temperature and vapor pressure data and thus make such data more worthy of consideration in weather analysis and numerical weather prediction studies, an improved method to obtain consistent vapor pressure and moist temperature data, potentially along the lines of that outlined in the next section, is required. 5. Towards Developing an Improved Moist Data Retrieval Method Currently, profiles of the moist quantities, specifically temperature and vapor pressure, are obtained using ancillary data from short-term forecasts or large-scale reanalysis data (UCAR 2004a). This introduces high sensitivities into these retrievals to small errors in the forecast or reanalysis temperatures (Wickert et al. 2001), an undesirable effect. Other methods using optimal estimation of or simple modeling techniques designed to replicate temperature and humidity data 20

22 have been proposed that have greater potential for improved retrieval of these quantities, as noted by Wickert et al. (2001). A procedure is proposed here to improve upon the retrieval of temperature and moisture data inspired by findings from section 4.3 to enhance the relationship between moist temperature and vapor pressure retrievals through regions of clouds. It should be noted that this technique is only valid within regions of clouds or high (i.e. saturated) moisture content due to assumptions in the derivation of the necessary relationship. Thus, for full benefit, cloud layers must be analyzed either using the vapor pressure data obtained from the GPS satellite, looking for regions in which the lapse rate is approximately -7 C km -1 or by using potentially more accurate ancillary data such as cloud-top pressure data. The need for additional data or analysis, however, does not diminish the benefit offered by this new data retrieval method. In deriving the necessary relationship, first, it is noted that a simplified relationship between refractivity N and temperature T exists taking into account wet atmospheric dynamics, as highlighted in equation (1). In vertical regions where clouds are present, a completely saturated atmosphere is assumed such that P w = e = e s. Equation (1) thus becomes: N p T e 5 s = x10. (3) 2 T The first term is the dry term from which profiles of dry temperature can be obtained (i.e. where specific humidity q = 0 and there is no moisture in the atmospheric column, a good approximation above the lowest few kilometers above the surface); the second is the moist term considering moist processes, necessary for accurate temperature and water vapor retrievals. An expression for e s can be obtained from the Clausius-Clapeyron equation: (ln es ) = t l R T v v 2, (4) 21

23 where l v is the latent heat of condensation and equal to x10 6 J, Rv the moist air gas kg constant and equal to J kg * K, and e s the saturation vapor pressure. Cloud temperatures are assumed to be sufficiently warm (generally above 30 C) where condensation, as opposed to deposition, processes dominate cloud formation and growth. Negligible (< ± 2.5%) variation in l v due to temperature is also assumed, allowing l v to be taken as a constant. Solving (4) by integration, the following results: e lv lv = eso exp[ ]. R T R (5) s + v This can be substituted into (3) for e s in the moist term. Now, the dependence on pressure p in the dry term in (3) must be eliminated. Consider the combination of the ideal gas law into the hydrostatic relationship, i.e. vt 0 p z pg = ρ g =. (6) R T d Note that temperature instead of a weighted virtual temperature is used in (5). This is a fairly good approximation to the weighted virtual temperature, particularly in the midlatitudes, and is more easily obtainable from the available data. Integration of (6) gives the following expression: p gz = p o exp( ), (7) R T d where p o is a reference initial pressure and z is the geometric height directly obtainable from the occultation data. The values of constants used in (7) are p o = 1 atm = Pa = hpa, 22

24 m g = and Rd = s J kg * K. Combining (5) and (7) into (3) and explicitly noting T as T wet, the desired relation is obtained: N = * T wet p o gz exp( R T d wet 3.730x10 ) + 2 T wet 5 *e so lv exp[ R T v wet lv + ]. (8) R T v 0 This gives the relationship of refractivity N to its constituents as a function of only wet temperature T wet Utilizing input values of T wet from the GPS occultation data, a model value of refractivity can be derived. A least-squares fit between simulated and GPS-derived refractivity can be conducted to derive new values of T wet given values of N at different heights. Equation (3) can then be used to obtain new values of vapor pressure. The wet temperature T wet and vapor pressure e s can be used to analyze for cloud layers, potentially offering better precision and results than the technique currently used in post-processing of CHAMP and SAC-C occultation data by eliminating the dependence on ancillary data or forecasts in the retrieval of saturation vapor pressure and wet temperature data. 6. Summary and Conclusions The CHAMP and SAC-C GPS RO missions provide high-quality meteorological data, particularly measurements of bending angle, refractivity, temperature and vapor pressure. This data has been shown in previous research (for instance, Zou et al. 2000) to positively impact numerical weather prediction by means of data assimilation and has further impacts beyond improving weather forecasts in terms of quantitative surveying of the atmosphere and particular atmospheric features. In this study, analyses are conducted to quantify impacts of clouds and 23

25 inversions as exhibited in the meteorological variables obtained from the RO technique. From these analyses, the following conclusions are made: Fractional differences in retrievals of bending angle and dry refractivity are well correlated to those expected from theory for particular types of clouds. Positive differences (from the mean) in bending angle and refractivity are observed with thicker, higher clouds while negative differences in the same variables are observed with lower, thinner clouds. Dry temperature profiles have the highest mean values and exhibit the greatest cold biases (due to negative impacts of moisture unaccounted for in the retrieval) with the convective cloud categories, the highest and often most moisture-laden clouds. The smallest mean values and relative warm biases are exhibited with the stratus and clear-air categories, featuring lesser amounts of cloud-based moisture. Again, noting the moisture biases associated with these clouds and in the GPS retrievals, this is as expected. Moist temperature retrievals offer better precision and accuracy than dry temperature retrievals, with lower values seen with cloud types that do not allow for large amounts of insolation (convective, stratus) and higher values with those that allow for greater amounts of insolation (cirrus, clear-air). The greatest values in mean vapor pressure retrievals by category are found in the highest (in altitude) cloud categories convective and cirrus while the lowest values are found in categories in which the clouds are not present or found near the surface clear-air and stratus. 24

26 The high resolution of the RO signals allows for precise determination of the tropopause. This shows great variation in the height of the tropopause in the midlatitudes, but little variation in the tropics. In inversion layers, as determined by means of an analysis of vapor pressure and wet temperature through regions of clouds, the vapor pressure and wet temperature data do not correlate well. This is likely due in part to the procedure used to obtain wet temperature from the dry temperature retrieval and reanalysis data. A new model utilizing a least-squares fit between satellite-observed and synthetically derived GPS data is developed to improve upon wet temperature and vapor pressure retrievals through regions of clouds. Results from this project can thus be further analyzed and expanded upon with a consideration of additional regions around the globe, for which archived and real-time satellite imagery is available from any number of sources, or by considering a bigger time window for example, several months in 2002 in the filtering process and actual data analysis. Furthermore, completion of the work towards an improved moist temperature and vapor pressure retrieval, as outlined in section 5, may be considered to improve upon the retrieval processes of meteorological data from the GPS RO technique. 7. Acknowledgements This research is supported by the Integrated Program Office of the NOAA under National Polar-Orbiting Operational Environmental Satellite System (NPOESS) Project No. 50-SPNA and the National Science Foundation (NSF) under Project No. ATM Satellite imagery for this project was provided by the University of Wisconsin Space Science and 25

27 Engineering Center (SSEC), available online at Occultation data files from CHAMP and SAC-C were obtained from UCAR by means of the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) project and are available online at The author wishes to express his gratitude to his advisor during this project, Dr. Xiaolei Zou, for all of her help and guidance. He also wishes to express his gratitude to his mentor in the lab, H. Shao, for her friendship, help and assistance with the aspects of GPS RO technology. 8. References Gerding, M. and A. Weisheimer, 2003: Water vapour profiles from GPS radio occultation Soundings in the Arctic. First CHAMP Mission Results for Gravity, Magnetic and Atmospheric Studies, C. Reigber, H. Luhr and P. Schwintzer, Eds., Springer-Verlag, Kursinski, E.R. et al., 1995: Observing tropospheric water vapor by radio occultation using the global positioning system. Geophys. Res. Lett., 22, Kursinski, E.R. et al., 1997: Observing Earth s atmosphere with radio occultation measurements using the Global Positioning System. J. Geophys. Res., 102, Kursinski, E.R. and G.A. Hajj, 2001: A Comparison of Water Vapor Derived from GPS Occultations and Global Weather Analyses. J. Geophys. Res., 106, Hajj, G.A. et al., 2004: CHAMP and SAC-C atmospheric occultation results and Intercomparisons. J. Geophys. Res., 109, D6-1 - D6-24. University Corporation for Atmospheric Research (UCAR), cited 2004: Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) website. [Available online at University Corporation for Atmospheric Research, cited 2004: GPS/MET Project Overview. [Available online at Wickert, J., et al., 2001: Atmosphere sounding by GPS radio occultation: First results from CHAMP. Geophys. Res. Lett., 28, Yunck, T.P., G.F. Lindal and C.H. Liu, 1988: The role of GPS in precise earth observation. Proc. 26

28 of IEEE Position, Location and Navigation Symposium, Orlando, FL. Zou, X., B. Wang, H. Liu, R. A. Anthes, T. Matsumura, and Y.-J. Zhu, 2000: Use of GPS/MET refraction angles in 3D variational analysis. Q. J. R. Meteorol. Soc., 126,

29 List of Tables & Their Captions Table 1: The number of occultations within each of the ten occultation categories in the defined region of consideration (30 W-100 W, 60 S-60 N) during May Table 2: Basic occultation information about each of the six occultation profiles represented in Figures 15 through

30 Occultation Category Occultations Occultation Category Occultations Tropical cirrus 25 Midlatitude cirrus 28 Tropical clear-air 47 Midlatitude clear-air 43 Tropical convective 139 Midlatitude convective 51 Tropical cumulus 86 Midlatitude cumulus 185 Tropical stratus 158 Midlatitude stratus 30 Table 1: The number of occultations within each of the ten occultation categories in the defined region of consideration (30 W-100 W, 60 S-60 N) during May

31 Group Date Time Latitude Longitude Satellite Min. alt. Cirrus Z N W SAC-C 0.83 km Cumulus Z N W CHAMP 1.11 km Clear Z N W CHAMP 3.91 km Stratus Z 6.73 S W CHAMP 2.49 km Cirrus Z N W CHAMP 6.14 km Convective Z S W CHAMP 1.63 km Table 2: Basic occultation information about each of the six occultation profiles represented in Figures 15 through

32 List of Figures & Their Captions Figure 1: Global distribution of all 6497 occultations obtained from COSMIC for the CHAMP (4306) and SAC-C (2191) missions during the month of May The region of consideration is outlined with a box. Figure 2: Example of a cloud categorization from the classification of an occultation profile passing through cirrus clouds on 31 May 2002 at 1459Z with perigee latitude and longitude of S, W east of Brazil. Occultation perigee point denoted in green. Visible image is at left, infrared at right with brightness scale included. Figure 3: Example of a cloud categorization from the classification of an occultation profile passing through convective clouds on 08 May 2002 at 1433Z with perigee latitude and longitude of N, W northeast of Canada. Occultation perigee point denoted in green. Visible image is at left, infrared at right with brightness scale included. Figure 4: Example of a cloud categorization from the classification of an occultation profile passing through cumulus clouds on 05 May 2002 at 1714Z with perigee latitude and longitude of S, W over southeastern Brazil. Occultation perigee point denoted in green. Visible image is at left, infrared at right with brightness scale included. Figure 5: Example of cloud categorization from the classification of an occultation profile passing through stratus clouds on 28 May 2002 at 1543Z with perigee latitude and longitude of N, W south of Greenland. Occultation perigee point denoted in green. Visible image is at left, infrared at right with brightness scale included. Figure 6: Depiction of the location and cloud type of all categorized occultations within the defined region of consideration from both CHAMP and SAC-C during May Figure 7: Number of occultation data points per height level for each of the ten cloudcategorized occultation categories during May The tropical categories are depicted in solid lines, while the midlatitude categories are depicted in dashed lines. Figure 8: Plot of the mean profiles of bending angle for each of the five cloud categories in the tropics (a) and midlatitudes (b), along with their corresponding standard deviation plots (c, d). Figure 9: Plot of the mean profiles of refractivity for each of the five cloud categories in the tropics (a) and midlatitudes (b) with their corresponding standard deviation plots (c, d). Figure 10: Plot of the mean profiles of dry temperature for each of the five cloud categories in the tropics (a) and midlatitudes (b) with their corresponding standard deviation plots (c, d). Figure 11: Plot of the mean profiles of wet temperature for each of the five cloud categories in the tropics (a) and midlatitudes (b) with their corresponding standard deviation plots (c, d). 31

33 Figure 12: Plot of the mean profiles of vapor pressure for each of the five cloud categories in the tropics (a) and midlatitudes (b) with their corresponding standard deviation plots (c, d). Figure 13: Fractional differences in bending angle (a), refractivity (b) and dry temperature (c) from the mean for each of the occultation categories in the midlatitudes. Figure 14: Fractional differences in bending angle (a), refractivity (b) and dry temperature (c) from the mean for each of occultation categories in the tropics. Figure 15: Vertical profiles between 2 km and 8 km of moist temperature (a) and vapor pressure (b) for the profiles denoted by Convective (solid lines) and Cirrus2 (dashes) in table 2. Figure 16: Vertical profiles between 2 km and 8 km of moist temperature (a) and vapor pressure (b) for the profiles denoted by Cirrus1 (solid lines) and Cumulus (dashes) in table 2. Figure 17: Vertical profiles between 2 km and 8 km of moist temperature (a) and vapor pressure (b) for the profiles denoted by Clear (solid lines) and Stratus (dashes) in table 2. 32

34 Figure 1: Global distribution of all 6497 occultations obtained from COSMIC for the CHAMP (4306) and SAC-C (2191) GPS radio occultation missions during the month of May The region of consideration is outlined with a box. 33

35 Figure 2: Example of a cloud categorization from the classification of an occultation profile passing through cirrus clouds on 31 May 2002 at 1459Z with perigee latitude and longitude of S, W east of Brazil. Occultation perigee point denoted in green. Visible image is at left, infrared at right with brightness scale included. 34

36 Figure 3: Example of a cloud categorization from the classification of an occultation profile passing through convective clouds on 08 May 2002 at 1433Z with perigee latitude and longitude of N, W northeast of Canada. Occultation perigee point denoted in green. Visible image is at left, infrared at right with brightness scale included. 35

37 Figure 4: Example of a cloud categorization from the classification of an occultation profile passing through cumulus clouds on 05 May 2002 at 1714Z with perigee latitude and longitude of S, W over southeastern Brazil. Occultation perigee point denoted in green. Visible image is at left, infrared at right with brightness scale included. 36

38 Figure 5: Example of cloud categorization from the classification of an occultation profile passing through stratus clouds on 28 May 2002 at 1543Z with perigee latitude and longitude of N, W south of Greenland. Occultation perigee point denoted in green. Visible image is at left, infrared at right with brightness scale included. 37

39 Figure 6: Depiction of the location and cloud type of all categorized occultations within the defined region of consideration from both CHAMP and SAC-C during May