Characterization of Mars seasonal caps using neutron spectroscopy

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114,, doi: /2008je003275, 2009 Characterization of Mars seasonal caps using neutron spectroscopy Thomas H. Prettyman, 1 William C. Feldman, 1 and Timothy N. Titus 2 Received 1 October 2008; revised 30 April 2009; accepted 19 May 2009; published 27 August [1] Mars seasonal caps are characterized during Mars years 26 and 27 (April 2002 to January 2006) using data acquired by the 2001 Mars Odyssey Neutron Spectrometer. Time-dependent maps of the column abundance of seasonal CO 2 surface ice poleward of 60 latitude in both hemispheres are determined from spatially deconvolved, epithermal neutron counting data. Sources of systematic error are analyzed, including spatial blurring by the spectrometer s broad footprint and the seasonal variations in the abundance of noncondensable gas at high southern latitudes, which are found to be consistent with results reported by Sprague et al. (2004, 2007). Corrections for spatial blurring are found to be important during the recession, when the column abundance of seasonal CO 2 ice has the largest latitude gradient. The measured distribution and inventory of seasonal CO 2 ice is compared to simulations by a general circulation model (GCM) calibrated using Viking lander pressure data, cap edge functions determined by thermal emission spectroscopy, and other nuclear spectroscopy data sets. On the basis of the amount of CO 2 cycled through the caps during years 26 and 27, the gross polar energy balance has not changed significantly since Viking. The distribution of seasonal CO 2 ice is longitudinally asymmetric: in the north, deposition rates of CO 2 ice are elevated in Acidalia, which is exposed to katabatic winds from Chasma Borealis; in the south, CO 2 deposition is highest near the residual cap. During southern recession, CO 2 ice is present longer than calculated by the GCM, which has implications for the local polar energy balance. Citation: Prettyman, T. H., W. C. Feldman, and T. N. Titus (2009), Characterization of Mars seasonal caps using neutron spectroscopy, J. Geophys. Res., 114,, doi: /2008je Introduction [2] The seasonal polar caps of Mars consist of CO 2 that condenses from the atmosphere to form surface ice at high latitudes following the autumnal equinox in both hemispheres [Leighton and Murray, 1966; Neugebauer et al., 1971]. The seasonal caps are prominent features of Mars, visible by telescope as bright polar spots [Herschel, 1784], extending as far as 40 S in the southern hemisphere and 55 N inthe northern hemisphere [James et al., 1992]. As insolation increases following winter solstice, the seasonal CO 2 ice begins to sublime, causing the polar caps to recede, gradually replenishing the atmosphere with CO 2 and revealing the underlying, high-latitude, water ice rich regolith and residual polar caps. Approximately 25% of the Martian atmosphere is cycled annually into and out of the seasonal caps [Tillman et al., 1993; Kelly et al., 2006]. Consequently, the seasonal CO 2 cycle is an important aspect of Mars general circulation [James et al., 1992; Zurek et al., 1992]. Questions about the seasonal caps that remain unresolved concern local cap properties (column abundance, volumetric density, geometric thickness, albedo, and emissivity), energy 1 Planetary Science Institute, Tucson, Arizona, USA. 2 United States Geological Survey, Flagstaff, Arizona, USA. Copyright 2009 by the American Geophysical Union /09/2008JE balance terms, and CO 2 condensation mechanisms [Titus et al., 2008a, 2008b]. [3] The rate of seasonal deposition and sublimation of CO 2 ice is determined by the local energy balance, which depends on insolation, atmospheric properties (for example, dust optical depth), emissivity and albedo of the surface, advection of energy by the atmosphere, and energy storage within the regolith [Leighton and Murray, 1966; James et al., 1992; Wood and Paige, 1992]. Mars General Circulation Models (MGCMs) have been calibrated by adjusting the emissivity and albedo of the seasonal caps to fit the model results to Viking pressure measurements [Hourdin et al., 1995; Haberle et al., 1999]. The albedo and emissivity of the seasonal ice were generally assumed to be spatially uniform and constant with time. This approach preserved the total amount of CO 2 cycled through the caps, consistent with Viking pressure measurements; however, the adjusted emissivity and albedo values are inconsistent with those observed by the Mars Global Surveyor (MGS) Thermal Emission Spectrometer (TES). TES observations reveal a cap that is spatially heterogeneous with time varying emissivity and albedo [Kieffer et al., 2000; Kieffer and Titus, 2001; Titus et al., 2001]. One of our goals is to measure the column abundance of seasonal CO 2 ice in order to constrain local cap properties and the polar energy balance. [4] Data acquired by the Mars Odyssey Gamma Ray Spectrometer instrument suite, which includes the Gamma 1of25

2 Table 1. Sensitivity of Neutron Spectroscopy to Surface and Atmospheric Parameters Adapted From Prettyman [2007] a Type Energy Range Major Interactions CO 2 -Free Surface Parameters Atmospheric/Seasonal Parameters Fast (Cat2, P1) >0.7 MeV Inelastic scattering, elastic scattering WEH abundance and stratigraphy, Average atomic mass Atmospheric mass, CO 2 ice column abundance < 100 g/cm 2 Epithermal (Cat1, P1) 0.5 ev (Cd cutoff) to 0.7 MeV Elastic scattering WEH abundance and stratigraphy Atmospheric mass, CO 2 ice column abundance up to about 400 g/cm 2 Thermal (Cat1, P2 P4) <0.5 ev (Maxwellian energy distribution) Elastic scattering, radiative capture (absorption) WEH abundance, Absorption by Fe, Cl, Ti. Stratigraphy of WEH and absorbers CO 2 ice column abundance up to about 400 g/cm 2, Absorption by N 2 and Ar a The prism identity (P1 4) (see Figure 1) and event category (Cat1 or Cat2) are indicated [Feldman et al., 2002a, 2002b; Boynton et al., 2004]. Note that thermal neutrons contribute partially to the response of the epithermal sensor (P1), as described in the text, which causes the Cat1, P1 signal to have the same overall range for CO 2 column abundance as the thermal neutrons. P4 is sheltered from thermal neutrons by the relative motion of the spacecraft and shielding by surrounding prisms and Cd. Consequently, the Cat1, P4 response is primarily due to epithermal neutrons. As shown in Figure 2, the counting rate for P4 saturates above 100 g/cm 2, which gives an upper limit on the column abundance of CO 2 ice that can be measured using epithermal neutrons. Ray Spectrometer (GRS), Neutron Spectrometer (NS), and High Energy Neutron Detector (HEND), have been used to directly determine the local column abundance of seasonal CO 2 ice, on a scale determined by the broad footprint of the instruments (roughly 10 of arc length or 600 km on the surface) [e.g., Feldman et al., 2003; Kelly et al., 2006; Litvak et al., 2007]. To date, nearly 3 Mars years of data have been collected, enabling interannual comparisons of local column abundances. Supplementing data from the GRS suite are measurements of the boundary of the cap edge using data from TES and thermal properties, which could be combined with CO 2 ice column abundance measurements to determine unknown terms of the local energy balance (for example, advection of energy by the atmosphere). In addition, data from the MGS Mars Orbital Laser Altimeter (MOLA) have been combined with CO 2 ice column abundance measurements by the GRS suite to determine the volumetric density of the seasonal ice [e.g., Smith et al., 2001; Feldman et al., 2003; Aharonson et al., 2004; Litvak et al., 2007]. The volumetric density of seasonal CO 2 ice, which was generally found to be less than that of solid CO 2, provides constraints on processes for deposition and alteration of surface ice [Titus et al., 2001; Hecht, 2008]. [5] The NS measures neutrons in three energy ranges, which have varying degrees of sensitivity to atmosphere and surface properties (see Table 1). All three energy ranges are sensitive to the column abundance of CO 2 ice and the abundance of water-equivalent hydrogen (WEH) within the underlying surface. Generally, neutron counting rates increase in response to surface seasonal ice deposits, because CO 2 has a low cross section for neutron capture and is a poor moderator in comparison to water, which is abundant at high latitudes. For all three energy ranges, the counting rates measured by the NS saturate for thick deposits of CO 2. For example, the fast neutron counting rate saturates for CO 2 ice column abundances greater than 100 g/cm 2, which is both a limitation, in that it is not possible to measure peak CO 2 ice column abundances near the pole using fast neutrons, and a benefit, in that the thick deposits can be used to calibrate models used to analyze the data [Prettyman et al., 2004a]. The calibration procedure used in this study is described in section 3. Thermal neutrons are sensitive up to about 400 g/cm 2, which is several times thicker than the maximum CO 2 ice column abundances predicted by GCMs; however, thermal neutrons are also sensitive to the presence of neutron absorbers in the surface (perhaps in the form of dust in the precipitated CO 2 ice) and the atmosphere, which contains the noncondensable gasses N 2 and Ar. The abundance of atmospheric N 2 and Ar has been found to vary seasonally, especially in the southern hemisphere, where a strong polar winter vortex inhibits meridional mixing, resulting in strong enrichment of noncondensable gasses as CO 2 condenses on the surface [Feldman et al., 2003; Sprague et al., 2004, 2007; Prettyman et al., 2004c]. Consequently, CO 2 ice column abundance cannot be determined uniquely from the thermal neutron measurements. [6] In this study, we will focus on the analysis of the Category 1 (Cat1) counting data for Prism 1 (P1), which is primarily sensitive to epithermal neutrons, has ample sensitivity and range for CO 2 frost at latitudes poleward of 60, and is not strongly sensitive to atmospheric mass and composition. A model of the Cat1 counting rate for P1 is presented, along with possible sources of error. The model is applied to counting data to determine the local column abundance of CO 2 ice. Systematic errors caused by spatial blurring are investigated using a spatial deconvolution algorithm. An important test of the accuracy of the neutron data analysis procedure is whether the total mass of CO 2 in the seasonal caps determined from the neutron data is consistent with the mass determined by GCM calculations that were calibrated using Viking pressure data. Consequently, we will compare results of the analysis of neutron data to a calculation by the Ames Research Center Mars GCM carried out by New Mexico State University (described by Feldman et al. [2003] and Prettyman et al. [2004a]). 2. Background [7] A review of neutron spectroscopy is beyond the scope of this work; however, some background information is provided here to help orient the reader. For readers unfamiliar with neutron spectroscopy, a general overview of nuclear spectroscopy techniques and their application to planetary science is provided by Prettyman [2007]. The application of neutron spectroscopy to Mars science is described in numerous publications, many of which are cited by this manuscript. A description of the Gamma Ray Spectrometer Instrument suite, which includes the GRS, NS, and HEND subsystems is given by Boynton et al. [2004]. [8] Throughout this manuscript, CO 2 ice refers to solid CO 2 present on the surface, independent of the emplacement mechanism (for example, snowfall or direct condensation), separate from CO 2 present as a gas or solid dispersed in the atmosphere (such as ice crystals in clouds). To a good 2of25

3 Figure 1. (a) An engineering drawing of the neutron spectrometer, which shows the placement of Cd filters around the spectrometer, is compared to (b) a cross-sectional diagram, which shows the orientation of the prisms relative to the spacecraft velocity vector (v * SC). Prism 1 (P1) is not completely covered by Cd, and the gap shown in Figure1b allows thermal neutrons to enter the prism. approximation, neutron production by cosmic rays is independent of volumetric density of solids, but is noticeably different between the atmosphere of Mars and the solid surface. In the thin atmosphere of Mars, secondary particles produced in cosmic ray showers, including charged pions, which would otherwise interact with nuclei to produce neutrons in solid materials, can undergo decay prior to interacting, resulting in reduced neutron production relative to the solid surface [Prettyman et al., 2004a]. The density effect accounts for the weak sensitivity of fast neutron measurements to atmospheric mass (see Table 1). In this study, we have not attempted to determine the atmospheric mass and the column abundance of CO 2 ice simultaneously from the nuclear spectroscopy data. Instead, a GCM, calibrated using Viking pressure measurements, was used to estimate atmospheric mass (g/cm 2 ) and scale height (km) in order to develop algorithms used to convert neutron counting rates to the column abundance of CO 2 ice. [9] In addition, we emphasize that the analysis of neutron spectroscopy data is dependent on models of the atmosphere and layered surface structure, based on observations and physical constraints. The details of surface layering cannot be determined uniquely using nuclear spectroscopy [e.g., see Boynton et al., 2002]. Neutron spectroscopy is sensitive to the column abundance (with units of g/cm 2 ) and weight fraction (g/g) of materials within the atmosphere and surface. Since column abundance is the product of volumetric density (g/cm 3 ) and geometric thickness (cm), the volumetric density of a layer can be determined from column abundance if the geometric thickness is known using another method (for example, photoclinometry or laser altimetry). [10] The NS consists of a boron-loaded plastic scintillator that is divided into four prisms, which are read out by separate photomultiplier tubes (Figure 1) [Feldman et al., 2002a, 2002b; Boynton et al., 2004]. Radiation interactions that produce detectable light are sorted by a field programmable gate array (FPGA) into event categories for which pulse height spectra are recorded. Thermal and epithermal neutrons can undergo capture with 10 B, a reaction that results in a well-defined peak in Cat1 (single interaction) spectra, which can be analyzed to determine the 10 B(n, a) reaction rate, from which the incident flux of thermal and epithermal neutrons can be determined. Fast neutrons produce a characteristic double-pulse signature that is recorded as Cat2 data. The first interaction of this pulse pair records the total energy lost by the incoming fast neutron, and the second interaction records the absorption of the neutron by the 10 B(n, a) reaction. [11] The Cat1 counting rate for neutrons in the thermal range is determined by exploiting the motion of the spacecraft relative to the neutrons. The most probable speed for thermal neutrons at Mars is 1860 m/s and the speed of the spacecraft is approximately 3400 m/s. The forward-facing prism (P2) rams into neutrons in the thermal energy range; however, neutrons in this energy range cannot enter P4, which is shielded by the surrounding prisms and faces opposite the direction of spacecraft motion. Both P2 and P4 have similar sensitivities to epithermal neutrons. Consequently, the counting rate for thermal neutrons is obtained by subtracting the counting rate measured by P4 from that of P2. [12] The Cat1 counting rate for incident neutrons in the epithermal energy range is measured by P1, the downward looking prism, which is covered by a Cd foil that absorbs incident thermal neutrons, but allows epithermal neutrons (greater than about 0.5 ev) to pass through; however, P1 is sensitive to thermal neutrons owing to the presence of openings the Cd foil covering P1 (shown as gaps in Figure 1) through which thermal neutrons can leak. The added sensitivity to neutrons in the thermal energy range accounts for the relatively wide dynamic range of the response of P1 to surface ice deposits. For example, P4, which is sensitive only to epithermal neutrons saturates (becomes insensitive to changes in the thickness of CO 2 ice) at about 100 g/cm 2 of CO 2 surface ice, whereas P1 saturates above 400 g/cm 2 (Figure 2). [13] The gaps are included in a detailed, end-to-end model of the spectrometer response, which treats the production of neutrons by cosmic rays in the surface, their transport within the surface and atmosphere, their ballistic trajectories in the exosphere, and detection by the orbiting spacecraft [Prettyman et al., 2004a]. The model fully accounts for the omnidirectional, anisotropic response of each prism. The field of view, which we sometimes refer to as the footprint, 3of25

4 Figure 2. The relative counting rates for P1 and P4 are shown for spatially uniform surfaces consisting of water ice covered by variable amounts of CO 2 ice. The counting rate for P4, which is primarily sensitive to epithermal neutrons, saturates above about 100 g/cm 2 CO 2 ; whereas, the counting rate for P1 continues to increase owing to the sensitivity of the prism to thermal neutrons. and spatial sensitivity of each prism depends on several factors that are treated by the model, including, but not limited to the altitude of the spacecraft, shielding by other prisms and materials, and the energy angle distribution of the incident neutrons, which is dependent on spacecraft velocity for low-energy neutrons [Feldman et al., 1989]. Because the sides of the prisms are shielded only by thin Cd sheets, the spectrometer is sensitive to epithermal and fast neutrons originating off the axis of spacecraft motion. For fast and epithermal neutrons, the spatial response function is approximately azimuthally symmetric about the nadir direction. For thermal neutrons, the spectrometer has greater sensitivity to neutrons originating ahead of the spacecraft, but is also sensitive to neutrons originating from locations off to the side of the spectrometer, which can arrive at orbital altitudes ahead of the spacecraft and enter the forwardlooking prism (P2). [14] On the basis of modeling, the added sensitivity of P1 to thermal neutrons due to gaps in the Cd foil could cause systematic errors in CO 2 ice column abundance when the abundance of noncondensable gasses is unknown, especially for thick frost deposits which produce copious thermal neutrons. In contrast, the sensitivity of P1 to thermal neutrons is not important in the analysis of CO 2 frost-free surfaces. The effect of noncondensable gasses on the determination of CO 2 ice column abundance using P1 counting data is described in this manuscript. [15] The model is also used to determine the spatial response function for each prism, which describes how the prisms respond to neutrons emitted from different locations within the field of view of the spectrometer. If the spatial response function is known, then the blurry maps of counting rates measured by the neutron spectrometer can be sharpened using spatial deconvolution to reveal spatial variations on a scale smaller than the resolution of the spectrometer. Spatial deconvolution is described in section 5. In principle, the spatial response function could be determined directly from measurements by making a map of counting rates from a strong point source of neutrons on the Martian surface, such as the CO 2 ice deposits in the south polar residual cap (SPRC). In practice, direct measurement of the spatial response function is challenging owing to various limitations, such as the location of the SPRC relative to the polar orbit of the spacecraft, and unknown contributions from regions within and surrounding the SPRC. In this study, measurements of the SPRC are used to verify that the calculated spatial response functions are accurate. [16] The spatial response of the prisms is illustrated in Figure 3 for a hypothetical case in which the spacecraft orbit passes directly over a circular source (5 of arc length in width) of neutrons on the surface of Mars with an incident energy distribution similar to that produced by a thick layer of CO 2 surface ice. No neutrons are produced outside the deposit. Owing to its forward orientation and the motion of the spacecraft, P2 responds to the source long before the other prisms and peaks well before the source is at the subsatellite point. P4 responds much later and peaks after the spacecraft has passed over the source. Owing to its orientation and sensitivity to epithermal neutrons, which are not strongly influenced by spacecraft motion, the P1 spatial response function is approximately azimuthally symmetric (about the nadir direction) and roughly centered on the source. [17] The response model was validated using data acquired by the NS for overflights of the south polar residual cap, which is a strong point source of neutrons relative to the Figure 3. The simulated response (relative counting rate) of P1, P2, and P4 is shown along an orbital trajectory that passes directly over a circular deposit of water ice (5 in diameter and centered at 0 arc length as indicated by the vertical lines). 4of25

5 Figure 4. Measured P1 and P2 counting rates, averaged over a collection of trajectories passing over the south polar residual cap (see inset map), are compared with modeled counting rates. The counting rates are given as a function of time, which is a proxy for arc length traversed by the spacecraft. The vertical line gives the approximate location of the center of the residual cap. Note the inset map is a stereographic projection (60 S to the pole). East longitude convention is used. surrounding water-rich regolith. For example, Cat1 P1 and P2 counting data averaged over selected orbits are compared to the model in Figure 4. The counting rates are given as a function of time, which is a proxy for arc length traversed by the spacecraft. [18] The modeled counting rates are based on a heterogeneous model of the residual cap, determined from TES observations, that describes the spatial distribution of exposed water ice and CO 2 ice deposits within the SPRC [Titus et al., 2006]. The CO 2 ice regions were assumed to cover a layer of pure water ice. Both the water ice layer underlying the CO 2 ice regions and the exposed water ice were assumed to be thick compared to the depth sensed by neutrons. The column abundance of the CO 2 ice layer was assumed to be 130 g/cm 2, consistent with the average column abundance of CO 2 ice within the SPRC determined by Tokar et al. [2003] and Prettyman et al. [2004a]. The regions surrounding the SPRC were modeled as an ice table covered by a lag deposit, consistent with models of the stability of ground ice [e.g., Mellon et al., 2004]. The model included the variation of ice table depth and water abundance with latitude determined by Prettyman et al. [2004a] from zonally averaged neutron counting data. The ice table parameters determined by Prettyman et al. [2004a] are valid from the pole to 50 S latitude, and, for the purpose of validating the spatial response model, are similar to those determined by other studies [e.g., Boynton et al., 2002; Tokar et al., 2002; Diez et al., 2008]. [19] The model for the thermal neutron counting rate (Figure 4) matches the measurements, indicating that the asymmetric shape, including the offset in the response from the cap center due to the relative motion of the spacecraft is accurately treated. Differences between model and measurements for the relatively weak epithermal peak (P1) probably result from uncertainties in the amount of exposed water ice in and around the cap or the area of the cap covered by relatively thin CO 2 deposits [Prettyman et al., 2004a]. Work is underway to combine models of the SPRC from thermal emission spectrosocopy and optical imagery with longitudinally resolved neutron counting data to further constrain SPRC parameters, such as the column abundance of CO 2 ice in different regions of the cap and portion of the cap consisting of exposed water ice. [20] Spatial blurring must be considered in the analysis of surface features such as the seasonal cap, especially when strong variations occur on scales comparable to or smaller 5of25

6 than the size of the footprint. During the advance, the seasonal cap is relatively uniform in thickness on scales much broader than the footprint; however, during the recession, CO 2 ice continues to build at the pole, while subliming at lower latitudes. We show that the sharp spatial variation, which is most pronounced during the recession, leads to systematic errors in CO 2 ice column abundance. By ignoring spatial blurring, both spatial and temporal artifacts are introduced. The column abundance of CO 2 ice is expected to be underestimated near the poles owing to spatial mixing with thinner ice at lower latitudes and overestimated at lower latitudes. During the recession, lower latitude regions that are frost-free are expected to be misattributed as having CO 2 ice owing to mixing with higher latitudes, resulting in a temporal lag. Spatial deconvolution will be used here to estimate the magnitude of systematic errors due to spatial blurring. 3. Model of Counting Rates [21] Counting rates (Cat1 and Cat2 for all four prisms) for representative surface and atmospheric parameters were modeled using the simulation codes developed by Prettyman et al. [2004a]. The surface and atmosphere of Mars was assumed to be uniform over the footprint of the spectrometer. The atmospheric mass and abundance of noncondensable gasses (N 2 + Ar, expressed as an equivalent abundance of N 2 [Feldman et al., 2003]) were varied along with surface parameters, which included the column abundance of seasonal CO 2 ice and regolith properties (soil composition, ice table depth, and abundance of water equivalent hydrogen). [22] As described by Prettyman et al. [2004a], the model was calibrated using measurements of the thick seasonal CO 2 ice in the northern and southern hemispheres. For the fast neutrons, the counting rate was observed to saturate during southern winter (see Figure 14a). The calibration constant was determined by dividing the observed saturation counting rate by the simulated counting rate for CO 2 ice thicker than 100 g/cm 2 distributed uniformly within the field of view of the spectrometer. For the thermal and epithermal neutrons, the model was calibrated using counting rates binned poleward of 85 N when the CO 2 ice was thickest in the northern hemisphere (L S =15 ). The surface was modeled as a uniform layer of CO 2 ice covering pure water ice, representative of the north polar residual cap. Although the water ice residual cap only covers 64% of the field of view of the spectrometer at the pole, the surrounding regolith is rich in water ice. Since the calibration was determined when the CO 2 ice column abundance was maximum, the calibration is insensitive to the abundance of water ice in the residual cap and surrounding regolith. The column abundance of CO 2 ice used in the model was 65 g/cm 2, determined by the attenuation of the gamma ray produced by neutron capture with hydrogen [Feldman et al., 2003; Kelly et al., 2006]. The calibration assumptions were verified by showing that the calibrated fast neutron model fitted the fast neutron counting data acquired at the north pole during winter [Prettyman et al., 2004a]. [23] Once calibrated, the simulations were used to determine the systematic variation of counting rates with CO 2 ice column abundance for different models of the atmosphere and frost-free surface (Figure 5). For each calculation, the surface and atmospheric properties were assumed to be constant over the field of view of the NS. Figures 5a 5c show trends for homogeneous, frost-free surfaces with a range of water-equivalent hydrogen abundances and an atmospheric mass of 10 g/cm 2. The equivalent N 2 mass mixing ratio was For thermal neutrons (Figure 5a), counting rate increases monotonically with CO 2 ice column abundance, tracing out a smooth curve from the value for the frost-free surface to the saturation value, for which the CO 2 ice is so thick that the neutron counting rate is insensitive to the underlying regolith. The fast neutron counting rate (Figure 5b) follows similar trends for surfaces with water abundances of 20% WEH or greater; however, for the 2% and 7% WEH surfaces, the counting rate decreases as CO 2 is added. For epithermal neutrons (Figure 5c), the trend is monotonic and increasing for all but the 2% WEH surface for which the counting rate initially decreases and then rises back up toward the saturation value. The nonmonotonic, variation for surfaces with relatively low water abundance is a consequence of the interplay between neutron production, moderation and leakage in the layered medium, which was modeled using the Monte Carlo radiation transport code MCNPX [Pelowitz, 2005]. [24] If the frost-free surface is assumed to be homogeneous, then the CO 2 ice column abundance can be determined given the counting rate observed for the frost-free surface during summer and the value measured when seasonal CO 2 ice is present. The frost-free counting rate uniquely identifies the curve that the counting rate will follow as CO 2 ice is added to the surface. As long as the curve is monotonic, there is a unique mapping between the observed counting rate and CO 2 ice column abundance (arrows in Figure 5c) and a single data band (for example, Cat1, P1) can be used in the analysis. Figure 5c shows that the curves are monotonic for epithermal neutrons (Cat1, P1) for WEH abundances of 7% or greater. Consequently, unique results can be obtained for observations poleward of 60 in the north and south where the abundance of WEH is high (greater than 20%). [25] The sensitivity of the measurements to changes in CO 2 ice column abundance depends on the WEH abundance of the underlying surface and the column abundance of CO 2 surface ice. For P1 (Cat1), the measurements are most sensitive for CO 2 ice column abundances between about 25 g/cm 2 and 100 g/cm 2 and least sensitive above 150 g/cm 2 and for thin layers of frost (<25 g/cm 2 ). Note that above 150 g/cm 2, changes in the P1 response are dominated by thermal neutrons, which gives P1 the same overall range as P2 (see Table 1). As the WEH abundance decreases, the sensitivity to changes in CO 2 ice decreases, especially for thin frost cover. [26] In order to determine CO 2 ice column abundance from the data, an interpolation algorithm was developed that gives the trend that the counting rate will follow as CO 2 ice is added to the surface. For a homogeneous regolith, the epithermal counting rate (C) is a function of the column abundance of CO 2 ice on the surface (A) and the summertime counting rate (C 0 ). The summertime counting rate is a proxy for the abundance of WEH in the material underlying the ice [Feldman et al., 2004]. For example, plots of C versus C 0 for different values of A for a homogeneous underlying regolith containing variable amounts of WEH form smooth 6of25

7 Figure 5. Systematic variation of counting rates as a function of CO 2 ice column abundance and the abundance of water-equivalent hydrogen (WEH) in the underlying surface for (a) thermal neutrons (P2 P4), (b) fast neutrons (Cat2, P1), and (c) epithermal neutrons (Cat1, P1). The curves shown in Figures 5a 5c were provided to guide the eye. The terms of equation (1) are illustrated in Figure 5c along with the inversion process in which the summertime counting rate (C 0 ), which is a proxy for WEH abundance in the underlying regolith, selects the trend of counting rate with CO 2 ice column abundance (A). When the trend is monotonic, the measurement of a seasonal counting rate (C) uniquely determines A. (d) The systematic variation in Cat1, P1 counting rates predicted by equation (1) is compared with modeled counting rates for three different regolith compositions (uniform surfaces with 7% and 100% WEH and a layered surface with 60% WEH covered by 15 g/cm 2 dry soil). The counting rates predicted using equation (1), given summertime counting rates, are labeled fit in the legend. Measurement of C 0 accurately determines the trend for seasonal counting rates when the regolith is homogeneous. When the regolith is layered, use of the homogeneous trend will result in errors in CO 2 ice column abundance of about 7 g/cm 2. curves that can be fitted to a quadratic (Figure 6a), with coefficients that depend on A: CðA; C 0 Þ¼a 0 ðaþþa 1 ðaþc 0 þ a 2 ðaþc 2 0 : The coefficients vary smoothly with CO 2 ice column abundance (Figures 6b 6d) and are given in Table 2 for two atmospheric masses, representative of the northern (20 g/cm 2 ) and southern (10 g/cm 2 ) high latitudes. The results show a weak sensitivity to atmospheric mass, such that the saturation value is lower in the north than the south. The ð1þ lower saturation value is caused by a combination of reduced production of fast neutrons by cosmic rays [Prettyman et al., 2004a] and increased absorption of thermal neutrons by noncondensable gasses in the thicker, northern atmosphere. [27] The procedure for determining CO 2 ice column abundance at any location is to construct the trend of counting rate with CO 2 ice column abundance given the observed summertime counting rate using equation (1). Then, the column abundance of CO 2 ice can be determined from the observed counting rate by interpolation (as illustrated in Figure 5c). Equation (1) is accurate for homogeneous surfaces over the range of water abundances expected at high 7of25

8 Figure 6. (a) Plots of modeled Cat1, P1 counting rates (C) as a function of the summertime, frost-free counting rate (C 0 ) are shown for different column abundances of overlying CO 2 ice (A). The counting rates were determined by modeling. The atmospheric mass was 10 g/cm 2. C 0 is a proxy for the abundance of WEH in the underlying regolith, which was assumed to be homogeneous. (b d) The coefficients of equation (1), which were determined by fitting a quadratic to each of the trends (C versus C 0 for constant A) shown in Figure 6a. The lines in Figure 6a are the fitted quadratic trends. Note that the trends for A = 5, 10, and15g/cm 2, for which coefficients are plotted in Figures 6b 6d, are not shown. The curves in Figures 6b 6d were provided to guide the eye. latitudes, as shown in Figure 5d, for surfaces with 7% and 100% WEH. [28] The high-latitude regolith is thought to consist of a relatively dry soil layer covering an ice table, the depth of which is thought to be controlled by exchange of water vapor with the atmosphere [e.g., Mellon et al., 2004]. Consequently, a source of uncertainty in the analysis of CO 2 ice column abundance is the assumption that the surface is uniform with depth. For example, in the southern hemisphere, the depth of the ice table varies with latitude, decreasing toward the pole, similar to that predicted by water ice stability models. On the basis of neutron spectroscopy, the ice table contains 60% ±10% WEH and is covered by less than 15 g/cm 2 of dry material [Prettyman et al., 2004a], which is similar to that determined by other studies that used data from GRS, HEND, and thermal emission spectroscopy [Boynton et al., 2002; Tokar et al., 2002; Prettyman et al., 2004a; Mitrofanov et al., 2004; Litvak et al., 2006; Titus and Table 2. Coefficients for Equation (1) for Surfaces With Uniform Composition Atmospheric Mass A 10 g/cm 2 20 g/cm 2 (g/cm 2 ) a 0 a 1 a 2 a 0 a 1 a of25

9 Prettyman, 2007; Bandfield, 2007; Bandfield and Feldman, 2008; Diez et al., 2008]. To determine the error caused by assuming a homogeneous surface, we simulated the trend for an ice table with 60% WEH covered by 15 g/cm 2 dry soil (Figure 5d). Given the summertime counting rate for this surface, we predicted the trend using equation (1) (for a homogeneous surface). The results, shown in Figure 5d indicate that the use of equation (1) would underestimate the column abundance of CO 2 ice by at most about 7 g/cm 2 if no other sources of error were present. [29] Stratigraphy can be removed as a source of error by modeling the epithermal counting rate as C = g(ajd, w), where D and w are the depth and WEH abundance of the ice table, respectively. The ice table depth and water abundance was determined as a function of latitude by neutron and gamma ray spectroscopy [Boynton et al., 2002; Tokar et al., 2002; Prettyman et al., 2004a; Mitrofanov et al., 2004; Litvak et al., 2006]. Recently, Diez et al. [2008] used neutron spectroscopy to map the ice table parameters as a function of longitude and latitude in the northern and southern hemisphere, excluding latitudes poleward of 75 S. The presence of an ice table strongly influences the thermal properties of the surface, and thermal emission spectroscopy (TES and THEMIS) has also been used to determine the depth of the ice table [e.g., Titus and Prettyman, 2007; Bandfield, 2007; Bandfield and Feldman, 2008]. Finally, geophysical models of water ice emplacement provide constraints on ice table depth that can guide the development of models used to interpret remote sensing data [Mellon et al., 2004; Schorghofer and Aharonson, 2005]. To determine g(ajd, w), we are in the process of calculating the systematic variation of counting rates with CO 2 ice thickness for the full range representative layered surfaces, based on available experimental and theoretical data. [30] A second source of error is the abundance of noncondensable gasses in the atmosphere at high latitudes, especially in the southern hemisphere for which meridional mixing is limited by the formation of a strong polar winter vortex, which results in the enrichment of N 2 and Ar during fall and winter [Sprague et al., 2004, 2007; Prettyman et al., 2004c]. Since N 2 and Ar are strong thermal neutron absorbers, the neutron spectrometer is sensitive to the abundance of N 2 and Ar in the atmosphere. The abundance of noncondensable gasses can be represented as the equivalent column abundance of N 2 (denoted N eq ) that would be needed in order to produce the same absorption of thermal neutrons as would be observed given the levels of N 2 and Ar present in the atmosphere [Feldman et al., 2003]. On the basis of data acquired by Viking Lander 2, the average Martian atmosphere contains 2.7% N 2 and 1.6% Ar [Owen et al., 1977], which we assume are molar fractions [e.g., see Lewis, 1997; Sprague et al., 2007]. From the standpoint of thermal neutron absorption, the average abundances for N 2 and Ar are equivalent to 3% N 2 by volume, which corresponds to an equivalent N 2 mass mixing ratio of [31] The equivalent N 2 abundance was calculated as the amount of N 2 that gives the same macroscopic thermal neutron absorption as the mixture of Ar and N 2 for the average Martian atmosphere. The macroscopic absorption cross section, with units of cm 1, for a selected element is given by S a = Nfs a, where f and s a are the molar fraction and microscopic absorption cross section for thermal neutrons (with units of barns per atom, 1 barn = cm 2 ), respectively, for the element of interest, and N (atoms/barn-cm) is the total number density of atoms. The microscopic, thermal neutron absorption cross sections for N 2 and Ar are = 3.78 barns (accounting for two nitrogen atoms per molecule) and 0.66 barns, respectively [Parrington et al., 1996]. The equivalent molar fraction for N 2 is then given by f = ( )/3.78 ffi 3%. [32] Note that Feldman et al. [2003] interpreted the abundances reported by Owen et al. [1977] as weight fractions. Consequently, the reference atmosphere used by Feldman et al. [2003] had an equivalent N 2 mass mixing ratio of From the standpoint of determining CO 2 ice column abundances from epithermal neutrons, the difference in the equivalent mass mixing ratios for N 2 in the reference atmosphere for Feldman et al. [2003] and this work is not significant; however, the difference is important when comparing results for noncondensable gas enrichment reported by Feldman et al. [2003] and Sprague et al. [2007]. [33] The value for N eq is a function of the atmospheric mass (total atmospheric column), which was calculated by the GCM as a function of time, longitude and latitude (on a grid). The maximum abundance of Ar in the southern hemisphere, determined by gamma ray spectroscopy [Sprague et al., 2007], was found to be about a factor of 6 (±1) times the average mixing ratio. Assuming N 2 and Ar were perfectly mixed, then the maximum equivalent mass mixing ratio for N 2 was approximately 6 (±1) = (±0.019). The atmospheric mass at high southern latitudes during winter is about 10 g/cm 2, which gives N eq = 1.14 (±0.19) g/cm 2 for the maximum column abundance of noncondensable gasses. Similarly, N eq = 0.19 g/cm 2 for an atmosphere with a mass of 10 g/cm 2 containing the average mass mixing ratio (0.019) of noncondensable gasses. [34] To demonstrate the sensitivity of thermal and epithermal neutrons to absorption by noncondensable gasses, the variation of thermal (P2 P4) and epithermal (P1) neutron counting rates with N eq is shown in Figure 7a for cases in which the underlying CO 2 ice was thick (100 g/cm 2 ) and for an atmospheric mass of 10 g/cm 2. From the fitted exponential trends, the P1 counting rate decreases by about 6% from the average value of N eq to the maximum, in comparison to a 26% decrease for P2 P4. The exponential variation is largely a consequence of the absorption of thermal neutrons escaping from the surface CO 2 ice by N 2 and Ar in the intervening atmosphere. The e-folding value for N eq depends on the energy distribution of neutrons in the surface and atmosphere, which in turn depends on surface composition and layering as well as atmospheric mass. CO 2 ice is a strong source of thermal neutrons, which are efficiently absorbed in the atmosphere, and, consequently, has relatively small e-folding values for N eq compared to ice-rich soil. [35] In Figure 7b, the variation of counting rate with CO 2 ice column abundance is shown for fast, epithermal, and thermal neutrons. The frost-free surface consisted of 15 g/cm 2 of dry soil covering a semi-infinite permafrost layer with 60% water equivalent hydrogen. The atmospheric mass was 10 g/cm 2. Considering the aforementioned uncertainty in the maximum N 2 equivalent column abundance, two cases, representing a range of possible effective N 2 column abundances, are compared: (1) N eq = 0.15 g/cm 2 and (2) N eq = 1.4 g/cm 2. Results show varying degrees of sensitivity to 9of25

10 Figure 7. (a) The exponential variation of counting rates with N eq is shown for a representative high-latitude surface (15 g/cm 2 of soil with 3% WEH covering soil with 50% WEH) covered by 100 g/cm 2 CO 2. The atmospheric mass was 10 g/cm 2. (b) Counting rates as a function of CO 2 ice column abundance covering a representative high-latitude surface with 15 g/cm 2 of dry soil (2% WEH) covering a water-rich medium (60% WEH). Results are shown for two column abundances of equivalent nitrogen: (1) N eq = 0.15 g/cm 2 and (2) N eq = 1.4 g/cm 2. The atmospheric mass was 10 g/cm 2 for both cases. changes in N 2 and Ar in the atmosphere: fast neutrons are not sensitive; epithermal neutrons are weakly sensitive; and thermal neutrons are strongly sensitive. If the effective column abundance of N 2 was not known, then fast neutrons would appear to be the best choice for determining the thickness of CO 2 ice; however, fast neutrons begin to saturate for relatively thin ice deposits (starting at about 50 g/cm 2 ), have relatively large statistical uncertainties, and are also sensitive to seasonal variations in atmospheric mass [Prettyman et al., 2004a]. In contrast, epithermal neutrons (Cat1, P1) are relatively insensitive to variations in atmospheric mass, have low statistical uncertainty, and are sensitive to changes in CO 2 over the expected range (up to 100 g/cm 2 ). [36] If the effective N 2 column abundance was assumed to be 0.15 g/cm 2, but was really 1.4 g/cm 2, then the error in the abundance of CO 2 determined using epithermal (P1) neutrons would be about 20 g/cm 2 if the CO 2 ice were 100 g/cm 2 thick. For thinner deposits of CO 2 ice, the absolute error would be smaller: approximately 10 g/cm 2 for an 80 g/cm 2 deposit; and <5 g/cm 2 for deposits <60 g/cm 2 thick. If the concentration of N 2 and Ar is greater than average, then using trends for epithermal counting rate versus CO 2 ice thickness calculated for the average concentration will give a lower bound on CO 2 ice column abundance. [37] Prettyman et al. [2004c] solved simultaneous equations to determine the zonally averaged column abundance of CO 2 ice and effective N 2 from thermal (P2 P4) and epithermal (P1) counting rates. In this study, we repeated the analysis of zonal data by determining the column abundance of CO 2 ice from P1 assuming N eq varied with the atmospheric mass calculated by the GCM, and using the N 2 mass mixing fraction for the average atmosphere. We then adjusted N eq to match the P2 P4 counting data using the model developed by Prettyman et al. [2004c], which depends on N eq, the CO 2 ice column abundance determined from P1, and the P2 P4 counting rate observed during summer. The modeled P1 counting rates using the N eq values determined from P2 P4 differed by less than the systematic error in the data from the values calculated assuming the average atmospheric composition. [38] Results of the analysis for Mars year 26 (Figure 8, poleward of 75 S) show a broad maximum in N eq between L S of 75 and 120, followed by a rapid decrease, similar to the results reported by Sprague et al. [2007] using gamma ray spectroscopy (see Figure 8 for a direct comparison between NS and GRS enhancement factors for year 26). The maximum CO 2 ice column abundance (>60 g/cm 2 ) occurs near the poles during the recession at approximately 170 L S, much later in time than the maximum in the N 2 mixing ratio. Consequently, P1 is not expected to be strongly affected by absorption of thermal neutrons, and the error in CO 2 ice column abundance determined from P1 counting data using equation (1) is expected to be relatively small, on the order of 5 g/cm Data Reduction [39] A discussion of errors would not be complete without describing the uncertainties introduced by the data reduction process. The data reduction algorithms used in this study were developed by Prettyman et al. [2004a, 2004b]. Several processing steps were used to convert raw telemetry data to counting rates suitable for mapping, including correction for variations in the gain of each prism, determination of net peak areas for the 10 B(n, a) reaction from the Cat1 spectra, and the normalization of counting rates to account for variations in the flux of galactic cosmic rays using data averaged over the belly band (between ±30 latitude). The algorithms were verified by comparison to codes independently developed by Tokar et al. [2002] and Maurice et al. [2007]. For epithermal neutrons, the difference between counting rates determined by Prettyman et al. [2004a] and Maurice et al. [2007] was less than 3%. The neutron counting data are subject to random variations, which result in fluctuations in derived quantities, such as CO 2 ice column abundance. In addition to Poisson noise, fluctuations in the mean counting rates are driven by variations in the galactic cosmic 10 of 25

11 Figure 8. (top) The column abundance of CO 2 ice and atmospheric N eq determined by neutron spectroscopy (see text) is shown as a function of time for year 26 poleward of 75 S along with the atmospheric mass (g/cm 2 ) calculated by the general circulation model (GCM). (bottom) The N 2 enhancement factor is shown. Following Sprague et al. [2007], the enhancement factor is the ratio of the column abundance of N eq determined from the Neutron Spectrometer (NS) data to the column abundance of N eq that would have been observed if the mass mixing ratio of noncondensable gas were constant with time and equal to the accepted average value measured by Viking Lander 2. For the reference case in which the mass mixing ratio was assumed to be constant, the value of N eq varied with the GCM-calculated atmospheric mass. For comparison, the enhancement factors determined from Gamma Ray Spectrometer data by Sprague et al. [2007] are shown for year 26. ray background and changes in the instrument response (for example, due to gain shifts), which are not fully corrected by the belly band normalization. The uncertainty in mapped, average counting rates varies inversely with the square root of the integration time. Consequently, the error introduced by random variations can be reduced by increasing the number of measurements used to determine average counting rates or by smoothing the data in the space or time domain. [40] For the time series, epithermal neutron counting data, systematic errors are associated with the determination of the 10 B(n, a) peak area from the P1, Cat1 spectrum. The background continuum underneath the peak is modeled as a power law, whose parameters are determined from channels on either side of the peak. A strong peak is visible when the spectrometer views thick CO 2 ice deposits; however, the peak to background ratio decreases substantially when the spectrometer views water-rich materials. If the functional form assumed for the background is incorrect, then errors will occur, particularly when the peak to background ratio is small. Consequently, the algorithm for determining net peak area is more accurate for thick deposits of CO 2 frost, which were also used to calibrate the model, than for waterrich materials. [41] Nonetheless, the systematic errors in epithermal net counting rates are thought to be no larger than ±15% for measurements of high-latitude, water-rich regions [Feldman et al., 2004]. Owing to continuous improvement in the data reduction algorithms and stable performance of the NS (in terms of gain variations), the uncertainty is probably smaller, on the order of 5%. If the calibration procedure is accurate, and there is reason to believe that it is based on independent analyses of neutron and gamma ray data, then a 15% 11 of 25

12 Figure 9. The uncertainty in CO 2 ice column abundance (s A ), determined using equations (1), (2), and (3), is shown as a function of CO 2 ice column abundance (A) for three different underlying WEH abundances for the case in which N = Note that the largest values for s A occur for A 20 g/cm 2 and A 80 g/cm 2, where the seasonal counting rates are least sensitive to changes in CO 2 ice column abundance (see equation (1) and Figure 5). In addition, s A increases as the WEH abundance in the underlying surface decreases. systematic error when counting rates are low would introduce a small error in derived CO 2 ice column abundances compared to other sources of bias, such as assumptions regarding depth of the ice table. For example, if the summertime counting rate (C 0 ) for a water-rich region of the northern hemisphere were 1.15 counts/s instead of 1.1 counts/s, then an observed seasonal value of C = 2 counts/s would correspond to 18 g/cm 2 instead of 20 g/cm 2. [42] The effect of uncertainties in the counting rate on the determination of CO 2 ice column abundance can be estimated using the Taylor series expansion method for error propagation [Bevington and Robinson, 1992]. The uncertainty in the CO 2 ice column abundance (s A ) in terms of the uncertainties in the seasonal and summertime counting rates, denoted s C and s C0, respectively, is given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2 C s A ¼ þ s2 C 0 ½a 1 ðaþþ2a 2 ðaþc 0 Š 2 da 0 da þ C da 1 0 da þ da 2 : ð2þ C2 0 da The derivatives of the coefficients of equation (1), which appear in the denominator of equation (2), can be determined from the values reported in Table 2. Note the seasonal and summertime counting rates were assumed to be uncorrelated in the derivation of equation (2). Consequently, equation (2) cannot be used to assess the effect of long-term, systematic variations in counting rate (for example, due to gradual modulation of the energy distribution of galactic cosmic rays during the solar cycle). [43] The population variance of mapped counting rates (for example, for a pixel or zone) is given by s 2 = (N 1) 1P N i¼1 (C i C) 2, where N is the number of 20s measurements for which the subsatellite point was within the pixel, C i is the ith measurement of counting rate, and C = N 1P N i¼1 C i. The uncertainty in the p ffiffiffiffiaverage counting rate for a pixel is given by s C ffi s/ N. If the counting rates were Poisson random variates, then the uncertainty in ptheffiffiffiffiffiffiffiffiffiffiffiffiffiffi average counting rate would be given by s CPoisson ffi C=ðNtÞ, where t is the measurement time (20s). [44] A comparison between these two estimates of uncertainty reveal that the counting errors are not distributed according to the Poisson distribution, which is expected, because of random variations introduced by the background subtraction and belly band normalization algorithms described by Prettyman et al. [2004a, 2004b]. For example, consider epithermal counting rates averaged poleward of 85 S asa function of time in 10 L S intervals (see Figure 14). For the minimum counting rate (C = 1.76 counts/s), which occurred during southern summer at L S = 3.96, the number of observations was N = 316 and the population standard deviation was s = 1.17 counts/s, for which s C = counts/s and s CPoisson = counts/s. For the maximum counting rate (C = 10.4 counts/s), which occurred at L S = 190.5, the number of observations was N = 875 and the population standard deviation was s = 1.37 counts/s, for which s C = 0.05 and s CPoisson = counts/s. [45] Taking all of the measurements into account, we find that the two estimates of the uncertainty are moderately correlated: s CPoisson = 0.37 s C with R 2 = Assuming the variation associated with the background subtraction algorithm is small, then the total uncertainty can be modeled as the quadrature of an unknown error (s u ), plus the Poisson error: s 2 C = s 2 u + s CPoisson.The unknown error was found to be weakly correlated with counting rate (R 2 = 0.015) with a mean value of approximately 0.04 counts/s for N ffi Assuming the unknown error is constant, the uncertainty in the average epithermal counting rate can be modeled as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi =N; s C ffi s 2 0 þ C=t ð3þ p where s 0 = 0.04 ffiffiffiffiffiffiffiffiffiffi 1000 = 1.26 counts/s and t = 20s. [46] Equations (1), (2), and (3) can be combined to estimate the sensitivity of CO 2 ice column abundance to errors in the seasonal and summertime counting rates as a function of the number of measurements (N), the column abundance of seasonal CO 2 ice, and the WEH abundance in the underlying regolith. For counting data averaged over 10 L S intervals and 5 latitude zones, N ffi 1000 (which is approximately independent of latitude). The variation of s A with A is shown for three different underlying WEH abundances in Figure 9 for the case in which N = One 10 L S interval was used to represent the uncertainty in the summertime counting rate, which was determined using equation (3). Several intervals (representing several thousand measurements) can be averaged during summer. Consequently, the values for s A shown in Figure 9 are higher than would be expected in practice. From Figure 9, the largest values for s A 2 12 of 25

13 occur for A 20 g/cm 2 and A 80 g/cm 2, where the seasonal counting rates are least sensitive to changes in CO 2 ice column abundance (see equation (1) and Figure 5). In addition, s A increases as the WEH abundance in the underlying surface decreases. For N = 1000, s A is much smaller than other sources of error over the entire range of CO 2 ice column abundances and WEH abundances expected at high latitudes. The values in Figure 9 can bep extrapolated ffiffiffiffi to other values of N by noting that s A / 1/ N. [47] The process of mapping CO 2 ice column abundance, described in section 5, involves smoothing time series counting data binned on a base map with 0.5 equal angle pixels by a 5 full width at half maximum (FWHM) spatial filter and rebinning the result on 2 equal area pixels for presentation. For the purpose of estimating uncertainties, the smoothing step, which dominates the intrinsic resolution of the resulting map, is roughly equivalent to binning data on 5 pixels of equal area. Equal area maps used in this study are described by Lawrence et al. [2004]. With the exception of the pole, the pixels have equal angle in latitude; however, to achieve approximate equivalent area, each pixel spans a number of 0.5 longitude intervals equal to N 8 = IPb360 sin(a eq )/(p cos(l 0 ))c, where IP refers to the integer part of the quantity in the brackets, a eq =5 is the resolution of the map, and l 0 is the center of the latitude band. In practice, N 8 is adjusted downward until an integer divisor of 720 is found. For the latitude bands centered on 60 N or S, N 8 = 19, resulting 40 equal-area pixels, each of which spans 9 in longitude. Note that the formula for N 8 presented here corrects an error found by Lawrence et al. [2004, also private communication, 2009]. [48] If the 1000 measurements per 5 zone were divided evenly among the pixels in the 60 latitude band, then N ffi 25 measurements per pixel. Since the latitude bands closer to the pole are divided into fewer pixels, N = 25 is a lower bound on the number of measurements per pixel ppoleward ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi of 60. Consequently, s A would be no more than 1000=25 ffi 6 times higher for map pixels than for the zonal values shown in Figure 9. In the worst case, s A for the pixels would be less than 10 g/cm 2 over the range of expected values for A and less than 5 g/cm 2 for values of A between 10 and 80 g/cm 2. [49] For mapped counting data, statistical fluctuations can cause C to be less than C 0 during early frost formation and near the crocus date. When this happens, the value for A is assigned to be zero; whereas, any time C is greater than C 0, a value for CO 2 ice column abundance is determined using the procedure described in section 3 (equation (1)). Since negative values cannot be introduced to offset fluctuations in counting rate above the mean value, a positive bias in CO 2 ice column abundance is introduced. In practice, the CO 2 ice column abundance for a pixel is not assigned unless (C C 0 )C 0 is greater than 10%. This approach avoids introducing bias in reported values of A; however, CO 2 ice deposits (below about 5 g/cm 2 ) are not included in the maps. In addition, zonally averaged values determined from maps of CO 2 ice column abundances may be biased when A is small. 5. Spatial Deconvolution [50] As illustrated in Figures 3 and 4, the spatial resolution of NS is asymmetrical, offset from the subsatellite point, and broad, roughly 10 FWHM of arc length. Spatial mixing can lead to analysis and interpretation errors when the composition of the surface varies significantly on a scale that is smaller than the footprint of the spectrometer. The asymmetrical shape and offset of the spatial response function result in blurring artifacts and registration errors when mapped neutron counting data are compared to other data sets. [51] For example, Figure 10a shows simulated, zonally averaged counting rates for the southern hemisphere of Mars during advance (L S =90 ) and recession (L S = 220 ) of the seasonal caps and during summer. The simulations included the spatial response of the spectrometer, and used an accurate model of the CO 2 frost-free surface described by Prettyman et al. [2004a] along with seasonal CO 2 ice column abundances calculated by the Ames GCM. Application of the algorithm described in section 3 (equation (1)) to the simulated counting rates gives results for CO 2 ice column abundance, which are compared to the GCM calculations in Figure 10b. The determined column abundances are underestimated near the poles and overestimated at lower latitudes. The errors are largest during the recession, for which the seasonal cap has a sharp gradient in the column abundance of CO 2 ice with latitude due to the sublimation of frost at lower latitudes and the continued accumulation of frost at high latitudes. [52] Spatial deconvolution techniques, such as Jansson s algorithm and the Pixon method, have been applied to planetary data sets to reduce or eliminate artifacts of spatial blurring from counting rate maps [Haines et al., 1978; Elphic et al., 2005; Prettyman et al., 2005; Lawrence et al., 2007; Elphic et al., 2007]. Here, we apply Jansson s algorithm [Jansson, 1997] to deconvolve maps of epithermal counting rates, with the primary goal of assessing the uncertainties introduced by spatial blurring in the analysis of CO 2 ice column abundance. [53] The observed map of counting rates (d) can be modeled as a convolution of the true map of the surface (i) with the response function of the spectrometer (r): d ¼ i r þ e; where denotes convolution and e represents noise in the map data, for example, due to Poisson noise. The boldface letters in equation (4) denote two-dimensional matrices. The convolution of the smoothed image with the two-dimensional spatial response function in spherical coordinates was carried out by a Monte Carlo calculation, which simulates the orbit of the spacecraft, the angular distribution of neutrons emitted from the top of the atmosphere, transport of neutrons though the exosphere along ballistic trajectories, the relative motion of the spacecraft, and a detailed model of the instrument response for each event category and prism [Prettyman et al., 2004a]. For epithermal neutrons, we found that the spatial response, which depends on the angular distribution of emitted neutrons, was not strongly sensitive to the composition of the surface and atmosphere (Figure 11). In this study, minor variations in the response due to surface composition were ignored, and the angular distribution for a single surface composition (pure water ice) was used to calculate the spatial response for all positions and times. [54] Jansson s algorithm amplifies noise through successive iterations. Therefore, it is expedient to smooth the data to ð4þ 13 of 25

14 where d k 1 = ~d i k 1 ~r is the difference between the model and the smoothed data, and Q k 1 i,i = k b1 (2/i max )(i k 1 i i max /2)c is a diagonal relaxation matrix that controls the growth of oscillations in the solution (via the relaxation parameter k) and imposes simple bounds on the solution, which is constrained to be between 0 and i max. Noise in the solution is controlled by the smoothing function and the relaxation parameter, both of which must be determined by experimentation. In addition, excessive iteration can result in a noisy solution. [55] In the present study, the optimal number of iterations and parameters for the relaxation matrix were determined using a simulated data set. We created a global map with sharp-edged, surface features with variable size, separation and counting rate spanning the range observed in the measured data. We convolved the image with the response function, and introduced Poisson noise to produce a blurry map with noise properties similar to the measured data. Jansson s algorithm was applied to the simulated data set. At each iteration, the magnitude of the difference between the model and the data kd k k 2 2 and the difference between true map and the solution ki i k k 2 2 was calculated. Note that kxk 2 2 denotes the sum of the squares of the elements of x. [56] Figure 12 shows that the difference between the model and data decreases with increasing iteration. The difference between the true map and the solution decreases at first, but reaches a point of diminishing return, finally increasing due to the amplification of noise in the solution by the iterative process. Consequently, a stopping criterion of 20 iterations was imposed on the application of Jansson s algorithm to the measured data. [57] The application of Jannson s algorithm is illustrated in Figure 13 for data acquired over an interval of 10 of L S, centered on L S =5. Figure 13a shows data binned at the subsatellite point on 0.5 equal angle pixels. Since the Figure 10. (a) Simulated, zonally averaged counting rates for the southern hemisphere of Mars during advance (L S =90 ) and recession (L S = 220 ) of the seasonal caps and during summer. The simulations included the spatial response of the spectrometer and used an accurate model of the frost-free surface described by Prettyman et al. [2004a] along with seasonal CO 2 ice column abundances calculated by the Ames GCM. (b) CO 2 ice column abundances determined by inverting equation (1) using simulated data in Figure 10a are compared to the GCM column abundances used to simulate the data. remove statistical variations prior to applying Jansson s algorithm. The smoothed map data can be represented as a double convolution of the true map: ~d ¼ d s ¼ ði rþs ¼ i ~r; ð5þ where ~r = r s and s is the smoothing function. The kth iteration of Jansson s algorithm is given by i k ¼ i k 1 þ Q k 1 d k 1 ; ð6þ Figure 11. The simulated response (relative counting rate) of P1 is shown along an orbital trajectory that passes directly over circular deposit (5 in diameter and centered at 0 arc length as indicated by the vertical lines). The response for a water ice deposit is compared to a CO 2 ice deposit. 14 of 25

15 the pole. As noted previously, this observation was used to calibrate the model used to analyze data acquired by the neutron spectrometer [Prettyman et al., 2004a]. [59] For comparison, the counting rate data from year 27 is superimposed on year 26 in Figures 14 and 15, revealing Figure 12. Convergence of Jansson s algorithm for simulated P1 counting data (see text for details). The difference between the forward model and the data monotonically decreases with increasing iteration. The difference between the reconstructed image and the truth (the image used to simulate the data) achieves a broad minimum after about 30 iterations and then steadily increases. spacecraft is in a polar orbit, the coverage is greater at the high latitudes. Some gaps in coverage can be seen at low latitude. The map in Figure 13b was produced by convolving the map in Figure 13a with the smoothing function (s), which was selected to be 5 FWHM, narrower than the P1 response function, but with approximately the same shape. The width of the smoothing function was selected to minimize the amplification of noise by the iterative process, based on experimentation with simulated data sets, and to fill regions poorly sampled by the ground track at lower latitudes. Application of Jansson s algorithm to the map in 13b, results in increased contrast and sharpened spatial features (Figure 13c). The selection of 10 L S intervals enables ample coverage of the high latitudes (within 60 of the pole). 6. Results and Discussion [58] Data acquired during two, successive Mars years were used to determine the seasonal variations in the thickness and distribution of CO 2 ice in the northern and southern hemispheres. The algorithms developed by Prettyman et al. [2004a, 2004b] were applied to reduce data acquired during Mars years 26 and 27 (April 2002 to January 2006, following the convention of Clancy et al. [2000]). The time series, averaged counting rates for all three neutron energy ranges are shown in Figure 14 for data acquired poleward of 85 in the northern and southern hemisphere. Zonal averages are shown for the 70 to 75 latitude band in Figure 15. Counting rates for fast, epithermal, and thermal neutrons change with seasonal ice thickness, which increases during autumn and winter and decreases in spring and summer in response to changes in insolation. The different shapes of the time profiles of the three energy ranges are primarily a result of differing sensitivities to CO 2 ice (Figure 5). In the southern hemisphere, the fast neutron counting rate saturates starting at about L S = 120 and maintains a constant value while the epithermal and thermal neutron counting rates continue to increase, which indicates that the CO 2 ice is very thick (>70 g/cm 2 ) in the regions seen by the spectrometer from Figure 13. Jansson s algorithm applied to P1 data acquired over an interval of 10 of L S, centered on L S =5 : (a) raw data binned at the subsatellite point on 0.5 equal angle pixels; (b) convolution of the raw data with the smoothing function (s), which was selected to be 5 full width at half maximum, with similar shape, but narrower than the P1 response function; (c) application of Jansson s algorithm to the smoothed map, resulting in increased contrast and sharpened spatial features. Note that the maps are stereographic projections extending from the pole to 45 N. The longitudes are given in east longitude convention. The color bar applies to all three maps. The raw data (Figure 13a), which is shown as a 0.5 equal angle map, shows how the orbital tracks sample the high-latitude region. The smoothed and deconvolved maps shown in Figures 13b and 13c, respectively, are presented as 2 equal area maps. 15 of 25

16 Figure 14. Average neutron counting rates measured poleward of 85 in the (a) southern and (b) northern hemispheres for two Mars years. The counting rates for the second year are superimposed on those for the first year as open symbols. relatively small interannual differences in the epithermal and fast neutron counting rates, which implies similar patterns of emplacement and removal of seasonal CO 2 ice each year. Small differences in the saturation value for the fast neutrons between the two years may be caused by differences in the production of neutrons with depth by galactic cosmic rays, whose energy distribution is modulated by the solar cycle. Perhaps a contribution may also come from a variable admixture of dust in the precipitated CO 2 ice, which may be considered in future studies. Variations in the intensity of galactic cosmic rays, which increased gradually with time, were normalized using the belly band averaging procedures described by Prettyman et al. [2004a, 2004b]. The peak thermal neutron counting rate in both latitude zones for year 27 is higher than in year 26. This may indicate that there was less N 2 and Ar in the polar atmosphere in year 27, which could mean that meridional mixing was inhibited by a stronger winter vortex in year 26. In addition, that the peak thermal neutron counting rates occur later in time than the peak in the column abundance of N eq (for example, see Figure 8 for year 26) may indicate that meridional mixing was suppressed for a longer period of time in year 26 than in year 27. Note that the thermal neutron measurements are consistent with GRS observations: The maximum counting rate at the south pole for the 1382 kev gamma ray line caused by neutron capture by Ti, which is proportional to Figure 15. Zonal average of neutron counting rates measured for the 70 to 75 latitude band in the (a) southern and (b) northern hemispheres for two Mars years. The counting rates for the second year are superimposed on those for the first year as open symbols. 16 of 25

17 Figure 16. Northern hemisphere: (left) Maps of deconvolved epithermal neutron counting rates are compared to (right) maps of CO 2 ice column abundances determined from the deconvolved counting rates using the procedure described in section 3. The physical quantities are superimposed on a shaded relief map. The maps are stereographic projections (extending from 45 N to the pole). East longitude convention is used. Pairs of maps at selected time intervals, approximately 10 L S in duration, are shown. The midpoints of the time intervals are indicated in blue. L S is an angular measure of season, with the following ranges for seasons in the northern hemisphere: spring (0 90 ), summer ( ), fall ( ), and winter ( ). Note that the CO 2 ice column abundance is not mapped unless the relative change in counting rate from the summertime average is greater than 10%. In addition, CO 2 ice is not mapped equatorward of 60 N. Pixels that are not mapped are shown in gray. The edge of the seasonal cap determined by Thermal Emission Spectrometer (TES) is shown as a red line [Titus, 2005]. During winter the boundary of the polar night is indicated as a dashed, aqua line. During spring (for example, see the maps of CO 2 ice column abundance for L S =14 and 44 ) the NS senses CO 2 ice outside of the physical cap as determined by TES, which implies that spatial deconvolution does not fully correct for the broad spatial response of the spectrometer. The highly asymmetrical appearance of the seasonal counting rates (the cap appears to be skewed toward Acidalia) is primarily a consequence of asymmetric summertime counting rates (for example, see the map of counting rates for L S = 155 ). The maps of CO 2 ice column abundance are more symmetrical and achieve their maximum values near the pole. During summer when seasonal CO 2 ice is absent, random variations in epithermal counting rates can cause CO 2 ice column abundances to be mapped at levels much less than 10 g/cm 2 (for example, see the map of CO 2 ice column abundance for L S = 155 ). A summary of uncertainties is given in Table of 25

18 Figure 17. Southern hemisphere: (left) Maps of deconvolved epithermal neutron counting rates are compared to (right) maps of CO 2 ice column abundances determined from the deconvolved counting rates using the procedure described in section 3. The physical quantities are superimposed on a shaded relief map. The maps are stereographic projections (extending from 45 S to the pole). East longitude convention is used. Pairs of maps at selected time intervals, approximately 10 L S in duration, are shown. The midpoints of the time intervals are indicated in blue. L S is an angular measure of season, with the following ranges for seasons in the southern hemisphere: fall (0 90 ), winter ( ), spring ( ), and summer ( ). Note that the CO 2 ice column abundance is not mapped unless the relative change in counting rate from the summertime average is greater than 10%. In addition, CO 2 ice is not mapped equatorward of 60 S. Pixels that are not mapped are shown in gray. The edge of the seasonal cap determined by TES is shown as a red line [Titus, 2005]. Where applicable, the boundary of the polar night is indicated as a dashed, aqua line. As in the northern hemisphere, the NS senses CO 2 ice outside the physical cap as a result of spatial blurring, which is not fully corrected by deconvolution (for example, see the map of CO 2 ice column abundance for L S = 234 ). The seasonal cap appears to be roughly symmetrical during the advance (for example, see the maps of CO 2 ice column abundance for L S =95 and 155 ); however, the maximum CO 2 ice column abundances occur in the vicinity of the residual cap, which is offset from the pole, resulting in an asymmetrical distribution of CO 2 ice during the recession (for example, see the maps of CO 2 ice column abundance for L S = 204 and 234 ). A summary of uncertainties is given in Table of 25