Cloud structure changes and their associated radiative property changes over the tropical Pacific Ocean during the strong 1997/98 El Niño are studied using a merged satellite data set from the Clouds and the Earth's Radiant Energy System (CERES) project. This one-degree by one-degree gridded data set provides monthly mean values of radiative fluxes at the top of the atmosphere in addition to cloud fraction, cloud top altitude and cloud optical depth for the first eight months of 1998. This time period includes much of the 1997/98 El Niño, which reached peak intensity in March 1998 and essentially subsided by August 1998. The west-to-east shift of the center of convection that occurred during the El Niño resulted in cloud fraction, cloud top altitude and cloud optical depth increasing in the eastern equatorial Pacific while decreasing in the western tropical Pacific. For both regions all three cloud parameters are strongly correlated with each other and contribute to the strong linear relationship between longwave (LW) and shortwave (SW) cloud-radiative forcings (CRFs). This strong El Niño serves as a suitable test case for climate models. Results using the National Center for Atmospheric Research (NCAR) Community Atmosphere Model (CAM) 4.0 show many of the observed changes in 500 hPa vertical velocity, cloud-radiative forcing, cloud top altitude and cloud fraction within the tropical Pacific during the El Niño event, but fail to capture the observed relationship between radiation anomalies and cloud optical depth anomalies.
 The large difference of climate sensitivity estimates among current climate models is mainly due to the inter-model difference in cloud feedbacks [Colman, 2003; Soden and Held, 2006] and cloud feedbacks are strongly affected by the representation of clouds and their radiative properties in climate models [Senior and Mitchell, 1993; Yokohata et al., 2005]. Clouds consist of various cloud types ranging from low-level boundary layer clouds and deep convective clouds and to thin cirrus. To fully understand cloud feedbacks, it is necessary to study the radiative properties of different cloud types and their impact on the change in the Earth's radiation budget not only globally but also regionally.
 Studies by Clement et al.  and Lauer et al. focus on regional and low-level cloud feedbacks on decadal time scales using both observations and models.Xu et al.  and Luo et al.  focus on the 1998 El Niño to study statistical characteristics of cloud properties and radiative properties and their relationships to large scale dynamics using CERES footprint data and a cloud resolving model. Bell et al.  and Cess et al.  showed that the 1998 El Niño event caused a collapse of the Walker circulation which resulted in fewer and lower clouds over the tropical western Pacific and more and higher clouds over the eastern Pacific. As emphasized by Cess et al. , these cloud structure changes should serve as a useful test of a climate model. A related study [Lu et al., 2004] demonstrated this by simulating the cloud structure changes using Version 3 of the Hadley Centre Atmospheric Model (HadAM3), and it was specifically shown that HadAM3 had produced the collapse of the Walker circulation, necessary for the model to produce the associated cloud structure changes. The model successfully produced top-of-the-atmosphere (TOA) radiative properties similar to the ERBE/CERES measurements and cloud top altitude change consistent with the collapse of the Walker circulation. However, the cloud top altitude in this study was approximated by the ratio of SW CRF to LW CRF since cloud top altitude data were not available at that time.
 In the present study we extend the analysis of Lu et al.  and Cess et al.  to show more features of the changes in cloud structure averaged, over the tropical Pacific during the 1997/98 El Niño, by using a recent satellite data set that includes not only radiative fluxes at the TOA, but also the associated cloud fraction, cloud top altitude and cloud optical depth. We then examine the changes of both radiative and cloud properties in the NCAR CAM4.0, as induced by the 1997/98 El Niño. Last, we will diagnose the effects of changes in the cloud structures and associated properties on the changes in radiative fluxes during that period.
2. Data Sets
 The data set used in this study is the SRBAVG-GEO Edition 2B, which includes monthly mean TOA radiometric flux averages and cloud properties produced by the CERES Project during the Tropical Rainfall Measuring Mission (TRMM) [Wielicki et al., 1996]. The product provides data with a monthly temporal resolution and a 1° × 1° spatial resolution. Each grid cell contains TOA fluxes and four layers of cloud fraction, cloud optical depth, cloud top height, cloud liquid and ice water path and other cloud properties. The four vertical layers are: low (P > = 700 hPa), lower middle (700 hPa > P > = 500 hPa), upper middle (500 hPa > P > = 300 hPa), and high (P < 300 hPa).
 For the TOA flux, the SRBAVG-GEO data set combines the CERES flux with the 3-hourly Geostationary (GEO) satellite flux between 60°N and 60°S. The GEO derived fluxes account for changes in radiation due to clouds between CERES measurements [Young et al., 1998], A region is typically only observed twice a day from the TRMM satellite, which is in precessionary orbit with a 46-day repeat cycle. The CERES TOA measured radiances are converted to fluxes using angular distribution models [Loeb et al., 2003] based on the scene identification information obtained from cloud retrievals from the Visible and Infrared Scanner (VIRS) imager (2-km nominal resolution) on the same TRMM satellite as the CERES scanners. GEO TOA fluxes are derived from observed pixel-level (8-km nominal resolution) narrowband radiances, which have been calibrated against the VIRS imager and are carefully normalized to CERES fluxes to maintain the CERES instrument calibration. More details about the SRBAVG-GEO data set can be found in the link: (http://eosweb.larc.nasa.gov/PRODOCS/ceres/SRBAVG/Quality_Summaries/CER_SRBAVG_Edition2D_Terra_Aqua.html#nature).
 The SRBAVG-GEO data set also combines the VIRS and GEO cloud properties to enhance overall data accuracy by taking advantage of the 3-hourly sampling provided by geostationary satellites. The VIRS cloud retrieval algorithm [Minnis et al., 2011] first uses a cloud mask algorithm [Trepte et al., 1999] to identify each pixel as either cloudy or clear. If a pixel is cloudy, then the cloud properties are retrieved by the Visible Infrared Shortwave-infrared Split-window Technique (VISST) [Minnis et al., 2004] during the day and by the Shortwave-infrared Infrared Split-window Technique (SIST) [Minnis et al., 2004] at night. All these methods iteratively solve for cloud effective temperature, phase, effective height, optical depth and particle size by correlating model-predicted and observed radiances within a prescribed uncertainty. Liquid water path (LWP) and ice water path (IWP) are calculated as a function of optical depth and particle size. More details about VIRS cloud retrieval are inMinnis et al. [2004, 2011]. The VIRS pixel cloud properties are convolved with the CERES footprint flux to produce the single scanner footprint (SSF) product [Geier et al., 2003], which is used as input in the monthly gridded SRBAVG data set.
 The 2-channel visible and infrared (IR) GEO cloud retrievals are less accurate than the multichannel VIRS retrievals. However, the GEO radiances are first calibrated using VIRS as a reference to ensure there are no radiance discontinuities between GEO satellite domains. The SRBAVG-GEO is the best currently available monthly gridded data set with coincident, collocated and consistent fluxes and cloud properties. These qualities are considered critical for cloud-climate feedback studies [Wielicki et al., 1996].
 The 500 hPa vertical velocity and other meteorological variables, such as pressure, temperature and specific humidity profiles, are from the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA 40) monthly mean data set [Uppala et al., 2005].
3. Analysis of the Observations
 Two regions were chosen for this study: the tropical western Pacific (120°E–170°E, 5°S–10°N) and the eastern equatorial Pacific (80°W–160°W, 7.5°S–7.5°N) as shown in Figure 1. The CERES data are only available from January to August 1998.
 The methods to calculate regional monthly averages are as follows. For radiative fluxes, the regional averages are simply the arithmetic averages of those grid cell values. For the CERES cloud properties, since they have four vertical layers, an average over vertical layers is needed.
 The averaging procedure for cloud fraction is slightly different from cloud top altitude and cloud optical depth. The cloud fraction regional average is obtained through equations (1a) and (1b), where fij represents a CERES monthly mean value at a grid cell j and a layer i and n denotes the total number of grid cells within the region. First, a regional mean for each layer, , is calculated by equation (1a) and then the monthly mean total cloud fraction is the sum of at the four non-overlapped layers (equation (1b)).
 The monthly regional means, , for cloud top altitude and cloud optical depth are obtained by first calculating cloud amount weighted layer mean, (equation (2a)) and then taking the cloud fraction weighted average over the layers (equation 2b). In equations (2a) and (2b), Aij denotes either cloud top altitude or cloud optical depth for a given grid cell and a layer, fij, i, j, n and are defined the same as those in equations (1a) and (1b).
 Shown in Figure 2 is the Niño 3 index, which is defined as the mean eastern tropical Pacific SST (5°N–5°S, 90°W–150°W) [http://www.esrl.noaa.gov/psd/data/climateindices/]. This index serves as one measure of the strength of an El Niño and is shown for March 1997 through October 1998. Note that the strength of the 1997/98 El Niño increases slowly with a small dip in August 1997, reaches a peak in March 1998, and then rapidly decreases. In contrast, the SST in the western tropical Pacific (not shown) exhibits little temporal variation.
 Monthly mean SW CRF and LW CRF for January to August 1998 are shown in Figures 3a and 3c for the western region and in Figures 3b and 3d for the eastern region. Black columns denote the observations while the gray represents the model results, which will be discussed in the next section. SW CRF and LW CRF are defined as
where S and Scdenote the TOA all-sky and clear sky reflected SW, respectively, while
where F and Fc, denote the all-sky and clear-sky TOA emitted LW, respectively. Typically the SW CRF is negative (cooling) and the LW CRF is positive (warming). Note that these quantities change significantly throughout the eight-month period, and that the minimum (maximum) magnitudes of both SW CRF and LW CRF for the western (eastern) region occur in March 1998 when the Niño 3 index is at the maximum. In addition to the radiative fluxes,Figures 3e–3h also show the temporal variations of cloud fraction, cloud top altitude and cloud optical depth for the two regions. All these cloud properties show similar trends much like the radiative properties during this period. For the western region, the cloud fraction, cloud top altitude and cloud optical depth all increase after March and reach a maximum in June. This is consistent with increasing cloud radiative forcing, since increasing both the cloud fraction and thickness leads to a greater cloud radiative forcing effect. For the eastern region, the opposite is true, where the cloud properties are decreasing, which are consistent with the associated radiative flux changes. The changes of both radiative and cloud properties are highly correlated with the Niño 3 index. The impact of the seasonal cycle is very small compared with the influence of the El Niño in the observed changes in clouds and fluxes.
 To further examine the relationships between these variables, scatterplots of monthly mean SW CRF versus LW CRF are shown in Figures 4a and 4b for the western and eastern region respectively. The solid line and dots represent the CERES observations while the dash line and circles are for the model results, which will be discussed later. Both regions exhibit highly correlated SW CRF and LW CRF relations during the strong El Niño. The relationship between SW CRF and LW CRF is affected by cloud fraction, optical depth and cloud top altitude. The changes of all three variables lead to the strong linear relationships of SW CRF and LW CRF over both regions.
 This strong linear relationship of the CRFs over both regions indicates that all the cloud properties are highly correlated with each other. Figure 5 demonstrates this point by clearly showing that the cloud fraction and cloud top altitude are strongly correlated (Figures 5a and 5b) and that cloud optical depth and cloud top altitude are also strongly correlated (Figures 5c and 5d). All three cloud properties work together to produce a strong linear relationship between LW CRF and SW CRF for two very different regimes, the western and eastern Pacific regions, during the strong El Niño period. Over the western Pacific, the decrease in cloud fraction, cloud top altitude, and optical depth occur simultaneously, leading to a decrease in both SW CRF and LW CRF. Over the eastern Pacific during the El Niño, the increase of these cloud properties strengthens both the SW and LW CRF.
 This interdependence of cloud parameters has a simple physical explanation. In the western region convection is suppressed during the El Niño, which results in lower clouds (smaller mean cloud top altitude), fewer clouds (smaller cloud fraction) and thinner clouds (reduced optical thickness). The reverse explanation applies to the eastern region.
4. Analysis of CAM4 Results
 In this section, a general circulation model is used to simulate radiative fluxes and cloud properties during the El Niño period and the relationships between these variables are analyzed. The model is the NCAR CAM4.0, which is the atmospheric component of the fully coupled Community Climate System Model 4.0 [Collins et al., 2006; Neale et al., 2010]. Since our focus is on the atmospheric radiation and cloud parameterization, CAM4 with the prescribed SSTs rather than the fully coupled model is chosen. The model is configured to have 64 × 128 (latitude × longitude) grid resolution and 26 vertical levels. The boundary is forced with the monthly mean observed sea-surface temperatures (SSTs) [Hurrell et al., 2008]. The model is run for a year beginning in September 1, 1997 and only the first eight months of 1998 are analyzed. Cloud fraction is computed from the ISCCP simulator, which uses CAM4 outputs to generate clouds that simulate those retrieved by satellites [Klein and Jakob, 1999; Webb et al., 2001]. Cloud top altitude is converted from cloud top pressure using the hypsometric equation. All parameters are averaged similar to either equation (1a) or (2a) since the CAM4 outputs are not stratified into multiple layers.
 The temporal variations of the monthly mean CAM4 SW CRF and LW CRF, cloud fraction, cloud top altitude and cloud optical depth are shown as gray columns in Figure 3alongside the CERES observations. The correlation coefficient, R, denotes the temporal correlation between CAM4 and CERES quantities, so R = 1.0 would mean that the temporal variation of a CAM4 quantity exactly matches that of the comparable CERES quantity, irrespective of differences in magnitude. All the R values, except for cloud optical depth, are significant at the 95% confidence level using the student's T-test.
 For the most part, CAM4 captures the main cloud and radiation features of the El Niño event. In terms of magnitude, CAM4 overestimates all radiative and cloud properties. Except for the cloud optical depth, the eastern region compares better with the observations than does the western region. Over both regions, the change in the simulated LW CRF is better correlated with observations than the change in SW CRF. Of the 3 simulated cloud properties, the change in cloud top altitude most resembles the observations, whereas the change in cloud optical depth is the least correlated to the observations in both regions. The cloud optical depths in JJA (Figure 3j) over the eastern region are nearly twice as large as the observations and therefore the model overestimates the SW CRF (the absolute value) in Figure 3b.
 CAM4 results are added to Figures 4 and 5 to further investigate the model and observation comparisons. As in the CERES data, the linear correlation between SW CRF and LW CRF in the model is strong for both regions (Figure 4). Also, a similar relationship between cloud fraction and cloud top altitude exists in the model as in the CERES data (Figures 5a and 5b). The exception is the relationship between cloud top altitude and cloud optical depth, which is poorly simulated.
 In order to explain the model versus observation differences shown in Figures 3–5, we compare CAM4 dynamic fields with the observations. We use the ECMWF ERA-40 500 hPa level vertical velocityω-500 to represent the dynamic fields [Bony et al., 2004] for the observations. CAM4 ω-500 is the vertical velocity linearly interpolated from the model layers just above and below the 500 hPa level.
Figures 6a and 6b show the regional monthly mean ω-500 for the first eight months of 1998 over both regions. The temporal variations ofω-500 in the model are very close to the observations over both regions. CAM4 produces almost perfectω-500 over the eastern region not only for the variation but also for the absolute magnitude. The western regionω-500 simulation shows good temporal variation with R = 0.93 but overestimates the magnitude for all months except June. This comparison of dynamic fields partially explains the overestimate of cloud properties for both regions. Shown inFigure 6a for the western region, the larger model ω-500 (absolute value) indicates stronger convection, which gives rise to more and higher clouds and ultimately larger CRFs as shown inFigures 3–5. Figure 6b shows CAM4 dynamics fields are more representative over the eastern region and thus provides better cloud and radiative properties that are more consistent with observations except for cloud optical depth.
 In order to investigate the poor simulation of cloud optical depth as shown in Figures 3 and 4, the total cloud water path (CWP) is compared. Figures 6c and 6d show CWPs for both CAM4 and the CERES observations over the two regions. CAM4 overestimates CWPs over both regions, and compared with the ω-500 inFigures 6a and 6b, the CWPs are not as well simulated. This points to possible problems in the model's convection scheme, which generates hydrometers.
 The simulated changes of CWPs, though not as good as the dynamics, are still much better than the simulated variations of cloud optical depth shown in Figure 3i and 3j. Cloud optical depth is proportional to cloud water path but inversely proportional to particle size. If CAM4 had perfect cloud microphysics, such as particle size and phase as the observations, one would expect the change in cloud optical depth to follow the change in cloud water path. However, Figures 3i and 3jshow that the simulated cloud optical depth and CWP are weakly correlated at best. The simulated cloud optical depths over the eastern region, are in fact, anti-correlated with the observations.
 The contrast between the rather good agreement between observed and simulated CWP and the rather poor agreement between observed and simulated cloud optical depth points to deficiencies in the CAM4 microphysics. A direct model-observation comparison of the cloud particle size would be very helpful to resolve this issue. Unfortunately, this variable is not currently available in the CAM4 output.
 The above discussion illustrates both the skill and weakness of the model. This clearly demonstrates the utility of using the strong 1997/98 El Niño as a suitable test case to evaluate the cloud-climate interactions within a climate model.
5. Decomposition of CRF Changes
 To illustrate how changes of the three cloud parameters impact the CRF and their relative contribution to the total CRF change, a one-dimensional radiative transfer model is employed. The model is the widely used NCAR Column Radiation Model (CRM) version 2.12 [Kiehl et al., 1996]. An introductory description of the model may be found online at http://www.cgd.ucar.edu/cms/crm/. The model assumes a constant 10 μm liquid water effective radius and a height dependent ice effective crystal size between 10 μm and 30 μm. Cloud ice fraction depends solely on temperature and it represents how much ice portion and liquid portion is in a cloud. In the model, the radiative properties such as optical depth, single scattering albedo, asymmetry parameter and forward scattering parameter depend on the cloud phase and particle size [Slingo, 1989].
 The experiment uses JFM (January, February and March) as the perturbed period and JJA (June, July and August) as a “normal” or “control” period. Cloud fraction and cloud top altitude inputs to the CRM are three-month averages from CERES during the respective periods. The vertical profiles of pressure, temperature and specific humidity are from the ECMWF ERA-40 data set. There are 23 vertical levels from 1000 hPa to 1 hPa. The ozone mixing ratio is from the standard tropical atmosphere [Anderson et al., 1986]. The surface air temperature is also from ECMWF while the sea surface temperature is from the National Oceanic and Atmospheric Administration (NOAA) Extended Reconstructed Sea Surface Temperatures, version 2 (ERSST.v2) monthly mean data set [http://www.ncdc.noaa.gov/oa/climate/research/sst/sst.php]. The same JJA mean cosine solar zenith angle is used for both the control and perturbed flux calculations to avoid the introduction of any angle dependences on the results. In the following experiments, only the cloud liquid phase is used to eliminate the impact of microphysics changes on CRF. Simple calculations show that this simplification has little impact on the ΔCRFs (perturbed CRF minus control CRF) discussed in this paper. The only exception is the cloud top height effect on the ΔSW CRF where the no-ice assumption shows about 25% less impact for both EST and TWP regions due to less reflectivity by liquid particles compared with ice particles. However, the difference does not change our conclusions. Since the CRM uses liquid water path (LWP) and not optical depth as the input for flux calculation. Thus, LWP will be used in the discussion for convenience. For water clouds, optical depth is a function of both LWP and water particle size [Liou, 2002]. As a constant liquid effective radius is assumed in the CRM, a linear relationship exists between LWP and cloud optical depth.
 The purpose of the investigation is to look at the relative contribution of each cloud property to the change in CRF under various climate regimes during the El Niño rather than to match the absolute values from the simple model output to those from the observations. In order to isolate the contribution to the CRF change from the three cloud properties and the atmospheric profile, only one factor is changed at a time. This is similar to the partial radiative perturbation method by Wetherald and Manabe  (WM). This method implicitly assumes the factors are independent, even though in reality, they are interdependent as shown in Figure 5.
 In our study, the cloud property inputs to the CRM are the regional monthly means. For each perturbed case, only one variable is set to the perturbed values while all the others use the control values. This method is straightforward if the column-averaged values are used as inputs. However, due to the interdependence between cloud fraction and other cloud properties whenequations (2a) and (2b) are used to calculate the averages, special steps are taken to avoid the impact of cloud fraction on the ΔCRF attributed to another cloud property. Take cloud top altitude as an example. The averaged cloud top altitude increase could be caused by the height increase in each layer, the cloud amount increase in the higher layer, or by both. When this vertically averaged cloud top altitude, which is weighted by the perturbed cloud fraction, is used as input to the CRM for perturbed fluxes calculation, the results are contaminated by contributions from cloud fraction.
 To mitigate this problem, we will carry out the CRM flux calculation for each layer assuming 100% cloud fraction. The total flux is the sum of the four fluxes weighted by their cloud fractions and the clear sky flux weighted by its area. This is the method used by the CERES SYN data product (F. Rose, personal communication, 2012) for the total flux calculation. For the cloud fraction experiment, in order to keep the column averaged cloud top altitude unchanged, the perturbed flux in each layer is weighted by the control cloud fraction adjusted by the ratio of the total perturbed cloud fraction to the total control cloud fraction. By doing this, we only change the total cloud fraction but keep the vertical structure and thus cloud top altitude the same as the control case. A similar technique is used for the cloud top altitude experiment, in which the perturbed flux is weighted by the perturbed cloud fraction as adjusted by the ratio of total perturbed cloud fraction to the total control cloud fraction, in order to keep the total cloud fraction unchanged. For the LWP and vertical temperature and humidity profile experiments, this kind of adjustment is not needed.
Figure 7 shows the changes in SW CRF and LW CRF (ΔSW CRF and ΔLW CRF) resulting from a change in each one of the following four properties: cloud fraction, cloud water path, cloud top altitude or the temperature and specific humidity profile.
Figures 7a and 7b show that the changes in cloud fraction and cloud top altitude produce the same sign changes in both LW CRF and SW CRF as previously discussed in section 3. For ΔSW CRF, a change in cloud fraction produce the largest change over both regions. The change in cloud top altitude is the dominant factor affecting the ΔLW CRF, whereas the increase in LWP, which affects the cloud emissivity, has little impact on LW CRF because the cloud emissivity in this case is already close to 1. Changes in LWP lead to positive ΔSW CRF, i.e., less cooling, over both regions. Whereas it seems reasonable for the western region where the total LWP is smaller during the perturbed period, it is counterintuitive for the eastern region where total perturbed LWP is larger than the normal LWP. Further investigation reveals that the LWP actually decreases on each of the four CERES layers during the perturbed period while the increase of the total LWP is due to an increase of cloud amount. The ΔSW CRF reflects the impact of LWP change only and the impact of the cloud fraction is purposely minimized in our experiment. The perturbation in the temperature and water vapor profile contributes much less to the changes in both the SW and LW CRF compared with cloud parameters such as the cloud fraction and cloud top altitude.
 Overall, all three cloud parameters change together in response to the El Niño to produce a strong linear relationship between SW CRF and LW CRF over different climate regimes. The cloud fraction and cloud height are the two largest contributions to the change of CRFs.
 The above analysis is only carried out for the CERES observation and it is highly desirable to do the same for CAM4 outputs and make model-observation comparison. Unfortunately, the current CAM4-ISCCP-simulator outputs do not have the CERES like four-layer cloud properties and would need different experiment designs. It is very difficult to make meaningful apple-to-apple comparisons between the two results.
 The strong El Niño of 1997/98 resulted in suppressed convection in the tropical western Pacific and enhanced convection in the eastern equatorial Pacific. This west-to-east shift of the center of convection resulted in cloud top altitude, cloud fraction and cloud optical depth collectively decreasing in the western region and increasing in the eastern region. These three cloud parameters, for both regions, are strongly correlated with each other. Among the three cloud parameters analyzed, the change in cloud top altitude dominates the change in LW CRF and the change in cloud fraction dominates the change in SW CRF. The change in cloud optical depth, represented by the change in LWP in the CRM and that of cloud top altitude play a secondary role in the change in SW CRF.
 The cloud property changes induced by this El Niño serve as one means of testing climate models, as is demonstrated using the NCAR CAM4. The model captures the major features of the El Niño when compared to the vertical velocity ω-500 and the CERES cloud fraction, cloud top altitude and TOA CRF measurements. The model does an excellent job simulating the dynamics over both regions with R = 0.93 and R = 0.99 for the eastern and western region respectively. For the TOA SW and LW CRF, CAM4 exhibits a weaker linear relationship compared to the CERES observation. The relationship between cloud fraction and cloud top altitude is well simulated in CAM4 but the optical depth simulation is very poor, especially for the eastern region. The model shows rather good agreement with the observation for the cloud water path simulation. Since cloud optical depth is proportional to CWP but inversely proportional to particle size, this points to possible model deficiencies in both the convection and microphysics schemes, which generates hydrometers and particle sizes respectively.
 In summary, the strong 1998 El Niño can be used as a necessary, but not sufficient test of a model.
 We thank Minghua Zhang for constructive comments concerning an earlier draft of this manuscript, in addition to an anonymous reviewer whose suggestions added considerable clarity to the final paper. This work was partially supported under the auspices of the Department of Energy's Office of Science, Biological and Environmental Research through grants DEFG0290ER61063 and DEFG028ER6013, and by the NASA CERES Project.