1. Introduction
Due to the uncertainty of the effects of cirrus clouds on the earth's radiation budget and feedback to atmospheric dynamics (Liou 1986), there has been an increased interest in the retrieval of cirrus macrophysical, microphysical, and radiative properties using both passive and active remote sensing techniques (Platt 1973; Ou et al. 1993; Smith et al. 1993; Matrosov et al. 1994). Knowledge of cirrus cloud properties and their inherent inhomogeneity will help to improve their representation in cloud models of all scales (e.g., cloud resolving, single column, and global climate models). Satellite retrieval algorithms also rely on knowledge of cloud radiative properties, therefore, improved measurements from surface-based instruments will enhance satellite cloud detection and analysis schemes.
Macrophysical properties obtained in this study include lidar-derived cloud base and top height, as well as cloud temperature inferred from radiosonde measurements. By combining lidar and infrared (IR) radiometric measurements, both visible optical depth τ and cloud emittance ɛ can be obtained. This combined remote sensor technique is commonly known as the LIRAD method and is described in Platt and Dilley (1981). In this paper, we will briefly outline the original LIRAD method, as well as the variations that we have made in the present algorithm. These modifications include a method for estimating the backscatter-to-extinction ratio for each lidar profile, rather than a single value for the entire observation period. Also described is a new technique for determining the amount of IR radiance that is emitted by the earth and reflected by the cloud into the radiometer field of view (FOV). Our results show that this value can be significant, particularly if the ice crystals in the cloud are relatively small.
A description of the instrumentation used in this study will be presented in section 2, followed by a review of the original LIRAD technique in section 3a. Our new retrieval of visible optical depth is presented in section 3b, which includes estimation of cloud boundaries, backscatter-to-extinction ratio k, and multiple-scattering parameter η. In section 4, the radiative transfer model used to estimate cloudless-sky downwelling radiance in the atmospheric window is presented, which is important in the calculation of ɛ. The retrieval of cloud radiative properties is detailed in section 5, including determination of the upwelling IR radiance that is reflected by the cloud into the IR radiometer FOV, which must be modeled for the ɛ calculations. A detailed sensitivity analysis is in section 6, followed by a case study demonstrating the abilities of the retrieval algorithm (section 7) and conclusions (section 8).
2. Instrumentation
In support of the First ISCCP (International Satellite Cloud Climatology Program) Regional Experiment (FIRE; Cox et al. 1987), ground-based remote sensing observations of high clouds have been recorded at the Facility for Atmospheric Remote Sensing (FARS) in Salt Lake City, Utah, since 1986. FARS is located at 40°46′00″N, 111°49′38″W at an elevation of 1.52 km above mean sea level. A complete list of FARS instrumentation and history is described in Sassen et al. (2001a).
The lidar system used in this study is a vertically pointing dual-polarization ruby lidar that operates at 0.1 Hz with a maximum vertical resolution of 7.5 m. Table 1 provides a complete list of instrument specifications for the ruby lidar, as well as the other instruments used in this study. Lidar calibrations are performed by positioning a randomly polarized light source at the minimum telescope focus distance (Sassen et al. 2001a). In order to ensure data quality, each lidar signal is examined using an algorithm that detects errors in both the background and the recorded backscattered energy (Barnett 2000). By inspecting the background signal, noisy background signals, offscale background settings, and pretrigger errors are identified. Errors identified by inspecting the recorded backscattered energy include instances when the oscilloscope falsely triggers, as well as when no data are recorded. The laser output power and photomultiplier tube voltage are also checked for proper values. In the event that an error is detected, the profile is not included in the data analysis.
The radiometer is a midinfrared Precision Radiation Thermometer (model PRT-5) that has been modified to have a narrow FOV. The PRT-5 is manufactured by the Pyrometer Instrument Company, Inc. and has a bandwidth that lies within the atmospheric window. The PRT-5 is designed to measure the vertical downwelling radiance emitted from water, ice, aerosols, clear-sky molecular background, and other substances that fill its FOV. The IR radiometer is coaligned with the ruby lidar so that both instruments are simultaneously sampling the same portion of the cloud. The radiometer has been calibrated by the manufacturer approximately once every two years, and comparisons with both spectral instruments and model-derived radiances ensure proper performance between calibrations (Barnett 2000).
Recently, FARS has acquired a model WVR-1100 dual-frequency radiometer manufactured by Radiometrics Corporation that measures microwave radiation emitted from the atmosphere at 23.8 GHz (K band) and 31.4 GHz (Ka band). The microwave radiometer (MWR) is used to derive column-integrated liquid water and water vapor from measurements of atmospheric brightness temperature. The 31.4-GHz channel mainly records microwave emission from cloud liquid while the 23.8-GHz channel is dominated by microwave emission from water vapor, allowing a simultaneous but separate retrieval of path-integrated liquid and vapor from the measured radiances. In this study, only the water vapor channel is used because cirrus clouds are primarily dominated by ice, and in the event that supercooled liquid water droplets are present, the emitted microwave energy is well below the detection threshold of the instrument (∼2.73 K). MWR measurements are used to correct variations in the column water vapor between radiosonde profiles to more accurately represent the actual water vapor mixing ratios, which are needed in the calculation of cloud IR emittance.
Radiosonde measurements are obtained from the Salt Lake City National Weather Service Forecast Office (SLC-NWSFO) and are available twice daily at 0000 and 1200 UTC. Prior to June 1998, the SLC-NWSFO used the Viz B-2 sonde, but more recently switched to the Vaisala radiosonde, which is equipped with the RS-80 H-humicap sensor. Recent studies have demonstrated that Vaisala sensors are approximately 10%–15% drier than water vapor profiles derived from Raman lidar measurements during the daytime, and 5% drier during the nighttime (Turner et al. 2000). Scaling radiosonde-derived water vapor profiles using MWR measurements can improve the daytime radiosonde dewpoint measurements to within 5% of the Raman lidar–derived values (Turner et al. 1998).
3. Methodology
The next section presents a brief account of the original LIRAD method, pioneered by C. M. R. Platt, followed by a detailed description of the current methodology used to estimate cirrus radiative and backscattering properties. The LIRAD method as described in Platt and Dilley (1981) is repeated for historical purposes and to provide the background needed to understand changes made to it in the present study. (A list of symbols is given in the appendix.)
a. Original LIRAD technique
b. Lidar signal processing and determination of visible optical depth
The following sections describe the new approach that is used in this study to determine cloud backscattering properties and visible optical depth.
1) Lidar backscattered energy and depolarization ratio
2) Estimation of cloud boundaries
Due to attenuation of lidar signals as cloud optical depths increase above τ ∼ 3 (Kinne et al. 1992; Sassen 2001), cloud-top heights of dense clouds become difficult to detect. This can also result from the limited dynamic range of lidar detectors, where weak signals are often lost when channel gains are reduced to accommodate cloud regions containing strong signals, especially from horizontally oriented plate crystals. Cloud radars, such as the FARS 3.2-mm (95 GHz) radar (Sassen et al. 2001a), are capable of penetrating through dense clouds; however, they are unable to detect small ice crystals due to their longer transmitting wavelength. Continuous radar measurements do not coincide with the ruby lidar dataset; therefore, only lidar is used to identify cloud boundaries.
Cloud heights are determined by first identifying the region where the cloud exists by inspecting height versus time displays of lidar backscattered energy measured for each observation period. For example, if the actual cloud base and top are 8 and 10 km, respectively, a window of 7.5 and 10.5 km would be chosen for the cloud height detection algorithm. Creating a window where only cirrus is located eliminates contamination of the dataset from lower water clouds or aerosol layers. A numerical algorithm then locates the actual cloud base using a running average of three consecutive points of the height normalized lidar signal, starting below cloud. The largest signal increase is determined by taking a ratio of the unaveraged signal to the average signal (Sassen and Cho 1992). If this ratio is greater than 1.3 (in our case), then zb is defined as the point where the largest signal increase occurs for the three points used in the average signal. Cloud-top height zt is determined using a reference cloud-free signal derived from Rayleigh scattering theory for molecules following Young (1995).
3) Cloud backscatter coefficient
4) Backscatter-to-extinction ratio k
The backscatter-to-extinction ratio k (sr−1) is equivalent to the normalized scattering phase function
The backscatter phase function primarily depends on ice crystal shape, as shown in Takano and Liou (1995). Sassen (1978) reports laboratory and field derived values of k obtained with a 0.6328-μm wavelength laser for various ice crystal types, concluding that k appears to vary with ice crystal habit and orientation. The results of both Sassen (1978) and Takano and Liou (1995) indicate that simple ice crystals, such as hollow columns, tend to have lower values of
Due to the inherent inhomogeneity of cirrus clouds, k will vary as the cloud evolves and ice crystal habits change. The present study determines k by first calculating the average backscatter coefficient above cloud top, expressed as
The maximum value of k was chosen based on the effect of horizontally oriented plate crystals on the lidar backscattered signal. Platt (1978) revealed that a maximum value of k = 800 occurs when there are a large number of precisely horizontally oriented plate crystals in the scattering medium. Ice crystals never fall with exactly 0° of wobble, but rather with a slight tilt from the horizontal (Sassen 1991). In this situation, δ will be low and the backscattered energy will be strong. Therefore, we have limited the maximum k derived from lidar observations of cirrus clouds to about 0.2, which corresponds to a tilt of approximately 10° off the horizontal (Platt 1978). The minimum value of k = 0.01 was chosen to help analyze weak signals that can occur in thin and subvisual cirrus clouds.
5) Multiple-scattering parameter η
The amount of multiple-scattered returns of a laser pulse that occurs in a cirrus cloud depends on the width of the diffraction peak in the phase function. Forward multiple-scattering contribution to lidar returns are also dependent on the angular FOV of the lidar receiver, cloud range, and cloud depth. Scattering phase functions for nonspherical ice crystals are highly forward peaked (Takano and Liou 1995), particularly at visible wavelengths. It is generally assumed that photons returning to the lidar receiver have undergone one large angle (∼180°) scattering event, which may be preceded and/or followed by multiple forward-scattering events. Nicolas et al. (1997) demonstrate that lidar signals penetrating cirrus clouds with optical depths less than 1.0 will be dominated by single or double scatterings, while multiple scattering will dominate for optical depths greater than 1.0, implying that exact shape of
The parameter that has been historically used to account for error in the single-scattering lidar equation due to multiple scattering is the parameter η (Platt 1973). Multiple-scattering corrections are required in the exponential attenuation term of Eq. (10). The parameter η(R) accounts for the multiple scattering as a result of captive diffraction. Due to the forward peak in cirrus ice crystal phase functions, scattering of the lidar pulse will be dominated by forward scattering, and thus some diffracted photons will remain indefinitely in the laser beam. The factor η(R) corrects the single-scattering lidar equation for the apparent decrease in the extinction rate, which causes an underestimation of cloud optical depth. However, η(R) does not correct for multiple scattering that includes a primary backscattering event. The parameter β′ in Eq. (10) does correct for this type of multiple scattering. There is no solution currently available describing β′, so we have neglected it rather than include it in the exponential attenuation term.
Platt (1981) shows that η generally increases in the first 1–2 km of the cloud, but then levels off as cloud penetration increases beyond that point. However, there is little information available that can help to correct for the variation of η with height. Therefore, in the present study, we assume that η is independent of height when analyzing lidar signal returns.
Values of η used in previous studies vary widely. Platt (1973) extracted a value of η = 0.41 ± 0.15 from cirrus observations, while Sassen and Cho (1992) used a value of 0.75 in their evaluation of optically thin clouds. Monte Carlo simulations of η performed by Platt (1981) produced values between 0.0 and 0.6, depending on the scattering phase function and cloud penetration depth. Platt et al. (1998) have subsequently developed a linear relationship between η and midcloud temperature. In this study, η ranges between 0.6 and 0.9. These values were derived from Mie calculations of forward multiple scattering using a similar method as described in Sassen and Zhao (1995). Figure 2 depicts the variation of η with FOV and effective radius of spherical ice particles. The forward diffraction peak of ice crystal phase functions increases as the size becomes larger for a constant wavelength. This is true for both spherical and hexagonal ice crystal shapes. The forward diffraction peak will not change significantly with ice crystal shape, as shown by theoretical simulations of phase functions reported in Macke et al. (1996). The ruby lidar was typically operated with a 1.0-mrad receiver FOV, but occasionally at 3.0 mrad. As Fig. 2 illustrates, at 1 mrad η will have a value ranging from approximately 0.7 to 0.98 depending on the particle radius. For a FOV of 3 mrad, the range is 0.6–0.95. Similar values are also reported by Eloranta (1998) using an analytical model that estimates multiply scattered lidar returns. Typically, using an η < 0.5 will result in unrealistically high values of τ, beyond the limit of the measurement capabilities of backscatter lidars using analog detectors, which occurs at τ ∼ 3.
In the present method, the appropriate value of η is chosen for each data period based on cloud observations reported in field notes and by examining height versus time displays of lidar backscatter returns. Each observing period was divided into sections based on apparent homogeneity. For example, a cloud system may begin as an optically and physically thin cloud, in which case a value of η = 0.9 was used because the scattering is dominated by single backscattering (with some forward scattering). As the cloud thickens, multiple scattering becomes more important, and η = 0.8 is used. If the cloud develops to the point where the lidar signal becomes attenuation limited (τ → 3), scattering will be dominated by multiple scattering, and therefore an η of 0.6 is used. The minimum and maximum values of η used are 0.6 and 0.9.
c. Radiative transfer model for the estimation of clear-sky radiance
The IR radiometer measurement includes emission from all absorbing gases, aerosols, and cloud particles in the FOV of the instrument. In the LIRAD method, the radiometer measurement is used to retrieve the emission from cloud particles only, which is needed to calculate cloud emittance ɛ. Hence, contributions from atmospheric gases and aerosols must be removed from the total downwelling radiance measurement. The amount of radiance emitted by atmospheric constituents can be estimated with a radiative transfer model, which is described in the following subsections. Aerosol absorption is generally assumed to be negligible; however, in cases where the lidar detected a dense aerosol layer, the case was either avoided or a temporally near-cloudless sky background IR radiometer measurement was used to obtain the cloud radiance. Generally, aerosols will not affect the measured IR radiance unless the aerosol is highly absorbing, such as carbon. Aerosols will influence the scattering of visible wavelength radiation; however, this will not affect the retrieval in this study.
1) Correlated K distribution method
The thermal infrared window between 9.0 and 12.5 μm is a region of continuous absorption primarily due to water vapor (see Fig. 3a). However, strong absorption due to ozone O3 exists at 9.6 μm, as well as weak absorption by carbon dioxide CO2 at 10.6 μm. The primary contributor to the downwelling IR radiance (for the IR radiometer bandwidth) at the surface is water vapor, which contributes about 88% of the total downwelling clear-sky radiance (using radiances calculated from Salt Lake City, Utah, soundings for a 1-yr period). Other gases, such as O3 and CO2 contribute approximately 9% and 3%, respectively. Therefore, these atmospheric gases are included in the estimate of IR radiance. A computationally efficient method for calculating absorption coefficients K for inhomogeneous atmospheres is the correlated K distribution (CKD) method (Lacis et al. 1991). Note that we use an uppercase K to represent absorption coefficient, whereas k denotes the backscatter-to-extinction ratio.
The FARS CKD model used in the present study was developed by Duffy (1996), following the method described in Fu and Liou (1992). Absorption coefficients were calculated using the HITRAN database and the Fast Atmospheric Signature Code 3 (FASCOD3) developed by the Air Force Geophysics Laboratory (Clough et al. 1986). Duffy (1996) tabulated absorption coefficients at a resolution of 0.0004 cm−1 for four temperatures (180, 220, 260, and 300 K) and 20 pressures between 12.6 and 1000 mbar for each absorbing species. There are 119 cumulative probability functions g(K) used in calculations of atmospheric transmittance.
The water vapor continuum is an important contributor to the downwelling radiance measured at the surface, but unfortunately there is still considerable uncertainty in representing continuum absorption in radiative transfer models. The continuum is attributed to the accumulation of absorption in the far wings of H2O lines, which results from self-broadening and foreign collision broadening. It has also been suggested that the water vapor dimer (H2O)2 may contribute to continuum absorption (Clough et al. 1989). The FARS CKD model uses a parameterization that estimates the continuum absorption as a function of wavelength, temperature, pressure, and partial pressure of water vapor following Roberts et al. (1976).
2) Transmittance and radiance calculations
3) IR radiometer filter function
In order to obtain a relationship between the filtered MODTRAN3 radiance and the nonfiltered CKD radiance, 83 cases were identified when clear sky conditions occurred near a 0000 or 1200 UTC balloon sounding launch from the nearby SLC-NWSFO. Cloudless sky conditions were determined using lidar backscatter profile measurements. The model downwelling clear-sky radiance at the surface is then calculated using both the FARS CKD model and the MODTRAN3 filtered and integrated results for each clear-sky sounding. A scatterplot of filtered to unfiltered model radiance yields a linear relationship with a correlation coefficient of 0.999. This relationship is used to correct the model downwelling radiance at the surface for the IR radiometer filter function. The FARS CKD model is approximately 56% faster than MODTRAN3 for calculations of a vertical profile of downwelling radiance under clear sky conditions, which greatly reduces the computation time when applying this retrieval to the FARS long-term dataset.
The above described method for adjusting model radiance to account for the radiometer filter function applies only to the model-derived downwelling radiance at the surface. It is also important to adjust the model radiance profile because an estimate of the radiance due to gases above and below the cloud is required for the calculation of the cloud radiance, which will be explained in section 3d. In this study, we correct the model radiance profile by using the gamma correction technique described in Smith et al. (1993), which iteratively adjusts the profile of atmospheric transmittance until the desired surface radiance is obtained (which, in our case, is a filtered radiance).
Comparisons have been performed between the FARS model and MODTRAN3 to exhibit the reliability of the CKD radiation code. The model-derived downwelling radiance, with the filter function and gamma correction included, agrees to 1.1% with MODTRAN3. In addition to the above comparison, Duffy (1996) provides extensive sensitivity studies and comparisons of the FARS CKD model with line-by-line calculations. The CKD model was found to be within 2% of FASCODE3 for both U.S. standard and midlatitude summer atmospheric profiles. Only in the subarctic winter case were errors larger (∼3.6%).
4) MWR correction of water vapor mixing ratios
d. Calculation of cloud radiative properties
The primary cloud radiative properties derived in this retrieval are IR emittance ɛ and visible optical depth τ. Cloud emittance is obtained by combining the IR radiometer and lidar backscatter measurements with the FARS CKD radiative transfer model, as we now describe.
1) Measured cloud radiance Ic and cloud emittance ɛ
The cloud IR absorption coefficient σa(z) is related to βc(z) using the expression σa(z) = ζβc(z), where ζ is an unknown constant that we initially set to 0.01. The theoretical cloud radiance Ict is then calculated using Eq. (6). The parameter ζ is varied until Ict ≅ Ic, and the final value of σa(z) is used to estimate ɛ following Eq. (8). The ratio of the layer mean visible extinction and IR absorption coefficients, σc and σa, respectively, is defined as α = σc/σa, and can be used to infer particle size (Mitchell and Platt 1998).
2) Upwelling radiance reflected by clouds Isr
Simulations of Isr for all 28 different size distributions reveal a distinct relationship between Isr and both IR optical depth τIR and ice crystal size (Fig. 4). Dividing ice crystal sizes into three groups labeled small, medium, and large (Table 2), we find that the amount of reflected radiance is generally higher for cirrus clouds with smaller particles. In fact, the magnitude of Isr varies substantially with τIR, surface ground temperature, atmospheric transmittance, ice crystal size, and, to a lesser extent, on cloud height.
In the present LIRAD retrieval, Isr is calculated for each cloud system using a “best guess” for the ice crystal size distribution based on the observed cloud type as revealed by lidar depolarization measurements and field notes. For example, an estimate of the particle size can be determined by the appearance of optical phenomena in cirrus clouds. Sassen (1997) explains how cirrus cloud layers that display a corona or aureole have relatively small particles (∼10–30 μm), whereas cirrus clouds that display halos and arcs generally contain large (at least 100 μm in maximum dimension) oriented hexagonal plate crystals (Sassen 1980). Based on criteria such as these, as well as cloud-base temperature, the size distribution is chosen for each cloud during periods where the cloud appears to be homogeneous. Once the size distribution is specified, the single-scattering properties used to determine Isr are chosen based on the average values indicated in Table 2.
4. Sensitivity analysis
a. Uncertainties in derived radiative properties
In order to assess the accuracy of the retrieval of radiative properties using the FARS–LIRAD algorithm, a detailed sensitivity analysis has been performed. Fractional uncertainties F in measured quantities are estimated using manufacturer supplied instrument specifications and calibration uncertainties (Table 3). For example, the fractional uncertainty in the temperature T and dewpoint Td are determined by the accuracy of the radiosonde sensors. The measured IR radiance has a combined F of 0.119, which includes instrument sensitivity and calibration uncertainty. Errors associated with the measured quantities are propagated to derived quantities, such as ɛ and τ, through the retrieval algorithm. The total uncertainty in the estimated cloud radiance is 0.173, which is a result of uncertainties in the measured radiance, cloud boundaries, the CKD model radiance, and other components of Eqs. (19) and (20). Uncertainties in the quantities k and η are also displayed in Table 3.
A variety of sensitivity tests were performed on a 1-yr period of lidar and IR radiometer data, amounting to 136 different observation periods with approximately 95 h of measurements. The uncertainties listed in Table 3 were applied to these measurements to estimate the errors in τ and ɛ. Our methodology was to first create a reference run for the 1-yr period of estimated cloud IR emittance and visible optical depth using the retrieval algorithm described in this paper. In each subsequent run, one quantity was perturbed by the amount listed in Table 4. For example, an 11.9% change in the measured radiance results in a 33.4% change in ɛ, which is the largest source of error. It is notable that overestimating the cloud base by 75 m results in an average change in τ and ɛ of only 3.4% and 0.57%, respectively. Similarly, overestimating zt by 150 m causes an average Δτ = 1.74% and Δɛ = 0.438%.
As displayed in Table 4, the largest uncertainty associated with calculating τ is the determination of k, otherwise, there is negligible change. Further calculations indicate that the average uncertainty in τ is approximately 24.5% and is independent of midcloud temperature and the magnitude of τ. This is mainly due to the physical and mathematical nature of the method used to derive k and τ. Although the overall uncertainty is high, the accuracy required for estimations of longwave fluxes is low. For example, Brown et al. (1995) studied the accuracy of τ required for calculations of outgoing longwave radiation (OLR) and model-derived surface fluxes for climate studies, and report that for OLR to be calculated within ±10 W m−2, the required accuracy of τ must be within +100% and −50% of the actual value. This value is sufficient for optical depths as low as 0.07 in midlatitude locations. The accuracy required for estimating downward fluxes within ±5 W m−2 is even less stringent according to Brown et al. (1995). Therefore, the average uncertainty in τ derived using the FARS–LIRAD method is well within the accepted accuracies needed for climate applications.
Changes in ɛ as a function of midcloud temperature Tm, determined from a radiosonde profile, are displayed in Table 5. There does not appear to be a large effect of midcloud temperature on the uncertainty in ɛ; however, errors in ɛ are most sensitive to perturbations in Im for Tm between −40° and −60°C. Also listed in Table 5 are the variations in uncertainty of ɛ for different ɛ intervals. The lowest ɛ interval has the largest uncertainty due to changes in Im. This is primarily caused by the small IR emission of cold, thin clouds that often radiate just above the cloudless background signal measured by the IR radiometer. Note that although changes in k/2η do not affect ɛ for different temperatures, there is a higher variation in ɛ for ɛ > 0.3 when perturbing k/2η.
b. Improvements using MWR-corrected water vapor mixing ratios
As described in section 3c, radiosonde-derived mixing ratio r can be corrected for temporal variations in column water vapor using MWR measurements. Adjusting r using the MWR also helps correct the apparent dry bias in radiosonde water vapor measurements mentioned in section 2. To assess the improvement of MWR corrections to derived radiances, downwelling IR radiance at the surface has been estimated using both radiosonde-derived and MWR-corrected mixing ratios. Observations of clear-sky radiance were identified using lidar backscatter profiles between October 1998 and June 1999. Downwelling clear-sky radiance at the surface is then calculated using both corrected and uncorrected mixing ratios at the radiosonde launch times (Fig. 5). Model radiances with the MWR correction are on average 7.8% higher than without the correction. Note that Fig. 5 also displays the tendency for the difference between corrected and uncorrected radiances to increase with increasing water vapor amounts. FARS is located in an arid climate and during cirrus observations WMWR is usually small, allowing for the retrieval of ɛ from low optical depth clouds. However, in moist climates, such as the Tropics, correcting for the dry bias in the radiosonde dewpoint measurement will be more important, particularly when deriving ɛ for small τ cases.
The correlation between ɛ estimated using radiosonde-derived and MWR-corrected mixing ratios is illustrated in Fig. 6. Cloud emittance is calculated for the same time periods as in Fig. 5, but for all cirrus observations rather than just clear sky observations. There is a noticeable bias toward higher ɛ when no MWR correction is used. The MWR corrected ɛ is on average 20% lower than the uncorrected ɛ. Although the MWR clearly provides an improvement to model-derived radiances, the overall average uncertainty in retrievals of radiative properties without MWR measurements is minimized when a large number of observations are analyzed. This result may differ for regions where column water vapor amounts are higher and vary significantly over time.
As mentioned previously, radiosonde data from the SLC-NWSFO are available only twice daily and the MWR can be used to adjust for the variability of water vapor between 12-h sounding data (Fig. 7). In Fig. 7, there is approximately a 0.4-cm change in the precipitable water vapor over the 5.5-h time period. The sounding is slightly lower than WMWR at the 0000 UTC launch time at the end of the period, as expected. During this time period, ɛ is up to 30% lower when using WMWR due to the overestimation of the downwelling radiance when the correction is not used. This example shows how 12-h soundings are not always representative of the atmospheric conditions at the time of LIRAD measurements, and how the MWR can be used to reduce the uncertainty in the model radiances and ɛ.
5. Case study
The following case study has been chosen to demonstrate the abilities of the FARS LIRAD algorithm to derive radiative and backscattering properties of cirrus clouds. Depolarization ratio and backscattered energy measured by the ruby lidar on 6 January 1999 at FARS are illustrated in Figs. 8a and 8b. The general synoptic conditions consist of a jet stream located to the northwest of Salt Lake City with local thin cirrostratus and fibratus, followed by denser bands. Figures 9 and 10 depict the Advanced Very High Resolution Radiometer satellite imagery and radiosonde data that correspond with the cirrus observations. Since the wind barbs in Fig. 10 indicate 28.1 m s−1 westerly winds at cirrus levels near 10 km, the cirrus to the east of FARS in Fig. 9 coincides with the lidar time-height display. According to the FARS lidar operator, several contrails were visible in the sky.
As indicated by Fig. 8, the cirrus was visibly thin until 2100 UTC, when the IR radiometer brightness temperature (Fig. 8c) began a slow increasing trend. (Note the small gap in the IR radiometer measurements between 2300 and 2310 UTC.) At 2230, when a weak 22° halo and broad sundogs became visible above FARS, the lidar signal appears to become attenuated. However, the region of strong backscattering near cloud base at this time led to a lowering of the gains of the detector channels, such that the weaker signals aloft were possibly no longer detected. Eventually, at 2320, the cloud becomes opaque and cellular as large cirrocumulus cells drift overhead. The atmospheric optical phenomena visible earlier ceased about this time as well.
The column water vapor W measured by the MWR and derived from the 0000 UTC 7 January 1999 radiosonde data is displayed in Fig. 8d. The MWR values are generally constant during the nearly 4-h time period. The sounding derived W is only slightly less than the MWR, which is typical when comparing the two measurements. In this case, an average discrepancy of 11% in W results in an average difference of 10% in the model clear sky radiance at the surface and a 14% difference in the derived ɛ.
Estimates of ɛ and τ using the FARS–LIRAD algorithm are depicted in Figs. 8e and 8f. During the first hour of the observing period, the IR radiometer brightness temperature is only slightly above the background signal due to emission of atmospheric gases, which is also indicated in the low values of ɛ ∼ 0.07 to 0.1 and τ ranging from 0.05 to 0.3. During this time period, k is quite small (Fig. 8g), which may indicate the presence of simple crystals, such as hollow columns that have been shown to have small backscatter phase functions (Takano and Liou 1995). Grund and Eloranta (1990) have also measured values of k as low as 0.01 sr−1 in a cirrus cloud with τ < 0.1 using a different technique. As denser cirrus cloud bands passed overhead, both ɛ and τ increased. Toward the end of the observation period, τ eventually approached the upper limit (τ ∼ 3.0) in lidar measurement capabilities of optical depth before complete attenuation. There are weak signals to cloud top between 2320 and 2345, indicating that the lidar signal is not attenuated and that τ of 2.5 is associated with the full depth of the cloud. During this period ɛ also reached approximately 0.8. The parameter k tends to be higher between 2150 and 2300 when the 22° halo and weak upper tangent arc were visible. The linear depolarization ratio δ in Fig. 8a appears to have patches of relatively low values at this time. Low δ values are an indication of the presence of horizontally oriented hexagonal plate crystals (Sassen and Benson 2001), which will have higher
The time series of α (Fig. 11) reveals slightly higher ratios in the first hour of observations, which can be an indication of the presence of smaller ice crystals in cirrus clouds. The large amount of scatter in α before 2100 is likely due to the uncertainty associated with estimating small ɛ. The thin cirrus cloud at this time has low ɛ and therefore the uncertainty (as discussed in section 4) in ɛ and σa is higher than later when ɛ and τ increase. As the cirrus becomes denser and the size of ice crystals increases, α oscillates around 2, which is in the geometric optics limit.
6. Conclusions
This paper describes extensions to the LIRAD retrieval algorithm originally developed by Platt (1973). The algorithm presented here includes several improvements, including the use of a detailed radiative transfer code that allows for more accurate estimation of the upwelling radiance reflected by the cloud. The current approach also uses a technique for estimating the backscatter-to-extinction ratio for each lidar profile, rather than a single value for the entire cloud system. This change allows for variations in the microphysical properties of cirrus as the cloud evolves, which will affect the derived k. This algorithm was designed to analyze the FARS high-cloud dataset (Sassen et al. 2001b; Sassen and Campbell 2001; Sassen and Benson 2001; Sassen and Comstock 2001) collected during our support of the extended time observations satellite validation effort of Project FIRE. However, this algorithm can be used by any backscatter lidar and IR radiometer combination intended to obtain τ and ɛ with sufficient accuracy for climate studies.
The sensitivity analysis details the uncertainties associated with both measured and derived quantities, identifying many sources of error that are a result of the assumptions in the LIRAD method. In particular, for cases with small ɛ, when the measured brightness temperatures are only slightly higher than the background, uncertainty in the radiative transfer model leads to increased uncertainty in the derived ɛ. This is mainly due to uncertainties in the estimation of the absorption coefficients for the water vapor continuum. We also show the utility of employing a microwave radiometer to obtain improved column water vapor amounts.
Results presented for a developing synoptic cirrostratus system reveal how the present LIRAD algorithm can be used to retrieve reasonable values of ɛ and τ, and also produce some information on the cirrus microphysics by combining measurements of δ, k, and α. This research illustrates the capabilities of ground-based observations for the verification of cloud properties derived from satellite radiance measurements, a major goal of our participation in Project FIRE.
The primary purpose for developing this algorithm was for the analysis of long-term observations of high clouds at FARS (Sassen and Comstock 2001). This dataset represents a climatologically representative sample of midlatitude cirrus clouds, from which we have developed a parameterization of their radiative properties (Sassen et al. 2001b) relating midcloud temperature and cloud thickness with IR absorption coefficient, and importantly, cloud visible optical depth and infrared layer emittance. These improvements to the LIRAD method and the development of radiative parameterizations from the extensive FARS dataset will contribute to better treatment of cirrus clouds in weather and climate models, and satellite cloud research.
Acknowledgments
This research has been funded primarily by NSF Grant ATM-9528287. The authors would like to thank Dr. Q. Fu for providing single-scattering properties and useful comments during the development of this algorithm. We also thank Dr. Z. Wang for useful discussions pertaining to this work and L. Wang for preparing the satellite imagery.
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APPENDIX
List of Symbols
Td Dewpoint temperature
T Atmospheric temperature
p Atmospheric pressure
ρ(ρυ) Density of dry (moist) air
r Water vapor mixing ratio
Ws, WMWR column-integrated water vapor derived from radiosonde and microwave radiometer measurements, respectively
zb, zt cloud-base and cloud-top heights
ztos Maximum height measured by the lidar
k Backscatter-to-extinction ratio
α Extinction-to-absorption ratio
η Forward multiple-scattering correction factor
P(R) Lidar backscattered power as a function of range
δ Linear depolarization ratio
σc Volume extinction coefficient at 0.694 μm
σa Volume absorption coefficient at 9.25–12.0 μm
β,β′ volume backscatter coefficient for single and mulitple backscattered photons, respectively
βm, βc molecular and cloud backscatter coefficients, respectively
T
υ K Absorption coefficient used in the correlated K distribution model
g(K) Cumulative probability as a function of absorption coefficient
P R(θ) Reflectance as a function of angle
τ Visible optical depth at 0.694 μm
τIR Optical depth at 10.0 μm
ɛ IR emittance
I↑,↓ υ Ib Blackbody radiance
Ic Radiance emitted by cloud ice particles only, derived from measured IR radiance
Im Radiance measured by IR radiometer
Isr Upwelling radiance reflected by cloud into radiometer FOV
Iac Downwelling radiance due to emission by atmospheric gases above the cloud
Iic Downwelling radiance due to emission by atmospheric gases in the cloud
Ibc Downwelling radiance due to emission by atmospheric gases below the cloud
Ict Theoretical cloud radiance
Isc Emitted radiance that is scattered in and out of the radiometer FOV
Isky Emission due to atmospheric gases used in original LIRAD method
Tbc Atmospheric transmittance between cloud base and surface
Tc Transmittance of layer between cloud base and top
Tm Midcloud temperature
Dge Generalized effective size of ice crystals as defined in Fu (1996)
g Asymmetry factor
(1 −
ω̃
Average βc between cloud top and the lidar signal maximum height estimated using various values of k/2η. Region I denotes the unstable solution, while region II denotes the stable solution, to Eqs. (12) and (13)
Citation: Journal of Atmospheric and Oceanic Technology 18, 10; 10.1175/1520-0426(2001)018<1658:ROCCRA>2.0.CO;2
Multiple-scattering parameter η as a function of forward-scattering angle (or FOV) and mean effective radius re for spherical ice particles
Citation: Journal of Atmospheric and Oceanic Technology 18, 10; 10.1175/1520-0426(2001)018<1658:ROCCRA>2.0.CO;2
Model downwelling radiance calculated by MODTRAN3 for (a) nonfiltered radiance and (b) with the PRT-5 radiometer filter function applied
Citation: Journal of Atmospheric and Oceanic Technology 18, 10; 10.1175/1520-0426(2001)018<1658:ROCCRA>2.0.CO;2
Fraction of upwelling radiance that is reflected off the cloud into radiometer FOV derived from model simulations. The different curves denote changes in scattered radiance due to generalized effective size Dge
Citation: Journal of Atmospheric and Oceanic Technology 18, 10; 10.1175/1520-0426(2001)018<1658:ROCCRA>2.0.CO;2
Comparison of model-derived clear-sky downwelling radiances at the surface for uncorrected and MWR-corrected water vapor mixing ratios
Citation: Journal of Atmospheric and Oceanic Technology 18, 10; 10.1175/1520-0426(2001)018<1658:ROCCRA>2.0.CO;2
Comparison of cloud emittance estimated using radiosonde-derived and MWR-corrected water vapor mixing ratios
Citation: Journal of Atmospheric and Oceanic Technology 18, 10; 10.1175/1520-0426(2001)018<1658:ROCCRA>2.0.CO;2
Column water vapor measured by the MWR and derived from radiosonde data. Note that the constant W from radiosonde data represents the case where the column water vapor is assumed to be constant between 12-h soundings
Citation: Journal of Atmospheric and Oceanic Technology 18, 10; 10.1175/1520-0426(2001)018<1658:ROCCRA>2.0.CO;2
Case study of a synoptic generated cirrostratus measured at FARS on 6 Jan 1999 (a) Time–height displays of δ and (b) lidar relative returned energy based on a logarithmic grayscale, (c) brightness temperature measured by the IR radiometer, (d) MWR and radiosonde measurements of W, (e) ɛ, (f) τ, and (g) k
Citation: Journal of Atmospheric and Oceanic Technology 18, 10; 10.1175/1520-0426(2001)018<1658:ROCCRA>2.0.CO;2
NOAA polar orbiter NOAA-14 image from the 10-μm channel taken at 2223 UTC 6 Jan 1999, displayed for the southwestern United States. FARS is located to the southeast of the Great Salt Lake, denoted with an “X.” There are several contrails visible in the satellite image
Citation: Journal of Atmospheric and Oceanic Technology 18, 10; 10.1175/1520-0426(2001)018<1658:ROCCRA>2.0.CO;2
SLC-NWSFO sounding for 0000 UTC 7 Jan 1999. Wind barbs are given in 2.5, 5.1, and 25.6 m s−1 intervals
Citation: Journal of Atmospheric and Oceanic Technology 18, 10; 10.1175/1520-0426(2001)018<1658:ROCCRA>2.0.CO;2
Extinction-to-absorption ratio α vs time for the case study displayed in Fig. 9
Citation: Journal of Atmospheric and Oceanic Technology 18, 10; 10.1175/1520-0426(2001)018<1658:ROCCRA>2.0.CO;2
FARS instrumentation used in the LIRAD-radiation method
Average single-scattering properties used in deriving IST and TC, where g is the asymmetry factor, 1 − ω̃ is the coalbedo, and σe is the extinction coefficient. The size categories are determined by the generalized effective size Dge (Fu 1996)
Fractional uncertainties in measured and derived quantities used in the sensitivity analysis. The parameter Tb denotes the measured brightness temperature
Results from the sensitivity analysis of ε and τ. The average change (Δε and Δτ-) is calculated for each perturbation in measured and derived quantities
Average change in ε in percent due to perturbations in radiances and k/2η as listed in Table 3. Averages are listed for three temperature and ε divisions