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  • View in gallery
    Fig. 1.

    Setup during the FIRE 1986 cirrus cloud field experiment. Little coordination among the aircraft never created collocations in time and space, yet profiles of radiation and microphysics are needed to verify models.

  • View in gallery
    Fig. 2.

    Setup during the FIRE 1991 cirrus cloud field experiment. Continuous ground measurements, when not obstructed by clouds at lower altitudes, guaranteed some collocations to aircraft measurements in vertical space. Case data were augmented by microphysical sondes and cloud radar.

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    Fig. 3.

    Comparison of three sets (MRI, PSU, NOAA) of downwelling solar and infrared broadband flux measurements at the ground site under cloud-free conditions on 4 December.

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    Fig. 4.

    Comparison of three sets (MRI, PSU, NOAA) of downwelling solar and infrared broadband flux measurements at the ground site under thin cirrus conditions on 5 December.

  • View in gallery
    Fig. 5.

    Comparison of two sets (MRI, PSU) of sunphotometer-derived cirrus cloud optical depths on 5 December. The included correction for forward scattering into the instrument’s field of view assumes small ice crystals.

  • View in gallery
    Fig. 6.

    Vertical (PSU) radar return signals for the 26 November cirrus cloud case over the ground site. Superimposed are locations of in situ microphysical measurements (solid line: King Air turboprop; double solid line: Sabreliner Learjet; dotted line: balloonsonde).

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    Fig. 7.

    Vertical (PSU) radar return signals for the 5 December cirrus cloud case over the ground site. Superimposed are locations of in situ microphysical measurements (solid lines: King Air; dotted line: balloonsonde).

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    Fig. 8.

    Vertical (PSU) radar return signal for the 6 December cirrus cloud case over the ground site. Superimposed are locations of in situ microphysical measurements (solid lines: King Air; dotted line: balloonsonde).

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    Fig. 9.

    Comparison of derived distributions for particle size and associated cross-sectional area from simultaneous cloud in situ measurements with an FSSP and a 2DC probe in a lower altitude cirrus on 25 November.

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    Fig. 10.

    Measured ice-crystal size distributions with 2D probes of the King Air aircraft on 26 November. One-minute samples near five selected cirrus altitudes during an ascent over the ground site are compared. The shading within each size-bin portrays, via its darkness, the compactness of detected crystals. Size distributions after a modeled breakup of larger compact crystals into many hexagonal columns are shown by the dashed lines and the increased values for ice-crystal densities.

  • View in gallery
    Fig. 11.

    Vertical variation in cirrus size distributions. Ice-crystal sizes are expressed by their extinction equivalent spheres. King Air and Sabreliner 2D-probe averages at selected altitudes in a cirrus over the ground site on 26 November are compared. Concentrations at 20 and 30 μm are not measured but result from the modeled crystal breakup.

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    Fig. 12.

    Variability on flight-leg averages for distributions of Fig. 11. Derived properties for characteristic size and extinction (averages are given in Tables 6 and 9) are presented with respect to a 6-km subscale. Also shown are other subsales for the 8.4-km altitude leg.

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    Fig. 13.

    Variability on flight-leg averages in an optically thin cirrus on 5 December. Derived properties for typical size and extinction (averages are given in Table 7) are presented with respect to a 6-km subscale.

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    Fig. 14.

    Vertical profiles of characteristic size and extinction from microphysical in situ measurements with 2D probes during rapid ascents and descents by the King Air over the ground site on 26 November. Also shown (dots) are properties derived from samples with the microphysical balloon sonde and properties representing horizontal flight-leg averages by King Air (K) and Sabreliner (S).

  • View in gallery
    Fig. 15.

    Vertical profiles of characteristic size and extinction from microphysical in situ measurements with 2D probes during a rapid ascent and descent by the King Air over the ground site on 6 December. Also shown (dots) are properties from microphysical balloonsonde samples.

  • View in gallery
    Fig. 16.

    Quantification of the importance of small ice crystals. Six balloon sonde microphysical samples on 26 November are separately analyzed for ice crystals with maximum dimensions above and below 50 μm. Though fewer in number, larger sizes have more area and dominate radiatively.

  • View in gallery
    Fig. 17.

    Comparison between modeled and measured downward solar and infrared broadband fluxes at cloud-free conditions. Model simulations are compared to three independent measurements at the ground site for the daytime of 4 December (see Fig. 3). The lower panel presents, based on NOAA data, model deviations for the direct solar irradiance.

  • View in gallery
    Fig. 18.

    Comparison between modeled and measured downward solar broadband fluxes for the 26 November cirrus cloud case. The deviation is illustrated in the lower panel. Also shown (dashed line) are model results that are purely based on the cloud boundaries detected by the radar.

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    Fig. 19.

    Comparison between modeled and measured downward solar broadband fluxes under optically thin cirrus conditions on 5 December. The deviation, illustrated in the lower panel, cannot be explained by the assumed crystal size.

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    Fig. 20.

    Sensitivity tests with modified model assumptions to improve the model–measurement comparison of Fig. 19.

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    Fig. 21.

    Whole-sky image at the ground site for the cirrus case on 26 November.

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    Fig. 22.

    Whole-sky images of the ground site for the cirrus case on 5 December.

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    Fig. 23.

    South–north scanning lidar return signals on 5 December for the times of the two frames of Fig. 22. The direction of the sun as seen from the ground site has been specially marked, as this path provides the basis for the sunphotometer-derived cirrus optical depth.

  • View in gallery
    Fig. 24.

    Modeling setup for three-dimensional (Monte Carlo) scattering simulations for the 5 December cirrus case. The atmosphere is approximated by (repetitive) sets of 3-km cubes, with one cirrus layer on top of three layers with Rayleigh scattering. Looking toward the sun (SSW direction), the ground site is located below the second column from the front. The horizontal dimension illustrates the (unchanged) atmospheric condition over time. The upper frame simulates an extrapolation of the sunphotometer optical depth (0.9) to the whole sky. The lower frame mimics a more realistic scenario with these optical depths only to the south but smaller cirrus optical depth over the ground site (0.3).

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    Fig. 25.

    Calculated visible transmissions at the ground for the two scenarios illustrated in Fig. 24.

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    Fig. 26.

    Cirrus inhomogeneity related deviations from 10-s measurements by using longer time averages; here for surface hemispheric downward solar and infrared fluxes of the 5 December cirrus case. Even though designed as an illustration for possible averaging errors, it is apparent that a comparison of different time averages contains information about inhomogeneity scales.

  • View in gallery
    Fig. 27.

    Experimental setup desirable for future experiments to understand the radiative transfer processes in cirrus. Continuous vertical colocation can be reached via multiple coordinated (unmanned) aircraft of identical speed. Balloon- or dropsondes may provide in situ data.

  • View in gallery

    Fig. A1. Distribution of average microphysical properties in (continental) midlatitude cirrus. The data constitute aircraft 2D-probe averages from horizontal flight legs in cirrus cloud fields below altitudes of 9 km during the FIRE 1986 and FIRE 1991 cirrus field experiments.

  • View in gallery

    Fig. A2. Relationship between temperature and extinction for midlatitude cirrus. Each symbol, categorized by date, represents a horizontal flight leg of at least 30 km in a cirrus layer. Data are based on 2D-probe measurements with the King Air aircraft during FIRE 1986 and FIRE 1991.

  • View in gallery

    Fig. A3. Relationship between temperature and particle size in midlatitude cirrus. Each symbol, categorized by date, represents a horizontal flight leg of at least 30 km in a cirrus layer. Data are based on 2D-probe measurements with the King Air aircraft during FIRE 1986 and FIRE 1991.

  • View in gallery

    Fig. A4. Relationship between mass extinction and particle size in midlatitude cirrus based on the same data that were used for Figs. A1 and A2. Also shown for comparison is a relation suggested by Ebert and Curry (1992).

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Cirrus Cloud Radiative and Microphysical Properties from Ground Observations and In Situ Measurements during FIRE 1991 and Their Application to Exhibit Problems in Cirrus Solar Radiative Transfer Modeling

S. KinneBay Area Environmental Research Institute/NASA Ames Research Center, Moffett Field, California

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T. P. AckermanDepartment of Meteorology, Pennsylvania State University, University Park, Pennsylvania

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M. ShiobaraMeteorological Research Institute, Tsukuba, Japan
Meteorological Research Institute, Tsukuba, Japan

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A. UchiyamaMeteorological Research Institute, Tsukuba, Japan

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A. J. HeymsfieldNational Center for Atmospheric Research, Boulder, Colorado

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L. MiloshevichNational Center for Atmospheric Research, Boulder, Colorado

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J. Wendell*National Oceanic and Atmospheric Administration, Boulder, Colorado

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E. ElorantaDepartment of Atmospheric Sciences, University of Wisconsin—Madison, Madison, Wisconsin

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C. PurgoldNASA Langley Research Center, Hampton, Virginia

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R. W. BergstromBay Area Environmental Research Institute, San Francisco, California

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Abstract

Measurements from the FIRE 1991 cirrus cloud field experiment in the central United States are presented and analyzed.

The first part focuses on cirrus microphysical properties. Aircraft 2D-probe in situ data at different cloud altitudes were evaluated for cirrus cases on four different days. Also presented are simultaneous data samples from balloonborne videosondes. Only these balloonsondes could detect the smaller crystals. Their data suggest (at least for midlatitude altitudes below 10 km) that ice crystals smaller than 15 μm in size are rare and that small ice crystals not detected by 2D-probe measurements are radiatively of minor importance, as overlooked 2D-probe crystals account for about 10% of the total extinction.

The second part focuses on the link between cirrus cloud properties and radiation. With cloud macrophysical properties from surface remote sensing added to the microphysical data and additional radiation measurements at the surface, testbeds for radiative transfer models were created. To focus on scattering processes, model evaluations were limited to the solar radiative transfer by comparing calculated and measured transmissions of sunlight at the surface.

Comparisons under cloud-free conditions already reveal a model bias of about +45 W m−2 for the hemispheric solar downward broadband flux. This discrepancy, which is (at least in part) difficult to explain, has to be accounted for in comparisons involving clouds.

Comparisons under cirrus cloud conditions identify as the major obstacle in cirrus solar radiative transfer modeling the inability of one-dimensional radiative transfer models to account for horizontal inhomogeneities. The successful incorporation of multidimensional radiative transfer effects will depend not only on better models but critically on the ability to measure and to define characteristic inhomogeneity scales of cloud fields.

The relative minor error related to the microphysical treatment is in part a reflection of the improved understanding on solar scattering on ice crystals over the last decade and of the available wealth on ice-crystal size and shape data for this study. In absence of this information, uncertainties from microphysical cirrus model assumptions will remain high.

Current affiliation: National Institute for Polar Research, Tokyo, Japan.

Corresponding author address: Dr. Stefan Kinne, NASA Ames, Mailstop 245-4, Moffett Field, CA 94035-1000.

Email: kinne@ice.arc.nasa.gov

Abstract

Measurements from the FIRE 1991 cirrus cloud field experiment in the central United States are presented and analyzed.

The first part focuses on cirrus microphysical properties. Aircraft 2D-probe in situ data at different cloud altitudes were evaluated for cirrus cases on four different days. Also presented are simultaneous data samples from balloonborne videosondes. Only these balloonsondes could detect the smaller crystals. Their data suggest (at least for midlatitude altitudes below 10 km) that ice crystals smaller than 15 μm in size are rare and that small ice crystals not detected by 2D-probe measurements are radiatively of minor importance, as overlooked 2D-probe crystals account for about 10% of the total extinction.

The second part focuses on the link between cirrus cloud properties and radiation. With cloud macrophysical properties from surface remote sensing added to the microphysical data and additional radiation measurements at the surface, testbeds for radiative transfer models were created. To focus on scattering processes, model evaluations were limited to the solar radiative transfer by comparing calculated and measured transmissions of sunlight at the surface.

Comparisons under cloud-free conditions already reveal a model bias of about +45 W m−2 for the hemispheric solar downward broadband flux. This discrepancy, which is (at least in part) difficult to explain, has to be accounted for in comparisons involving clouds.

Comparisons under cirrus cloud conditions identify as the major obstacle in cirrus solar radiative transfer modeling the inability of one-dimensional radiative transfer models to account for horizontal inhomogeneities. The successful incorporation of multidimensional radiative transfer effects will depend not only on better models but critically on the ability to measure and to define characteristic inhomogeneity scales of cloud fields.

The relative minor error related to the microphysical treatment is in part a reflection of the improved understanding on solar scattering on ice crystals over the last decade and of the available wealth on ice-crystal size and shape data for this study. In absence of this information, uncertainties from microphysical cirrus model assumptions will remain high.

Current affiliation: National Institute for Polar Research, Tokyo, Japan.

Corresponding author address: Dr. Stefan Kinne, NASA Ames, Mailstop 245-4, Moffett Field, CA 94035-1000.

Email: kinne@ice.arc.nasa.gov

1. Introduction

Cirrus clouds represent only a small fraction of the total cloudiness in the earth’s atmosphere. Nevertheless, ice clouds are unique in the sense that they can contribute to a warming of the earth–atmosphere system by increasing the radiative energy. The combination of a small optical depth and a low temperature enables cirrus to preserve more space-directed infrared radiation (greenhouse effect) than radiation concurrently lost to space by an increase in solar reflection (albedo effect). Yet predictions of a possible warming, which might result from an increase in cirrus cloud cover, are difficult. Cirrus cloud microphysical (crystal size and shape) and macrophysical (structure, thickness) properties, which characterize the solar scattering and determine the albedo effect, are highly variable (Heymsfield and Platt 1984; Foot 1988; Francis et al. 1994) and poorly represented in current radiative transfer and/or climate models (Stephens et al. 1990). The strong uncertainty in cirrus solar radiative properties (Stackhouse and Stephens 1991) opened the door to speculations on the climatic role of cirrus (e.g., Ramanathan and Collins 1991; Fu et al. 1992).

Several cirrus cloud field experiments have been conducted in Europe (ICE/EUCREX—see Raschke et al. 1990) and in the United States (FIRE—see Heymsfield and Ackerman 1990 or Stephens 1995). One of the major goals of these experiments sought to provide better insights into the effects of cirrus on solar radiative transfer. Simultaneous measurements of radiation and cirrus microphysical and macrophysical properties were conducted, though hardly for the entire cloud field, as needed. In reality, just the derivation of related vertical profiles for radiation and microphysics from field experiment data has proven to be difficult, if not impossible.

Cirrus in situ measurements in the past, during the FIRE 1986 field experiment [First (International Satellite Cloud Climatology Project) Regional Experiment], as illustrated in Fig. 1, were usually conducted by a single aircraft. Commonly, straight horizontal flight-leg patterns were chosen to permit hemispheric flux measurements and to minimize the temperature sensitivity of flux radiometers. Such in situ measurements from a single platform may provide some data for a statistical analysis; however, they are generally ill suited for the composition of vertical profiles: The time-delayed nature of measurements at different altitudes may not allow a comparison in light of a fast changing (wind-shear driven) cirrus structure over time. Thus, data collected by the same aircraft at different altitudes for a particular atmospheric vertical column may not relate to each other, even if location adjustments, based on the average wind advection of the environment, are included. In addition, many aircraft are unable to reach the highest cirrus altitudes. Thus, a derivation of vertical profiles for radiation and microphysics in cirrus clouds from in situ measurements by a single aircraft are almost impossible. Although the FIRE 1986 campaign operated with several aircraft, their coordination in both time and vertical column remained poor, in part due to the different aircraft velocities. With essentially no collocation in time and (vertical column) space, the creation of vertical profile approximations for radiation and microphysics became an incomplete puzzle (Kinne et al. 1992).

A different approach was pursued for the FIRE 1991 field experiment, as illustrated in Fig. 2. Groups of instruments at selected surface sites provided continuous data of atmospheric (and cirrus cloud) properties via remote sensing. These instruments also defined the lower boundary values of vertical radiation profiles. Occasional cirrus cloud in situ data by aircraft or balloonsondes over the ground site could at least guarantee a limited number of vertical collocations in time. After the elimination of cases, where water clouds interfered with cirrus observations from the ground, a few “cirrus-only” cases remained.

Our analysis for some of the cirrus cases from the FIRE 1991 campaign are presented below. First, we introduce the ground-based measurements. Next, we summarize the microphysical cloud in situ data and present their derived cirrus optical properties. Then, applying these cloud properties in a model, we compare calculated radiative fluxes to actual flux measurements at the surface. Finally, we discuss the (dis-)agreement and we give an outlook to future cirrus field experiments.

2. Instrumentation and data

We limited our data analysis to a few important cirrus cloud properties and focused more on the validation of these properties with independent measurements, if possible. Instruments at the ground provided continuous data of downward solar and infrared radiative fluxes, of atmospheric (sunphotometer-derived) optical depths and of (radar-derived) cloud boundaries. Our analysis of cirrus in situ microphysical data concentrated on samples by aircraft or occasional balloonsondes over (or near) the primary ground site. The instruments we used in our study and their relative location is summarized in Table 1.

a. Surface measurements

Measurements of the atmosphere were continuously collected (on precipitation free days) at several sites on the Coffeyville airfield, hereafter referred to as “ground site.” The cloud radar was located near the main hangar (site A). Sunphotometer measurements were conducted 500 m to the north (site B). This was also the launch site for radiosondes, the site of the whole-sky-image camera, and the location for two of our broadband radiative flux measurements. Additional radiation measurements were taken 1000 m northeast of the main hangar (site C). Finally, there was a scanning lidar about 21 km south-southwest of the main hanger. We limited our data analysis to eight daytime periods with good sunphotometer support. We chose four cloud-free days (18 November, 21 November, 24 November, and 4 December) and four days when cirrus was at least temporarily detected over the site (25 November, 26 November, 5 December, and 6 December).

1) Broadband fluxes

Hemispheric downward radiative fluxes for both solar and infrared broadband spectral regions were recorded by multiple pyranometer–pyrgeometer sets at site B and site C (Table 1). The instruments of the Meteorological Research Institute of Japan (MRI) provided averages over 10 s, while 30-s averages were recorded by the Pennsylvania State University (PSU) data system, and only 3-min averages were logged with the instruments of the National Oceanographic and Atmospheric Administration (NOAA). The longer time averages are unfortunate for the analysis of cloudy conditions, as information regarding the variability in cloud cover and cloud optical depth were lost.

A comparison of measured flux (3-minute) averages under cloud-free conditions is illustrated for the daylight hours of 4 December in Fig. 3. The agreement is within the expected uncertainty. For the downward broadband solar fluxes, a 4% error must be expected from the poor characteristic on the cosine response and from the temperature dependence of the pyranometer (Meyers et al. 1989). For the downward infrared fluxes, we should expect errors of up to 10% with accuracies at best at 20W m−2 (DeLuisi et al. 1992.)

For the comparison of measured fluxes under cloudy conditions we selected with Fig. 4 an optically thin cirrus event at noontime on 5 December. This cirrus case will be addressed later in more detail. We used 1-min averages, if available. The agreement for the independent solar and infrared flux measurements is better than expected, and the slight offsets in time are attributed to independent time references.

2) Sunphotometer data

Sunphotometers measure the direct solar radiation; thus they provide data about atmospheric attenuation or atmospheric optical depth. Two independent datasets from collocated sunphotometers were recorded. The MRI instrument had a field-of-view half angle of 1.2° and the PSU instrument had a half angle of 1.0°. These half angles exceed that of the sun (0.25°). Thus, the measured solar radiation includes not only the directly attenuated solar flux but also contributions of forward-scattered solar radiation into the instrument’s field of view. Hence the apparent optical depth, derived from the assumption of direct attenuation only, will, with the presence of atmospheric scatterers, be smaller than the actual optical depth. We calculated ratios between the actual and the apparent optical depth with our Monte Carlo code. We also listed values of an approximation (Shiobara and Asano 1994). Forward-scattering contributions increase with the instrument’s field of view and with particle size, as illustrated in Table 2.

For cloud-free events, we determined average aerosol optical depths from sunphotometer measurements. Detected aerosol optical depths for cloud-free cases and for cirrus cases are summarized in Table 3 (more details are available in Shiobara et al. 1996). The derived aerosol optical depths are larger in early December, as pockets of increased stratospheric aerosol concentrations from the June 1991 eruption of Mt. Pinatubo in the Tropics arrived over Coffeyville (Sassen et al. 1995). The detected optical depth variations, even during the day, are mainly due to changes in concentration, because the ratios of derived optical depth at different wavelengths remained similar. These ratios reveal the presence of submicrometer size particles only. For these sizes and for the viewing solid angles of our sunphotometer, the forward-scattering contributions in the aerosol optical depth derivation can be neglected.

For cirrus (and the presence of much larger particles), sunphotometer-derived optical depth estimates have to include forward-scattering effects. Monte Carlo scattering simulations are summarized in Table 2. Our results for cirrus and 1.0° (PSU) or 1.2° (MRI) field of view half angles show that the correction factors vary between 1.6 and 2.5 depending on ice-crystal size. Thus, for our cirrus case the actual optical depth is about twice the apparent (DeBeer law) optical depth.

Simultaneous measurements of both sunphotometer instruments were compared for the 5 December noontime cirrus event. Figure 5 shows that the independently derived visible optical depths for cirrus agree well. Attenuations due to aerosol (aerosol optical depths are indicated in Table 3), molecular scattering, and ozone absorption had been subtracted. For the forward-scattering correction we assumed (120-μm length and 30-μm half-width) hexagonal ice columns. This ice-crystal size is consistent with standard cloud in situ data for that day, which we will address below in more detail. We will also show that limitations to these in situ measurements allow for the possibility of a smaller characteristic ice-crystal size. This would reduce the scattering correction and the cirrus optical depths would be slightly smaller than those given in Fig. 5.

3) Cloud radar data

The PSU 94-GHz (or 3-mm) radar provided continuous vertical profiles of clouds as they drifted over Site A. Although most corresponding flux and sunphotometer measurements were taken at site B, 500 m to the north, we believe that 3-mm radar return signals illustrated very well the character of the cloud field as it related to our radiometer measurements. We present radar return signals, with superimposed locations of cloud in situ measurements for cirrus events on 26 November in Fig. 6, on 5 December in Fig. 7, and 6 December in Fig. 8.

The detection of cloud positions by radar, however, has its limitations. Optically thin cloud layers remain undetected and strong attenuations in the lower part of the cloud can prevent a 3-mm radar from detecting the upper parts of the cloud. This explains detected ice-crystal concentrations by the Sabreliner aircraft on 26 November and by balloon sondes on 5 and 6 December above the cloud top height suggested by the radar. It also explains the lack of a signal for part of the optically thin cirrus case on 5 December despite the detection by the sunphotometer, as shown in Fig. 5 and visual observation from the ground.

Radar deficiencies could be largely eliminated with the simultaneous use of lidar and longer wavelength (8 mm) radar systems. Lidar–radar combinations, even more so with a scanning ability, promise to be an exciting tool to visualize and quantify cloud structures and their scales. We will illustrate later the importance of cloud images from a scanning lidar and from a whole sky image camera for one of our cirrus cases.

b. In situ measurements

Several aircraft and occasional balloon sondes sampled ice-crystal concentrations in cirrus clouds above the Coffeyville airfield. We analyzed these microphysical measurements in detail, because size, shape, and concentration of ice crystals are critical parameters in cirrus (solar) radiative transfer modeling. The airplanes also provided in situ radiation data and hemispheric broadband fluxes. However, we did not analyze these data in this study. We felt that uncertainties of reconstructed vertical profiles for broadband radiative fluxes would be too large to be meaningful in model verification tests.

First, we present a comparison of simultaneous measurements by two different particle detectors, the two-dimensional Diode Array Probe (2D probe) and the Forward Scattering Spectrometer Probe (FSSP). Most of our analyzed cirrus in situ data is based on 2D-probe ice-crystal measurements of the two NCAR aircraft, King Air and Sabreliner. These data will be introduced next, and we will explain our data processing. Our presentation of derived cloud properties will concentrate around cirrus events on 26 November, 5 December, and 6 December. We will finish this section with a comparison of cirrus microphysical properties from 2D probes to those derived from balloonsondes in the same cirrus. This comparison allowed us to investigate the importance of smaller ice crystals, which are overlooked by 2D probes. The altitudes of our microphysical samples with respect to the two-dimensional radar images of our three local cirrus events are superimposed in Figs. 6–8.

1) Comparison of 2D-probe and FSSP-probe data

The FSSP probe detects particle sizes in the 1- to 50-μm size range based on the assumption that particles are spheres. Ice crystals of that size, though not spheres, lack a preferred dimension. Thus we wondered if FSSP measurements can complement 2D-probe data, which fail to detect the small ice-crystal sizes. Simultaneous measurements with an FSSP and a 2D probe were taken in a midlevel cloud layer at a 3-km altitude over the Coffeyville airfield on 25 November. Even though the cloud was expected to be composed of water droplets only (FSSP measurements were intended to provide a radar calibration), ice crystals were detected.

We compared six 1-min averages of size distributions for particle concentration and their cross section in Fig. 9. We found that in the overlapping size region, FSSP concentrations are much larger than those from 2Dprobe data. FSSP overcounting, not limited to the overlapping region, is expected from the presence (and forward-scattering contributions) of large particles beyond the FSSP probe detection limit (Gardiner and Hallett 1985). We also do not know if the high concentrations for sizes below 20 μm are caused by the possible presence of water droplets. In any case, the usefulness of FSSP-derived particle size concentrations is questionable, even in the absence of both water droplets and larger crystals (as for cirrus in tropical regions or near cirrus tops at midlatitudes): Modeling studies have shown that expected FSSP signals (forward scattering between 5 and 25 degrees) for ice crystals are not only different from spheres but also highly shape dependent (Macke 1993). Thus FSSP measurements in cirrus seem to have a limited value. Additional comparisons, involving simultaneous microphysical measurements with other microphysical instruments, such as replicators or videosondes, are certainly desirable.

2) Aircraft 2D-probe measurements

Most of our 2D-probe in situ microphysical data are based on measurements by the King Air. The King Air is a slow flying (100 m s−1) turboprop with a 9.5-km altitude ceiling. This often prevented the aircraft from reaching the cirrus cloud top. Thus, for the 26 November cirrus case, we also evaluated microphysical measurements obtained by the Sabreliner. The Sabreliner Learjet could fly at higher altitudes; however, it operated at twice the speed (200 m s−1) of the King Air.

The King Air had two probes, a 2DC probe with a finer size-bin resolution for the submillimeter sizes and a 2DP probe more optimized for the largest crystals. The Sabreliner was equipped with a 2DC probe only. As a combined result of 2D-probe design and aircraft velocity, ice-crystal sizes below 35 μm for the King Air and below 50 μm for the Sabreliner remained undetected. In addition, 2D-probe concentrations for crystal sizes below 100 μm for the King Air and below 150 μm for the Sabreliner must be considered as inaccurate and too low. The concentration of these undetected smaller ice crystals and their impact on our derived cirrus properties will be addressed later.

The initial rapid King Air ascent through a cirrus layer on 26 November (see Fig. 8) has been selected to illustrate 2D-probe cirrus in situ measurements. One-minute averages (climbing rate: 300 m min−1) at five altitudes are presented in Fig. 10. The shaded areas outline the measured particle concentrations, with respect to the detected maximum crystal dimension. The different shading tones within a particular size-bin column separate particle cross sections (in terms of fractions to the largest possible cross-section area of a circle, whose diameter is the maximum dimension). The darker the shading, the larger the area fraction. Thus the darkest shades reflect compact crystals with no preferred dimension and the lightest shades indicate needlelike crystals. All five panels illustrate that small sizes are compact, but as their maximum dimension or length increases, ice crystals become more needlelike. For crystal lengths between 175 and 600 μm increasingly darker shadings, thus larger cross sections, reflect the presence of complex particles, mainly bullet rosettes (3D aggregates of hexagonal columns). The panels also display an overall increase in large particle concentrations at the expense of small particle concentrations towards the cloud base.

3) Processing of aircraft 2D-probe data

Our derivation of optical properties from 2D-probe data assumed that all ice crystals have the shape of a single hexagonal column, with the exception of complex ice crystals. Complex crystals are treated as a set of many (subsized) hexagonal columns. We considered a crystal as “complex” if its ratio between cross-sectional area and maximum length, from now on referred to as s/c ratio, exceeded observed ratios for hexagonal columns (Heymsfield 1972; Auer and Veal 1970) by at least 15%. We reconstructed a complex crystal as a double column with as many branches attached to the center as it took to satisfy the cross-section requirement. Thereby, we also accounted for the three-dimensional nature of these ice crystals: Many branches in a two-dimensional image are partly or completely hidden or not represented by the detected cross sections. We then considered all columns and branches to be individual crystals. This break-up procedure is supported by geometrical optics ray-tracing results: The scattering for a (hexagonal) bullet rosette ice crystal is almost identical to scattering of its individual (hexagonal) branches (Macke 1993). Thus, scattering properties for complex crystals are not determined by their overall size but by the size of their much smaller branches. Thus in terms of solar scattering, complex ice crystals behave smaller (stronger backscattering) than their maximum dimension would suggest.

The breakup of complex crystals increases the concentration and modifies the particle size distribution, as indicated in Fig. 10. The effective shift in the particle concentration distribution to smaller sizes, as illustrated by the dashed lines in Fig. 10, seems to fill the gap between the small and the large particle mode. Those two modes are frequently observed for convective cirrus (Cirrus uncinus; Heymsfield 1975). Thus it seems possible to approximate cirrus particle size distributions for the analysis of radiative effects by a monomodal analytical function.

To determine the single scattering properties for radiative transfer calculations, our distributions of hexagonal columns were transformed into distributions of surface area equivalent spheres characterized by their effective radius (reff). Spherical shapes permit rapid Mie calculations. We chose an equivalency in surface area, because it provides correct values for extinctions (βex), assuming that ice crystals have no preferred orientation. This assumption seems justified as the small crystals are compact and the branches of larger complex crystals point in all directions. Necessary adjustments at solar wavelengths to single-scattering albedo (w0) and asymmetry factor (g) were based on published differences between spheres and hexagonal columns (Takano and Liou 1989; Kinne and Liou 1989). Our calculated ice water contents (IWC) account for hollowness by assuming a reduced density with increased crystal length for all single columns and all detached branches that exceed 50 μm in length.

4) Accuracy of our processed 2D data

We performed some sensitivity studies to test the accuracy of our calculated optical properties. A summary is given in Table 4. For 2D-probe measurements, we face the problem of undetected small ice crystals, which will increase the extinction. However, the severity of the problem depends on the presence and concentration of larger ice crystals. In the company of many large ice crystals [as for the crystal-size distribution from FIRE 1986 shown in Fig. 13 of Kinne et al. (1992)], only a modest impact of less than 10% is expected. For that distribution detected crystals in the 25–50-μm and 25–100-μm maximum dimension range account for only 4% and 7% of the entire extinction. An artificial tenfold increase of the 25–50-μm range concentration for an imagined 10–25-μm size bin only lifts the extinction by 6%. However, if large crystals or aggregates are rare, the impact of undetected small sizes will be larger. In comparison with simultaneous balloonsonde data, we will show later that for the 26 November cirrus case study crystals smaller than 50 μm contribute about 20% to the total extinction. As the 2D probe of the slower (King Air) aircraft detected a few sizes below 50 μm, we deduced a 5%–20% underestimate for our calculated cirrus extinctions from 2D-probe data due to overlooked small sizes.

We also tested the sensitivity of several model assumptions. During the reconstruction of a complex crystal we considered that the two-dimensional cross-section area originates from a three-dimensional particle. We had to make some assumptions about the hidden surface area, which introduces uncertainties of about 5% for IWC and extinction. A similar uncertainty for the calculated IWC relates to our assumed partial hollowness for hexagonal columns or branches longer than 50 μm.

In summary, we estimate that our calculated extinctions and ice-water contents could be off by as much as ±15%. There is a tendency towards larger extinctions due to the possibility of undetected small particles in the 2D-probe measurements.

5) Accuracy of other 2D-data processing techniques

A common approach avoids the breakup of complex particles. Then the measured cross section for one particle is always substituted with one sphere that conserves that cross section. This may only provide a good estimate for the extinction. However, the IWC gets artificially large and the typical particle size doubles, with severe consequences on derived properties for (solar) scattering: Too much solar transmission and too little solar reflection or cloud albedo.

Another interesting approach (suggested by S. Warren 1990, personal communication) adopts the complex particle breakup but represents all hexagonal columns or columnar branches by chains of spheres whose diameter is the columnar width. This approach reproduces our hollowness (reduced density) and extinction (if we add spheres to cover the neglected surface area of the end plates of hexagonal columns). The main difference is a sharp (50%) reduction of the effective particle size. In light of the fact that our crystal modeling is based around simple (and smooth) shapes, which rarely exist in nature, and that we underestimate small crystal concentrations in 2D-probe measurements, this suggested sphere–chain approach seems interesting and warrants further investigation.

6) Properties derived from aircraft 2D-probe data

Calculated cirrus cloud optical properties are determined for consecutive samples as well as long-term averages. Since our microphysical analysis is primarily intended to supply cirrus optical properties for (local) case studies, this section focuses on samples that can be related to each other with respect to the cirrus cloud field. We will compare consecutive 1-min averages to demonstrate the horizontal and vertical variability in cirrus.

Nevertheless, since there is an interest in characteristic cirrus cloud properties from a statistical point of view, a summary of derived averages in tables and an analysis in the appendix was provided. We averaged 2D-probe data over horizontal flight legs of at least 30 km in distance to define altitude (and temperature) specific cirrus properties. The derived properties for the four cirrus cloud cases during FIRE 1991 are summarized in Tables 5–9. These tables also provide information about measurement duration, aircraft heading, wind direction, and wind speed. For the analysis of (continental) midlatitude cirrus below 9 km we also included flight-leg averages from 4 days (22 October, 28 October, 1 November, and 2 November) during FIRE 1986. Distributions for cloud temperature, effective radius, ice-water content, and extinction, as well as relationships among these variables, are presented and discussed in the appendix.

For local case studies, vertical profiles of microphysical properties are desirable. In light of the shear-induced changing structure of cirrus cloud fields, rapid ascents and descents through cirrus layers are desirable. Microphysical measurements from long horizontal flight legs seem only useful when multiple aircraft sample in the same cloud-field column at different altitudes, as did the Sabreliner and King Air over the ground site on 26 November, illustrated in Fig. 6.

Altitude-related “average” size distributions for 26 November are presented in Fig. 11. The selected altitudes also include those of 2D-probe data samples of Fig. 10. The comparison of the size distributions revealed a strong increase in particle size toward the cloud base, though primarily in the upper part of the cirrus. Average crystal concentrations reached a maximum in the lower part of the cirrus. Reduced concentrations near the cloud base can be explained by sublimation processes. A cloud base size distribution is depicted by the dotted line in Fig. 11. Lower concentrations toward the cloud top are attributed to the increased inhomogeneity, as considerable cloud-free fractions contribute in the averaging process. Differences in the size distribution between the Sabreliner and King Air at 8.5 km could be explained by inhomogeneity and associated changes over time. Yet there is good agreement at 7.3 km, despite the considerable time delay. The detection of fewer small ice crystals by the Sabreliner can be attributed to its higher speed. The lack of the Sabreliner data to define the largest ice-crystal concentrations (which are very important for ice-water estimates and remote sensing retrievals) underscores the importance of 2DP-probe measurements, which were only made by the King Air.

The inhomogeneity of the cirrus cloud fields severely limits an intercomparison of average properties from different altitudes for local studies, be it the size distributions of Fig. 11 or the derived properties summarized in Tables 5–9. To illustrate this, we resolved horizontal flight-leg averages for extinction and characteristic size into consecutive 1-min mean values. The optically thicker cirrus case on 26 November of Fig. 12 relates to previously discussed size distributions in Fig. 11, while the optically thinner cirrus case on 5 December of Fig. 13 relates to ground-based measurements of Figs. 4 and 5. Such resolution still averages over a distance of 6 km and hardly depicts the actual variability. For example, we compared in the lower panel of Fig. 12 averages over 12, 4, and 1 km from the Sabreliner flight leg at 8.4 km. (The instrument’s sampling volume restricts resolutions to above 1 km).

Rapid ascents and descents (preferably in a spiral fashion while drifting with the ambient wind) through a cirrus cloud layer is probably the best way to determine vertical profiles of microphysics and vertical variability with a single aircraft. For selected ascents and descents, a few characteristic properties in the upper part and lower part of the cirrus layer are compared in Table 10. Toward the cloud base we noticed trends to larger and more complex particles, to elevated extinctions, and to sharply increased ice-water contents. These trends were already apparent from Fig. 10, which depicted the initial ascent by the King Air on 26 November.

Comparisons among rapid profiles through the same cirrus cloud are given in Fig. 14 for the 26 November case and in Fig. 15 for the 6 December case. For the extinction profiles, the vertical variations are much stronger than the overall trend. The data seem to support a cellular (as compared to a layered) cloud structure, because extinction profiles within the same cirrus layer undergo rapid changes over time.

Thus models, which are incapable of including effects of horizontal inhomogeneity, such as one-dimensional radiative transfer models, will be a poor choice under cirrus conditions. This is especially true for local case studies and will be addressed later.

7) Balloonsonde microphysical samples

Balloonsonde measurements lack the spacial coverage of aircraft measurements. Nevertheless, microphysical balloonsonde data define vertical profiles of particle size distributions, they reach (in contrast to many aircraft) higher cirrus altitudes, and, most importantly, they provide data on small crystal concentrations. Thus, despite their small sampling volume (about 0.005 m3), balloonsonde data are an important extension to aircraft 2D-probe data, which cannot detect small ice crystals. The microphysical balloonsondes can record optical images of ice crystals as small as 10 μm in size (Miloshevich et al. 1997). Ice crystals were collected on a Formvar film, videotaped, and (optically) counted. Problems associated with particle breakup upon impact, as for replicator aircraft data (Arnott et al. 1994), were minimized due to the relatively slow ascent velocity of the Fig. 11. Vertical variation in cirrus size distributions. Ice-crystal sizes are expressed by their extinction equivalent spheres. King Air and Sabreliner 2D-probe averages at selected altitudes in a cirrus over the ground site on 26 November are compared. Concentrations at 20 and 30 μm are not measured but result from the modeled crystal breakup. balloonsonde. The analysis confirmed that the majority of the detected larger ice-crystal shapes are irregular or complex, and not just hexagonal columns. For these irregular particles, we adopted characteristic 2D-probe ratios between maximum dimension and cross-sectional area. We performed a similar breakup procedure into individual branches as for the 2D-probe data.

We compared derived cirrus properties from balloonsondes, indicated by dots in Figs. 14 and 15, to those derived from 2D probes in Table 10. We picked events on 26 November and 6 December, when measurements occurred at about the same time and location, as shown in Figs. 6 and 8. The agreement is within the expected variability. The effective radii from the sonde data are only slightly smaller than those from the 2D-probe data. This is a first indication that overlooked small particle concentrations are not too important, radiatively, at least for the cirrus cases on 26 November and 6 December.

To quantify the influence of small particles, we investigated six balloonsonde samples for the 26 November cirrus case. We separated these size distributions at 50 μm into small particles and large particles. Figure 16 shows that the concentrations for small particles are higher, with effective radii peaking near 20 μm. However, the larger particles, which can be detected by 2D probes, provide more cross section; thus they dominate radiatively. The comparison of calculated properties in Table 11 showed that particles smaller than 50 μm in maximum dimension contribute only to about 20%, at most to 35%, to the total extinction. Since 2D-probe measurements can detect at least a few ice crystals smaller than 50 μm, the expected extinction underestimate due to undetected small particles is smaller. Our estimate for small particle contributions to extinction is between 5% and 20%, as indicated in Table 4.

Small ice-crystal concentrations, which 2D probes fail to detect, however, will be much more important for very cold cirrus, where larger ice crystals are rare or missing. This includes cirrus in tropical regions, the cloud top regions of midlatitude cirrus, and young contrails. In those cases 2D-probe data can give a very distorted picture of the microphysical properties (smaller extinction, larger characteristic size) and can lead (via poor assumptions) to inaccurate model results. Unfortunately, current aircraft instrumentation is unable to quantify small size concentrations. This leaves room for speculation on microphysical processes and on the climatic impact of cirrus. Microphysical balloon- or dropsondes, even if limited to a few samples, could reduce this uncertainty by complementing and extending aircraft measurements.

8) Summary

In situ microphysical measurements provided the necessary particle size information for the modeling studies of our selected cirrus cloud cases. The extinction can be expressed by ice spheres with radii of about 85 μm for 6 December, of about 70 μm for 26 November, and of 40 μm for 5 December. As these sizes are based on 2D-probe data, which are unable to detect the smallest ice crystals, a shift to smaller sizes cannot be ruled out, particularly if large ice crystals are rare. This applies for the 5 December case. Balloonsonde data on that day suggest radii of only 25 μm near the cloud top at 13-km altitude.

3. Comparison

The data we introduced in the previous section can be used to define the atmospheric state in radiative transfer models. Once processed in such a model, calculated results can be compared to actual measurements. To test the ability of widely used one-dimensional two-stream models to describe atmospheric radiative transfer processes, we compared downwelling hemispheric broadband fluxes at the surface. We were aware that 1D radiative transfer models cannot account for horizontal inhomogeneities, which is an important cirrus feature, as we have already illustrated. Since inhomogeneity effects from different (cloud) altitudes at times cancel in part, time periods may be found when an inhomogeneous cloud field can be approximated by a homogeneous cloud layer. We limited our comparisons involving cirrus clouds to these cases, with the primary goal being to validate the cirrus microphysical treatment in our model. Prior to the presentation of the cirrus cases, we will briefly introduce the model and we will conduct comparisons under cloud-free conditions to detect any possible model bias.

a. Model

Radiative fluxes were determined with a two-stream model. The model assumes plane-parallel layers. This means that only vertical inhomogeneities can be considered. Our broadband results are based on 50 calculations at 8 solar wavelengths and 70 calculations at 12 infrared wavelengths. Absorption by atmospheric gases is expressed via an exponential sum fitting for the transmission. Atmospheric conditions are prescribed by data of the National Center for Atmospheric Research (NCAR) CLASS-type radiosondes, which were launched at least four times each day at the ground site. For times between launches, we performed linear interpolations of the sonde data.

b. Cloud-free cases

To detect a possible bias by the model, we conducted a comparison of hemispheric downward fluxes under cloud-free conditions. We included the effects of aerosol. Aerosol optical depths and aerosol sizes were based on the sunphotometer-derived data, which we summarized in Table 4. We also distinguished between weakly absorbing tropospheric aerosol and nonabsorbing stratospheric aerosol. The strong variations in optical depth from day to day (and even during some days) were attributed in part to the stratospheric component, as initial aerosol pockets from the Mt. Pinatubo eruption appeared over the ground site.

Cloud-free model calculations were conducted every 3 min for the sunlight hours on 18, 21, and 24 November and 4 December. We summarized in Table 12 our model deviations with respect to the three independent measurements for a morning, noon, and afternoon time. Deviations for an entire daytime period were presented in Fig. 17. We picked the 4 December case, as we already had introduced the measurement datasets in Fig. 3. In comparison to all three flux measurements, our model overpredicts solar and infrared broadband fluxes.

The infrared model bias of about 6% or 15 W m−2 is within the expected measurement uncertainty. Also, our modeling results are based on a few humidity measurements. Downward infrared broadband fluxes are very sensitive to changes in atmospheric water vapor near the surface. The overall larger infrared fluxes of the model (assuming the model’s absorption coefficients for water vapor are correct) indicate that we probably overestimate the water vapor amount in our model. With this in mind, the disagreement of the solar downward broadband fluxes is even more alarming.

The solar model bias is strong and similar for all four days: Disregarding larger deviations after dawn and before dusk, our model strongly overpredicts measured downward solar broadband fluxes by about 45 W m−2 or 9% around noon. This error is far beyond expected measurement uncertainties. To illustrate the problem a match between measurements and model results would require a quadrupling of either the aerosol optical depth or all water vapor absorption coefficients. We acknowledge that our model probably underestimates the trace gas absorption in the near-infrared spectral region. However, that can only explain about half of the model deviation due to the limitation by the much smaller deviation for direct solar irradiances, as indicated in the bottom panel of Fig. l7. It is unclear whether the remaining solar bias is a measurement problem (such as an underestimate of the diffuse flux component) or whether it is a model-related problem (such as an underrepresentation of the aerosol absorption). These strong deviations under cloud-free conditions are currently being investigated (e.g., Kato et al. 1997). As we did not understand the details of the solar model discrepancy, we adopted a 9% solar model bias for our cloud simulations.

c. Cirrus cases

Our model-measurement comparisons under cirrus conditions concentrated on solar radiative transfer modeling, where (uncertain) scattering processes dominate. Cirrus are positioned in our model according to the radar data. Cirrus cloud optical depths were derived from sunphotometer data. The necessary information on ice-crystal size and shape is taken from microphysical in situ measurements.

Our radiative treatment of any complex crystal (such as a bullet rosette shape) is based on a simulated breakup into its individual branches. This reduction to one ice-crystal shape, that of a hexagonal column, greatly simplifies the derivation of (single) scattering properties. As differences in the scattering behavior between spheres and hexagonal columns are well known from geometrical optics calculations (Takano and Liou 1989), rapid MIE theory can be applied. The extinction βex is well approximated by surface area equivalent spheres. To capture the correct scattering properties of hexagonal columns, reductions to the cosingle scattering 1 − w0 and the asymmetry factor g of surface equivalent spheres are required. Parameterizations exist (Ebert and Curry 1992). The reductions in absorption (1 − w0) are larger (up to 40%) for the elongated (and larger) particles than for (generally small) particles with no preferred dimension (about 10%). The more important correction, however, is the reduction of the solar asymmetry factor. At visible wavelengths, we need reductions from 0.86 to about 0.78 for small ice crystals and from 0.90 to about 0.83 for large ice crystals.

For the model versus measurement comparison of solar fluxes under cirrus conditions, we picked two near-noon events, when small mass-amplification factors increase our confidence in sunphotometer data and derived optical depths. Contributions by aerosol optical depths of Table 3 were considered.

Our two cirrus cloud cases in Figs. 18 and 19 for 26 November and 5 December, respectively, revealed, despite a good correlation for flux minima and maxima, at times significantly different amounts for calculated and measured solar broadband hemispheric fluxes at the ground site. We attributed the alternating nature of deviations to horizontal inhomogeneities of the cirrus cloud field, which could not be treated by our simple 1D model. Horizontal inhomogeneities of a cloud field can temporarily create hemispheric solar fluxes at the ground that are alternating larger or smaller than fluxes under horizontal homogenous average conditions, due to either a surplus or a lack of diffuse scattered radiation, respectively. In that sense, inhomogeneities can also explain measured solar flux values that at times exceed model predictions for cloud-free conditions. Accurate model simulations involving inhomogeneities require a measure for the inhomogeneity and a three-dimensional radiative transfer model. Without both, we limited our comparison with the 1D model to the final sections of our two cirrus cloud case time periods, when solar broadband fluxes and sunphotometer-derived cirrus optical depths varied less over time. This suggested to us that effects of inhomogeneity were not significant.

For the 26 November case in Fig. 18, the agreement between model results and measurements was surprisingly good. Alternating deviations of up to 5%, as were detected for the last 45 min of that case, were expected as the cirrus cloud field was not completely homogeneous. We also tried to reproduce solar flux surface measurements based on cloud boundary information by the radar and assumed cloud microphysical properties as a function of temperature, as illustrated in Table 13. The agreement based on such simulation was not very satisfying. However, better results could be expected if additional information about the vertical extinction profile and the typical cloud particle size were available. We could not test to see if an extinction profile alone would be sufficient because the cloud radar was not calibrated.

For the 5 December case already introduced in Figs. 4 and 5, the comparisons between model results and measurements were poor, as illustrated in Fig. 19. The last hour revealed an offset, as the model consistently overpredicts the solar transmission, on average by 6%.

In summary, for one case our cirrus model agreed well with the measurements; the other times our model performed poorly.

4. Discussion

The poor modeling effort for the 5 December case is very disturbing. However, this is in line with overpredictions of the solar transmission under cirrus conditions by radiative transfer models, which had been reported in the past (Stackhouse and Stephens 1991; Francis et al. 1994; Shiobara and Asano 1994). As scattering on nonspherical ice crystals was, and still is, not completely understood, it was often suggested that the forward-to-backward scattering ratio on ice crystals should be reduced. To force an agreement to the measurement, however, frequently the authors suggested a scattering behavior, which theory could not explain.

The 5 December cirrus case, for example, would require a solar asymmetry factor of about 0.65, whereas geometrical optics for hexagonal shaped particles (Takano and Liou 1989; Macke et al. 1995) suggests solar (visible) values between 0.78 and 0.82 for midlatitude cirrus cloud particles. Even the overlooked hollowness is not expected to cause smaller values (Stephens 1987; Takano and Liou 1995). In any case, just adopting a model parameter, which cannot be explained by theory, is not very satisfying.

We have confidence in the measurements, which is supported by the agreement of independent datasets in Figs. 4 and 5. Possible errors from the use of 1-min averages, as investigated in Table 14, remain small. Thus, we examined possible errors in the model assumptions. Our model-measurement comparisons were conducted at solar zenith angles of about 65°. Under these conditions, we introduced only small errors by using an approximate (two-stream quadrature) radiative transfer method (King and Harshvardan 1986) and by using an asymmetry factor in place of the accurate phasefunction to describe solar scattering (Fu and Takano 1993). We also found that our choice of particle size is immaterial, as larger sunphotometer optical depths offset the stronger transmissions for larger crystals, as indicated in Fig. 19. Finally, we performed three sensitivity tests. We investigated effects of doubled aerosol, we replaced the solar asymmetry factor in the model with the smallest theoretically possible value for ice crystals (0.75), and we increased the near-infrared absorption for cirrus by a factor of 4. Figure 20 shows that each of these model modifications helps to reduce the disagreement. However, even when we combined the effects of all three (extreme, thus unlikely) assumptions, our “average” modeled transmission was still too large.

A serious shortcoming is the model’s inability to account for horizontal variability. However, there is the perception that inhomogeneity effects average out over time. A substitution of inhomogeneities by their average property results in a smaller overall solar transmission. Thus the inability of our model to account for horizontal inhomogeneity seems an unlikely candidate to explain why solar transmissions should be larger than the measurements. Yet, a closer inspection of the 5 December cirrus case revealed that, in fact, the model’s overprediction for the solar transmission was related to cirrus inhomogeneity, which was not detected and led to a poor model assumption.

We assumed in our model calculations that the cloud, which attenuated the direct sunlight represented the average cirrus optical depths. In selecting potential cases to validate our 1D model, we were aware that the extension of a single measurement to the entire cloud field would depend on the scales of the inhomogeneity. This is especially true for the low sun-elevation angles of at most 30° for our cirrus cases. If inhomogeneity scales were such that cloudiness or cloud optical depth towards the sun were quite different from that overhead, which largely defines the diffuse flux component, an average model cannot reproduce measured solar flux minima and maxima, as those during the first hour of our two cirrus case studies in Figs. 18 and 19. However, if inhomogeneity scales are smaller such that average cloudiness or optical depth towards the sun is similar to that overhead, then the hemispheric solar flux variations remain small and an approximation by a homogeneous layer can be justified.

We assumed always smaller-scale inhomogeneities, when sunphotometer and broadband flux measurements varied less over time in Figs. 18 and 19. Whole-sky images of the cirrus cloud fields in Fig. 21 reveal that this assumption may be valid for the 26 November case. The 5 December case, however, demonstrates that weaker variations in the sunphotometer or flux measurements do not necessarily eliminate larger-scale inhomogeneities. On that day there appeared a cirrus cloud field with consistently larger optical depth to the south (and sun), as documented by whole-sky images for two different times in Fig. 22. It moved in an easterly direction, thus perpendicular to the direction of a sunphotometer measurements. This way, the large-scale inhomogeneity, judged by variations of sunphotometer data and broadband solar flux measurements, remained undetected. The persistent larger optical depths to the south were also confirmed by scanning lidar images (Eloranta and Forrest 1992), as illustrated in Fig. 23.

We applied a Monte Carlo scattering program to illustrate the impact of our modeling error, the inappropriate extension of the large (sunphotometer) cirrus optical depth to the whole sky. We approximated the atmosphere by four 3-km layers. The layer properties were defined by arrays of 12 × 12 3-km cubes whose optical properties could be independently chosen. We prescribed a solar zenith angle of 60°. We compared the results of two simulations with only changes to the top cirrus cloud layer, as illustrated in Fig. 24: The first simulation extended the large sunphotometer optical depth (0.9) to the whole sky, as we did in our radiative transfer model. The second simulation assumed a cirrus cloud band with a larger optical depth only in the direction of the sun, while everywhere else, including overhead, we assumed a lower cirrus cloud optical depth (0.3). This is a better characterization for the last hour of the 5 December case. In Fig. 25 the calculated transmissions at the surface are compared for both cases. Despite the overall larger transmission for the more realistic case, locally over the ground site the transmission is smaller by about 15%, due to a lack of diffuse radiation. This difference, even though here simulated only for visible light, is large enough to easily explain the detected solar broadband flux offset between model results and measurements for the 5 December cirrus case.

In summary, the cirrus cloud comparisons showed that in order to test current cirrus cloud models in case studies, the cirrus cloud structure must be well understood and represented in the model. If we use plane-parallel radiative transfer models, which are unable to treat horizontal inhomogeneities, we have to make sure that we characterize the cloud field at least by the correct average cloud optical depth. One measurement series across the cloud field is not sufficient, be it by an aircraft or by a single ground measurement (as the cloud moves by), such as a sunphotometer measurement time series. The cirrus cloud comparisons also showed that in order to correctly model cirrus solar radiative transfer, the cloud structural characterization may be at least as important as the characterization of the scattering properties on ice crystals. In light of all the recent advances in our understanding of the scattering on ice crystals, which are, at least partly, reflected in our radiative transfer model, we need to focus on measurements and definitions of inhomogeneity, preferably definitions that can be applied to plane-parallel radiative transfer models.

5. Conclusions

We presented simultaneous ground-based measurements and in situ data of cirrus clouds from the FIRE 1991 field experiment. We used these data to test the ability of current (simple) models to simulate solar radiative transfer processes in cirrus clouds.

The characterization of the macrophysical (cloud structural) properties by its average quantity appeared to be the biggest problem. We demonstrated that averages from measurements along a single path in an inhomogeneous cloud field do not necessarily apply to the entire cloud field. The use of such averages can cause serious misinterpretations. The definition of inhomogeneity in deterministic radiative transfer models is another problem. Even with measurements that capture the structure of the entire cloud field (such as scanning remote sensors) or give cloud-scale information by comparing different measurement averages, as in Fig. 26, we still have to find ways to implement the detected variability statistics into deterministic radiative transfer models.

The characterization of the microphysical (ice crystal) properties contributes to the uncertainty as well. Of particular concern is the frequent failure to reach the cirrus cloud top and the inadequate instrumentation to quantify the smaller ice-crystal concentrations. In addition, the scattering behavior of complex crystals is not completely understood. The simplifying breakup of complex shapes into individual independent pieces, as assumed in this study, may give at least an approximate answer.

Another uncertainty in solar radiative transfer modeling, unrelated to cirrus, is introduced with the inability of our model to simulate cloud-free conditions. Our model overpredicts the solar transmission by about 30 W m−2. There does not seem an easy explanation and it warrants further investigation, if this discrepancy is related to measurements or treatment in the model.

For future cirrus cloud field experiments, it is desirable to have observations under high sun-elevation angles. Most cirrus field experiments in the past, such as FIRE 1986 and FIRE 1991, were conducted at low sun-elevation angles, partly because during the late autumn season cirrus altitudes could be reached by most participating aircraft. However, at these low sun angles it is very difficult to quantify the cloud macrophysical effects; thus a successful separation of cloud microphysical effects, to verify microphysical model assumptions, is less likely. At required (sub-)tropical locations cirrus would be found at much higher altitudes. This eliminates many research aircraft used in past cirrus experiments. Aircraft that can reach and remain for extended time periods in the lower stratosphere are needed.

For future cirrus cloud field experiments, there has to be an emphasis on coordinated aircraft measurements. A coordination in time and vertical space was almost never achieved during past cirrus aircraft missions. However, in a quickly changing (cirrus cloud) environment, a coordination of measurements in time and vertical space is vital. Airspeed-coordinated flights, as illustrated in Fig. 27, should be designed to measure the (not only hemispheric) radiation simultaneously above the cloud top and below the cloud base. Then radiation measurements would define the radiative properties of the cloud in between and thus provide a framework in which microphysical and macrophysical model assumptions can be tested. Information on cloud boundaries, cloud structure, cloud optical depth, and even cloud particle size could be retrieved from (scanning) remote sensing equipment on these airplanes. In the absence of an additional in situ aircraft, a few balloon- or dropsondes could provide microphysical samples. There have been efforts to work towards such a setup during recent aircraft experiments (such as TOGA COARE, ARESE, or SUCCESS). Experiences from these field experiments should assist in the design of future cirrus multiple aircraft missions.

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APPENDIX

Microphysical Properties for Midlatitude Cirrus: Averages, Temperature Dependencies, and Correlations

Two-dimensional-probe measurements with the NCAR King Air aircraft below altitudes of 9.5 km (the ceiling for the aircraft) provide a good representation of cirrus cloud microphysical properties at midlatitudes. Balloonsonde samples indicated that the smallest sizes, which are overlooked by the 2D probes, are radiatively not very important at these altitudes. Thus, we used 2D-probe data to derive average properties for midlatitude cirrus.

The data of 60 horizontal flight legs from two cirrus cloud field experiments, FIRE 1986 and FIRE 1991, have been combined. Each flight leg was at least 30 km long. Histograms are given in Fig. A1 and average properties are summarized in Table A1.

The ice-crystal size was defined in terms of a radius. Ice crystals were considered to have the shape of a hexagonal column or that of a complex crystal. Complex crystals were approximated by an array of many individual hexagonal columns. We represented each column by a sphere with the same surface area. Such equivalency preserves the extinction. Our mean radius of 70 μm corresponds to hexagonal columns 240 μm long. Such sizes were already assumed in cirrus modeling studies decades ago (e.g., Wendling et al. 1979). Characteristic ice-crystal sizes from FIRE 1986 are usually larger than those from FIRE 1991. We attribute this to the stronger vertical windshear during FIRE 1986.

We calculated an average extinction of about 1.0 km−1, an average ice-water content of about 0.02 g m−3, and an average crystal concentration of about 0.05 m−3. Our simulated breakup of complex crystals (such as bullet rosettes) into individual crystals increased the concentration to 0.08 m−3. This breakup is necessary to capture the radiative effects of complex particles, whose scattering properties are much less understood than those of hexagonal columns. Table A1 also presents averages without the larger (>800 μm) and smaller (<150 μm) ice crystals. Clearly, the ice-water content is highly sensitive to the number of (even a few) large ice crystals, whereas the extinction is more sensitive to (somewhat uncertain) small crystal concentrations.

Using average properties from all 60 horizontal flight legs, we displayed in Fig. A1 histograms for four important cirrus cloud properties: ice-crystal sizes [again, in terms of radii of extinction (surface area) equivalent spheres], extinction, ice-water content, and temperature. Unfortunately, there were no clear relationships between these properties. We only noticed general trends, such as larger extinctions and larger sizes toward warmer temperatures. This is in agreement with other observations (e.g., Heymsfield and Platt 1984). The extinction trend, though, as illustrated by Fig. A2, seems too disperse to justify a general fit (as suggested by Platt and Harshvardan 1988). A size trend to larger ice crystals at warmer temperatures, as shown in Fig. A3, remains valid even after our modeled breakup of complex particles. While the overall picture in Fig. A3 is rather diffuse, individual cases display a clear trend, if we neglect the warmest cloud(-base) region where sublimation processes occur. We blame difference in dynamics and available moisture for the wide range for detected radii (±25 μm) for any given cirrus cloud temperature or altitude.

The wide range of possible sizes makes it impossible to determine a single characteristic relationship between extinction and ice-water content. A relationship between these properties, however, can be defined, if we specify the associated particle size. In Fig. A4 our data follow a simple relationship:
βexre0.755
where βex is the volume extinction (1 m−1), IWC is the ice-water content (g m−3), and re is the extinction equivalent effective radius (μm).

Our values for mass extinction (the ratio between extinction and ice-water content) at a particular size are slightly larger than those of the Ebert parameterization (Ebert and Curry 1992). Ebert also defines particle size via surface area equivalent spheres of hexagonal columns. Their parameterization, however, is based only on a few data and, more importantly, their assumed ice density of 0.85 g cm−3 seems too large, which can explain the discrepancy of their fit to our data.

Fig. 1.
Fig. 1.

Setup during the FIRE 1986 cirrus cloud field experiment. Little coordination among the aircraft never created collocations in time and space, yet profiles of radiation and microphysics are needed to verify models.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 2.
Fig. 2.

Setup during the FIRE 1991 cirrus cloud field experiment. Continuous ground measurements, when not obstructed by clouds at lower altitudes, guaranteed some collocations to aircraft measurements in vertical space. Case data were augmented by microphysical sondes and cloud radar.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 3.
Fig. 3.

Comparison of three sets (MRI, PSU, NOAA) of downwelling solar and infrared broadband flux measurements at the ground site under cloud-free conditions on 4 December.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 4.
Fig. 4.

Comparison of three sets (MRI, PSU, NOAA) of downwelling solar and infrared broadband flux measurements at the ground site under thin cirrus conditions on 5 December.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 5.
Fig. 5.

Comparison of two sets (MRI, PSU) of sunphotometer-derived cirrus cloud optical depths on 5 December. The included correction for forward scattering into the instrument’s field of view assumes small ice crystals.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 6.
Fig. 6.

Vertical (PSU) radar return signals for the 26 November cirrus cloud case over the ground site. Superimposed are locations of in situ microphysical measurements (solid line: King Air turboprop; double solid line: Sabreliner Learjet; dotted line: balloonsonde).

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 7.
Fig. 7.

Vertical (PSU) radar return signals for the 5 December cirrus cloud case over the ground site. Superimposed are locations of in situ microphysical measurements (solid lines: King Air; dotted line: balloonsonde).

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 8.
Fig. 8.

Vertical (PSU) radar return signal for the 6 December cirrus cloud case over the ground site. Superimposed are locations of in situ microphysical measurements (solid lines: King Air; dotted line: balloonsonde).

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 9.
Fig. 9.

Comparison of derived distributions for particle size and associated cross-sectional area from simultaneous cloud in situ measurements with an FSSP and a 2DC probe in a lower altitude cirrus on 25 November.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

 Fig. 10.
Fig. 10.

Measured ice-crystal size distributions with 2D probes of the King Air aircraft on 26 November. One-minute samples near five selected cirrus altitudes during an ascent over the ground site are compared. The shading within each size-bin portrays, via its darkness, the compactness of detected crystals. Size distributions after a modeled breakup of larger compact crystals into many hexagonal columns are shown by the dashed lines and the increased values for ice-crystal densities.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 11.
Fig. 11.

Vertical variation in cirrus size distributions. Ice-crystal sizes are expressed by their extinction equivalent spheres. King Air and Sabreliner 2D-probe averages at selected altitudes in a cirrus over the ground site on 26 November are compared. Concentrations at 20 and 30 μm are not measured but result from the modeled crystal breakup.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 12.
Fig. 12.

Variability on flight-leg averages for distributions of Fig. 11. Derived properties for characteristic size and extinction (averages are given in Tables 6 and 9) are presented with respect to a 6-km subscale. Also shown are other subsales for the 8.4-km altitude leg.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 13.
Fig. 13.

Variability on flight-leg averages in an optically thin cirrus on 5 December. Derived properties for typical size and extinction (averages are given in Table 7) are presented with respect to a 6-km subscale.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 14.
Fig. 14.

Vertical profiles of characteristic size and extinction from microphysical in situ measurements with 2D probes during rapid ascents and descents by the King Air over the ground site on 26 November. Also shown (dots) are properties derived from samples with the microphysical balloon sonde and properties representing horizontal flight-leg averages by King Air (K) and Sabreliner (S).

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 15.
Fig. 15.

Vertical profiles of characteristic size and extinction from microphysical in situ measurements with 2D probes during a rapid ascent and descent by the King Air over the ground site on 6 December. Also shown (dots) are properties from microphysical balloonsonde samples.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 16.
Fig. 16.

Quantification of the importance of small ice crystals. Six balloon sonde microphysical samples on 26 November are separately analyzed for ice crystals with maximum dimensions above and below 50 μm. Though fewer in number, larger sizes have more area and dominate radiatively.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 17.
Fig. 17.

Comparison between modeled and measured downward solar and infrared broadband fluxes at cloud-free conditions. Model simulations are compared to three independent measurements at the ground site for the daytime of 4 December (see Fig. 3). The lower panel presents, based on NOAA data, model deviations for the direct solar irradiance.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 18.
Fig. 18.

Comparison between modeled and measured downward solar broadband fluxes for the 26 November cirrus cloud case. The deviation is illustrated in the lower panel. Also shown (dashed line) are model results that are purely based on the cloud boundaries detected by the radar.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 19.
Fig. 19.

Comparison between modeled and measured downward solar broadband fluxes under optically thin cirrus conditions on 5 December. The deviation, illustrated in the lower panel, cannot be explained by the assumed crystal size.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 20.
Fig. 20.

Sensitivity tests with modified model assumptions to improve the model–measurement comparison of Fig. 19.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 21.
Fig. 21.

Whole-sky image at the ground site for the cirrus case on 26 November.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 22.
Fig. 22.

Whole-sky images of the ground site for the cirrus case on 5 December.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 23.
Fig. 23.

South–north scanning lidar return signals on 5 December for the times of the two frames of Fig. 22. The direction of the sun as seen from the ground site has been specially marked, as this path provides the basis for the sunphotometer-derived cirrus optical depth.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 24.
Fig. 24.

Modeling setup for three-dimensional (Monte Carlo) scattering simulations for the 5 December cirrus case. The atmosphere is approximated by (repetitive) sets of 3-km cubes, with one cirrus layer on top of three layers with Rayleigh scattering. Looking toward the sun (SSW direction), the ground site is located below the second column from the front. The horizontal dimension illustrates the (unchanged) atmospheric condition over time. The upper frame simulates an extrapolation of the sunphotometer optical depth (0.9) to the whole sky. The lower frame mimics a more realistic scenario with these optical depths only to the south but smaller cirrus optical depth over the ground site (0.3).

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 25.
Fig. 25.

Calculated visible transmissions at the ground for the two scenarios illustrated in Fig. 24.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 26.
Fig. 26.

Cirrus inhomogeneity related deviations from 10-s measurements by using longer time averages; here for surface hemispheric downward solar and infrared fluxes of the 5 December cirrus case. Even though designed as an illustration for possible averaging errors, it is apparent that a comparison of different time averages contains information about inhomogeneity scales.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Fig. 27.
Fig. 27.

Experimental setup desirable for future experiments to understand the radiative transfer processes in cirrus. Continuous vertical colocation can be reached via multiple coordinated (unmanned) aircraft of identical speed. Balloon- or dropsondes may provide in situ data.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

i1520-0469-54-18-2320-fa1

Fig. A1. Distribution of average microphysical properties in (continental) midlatitude cirrus. The data constitute aircraft 2D-probe averages from horizontal flight legs in cirrus cloud fields below altitudes of 9 km during the FIRE 1986 and FIRE 1991 cirrus field experiments.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

i1520-0469-54-18-2320-fa2

Fig. A2. Relationship between temperature and extinction for midlatitude cirrus. Each symbol, categorized by date, represents a horizontal flight leg of at least 30 km in a cirrus layer. Data are based on 2D-probe measurements with the King Air aircraft during FIRE 1986 and FIRE 1991.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

i1520-0469-54-18-2320-fa3

Fig. A3. Relationship between temperature and particle size in midlatitude cirrus. Each symbol, categorized by date, represents a horizontal flight leg of at least 30 km in a cirrus layer. Data are based on 2D-probe measurements with the King Air aircraft during FIRE 1986 and FIRE 1991.

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

i1520-0469-54-18-2320-fa4

Fig. A4. Relationship between mass extinction and particle size in midlatitude cirrus based on the same data that were used for Figs. A1 and A2. Also shown for comparison is a relation suggested by Ebert and Curry (1992).

Citation: Journal of the Atmospheric Sciences 54, 18; 10.1175/1520-0469(1997)054<2320:CCRAMP>2.0.CO;2

Table 1.

Instrumentation and its location.

Table 1.
Table 2.

Multipliers to apparent sunphotometer optical depths for three (1.0°, 1.2°, and 2.5°) field of view half angles. The derivation of a correct optical depthτc from a sunphotometer measurement requires the apparent optical depth τa, defined by the assumption of direct attenuation only [τa = −ln (I/I0)cosθ], to be increased by some multiplier M[τc = Mτa]. The multiplier, presented in the table, depends on the characteristic atmospheric particle size and the instrument’s field of view (FOV). For FOV half angle of 1° and cirrus with small ice crystals, M is about 2.

Table 2.
Table 3.

Aerosol optical depth averages from sunphotometer data.

Table 3.
Table 4.

Uncertainty for 2D-probe-derived cirrus properties.

Table 4.
Table 5.

King Air (100 m s−1) cirrus in situ constant altitude flight legs across Enid, Oklahoma, on 25 November.

Table 5.
Table 6.

King Air (100 m s−1) cirrus in situ constant altitude flight legs across Coffeyville, Kansas, on 26 November.

Table 6.
Table 7.

King Air (100 m s−1) cirrus in situ constant altitude flight legs across Coffeyville, Kansas, on 5 December.

Table 7.
Table 8.

King Air (100 m s−1) cirrus in situ constant altitude flight legs across Coffeyville, Kansas, on 6 December.

Table 8.
Table 9.

Sabreliner (200 m s−1) cirrus in situ constant altitude flight legs across Coffeyville, Kansas, on 26 November.

Table 9.
Table 10.

Cirrus properties from microphysical ascents and descents.

Table 10.
Table 11.

Importance (extinction) of small vs large ice crystals.

Table 11.
Table 12.

Model disagreement under cloud-free conditions.

Table 12.
Table 13.

Cloud microphysical assumption for cloud radar data.

Table 13.
Table 14.

Inhomogeneity and averages: Variations in inverted cirrus optical depths due to solar flux averages.

Table 14.

Table A1. Average cirrus properties from horizontal flight legs.

i1520-0469-54-18-2320-t101
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