Investigation of the effect of surface heterogeneity and …gautier/CV/pubs/Ricchiazzi_Gautier_Palmer_1998.pdf · zenith angle, and surface albedo are presented. Comparisons of the

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 103, NO. D6, PAGES 6161-6176, MARCH 27, 1998

Investigation of the effect of surface heterogeneity and topography on the radiation environment of Palmer Station, Antarctica, with a hybrid 3-D radiative transfer model

Paul Ricchiazzi and Catherine Gautier •

Institute for Computational Earth System Science, University of California, Santa Barbara

Abstract. We have developed and used a Monte Carlo radiative transfer code to investigate how surface topography and heterogeneous snow/ice distributions affect the downwelling irradiance at Palmer Station, Antarctica (64.76øS, 64.07øW). The Monte Carlo calculations treat a three-dimensional (3-D) atmospheric volume which extends from the surface to 100 km altitude and has a 20 km x 20 km footprint on the southwest coast of Anvers Island. The radiative transfer calculations include the effects of molecular

absorption, Rayleigh scattering, and clouds. The surface interaction is modeled explicitly. The trajectories of reflected photons are computed from stochastic bidirectional- directional reflectance functions, and their paths are traced through multiple interactions with complex surface features. Computed results for a range of cloud optical depth, solar zenith angle, and surface albedo are presented. Comparisons of the 3-D model calculations to plane-parallel model predictions show that the effective albedo which characterizes a given ice distribution is affected by regions surprisingly far from the point of interest. Under low clouds (Zclou d = 1 km), surface irradiance measurements over a snow surface are significantly affected by the dark ocean surface more than 7 km away. For the opposite case of irradiance observations over ocean, the effect of a distant snow surface is not significant at ranges greater than 2 or 3 km. Since the radius of influence depends on atmospheric transmission and surface albedo, the effective albedo varies spectrally. Neglect of this nonlocal albedo effect may significantly degrade the accuracy of radiation diagnostics that depend on spectral intensity ratios.

1. Introduction

The environment in high-latitude regions presents an un- usual challenge to remote sensing and surface radiation measurements interpretation. In addition to the well-known prob- lems discriminating between clouds and high-albedo surfaces, the low Sun angles make satellite observations of the surface difficult to interpret. Even areas of modest topographic relief are subject to large variations in the surface insolation due to shadowing and shallow angles of illumination. These geometrical effects must be properly considered in order to make quantitative use of the satellite observations.

The analysis and interpretation of surface radiation measurements in high-latitude regions represents an important challenge. The extensive surface coverage of snow and ice increases multiple reflection and causes a significant sensitivity of downwelling irradiance on the surface reflectivity. Under cloudy conditions the contrast between a snow surface and a dark ground cover can make a factor of 2 difference in the downwelling shortwave (SW) irradiance [Leontyeva and Stamnes, 1993; Gatdiner, 1987]. Rayleigh scattering of blue light causes a somewhat smaller enhancement in clear skies. Even if a measure of the spatially varying reflectance is available, it is not obvious how the information should be used to

•Also at Geography Department, University of California, Santa Barbara.

Copyright 1998 by the American Geophysical Union.

Paper number 97JD03629. 0148-0227/98/97JD-03629509.00

produce an effective surface albedo that could be used in plane-parallel radiative transfer (RT) models. In overcast conditions, physical considerations of cloud and surface reflectance suggest that the radius of influence of a given surface element is of the order of the cloud base height. Presumably, surface regions that remain uniform over a horizontal scale much larger than the cloud base height should be well charac- terized by the local surface albedo. However, in areas where the snow or sea ice coverage may vary on the kilometer scale, it is difficult to know how to weigh the importance of contributions at different radii around the sensor.

In an effort to quantify these effects we have developed the SAMCRT (Surface-Atmosphere Monte Carlo Radiative Transfer) code, which is designed to model radiative interactions of atmospheric radiation with complex surface features. During the austral spring, Palmer Station is subjected to episodes of significant UVB enhancements as the outer edge of the ozone hole passes over it. We have undertaken a thorough study of the radiation environment at this site [Lubin et al., 1994; Ricchiazzi et al., 1995] in hopes of developing insight into how surface radiation levels of UVB, UVA, and visible radiation can be derived from satellite imagery. Palmer Station is the home of the NSF UV spectrometer, which has provided spectral irradiance data in the UV and visible since May 1988 [Booth et al., 1994]. In addition, we have installed a Biospheri- cal Instruments GTR-100 radiometer which has two narrow-

band sensors at 410 and 936 nm and two wideband sensors

designed to match AVHRR channels 1 and 2. One of the motivations of undertaking this study is to help reconcile the

6161

6162 RICCHIAZZI AND GAUTIER: ALBEDO HETEROGENEITY AND RADIATION

satellite observation with surface measurements made with this

instrument.

The remainder of this text will describe the model and

present our computational results for the radiation environment of Palmer Station, Antarctica (64.767øS, 64.067øW). We describe our treatment of atmospheric and surface scattering in section 2. The effects of surface heterogeneity and topography on satellite remote sensing of surface albedo and cloud optical depth are discussed in sections 3.2.1 and 3.2.2. We discuss how surface irradiance varies in relation to the distance

from the snow/ocean boundary in section 3.3. While our computations are based on specific topographic characteristics in the vicinity of Palmer Station, we show in section 3.4 that the predictions of offshore surface irradiance have general appli- cability.

2. Radiative Transfer Model

2.1. Overview

A great deal of effort has gone into the exploration of how 3-dimensional morphology of clouds affects the Earth's radiation environment [e.g., Barker and Davies, 1992; O'Hirok and Gautier, 1997]. These effects may play an important part in explaining some of the disparities between current plane- parallel radiative transfer models and observational measures of atmospheric absorption [Cess et al., 1996]. However, in high- latitude regions, the strongest departure from one-dimensional (i-D) radiative transfer assumption is associated with the spatial distribution of high-contrast ocean and snow-covered surfaces. The prevalence of stratus clouds and the scarcity of vertically developed convective clouds decreases the importance of 3-D cloud effects.

In typical Monte Carlo simulations of 3-D cloud radiative transfer, photon trajectories are followed in detail through interactions with a large ensemble of Mie scattering centers [e.g., O'Hirok and Gautier, 1997]. For optically thick clouds a single photon may undergo hundreds of scattering events. Fol- lowing the photon trajectories in a Monte Carlo simulation at this level of detail is computationally expensive but is required to simulate photon transport through a cloud of irregular geometry, where it is not known in advance whether the next random scattering trajectory could be in directions conducive to photon escape. However, high-latitude clouds tend to have limited vertical extension and conform closely to idealized plane-parallel morphology [Lubin and Frederick, 1991]. Hence in SAMCRT we have avoided much of this computational burden by lumping together the multitude of interactions that take place within the cloud into a single computation that specifies the new trajectory of the reflected or transmitted photon. The rules that specify how the photon interacts with the cloud layer are then simply derived from plane-parallel radiative transfer.

The validity of this approach depends on the assumption that no horizontal transport takes place within the cloud. That is, the horizontal position of the photon remains fixed immediately before and after the cloud interaction. For optically thick clouds the horizontal displacement a photon undergoes in passing through the cloud layer is roughly approximated by the vertical thickness of the cloud [Marshak et al., 1997]. Hence disabling horizontal transport is equivalent to assuming that the cloud layer opacity is compressed to a scattering layer of zero thickness. This assumption limits us to cases where both the horizontal mean free path of photons within the cloud and

the cloud geometric thickness are much less than the horizontal length scale of cloud or surface variations.

2.2. Cloud Model

The microphysical properties of Antarctic stratus clouds have been measured near McMurdo Station, 75øS, by Saxena and Ruggiero [1990]. Their results indicate that cloud droplets consist mostly of liquid water. They measured a bimodal drop size distribution with a significant fraction of the droplets having an effective radius, R eff, less than 2 /xm. (The effective radius is defined as the ratio of the third to second moments of

the particle radius distribution function.) The effective radius of droplets in the second peak of the distribution is between 6 and 9 /xm, which is closer to the typical values reported by Paltridge [1974] for stratus clouds off the Australian coast (31øS to 37øS). Lacking in situ microphysical cloud measurements, in the present study we will assume clouds composed of liquid water droplets. The particle size probability function is assumed to follow a gamma distribution,

(r/ro)P-le -r/ro N(r) = r0F(p) (1)

where F is the gamma function, p is a fitting parameter, and r o - Reff/(p + 2). In our baseline set of calculations we chose values ofp = 7 and Ref f -- 10 /xm. In addition, to assess the sensitivity of our results to drop size distribution, we made a series of runs with an effective radius of 2/xm. The radiative scattering parameters, volume extinction coefficient, single- scattering albedo, and phase function moments, were calculated by using a Mie-scattering algorithm provided by Wis- combe [1980].

The discrete ordinates radiative transfer (DISORT) [Stamnes et al., 1988] model was used to compute the radiance field above and below the cloud layer for different solar zenith angles and for a range of total optical depth. In these calculations the radiance distribution was computed with 20 zenith angles and 20 azimuthal modes. In section 2.4 we discuss how these plane-parallel radiative transfer results are used to derive the probability functions for photon reflection, absorption, and transmission through the cloud layer.

2.3. Surface Model

The main issue we wish to address in this study is the effect of large albedo contrasts on the radiation environment. To limit the scope of the study, we will focus consideration on the two basic surface types that display maximal contrast: open ocean and snow-covered land or ice. Compared to the extensive set of spectral albedo measurements of either snow or ocean, there are relatively few data sources for bidirectional reflectance. For the ocean spectral reflectance we take the value provided by Reeves et al. [1975]. The strong winds, which are common to the Southern Ocean, roughen the water surface and diffuse the specular component of the surface reflection, strongly reducing the anisotropy of the reflected radiation. The exact form of the ocean bidirectional reflectance distribution

function (BRDF) will therefore depend on wind speed and direction. To avoid introducing these extra free parameters into our modeling study, we assume the sea surface acts as a Lambertian reflector. Since the overall reflectivity of the ocean is less than about 0.05 and is much smaller than the snow

albedo, the computed radiation parameters are insensitive to the details of the ocean reflectance.

RICCHIAZZI AND GAUTIER: ALBEDO HETEROGENEITY AND RADIATION 6163

Figure 1. Shaded relief map of the region included within the Monte Carlo computation grid. Palmer Station is located at the center of the grid.

Antarctica is one of the few places in the world where snow is essentially free of contamination from industrial pollution. There are only a few measurements of snow BRDF available, and there are no data sets available for fresh Antarctic snow

that provide information for the full range of incident zenith angle required by our model. Fortunately, the ability to model light reflection from a flat snow surface appears to be well developed [Wiscombe and Warren, 1980] and may, in some cases, be more reliable than in situ observations. Our approach will be to obtain the snow BRDF from explicit calculations made with DISORT. This technique was applied by Li [1982], who showed that the angular integrations of the resultant BRDF agrees very well with measured distributions of snow spectral albedo. Episodes of snow precipitation are quite fre- quent on Anvers Island and little time is available for snow particle growth through metamorphosis. Hence we assume the snow layer is composed of clean, fresh snow, with a small effective radius of 100 ktm. A Mie scattering code [Wiscombe, 1980] is used to derive the scattering properties of the ice particles. The scattering phase function resulting from these calculations are used in DISORT, after expansion in terms of Legendre and Fourier series. To limit the parameter space, we assume snow layers are semi-infinite, which for practical pur- poses requires a layer thickness greater than ---20 cm. In the next section we discuss how the radiance distributions com-

puted by DISORT are used to construct probability functions for reflection of photons off the snow surface.

We have exercised SAMCRT on several surface models, including cases displaying l-D, 2-D, and 3-D variations in both topography and surface type. We have also modeled the radiative effects of a 3-D surface grid with no topography but with snow/ocean surface contrast. Our first set of runs were based

on a surface grid that includes topographic information of the southwest corner of Anvers Island, over a 20 km x 20 km square centered on Palmer Station (Figure 1). The surface grid contains 10,000 facets, each of which is 200 m on a side. The vertical placement of the surface elements conforms to the topography of the island. The geometry of each surface ele-

ment is defined by the z-coordinate values at the four corners of the facet. The altitude within the facet is assumed to vary as a bilinear function (z - ax + by + cxy + d)of the E-W (x) and N-S (y) coordinates, ensuring a continuous surface across the facet boundaries. The slope of the surface at the point of intersection with a given photon trajectory is used to establish a local rotated coordinate system in which to apply the reflectance probability functions. The surface topography is obtained from contour maps published in 1963 by the British Directorate of Overseas Surveys. The maps have a horizontal resolution of about 100 m and are based on vertical air pho- tography performed by Hunting Aerosurveys Ltd. in Decem- ber 1956. It is unfortunate that a more recent survey of the Palmer Station area is not available. While general aspects of the surface shape are probably unchanged over the four decade interval since the British survey, small-scale features of the glacier are probably quite different, especially near the coast. For example, casual observations by station personnel indicate a 200 m recession of the glacial terminus immediately behind the station within the past decade. However, as shown in section 3.4, many aspects of the model results are insensitive to the details of the surface topography.

To properly model the surface interaction with a Monte Carlo model, statistical noise must be reduced by sampling each surface element a great number of times. In the runs presented here we use 108 photons. Thus 10,000 photons are potentially available to sample each surface element, though Rayleigh and cloud scattering tend to reduce this number. Each calculation required about 9 hours of processing time on a DEC Alpha workstation.

Since the photon trajectories obey cyclic boundary conditions, surface features within the model have a spurious 20 km periodicity. This means that the modeled region should be considered as one of an infinite planar array of identical islands. The radiation environment of Palmer Station is ade-

quately simulated if the influence of surface elements farther than 10 km have a small impact on local conditions. We will return to this question in section 3.


2.4. Photon Interaction With Scattering Plane

The angular probability distribution of reflection or transmission trajectories for a single photon incident on a scattering plane is directly related to the reflected radiance distribution produced by an incoming beam of radiation. The reflected energy per unit time and wavelength interval within a given differential solid angle, dfl, is given by [Lieu, 1980, equation

dE = txI(0o; Ix, (b)dD. (2)

where/x is the cosine of the angle between the outgoing propagation direction and the normal to the scattering plane, and I(00; •, 4>) is the reflected radiance distribution associated with the incoming beam of radiation incident on the surface at zenith angle 00. Since photon number is proportional to energy, the probability that a photon scatters within solid angle d/x d (b is given by

P(0o; •, &)d• d& = •I(0o; I•, (k)dl• drk/Fo (3)

where the azimuth angle 4> is measured relative to the vertical plane which includes the surface normal and the original propagation vector, and F 0 is the energy flux of photons incident on the scattering plane at zenith angle 00. Since some photons may be absorbed within the scattering plane, the integral of P(00; •, 4>) over solid angle may be less than 1.

To be of use in the Monte Carlo code, this probability distribution must be converted into a pair of probabilistic trajectory functions that specify the value of • and 4> of the scattered photons. This involves comparing the values of a series of uniform random numbers RNi in the interval [0, 1) to various test functions which determine the trajectory of the photon. First, the photon is either reflected or transmitted by the scattering plane depending on a comparison of RN• to the factors F ']'/F o and F ,l,/Fo, which are the transmission and reflection fractions computed from DISORT.

Next, the zenith angle is obtained by equating RN2 to the cumulative probability that the scattering zenith angle lies between 0 and

f o l'Xr • 2 7r Id6 I ( 0 0 ; Id6 , (•) ) d ck dO

RN2 = (4)

fo--1fo2'lI(Oo;l,4))d4)dl In this equation the /x integration is in the upper or lower hemisphere depending on the results of the first step (transmission, or reflection). The cosine of the zenith angle/xr of the reflected photon is obtained by using (4), solving for •r as a function of RN 2. The equation is solved numerically by interpolation on a precalculated radiance distribution table. The azimuthal direction is obtained by equating another random number to the conditional cumulative probability that a photon is scattered at zenith angle a cos (•) in the azimuth range 0 to

(Oo; 4,)a4,

= (5)

(0o; 4,)a4,

Finally, comparison with a fourth random number determines the sign of the relative azimuth angle. A different equation with integration limits from -,r to 4> could have been used to find 4> directly instead of just its absolute value. However, deciding the sign of 4> with a new random number ensures that the numerical evaluation of 4> does not introduce a statistical bias with respect to the left-right symmetry of the scattering process.

In our scheme, "photons" are never destroyed by interaction with the atmosphere or surface. Instead, a weighting factor Wp is used to carry forward the attenuation accumulated by the photon along its trajectory. Each interaction with the scattering layer causes a reduction in the photon weighting factor by an amount (F ,l, + F ']' )/F o.

2.5. Rayleigh Scattering

Because we are particularly interested in effects in the ultraviolet (UV) part of the SW spectrum, it is essential to include an accurate model of Rayleigh scattering. This introduces a bit more complexity into our model because Rayleigh scattering may occur at any altitude, in contrast to our assumption of a fixed altitude for cloud scattering. The distance to the next Rayleigh-scattering event along the current photon trajectory can be derived from

RN = 1 - e "r(N(z)-Nø)/t• (6)

where N(z) is the atmospheric column density, No is the column density at the current location of the photon, cr• is the Rayleigh-scattering cross section, and • is the cosine of the photon trajectory zenith angle. Note that • is negative for downwardly directed photons, making the quantity (N(z) - No)/lx negative for any photon trajectory. Also note that for upwardly directed photons, values of RN greater than 1 - e -ø'rNø/" do not yield a physical, nonnegative solution for N(z). These values of RN correspond to the population of upwardly directed photons that escape the atmosphere without undergoing a Rayleigh scattering.

The computation of the altitude at which the Rayleigh scattering occurs can be quite burdensome due to the time- consuming table lookup relating N to z. However, this over- head can be minimized by assuming an exponential air density profile. With this assumption the distance d to the next Ray- leigh-scattering event may be written as

h d = - I-•T log - log (1 - RN) + e -zø/h Tr (7)

where ,• is the Rayleigh-scattering optical depth at the surface, z 0 is the current photon altitude, and h is the number density scale height. A Rayleigh-scattering event will occur if the distance along the photon trajectory computed from this equation is less than the distance to the top of the atmosphere (TOA set at 100 km), or the nearest scattering surface (either a cloud layer or a surface element). In this case, the photon is moved to the scattering point and a new random trajectory is computed on the basis of the Rayleigh-scattering phase function [Lieu, 1980, equation (3.62)].

A similar scheme could be used to implement aerosol absorption and scattering. However, the visibility in the vicinity of Palmer Station commonly exceeds 30 km, even under the high- wind conditions that promote marine aerosol production. The vertical optical depths implied by this observation are too small to have a significant effect on the surface irradiance levels.


Hence we have decided not to include aerosols in this initial

version of the model.

2.6. Gas Absorption

The vertical distribution of gaseous absorbers is assumed to follow simple algebraic functions of altitude. This simplifies the computation and provides for an expedient method to compute the attenuation suffered along any given segment of the photon trajectory. We assume an exponential variation with height for water vapor and the uniformly mixed gases. For the calculations presented here, the total precipitable water and water vapor scale height is set at 0.2 g/cm 2 and 3.0 km, respectively. The uniformly mixed gases are set to standard number density ratios [McClatchey et al., 1972]. The ozone density distribution is specified as two piecewise constant values, with 25 Dobson units (DU) in the troposphere (z < 15 km) and 300 DU in the stratosphere (15 < z < 30 km). Absorption by gases is computed from analytic integrations of these constant or exponential functions between each photon scattering and is carried forward through successive scatterings in the photon weighting factor.

We have modeled the heterogeneous surface effect for radiation in four bands: narrow spectral bands at 300 and 410 nm and relatively broad bands centered at 630 and 875 nm that duplicate the filter functions of NOAA AVHRR channels 1 and 2. The three longest wavelength channels were chosen because they match the spectral channels of our Biospherical Instruments GTR-100 radiometer, with which we have obtained surface irradiance data at Palmer Station in austral

Spring of 1991 and 1994 [Lubin et al., 1994]. In addition, observational results for the 300 nm channel are available from

the NSF UV spectrometer. These bands are also interesting because they manifest interesting contrasts in their radiative transfer characteristics: (1) the snow reflectivity in both the 410 nm and the 300 nm bands is very large (over 95%), but the 300 nm band is subject to strong atmospheric absorption (due to ozone), while the 410 nm band is not; (2) snow reflectivity is also high in the AVHRR-1 channel, but Rayleigh scattering is much less than either the 300 nm or the 410 nm bands; and (3) compared to AVHRR-1, AVHRR-2 has greater atmospheric absorption due to water vapor and oxygen and significantly lower snow surface reflectivity.

To model the gas absorption within the 300 nm channel and two AVHRR channels, we use simple analytic curve fits to band-integrated LOWTRAN 7 transmission functions. The decrease in the photon weighting factor due to absorption by a single gas species is computed by multiplication by a transmission factor of the form

r(u) = exp (-au b) (8)

where a and b are the fit coefficients, and u is the path integral of the absorbing species. The photon weighting factor is reduced by the product of such transmission factors if more than one molecular species contributes to the absorption within the band. The double-exponential functional form of the transmission factor is the same as used to parameterize molecular line data in LOWTRAN 7. To reduce computational effort in the SAMCRT, we use a single-function evaluation to predict transmission over wide spectral bands, which in the case of the AVHRR-1 and AVHRR-2 channels, LOWTRAN would treat as hundreds of separate 20 cm- • intervals. Hence we should not expect this approach to match the LOWTRAN results

exactly. However, as Figure 2 shows, this simple parameterization does a good job of matching the ozone absorption at 300 nm and in AVHRR-1 and also accurately fits the water vapor absorption in AVHRR-1 and AVHRR-2. The oxygen A-band absorption in the AVHRR-2 channel is somewhat less well represented. However, this discrepancy only becomes large for trajectories that pass through more than 10 air masses.

3. Results

3.1. Verification for a Plane-Parallel Case

We have described several simplifications used within SAM- CRT that have been included to avoid excessive computational run times. The impacts of these approximations can be as- sessed by comparing results from SAMCRT for a strictly uniform and plane-parallel surface and cloud configuration with predictions from a plane-parallel model. Figure 3 shows the surface irradiance for a snow or ocean surface as predicted by SBDART (Santa Barbara DISORT atmospheric radiative transfer) [Ricchiazzi et al., 1997], a detailed plane-parallel radiative transfer code based on the DISORT radiative transfer

module and the LOWTRAN 7 gas transmission model. The SBDART computations were carried out at a spectral resolution of 5 nm on the standard subarctic winter atmosphere [McClatchey et al., 1972]. A solar zenith angle of 59 ø was used. Diamonds indicate the SAMCRT results for the same surface

conditions and solar angle but with the exponential atmospheric profiles discussed in section 2.5. The two codes are in good agreement over a large range of cloud optical depth and surface albedo. The results for the AVHRR-2 channel over a

snow surface show the greatest discrepancy, with the SAM- CRT predictions only a few percent greater than those from SBDART. It is interesting to note that this channel would also be the one most difficult to represent by a plane-parallel calculation at a single effective wavelength. The snow spectral reflectance varies significantly over the AVHRR-2 wavelength range, making it difficult to estimate an effective surface albedo which would apply for a wide range of cloud optical depths. Other sources of uncertainty in the treatment of AVHRR-2 is the less than ideal parameterization of the oxygen A-band absorption and the use of a simple exponential water vapor profile.

3.2. Implications for Satellite Remote Sensing

3.2.1. Retrieval of surface albedo. SW energy input in the summer season is one of the most important factors in deter- mining the annual mass balance of glacial ice sheets JAmbach, 1963]. Hence models which attempt to predict glacier dynam- ics must rely on accurate estimates of the surface albedo, particularly below the equilibrium altitude where most of the summer melt occurs. Satellite remote sensing of the surface is an important data source for the development of surface albedo parameterization in climate models used to predict surface albedo variations. It provides a high temporal resolution and global to regional scale spatial coverage which cannot be matched by in situ measurement. However, in some cases the relationship between TOA observations and surface albedo is difficult to obtain because standard plane-parallel radiative transfer models used in some current glaciology studies do not include the effects of surface topography or heterogeneity and assume a Lambertian BRDF for snow [e.g., Knap and Oerle- mans, 1996]. Retrieval schemes that ignore these 3-D effects may only be applied with confidence far from the glacial


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boundaries and where the surface slopes are small. This se- verely limits the utility of the plane-parallel technique since it cannot be used to obtain energy budget parameters near the ice edge. Since ablation occurs most rapidly in the boundary regions, this part of the glacier is also the most dynamic and least likely to have been sampled by up-to-date in situ measurements, making improved remote sensing methods even more important. In this section we investigate how 3-D surface effects degrade the accuracy of traditional plane-parallel retrieval methods and the extent to which they may be mitigated by geometrical corrections.

The Piedmont Glacier of Anvers Island, which occupies most of the land area of our surface grid, provides a good test case for the 3-D surface effect. Toward the northwest corner of

the surface grid the Piedmont Glacier reaches an altitude of about 300 m. The surface slope is small over much of the glacier but increases monotonically toward the coast, which runs diagonally from the northwest to the southeast corners of the grid. The surface altitude within a few kilometers of the north and east grid edges is ramped to zero to satisfy cyclic boundary conditions.

Figure 4 shows TOA radiance in AVHRR channel 1 simulated by SAMCRT under clear-sky conditions. These calculations are for the solar ephemeris of October 31, at 1300 and 1900 UTC. This corresponds to a solar zenith angle of 59.25 and azimuth angles of _+53.0 ø . North is toward the top of the image. Radiance is computed by binning the photons leaving the top of the numerical volume (at 100 km altitude) in terms of both propagation direction and horizontal position. To avoid introducing too much statistical noise, the angular bins are large, with the upper hemisphere divided into five equal solid angle bins, representing the radiation directed in the upward direction (zenith angle less than 37ø), as shown in Figure 4, and also in the forward, back, left, and right quadrants with respect to the solar beam. The x-y spatial bin to which a photon is assigned is obtained by extrapolating the trajectory back to sea level. Though the surface relief is not very large for this part of the island, the simulation shows a noticeable reduction of radiance for regions that slope down away from the illumination direction.

Figure 5 shows morning and afternoon transects of TOA radiance in AVHRR channels 1 and 2 for radiation within

several solid angle bins. The transect extends diagonally 10 km southwest to 10 km northeast of Palmer Station. The solid lines

indicate scaled radiance levels for radiation propagating in the forward and upward directions. Also shown is the average of the left, right, and back directions, which in these calculations are essentially equal. The significance of the dotted lines will be discussed below. The radiance levels are scaled so that the

incident solar flux reflecting from a perfect Lambertian reflector at the TOA produces a radiance value of 1. Clearly, for this example, topography has a significant effect on the observed radiance. As shown in Figure 5a, the radiance in the up direction 1 km northeast of the station is 25 % smaller than would be

observed 9 km farther toward the center of the island. The

underestimate of the surface BRDF would be larger than 25% after atmospheric effects are removed. As expected from considering the illumination geometry, the afternoon case (Figure 5b) shows less variation in radiance between 1 km and 10 km northeast of the station. Deviations from the Lambertian re-

flection model is most apparent for the forward scattering direction, which has a scaled radiance larger than the average for the other quadrants by 17 and 60% for AVHRR channels


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Figure 3. (a) Surface irradiance predictions in the 300 nm spectral band for a range of cloud optical depth over a homogeneous surface covered by snow (top curve) or ocean (bottom curve). The solid lines indicate model prediction from SBDART, a DISORT-based 1-D radiative transfer code. The diamond symbols show results from the Monte Carlo calculations. (b) Same information for the 410 nm spectral band. (c) Same information for the AVHRR-1 channel. (d) Same information for the AVHRR-2 channel.

1 and 2, respectively. The ratio of the forward radiance to the radiance in the other quadrants is nearly constant over a wide distance range northeast of the station in both AVHRR channels and for either the morning or the afternoon cases.

In these clear-sky calculations the atmospheric effect is en- tirely due to Rayleigh scattering. Since the atmospheric path length is greater for trajectories with larger zenith angles, the

scattering tends to decrease the anisotropy of reflected radiation at the TOA compared to that at the surface. For example, the AVHRR channel 1 radiance in the forward direction is

25% less at TOA than at the surface, while the difference for radiance in the upward quadrant is only 3.5% less. Because of the decrease in Rayleigh-scattering cross section with wavelength the atmospheric effect for AVHRR channel 2 is about

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0.00 0.200 0.400 0.600 0.800 1.00 1.20 1.40

Pl,•n•tory

Figure 4. Clear-sky planetary albedo predicted by SAMCRT in the AVHRR-1 spectral channel for (a) morning and (b) afternoon solar illumination angles. This figure shows results for the "upward" radiance bin, i.e., for photons with propagation zenith angle less than 36 ø .


O) 1.2 1.0

0.8

0.6

0.4

0.2

0.0

AVHRR- 1 AM

Radiance Bin . - -- Forward /•'•" --- Upward /

0 -5 0 5

1.0

0.8

0.6

0.4

0.2

0.0

-10

AVHRR- 1 PM

-5 0 5

C) 1.2 1.0

c 0.8 .o_

a: 0.6

o 0.4

0.2

0.0

0 -5

AVHRR-2 AM

Range (km) 10

AVHRR-2 PM d) 1.2

1.0

0.8

0.6

0.4

0.2

0.0

-10 -5 0 5 10

Range (km)

Figure 5. (a) Transect of the morning-case planetary albedo from Figure 4. The transect extends diagonally from the southwest to the northeast corners of the grid. Results for the forward and upward radiance bins are shown with black and dark gray lines, respectively. The average of the right, left, and backward radiance bins is indicated by the light gray line. The dotted lines show results for a simple linear fit to the Monte Carlo calculations. (b) Same a Figure 5a but for the afternoon solar geometry. (c) Same information as Figure 5a but for the AVHRR-2 channel. (d) Same as Figure 5b but for the AVHRR-2 channel.

half as large, and the TOA channel 2 radiance anisotropy is much larger than for channel 1.

Next we consider how to derive surface properties from satellite radiance measurements of regions with significant altitude variations. In order to derive surface albedo from sat-

ellite radiance measurements it is necessary to correct for atmospheric effects. In plane-parallel situations this may be accomplished either by applying 1-D radiative transfer methods or by assuming a simple linear relationship between the planetary albedo (TEA) and the surface albedo [Koepke, 1989]. It should be noted that the linear relationship between the surface and the planetary albedo is theoretically well founded only in plane-parallel situations, where the relationship follows from energy balance of the TeA and surface irradiance. Since it is not usually feasible to undertake a series of Monte Carlo runs to derive a more complicated relationship in the 3-D case, we need to determine whether a linear equation is adequate to relate surface reflectance to TeA radiance over a nonuniform surface. Consider a simple linear relationship of the form

COS • pt(O, 49)= a + b R(0o, 4>0; 0, 4>) (9)

cos 00

where pt(O, ok) is the planetary albedo, R(0o, qbo; 0, qb) is the surface BRDF, and the constants a and b are coefficients of

the linear fit. The angular coordinates (0, qb) and (0o, qbo) denote the zenith and azimuth angles of the satellite and Sun, respectively. The geometric factor (cos D/cos 0o), where/3 is the angle between the surface normal and the sunward direction, provides a correction for the solar illumination on a sloped surface.

A retrieval scheme based on (9) depends on having good in situ measurements of the BRDF. In order to fix the values of

the two fit coefficients the surface reflectivity for a given solar and satellite-viewing geometry must be accurately determined for at least one bright and one dark surface region. (Of course, a least squares fit on a greater number of data points would help reduce sampling bias.) If Pt is obtained from AVHRR imagery, the surface regions must be uniform over the scale of at least 1 or 2 km. In the Anvers Island case, in situ observations over the ocean and near the center of the glacier provide a good baseline to compute the fit coefficients. Taking the transect shown in Figure 5 as an example, we have computed the fit parameters which apply to surface regions at x - +_ 10 km. Each point on the transect was assigned the reflectivity of either ocean or snow depending on the underlying surface type. The quality of the fits are indicated by the dotted lines shown in Figure 5. Evidently, a simple parameterization of this type is adequate to capture most of the radiance variation computed by SAMCRT. The parameterization reproduces the


detailed Monte Carlo results to within a few percent over the entire range of radiance variations. This suggests that the technique could be used in inverse mode to derive the spatial distribution of BRDF as a function of Pt' A relationship between the BRDF and the angle-averaged surface albedo would then follow from available in situ measurements.

Clearly, this simple scheme is limited to situations with mild surface topography and is inappropriate where surface shadowing (/3 > 90) or direct surface-to-surface reflection is important. In these more complicated cases it may be necessary to use SAMCRT to derive a more complicated relationship between the planetary and the surface albedo. Of course, before we can rely on SAMCRT for this purpose, it must be validated against satellite and in situ observations. We intend to address this issue in future work.

3.2.2. Retrieval of cloud optical depth. Since the discov- ery of the Antarctic ozone hole in 1980, a number of research efforts have been initiated to assess the effects of increased

ultraviolet (UV) radiation on the biomass productivity of the Southern Ocean. These studies have been impeded by the large size and remoteness of the affected area and the inability of in situ measurements to provide accurate large-scale information on UV and visible surface radiation. Satellite observa-

tions may be the key to providing information on the required spatial and temporal scale. We [Lubin et al., 1994 (hereinafter referred to as LRGW)] have described a satellite-based surface irradiance mapping algorithm that uses observations from the total ozone mapping spectrometer (TOMS) together with several AVHRR channels to predict total atmospheric transmission. This algorithm depends on the fact that the ozone depletion occurs mainly in the stratosphere. Hence the total ozone measurements can be converted directly to maps of UV-B irradiance at the top of the troposphere. The transmission of the troposphere is derived in two steps. The first step is similar to the cloud optical depth retrievals carried out by the Inter- national Satellite Cloud Climatology Project (ISCCP) experi- ment [Rossow and Schiffer, 1991]. A plane-parallel radiative transfer model is run in inverse mode to obtain cloud optical depth from the AVHRR channel 1 measurements. Second, the RT model is used again in forward mode to obtain the transmission to the surface at various UV and visible wavelengths. The ISCCP derivation of cloud optical depth from TOA observations depends on an assumed value of surface albedo. Since the algorithm uses a 1-D radiative transfer model, the assumed surface albedo is assigned on the basis of the surface type of the associated pixel. The algorithm does not account for adjacency effects between bright and dark surface elements. In this section we discuss how such gradients in surface reflectance may affect the accuracy of the cloud optical depth retrieval used in the LRGW method.

Figure 6a shows the simulated TOA radiance in AVHRR-1 for cloud optical depth 10 and cloud height 1 km. We plot only the central 8 km x 8 km region around the station. The outer edge is clipped to exclude the spurious effects introduced by our use of cyclic boundary conditions. The planetary albedo decreases from a maximum value of about 0.70 a few kilome-

ters inland to a minimum of 0.42 at distances greater than --•2 km off the coast. This behavior is analogous to the blurring produced by a translucent screen placed a small distance above a high-contrast surface and is caused by the horizontal transport of photons below the cloud layer. More than a few kilometers from the coast, the photons that escape the island interior are essentially quenched by multiple reflections with

the dark ocean surface and make only a small contribution to the upwelling radiance above the cloud.

Following the LRGW procedure outlined above, we derived the cloud optical depth implied by this simulated radiance distribution. This involved using SBDART to compute radiance in the upper hemisphere at several cloud optical depths, assuming an oceanic surface albedo. To reconstruct the radiance parameter computed by SAMCRT, we integrated SB- DART's radiance output over the upward solid angle within 37 ø of zenith. The cloud optical depth was then obtained by table interpolation using the radiance field of Figure 6a as input. The results of this simulated retrieval are shown in Figure 6b. Because the LRGW algorithm uses a different and more complicated methodology to derive transmission over high albedo areas, we have masked out the radiance contours over Anvers Island and some smaller islands off the coast. Far

from the coast, the retrieval yields an optical depth of 10, i.e., the original input value. However, within about 2 km of the coast the retrieved optical depth is greater than the input, increasing to maximum values between 18 and 20 within Arthur Harbor (the inlet just north of the station).

Completing the final step in the LRGW procedure, we used the 1-D radiative transfer model in forward mode to retrieve

the tropospheric transmission shown in Figure 6c. For comparison we show in Figure 6d the simulated transmission to the ocean surface predicted by SAMCRT. Far from the coast, the retrieved transmission and the SAMCRT value are in good agreement and have values close to 0.41. However, the values diverge as the coast is approached, with the retrieved transmission decreasing due to overestimated optical depth near the coast and the simulated values increasing due to the contribution of photons below the cloud layer escaping from the island interior. Immediately adjacent to the coast, the two values differ by as much as a factor of 2. Though fairly large, the disagreement for low clouds is limited to narrow regions near the coast. If AVHRR imagery is used as the source of the planetary albedo, the effect would be difficult to observe, considering that this sensor has at best a 1 km resolution and often suffers from imprecise geographic registration. In any case, since the effect is confined to narrow areas near coastlines, it is probably unimportant when analyzing large areas of ice-free ocean. However, it may be important when considering the effect of ozone depletion on the phytoplankton bloom in early spring, which is initiated in narrow leads that form when large ice sheets break up.

It seems physically reasonable, considering the translucent screen analogy, to assume that the horizontal scale of the gradient effect may increase with cloud altitude. To test this hypothesis, we repeated the analysis for a cloud at 5 km altitude and the same cloud optical depth. The results are shown in Figure 7. In this case, simulated TOA radiance (Figure 7a) shows less contrast between the island interior and the ocean

and has a weaker gradient at the coast. The retrieved optical depth (Figure 7b) is close to the input value only when the distance from the coast is greater than about 3 to 5 km, but unlike the results of Figure 6, it increases to only 50% greater than the input value immediately adjacent to the coast. The retrieved transmission (Figure 7c) shows the same gradual variation with distance from the coast, decreasing from a maximum value of 0.40 in the "center" of the ocean to below 0.33

near the coast. The simulated transmission (Figure 7d) shows very little variation over the area of the grid. Compared to the simulated transmission, the retrieved values are 15% smaller


o)

o

-5

c) 5

o n,'

-5

TOA AVHRR-1 Radiance = . . i .... i .... i . i

...... ? •'"•:'•: 0.65

ø '"":•1 ........ • 0.60

:; :.

• !m r Station,, ,,,!Q. •/ ............ •0.55 o.so 0.45

b) .Re, tr!e.ve.d .Opt!c?l. D.ep, th,

..

'/-•, :?•?•.: ....... Palmer Station

-5

20.0

18.0

16.0

14.0

12.0

0.40 10.0

-5 0 5 -5 0 5

Retrieved Transmission

............

,

Max--"0.44

-5 0 5

Range E-W (km)

__0.74

__0.70

__0.66

__0.62

__ 0.58

__ 0.54

__ 0.50

__0.46

0.42

0.38

0.34

0.30

d)

-5

Actual Transmission i?--•"•"•'¾•:'"' "•. • -•,,: •'•:.:' ':':..;;" ' .... ' ' ' 0.74

........ :•-:•-. 0.66 '• •'•"••,:• Max =0.73

:..:.... .::

..... ':::::•::)....-:::• . ,•.....,.,..•

:" 0.42

Min=0.40 0.•8

0.•4

0.•0

-5 0 5

Range E-W (km)

Figure 6. (a) Monte Carlo prediction of AVHRR-1 planetary albedo for a cloud of optical depth 10 and height I km. (b) Retrieved cloud optical depth assuming radiance field of Figure 6a and assuming independent pixel approximation, i.e., no horizontal transport of photons. (c) Transmission to surface assuming cloud optical depth field of Figure 6b and 1-D radiative transfer. (d) Actual transmission include 3-D effects, computed by SAMCRT.

far off the coast and 45% smaller near the coast. Though these results are indicative of the horizontal scale of the nonlocal

effect, they are probably less accurate than the results for the 1 km cloud. Since SAMCRT uses cyclic boundary conditions, areas near the grid boundary will be influenced by artificial surfaces just outside the grid. The ocean location about 7 km southwest of the station is more than 5 km from any substantial high-albedo area. Yet this location shows significant nonlocal influence, much of which is probably due to regions outside the grid. Despite this source of inaccuracy, these results indicate that the horizontal range of nonlocal effects is greater than 5 km. This suggests that the spatial resolution of the LRGW or ISCCP methodologies may be poor when applied to high- contrast scenes with substantial cirrus or altostratus cloud lay- ors.

3.3. Implications for Surface Radiation Diagnostics

In 1988 the National Science Foundation initiated a program to monitor levels of surface UV and visible radiation at several high-latitude sites in the southern hemisphere. The main goal of this program is to assess the effect that springtime

ozone depletion has on the radiation environment at the surface. To carry out the observations, scanning spectroradiom- eters were deployed at four sites: McMurdo Station, Amund- sen-Scott Base (south pole), Ushuaia, Argentina, and Palmer Station. Of these installations, Palmer Station most closely represents the maritime Antarctic region and is most relevant for assessing ecological impacts. With the UV spectrometer providing an irradiance measurement standard the ocean area within several kilometers of the station has attracted intense

research scrutiny [Smith et al., 1995]. However, as shown in Figure 8, the irradiance measured at the station may misrep- resent the radiation environment offshore. This SAMCRT cal-

culation for cloud optical depth of 20 shows that surface irradiance at 300 nm (normalized to one at Palmer Station) decreases by nearly a factor of 2 within about 3 km of the coast. Hence it is crucial to understand how the spectral irradiance varies with distance from the coast in order to help tie the UV and visible radiation measurements taken at the station to

nearby offshore observations. In addition, since ocean ice may partially or completely fill the area around the station at any time during the spring season, a proper interpretation of the


o)

I z

-5

TOA AVHRR-1 Radiance ß 0.60

•0.58

• 0.54 '• 0.52

0.48

0.46

0.44

b) Retrieved 0 tical Depth

o

-5

0 .. Palmer Station

-5 0 5

16.0

15.0 14.0

13.0

......... 12.0

11.0

10.0

Retrieved Transmission

............. , , , 0.50 C I [ 0.4•

5 •-•__•, o.4• . 0.44

t½ 0 "'•x.-. Palmer Station """'•'•• 0.40 0.38

...... ...... ""J 0.36 ;:!'::':'••'O :•'•:••!:• 0.34 -5 ..• ß ,:./ai;"'"'"':.:;;:.:::::::.":':'.•.:::•:.•:::i.',':. "":..'.:' o - 0.32

d)

-5

• ,--'-'-"•. 0.30 ...... i 'il" ß - - "-' i

-5 0 5 -5 0 5

Ronge E-W (kin) Ronge E-W (kin)

Figure 7. Same as Figure 6 but for a cloud height of 5 km.

Actual Transmission ............ , . , 0.50

.__.q 0.48 ø 0.46

'•"'• o.4o -- .• 0.38

' 0.36

0.34

0.32

.... 0.30

UV monitor data is not possible without knowing how nearby ocean ice distributions affect the surface radiation. Hence it is

equally important to understand how irradiance depends on distance inland from the ice edge.

In this section we discuss surface irradiance predictions generated by SAMCRT for a range of clear-sky and overcast conditions. A nominal cloud height of I km will be assumed, consistent with the observed low cloud heights around the station. The cloud optical depth used in the calculations are referenced to a standard wavelength of 0.55 /.•m, so all simulations at a given cloud optical depth have the same precipitable water amounts. The results shown in Figure 6, for AVHRR-1 and a 1 km, optical depth 10 cloud, are generally representative of the predictions for other channels and cloud optical depths. All the simulations had maximum variation within a few kilometers of the coast, with a gradient direction roughly perpendicular to the coast. The details of the spatial dependence is presented in Figure 9, which shows transects of the surface irradiance (solid lines) in four spectral bands, AVHRR-1, AVHRR-2, and 410 and 300 nm. The transoct path runs diagonally from the southwest to the northeast corner of the surface grid, and each line is labeled on the right with the cloud optical depth used in the calculation. These calculations assume a solar zenith angle of 59.25 ø and a solar

Surface Irradiance, 500nm

0 ........ .....-.....'"' + Palmer Stodon ..

-5 { ""• 0.75

-4

Min=0.68

0.70

..

-• 0.65

,,.,

-5 ., 0.60

-5 -4 -5 -2 -1 0 1 2

Ronge E-W (kin)

Figure 8. Surface irradiance at 300 nm for cloud optical 20 and cloud height 1 km. Irradiance values are scaled to ] at Palmer Station.


AVHRR-2 AVH RR- 1 ... b) 500 Cl) lOOO ................

800 ..... . . .. 400

E• 600 300

400

200 • 1 O0 o o

-20 -10 0 10 20 -20 -10 0 10 20

410nm c) lOOO ...................

8OO

600

400

2OO

...................... d) 0.40

• -'-D ..... "• o : 0.30 5 ':

• 1 o : 0.20 2o •

• 40: O. lO 0.00

-20 -10 0 10 20 -20 -10 0 10

SW •- Range (km) ---> NE SW •- Range (km) ---> NE

30Ohm

0

5

10 . 20

." 4-0 2O

Figure 9. (a) Surface irradiance transects AVHRR-1 for cloud optical depths of 0, 5, 10, 20, and 40. The transect line runs from the southwest to the northeast corners of the surface grid. Results for a homogeneous surface of 0, 50, and 100% snow are indicated by squares, triangles, and diamonds, respectively. (b) Same information for AVHRR-2. (c) Same information for the 410 nm band. (d) Same information for the 300 nm band.

azimuth of 53 ø (under cloudy skies, other values of solar azimuth produced nearly identical results). For comparison, we also show plane-parallel results generated by running SAMCRT with horizontally uniform surface configurations composed of homogeneous mixtures of snow and ocean. Plane-parallel results for 0, 50, and 100% surface snow fraction are indicated by the squares, triangles, and diamonds, respectively. If the distance to a contrasting surface type is large enough, the effects of the snow/ocean albedo contrast should be negligible, and the 3-D results should approach the predictions for 0 or 100% snow fraction. Taking into account the cyclic boundary conditions (and the artificial surface contrast at the grid boundaries), the points at _+7 km should most closely approach the plane- parallel limit. With regard to radiation measurements obtained right at the station, it has been assumed in previous research [Lubin and Frederick, 1991] that the radiation environment is well modeled by assuming a surface albedo between 0.4 and 0.5, representing a sort of local area average of the surface albedo.

Consider first the AVHRR channels. In the clear sky case (r = 0) the SAMCRT transects for AVHRR channel 1 (Figure 9a) show very little dependence on surface condition and agree well with the plane-parallel results. As the cloud optical depth is increased, the effect of the underlying surface becomes more apparent, with the effects of multiple reflection significantly enhancing the irradiance over the snow-covered areas. The irradiance approaches its mid-ocean value just a few kilometers southwest of the station. Near the center of the ocean

(range = -7 km) and at the coast the SAMCRT results are just slightly less than plane-parallel predictions for 0 and 50% snow. In contrast, the irradiance transect to the northeast of

the station continues to increase until nearly the mid-island point (range = +7 km) is reached. Here the irradiance must begin to decrease again because of the cyclic boundary conditions. The simulated irradiance at +7 km is significantly less than the plane-parallel predictions for 100% snow. This is due to the influence of the ocean surface to the south and west and

also to the artificial ocean areas at the northern and eastern

edges of the grid. We have repeated these calculations with a surface grid artificially enlarged in the horizontal dimension by a factor of 5 but otherwise the same as the grid used in the runs shown in Figure 8. These enlarged grid calculations (not shown) indicate that the AVHRR-1 irradiance predictions on the nonuniform grid do indeed attain the values predicted for a homogeneous surface but only when the distance from the coast exceeds about 10 km. The nonlocal effect is of much

longer range over a high-albedo surface. Since the snow reflectance is very high, photons originating near the island center easily escape to dark surface regions where they are even- tually absorbed. In contrast, the area near the ocean "center" is not easily affected by brighter regions. Any photons escaping the island interior are absorbed by the nearshore ocean surface before they can contribute significantly to the downwelling irradiance further offshore.

The irradiance transects for AVHRR-2 (Figure 9b) match the 0 and 50% predictions about as well as for AVHRR-1 but approaches the 100% snow value more closely. The range of the nonlocal effect over snow is reduced mainly because the reflectivity of snow in the AVHRR-2 channel is significantly smaller than that of AVHRR-1. In addition, there is greater absorption by water vapor and oxygen. Both factors decrease


the importance of multiple reflection and cause a decrease in the influence of distant surface elements.

A similar line of reasoning explains the behavior of the 410 and 300 nm channels. In these spectral bands the snow albedo is very high and nearly the same for both channels. There are no significant atmospheric absorbers in the 410 nm band (Fig- ure 9c). As a result, the irradiance transects show large deviations from the 100% snow predictions, an indication of strong nonlocal influence. In contrast, the 300 nm spectral band (Fig- ure 9d) is absorbed by tropospheric ozone. As for the case of the AVHRR-2 channel, this tends to suppress the nonlocal effect and causes the inland results to approach the 100% snow value at large cloud optical depth. Both the 300 and the 410 nm bands show large deviations from the uniform surface results that actually increase with decreasing cloud optical depth over the ocean. The relatively greater importance of Rayleigh scattering compared to the two AVHRR channels causes these strong nonlocal surface effects. For example, at the 300 nm band under clear skies, Rayleigh scattering may cause the surface irradiance over a bright surface to be up to 50% greater than over a dark surface. Since the average altitude at which reflected photons are Rayleigh scattered is greater than 4 km for either the 300 nm or the 410 nm bands, the effective horizontal range of influence of distant surface elements can be much greater than for low clouds.

To assess the effect of cloud microphysics, we also made a series of runs with the cloud drop size effective radius set to 2 /•m, instead of the nominal 10/•m size used for the rest of the simulations. According to Mie-scattering theory the smaller drop size should result in slightly less forward scattering and slightly greater extinction efficiency (resulting in about 5% greater cloud optical depth than the nominal case). As shown in Figure 10, the results for the AVHRR-1 band are qualita- tively very similar to the nominal case shown in Figure 9a.

Recent studies have shown that biological production in the maritime Antarctic is affected by the ratio of irradiance in the UVB band to that in the UVA or the photosynthetically active radiation (PAR) bands [Smith and Cullen, 1995]. We have not calculated the surface effect for the UVB or PAR spectral profiles, which are thought to be important to biological productivity. However, we can estimate the expected surface effect using a ratio of the 300 nm and AVHRR-1 bands. Figure 11 shows a transect of this quantity (normalized to 1 at Palmer Station) for the same conditions as used for Figure 9. Inter-

AVHRR- 1,

1000 I ................... 800 , ß

E • 600 '

• 5 E

• 400 10

• 20 20o 40

.............. ! .........

-20 -10 0 10 20

SW ,- Ronge (km) -, NE

Figure 10. Same as Figure 9a except for a cloud drop effective radius of 2/•m.

1.15

1.10

1.05

1.00

0.95

0.90

- 0

500nm/AVHRR 1

Optical Depth

½ • 0 ,• ,.• 5 [] [] lO • • 20

• • 40

-5 o 5

Range (km)

Figure 11. Ratio of surface irradiance in the 300 nm and AVHRR-1 channels. Results for cloud optical depths between 0 and 40 are shown.

estingly, this ratio shows a larger ocean-island gradient under clear skies, with the ratio decreasing with increased distance from the coast. In the clear-sky case, the ratio drops by 10% within about 4 km southwest from the coast. For the overcast

conditions that are more typical of the region (optical depth 10 and greater [Lubin, 1994]), the spectral ratio remains within 5% of the coastal observations. Over snow the ratio increases

by about the same factors. This result indicates that the relative strength of Rayleigh scattering has the largest effect on the spatial variation of the band ratio. Each spectral band sepa- rately has a large spatial variation when moving from a dark to bright surface, but since the radiative properties of snow and clouds are nearly the same for both channels, these variations tend to be suppressed in the ratio.

3.4. Comparison to a 2-D Surface Model

The 3-D results discussed above would be more generally useful if the surface irradiance predictions are relatively independent of the specific features of the surface topography near the station. We have explored this issue by comparing the 3-D results with a simple 2-D model consisting of a straight coastline separating uniform regions of ocean and snow. To model this situation, we use a linear surface grid made up of 160 surface cells and covering a total distance of 80 km. The left and right half of the grid is filled with ocean and snow, respectively. All surface elements throughout the grid are at sea level, eliminating any surface topography effects. Since cyclic boundary conditions still apply, photons passing out of a cell in a direction perpendicular to the long axis of the grid will reenter that cell from the opposite face. The variation along the long axis is also cyclic. A relatively long grid is used, so a small influence is felt from cyclically repeated, contrasting surface elements. We have noted above that the results of our first set

of 3-D runs suggest that the 20 km x 20 km surface grid may have been too small to properly simulate conditions far from the grid center, especially over the glacier. Hence to ensure a valid comparison with the 2-D model, we reran several 3-D


2O

10

-10

-2O

0.40

0.35

0.30

0.25

0.20

0.15

Figure 12. Contours of surface elevation for the enlarged surface grid. Palmer Station is located at the center of the grid. The solid dots indicate the placement of grid cell centers that lie on the island boundary. Transects of surface transmission (or irradiance) within this grid are used in the comparisons of Figure 13. The transect path is indicated by the solid diagonal line.

simulations on an enlarged surface grid that covers a geograph- ical area of 50 km x 50 km centered on the station. Contours

of surface elevation within this area is shown in Figure 12. The dotted line indicates the boundaries of the snow-covered region.

A comparison of the surface transmission in the 300 nm and AVHRR-1 channels is shown in Figure 13. These calculations are for a solar zenith angle of 59.25 ø. We have verified that the predictions do not depend on solar azimuth for the cloud optical depths 10 and greater. The plotted quantity is the total transmission to the surface, defined as the ratio of the surface irradiance (onto a horizontal surface) divided by the solar irradiance at the top of the atmosphere. The results from the 2-D simulation are indicated with a solid line, while the two horizontal gray lines indicate 1-D results for 100% ocean or snow. The dotted line represents the surface transmission from the 3-D simulation, along a transect indicated by the diagonal line in Figure 12, while the dashed line shows results for another 3-D calculation for which the surface elevations throughout the grid are zero. The 2-D and both 3-D calculations produce very similar predictions for the net transmission to the ocean surface, and all tend to saturate to the 100% ocean value within about 8 km of the coast. These results imply that the offshore surface irradiance predictions discussed in section 3.3 are not very sensitive to the surface topography of the island. Hence they should be representative of any ocean region bor- dering an extensive snow-covered area, assuming a relatively straight coastline.

Over snow, the predictions diverge to a greater extent. The 2-D model results closely approach the 1-D predictions for uniform snow at a horizontal range greater than about 15 km. In the AVHRR-1 channel (Figures 13a and 13b) both the nominal and the zero-altitude 3-D results drop below the 2-D predictions, mainly because photon diffusion from the island center toward the ocean is more efficient in the 3-D case.

When topographic effects are included, the transmission to the surface drops noticeably, especially for thick clouds and at

ranges greater than 10 km (Figure 13b). The reduced transmission is due to the downward slope of the surface just past the 10 km range. The inclined surface introduces a bias into the photon random walk which causes enhanced diffusion away from the island apex. The sloping surface tilts the central axis of the BRDF distribution so that more scattered photons are reflected in a more horizontal direction toward the ocean.

Though this same mechanism is active in the 300 nm channel (Figures 13c and 13d), the irradiance predictions for the 3-D model with surface topography exceed both the 2-D and the flat 3-D models. In this case, the increased surface altitude at the + 10 km range reduces the photon path length between cloud and surface and thereby decreases absorption due to tropospheric ozone. This effect more than compensates the enhanced downslope diffusion.

The 2-D model and both 3-D calculations predict that the transmission directly at the coast is greater than obtained by assuming 1-D radiative transfer (RT) and a uniformly mixed surface composed of equal parts of snow and ocean. The 1-D RT result for uniformly mixed snow, and ocean is indicated in the figure by "x." Interestingly, the coastline value predicted by the 2-D model, marked with a diamond symbol, is within a few percent of the geometric average of the 1-D results for 100% ocean and 100% snow. This result appears to be quite general. It is accurately replicated in a series of 2-D simulations of the 300 nm and AVHRR-1 channels, for cloud optical depths between 5 and 40, for cloud heights between 1 and 5 km, and for clean and "dirty" snow (i.e., snow albedo reduced 20%). The coastal transmission values from the two 3-D models are

less than the geometric average but still significantly greater than that obtained by using 1-D RT and an equal mix of ocean and snow.

4. Summary and Conclusions We have carried out a modeling study of the radiative effects

of surface albedo contrast in the vicinity of Palmer Station. The analysis is based on a newly developed 3-D radiative transfer model that explicitly includes radiative interactions between plane-parallel clouds and heterogeneous surface topography and also includes the effects of gas absorption and Rayleigh scattering. Applied to the coastal area around Palmer Station, results from the model indicate a number of new effects that

bear on both satellite and surface data interpretation. Satellite remote sensing of cloud optical depth requires reg-

istration of satellite images with a surface albedo map. We have found that bright surface features affect the planetary albedo beyond the coastal margins delineated by the albedo map. The width of the affected region appears to be about twice the cloud altitude, which implies significant degradation of spatial resolution in cases of high clouds over high-contrast surfaces.

The downwelling irradiance below a cloud is affected by the brightness of distant surface elements. The radius of influence of this surface effect is greater near the center of a large high-albedo surface than over an extensive dark region. On the basis of calculations with low clouds (1 km altitude) we found that any dark surfaces within a 7 km radius can lower the irradiance below the value expected for a uniform snow- covered region. In contrast, irradiance values close to that expected from a uniform ocean surface are obtained at offshore locations more than about 2 km from the coast. These

estimates scale with cloud altitude. In clear skies and at shorter


o)

0.6

E 0.4

0.2

0.0

b)

0.6

E 0.4

0.2

0.0

AVHRR- 1 -7-- 10 c) 5OOnm '7-= 10 0.0020

100% snow .•- ......... :-. -.•..-...-..,

-

- . ............. 100,.% oceon -

2D

3D z=O

.... i .................. i ......... i ....

//,"';;• "' ..... ,•.,.. - 100% snow ..>. • --..--7

- j( - .... 100% oceon

-- _

.... i .................. i ......... i . . . I

O.O015

O.O010

0.0005

0.0000

-10 0 10 20 -10 0 10 20

Ronge (kin)

.... i .................. i ......... i ....

100% snow •. -• ''-"--'--.T "" - -

- 100% oceon - .

.... i .................. i ......... I ....

AVHRR- 1 'r=40 d) 500nm 'r=40 0.0020

O.O015

O.O010

0.0005

0.0000

.... i .................. i ......... i ....

.

_ _

100% snow ...... :; "'-...-. ....

_ /..;';"•••'-• _ /

- • _

...... 100%. oceon

.

.... i .................. i ......... i ....

-10 0 10 20 -10 0 10 20

Ronge (km) Ronge (km)

Figure 13. Comparison of 3-D and 2-D simulations for the coastal region near Palmer Station. Figures 13a and 13b show results for AVHRR-1 at cloud optical depths of 10 and 40, respectively. The same comparison is shown for the 300 nm channel in Figures 13c and 13d. In each plot, the results from the 2-D simulation are indicated with a solid line, while the two horizontal gray lines indicate 1-D results for 100% ocean or snow. The dotted line represents the surface irradiance from the 3-D simulation, along a transect indicated by the diagonal line in Figure 12, while the dashed line is a similar calculation with the surface elevations throughout the grid set to zero. The diamond symbol indicates a transmission value of V'T ... T ..... where T .... and T .....are the transmission factors computed assuming 1-D RT and a uniform snow and ocean surface, respectively. The "x" symbol indicates the transmission value computed by assuming 1-D RT and a uniform and equal mix of snow and ocean.

wavelengths, Rayleigh scattering of reflected radiation can significantly increase the surface irradiance. The effective scattering altitude of reflected radiation between 300 nm and 400 nm is greater than 4 km. Hence increasing the optical depth of low clouds may actually decrease the irradiance contribution from surface elements more than 5 km away. These nonlocal effects need to be considered when relating the measurements obtained with the NSF UV monitor system at Palmer Station to ocean measurements taken far from shore or in the vicinity of the station. Furthermore, it should be noted that seemingly intuitive estimates of an "effective" surface albedo to be used

with 1-D RT do not faithfully represent the surface radiation at a coastal location. According to our 2-D Monte Carlo simulations the surface transmission at the coast is close to the geometric average of the "pure ocean" and "pure snow" values. Assuming 1-D RT and using an effective surface albedo between 0.4 and 0.5 [Lubin and Frederick, 1991] significantly underestimates the transmission.

The radius of influence of the nonlocal effect is smaller for

wavelengths with significant atmospheric absorption or reduced snow reflectivity. This brings into question a wide range

of spectral diagnostic procedures that have been developed and applied to data from coastal radiation-monitoring facili- ties. For example, total ozone amount above Palmer Station is obtained by the ratio of two narrow UVB bands [Lubin and Frederick, 1991]. We have noted in another study [Gautier et al., 1996] that surface ozone retrievals based on spectral ratios are sensitive to cloud amount and surface albedo. Since the

two channels have different ozone absorption cross sections, their response to distant surface features will be different. This introduces a dependence on the snow and ice distribution around the station which could distort ozone retrievals.

In future work we intend to validate the predictions of SAMCRT by comparison with observations obtained in the area around Palmer Station. If the model results prove valid, we will begin a program to develop simple parameterizations of the nonlocal surface effect.

Acknowledgments. This work was supported in part by the Atmo- spheric Radiation Measurement (ARM) Program of the U.S. Depart- ment of Energy (DOE) under grant 90ER61062 and in part by the National Science Foundation under grant OPP9317120. We would like


to thank William O'Hirok for several helpful suggestions which con- tributed to the design of the Monte Carlo model.

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C. Gautier and P. Ricchiazzi, Institute for Computational Earth System Science, University of California, Santa Barbara, CA 93111. (e-mail: [email protected])

(Received June 9, 1997; revised December 4, 1997; accepted December 11, 1997.)

Investigation of the effect of surface heterogeneity and …gautier/CV/pubs/Ricchiazzi_Gautier_Palmer_1998.pdf · zenith angle, and surface albedo are presented. Comparisons of the

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