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A feasibility study of the estimation of net solar radiation at the sea surface using NOAA-9 AVHRR data Gu, Jiujing 1991

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A FEASIBILITY S T U D Y O F T H E E S T I M A T I O N OF N E T S O L A R R A D I A T I O N A T T H E S E A S U R F A C E USING N O A A - 9 A V H R R D A T A By Jiujing Gu B. Sc. in Physics, Shandong Colledge of Oceanography, 1984 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E in T H E F A C U L T Y O F G R A D U A T E S T U D I E S A T M O S P H E R I C S C I E N C E We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A Aug. 1991 © Jiujing Gu, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of AtwQfiphlVe •& , ie infg ^YO^YIMAA The University of British Columbia Vancouver, Canada Date DE-6 (2/88) Abstract A feasibility study is presented of the use of a simple physical parameterization to esti-mate sea-surface net solar flux from radiance measurements taken by the Advanced Very High Resolution Radiometer (AVHRR) on board National Oceanic and Atmospheric Ad-ministration (NOAA) polar orbiting satellites. The scheme, which is based on Gautier's parameterization for geostationary satellite data, is revised for application to AVHRR data at high latitudes. The revised technique employs relationships among cloud optical and microphysical parameters, cloud broadband radiative properties, and the AVHRR channel radiances derived using a 24-band ^-Eddington radiative transfer model. The <5-Eddington model is used to test the sensitivity of the daily mean surface net flux to variations in ozone amount, column water vapor amount, surface albedo, cloud optical thickness, cloud fraction and droplet size. Over typical ranges of these variabilities, the uncertainty of daily mean surface net solar flux is less than 6 W ro-2 for the clear case. For the cloud case, the main uncertainty of surface net flux is due to the variations in cloud optical depth and cloud fraction. The typical sensitivities in cloud optical depth and cloud amount introduce variations in the surface net flux of 17 Wm~2 and 9 W ra-2, respectively. Based on these sensitivity studies, a modification of Gautier's simple physical model is proposed. This modification calculates cloud optical depth and droplet effective radius from the top of the atmosphere (TOA) upward fluxes in AVHRR channel 1 and 3, and then uses these derived parameters, with solar zenith angle, to estimate cloud albedo and absorptance. To compare the original and the modified Gautier model, the Slingo 6-Eddington model is used to simulate the satellite and pyrometer measurements in the ii real world. Simulation studies under standard midlatitude summer conditions show that the original model may produce surface net flux errors of over 30 Wm~2, mainly due to the poor estimation of cloud broadband absorptance. In contrast, the modified model produces errors of less than 3 W m~2 . However, both models produce errors of similar magnitude when the standard atmospheric condition is perturbed. This shows the need to accurately estimate atmospheric parameters. In recognition of 1) the large sensitivity of the satellite measurements to the atmo-spheric scattering, 2) the low sensitivity of the surface net flux to the sea surface albedo found from these sensitivity studies, an alternative clear sky retrieval scheme is proposed. Several existing techniques for estimating radiatively important cloud and atmo-spheric parameters by means of remote sensing are applied to the AVHRR data collected during the First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment in marine stratocumulus clouds in the western Pacific. The results are com-pared with in situ measurements made by the aircraft and radiosonde during the same experiment. The preliminary comparisons show promise in retrieving these parameters from the AVHRR data. iii Table of Contents Abstract ii List of Tables vii List of Figures viii List of Main Symbols xiii Acknowledgements x v i i 1 Introduction 1 1.1 Overview of satellite sea surface solar radiation estimation 3 T . l . l Motivation 3 1.1.2 Previous work 6 1.2 Overview of Satellite Cloud and Atmospheric Parameter Retrieval . . . . 10 1.3 Objectives 13 1.4 Preview of subsequent chapters 15 2 Estimation of Sea-Surface Net Solar Flux: Model Studies 17 2.1 Description of the Slingo Model 17 2.2 Description of the Gautier Model 20 2.2.1 Gautier Clear Model 20 2.2.2 Gautier Cloudy Model 22 2.3 Sensitivity Studies 26 2.3.1 Model Atmospheric and Surface Conditions 26 2.3.2 Sensitivity of Fluxes under Clear Conditions 27 iv 2.3.3 Sensitivity of Fluxes under Cloudy Conditions 36 2.3.4 Sensitivity of Cloud Optical Properties . 41 2.3.5 Summary and Discussion 46 2.4 A Variant of the Gautier Cloudy Model 50 2.4.1 Alternative Algorithm for Cloud Albedo and Absorptance Calcu-lations . . .-. 50 2.4.2 Simulation Study 54 2.4.3 Discussion 57 2;5;'>- A•••Plausible'Scheme for the Clear Case 57 3 Retrieval of Key Parameters for Net Solar Flux at the Sea Surface from A V H R R Data 61 3.1 Cloud Optical Depth and Effective Radius Retrieval . 61 3.1.1 The Method 61 3.1.2 Retrieval with the Slingo Model 65 . 3.1.3 Comparison with Aircraft Data 66 3.1.4 Discussion 72 3.2 Cloud Detection and Cloud Fraction Estimation 74 3.2.1 The Method 74 3.2.2 Limitation of the Spatial Coherence Method 75 3.3 Column Water Vapor Amount Retrieval . 77 3.3.1 The Method . 77 3.3.2 Comparison of Satellite Retrieved Column Water Vapor with Ra-diosonde Measurements 77 3.3.3 Discussion 79 4 Conclusions and Future Extensions 81 Appendices 86 A Elementary Facts from Two-stream Radiative Transfer 86 B Variability of Atmospheric and Surface Conditions 89 C A V H R R data Calibration 9 1 C.l Visible Channel Calibration . . 91 C. 2 Infrared Channel Calibration . 92 D Comparisons Between Slingo Model Results and in situ Measurements 94 D. l Comparison with Surface Flux Measurements under Clear Case . . . . . 94 D.2 Comparison with Aircraft Flux Measurements 95 Glossary 98 Bibliography 100 vi List of Tables 1.1 Band differences between the A V H R R and V I S R R 15 2.1 Band limits (um), incident solar irradiance at T O A (%) and the gaseous absorption considered in Slingo model 19 2.2 Wavelength.es of A V H R R channels and wavelength limits used in the Slingo model for simulation (unit: fim) 20 2.3 Sensitivity of surface net flux (AFnet) at 12:30 and daily mean surface net flux (Fnet) for midlatitudes due to the variation of column water vapor W v , ozone amount W0 and surface albedo Ag under clear case (unit: Wm~2). 35 2.4 Sensitivity of surface net flux (A-F^t ) at 12:30 and daily mean surface net flux (AFnet) for midlatitudes summer due to the.variation of various parameters under cloudy case (unit: Wm~2). . . 40 3.1 Comparison between satellite inferred cloud droplet effective radius r* and airplane measurements r™ in am. 9Q, 6 and c6 are the area averages of solar zenith angle, satellite viewing angle and relative azimuth, respectively. The values in brackets are variances of measurements. The numbers under the measurements are the times the measurements taken 68 vii 2.5 The solid curves are a) surface net flux Fnet , b) TOA upward fluxes in the AVHRR channel 1 chl f, c) channel 2 ch2 T , and d) channel 3 ch3 f from sunrise to sunset, during which the solar zenith angle changes from 90° to minimum and returns to 90°. The error bars are uncertainties of these fluxes due to 50% variation in column water vapor amount (mid-latitude summer clear condition). The 'x' in (c) is discussed in section 2.3.5. . . . 29 2.6 Similar to figure 2.5 except that the error bars are uncertainties of the • fluxes due to approximately 90% variation in column ozone amount. The - V in' (b)' is"'di's'cussed^ n*' section--2^ .3.5 30 2.7 Similar to figure 2.5 except that the error bars are the uncertainties of the fluxes due to 20% variation in surface albedo. The 'o and x' in (b) and (c) are discussed in section 2.3.5 31 2.8 Similar to figure 2.5 except for under cloudy case 37 2.9 Similar to figure 2.6 except for under cloudy case 38 2.10 Similar to figure 2.7 except for under cloudy case . 39 2.11 Cloud channel 1 albedo Rci vs. (a) cosine of solar zenith angle yu0; (b) cloud optical depth r c; (c)water vapor amount above cloud Wv\ (solid line), within cloud Wv2 (dash line), under cloud Wv$ (dotted line); and (d)surface albedo Aa. r\ is the cloud droplet effective radius at cloud top. 43 2.12 Cloud channel 3 albedo i?^ vs. (a) cosine of solar zenith angle fi0; (b) cloud optical depth Tc; (c)water vapor amount above cloud wv\ (solid line); within cloud wv2 (dash line), under cloud wv$ (dash-dotted line); (d)i?c3 with homogeneous cloud droplet effective radius vs. r c. r\ is the cloud droplet effective radius at cloud top. 44 viii 2.5 The solid curves are a) surface net flux Fnet , b) TOA upward fluxes in the AVHRR channel 1 chl | , c) channel 2 ch2 | , and d) channel 3 chZ | from sunrise to sunset, during which the solar zenith angle changes from 90° to minimum and returns to 90°. The error bars are uncertainties of these fluxes due to 50% variation in column water vapor amount (mid-latitude summer clear condition). The 'x' in (c) is discussed in section 2.3.5. . . . 29 2.6 Similar to figure 2.5 except that the error bars are uncertainties of the fluxes due to approximately 90% variation in column ozone amount. The 'o'in (b) is discussed in section 2.3.5 30 2.7 Similar to figure 2.5 except that the error bars are the uncertainties of the fluxes due to 20% variation in surface albedo. The 'o and x ' in (b) and (c) are discussed in section 2.3.5 31 2.8 Similar to figure 2.5 except for under cloudy case 37 2.9 Similar to figure 2.6 except for under cloudy case 38 2.10 Similar to figure 2.7 except for under cloudy case 39 2.11 Cloud channel 1 albedo Rc\ vs. (a) cosine of solar zenith angle /z0; (b) cloud optical depth r c; (c)water vapor amount above cloud Wv\ (solid line), within cloud W„2 (dash line), under cloud Wvz (dotted line); and (d)surface albedo Aa. r\ is the cloud droplet effective radius at cloud top. 43 2.12 Cloud channel 3 albedo R& vs. (a) cosine of solar zenith angle fio; (b) cloud optical depth r c; (c)water vapor amount above cloud wv\ (solid line); within cloud i w v 2 (dash line), under cloud wv3 (dash-dotted line); (d)i?c3 with homogeneous cloud droplet effective radius vs. r c. r\ is the cloud droplet effective radius at cloud top 44 ix 2.13 Cloud albedo Rc vs. (a) cosine of solar zenith angle fiQ at r\ = 16.6^m; (b) cloud optical depth T c at \IQ = 0.78; (c)water vapor amount above cloud wvi (solid line), within cloud wv2 (dashed line), under cloud itfv3 (dotted line) at r\ = 16.6/jra and U-Q = 0.78; and (d) surface albedo Ag at r\ = 16.6/jm and uQ = 0.78 47 2.14 Cloud absorptance absc vs. (a) cosine of solar zenith angle fio at r\ = 16.6/zm; (b) cloud optical depth r c at u-0 = 0.78; (c) water vapor amount above cloud wvi (sohd line), within cloud wv2 (dashed line), under cloud iu v 3 (dotted line) at r\ = 16.6^m and fio = 0.78; and (d) surface albedo Ag at r\ — lQ.Qfim and n0 = 0.78 48 2.15 Cloud broadband albedo Rc vs. cloud channel 1 albedo RcX for (a) varying cosine of solar zenith angle (0.087 < /x0 < 1) at a certain r c; (b) varying cloud optical depth (0.01 < r c < 32) at a certain / J 0 ; (c) varying surface albedo (0.05 < Ag < 0.2) at r c = 2 and a certain r\; (d) varying water vapor above cloud (0.20cm < Wv\ < 2.37cm) and within cloud (0.18cm < Wv2 < 1.92cm) at r c = 16 and r* = 16.6/im. "L" ("H") is for low (high) value of the varying variable. '+' is from the plot of equation (2.7). . . . 52 2.16 Similar to figure 2.15 except the vertical axis is cloud broadband absorp-tance absc. '+' is from the plot of equation (2.8) 53 2.17 The error of surface net flux (a) in the Gautier model (b) and the variant one for midlatitude summer condition at ^ 0 = 0-78 (unit: Wm~2). . . . . 55 2.18 Errors of the Gautier model (Gautier minus Slingo) in predicting (a) cloud broadband albedo and (b) cloud broadband absorptance for cloud droplet effective radius at cloud top r\ = 4.4^m (solid), r\ = 10.4/jm (dashed), r\ = 16.4/jm (dash-dotted) at fi0 = 0.78 56 x 2.19 Similar to figure 2.17, except that the column water vapor amount is changed by 50% 57 3.1 Similarity parameter for liquid water as a function of wavelength A for particle radius = 10/im (solid), 3//m (dashed) and lfim (dash dotted). . . 63 3.2 Sketch for retrieval of r* and r* from a given pair of cloud albedo in visible and near IR (R*vU, R*nir) 64 3.3 X and Y axes are cloud channel 1 and 3 isotropic albedo, respectively. Lines are obtained from the Slingo model for various values of cloud optical depth r c (dash lines) and droplet effective radius at cloud top r* (solid lines) at 60 = 35.0°. Dots are calculated from the AVHRR data on July 7 1987 for longitude between 120.9° and 122.6°W, and latitude between • 31.0° and 32.0°N 66 3.4 Relative geometry between sun and satellite. Pixels in region I have rela-tive azimuth between sun and satellite c6 close to 180°, whereas pixels in region II have <f> close to 0° 68 3.5 Lines show relationship between the albedo in the AVHRR channel 1 and. 3 from the Slingo model for various values of r c (dash lines) and r\ (solid lines) for 80 = 39° . The dots are from July 14 1987 satellite measurements of cloud isotropic albedo in the relevant channels, a) for pixels from the area with <6 = 179° , and b) for pixels from the area pixels with 4> = 5.5° . 70 3.6 Intensity of the radiation diffusely reflected by a plane-parallel homoge-neous atmosphere containing spherical monodispersion; TJ is scattering optical depth; the size parameter x (defined in appendix A) equals 10, the refractive index m = 1.342,60 = 60° (after Dave, 1970) 71 xi 3.7 Sketch for spatial coherence method. The x-axis is local mean radiance, and y-axis local standard deviation. The cluster around A and B represent 3.8 Local standard deviation vs. local mean radiance obtained from calcula-tion to 2x2 arrays of July 7 1987 the AVHRR LAC data. The area is the same as figure 3.3. . 76 3.9 Comparison of the column water vapor amount obtained from the CLASS (solid line) and the AVHRR (dots) for the area over the San Nicholas Island from June 30 to July 19,, 1987. 79 D.l Surface downward a) total flux and b) diffuse flux from the Slingo model (solid) and from observations (dashed) for July 19, 1990. . . . . . . . . . 96 D.2 Flux profiles from July 2 1987 cloud sounding (solid) and from Slingo model (dashed) 97 xii List of Main Symbols Symbol Ac Cloud fraction (page 11, 74) Ag Sea surface albedo (page 21, 25) Ai Reflectance factor of the earth-atmosphere system in AVHRR channel i (page 91) A* Reflectance factor of the NASA 30-inch integrating sphere source (page 92) d AVHRR measured counts in channel i (page 91) Eabs Flux absorbed in the atmosphere (page 59) Fd Downward solar flux at the surface (page 21) Fv Downward flux in the VISSR visible channel at the TOA (page 21) FQ Downward solar flux at the TOA (page 21, 28) Fnet Net solar flux at the surface (page 21) Ke Mass extinction coefficient (page 86) K3C Mass scattering coefficient (page 86) 70 Solar constant (page 20, 26) Ii Filtered extraterrestrial solar irradiance in AVHRR channel i at mean earth-sun distance (page 91) L{ Filtered radiance measured by channel i of AVHRR (page 91) LWC Liquid water content (page 88) LWP Liquid water path (page 88) N Number of cloud droplets per unit volume (page 88) P(i>) Phase function (page 86) Qext(x) Efficiency factor (page 87) Rc Cloud albedo for solar flux (page 24, 41) xiii Rd Cloud albedo for flux in the AVHRR (or VISSR) channel 1 (page 24, 42) Rc3 Cloud albedo for flux in the AVHRR (or VISSR) channel 1 (page 42) Rnir Cloud bidirectional reflectance for flux in near infrared (page 63) Ruis Cloud bidirectional reflectance for flux in visible (page 63) SW I Radiance received by VISSR visible channel (page 21) T Air temperature (page 78) T\ Brightness temperature calculated from the AVHRR channel 4 (page 77) T$ Brightness temperature calculated from the AVHRR channel 5 (page 77) T\ Transmittance of the sensor (page 92) U Relative humidity (page 78) V Ratio of F0 to F (page 21) Wv Effective column water vapor amount (page 27) W0 Column water vapor amount (page 27) a Albedo of the atmosphere for solar flux (page 59) a ( « i ) Absorptance of slant path of water vapor U i for the direct solar flux (page 21) a(uia) Absorptance of slant path of water vapor above the cloud for the direct solar flux (page 24) a(uif,) Absorptance for slant path of water vapor below the cloud to the direct solar flux (page 24) absa Absorptance of the atmosphere for solar flux (page 59) absc Cloud absorptance for solar flux (page 24, 41) b Transmittance of the atmosphere for solar flux (page 59) e Vapor pressure (page 78) es Saturation vapor pressure (page 78) g Asymmetry factor (page 62, 86) xiv m,- Imaginaxy part of the index of refraction (page 87) mr Real part of the index of refraction (page 87) n(r) Cloud drop size distribution (page 87) ozl Absorptance of ozone in the visible bands for direct solar flux (page 21) oz2 Absorptance of ozone in the visible bands for diffuse solar flux (page 21) ozZ Absorptance of ozone in the ultraviolet bands for direct solar flux (page 21) P Air pressure (page 78) Water vapor mixing ratio (page 78) r Cloud droplet radius (page 87) re Cloud droplet effective radius (page 88) rl Cloud droplet effective radius at cloud top (page 41) s Similarity parameter (page 62) z Height (page 86) <* Solar altitude (page 26) <*o Albedo of the earth-atmosphere system for solar flux (page 59) CCi Albedo of the earth-atmosphere system for flux in AVHRR channel 1 (page 60) a2 Albedo of the earth-atmosphere system for flux in AVHRR channel 2 (page 60) OCR Rayleigh scattering coefficient for direct solar flux (page 21) Rayleigh scattering coefficient for diffuse solar flux (page 21) ow(A) Rayleigh scattering coefficient for direct flux in VISSR visible channel (page 21) OCRl(X) Rayleigh scattering coefficient for diffuse flux in VISSR visible channel (page 21) PaX Volume absorption coefficient (page 28) X Size parameter (page 86) X V « Diffusion length (page 71) A Wavelength (page 17, 28) ho Cosine of solar zenith angle (page 41) Single scattering albedo (page 62, 86) Relative azimuth angle between the sun and the satellite (page 67) + Scattering angle (page 86) p Density of the medium (page 86) pi Density of liquid water (page 88) T Optical depth (page 86) Absorption optical depth (page 45) Ta\ Monochromatic absorption optical depth (page 28) Tc Cloud optical depth (page 13, 41, 87) i Tc Scaled cloud optical depth (page 62) TRX Monochromatic Rayleigh scattering optical depth (page 28) T\ Cloud scattering optical depth (page 45) 6 Satellite viewing angle (page 5, 67) Oo Solar zenith angle (page 5, 67) xvi Acknowledgement First of all, I would like to acknowledge gratefully Dr. Phil Austin, my supervisor, for his guidance of the thesis project, and also for his help in many aspects of my academic life. I would also like to thank the following: Dr. Bill Large for his initiating the interesting topic as well as the financial assistant at the early stage of the work, Dr. William Hsieh for many discussions along the way, and Dr. Howard Freeland for his encouragement and interest in the work. The assistance from Mr. Denis Laplante and Mr. Jim Mintha in using computing resources is also deeply appreciated. The association with my fellow students at the Departments of Oceanography and Geography will long be remembered. On more a personal note, I am grateful for the emotional comfort and moral support from my family over these years, which has been much of the source of impetus in my life. xvii Chapter 1 Introduction Two factors in the earth's climate system have been identified to be of crucial im-portance. One is the oceans, especially their role in the global energy cycle. The other is clouds, in particular, their influence on the radiation field. The significance of the oceans is due to their capacity to serve as a huge heat reservoir, e.g., 25-30% more heat is stored in the oceans than in the land at the same latitude (Tolmazin, 1985), and the fact that the oceans act as effective meridional heat transport agents via vigorous oceanic circulations (e.g., the Gulf stream). The importance of clouds lies in their large spatial coverage, and their unbalanced effects on the earth's radiation budget. For example, due to the higher albedo of the stratrocumulus (30% - 40%) than sea surface (10%), the solar radiation absorbed by the sea surface is considerably reduced in the presence of clouds. On the other hand, the incident longwave radiation at the sea surface is slightly enhanced due to the thermal emission of cloud base. Thus, the presence of the low level clouds results in a cooling effect on the sea surface. However, it is in these two factors that our understanding of the earth climate is fragmentary. For oceans, figure 1.1 shows that it remains uncertain whether the heat transport in the Pacific and Indian oceans is poleward or equatorward. One of the difficulties in making such calculations is estimation of the solar energy absorbed by the sea which, in turn, depends crucially on correct estimation of the incident solar radiation (insolation) at the sea surface (Bretherton, et al. 1982; Dobson and Smith, 1988). For clouds, the uncertainties are in their coverage and radiative effects. Even with the satellite 1 Chapter 1. Introduction 2 Figure 1.1: Oceanic heat transport in units of 101 5W from a variety of sources. In some cases authors give more than one value (giving an indication of error bounds). Different characters stand for different authors. Note the different sign of heat transport in the Pacific and Indian Oceans (from Anderson, 1983). data, the accurate estimate of cloud amount is still difficult due to the limited spatial and temporal resolution of the measurements, and a lack of the sensitivity of the sensor to the outgoing radiance (Shenk and Salomonson, 1972). The competing shortwave and longwave effects of clouds on both the top of the atmosphere (TOA) and surface, which vary with cloud type, surface type and atmospheric conditions, are not well understood. In the next two sections, we present brief overviews of the efforts made to obtain a better estimation of sea-surface solar radiation and to retrieve cloud parameters from satellite data. Chapter 1. Introduction 3 1.1 Overview of satellite sea surface solar radiation estimation 1.1.1 Motivation Given that the present uncertainty in determining the oceanic meridional heat trans-port is the consequence of the poor estimation of the energy input from the sun, it becomes necessary to impose a stringent accuracy requirement on its determination. Suppose that the total amount of heat within an ocean basin remains constant over the time period pertinent to climatological studies. It then follows from the conservation of energy that a required accuracy of 20% (or 0.2 petawatts) for the meridional heat transfer at 24° N across the Atlantic corresponds to a 10Wm~ 2 accuracy for the long-term mean sea surface net flux, which is downward flux (i.e., insolation) minus upward flux (Bretherton, et al. 1982). The latter in turn imposes at least 1 0 W m ~ 2 accuracy on estimates of the sea surface insolation. - However, it is impossible to get this accuracy using in situ measurements due to the inadequate spatial and temporal resolutions of current sea surface observations. It is also impossible to achieve this accuracy with empirical formulae which relate surface fluxes to hourly cloud amount and cloud type from standard meteorological surface observations. Dobson and Smith (1988) tested six empirical formulae for sea surface insolation with long time-series radiation measurements at several ocean weather stations, concluding that none of these, formulae are able to achieve the 10 Wm~2 accuracy for long-term mean insolation required for climate studies. They further suggested that it is the con-siderable spatial and temporal variability within any observational category of clouds which resulted in the poor insolation estimation. A variety of alternative approaches using satellite data have recently emerged, with Chapter 1. Introduction 4 results which indicate the possibility of obtaining the desired accuracy of surface insola-tion (Bretherton, et al. 1982). Such a possibility exists largely due to the higher temporal and spatial resolution of satellite data in comparison with the in situ measurements. On the other hand, unlike the conventional measurements, satellite sensors measure nearly instantaneous radiance at the top of the atmosphere (TOA) within a certain bandwidth, viewing angle and area. Thus, a successful use of the satellite data for daily mean surface insolation involves the following steps: • calibration of satellite data • inference of surface insolation using the TOA narrow band radiances • estimation of daily mean insolation by extrapolating the available satellite data points over the relevant period of time and integrating Given that the calibration is done properly, and that the extrapolation of the inso-lation over daytime can be accomplished reasonably well with the Geostationary Oper-ational Environmental Satellite (GOES) data by virtue of its high temporal resolution (one image, per 30 minutes), then the whole task of estimating daily mean sea surface insolation with satellite data essentially reduces to the second step. Even then, the infer-ence of surface insolation is still complicated since satellite sensors measure the combined radiative effects of all the physical processes shown in figure 1.2 in several wavelengths. The uncertainties of the atmospheric conditions (e.g., amount of absorbing gases, clouds, aerosols, and surface albedo), and the enormous computer requirement for accurate ra-diative transfer calculation make global estimates infeasible in the near future. Chapter 1. Introduction 5 reflection subsurface scattering Figure 1.2: Processes influencing the solar radiation over ocean. The solar zenith angle 8Q is the angle between the, direction of the incident solar radiation and the direction of zenith. The satellite viewing angle 9 is the angle between the direction of the outgoing radiance towards the satellite and the direction of zenith. Chapter 1. Introduction 6 1.1.2 Previous work A variety of methods have been developed to simplify the problem, which may be classified into three categories on the basis of how these physical processes are dealt with. The first, hereafter referred to as the statistical approach, ignores the complicated physical processes and makes direct use of simple or multiple linear regression of normal-ized satellite-measured brightness and normalized atmospheric transmittance obtained from in situ radiation measurements (e.g., Hay and Hanson, 1978; Tarpley, 1979). While conceptually simple, a statistically optimized relation hides the relationship among at-mospheric, cloud, and surface conditions and atmospheric transmittance. Furthermore, a statistical relation may change with time and location (Raphael and Hay, 1984). The second, involves radiative transfer modeling (e.g., Pinker and Ewing, 1985). In contrast to the statistical approach, many radiatively important physical processes and the interactions among them are incorporated into the model. For example, Pinker and Ewing (1985) use a twelve-band £-Eddington radiative transfer model, a simplified radiative transfer model (see appendix A for detail). Parameterizations are made for the parameters describing the absorbing and scattering processes associated with gasses, aerosols and clouds in each band and each atmospheric layer. However, they are limited mainly by the difficulty of providing input model parameters (e.g., profiles of temperature, humidity and liquid water content), especially for the poorly observed oceanic context. The third, known as the simple physical approach, may be viewed as a compromise be-tween the statistical approach and radiative transfer modeling (e.g., Gautier, et al. 1980; Diak and Gautier, 1983). It is based on highly simplified parameterizations of the major radiative processes. For example, in Diak and Gautier (1983), aerosol scattering and absorption are ignored, and scattering processes are assumed to be independent of ab-sorption. The few input model parameters are inferred from the satellite data (e.g., cloud Chapter 1. Introduction 7 albedo), or from climatological mean data (e.g., column water vapor and ozone amount), or simply treated as tuning parameters (e.g., cloud absorptance). It is preferable to use the simple physical approach for oceanic application since a physically based procedure explicitly describes individual radiative process and hence can be easily adapted to dif-ferent areas and allows potential improvements by introducing more accurate parameters from observations or by modifying the parameterization of radiative processes. It is based on these considerations that the model developed by Gautier (1980) and improved by Diak and Gautier (1983) (hereafter called the Gautier model) using GOES Visible and Infrared Spin Scan Radiometer (VISSR?) data is employed in t^his study. Comparisons between model results and in situ measurements are made in the pre-vious studies to test the performance of the models. The root mean square difference between the surface daily mean insolation inferred from satellite and that observed from in situ measurements is around 10% no matter what kind of scheme is used (e.g., Raphael and Hay, 1984; Gautier, et al. 1980; Pinker and Ewing, 1985). It has been argued that the discrepancy may have its origin in: • the mismatch between the spatially and temporarily averaged measurements; • errors in the in situ and satellite measurements; • imperfection of the models themselves; • uncertainties in specifying the model parameters (e.g., column water vapor amount . and cloud absorptance for physical models; water vapor profile and cloud single scattering parameters for radiative transfer models). While it is reasonable to assume that the discrepancy has much to do with the first and second sources as suggested in Gautier and Katsaros (1984), it remains uncertain to Chapter 1. Introduction 8 what degree the disparity can be ascribed to the third and the fourth sources. Several investigations have been conducted to address these uncertainties (e.g., Buriez, et al. 1986; Chou, 1989; Li, et al. 1991). The theoretical study of Buriez et al. (1986) is based on a 183-band <5-Eddington ra-diative transfer model for midlatitude summer conditions. The model results are used to simulate the narrow band measurements of satellite sensors and the broadband measure-ments of pyrometer. Attention is directed to the validity of a linear relationship between broadband atmospheric transmittance and narrow band albedo at the TOA used in some form in both statistical and simple physical-models (e.gvyHay and Hanson, 1978; Gautier, et al. 1980) over a range of atmospheric conditions corresponding to observed variations about a climatological mean. It is found that such a relationship holds for a given solar zenith angle 0O (defined in figure 1.2). They test the sensitivity of the linear relationship between the transmittance and albedo by holding 80 constant and perturbing atmospheric parameters (e.g., column gases and aerosol amount, the cloud height and type) over a range corresponding to their possible natural variability. The results of Buriez' sensitivity study show that the linear relation is most sensitive to the amount of water vapor and aerosols but is insensitive to cloud type and cloud fraction. Moreover, one conclusion reached is that the errors in the broadband transmittance introduced by the uncertain-ties of the atmospheric or surface conditions are larger than the errors introduced by the linear assumption. Based on these findings they suggest that increasing the complexity of the model will not necessarily improve the accuracy of surface insolation estimation. A similar sensitivity of the surface net flux to 60 and water vapor amount is observed by Chou (1989). In addition to a sensitivity study, Chow (1989) argues that, given atmospheric and surface conditions, surface insolation can be obtained more accurately from a radiative transfer model and satellite inferred cloud parameters than is possible from a statistical Chapter 1. Introduction 9 approach. He shows that although the satellite inferred cloud parameters are subject to errors, the effects of the errors from different cloud parameters on surface insolation are likely to offset considerably if the fluxes are consistent with satellite measurements. For example, if a brightness threshold is used as an indicator of the presence of cloud, an overestimate of this threshold would result in an underestimate of cloud amount, which in turn would results in an overestimate of surface insolation. On the other hand, the higher threshold would lead to an increased estimate in cloud optical depth, which determines the amount of radiation attenuation when passing through the cloud (defined in appendix A). This overestimate of cloud optical depths, would, in .turn cause a decrease in the estimate of surface insolation. Thus the net effect of overestimation of the cloud threshold value on the surface insolation is compensated for. Chou numerically demonstrates this compensation for a large range of cloud optical depth. Specifically, he finds that the typical error after the cancellation of the opposing effects is as small as 7Wm~2, a value a tenth of the possible uncertainty of surface net flux which accompanies a statistical model. The above two studies suggest that in spite of the potentially complex radiative effects of clouds, the net effect of clouds on surface shortwave flux can be accurately estimated using the satellite data. However, different studies reach different conclusions about the importance of factors such as cloud type (e.g., stratocumulus, cumulus, cirrus) on the surface .fluxes. One example may be found in Li et al. (1991), who verify the linear relationship between the broadband net flux at the TOA and the surface using a detailed radiative transfer model. Li's result shows that the linear relationship depends as much on cloud type as on column water vapor variation, in contrast, Buriez et al. (1986) who find less importance of cloud type in the same range of column water vapor variation. One possible explanation for this discrepancy is that the parameterizations for cloud single scattering properties in the two studies are different. Chapter 1. Introduction 10 1.2 Overview of Satellite Cloud and Atmospheric Parameter Retrieval In light of the importance of the clouds and some atmospheric parameters (e.g., column water vapor amount) to the earth's radiation budget, as well as the limitation in temporal and spatial resolution associated with conventional observations, much effort has been made to infer the radiatively important parameters from satellite data. The first step of satellite image analysis is to tell the cloudy pixels from the clear ones for cloud amount estimation- All the cloud detection schemes are developed based on two facts seen from satellite images: • cloud top is brighter than most surface types in visible images • cloud top is usually colder than the earth's surface in infrared (IR) images Retrieving schemes may be classified into the following three types according to whether the detection is based on the satellite measurements of one pixel or pixel aggregations or the spatial variation of the measured radiance. The first, known as the threshold method, detects the cloud from the radiance of one pixel in the visible or IR. Making direct use of the above facts, a value of radiance R in the visible (or IR) is chosen to distinguish clear pixels from cloudy ones. To take into account the possible atmospheric and surface influence on the satellite sensed radiance, a threshold Ai? is introduced. A pixel is then called cloudy if its visible radiance is larger than R-\-AR (or if its IR radiance is smaller than R — A R ) . Based on this idea, several schemes using one channel or multiple channel satellite data have been developed to determine the R and Ai? from the minimum reflectance in visible (or maximum radiance in IR) over a certain area (or during a period of time), or from radiative transfer model calculations (Rossow, et al. 1985). Although the method is conceptually simple it is limited in its handling of clouds smaller than the resolution of data (Shenk and Salomonson, 1972; Chapter 1. Introduction 11 Coakley and Bretherton, 1982). The second, referred to as the statistical method, adds information obtained from one or multiple-dimensional radiance space to the above facts for a better classification. The implicit assumption in this method is that the variation of radiance within each type of surface or cloud results is smaller than the radiance difference among different types of surfaces and clouds. Thus, completely clear or cloudy pixes tend to cluster and form peaks in the histograms in radiance space, whereas, partially cloud filled pixel will spread out. Schemes falling into this category differ in their ways of separating clusters (Rossow, et al. 1985). The advantage of thisvmethod.over the threshold method is that it allows the existence of several types of surfaces and clouds in one scene. Based on this method, Arking and Childs (1985) developed the maximum clustering scheme which can determine the cloud fraction A c for partially cloudy pixels. After the identification of clusters, they vary the A c of partially cloudy pixels from 1 to 0 in order to find the A c which results in the retrieved cloud.parameters (e.g., temperature) most consistent with a certain type of completely cloud filled pixel. The third, called the spatial coherence method, is developed by Coakley and Brether-ton (1982). It makes a judgement based on the additional information obtained from the spatial variation of the IR radiation field. Areas of uniform IR radiance are considered as completely clear or cloudy, whereas areas with large spatial variation of radiance are regarded as partially cloudy (see section 3.2 for detail). This method is advantageous in that A c can be calculated without radiative transfer modeling, and hence the pertur-bation of the atmospheric conditions will not affect the retrieval. Although limited to uniform background and layered clouds (such as the ocean and stratiform clouds), this method is desirable since about 71% of the earth's surface is cover by the oceans and most clouds over the ocean are stratiform. Chapter 1. Introduction 12 After the cloud amount calculation, further retrieval of other atmospheric and cloud parameters are carried out using models of different degrees of complexity. The major concerns for solar radiation studies are the quantitative determination of surface albedo, aerosol optical depth and column water vapor amount from clear pixels, and of cloud optical depth and drop size information from cloudy pixels. Due to the complexity of the satellite measured radiances seen in figure 1.1, the retrieval of any physical parameter is possible only when 1) the relevant parameter can produce a detectable radiative effect at the TOA; 2) the radiative effects of other parameters are known. For clear pixels, surface albedo and aerosol optical depth are, estimated with visible and near IR data. The simplest sea surface albedo retrieval scheme uses the minimum radiance during a certain period of time (Dedieu, 1987). The absorption and scattering by the atmosphere are calculated from the climatological mean atmospheric conditions with a simple physical model. Other schemes are based either on a prior knowledge of the albedo of neighboring areas (Pinty and Ramond, 1987) or on an assumed relationship between the surface albedo and planetary albedo (Koepke, 1989). For example, Koepke . assumes that the relationship between the surface albedo and planetary albedo is linear. Then he derives 12 sets of coefficients for the linear relationship by fitting results from numerical simulations under two aerosol optical depths, two ozone amounts and three water vapor amounts. -The aerosol optical depth is obtained by assuming that the surface albedo and the amount of major absorbing gases are known (Kaufman and Joseph, 1982; Rao, et al. 1989). For example, the method developed by Rao et al. (1989) for an oceanic context is based on the assumption that changes of TOA radiance are solely determined by the atmospheric aerosol. ••.;.**.<.••.••-• . - •• The basis for column water vapor amount estimation from the AVHRR imagery is the differential absorption of water vapor in the two adjacent IR channels which have been Chapter 1. Introduction 13 used successfully in the split window technique for estimation of sea surface temperature. While numerical simulations by Dalu (1986) and Schluessel (1989) have shown that the column water vapor amount can be linearly related to the AVHRR channel 4 and 5 brightness temperature difference, no test with real satellite data had been conducted in the previous studies. . The cloud optical depth and cloud droplet effective radius,, which is a parameter con-taining cloud drop size distribution information (defined in appendix A), are determined from cloud albedo in the visible and near IR measured by radiometers on board the satellite (Arking and Childs, 1985) or aircraft (Twomey and,Cocks, .1989; Nakajima and King, 1990). These schemes are based on the following facts obtained from numerical simulations: • the cloud reflection is dominated by such cloud parameters as cloud optical depth and cloud droplet effective radius, with its dependence on other parameters (e.g., column water vapor amount) ignored; • the variation of cloud reflection in nonabsorbing channels indicates the variation of cloud optical depth; • cloud drop size information can be obtained from cloud reflection in near IR chan-nels where absorption varies with drop size. A more detailed description of these methods is presented in section 3.1. 1.3 Objectives Our first objective is to examine, from a theoretical point of view, the feasibility of using the Gautier model to estimate sea-surface net solar flux from the AVHRR data. The work is based on a 24-band cS-Eddington radiative transfer model developed by Slingo Chapter 1. Introduction 14 and Schrecker(1982, 1989, hereafter, Slingo model). To achieve the goal, we carried out a sensitivity study and a simulation study. The sensitivity study focuses on the the effect of variations in water vapor,ozone, cloud reflectivity and cloud properties of solar fluxes. Unlike the general study of Chou (1989), our study is oriented toward a validation of a simple physical model - the Gautier model for sea surface net solar flux from the AVHRR imagery. Therefore, we include not only the sensitivity of surface solar flux to atmospheric, cloud and surface parameters but also the sensitivity of the TOA fluxes in AVHRR channels. Based on this sensitivity study we construct a variant of the Gautier's model. The variant consists of two aspects; 1) a calculation of the cloud optical depth and cloud droplet effective radius at cloud top from the multiple channels of the AVHRR data; 2) estimates of the broadband cloud albedo and absorptance from the derived cloud optical depth and droplet effective radius. The resulting improvements in estimating sea surface net flux estimation from this variant is demonstrated with respect to the Gautier model. Instead of using VISSR data, for which the Gautier model is designed, we chose the AVHRR data, because the AVHRR data is the only operational satellite data available for high latitude. Despite the poor temporal resolution of the AVHRR data (between 2 and 4 daytime passes at present), it has five channels which span wavelengths from the shortwave to infrared region, whereas, VISSR data-only has two (table 1.1). Therefore, there is the potential to extract more information about the atmospheric condition by utilizing the extra channels of the AVHRR data. Although the VISSR sounder channels may be used for more information, there are difficulties with the collocation of the sounder footprints to the VISSR imagery. The second objective of this study is the retrieval of some radiatively important param-eters from the AVHRR data. This work aims at our long term goal: satellite estimation of net solar flux at the sea surface. We use the spatial coherence method to retrieve cloud Chapter 1. Introduction 15 NOAA-9 AVHRR GOES VISRR Channel Wavelength(/zm) channel Wavelength (/z m) 1 0.59-0.69 visible 0.55-0.7 2 0.73-0.92 3 3.55-3.93 4 10.5-11.5 IR 10.5-12.6 5 11.5-12.5 Table 1.1: Band differences between the AVHRR and VISRR fraction. The scheme developed by Nakajima and King (1990) is employed for cloud op-tical depth and cloud droplet effective radius fetrieval.~The~columri wafer vapor amount is estimated as a linear function of the brightness temperature difference between the AVHRR channel 4 and 5, which is suggested by the previous model studies. The data used for these tests is collected during the First International Satellite Cloud Climatology Program Region Experiment (FIRE, Albrecht et al. 1988). We chose FIRE data for following reasons: • the single-layered stratocumulus cloud studied in that experiment is a simple system that is described well by <5-Eddington radiative transfer calculations; • stratocumulus is the most radiatively important cloud over the ocean in terms of extensive coverage and high albedo; • aircraft, radiosonde and surface radiation measurements during the.experiment are available. -1.4 Preview of subsequent chapters In chapter 2, we study the feasibility of the estimation of net solar flux at the sea surface using the AVHRR data and the Gautier model. The Slingo model is briefly Chapter 1. Introduction 16 described in section 2.1, and is subsequently used for the sensitivity study in section 2.3. The Gautier model is introduced in section 2.2. Its limitations are identified upon comparing it with the Slingo model results, which leads to the construction of its variant for cloudy case in section 2.4. A plausible scheme for the clear case is discussed in section 2.5. In chapter 3, we infer the parameters required by the variant of the Gautier cloudy model using existing techniques. Specifically, the techniques used for cloud optical depth and cloud droplet effective radius, cloud fraction, as well as column water vapor amount retrieval are described in section 3.1, 3.2, and 3.3* respectively. We include also the comparison of the satellite derived parameters with in situ measurements. The problems and possible solutions related to these retrieving techniques are discussed. In chapter 4, we present the conclusion and propose possible extensions. Chapter 2 Estimation of Sea-Surface Net Solar Flux: Model Studies The objective of this chapter is to examine the influence of atmospheric, cloud and surface parameters (e.g., column water vapor amount, cloud amount and surface albedo) on the estimation of the net solar flux at the sea surface from the AVHRR data and the Gautier model. We use the Slingo model to simulate the net surface flux and the TOA fluxes in the AVHRR channels over a range of these parameters corresponding to their observed variabilities. The results serve to assess the relative importance of these parameters on the determination of surface net flux from the AVHRR data. They also provide a measure of the adequacy of some assumptions made in the Gautier model. We begin with a description of the Slingo model, which is not intended to be complete, but rather to serve as a preliminary to the subsequent work. The same remark applies to the description of Gautier model. 2.1 Description of the Slingo Model The Slingo model is a 24-band radiative transfer model based on the 6-Eddington approximation (see appendix A for detail). The model includes parameterized Rayleigh scattering, cloud Mie scattering, ozone absorption in the shortwave (0.25^m < A < 0.69/im) and water vapor absorption in the near IR (0.69/zm < A < 4.0/jm). The absorp-tion of oxygen and carbon dioxide are assumed to be negligible (cf., Lacis and Hansen, 1974; Pinker and Ewing, 1985; Buriez et al., 1986; Chou, 1989), although Liou et al. (1978) proposes that oxygen absorption may be important. LOWTRAN 3B subroutines 17 Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 18 (Selby et al., 1976) axe used to calculate the transmittance of the fluxes in each band when passing horizontally through water vapor and ozone at standard temperature and pressure. The correction for conditions which deviate from standard temperature and pressure is made by using the effective water vapor amount (Lacis and Hansen, 1974). To incorporate the interaction between gaseous absorption and multiple scattering, the exponential-sum fitting of transmissions technique (Wiscombe and Evans, 1977) is ap-plied to fit the transmission function in a given spectral interval to a sum of exponentials. The single scattering albedo, asymmetry factor and optical depth of clouds are param-eterized as linear or hyperbolic functions of cloud liquid water path and cloud droplet effective radius using results from Mie calculations (Slingo, 1989). The model calculates radiative flux within the 0.25 to 4.0/im wavelength interval, which contains nearly 98% of the solar energy reaching the TOA. Therefore, we will call the energy between 0.25 and 4.0/xm solar radiation. Table 2.1 shows the band division used in the Slingo model and the percentage of the insolation at the TOA in each band (Thekaekara and Drummond, 1971). With the Slingo model, the radiative properties of vertically inhomogeneous layer clouds can be studied with much less computational demand than is required by Mie theory. The range of cloud droplet effective radii param-eterized in the model is between 4.2 and 16.6/xm, a range covering droplets in maritime clouds and in clouds in the transition from continental clouds to maritime clouds. Although efficient, the Slingo model has the following limitations: • the model calculates flux, whereas the satellite sensors measure radiance; • limited by the band division of the Slingo model, the simulated AVHRR channels are not exactly the same as the real ones (cf., table 2.2); In spite of the limitations, the 6-Eddington approximation marks an improvement in accuracy over the two-stream and Eddington approximations for flux calculations for Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 19 Band 1-12 Band 13 - 24 Band limits Irradiance Absorber Band limits Irradiance Absorber 1 0.25-0.30 1.0094 ozone 13 0.78-0.87 6.8135 water vapor 2 0.30-0.33 1.7224 ozone 14 0.87-1.00 8.3962 water vapor 3 0.33-0.36 2.4017 ozone 15 1.00-1.10 4.9082 window 4 0.36-0.40 3.4645 window 16 1.10-1.19 3.9072 water vapor 5 0.40-0.44 5.0524 window 17 1.19-1.28 2.9133 window 6 0.44-0.48 5.9520 window 18 1.28-1.53 6.5845 water vapor 7 0.48-0.52 5.7464 ozone 19 1.53-1.64 2.0611 window 8 0.52-0.57 6.6188 ozone 20 1.64-2.13 5.0793 water vapor 9 0.57-0.64 8.5882 . ozone 21 2.13-2.38 1.4226 water vapor 10 0.64-0.69 5.4202 ozone 22 2.38-2.91 1.8681 water vapor 11 0.69-0.75 6.0863 water vapor 23 2.91.3.42 .0.9588 water vapor 12 0.75-0.78 2.5044 window 24 3.42-4.00 0.5205 water vapor Table 2.1: Band limits (um), incident solar irradiance at TOA (%) and the gaseous absorption considered in Slingo model. moderately thick clouds over a wide range of solar zenith angles (King and Harshvardhan, 1986). The possible error of the model in cloud base flux is only 0.8% of the incident flux at cloud top when compared with calculations done using the more elaborate adding-doubling method (Wiscombe, 1977). Appendix D presents our comparisons between the Slingo model results and in situ observations. Although the detailed structure in the aircraft measurements may be difficult to account for, its general trend is clearly in accordance with the Slingo model results. While both the Slingo model and the Gautier model (see next section for detail) fail to treat the effects of finite-size clouds and aerosols, the Slingo model has the advan-tage of explicit physical treatment of the interaction between absorption and scattering. Therefore, the Slingo model is appropriate for determining the relative importance of the parameters in the Gautier model and testing the adequacy of some of the assumptions made in the Gautier model. Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 20 channel 1 channel 2 channel 3 AVHRR 0.57-0.69 0.72-0.98 3.55-3.95 Slingo Model 0.57-0.69 0.75-1.00 3.42-4.00 Table 2.2: Wavelengthes of AVHRR channels and wavelength limits used in the Slingo model for simulation (unit: p m ) . 2.2 Description of the Gautier Model The simple physical model presented in the following section was originally developed by Gautier et al. (1980) and refined by Diak and Gautier (1983). The model was constructed for estimation of surface radiation from the GOES VISSR imagery for both clear and cloudy cases. 2.2.1 Gautier Clear Model Figure 2.1 shows that physical processes such as Rayleigh scattering, water vapor absorption, ozone absorption, and surface reflection are incorporated in the clear model, with aerosol scattering and weak absorption of water vapor in the GOES VISSR vis-ible channel neglected for simplicity. Absorption, scattering and surface reflection are assumed to act independently to deplete the direct beam and to produce the diffuse flux. With the above simplifications, the satellite-received visible radiance SW | and surface downward solar flux Fd may be obtained (Diak and Gautier, 1983): S W T = Fv(l ~ ozl/.V){l- oz2/V)ctR(\\ A + FV{1 - ozl/V)(l. -oz2/V)[l - aR{\)][l - am{X)]Ag (2.1) v „ ; -r . B F d = F0{1 - aR)(l - 02 l ) ( l - oz3)[l - a(«i)](l + A g a R l ) (2.2) Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 21 Ocean Figure 2.1: Gautier clear model. Symbols A and B represent terms in equation (2.3). 7o is the solar constant. where FQ,FV: TOA downward solar fluxes (total and in the VISSR visible channel, respec-tively). V: ratio between FV and F0; ozl, oz2: direct and diffuse absorptances of ozone in the visible bands; oz3: direct absorptance of ozone in the ultraviolet; a(ui): absorptance of water vapor for the direct solar radiation; ctfi(X), ctRi(\): .coefficients for direct and diffuse Rayleigh scattering in the VISSR visible channel; C*R,<XRI'- coefficients for direct and diffuse Rayleigh scattering for solar radiation; A g : surface albedo; A and B terms in (2.1) represent different parts of radiance received by the satellite Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 22 sensor shown in figure 2.1. Surface net flux Fnet can be calculated from Fd according to: Fnet = Fd(l-Aa) = F0(l - aR){l - ozl)(l - oz3)[l- a(ux)](l - Ag + AgaRl - A2gam) (2.3) The absorptance of ozone ozl,oz2 and oz3 are parameterized as functions of slant ozone path (Lacis and Hansen, 1974). The water vapor absorptance a(ui) is approxi-mated as a function of slant precipitable water path u\ (Paltridge, 1973). The column - -water vapor and ozone amount for oceanic applications,are obtained from climatological means (Gautier and Katsaros, 1984). The Rayleigh scattering coefficients a, cti and o:1(A) are obtained from the tables of Coulson (1959). The ct(\) is calculated as a function of optical depth of Rayleigh scattering, solar zenith angle 6Q and satellite viewing angle 9 (defined in chapterl figure 1.2) with a single scattering assumption (Coulson, 1959) and with the Rayleigh scattering optical depth of the atmosphere obtained from Allen (1973). The only unknown for Fd or (Fnet) is the surface albedo Ag, which can be determined from equation (2.1) • • SW^ - F 0 ( l - ozl/V)(l -oz2/V)aR(\) 9 F0(l - ozl/V)(l - oz2/V)[l - aR(X)][l - aR1(X)] K ' ; 2.2.2 Gautier Cloudy Model Figure 2.2 shows how the Gautier cloudy model is constructed by adding a cloud layer and invoking the following additional assumptions. First, the cloud top is fixed at a height such that 30% of column water vapor is contained above the cloud top. Second, Rayleigh scattering exists only above the cloud top; with the scattering coefficients for the total atmosphere scaled by the fraction of the atmospheric mass above the cloud top. Third, the broadband radiative effect of the cloud is parameterized via the cloud Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 23 Ocean Figure 2.2: Gautier cloudy model. Symbols A, B, C and D represent terms in equation (2-6) Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 24 albedo Rc and the cloud absorptance absc. Fourth, the cloud radiative effect in the VISSR channel is represented as the cloud visible albedo Rc\, with cloud absorption in the channel neglected. The counterparts of (2.1) and (2.3) for the cloudy case thus follow from these assumptions: SW-T = Fv(l-ozl/V)(l-oz2/V)aR(X) > v ' A + FV{1 - ozl/V){l - oz2/V)[l - aR(X)][l - aRl{X)}Rcl v : v / B + FV(1 - ozl/V)(l- oz2/V)[l - aR(X)}R2claR1(X) v v . / C + FV(1 - ozl/V)(l - oz2/V)[l - aR(X)][l - aRl{X)](l - RcX)2Ag (2.5) v :—, v • D Fnet =. F 0 ( l - ozl)(l - oz3)(l - aR)[l - o(tx l a)](l -Rc- absc)[l - a ( « u ) ] ( l - Ag) (2.6) where u\a and un are slant precipitable water vapor path above and below cloud, respec-tively. Terms A, B, C and D represent different parts of the TOA upward flux shown in figure 2.2. To get Fnet from (2.6), they further assume that the surface albedo Ag for the cloud case takes the same value as for the clear case. Moreover, cloud albedo for all solar wavelengths is assumed equal to the albedo in the VISSR visible channel: Rc " R& (2-7) and cloud absorptance is fixed at 20% of cloud albedo: absc = 0.2Rd (2.8) Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 25 20 30 40 SO 60 SUN ALTITUDE. DEGREES 10 20 JO 40 SO' S O . SUN ALTITUDE, DECREES Figure 2.3: Sea surface albedo as a function of solar zenith angle for clear (a) and cloudy (b) cases (after Payne, 1972). Points are from measurements. Solid lines are fits to the data points Additional constraints for R c and absc are imposed. The minimum of R c is set to be 7% , a value that gives a best-fit between the final estimated downward flux Fd and in situ measurements. The maximum absc is also assumed to be 7% , a value which, similarly, gives the best agreement with surface observations under thick cloudy cases. Of the assumptions above, the use of the surface albedo A g calculated from clear pixels for cloudy ones is obviously inadequate for the ocean surface according to observations near the sea surface. Figure 2.3 (a) and (b) shows the in situ measurements made by Payne (1972) for clear and thick cloudy conditions, respectively: Points in these figures are from measurements. Lines are from fits to the measured data. The figure shows that for clear conditions A g may vary with sun.altitude from 0.04 to 0.4, while for thick cloudy conditions A g is approximately 0.06. The validity of the use of the climatological mean ozone and water vapor amount, Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 26 and of the assumption of the linear proportionality between cloud albedo and cloud absorptance, will be examined below in light of the results of our sensitivity studies. 2.3 Sensitivity Studies The objective of this section is to assess the sensitivities of the surface net flux and the TOA upward fluxes in the AVHRR channels at midlatitudes to the largest estimated uncertainties of atmospheric and surface conditions for the Vancouver area (cf., appendix B) using the Slingo model introduced in section 2.1. Key parameters for estimating sea-•surface net solar flux from the AVHRR data are identified. 2.3.1 Model Atmospheric and Surface Conditions The climatological mean profiles used for temperature, water vapor and ozone mixing ratio are mid-latitude summer (figure 2.4 (a)) and winter profiles from McClatchey et al. (1972). For the cloudy layers, the liquid water content and droplet effective droplet radius (defined in appendix A) are assumed to increase linearly with height, which is consistent with in situ measurements in marine stratocumulus (e.g., Slingo, et al.T982; Stephens and Piatt, 1987; Foot, 1988). One example of the profiles is shown in figure 2.4 (b) which shows the droplet effective radius and liquid water content for a stratocumulus cloud of roughly 1 km thickness. The solar constant I0 and solar zenith angle OQ are calculated from the equations provided by Dogniaux (1976). They are functions of the day of the year, time of the day, and latitude, longitude, with the variation of I0 during a day neglected. The location assumed in the sensitivity study is Vancouver (49°.20' N, 125° W). Sea surface albedo A g is from Payne (1972). For clear conditions, we represent Payne's Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 27 0.0 o o o CO o <0 o o CM density (gm~3) 0.0001 0.0002 0.0003 2 4 6 8 10 12 mixing ratio (g/kg) E CM droplet effective radius (/xm) 0 5 10 15 0.0 0.04 0.08 0.12 liquid water content (gm~3) Figure 2.4: Representative profiles used for sensitivity study, (a) water vapor mixing ratio: solid, ozone density: dashed, (b) liquid water content: solid, cloud droplet effective radius: dashed. where a (= 90° — 0Q) is the solar altitude, the angle between the direction of the solar radiation and its projection at the earth's surface. For the cloudy case, a constant value of A g = 0.07 is used. 2.3.2 Sensitivity of Fluxes under Clear Conditions Figures 2.5 - 2.7 show the results of our sensitivity study for the surface net flux Fnet (downward minus upward) and the TOA upward fluxes in the AVHRR channels 1, 2, and 3 under clear conditions. The data points are obtained from the Slingo model during the daytime at half hourly intervals. At each solar zenith angle Oo, seven cases corresponding to the mean midlatitude summer condition and the largest deviations of column water vapor amount Wv, ozone amount W0, and surface albedo Ag are calculated, forming a set of 217 separate results. In particular, we consider a 50% deviation of Wv from mean conditions (i.e., 1.49 - 4.42 cm for summer, 0.86 - 2.70 cm for winter), an Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 28 approximately 90% deviation of mean W0 (i.e., 32.5 - 650 Dobson units for summer, 40.4 - 808 Dobson units for winter), and a 20% deviation of mean A g (i.e., ± Q . 2 A g ( a ) from equation (2.8) for clear conditions, 0.056 - 0.084 for cloudy conditions). Appendix B explains the (somewhat arbitrary) choice of limits of these deviations. The solid lines in figure 2.5 (a), 2.6 (a) and 2.7 (a) show FNET during daytime under climatological mean atmospheric conditions. The error bars show the possible variations of FNET from the solid line due to the uncertainties of the atmospheric conditions. The remaining three panels (panel b-d) in these figures show corresponding results for the TOA upward fluxes in the AVHRR channels 1, 2,and 3, respectively. To understand the features seen in the above figures, we note that the incident solar flux at the TOA JFO> which sets an upper bound on surface and TOA fluxes, is given by FQ = Iocosd0 (2.10) In addition, the surface and TOA fluxes are modified by Rayleigh scattering, gaseous absorption and surface reflection. Considering them in turn, the optical depth of Rayleigh •: scattering TR and gaseous absorption r a have the following forms: TRX<X—1—, (2.11) A*COSUo r a X oc — . (2.12) cos Vo where A ( p m ) is the wavelength, j3a\ (cm - 1) the volume absorption coefficient, and Wa (cm) the volume of any absorber per unit area of air column. The larger the TR\ ( or ra\) the larger the amount of radiative flux being scattered (or absorbed) by the atmosphere. The albedo of the sea surface, A g , is shown in figure 2.3 (a). The larger the A g , the larger the amount of flux been reflected at the sea surface. For the surface net flux, we see from panel a of figures 2.5 to 2.7 that Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 29 5 10 15 20 5 10 15 20 (a) time (hr) (b) time (hr) 5 10 15 20 5 10 15 20 (c) time(hr) (d) time(hr)""• Figure 2.5: The solid curves are a) surface net flux F n e t , b) TOA upward fluxes in the AVHRIt channel 1 chl f, c) channel 2 ch2 T., and d) channel 3 ch3 T, from sunrise to sunset,- during which the solar zenith angle changes from 90° to minimum and returns to 90°. The error bars are uncertainties of these fluxes due to 50% variation in column water vapor amount (mid-latitude summer clear condition). The 'x' in (c) is discussed in section 2.3.5. Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 30 10 15 20 5 10 15 (c) time(hr) (d) time (hr) Figure 2.6: Similar to figure 2.5 except that the error bars are uncertainties of the fluxes due to approximately 90% variation in column ozone amount. The V in (b) is discussed in section 2.3.5. Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 31 5 10 15 20 5 10 15 20 (c) time (hr) (d) time (hr) Figure 2.7: Similar to figure 2.5 except that the error bars are the uncertainties of the fluxes due to 20% variation in surface albedo. The 'o and x' in (b) and (c) are discussed in section 2.3.5. Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 32 • the surface net flux Fnet first increases with time (or with decreasing 0O) and then decreases. This increase of Fnet with the decrease of 60 is expected since the energy available at the TOA, Fo, (cf., equation (2.9)) increases with the decrease of 6Q. At the same time, the decrease of 60 produces a decrease in Rayleigh scattering and gaseous absorption, which enhance Fnet by increasing the energy reaching the sur-face, and produce a decrease in Ag, which enhance Fnetby decreasing the reflected flux at the surface. • under perturbed conditions, although the variation of absorption optical depth (ATAA OC is larger when the sun is low, the uncertainty of Fnet due to the uncertainties of the absorber amounts in atmosphere reaches a maximum when the sun is highest. The reason that Fnet reaches its maximum at high sun is that the increase of Fo with decreasing 0o happens in the whole solar wavelength, while the effect of absorber amount can be seen only in several absorption bands. Therefore, the effect of increasing Fo dominates the variation of Fnet. (Later we will show cases in narrow bands where the effect of absorber amount overwhelms the effect ofF 0 .) • the ambiguity of any atmospheric and surface parameter (i.e., Wv, W0 and Ag) has an effect on surface net flux under clear conditions although the magnitude of these effects is relatively small ( < 3 % of total surface flux in general). Among these parameters, Wv exhibits the most pronounced effect which reaches a maximum difference in Fnet of 20.3Wm~2 (cf., heights of error bars in figure 2.5 (a), 2.6 (a) and 2.7 (a)). Panel b, c and d in the above figures shows the TOA upward fluxes in the AVHRR channels and their uncertainties due to the uncertainties of atmospheric and surface conditions. Unlike the monotonic relation between Fnei and 0O, the narrow band upward Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 33 flux reaches three local maximums during the daytime. These patterns are results of the competition among the different processes discussed in above. On the one hand, a decrease in OQ leads to a larger amount of F0 and a smaller ra> (cf., equations (2.10) and (2.11)), which enhance the upward flux at the TOA. On the other hand, the decease in 6o results in a smaller TR\ and AG (cf., equation (2.12) and figure 2.3 (a)), which reduces the flux been scattered and reflected back to the space. We see from these panels that • as is expected from equation (2.11), the upward flux in shorter wavelengths, on the whole, is larger than that in longer wavelengths (i.e., upward flux in channel 1 is the largest, and in channel 3 is the smallest). • the largest effects on the amount of the incident flux and the effect of Rayleigh scattering are seen in the early morning (points A to B in figure 2.5 (b)). The sharp increase of the upward flux is due to: 1) the rate of the increase of Fo with the decrease of the OQ reaches maximum, as evidenced by the derivative of FQ with respect to 0O from equation (2.10) at 0O « 90°; 2) TR\ from equation (2.11) is very large during this period. • the larger effect of Rayleigh scattering under lower sun conditions can also be seen from the error bars in figure 2.5 (c) and. figure 2.7, where the larger uncertainties of WV and AG (AW„ oc -^jjjj-, A A G oc AG) do not lead to larger uncertainties in TOA upward fluxes, since a large amount of the flux has been scattered by the atmosphere before being absorbed by water vapor in the lower atmosphere and being reflected by the surface. • the maximum uncertainty of upward flux due to the uncertainty of ozone amount in figure 2.6 (b) is obtained at low sun when the AW0 is maximum. The effect of Rayleigh scattering is not seen at low sun since the ozone is concentrated in the er 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 34 upper atmosphere. the largest effect of Ag on TOA fluxes is seen along the curve in figure 2.5 (b) from point B to C. In this period, the rate of the increase of Fo decreases, and the decrease of surface albedo Ag (shown in figure 2.3 (a)) becomes the dominant effect which, in addition to the decreasing Rayleigh scattering, leads to the depletion of the upward flux. This point can be demonstrated numerically by setting Ag to a constant, which results in the single maximum pattern of upward fluxes similar to Fnet in panel a. equation (2.11) indicates that the effect of Rayleigh scattering is larger when the wavelength is shorter. We see the relatively smaller effect of decreasing Ag in panel b (0.69//m) compared to panel c (lAfim) and d (3.7^m). Due to the larger water vapor absorption in channel 3 compared to channel 1, the downward flux reaching the surface in channel 3 is relatively small, and therefore, the effect of decreasing Ag in channel 3 is seen to be no larger than that in channel 2. from C to D, the enhancement of the upward flux due to increasing Fo and decreas-ing gaseous absorption is slightly larger than the effects of the decreasing surface albedo and Rayleigh scattering, resulting in the small maximum slightly after noon (D in figure 2.5 (b)). error bars in panel b, c and d of the above figures show that the uncertainties of Wv, W0 and Ag have much larger relative effects on the upward fluxes at the TOA than on Fnet- Moreover, ozone affects channel 1 and water vapor affects channel 2 and 3 of the AVHRR. Each channel is affected by at least two factors, one from the atmosphere and one from the surface, by amounts of the same order. (This point will be discussed in section 2.5.) Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 3 5 and 3 of the AVHRR. Each channel is affected by at least two factors, one from the atmosphere and one from the surface, by amounts of the same order. (This point will be discussed in section 2 . 5 . ) Table 2 . 3 summarizes the results in panel a of figure 2 . 5 , 2 . 6 and 2 . 7 , as well as the results for midlatitude winter conditions in terms of the maximum sensitivity of surface net flux ( A F n e t ) , which is obtained around 1 2 : 3 0 when the solar zenith angle reaches min-imum. Also shown are the uncertainties of the daily arithmetic mean net fluxes (AFnet) to the uncertainties of atmospheric and surface conditions if we use the climatological mean Wv, W0 and A g . The largest uncertainty of any one parameter (i.e., A W V = 1 . 4 9 and 1.84 cm for summer and winter, respectively; A W o = 3 2 5 and 4 0 4 Dobson units for sum-mer and winter, respectively; and AAg(a) = 0.2Ag(a)) will lead to a A F n e ( < 10Wm~2. However, if the Wv. and W0 are all larger (or smaller) than their climatological means, the uncertainty in surface net solar fluxes will add since the main absorption bands of these two gases do not overlap, which results in an error larger than 10 Wm~2. The implication of this result is that the improvements in the accuracies of column water vapor and ozone are more beneficial than that of surface albedo to accurate estimates of Fnet. The lower sensitivities for winter compared to summer seen in the table are mainly due to the lower solar zenith angle OQ in winter, and the fact seen in figure 2 . 5 to 2 .7 that 0 O dominates the surface flux and its sensitivity. The slightly larger sensitivity of surface flux around noon A F n e t in winter than in summer is due to the dryer mean clear condition in winter. 2.3.3 Sensitivity of Fluxes under Cloudy Conditions Sensitivity studies under cloudy conditions are carried out, first, by keeping the cloud liquid water content and cloud droplet effective radius r e profiles (figure 2 . 4 (b)) fixed Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 36 2.3.3 Sensitivity of Fluxes under Cloudy Conditions Sensitivity studies under cloudy conditions are carried out, first, by keeping the cloud liquid water content and cloud droplet effective radius r e profiles (figure 2.4 (b)) fixed and varying Wv, W0 and A g as in the figure 2.3 to 2.5. The cloud optical depth r c is 16, and the cloud droplet effective radius at the cloud top r\ is 16.6pm. These values are typical for many thin stratiform clouds (Twomey and Cocks, 1989; Nakajima and King, 1990). By definition, r c is a function of wavelength. In this thesis, however, r c refers to the average optical depth in the AVHRR channel 1. This value is very close to the intensity weighted average of r c in the wavelength range of solar radiation. The results of the sensitivity study for the cloudy mid-latitude summer case are shown in figure 2.8 to 2.10 . The high cloud albedo reduces the magnitude of F n e t to less than half of its clear value. The magnitude of the TOA upward fluxes in the AVHRR channels 1, 2 and 3 are correspondingly increased by factors of 8, 10 and 2, respectively. Furthermore, the uncertainties of surface and TOA fluxes due to the uncertainties of the amounts of absorbing gases and the magnitude of the surface albedo are reduced in a relative sense. These phenomena suggest that the existence of cloud has a dominant effect on the surface and TOA fluxes in comparison to other parameters. To see the effects of varying cloud parameters on the foregoing results, calculations are made by keeping the atmospheric and surface conditions unchanged and changing the slopes of cloud liquid water content and droplet effective radius profiles in figure 2.4 (b) so that r c and r\, vary by amounts representative of their estimated sensitivities when retrieved from remotely sensed data (i.e., A r c = 4 and Ar\ = 6pm, see Nakajima and King, 1990 for detailed discussion). While the realistic simulation of cloud side effects that accompany changing A c is impossible due to the limitation of the Slingo model discussed earlier, the effect of A c is roughly estimated by linearly combining the surface Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 37 Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 38 Figure 2.9: Similar to figure 2.6 except for under cloudy case Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 39 5 10 15 20 5 10 15 20 (a) time (hr) (b) lime (hr) 5 10 15 20 5 10 15 20 (c) time (hr) (d) time (hr) Figure 2.10: Similar to figure 2.7 except for under cloudy case Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 40 A F n e t A r c = 1 -12.5 -4.3 A A C = 1% -5.8 -2.3 Ar* = — 1pm -1.3 -0.4 AWV = 1 cm -3.0 -1.0 AW0 = 100 Dobson units -0.7 negligible A A g = 1 % -1.4 -0.5 Table 2.4: Sensitivity of surface net flux ( A F n e i ) at 12:30 and daily mean surface net flux ( A F n e t ) for midlatitudes summer due to the variation of various parameters under cloudy case (unit: W m ~ 2 ) . retrieved from remotely sensed data (i.e., A r c = 4 and Ar* = 6pm, see Nakajima and King,.1990 for detailed discussion). While the realistic simulation of cloud side effects that accompany changing A c is impossible due to the limitation of the Slingo model discussed earlier, the effect of A c is roughly estimated by linearly combining the surface fluxes determined under completely clear and cloudy conditions. The A A C is taken as 0.04 which is the typical sensitivity of cloud fraction derived from the spatial coherence method (Coakley and Bretherton, 1982). It is found (not shown here) that while the general pattern bf surface and TOA fluxes are the same as figure 2.8, 2.9 and 2.10, the effects of varying cloud parameters are larger than those produced by varying atmospheric parameters. These larger effects are shown in table 2.4 and will be discussed in detail in the next subsection. The above sensitivity studies for midlatitude summer cloudy conditions are sum-marized in table 2.4 as partial derivatives of the surface net flux with respect to the variations of the physical parameters. It can be seen from the table that the maxi-mum uncertainties of Wv (1.49 cm), W0 (325 Dobson units) and A g (0.014) lead to an error in F n e t < bWm~2 (or F n e t < 2Wm~2 ). Whereas, uncertainties of r c of 4, A c of 4% and r* of 6pm result in A9.9Wm~2,23.2Wm-2 and 7.9Wm~2 errors in F n e t (or Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 4 1 available at the TOA and affects the amount of energy been absorbed and scattered by the atmosphere. We found that the sensitivity of surface flux to Wv from our results is smaller than that from Li et al. (1991). This discrepancy may due to the differences between the LOWTRAN 6 and 3B used in the two studies. 2.3.4 Sensitivity of Cloud Optical Properties It is obvious from table 2.4 that the cloud parameters are much more important to surface fluxes than the other parameters. A better understanding of the relationships ambhg'the cloud parameters'(e.g, cloud optical depth r c, droplet effective radius r e), the cloud albedos in the AVHRR channels and cloud broadband optical properties (i.e., cloud albedo and cloud absorptance) is a key to the successful use of satellite data for surface net flux estimation. The definitions of the cloud optical properties in the thesis are as follows. The cloud albedo Rc is the ratio of upward flux to downward flux at cloud top. It is actually the total albedo of both the clouds and the underlying surface. The cloud absorptance absc is defined as the ratio of shortwave flux divergence between cloud top and cloud bottom to total downward flux at cloud top, thus representing the ratio of the total energy lost within the cloud to the energy incident on the top of the cloud. It then follows that the effect of multiple scattering between cloud bottom and sea surface, and the effect of gaseous absorbers within the cloud are taken into account. The results are grouped into two sets corresponding to relations between: 1) cloud physical parameters (i.e., cloud optical depth r c and cloud droplet effective radius at cloud top r*e) and cloud albedo in the AVHRR channels, and 2) cloud physical parameters and cloud broadband optical properties (i.e., Rc and absc). The variables r c and re are assumed to be independent, although they may be coupled in real clouds. Some cases calculated in this subsection may lead to unrealistic cloud Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 42 top r*) and cloud albedo in the AVHRR channels, and 2) cloud physical parameters and cloud broadband optical properties (i.e., R c and absc). The variables r c and re are assumed to be independent, although they may be coupled in real clouds. Some cases calculated in this subsection may lead to unrealistic cloud droplet number concentrations. For example, with the approximate relation (A.12), the extreme case discussed in this subsection (i.e., r\ = lQ.Qfim,TC = 0.01, and cloud height 1 km) would lead to the number of cloud droplets N < 6cm - 3 , while in real stratrocumulus N > 100cm"3 (Stephens, 1978). * We'-start with the first set of the results which show ways in which the cloud albedo in the AVHRR channels varies with T c , r e , Wv, W0 and A g . For channel 1, figure 2.11 shows that cloud channel 1 albedo Rcl is mainly determined by r c and the cosine of the solar zenith angle fio. A decrease in U.Q has the same effect on Rci as an increase in r c. This observation may be accounted for by noting that a decrease in fj,Q corresponds to an increase in the optical depth. Also note from figure 2.11 (b) that R c i is rather insensitive to the variation of cloud droplet effective radius at cloud top r\. From figure 2.11 (d), we observe that the effects of A g on Rc\ is small. In contrast to the sensitivity of the channel 1 radiance at the TOA to W0 seen in figure 2.9 (b)), the reflectance at cloud top Rc\, does not vary with W0 since most of the ozone is above the cloud top, and therefore, the relevant plot is not shown here. Similar calculations are made for channel 3, with the results displayed in figure 2.12(a-c). It is noted in figure 2.12 (b) that the cloud channel 3 albedo R& varies sharply when r c is small, it quickly levels off to a certain value depending on cloud drop size distribution. The maximum Rcz at r c « 2 for r\ = 16.6fj.rn in figure 2.12 (b) is due to the decrease of the cloud drop size with decreasing height shown in figure 2.4 (b)..To prove this point, we plot R^ against Tc for clouds with vertically homogeneous droplet effective radius r e in figure 2.12 (d). As we expected, Rc3 increases sharply with r c and quickly forms a Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 43 0.2 0.4 0.6 (a) po 0.8 1.0 10 15 20 ( * ) T e 25 0.0 0.5 1.0 1.5 (c) Wv {cm) 2.0 0.05 0.10 0.15 {d) Ag 0.20 Figure 2.11: Cloud channel 1 albedo Rci vs. (a) cosine of solar zenith angle /*o; (b) cloud optical depth r c; (c)water vapor amount above cloud Wvi (solid line), within cloud Wv2 (dash line), under cloud W v 3 (dotted line); and (d)surface albedo Ag. r\ is the cloud droplet effective radius at cloud top. Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 44 to o d o •— d m o o 0.2 0.4 0.6 (a) / z 0 0.8 1.0 8 d ft? d o d / ' / * / r* = 6/xm • » r e = 10/xm ;/ ^ — . |f r e = 16.6/im 10 15 20 25 s o d CM O o J3 CO in p o 0.0 0.5 1.0 1.5 • '(c) Wv (cm) 2.0 8 d o=5 d o d r. = 16.6/im 0 5 10 15 20 25 30 (d) TC Figure 2.12: Cloud channel 3 albedo vs. (a) cosine of solar zenith angle (J.Q] (b) cloud optical depth rc;. (c)water vapor amount above cloud w v i (solid line); within cloud wv2 (dash line), under cloud tuv 3 (dash-dotted line); (d)Rcz with homogeneous cloud droplet effective radius vs. T c . r e is the cloud droplet effective radius at cloud top. Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 45 simple physical explanation to understand the effect of vertical inhomogeneity. The cloud optical depth in a water absorbing channel, such as AVHRR channel 3, consists of two parts: one is scattering optical depth r3 and the other is absorbing optical depth r„. The larger the r a , the larger the cloud albedo in the channel, and the larger the r c (= T5 + T„) the shorter the distance the radiation can penetrate the cloud. What can be inferred from figure 2.12 (d) are: 1) for the same r c , r3 for smaller cloud droplets is larger than ra for larger droplets, which results in the higher R& for smaller droplets; 2) the diffusion length for cloud with r e = 16.6/mz is at r c ' « 2, and as r e decreases the diffusion length decreases. For the "vertically inhomogeheous cloud in figure 2.12 (b), R^ increases with increasing r c at first due to the increase of TS. As Tc continues to increase over its diffusion length (i.e., r c > 2 for r e = 16.6pm), the radiation cannot penetrate through the whole cloud, and thus only the larger droplets in the higher layer can affect i?^, resulting in the decrease of R& with the increase of r c . As r c further increase, only the droplets at the top can affect R&, and therefore, R^ levels off. As in the case of channel 1, figure 2.12 (a) shows a similar monotonic dependence of RC3 on po. In comparison to the previous channel, Wv has a noticeable effect on channel 3 albedo. The effect of A g on R& is very small, and is omitted here. The results for channel 2 are similar to those observed from channel 1 except that channel 2 albedo is affected slightly by water vapor absorption, and hence there is a slightly larger effect on cloud droplet effective radius. Our observations on the high sensitivity of cloud albedo to r c in the non-water vapor absorbing channel (i.e., AVHRR channel 1), and to r e in the water vapor absorption channel (i.e, AVHRR channel 3) are in agreement with the results of Nakajima and King (1990), and Arking and Childs (1985). The importance of these sensitivities will be seen in the retrieval of r c and r e in section 3.1. The second set of our results are presented in figure 2.13 and 2.14. Figure 2.13 shows Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 46 that the broadband cloud albedo Rc is dominated by Tc and fxQ . The effects of other parameters are relatively small. Figure 2.13 (c) shows that increasing Wv above and within the cloud produces opposing effects on Rc because an increase in water vapor amount above the cloud Wv\ decreases the water vapor absorption within the cloud, which results in an increase in Rc. However, an increase in water vapor amount within the cloud WV2 increases the cloud absorption, which results in a decrease in Rc< Panel (d) shows that the effect of surface albedo on Rc is seen only when the cloud is thin. The solid curve in figure 2.13 (a) shows unphysical albedo (i.e., Rc > 1) for thick clouds under low sun conditions (i.e., fio < 0.1) where the 6-Eddington approximation breaks down. This overestimation of cloud albedo under low sun conditions is also observed by Wiscombe and Joseph (1977) when comparing the results from the £-Eddington approximation with those from more elaborated diamond-initialized doubling method. Figure 2.14 shows how the broadband cloud absorptance absc varies with the condi-tions of the sun, atmosphere and cloud. It is seen in figure 2.14 (a) that absc is generally larger when the sun is higher. Moreover, the effects of r\ on absc shown in panel (b) is larger than that on Rc. The effects of varying water vapor amount above and within the cloud on absc illustrated in figure 2.14 are in opposite directions as in the the case for their effects on Rc. The effect of Ag on absc is negligible. On the whole, /io,Tc,r* are all important to the determination of the broadband cloud absorptance absc. 2.3.5 Summary and Discussion Results in section 2.3.2 show that it is difficult to determine the clear surface net flux Fnet to within 10Wm-2 accuracy using the climatological mean water vapor and ozone amounts due to their large variabilities. For example, if the Gautier clear model is used to calculate Fnet, a decrease in column ozone amount W0 in the atmosphere would be misinterpreted as an increase in Ag according to equation (2.4), which in turn would Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 47 0.2 0.4 0.6 0.8 1.0 0 5 10 15 20 25 (a) /*0 (6) TC o d in d o in in d d T e = 32 I 0.5 0.6 / « d CM d • • * TC = 2 0.0 0.5 1.0 1.5 2.0 (c) W u (cm) 0.05 0.10 0.15 (<*) Aa 0.20 Figure 2.13: Cloud albedo Rc vs. (a) cosine of solar zenith angle po at r\ — 16.6//m; (b) cloud optical depth T c at p0 = 0.78; (c)water vapor amount above cloud wvi (solid line), within cloud wV2 (dashed line), under cloud wvz (dotted line) at r* = 16.6/zm and po = 0.78; and (d) surface albedo Ag at r* = 16.6/im and /z0 = 0.78. Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 48 o d s d s O d o d o d t — 6 t » r n /•' ' /'* * 5 10 15 20 25 0.0 0.5 1.0 1.5 (c) W„ (cm) ' 2.0 0.05 0.10 0.15 0.20 («0 Ag Figure 2.14: Cloud absorptance abse vs. (a) cosine of solar zenith angle t\t0 at r* = 16.6/zm; (b) cloud optical depth T c at /zo = 0.78; (c) water vapor amount above cloud wv\ (solid line), within cloud wvi (dashed line), under cloud wvz (dotted line) at r\ — 16.6/zm and u0 = 0.78; and (d) surface albedo Ag at r* = 16.6/zm and /z0 = 0.78. Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 49 result in a decreased estimate of Fnet from equation (2.3) (ignoring the small terms Aga\ and -Ajjai). However, in the real world, less ozone in the atmosphere would increase the amount of flux reaching the surface, and therefore, increase the Fnet. A quantitative estimate of the error in surface net flux due to the use of the clima-tological mean data may be obtained by assuming that the Gautier model can exactly estimate the radiative effects of physical processes (i.e., it produces the same results as the Slingo model under the same conditions). Then, the effect of using these climatolog-ical means on the estimation of Fnet may be seen from figures 2.5 to 2.7. For example, according to figure 2.6 (b) and figure 2.7 (b), a 90% decrease of ozone amount around noon (cf, the V in figure 2.5 (b)) in the real world may be misinterpreted as a 14% in-crease in Ag (cf., the 'o' in figure 2.7 (b)) by the Gautier model. From figure 2.5 (a) and figure 2.7 (a), this misinterpretation may lead to an error of 17.5Wm~2 in Fnet. Similarly, if we estimate Ag from the AVHRR channel 2 measurement a similar equation as (2.1) may be written with absorptance of ozone replaced by the absorptance of water vapor. Then, a 50% decrease of the water vapor amount around noon (cf., the 'x' in figure 2.5 (c)) may be. misinterpreted as a 5.2% increase in surface albedo (cf., the 'x' in figure 2.7 (c)), resulting in a 22AWm~2 error in Fnet. To get a better estimate of surface insolation over the ocean, improved accuracies in gaseous absorber amounts, especially water vapor amount, are needed. Such improve-ments may be obtained through incorporating the TIROS Operational Vertical Sounder (TOVS) data on board the NOAA'satellite or using the retrieval technique to be discussed in section 3.3. Under the cloudy case, results in section 2.3.3 show that the accuracies in cloud optical depth r c and cloud amount Ac are crucial to the determination of F n e j . For the relatively thin cloud case studied (rc = 16), accuracies of, at least, 2.3 (i.e., 14%) in r c and of 5% in Ac are needed to reach the required 1 0 W m ~ 2 accuracy for the climate studies. Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies, 50 gaseous absorber amounts, especially water vapor amount, are needed. Such improve-ments may be obtained through incorporating the TIROS Operational Vertical Sounder (TOVS) data on board the NOAA satellite or using the retrieval technique to be discussed in section 3.3. Under the cloudy case, results in section 2.3.3 show that the accuracies in cloud optical depth r c and cloud amount A c are crucial to the determination of Fnet- For the relatively thin cloud case studied (rc = 16), accuracies of, at least, 2.3 (i.e., 14%) in r c and of 5% in A c are needed to reach the required 1 0 W m ~ 2 accuracy for the climate studies. "Section 2.3.4 showed that it is possible to determine r c from the AVHRR'charinel 1 since cloud channel 1 albedo is dominated by r c and a known parameter, the solar zenith angle. For relatively thick clouds, it is also possible to estimate cloud droplet effective radius at the cloud top, r e , from the AVHRR channel 3. Although r\ seems unimportant to F n e t according to table 2.4, its importance lies in following aspects: • r c , which dominates the amount of the incoming solar energy of the earth-atmosphere system, is "strongly dependent on r e (cf., equation A. 10) • r e affects cloud absorption absc (cf., figure 2.14 (b) and (d)) • r\ gives cloud thickness information which could be used to described its emission All the above factors working together determine the amount of energy being absorbed by the atmosphere and the ocean, and hence provide the fundamental driving force of the atmospheric and oceanic circulation. 2.4 A Variant of the Gautier Cloudy Model The objective of this section is to construct a variant of Diak and Gautier (1982) for the cloudy case, in light of the limitations of the original cloudy model. A comparison of Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 51 Rci (equation (2.7)) and the linear relationship between absc and Rci (equation (2.8)). To show the adequacy of these assumptions, we replot, in figures 2.15 and 2.16, the results of section 2.3.4 in terms of relations: R c vs. R & and absc vs. Rc\, respectively. Also shown, by the symbol '+', are Gautier's assumptions (i.e., figure 2.15 shows the assumption R c — Rc\; figure 2.16 shows the assumption absc — 0.2i?cl and maximum absc = 0.07). It is seen in figure 2.15 that the tendency of R c with Rc\ revealed from the Slingo model is in accordance with the Gautier assumption (2.7) although there are large discrepancies for low sun angles. However, figure 2.16 show that Gautier's assumptions on a6sc'are qualitatively different from the Slingo model. It is seen from figures 2.16 (a-b) that Gautier's assumptions underestimate absc for small and large cloud optical depths r c , but overestimate absc for moderate values of r c. It is noted from figure 2.16 (c-d) that the influences of cloud droplet effective radius at cloud top rfe, surface albedo A g , water vapor amount within the cloud W„2, and especially water vapor amount above the cloud Wv\ on absc are not appropriately accounted for in the Gautier model. Motivated by the foregoing numerical observations of limitations in the original model, we consider the following as an alternative to the linear relations in (2.7) and (2.8). Specifically, we first extract Tc and r\ from the AVHRR channel 1 and 3 measurements (to be discussed in section 3.1). Then we use these satellite derived cloud microphysical parameters to interpolate R c and absc from two look-up tables constructed from the Slingo model. We used 18 x 14 x 7 values for 2 < r c < 36, 4.2^m < r\ < 16.6pm and 0.6 < po < 0.9, respectively, a range appropriate for the FIRE data. Due to the large effect of Wv\ on R c and absc shown in figure 2.15 (d) and 2.16 (d), one more dimension should be added if Wv\ can be properly determined by the satellite data or by other means. Chapter 2. Estimation of Sea-Surface Net Solax Flux: Model Studies 52 CM ^ CM CD d 0.14 0.16 0.18 0.20 0.22 0.24 0.26 Rci © CO in o r-in ft! -o to to d o m in d d 1 :+ H h H "~ 4 Wvl  Ww2 * * a • + L 0.45 0.50 0.55 0.60 0.65 Rci 0.70 Figure 2.15: Cloud broadband albedo Rc vs. cloud channel 1 albedo Rci for (a) varying cosine of solar zenith angle (0.087 < no < 1) at a certain r c; (b) varying cloud optical depth (0.01 < r c < 32) at a certain fi0; (c) varying surface albedo (0.05 < Ag < 0.2) at T c = 2 and a certain r*; (d) varying water vapor above cloud (0.20cm < Wv\ < 2.37cm) and within cloud (0.18cm < W v 2 < 1.92cm) at r c = 16 and r< = 16.6/zm. "L" ("H") is for low (high) value of the varying variable. '+' is from the plot of equation (2.7). Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 5 3 Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 54 parameters to interpolate Rc and absc from two look-up tables constructed from the Slingo model. We used 18 x 14 x 7 values for 2 < rc < 36, 4.2/zm < r[ < 16.6/zm and 0.6 < uQ < 0.9, respectively, a range appropriate for the FIRE data. Due to the large effect of Wvi on Rc and absc shown in figure 2.15 (d) and 2.16 (d), one more dimension should be added if Wv\ can be properly determined by the satellite data or by other means. 2.4.2 Simulation Study To test the impact of Rc and absc information on a simple physical retrieval of surface net flux, F n e t, we calculate F n e t using equation (2.6) for two sets of calculations of R c and absc. The standard for the comparison is the surface net flux given by the Slingo model F°et for the midlatitude summer atmosphere with a cloud layer that spans a range of r c and r*. In the first set of calculations, which we will call 'original' and denote by superscript 'o', Rc and absc are obtained from Gautier's linear assumptions (i.e., equations (2.7) and (2.8)) using Rc\ calculated from equation (2.5) with simulated TOA channel 1 upward flux from the Slingo model and a maximum absc = 0.07. The second set, which we will call 'variant' and denote by superscript V , calculates Rc and absc as functions of r c and r\ by table lookup. The r c and r\ are estimated with TOA channel 1 and 3 upward fluxes simulated by the Slingo model. Figure 2.17 shows contours of F°et - F^et in 2.17(a), and of F%et - F* e t in 2.17(b) at Ho = 0.78. We choose this value of fi0 since most of the satellite images during FIRE are collected around such a fi0, and since the Gautier model probably gives the best performance in estimating Rc at such a value of u0 (cf., figure 2.15 (b) which shows that Rc from the Gautier's assumption is very close to the Slingo model results at /z0 = 1 and 0.698). We see clearly that to the extent that the Slingo model describes the true behavior of the atmosphere, the variant leads to a better result for surface flux. The Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 5 5 CO CM IT co CD 15 -30 10 20 T c (a) 30 10 20 30 Figure 2.17: The error of surface net flux (a) in the Gautier model (b) and the variant one for midlatitude summer condition at po = 0.78 (unit: Wm~2). small errors in the variant shown in figure 2.17 (b) are probably due to the neglect of the interaction between scattering and absorbing processes by the simple physical scheme. It is seen in figure 2.17 (a) that the original model underestimates surface flux on the whole. To understand the error pattern in figure 2.17 (a), we show in figures 2.18 a similar plots to figure 2.15 (b) and 2.16 (b), but in terms of R°c — R\ vs. r c and abs°c — abs'c vs. r c at three values of r* and p0 = 0.78. Also, we note from equation (2.6) that the Gautier model estimates surface flux from following relation: F°et = constant x (1 - R°c - abs°c) (2.13) Therefore, an underestimate (overestimate) of Rc or absc will lead to an overestimate (underestimate) of Fnet. Thus, the independence of the error to rf. in figure 2.17 (a) is due to the counterbalancing effects of r\ on Rc and absc seen in figures 2.18 (a) and (b). The underestimate of absc by the Gautier model for r c « 2 in figures 2.18 (b) causes the slight overestimate of F n e t (positive value). As r c increases, the large increase of negative error in Fnet for r c < 5 is due to the net effect of sharp decreasing negative errors in Rc Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 56 10 20 30 10 20 30 (a) Cloud optical depth (b) Cloud optical depth Figure 2.18: Errors of the Gautier model (Gautier minus Slingo) in predicting (a) cloud broadband albedo and (b) cloud broadband absorptance for cloud droplet effective radius at cloud top re = AAfim (solid), r\ = lQAum (dashed), r\ — 16.4*zm (dash-dotted) at Ho = 0.78. and surface conditions perturbed. Figure 2.19 shows an example for decreasing column water vapor amount by 50% . Though smaller than the original model in general, the error of the variant is increased due to the errors in estimating r c and r\. Larger errors in F n e t than under the standard conditions for the variant are also found when varying column ozone amount and surface albedo. These results indicate that although the alter-native scheme does.give better estimate of F n e t for. the standard atmospheric condition, it is still affected by the uncertainties of the atmospheric and surface conditions. This behavior is in line with the results of Buriez (1986), who found that the uncertainty of the atmospheric condition is a more severe problem to F n e t prediction than the imperfection of the simple models. Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 57 10 20 30 10 20 30 Figure 2.19: Similax to figure 2.17, except that the column water vapor amount is changed by 50%. behavior is in line with the results of Buriez (1986), who found that the uncertainty of the atmospheric condition is a more severe problem to Fnet prediction than the imperfection of the simple models. 2.4.3 Discussion It should be noted that in section 2.4.1 the Slingo model which is used to examine the performances of the simple physical means has also been employed to parameterize the cloud albedo and cloud absorptance in the alternative scheme. Thus, the better performance of the alternative scheme is only on condition that the Slingo model can exactly describe the radiative processes in the real world which is not true according to our comparisons between model results and in situ measurements in appendix D. However, such an alternative simple scheme seems applicable as long as calculations from a more accurate radiative transfer model is available. Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 58 radiating as an electric dipole) for estimating the Rayleigh scattering of the direct beam in the satellite visible channel, and is thus considered to be anisotropic, whereas the Slingo model is built on the assumption of isotropy. Second, Rayleigh scattering is a dominant term in the energy received by satellite shortwave channels under clear case. Therefore, there is no simulation study for the clear condition. The following description of a modified model for clear case can be regarded as a discussion. Under the cloudy case, the Rayleigh scattering by the atmosphere above the cloud is much less than the reflection of the cloud, and therefore, the isotropic assumption made by the Slingo model will practically not affect the result. . The basic idea of the Gautier clear model is that the variation of the TOA flux ( S W |) is dominated by the variation of the albedo of the surface. Therefore, they parameterized the scattering coefficient by Rayleigh scattering and estimated the water vapor and ozone absorptances from their climatological means. Then they used satellite measurements with equation (2.4) for the visible albedo of the surface to solve equation (2.3) for the surface net flux. From the above description and our sensitivity study it is not difficult to see the inadequacies of the Gautier model which ascribes all the variation of TOA radiance to the variation of surface albedo. First, out of the glint direction, less than 10% of the radiance is due to the reflection of the ocean, while around 20% of the radiance in the channel is from the scattering of the aerosols that is variable both in time and space, and the rest is from the Rayleigh scattering that is essentially constant in both time and space (Kaufman and Holben, 1990). Second, our sensitivity studies show that the uncertainty of the TOA fluxes over clear ocean due to the uncertainty of gaseous absorption has the same magnitude as the uncertainty of the TOA fluxes due to the uncertainty of surface albedo. In light of this inadequacy as well as the dominate radiative effect of aerosols (Masuda Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 59 and Takashima, 1988) under clear case, it appears that the following algorithm would be more appropriate to sea surface net flux estimation under clear case. From the view point of energy conservation, the insolation at the TOA, Fo, will either be reflected back to space or absorbed by the atmosphere and surface, i.e., . Fo = a0Fo + Eabs-rFd{l-Ag): ' (2.14) where Fd is the downward solar flux at the surface, Eabs the flux absorbed in the atmo-sphere, and ao the albedo of the earth-atmosphere system. From the equation above, ao c a n be written as a0 = a + bAg (2.15) with Fo — Fd — Eaba / 0 1 M a = (2.16) -TO * = (2-17) -TO where a represents the relative amount of radiation scattered back to space by molecules and aerosol particles and b represents the flux transmittance of the atmosphere. The linear relation (2.15) was used in Koepke (1989) to get empirical relations for satellite surface albedo retrieval. The transmittance b can also be written as b = (1 - o)(l - absa) (2.18) where absa is the absorptance of the atmosphere to solar radiation. Thus the incident net solar radiation at the sea surface is Fnet = Fd{l-Ag) = F 0 ( l - a)(l - absa){l - Ag) (2.19) Chapter 2. Estimation of Sea-Surface Net Solar Flux: Model Studies 60 Here the net effect of aerosol and molecular scattering is taken into account by one parameter a. To get the Fnet from (2.18), there are three parameters (i.e., the coefficient of atmospheric scattering a , absorptance absa and sea-surface albedo Ag ) which need to be determined. Based on the previous studies, the atmospheric scattering is probably the most significant and the most variable one for surface and TOA fluxes over low albedo surface like the sea. Therefore, our suggested practise is to determine the coefficient of atmospheric scattering a from the AVHRR data, with other parameters given by climatological means. Solving (2.15) and (2.17) for a we obtain „ Qo - (1 - absa)Ag a = ~5 n , x A (2.20) 1 - (1 - absa)Ag where ao, the albedo of the earth-atmosphere system for solar radiation can be obtained from the albedos of the earth-atmosphere system in narrow bands, which are the mea-surements of the satellite sensors. The narrow band to broadband conversion used in this study is from Wydick (1987), which relates AVHRR channel 1 and channel 2 isotropic albedo ai and cx2 to the albedo of solar radiation with the following statistical relation a 0 = -6.219 + 0.73a! + 0.406a2 (2.21) Although the revised clear model appears to be more appropriate in the sense that the effect of aerosol scattering can be included, verification with a more complete model or real data is needed. Chapter 3 Retrieval of Key Parameters for Net Solar Flux at the Sea Surface from A V H R R Data In section 2.4.2, we used the cloud optical depth and droplet effective radius as essen-tial parameters in our alternative means of estimating sea surface insolation. Moreover, an accurate estimate of the cloud fraction, of water vaporabibve"and'"within"the: cloud, and of the column ozone amount is also desirable for a better performance of the al-ternative scheme. While the measurements of the satellite radiometer are narrow band radiances, it is has been recognized for some time that these radiances, with some phys-ical constraints, may be used to infer model parameters such as the cloud optical depth (Twomey and Seton, 1980; Coakley and Bretherton, 1982; Twomey and Cocks 1982). The objective of this chapter is to retrieve cloud optical depth, droplet effective radius, cloud fraction and column water vapor amount using the AVHRR data. The retrieval for the cloud optical depth and droplet effective radius is made in section 3.1, with work on cloud fraction in section 3.2 and the column water vapor amount in section 3.3. 3.1 Cloud Optical Depth and Effective Radius Retrieval 3.1.1 The Method There have been several investigations using the visible and near IR channels for retrieval of cloud optical depth as well as cloud drop size and water phase information (Arking and Childs, 1985; Twomey and Cocks, 1989; Nakajima and King, 1990). While 61 Chapter 3. Retrieval of Key Parameters . 62 in the cloud physical and microphysical parameters lead to differences in the cloud single scattering properties, and hence differences in reflected radiances in satellite channels (Twomey and Cocks, 1982). The principle findings from sensitivity studies are: 1) cloud reflection is most sensitive to cloud optical thickness when the scattering is conservative and the albedo of the underlying surface is small (King, 1987); 2) cloud reflection is sensitive to cloud drop size and water phase information when the scattering is noncon-servative and the absorption varies considerably with cloud drop size and phase (Twomey and Cocks, 1982). It is known (see e.g., van de Hulst, 1974, 1980) that-the-eloud~reflection-field4n thick clouds can be approximately determined by the single scattering albedo w, asymmetry factor g , and cloud optical depth r c (defined in appendix A). According to the following similarity relations: (van de Hulst, 1974), these parameters can be reduced to two: < = { i - g ) T c (3.1) V 1 -ug In figure 3.1, we plot s calculated from (3.2), with UJ and g obtained from Mie calculations (cf., Irvine and Pollack, 1968), as a function of wavelength A and water particle radius r. Figure 3.1 shows that s approaches zero for all cloud droplet sizes for A < 0.9pm . Therefore the cloud reflection in these channels is primarily determined by the single parameter r'c which is given by (3.1). This sets up the basis for determining r c by measuring the cloud reflection. If is also seen from the figure that s is sensitive to the cloud drop size at several near IR wavelengths such as at 1.5,2.0, and 3.7pm . Therefore, the reflectances in these near IR channels are indicators of cloud drop size r (or droplet effective radius r e for cloud with a certain drop size distribution). Our retrieval of the cloud optical depth and droplet effective radius is based on the Chapter 3. Retrieval of Key Parameters ... 63 o 'E CO CM O E <o 2 o CO o o d \ \ \ 1 2 3 4 Wavalength (um) Figure 3.1: Similarity parameter for liquid water as a function of wavelength A for particle radius = lOfim (solid), 3/zm (dashed) and lfim (dash dotted). technique originated by Nakajima and King (1990) and tested by aircraft remote sens-ing using visible wavelengths centered at 0.75/zra and near-IR wavelengths centered at 2.16/xm. The essential physics behind the technique may be described symbolically as fol-lows. First, based on the above similarity relations, two working channels are chosen: one in the visible band and one in the near IR. Let Rv{s and Rnir denote the cloud reflection functions in the two channels respectively. It then follows from the asymptotic theory at large optical depth (Nakajima and King, 1990) that Rvis and i?„,> can be written as where 6Q,0,<f> are the solar zenith angle, the satellite viewing angle and-the relative azimuth between sun and satellite (shown in figure 3.4), respectively. In the forward problem, one seeks the reflectances Rvis and i? n t r for a given r c and r e . In the inverse Rvis = / i ( r c , r e ; #o, 0, <t>) (3.3) Rnir = /2 ( r c , r e ; #o, 6,4>) (3.4) Chapter 3. Retrieval of Key Parameters .. 64 92 = r e i Reflectance in Visible fU* Figure 3.2: Sketch for retrieval of r* and r* from a given pair of cloud albedo in visible and near IK {R'vU, Rnir). problem, one solves for r c and r e given specified reflectances. It is shown by Nakajima and King (1990) that the parameters of interest can be extracted as inverse functions (gx and g2) of / : and f2 (cf., equation (3.3) and (3.4)) i.e. Tc = 9l(Rm,, Rnir] 0o,0,<f>) (3.5) re = g2(Rvi„ Rnir] 0o,O, <f>) (3.6) A unique inverse exists for the range of optical parameters we are interested in (i.e., T C between 2 and 40, r e between 4.2 and 16.6/xm). To see how it works more closely, let us assume that two sets of curves in figure 3.2 corresponding to constant values of the gx and g2 are obtained on the plane (Rvis, Rnir) from a model study. Then, the task of retrieving the cloud optical depth and droplet effective radius is simply to locate the point (T*, r*) corresponding to the measurements R*vis and R*nir . Chapter 3. Retrieval of Key Parameters . 65 3.1.2 Retrieval with the Slingo Model We use the AVHRR channel 1 (0.59 - 0.69/zm) and channel 3 (3.55 - 3.93/zm) for r c and re retrieval. To generate the grid (cf., figure 3.2) for the retrieval, we run the Slingo model for the McClatchey midlatitude summer profiles (cf., figure 2.4 (a)), with the rest of the model parameters chosen as in the section 2.3.1 (i.e., the liquid water content and cloud droplet effective radius are increasing functions of height). For the satellite data, we first convert the satellite measured counts into isotropic albedo of the earth and atmospheric system ao (see appendix C for details). Fully cloudy pixels are detected using the spatial coherence method described in next section. We then calculate the albedo of the cloud under the assumptions: • the magnitude of the radiance which is reflected at the low albedo sea surface, penetrates the clouds and reaches the satellite sensor is negligible; • the water vapor amount above the cloud top is proportional to the brightness temperature difference between channel 4 and 5 (Section 3.3); • column ozone amount is set to its seasonal mean (i.e., 325 Dobson units); • the atmospheric scattering in channel 1 acts as Rayleigh scattering (Paltridge and Piatt, 1976). We neglect the atmospheric scattering in channel 3 (3.7/zrn). • the emission in channel 3 is subtracted using the black body assumption, with the temperature-of the cloud determined from channel 4. The retrievals are made using AVHRR data from June 30, July 7, 11 and 14 1987 for the area off the California coast. Figure 3.3 presents the results for July 7. It is1 seen that the satellite retrieved cloud optical depth at the AVHRR channel 1 ranges from 2 to 12, and that r e is less than 8/zm , with some values smaller than the range of applicability Chapter 3. Retrieval of Key Parameters . 66 0.2 0.4 0.6 0.8 cloud channel 1 isotroDic albedo Figure 3.3: X and Y axes are cloud channel 1 and 3 isotropic albedo, respectively. Lines are obtained from the Slingo model for various values of cloud optical depth r c (dash lines) and droplet effective radius at cloud top r\ (solid lines) at 90 = 35.0°. Dots are calculated from the AVHRR data on July 7 1987 for longitude between 120.9° and 122.6°W, and latitude between 31.0° and 32.0°N. of the Slingo model (4.2pm < re < lQ.6pm). Moreover, cloud droplet effective radius at the cloud top increases as the optical depth increases, which is in agreement with observations of large droplets in thicker clouds. 3.1.3 Comparison with Aircraft Data Next, we compare satellite retrieved cloud parameters with aircraft measurements. The data consists of cloud drop size distribution measurements taken using the Forward Scattering-Spectrometer Probe (FSSP) on board the NCAR Electra aircraft at the same Chapter 3. Retrieval of Key Parameters . 67 region. The range of FSSP cloud diameter measurements is between 2.0 and 47.0pm, with a bin size 3.0pm. The calculation of cloud droplet effective radius from FSSP measurements r™ follows (A.8) with corrections for beam inhomogeneities (Baumgardner and Spowart, 1991). The optical depths from the airplane measurement r™ are obtained using the integrated liquid water content, LWC(gcm~3), from the FSSP measurement and using the approximate relation from (A.10). The comparisons for results from July 7 and 14 show that five airplane-measured cloud optical depths, T™, are within the range inferred from the satellite measurements. •^ For example, the airplane sounding taken between 21:55 and 21:57 July 7 shows .that-the T is 3.5, a value within the range of satellite inferred cloud optical depth as shown in figure 3.3. Since there are only 5 soundings around the time of the satellite passing, we do not have statistical results for the comparison between r™ and rc s . Before presenting the results of our comparison for cloud droplet effective radius, we define a few terms. Let plane TT in figure 3.4 be the one tangential to the earth's surface at the point of interest B; and the points S' and P' be the projections of the sun and the satellite on plane TT, respectively. Then, the satellite zenith angle 0 is the angle between the direction of the reflected radiance (i.e., PB) and the direction of zenith. The solar zenith angle 0Q, defined in chapter 1, is the angle between SB and zenith. The azimuth angle of the sun (satellite) is defined as the angle made when line B N turns to line S B ( P ' B ) clockwise, and the relative azimuth (j) is simply the difference between the azimuth of the sun and the satellite. The result of our comparisons for the cloud droplet effective radius is shown in table 3.1. It seems that r* is close to in situ measurements r™ when <j> is large (e.g., the case for June 30), and that the satellite significantly underestimates the droplet effective radius' when <j> is small (e.g., the case for July 7). To show this point more clearly, we present our retrieval with data obtained on July 14 1987 in figure 3.5 . Chapter 3. Retrieval of Key Parameters ... 68 Figure 3.4: Relative geometry between sun and satellite. Pixels in region I have relative azimuth between sun and satellite cj) close to 180°, whereas pixels in region II have <f> close to 0°. 0o 9 e rt June 30 29.7° 58.3° 170° 7.2 (3.2) 22:13 - 22:34 5.5 (2.7) 22:19 July 7 35.0° 25.8° 171° 7.4 (0.9) 20:14 - 20:32 5.6 (1.3) 22:43 July 11 48.3° 53.7° 8° 10.1 (3.3) 21:02 - 21:25 < 4.2 23:42 July 14 39.0° 4.6° 179° 5.5° 11.0 (0.9) 21:08 - 21:27 8.0 (3.2) < 4.2 23:09 Table 3.1: Comparison between satellite inferred cloud droplet effective radius r'e and airplane measurements r™ in u-m. 0o, 9 and <f> are the area averages of solar zenith.angle,., satellite viewing angle and relative azimuth, respectively. The values in brackets are variances of measurements. The numbers under the measurements are the times the measurements taken. Chapter 3. Retrieval of Key Parameters . 69 The unique feature of the results on July 14 is that there are two clusters of pixels in figure 3.5. The one corresponding to <f> = 179° has r3e ranging from 5/zm to 12/rni, which is close to the aircraft measurements r™ (table 3.1). In contrast, the one with <f> = 5° gives much smaller r"e values than the measurements. It is known from previous studies (cf., Stephens, 1978; Slingo, 1982 etc. ) that the droplet effective radius for marine stratrocumulus is in a range between 4 and 16izm, thus implying that figure 3.5 (b) is unrealistic. It can also be seen from figure 3.5 that although the value of r3e for these two clusters differs greatly, the range of r* for the former cluster is only slightly smaller than that of the later. This:• observation--suggests' thatr-'the'responses of the cloud channel 1 and 3 reflectances to the variation in <f> are different. To explain the results of July 14 1987 qualitatively, we first refer to figure 3.4, to illustrate the reason for the large difference in (j) within a small area. For this particular image, the satellite is right above the area of our interest. Therefore, the pixels in the west and east (region I and II of figure 3.4 , respectively) have completely different <f>. One is close to 0° and the other is approximately 180°. Second, we show the reflected radiation in the meridian plan (i.e., the plane with <f> = 0°,180°) from Dave (1970) as representative of the pattern of the reflected radiation. This case is equivalent to water drops with radii 5.7/zm at AVHRR channel 3 wavelengths. The part to the left (right) of the zero 9 line is relevant to the region II (region I) in figure 3.4 ). It is seen from this figure that the reflected radiance shows strong angular dependence when the scattering optical depth r\ is 0.1 since the reflected photons undergo low orders of scattering. In the part close to nadir, which is similar to the case of figure 3.5, the back scattered radiation (i.e., 4> ~ 0°) is larger than that of the forward scattered. It can also be seen that as TJ increases the angular dependence of the feflected radiance decreases due to the averaging effect of multiple scattering. (This calculation is made at 9Q = 60° , an angle larger than the July 14 case. According to another calculation at 0O = 0° made in Dave (1970), the Chapter 3. Retrieval of Key Parameters . 70 0.2 0.4 0.6 0.8 cloud channel 1 isotropic albedo 0.2 0.4 0.6 0.8 cloud channel 1 isotropic albedo Figure 3.5: Lines show relationship between the albedo in the AVHRR channel 1 and 3 from the Slingo model for various values of r c (dash lines) and r[ (solid lines) for 6Q = 39° . The dots are from July 14 1987 satellite measurements of cloud isotropic albedo in the relevant channels, a) for pixels from the area with 4> = 179° , and b) for pixels from the area pixels with <f> = 5.5° . Chapter 3. Retrieval of Key Parameters . 71 4 0 2 0 0 2 0 4 0 NADIR A N G L E IB) Figure 3.6: Intensity of the radiation diffusely reflected by a plane-parallel homogeneous atmosphere containing spherical monodispersion; T\ is scattering optical depth; the size parameter x (defined in appendix A) equals 10, the refractive index m = 1.342,9o = 60° (after Dave, 1970). reflection may show larger angular dependence when 90 is smaller, making anisotropy important at larger optical depth.) Next, we explain why in figure 3.5 Rc\ did not show strong (f> dependence, while i?c3 showed this dependence. This follows from the fact that the solution to the two-stream radiative transfer equation (A.l) has a term with an exponentially decaying factor exp(—KT), thus implying a typical optical depth 1 r = K-1 = (3.7) which is the optical depth at which the flux attenuate to 1/e (called the diffusion length by Coakley and Davies (1986)). With ui and g values from Irvine and Pollack (1968), we obtain from the above equation that this optical depth for the AVHRR channel 3 is around 3 to 5 (depending on cloud drop size), a range equivalent to a scattering optical depth r/ (= TU, see figure 3.6) from 2.4 to 4.4. In contrast, this optical depth for the Chapter 3. Retrieval of Key Parameters . 72 AVHRR channel 1 is large since the value of u is close to 1. Due to the small « for channel 3 the radiation in channel 3 can only penetrate a small distance in clouds before being scattered back or absorbed. Therefore, the reflected radiation only has the chance to have low orders of scattering; and hence the reflection shows anisotropy. In contrast, the radiation in channel 1 can penetrate deeply and experience high orders of multiple scattering, therefore the reflection is more isotropic than that of the channel 3. The results in figure 3.5 reveal that it is not appropriate to use the isotropically based Slingo model directly for cloud droplet effective radius retrieval. We used the Slingo model for this test since the aircraft measured cloud reflection in 0M5pm shows a fairly isotropic reflection field for observational zenith angle within ±50° (King, 1987), and the range of the AVHRR viewing angle is (-55.4° < 6 < 55.4°). . • . 3.1.4 Discussion The differences between r* and r™ may come from other sources: • difference in physical meanings of the two types of measurements The satellite inferred r3e corresponds to an equivalent radius for a certain area (pixels > 1.1 x l.lkm in this study) and the whole cloud layer (Nakajima and King, 1990), whereas the aircraft measurements are averages along a line at the height of the airplane which varies with time. However, as we pointed out earlier, the in situ measurements show that the r e for marine stratrocumulus is almost always larger than 4pm, hence the result in figure 3.5 (b) is unrealistic. • difference in time between satellite passing and in situ measurement Although the area we calculated for the satellite image accounted for advective transport over the observation period, according to the wind velocity and the dif-ference of the measurements in time, the cloud parameters may change with time Chapter 3. Retrieval of Key Parameters . 73 (the largest time lag in table 3.1 is over two hours). Again according to the mea-surements, the cloud drop size would not become smaller than Aum. • noise in the AVHRR channel 3 One problem with any application of the AVHRR channel 3 data is that the data may be seriously contaminated with noise. Fortunately, the noise of channel 3 on board NOAA-9 is found to be greatly reduced in comparison with the NOAA-7 (Dudhia, 1989). The noise pattern can hardly be seen on our image after averaging for every 4 neighboring pixels. • the emission associated with the AVHRR channel 3 The thermal emission in channel 3 (3.7/im) is removed by assuming blackbody emission at cloud top temperature Tc, where Tc is given by the brightness tempera-ture of the AVHRR channel 4 (12/zm). The consequence of the assumption is that the contribution of differential absorption and emission of atmospheric gases (e.g., nitrous oxide, water vapor) to the brightness temperatures in these two channels is ignored (Coakley, 1986). According to Saunders and Edwards (1989), the effect of this simplification to the TOA channel 3 brightness temperature is less than IK, corresponding to a channel 3 radiance difference of Q.02mWm~2 (i.e., an error in rae of around lfim ). We conclude that the unphysically small values of result from ignoring azimuth dependence in the two-stream Slingo model. One solution to this problem is to use a more realistic radiative transfer model which calculates radiance instead of irradiance. One example for such a model is the discrete ordinate^radiative transfer model (Stamnes, et al. 1988). The other solution is to apply an anisotropic correction to satellite data. One example may be found in Buriez et al. (1986) in which relationship between the Chapter 3. Retrieval of Key Parameters . 74 satellite measurements at any direction and that at nadir in a certain atmospheric trans-mittance range is derived empirically. The data used to derive these relationships are from satellite measured albedo and atmospheric transmittance calculated from surface flux measurements. 3.2 Cloud Detection and Cloud Fraction Estimation 3.2.1 The Method To identify fully clear, cloudy and partially cloudy pixels, we employ the spatial coherence method developed by Coakley and Bretherton (1982). The method calculates cloud fraction for layered clouds over uniform surfaces using global area coverage (GAC) data constructed from AVHRR channel 4 (Wpm) data. The physics underlying the method can be stated as follows. If the cloud is thick, and if the sea and cloud surface are blackbody emitters, IR radiation fields over completely clear or cloudy regions are locally uniform, and hence correspond to areas of uniform brightness at two distinct temperatures on the satellite image. On the other hand, those over cloud edges exhibit large spatial variations, which results in sharp contrasts on the image. Therefore, if we calculate the means and standard deviations of IR radiances for several neighboring pixels, and plot the local standard deviation against local mean radiance, the results would show an arch structure when the image contains both completely clear and cloud pixels (figure 3.7). Pixels in the foot with higher radiances (Is) correspond to clear sea surface, while pixels in the foot with lower radiances (7C) correspond to fully cloudy pixels. Other pixels with high local standard deviation of radiance are interpreted as partially cloud covered and their cloud fraction are determined from (3.8) Chapter 3. Retrieval of Key Parameters . 75 co "> CD "O c. CO "D c co ••—* CO co o o pH»-s'.siV-'«i«.'..'r '4--' Local mean radiance Figure 3.7: Sketch for spatial coherence method. The x-axis is local mean radiance, and y-axis local standard deviation. The cluster around A and B represent completely clear pixels, Other pixels (e.g., C) represent partial cloudy pixels. Figure 3.8 shows the results when this technique is applied to the AVHRR channel 4 data taken on July 7 1987 AVHRR. The clear sky radiance in channel 4 is 94.6 ± 1 m W m - 2 , corresponding to the blackbody temperature of 289 ± 0.7/^ ; cloudy sky radi-ance is 87.5 ± 1 W m - 2 , corresponding to the blackbody temperature 284.3 ± 0.7K. The difference between the two temperatures indicates that the height of the cloud is 780±230 meters if the atmospheric lapse rate is 6 degrees per kilometer. The cloud amount for the whole area can be obtained from averaging the cloud fraction. The uncertainty in cloud amount is associated mainly with the width of the two feet. Its typical value according to Coakley and Bretherton (1982) is 4% . 3.2.2 Limitation of the Spatial Coherence Method Like many other techniques developed to deduce cloud cover, this method fails to give accurate estimation of cloud cover under the following circumstances: Chapter 3. Retrieval of Key Parameters ... 76 P 'a O d 88 90 92 94 Local Mean Radiance Figure 3.8: Local standard deviation vs. local mean radiance obtained from calculation to 2x2 arrays of July 7 1987 the AVHRR LAC data. The area is the same as figure 3.3. • the clouds do not show a layered structure (such as clouds associated with a frontal system) • the clouds in the scene are everywhere smaller then the resolution of the analysis (« 2km)2 in this study) • the clouds are too low, so that there is no clear distinction between clouds and sea surface • clouds have variable emissivities (such as cirrus) We applied the technique to the FIRE data and found the main problem with this method and this data set is that in 12 out of 21 cases the cloud is too low to differentiate between cloud and sea. Under this circumstance, the data in the visible channel can be used for cloud detection. Chapter 3. Retrieval of Key Parameters ... 77 3.3 Column Water Vapor Amount Retrieval 3.3.1 The Method It is desirable to get the column water vapor amount Wv from the AVHRR data since the TOVS has a field of view roughly 60 km in diameter which makes the collocation of the TOVS data to the AVHRR difficult. In this section, we test the use of differential absorption by water vapor in the two adjacent AVHRR IR channels for Wv retrieval. This idea has been used successfully in the split window technique for atmospheric correction of sea surface temperature. The possibility of. using, this, ijlea .to jjdet. Wfv^ has, ...been numerically studied with radiative transfer models (Dalu, 1986; Schluessel, 1989 etc.). It is found from these studies that in spite of the influences of the atmospheric conditions (e.g., vertical structure of water vapor, temperature) Wv can be linearly related to the brightness temperature difference between the AVHRR channel 4 and 5, with coefficients that depend on 8Q. The standard error due to the variation of the atmospheric conditions and. the simulated noise of the instrument is within 0.59 cm water (Schluessel 1989). 3.3.2 Comparison of Satellite Retrieved Column Water Vapor with Ra-diosonde Measurements To verify the linear relationship, we compared the water vapor amount obtained from satellite retrieval with that from radiosonde measurements. The relationship we used for the satellite retrieval takes the following form: W* = [ao + ai(T 4-T 5 )]c O s0 (3.9) with ao = 0.15cm, a\ = 2.23g/Kcm 2 (3.10) * Chapter 3. Retrieval of Key Parameters . 78 where 9 is the satellite viewing angle, and the coefficients are from a fit to the results of Shin (1986). The satellite data is from NOAA-9 AVHRR imagery between June 30 and July 19 1987 for areas from 33° to 33.5°N and 119.2° to 119.7°W. Twelve out of 20 of the images contain clear pixels (as indicated by the spatial coherence method) in the area we are interested in. The in situ measurements of column water vapor amount W ™ are calculated from the temperature and relative humidity soundings taken by the cross-chain Loran atmospheric sounding system (CLASS) at the northwest end of San Nicholas Island (33.3°N and 119.5°W) during the same period. There are 69 soundings in total. We consider the 63 soundings which reached at least lOOmb. The column water vapor amount from the CLASS is computed from the following integration with pressure p: w?=rqdP (3.H) where pi,p2 are pressures of the bottom and top of the sounding, and q is the water vapor mixing ratio computed from measured relative humidity U (in percent) and temperature T (in degree Celsius) from the following equation (Schubert, et al. 1987) 9 = 2 ^ £ i (3.12) p — e e = e.{T)U = 6 . 1 1 2 e s p ( r ^ 6 2 ^ ( 3 . 1 3 ) where e and e3 are vapor pressure and saturation vapor pressure, respectively. Neglecting the time lag of the humidity and temperature sensors, the error in W ™ due to the measurement error in temperature, humidity and pressure is less than 2% of the total. The results of our comparison are shown in figure 3.9. Although it is hard to make any conclusion due to the limited number of satellite soundings, the comparison seems to show larger errors than those from the simulation studies (Dalu, 1986; Schluessel, 1989). Moreover, there is a tendency to underestimate VKJ from the fifth to the fifteenth day. Chapter 3. Retrieval of Key Parameters . 0 5 10 15 20 y Time (day) Figure 3.9: Comparison bf the column water vapor amount obtained from the CLASS (solid line) and the AVHRR (dots) for the area over the San Nicholas Island from June 30 to July 19, 1987. 3.3.3 Discussion Our results for tendency to underestimate W* from satellite data are in contrast to the only case study found in the literature (Schluessel, 1989). Schluessel found from one pass of NOAA-7 data that this simple method systematically overestimates column water vapor amount for relatively dry atmospheres. From the numerical simulation of Dalu (1986), the coefficients for equation (3.9) are a 0 = 0cm, a i = 1.96g/Kcm2, which are different from the values given in equation (3.10). This difference may due to the differences in their model. However, from another point of view, this difference may suggest that the coefficients are data-set dependent. Therefore, these coefficients may change with time or location. Possible sources that could lead to the bias towards an underestimate of W ° from our results are: . Chapter 3. Retrieval of Key Parameters . 80 • absorption and emission of atmospheric gases It is shown in Saunders and Edwards (1989) that the modification by the gases of the TOA channel 4 and 5 brightness temperature under the U. S. standard atmosphere are not the the same. The differential influence of water vapor is the largest, which is the basis of the retrieval. However, the differential influences of other gases, though small, are nonnegligible. For example, the effect of carbon dioxide introduces around a 0.18 K brightness temperature difference, which corresponds to a 0.4 cm difference in W ° if (3.8) is used. • nonlinear response of the AVHRR IR channels to radiance The calibration for AVHRR channel 4 and 5 data for the present study is linear (appendix C). It was found, however, that the AVHRR on board NOAA 9 suffered from higher nonlinearity than the NOAA 7 (Brown, et al. 1985). According to tables published for the nonlinear correction (Brown, et al. 1985; Weinreb, et al. 1990), the difference of the brightness temperature correction needed for channel 4 and 5 can be as large as 0.2 K at the scene temperature we are interested in. This temperature difference results in 0.44 cm difference in W*. We corrected our data with tables in Weinreb et al. (1990). However, we found no improvements in the retrieval. Chapter 4 Conclusions and Future Extensions We have investigated the feasibility of estimating the sea-surface net solar flux from the AVHRR data based on a hierarchy of physical models, including a tf-Eddington radiative transfer model (Slingo and Shrecker, 1982), a simple physical model (Diak and Gautier, 1982) and its variant. The sensitivity studies based on the radiative transfer model were separated into clear and cloudy cases. For the clear case, we found: • The uncertainties in daily mean sea-surface net solar flux due to the uncertainty of individual atmospheric and surface parameters is less than 5.4 Wm~2 (see table 2.3 for detail). The potential uncertainty is close to 10 Wm~2, which is the accuracy requirement for climate studies, due to the combined effect of the uncertainties in column water vapor and ozone amount. • If the daily mean sea-surface net solar flux is retrieved from the satellite measure-ments, imperfections in the retrieving scheme may result in larger uncertainties. As an example, we showed that if the Gautier clear model were applied to the AVHRR data for daily mean sea-surface net solar flux, a change in column water vapor amount would be misinterpreted as a change in the sea surface albedo, resulting in a larger uncertainty in the surface flux. For cloudy conditions, we observed from the sensitivity study that: • The uncertainties in daily mean sea-surface net solar flux is larger than for the clear 81 Chapter 4. Conclusions and Future Extensions 82 case, mainly due to the uncertainties in cloud optical depth and cloud amount. These uncertainties due to the typical sensitivities of the cloud optical depth and cloud amount when retrieved from remotely sensed data are 17.2 Wm~2 and 9.2 Wm~2, respectively (see table 2.4 for detail). • The broadband cloud albedo and absorptance, which are important parameters in the Gautier cloudy model, depend heavily on the cloud optical depth, and the solax zenith angle. The cloud absorptance depends also on the cloud droplet effective radius. • Our sensitivity study showed that cloud albedo in the AVHRR channels 1 and 3 are most sensitive to cloud optical depth and droplet effective radius. These results confirm the applicability of the AVHRR data for cloud optical depth and drop si2;e information retrieval (Arking and Child, 1984). From the sensitivity study, we found also that Gautier's cloudy model may introduce large errors in surface flux estimates due to its oversimplification of the calculation of cloud albedo and absorptance. Therefore, we constructed a variant of Gautier's cloudy model. The variant, first, calculates cloud optical depth and droplet effective radius from TOA upward fluxes in AVHRR channel 1 and 3, and then uses these derived parameters, with solar zenith angle, to estimate cloud albedo and absorptance. To compare the original and the variant, the Slingo <5-Eddington model is used to simulate the satellite and pyrometer measurements in the real world. It is found from this simulation study that • A direct use of the Gautier's simple physical approach for the cloudy case at = 0.78 may introduce an error in surface net flux over 30 Wm~2 (cf., figure 2.17 (a)) for a large range of cloud optical depths and droplet effective radius. At this solar Chapter 4. Conclusions and Future Extensions 83 zenith angle, Gautier's model is expected to give the best estimation of surface net flux. The implication of this result is that the 4 Wm~2 accuracy of the approach, which is suggested in Gautier and Katsaros (1984), may be over-optimistic. • The variant of the original scheme incorporates the dependence of solar zenith angle and cloud droplet effective radius into the calculation of cloud broadband optical properties, and hence reduces the error in surface net flux to less than 3 Wm~2 at fi0 — 0.78 (cf., figure 2.17 (b)). The relationships between cloud broadband optical properties and the AVHRR narrow band measurements for the variant are obtained from radiative transfer modeling under standard atmospheric and surface conditions. • Both the original simple physical model and its variant are subject to the pertur-bations of the atmospheric conditions.. For example, if the column water vapor amount is changed by 50%, the maximum error in the original, and its variant are increased to 41 and 12 Wm~2, respectively. In light of the inadequacies of Gautier's original clear model for the low-albedo ocean surface recognized from our sensitivity study, we proposed an alternative scheme for the clear case. More specifically, we proposed to determine the atmospheric scattering, instead of determining surface albedo in the original model, from the satellite data. In chapter 3, we investigated the feasibility of retrieving some cloud and atmospheric parameters from the real AVHRR data for the estimation of sea-surface net solar flux. This is done using existing methods (e.g., Nakajima and King, 1990; Coakley and Brether-ton, 1982), with the retrieved parameters compared with in situ measurements for some cases. Our principle findings are • Comparisons between the satellite inferred and the in situ measured cloud optical depth and droplet effective radius show the potential capability of the AVHRR data Chapter 4. Conclusions and Future Extensions 84 for retrieval of these cloud parameters (cf., figure 3.3). However, unrealistic results of cloud droplet effective radius are obtained using the Slingo 6-Eddingtdn model due to the anisotropic scattering of clouds in the AVHRR channels, especially in channel 3 (cf., figure 3.5). • The spatial coherence method can be used successfully in detecting cloud filled, partially filled and clear pixels for most cases (cf., figure 3.8). However, there are 12 out of 21 cases in which the spatial coherence method fails to distinguish the clear pixels from cloudy ones due to the low height of the cloud top. • The comparison between satellite-estimated column water vapor amount and ra-diosonde measurements shows a tendency for the underestimation of vapor amount by the satellite. It is unclear if this underestimate is caused by the absorption and emission of trace gases or by the nonlinear response of the AVHRR to the radiance;. Future Extensions The limitations in the present studies suggest a number of plausible extensions: • There is a considerable disparity between the Slingo model predicted cloud broad-band absorptance and the in situ measurements (cf., figure D.2). The possible reasons for this disparity are discussed in appendix D. A convincing explanation for our observed discrepancy requires additional in situ measurements and radiative transfer modeling. • The climatological mean column water vapor and ozone amount needs to be re-placed with more accurate values due to their effects on surface flux estimation (cf., figure 2.19, table 2.3). The parameter that may introduce the largest error in estimating the surface net flux under the cloudy case is the stratospheric ozone amount which affects the calculation of cloud albedo in the AVHRR channel 1. Chapter 4. Conclusions and Future Extensions 8 5 The cloud channel 1 albedo, in turn, influences the estimation of cloud broadband properties in the original model as well as the extraction of cloud optical depth in the alternative one. One possible solution to the uncertainty of water vapor and ozone amount is to use the profiles inferred from the sounders onboard the satellite (Cunnold, ef al. 1989). • The dependence of channel 3 albedo on the satellite viewing angle indicates that a correction for the anisotropy of the satellite measured radiance is required for the cloud droplet effective radius retrieval. Nevertheless, such a correction obtained empirically at several discrete atmospheric transmittance may change when the time, location, atmospheric and surface conditions are changed. Another possible solution is to derive the relation for the anisotropic correction on the basis of the sensitivity study using an azimuth-dependent radiative transfer model. • Other cloud detection schemes reviewed in the introduction need to be used when the cloud top is too close to the sea surface. More possible problems may emerge if the spatial coherence method is used in the Arctic since the ice may be as bright and cold as the cloud. Under such circumstances, the difference in spectral reflectance associated with different surface types can be used to tell ice pixels from cloudy ones (Sakellarion, et al. 1990). Appendix A Elementary Facts from Two-stream Radiative Transfer We summarize some terminologies, originated in the field of two-stream radiative transfer and used frequently in this thesis, for the convenience of reference. (See Paltridge and Piatt, 1976; Shettle and Weinman, 1970; Wiscombe, 1977; Goody and Yung, 1989 for more detailed description.) Two-stream model is a simplified version of the equation of radiative transfer. Two-stream models calculates only the radiative fluxes in two opposite directions (i.e., upwards and downwards). It is assumed, in two-stream models, that for plane parallel medium the phase function P, a function describing the angular dependence of the scattered radiation field, takes a specific azimuth averaged form. Under this assumption, the equation of the two-stream radiative transfer can be written as d2F dr2 with = 3 ( l - u O ( l-i ^ ) F + / ( l -u, ) ( l//i 0 -3^o) (A.l) F = F + u.Qf (A.2) l r+1 g = - I P(il))cosi>d(cos4>) (A.3) .2 J-i » = % (A.4) T S S /' KeP(z)dz (A.5) Jo where F is the total flux, g the asymmetry factor, UJ the single scattering albedo, r the optical depth, and fio the cosine of solar zenith angle (defined in figure 1.2). Physically, 86 Appendix A. Elementary Facts from Two-stream Radiative Transfer 87 F and / represent the diffused and direct part of the flux, respectively; the g in (A.3) describes the anisotropic scattering of the radiative flux by the medium, with ip the scattering angle; the u> in (A.4) is the probability of a photon scattered when interacting with a medium, with Kac and Ke mass scattering coefficient and extinction coefficient; and finally, the r describes the quantity of radiance attenuates when the radiation go though a medium, with p(s)ds the total mass of the medium per unit cross-sectional area (g/cm2) along ds. <5-Eddington approximation Provides an approximate phase function for predom-inately forward scatterers. It is assumed, in this theory that the phase function can be represented as a sum of two parts: one for a nearly isotropic part representing the broadly scattered part of the radiation field, and one for a 6-function part representing the radiation scattered in the forward direction. This approximation is widely used for its accuracy and efficiency. Determination of g,u> and r for cloudy layer In the presence of water clouds, the basic cloud parameters for the two-stream model (i.e., cloud optical depth, asymmetry factor, single scattering albedo) can be determined with Mie theory as functions of drop size distribution n(r) and efficiency factors, which depend upon the refractive index m = mT + im; . For example cloud optical depth may be defined as: rcloud top roo TC= / n{r)Qext(x)*r2drdz (A.G) J cloud base JO where x = 2irr/X , with A wavelength, is the size parameter, Qext{x) t n e efficiency factor for extinction determined from the Mie theory and n(r) the cloud drop size distribution. To avoid the time consuming Mie calculation, these basic parameters in the Slingo model are parameterized as functions of cloud liquid water path (LWP) and cloud droplet effective radius re by fitting to the results of Mie calculation. The LWP is calculated Appendix A. Elementary Facts from Two-stream Radiative Transfer 83 from rcloud top LWP= / LWCdz (A.7) J cloud base where LWC is the liquid water content (gm~3) at height z (m). The effect of cloud with drop size distribution n(r) on radiation is simplified to a single parameter cloud droplet effective radius re. Given that the amount of radiation scattered by each particle is proportional to 7rr2, re is defined as _ Jo° rxr2n(r)dr E ~ / Q 3 0 7rr2n(r)dr or a r n ( r ^ ( A g ) $rTn(r)r2dr K } According to Stepens (1978), if Qext{x) m (A.6) is set to its large K asymptotic value 2, a value corresponding to shortwave limit, (A.6) can be simplified to: rcloud top roo r c « / 2TT / n(r)r2drdz. (A.9) J cloud base JO With the definition of r e , a widely used approximate form for r c is obtained rcloud top ZLWC , , . i r N TC « / fl* (A.10) J cloud base 2r e where r e is in /zm, L W C in g/ra3 and z in meter. With further approximation LWC — / -7rn(r)r /)jaV Jo 3 • « ^ r ^ , , (A.ll) where N is the number of cloud droplets in a cubic meter and pi the density of the liquid water in g/um3, we have an alternative form for (A.10) in terms of N, rcloud top •c rcloua top / 2i:NrlPidz. (A.12) J cloud base Appendix B Variability of Atmospheric and Surface Conditions We list the variability of column water vapor, ozone amount and sea-surface albedo used in chapter 2, as well as our choice of reference values. Variability of column water vapor amount The variability of column water vapor amount assumed in this study is chosen based on a comparison between the in-tegration of the McClatchey midlatitude water vapor profiles and the radiosonde data between 500mb and the surface obtained from Vancouver Island (Lott, 1976; Ho and Riedel, 1979). Based on the Vancouver Island observations, we choose a 50% variation about the McClatchey midlatitude summer profile (2.94 cm) as the possible range of column water vapor amount variation in summer. As a result, the range of water vapor amount in summer is from 1.49 to 4.42 cm. In winter, we choose 0.86 cm from Mc-Clatchey midlatitude winter profile as the lower limit and the maximum water vapor amount 2.70 cm from observation as the upper limit of total water vapor amount. Variability of column ozone amount From the McClatchey profiles, the col-umn ozone amount for midlatitude summer is 325 Dobson units and for midlatitude winter is 404 Dobson units. Since the balloon observed variability of tropospheric ozone is of the order of 50%, and the variability increase with height, reaching a maximum in excess of 100% at 10 km ( Krueger and Minzner 1976), the range of column ozone amount is chosen to vary from one tenth to two times of the value obtained from McClatchey mid-latitude profiles. Therefore, the ranges of column ozone amount for summer and winter are from 32.5 to 650 Dobson units and from 40.4 to 808 Dobson units, respectively. 89 Appendix B. Variability of Atmospheric and Surface Conditions 90 Variability of sea surface albedo According to the observation of Payne (1972), the uncertainty of sea surface albedo is primarily from the roughness of the sea surface, and the maximum effect of the sea surface roughness is less that 20% . We take this maximum value as the uncertainty of sea surface albedo under the clear case. Under cloudy conditions, we change the albedo 0.07 by 20% (from 0.056 to 0.084) according to Payne's measurements under thick cloudy conditions. Appendix C A V H R R data Calibration The AVHRR went though pre-launch and post-launch tests and calibrations. In this appendix, we describe briefly, how to get the channel radiances from instrument measured counts, using these calibrations. For those particularly interested in the procedure of AVHRR calibration, the suggested references are Rao (1987), Lauritson (1979), Weinreb, et al. (1990) and Kaufman and Holben (1990). C . l Visible Channel Calibration The AVHRR has no onboard calibration system for visible wavelengths. The common practice is to use the following linear regression relationship to convert the AVHRR digital counts to reflectance factors of the earth-atmosphere system A,-where i denotes the AVHRR channels 1 and 2, d is the AVHRR counts and A,- is the with the filtered radiance measured by AVHRR visible channels when viewing the earth-atmosphere system in orbit Lt- and the filtered extraterrestrial solar irradiance at the mean earth-sun distance defined as: A{ — a,-(%) + b{(% j count)C{(counts) (C.l) reflectance factor of the earth-atmosphere system defined as (C.2) (C3) 91 Appendix C. AVHRR data Calibration 92 7, = / IoxTxd\ (C.4) where L\ is the radiance towards the satellite sensor at wavelength A, T\ transmittance of the sensor; IQ\ the extraterrestrial spectral solar at wavelength A, and Ai, A2 the cut-on and cut-off wavelength of the passband of the AVHRR channel. The coefficients a,- and 6; in (C.l) are determined from the pre-launch calibration, which linearly relates the reflectance factor of the NASA 30-inch integrating sphere source A3i to the AVHRR counts. The definition of reflectance factor of the integrating sphere A* is as follows: where L* is the filtered radiance measured by AVHRR visible channels when viewing cit the integrating sphere source at laboratory (defined similar to Li). The averaged signal degradations of AVHRR channel 1 and 2 onboard NOAA-9 are found to be around 0.4% per month and 0.2% per month, respectively. The following expressions from Kaufman and Holben (1990) are used to compensate for these degra-dations A° = Ii (C.5) (C6) 0.953 - 0.00425x L2 (C.7) 0.86633 - 0.0021667x where x is the number of months since Dec 31, 1984. C.2 Infrared Channel Calibration The calibration of infrared channels, known as channel 3, 4, and 5, is performed in-flight and is based on the assumption that the radiance in each channel L{ is linearly Appendix C. AVHRR data Calibration 93 related to the AVHRR counts C,-. i. e., Li = aiCi + bi (C.8) where a,- and 6,- are the gain and intercept of the relevant channel. They are determined from two measurements of radiance in orbit. One is from an internal calibration target at temperature approximately 288K and the other is from cold space at temperature approximately 3K. Due to the deviation of the real relation between radiances and outputs of AVHRR channel 4 and 5 from the linear relation (C.8), especially for NOAA 9, several sets of nonlinearity correction data based on pre-launch tests were published for studies needing accurate surface temperature. It is well known that the channel 3 data is frequently contaminated by periodic noise from an unidentified source. With the AVHRR from NOAA-9, the noise is found to be greatly reduced in comparison to the earler AVHRRs. The noise pattern was found to show regular vertical bands suggesting that the noise from NOAA-9 AVHRR channel 3 is more stable and synchronized with the scan rate. While various Fourier analysis techniques have been used to remove this noise, channel 3 images for this study are obtained simply from averages of every four pixels. The ver-tical noise pattern described by other investigators is hardly noticeable from our images (Warren, 1989). Appendix D Comparisons Between Slingo Model Results and in situ Measurements Comparisons between Slingo model results and aircraft measurements have been made by Slingo et al. (1982). They found that fluxes calculated from Slingo model and mea,-sured from aircraft are in good agreement, although there is a consistent overestimation of the downward flux at cloud top. In this section, we present further comparisons between measured and modeled fluxes. D . l Comparison with Surface Flux Measurements under Clear Case The measurements under the clear case were made above a forest near the coast of Vancouver Island (125°W, 49.3°N) in summer 1990 (Chen and Black, 1991). The wavelength range of the pyrometer is from 0.285 to 2.8/ira. The precision of the total and diffuse fluxes are 2% and 5% , respectively. The Slingo-model-predicted flux between the wavelengths 0.30 and 2.91/zm is used for the comparison. Figure D.l , show the results for July 19, 1990. It is seen that the Slingo model overestimates total flux and underestimates diffuse flux at the surface for this clear case. This discrepancy is due to the underestimate of the atmospheric scattering by aerosols. The effect of aerosol on surface radiation inferred from this figure is around 10 to 30 Wm~2 , which is approximately equivalent to an aerosol optical depth of 0.02, a value typical for mid-latitude relatively clean atmosphere. The several local minima in the total flux and maximum diffuse flux measured in the afternoon were due to scattering by small clouds. 94 Appendix D. Comparisons Between Slingo Model Results and in situ Measurements 95 D.2 Comparison with Aircraft Flux Measurements We also compared also the model results of downward, upward and net fluxes with aircraft cloud soundings at San Diego on July 2 and July 14 1987. Figure D.2 shows one example of the comparison. The input cloud LWC and r e profiles to the Slingo model are 2 mb averages of the aircraft soundings. The model-produced downward and upward flux profiles compare well with the measurements above the cloud, whereas, the depletion of net flux from cloud top to cloud bottom predicted by the model are obviously less than the measurements. This result means that the model predicted cloud albedo is in agreement with in situ measurements but the cloud absorption from the model is less than the measurements. A similar disparity is observed by Foot (1988) who found that in situ measured cloud absorption is about double the Slingo model predicted values. The possible reasons for this discrepancy, as pointed out in Stephens and Tsay (1990), are: • cloud absorption enhanced by a small number of large drizzle sized droplets unde-tected by aircraft • additional absorption by other particles (e.g., aerosols) embedded in or interstitial to cloud drops • possible existence of a near IR water vapor continuum absorption • energy loss due to the reflection of cloud sides • the technical difficulty of comparing the model results which are based on the plane-parallel assumption with the slanted aircraft measurements taken from a spatially varying clouds. For the two cases we compared, large drizzle amounts are found from the measurements. Appendix D. Comparisons Between Slingo Model Results and in situ Measurements 96 5 10 15 20 a) time (hr) 5 10 15 20 b) time (hr) Figure D. l : Surface downward a) total flux and b) diffuse flux from the Slingo model (solid) and from observations (dashed) for July 19, 1990. Appendix D. Comparisons Between Slingo Model Results and in situ Measurements 97 Figure D.2: Flux profiles from July 2 1987 cloud sounding (solid) and from Slingo model (dashed). Glossary A V H R R advanced very high resolution radiometer. C L A S S cross-chain Loran atmospheric sounding system E R B E Earth Radiation Budget Experiment. FSSP forward scattering-spectrometer probe. F I R E First ISCCP (International Satellite Cloud Climatology Project) Regional Exper-iment. G A C global area coverage data. G O E S Geostationary Operational Environmental Satellite. IR infrared. insolation incident solar radiation. L O W T R A N a model calculates atmospheric transmittance and radiance at moderate spectral resolution (20cm-1). N A S A National Aeronautics and Space Administration (Washington, D.C). N C A R National Center for Atmospheric Research (Boulder, Colorado). NESDIS National Environmental Satellite and Data Information Services (NOAA) (Washington, D.C). 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