DOC. C 55.13: NESDIS-4 8 a c / ^<«° r c „ F/dT , o S dA /dT must be equal or very close to zero, i.e, A and T must not be correlated. This, indeed, is the case except in the annual zonal case for both Northern Hemisphere and ocean where high correlation was found to exist between A and T (3^=0.84 and 0.76 respectively). And it is exactly these two instances in which dF/dT and 9F/9T are significantly different. We, S o however, hesitate to attach any physical significance to this finding since the sample size, only 9, is small. In order to examine in more detail the sensitivity that clouds demonstrate, Table 4 was generated. All data employed to produce numbers in Table 4 are identical to those used for Table 1 except that the cloud fraction is based on London (1957). London's cloud amounts are lower at all latitudes compared to those of Berlyand et al. (1980) used for Table 1. The differences in c between Table 4 and Table 1 are very significant especially for the Northern Hemisphere where differences in b=(9F/9T g ) are also very noticeable. This demonstrates again the delicate nature of cloud sensitivity to the cloud data set used, as was discussed earlier. An alternative way to estimate b and c is to look at the variation of longwave radiation with respect to surface temperature and cloud cover at each latitude zone. Table 5 lists these values, using surface temperatures from Warren and Schneider (1979), NOAA's SR longwave fluxes from Gruber and Winston (1978) and fractional cloud data from Berlyand et al. (1980). To ensure the 2 reliability of these estimates, only those values with r >0.85 are kept. Because of the small annual variation of temperature at low latitudes and -6- uncertainties in the data, which lead to low correlations, it is primarily these latitudes that are excluded by the above constraint. Further, if the standard error of a coefficient (SE) is comparable to the magnitude of the coefficient itself, the true value of such a coefficient must be viewed as unreliable. It is quite clear that b=(dF/dT s ) is not constant but has significant meridional variations, generally decreasing from equator to pole. Similar variations of b with latitude occur in the Southern Hemisphere. Such variations have also been found by Warren and Schneider (1979), who used the Ellis and Vonder Haar (1976) radiation data set, and by Ramanathan (1977) from simulations. However, the larger value of b obtained at higher latitudes in the Southern Hemisphere by Warren and Schneider (1979) is contrary to our result. A decrease of b toward the poles might be expected from the meridional variation of the effective emission temperature (T ) of the Earth-atmosphere system. In general, T e decreases with latitude, at least for latitudes greater than 20-30 . If the outgoing longwave flux is represented by (fT , where U is the Stefan-Bol tzmann constant, then dF/dT would decrease with increasing latitude. Since the effective emission temperature is positively correlated with surface temperature, one might also expect that b = dF/dT would also decrease toward the poles. 3-2 Relationship between surface and planetary albedo for clear skies. Regression equations linking the planetary to surface albedo for clear skies were derived by employing data obtained from model calculations as described in Section 2. These relationships were then tested with real data from satellite observations and ground measurements. The method of assessing the derived equations was to compute the root-mean-square-error (RMSE) of the -7- planetary albedo defined by, RMSE = A4 where n is the number of observations , oC > t-he observed planetary albedo, and o^the predicted planetary albedo defined as follows, c£ - 0.0587 + 0.7301 JT (6) tf( = 0.0410 + 0.7610 If (7) where f denotes the surface albedo. It is necessary to point out here that the (G\. \ ) relationship in Eq . (6) was derived for all solar zenith angles, whereas Eq . (7) was only for a solar zenith angle of 40°. Both Eqs. (6) and (7) show that at low surface albedos the planetary albedo is greater than the surface albedo; this is a result of the importance of the contribution of Rayleigh scattering to the planetary albedo when the surface albedo is small. At large surface albedos, the planetary albedo is less than the surface albedo; this is due to the depletion of the solar radiation by atmospheric absorption, which reduces the reflected solar radiation reaching the top of the atmosphere. There is a crossover point at which the planetary and surface albedos are equal. For Eq. (6), this occurs at an albedo value of 0.22, for Eq.(7), at an albedo of 0.17. Table 6 shows that the RMSE is 0.05, except when the Hummel and Reck (1979) values of |f are used in Eq.(7), in which case RMSE is 0.06. This may be attributable in part to the fact that Hummel and Reek's seasonal data were interpreted as representing the mid-seasonal month. Table 7 lists two regression equations derived from the observational data, using respectively, Robock and Hummel and Reck for surface albedo. In each case the standard error is 0.05. These two equations are to be compared -8- with Eqs. (6) and (7) which were previously derived using theoretical data. Notice that both the intercept and slope of the first equation in Table 7 are comparable to their counterparts in Eq (6). This indicates again that Robock's data are in somewhat better agreement with the theoretical equations. Fig. 1 shows the plot of the four individual regression lines, two from the simulations and two from the observations. At the higher and lower ends of both oCand f , there is a difference of about 0.05 between the highest and lowest of these lines. In the middle range, (.0= 0.2 to 0.4), the differences among the regression lines are very small. Overall, the line representing Eq. (6) agrees best with the other three lines. Further, these three lines certainly would fall inside the domain bounded by upper and lower lines drawn parallel to the line representing Eq. (6) to distance equal to ± 0.05. A somewhat similar study was made by Preuss and Geleyn (1980). For given model atmospheres, and using the two stream approximation, they calculated the reflected solar radiation for two different surface albedo values. For each model atmosphere they then derived a linear relation between the planetary albedo and surface albedo. The average values of the intercept and slope of their equation are, respectively, 0.101 and 0.59 for June and 0.108 and 0.57 for January/February. These numbers differ quite significantly from our observational and theoretical results discussed above. The agreement of the NOAA SR albedo observations with the theoretical regressions suggests that although the SR albedos are based upon measurements in the visible region of the spectrum they yield, at least for zonal averages, reasonable values for the total albedo. Recently, in connection with climate modeling studies some interest has been generated in the magnitude of the surface albedo of the Sahara desert -9- region. Based on observations of 16 target areas (^^500k.m x 500km each) over the Sahara desert area for a period of 12 days, the ERB (NIMBUS 7) gave an average minimum albedo of 36.7%. If one inserts this value into Eq. (6), one obtains a surface albedo of around 0.42. Similarly, if one uses the regression of ^fonoC, i.e.,y= -0.0724 + 1.34640L, one also obtains a surface albedo of 0.42, since in this case qJC and y fell nearly precisely on the same straight line. Since the NIMBUS 7 observations are close to local noon and since there is a tendency for the surface albedo to increase with increasing solar zenith angle, the actual mean daily surface albedo is probably a few hundreths higher than 0.42. Interestingly, an even higher value is predicted by Preuss and Geleyn (1980) equation. These albedos are much higher than those usually attributed to desert regions (e.g., Budyko, 1974, p. 55, gives a value of 0.28, and Hummel and Reck, 1979, give values of 0.25 to 0.31 for the Sahara region ), although Otterman and Fraser (1976) have derived a value of 0.44 from Landsat observations. 4. Conclusions The results presented here show that the cloud sensitivity coefficient ( 5F/3A ) as determined from multiple regression analysis of highly averaged data, is strongly dependent on the radiation and cloud data sets used in the analysis and also on whether one uses annual or monthly means. To a much smaller extent this is also true of the temperature sensitivity coefficient. There are a number of implications for climate models and climate theory. 1) Presently available radiation and cloud data sets yield different values for longwave radiation sensitivities causing uncertainties in the true values of these coefficients. -10- 2) Because of the uncertainty in the value of dF/dT to be used in energy balance climate models, the results of such models are subject to uncertainty (see Warren and Schneider, 1979 for sensitivity of climate model results to dF/dT ). Our results suggest that rather than using a single value of the coefficient dF/dT in such models, a latitude dependent or, even better, a temperature dependent coefficient should be used. 3) The strong sensitivity of 9F/9A to radiation and cloud data sets and to time averaging period suggest that it was fortuitous that Cess (1976) obtained a value of^-" -90 W"m for ^F/3A — a value almost exactly balancing the cloud albedo effect. It would appear that, if one were to try to obtain a mean hemispheric or global value of 9F/9A c from a regression of the sort used here, it would be more appropriate to use the monthly data, which allow for seasonal and latitudinal variations, rather than the annual data, which allow only for latitudinal variations. In almost all cases the 3F/9A values for J c the monthly data are lower than for the annual data and are well below the value required to balance the cloud albedo effect. 4) To obtain better estimates of these important sensitivity parameters, more accurate earth radiation budget and cloud climatological data are required. A simple linear relationship has been derived between the planetary albedo and the surface albedo for the case of clear skies. Such a relationship has important applications in climate modeling and in the use of satellite observations for cloudiness estimates and surface energy budget determinations. Application of this relationship to satellite albedo observations over the Sahara desert region yields a surface albedo of 0.42, significantly higher than previous estimates. -11- 4-1 TJ (D C CO T3 T) •O C C CO •> CO CO-I pi •>^»' a; *> — « a) 3 C •U CC CO u 0) P-On e r- Ol ON pi CO o 0) o CO 14-1 3 en CO E- > ft) J-l 0) 13 •H 0> c X- O • CO 0) CC T3 CD c ■H CO i— I a 0) 0) ej C CO ■H CO > c CO S-l o t-l >jCM ai l 0) T3 CO 3 P c CO 01 X- c «0 G 01 s- J-l 6 o <4-4 T3 c CC S-J CO T) c CO 4JrH CO I CJ> OJ o 10 4-1 •H OCM ■-i C I h ]) e w -oS BCN O MCM I C 13 CO J-i CO fx3 CO CO c o . NO Ol < CO 4-i be T3 3 o u OJ M3 c c o o H > 0) > •H 4-1 U 0> a CO 01 u 0) s- co CJ 01 X. iH E~ CO c o • •H /~* 4J O CJ 00 CO ON U — I -a C CO O 14-, BO OJ ,o a 4-i E -h co B U Pj fn < CJ H ,0. + CO Xi + CO II CO CO 3 C c o C N NO •— i in • • • 00 ON NO on on a- o o o r^ m on o o o o o o O ro co no in no rv o pi no O W CO 'Z t— I o r- o r^ • • • -^ co co On On On On On On O O O r>* cn -j- o •— « ■— < o o o o co m in — I oo .— i i— i o 00 On CO rv oo cn CM CM CO on oo r» • • • in m on r» no o On ON On O C O CO CM O i— I i— I CM O O O • > Pi NO a: u v. z NO 00 00 • • • CM CM NO ON ON 00 ON ON ON o o o LO —I o co cn 00 r- i 1— 1 i — 1 CM co CM i—4 CM ON 00 ON CM ON NO CM ■— i O r^ NO o r-« CO 1 1 NO 1 1 i — i 1 1 00 1 m 1 NO 1 sr Pi'. NO tc w co 2: -12- ph on <— i r~~ CN NO CO NOfO ^_- • • • • • • • • • UJ CO NO O O vO ON m m — < on 1 — t 1 — 1 i— I i— i . — i ^ I — CO to in cm on oo 00 ON On < o H -O /—v < CM CO \o -^ in VD cm m + rd O O O o o o O o O ■»— • • • • • • • • • • CO w o o o o o o o o o II C/N Pn oo o o o on -j- r^ co oo in no co m I I I o o o NO ON 00 N O — I 1— 1 i — I I-H 1 — 1 , — ■-H i— 1 r— 1 CO ed CJ o m O -^ • • • • • • • • • B c/? in r^ CM "" * r^ i— i r^ 1^ CN 1h o 14-1 NO vO O i-H -a- r^ NO VO CN XJ CO ON 0> ON ON 00 00 ON ON a CM • • • • • • • • • 0) (-1 o o o o o o o o o o X H ■—* ^5 /""V .O in CM -d- NO CO i— 1 I— 1 r-{ H X CO CO ■u C .O > C* NO • > Oi NO C o O w CO Z sc w w z jr w C/3 ^ O N i-H • • X o :z cyN -13- I-l 0) ■U (0 re a a; c 0) o o c 4J a 0) o x Xs to w g re C/N co <3J r-l re E- o H JO + re n + re ii fa &-, -^ vO CO in r^ ^a- •J- CM ^ • • • • • • • • UJ oo i— i r~- o m r^ co LTv en «-H 1— 1 iTl co CO 00 00 CN o> r^ ON ON on 00 ON ON ON ON cm o o m i-v. co vj- O o o o ON ON O i— i m m 00 m l>» m 00 SO r-. • • • • ■ • • • f-H o CM co OJ o CM CM f— t CM o n i—i CM O CM CM CJ CM CI CM CN CM y^ ^ «H H •-<. y^ re re H H c c re re o o c C N 5Z N o 5S o a pi NO < C* NO O N as NO < N pi NO S ►> w SB W t^ cr. 5z z C/J 5S w V) 53 < t-> CJ> H < f* u i—( .J X. c § o X *J c 5 B hJ re c (= re c re C C re -14- w CD CO — • CN • • • r*. vj- r^ ooui s • • • —I >* -3- CO - r^ o> o> o> o o o ON CO CO On On On o o o CT\ CTn 00 ON ON On O O O w CD m On c o *o c o •J E o 3 O H + <0 cd r^ o r-> O cn O r- -» (0 CO 3 3 3 + CO W CD cn rs no no r^ no o m — < cm o CM CM CM XI CO H CO X > PS NO O W CD z o > p> NO • > &, NO IX W cd 2: -15- co o z s o l-l TD O N <1J 1—1 X T3 <-> C c C co H O to 43 E -i i-i + E a» o pa CO u u-. B II O CO Lj ta 4-t y-i H 3 ctJ CD 4-1 CU CO Od T3 T3 • 3 lo o i— i cu o — i & -a CO c H co co CO 3 C c o CN N O r-» (N M on a\ o> o o o o O H \0 CO CJ o oo in oo CO M3 CN LO ON —1 CO -o 3 o CNI 1 1 1 lo l CO 1 0O in 1 1 I 1 co co 1 1 c 1 o + •H -J co CO H •H 43 X! >~» LO ON 00 i — i CN O II CO & fe co CM CN o CO 00 LO ^o LO o CO CJN OS C3N C3N ON CJN O O O O O O CO Ov o> CO IN CO O O O O O -h o o o o o o CN O O ON lo »i) vO in in n, cn in when there is no atmosphere. -18- References Berlyand, T.G. , L.A. Strokina, and L. Ye. Greshnikova, 1980: Zonal cloudiness distribution over the globe. Meteorologia 1 Hidrologia , No. 3, 15-23. Budyko, M. I., 1969: The effect of solar radiation variations on the climate of the earth. Tellus , 21, 6ll-6l9. Budyko, M.I., 197^: Climate and Life. Academic Press, N.Y., 505pp. Campbell, G.G. , and T.H. Vonder Haar, 198O: An analysis of two years of NIMBUS 6 Earth Radiation Budget Observations: July 1975 to June 1977. Atmos. Sci. Paper 320, Colorado State University, 83pp. (Available from Department of Atmospheric Science; Colorado State University, Fort Collins, Colorado 80523. ) Cess, R.D. , 1976: Climate change: An appraisal of atmospheric feedback mechanisms employing zonal climatology. J. Atmos . Sci. , 33, 1831-183^-. Cess, R.D., B.P. Briegleb, and M.S. Lian, 1982: Low-latitude cloudiness and climate feedback: Comparative estimates from satellite data. J. Atmos. Sci. , 39, 53-59. Ellis, J.S., and T.H. Vonder Haar, 1976: Zonal average earth radiation budget measurements from satellites for climate studies. Atmos. Sci. Paper 2^+0, Colorado State University, 50pp. (NTIS N77-1^588/7GA. ) Gruber, A., and J.S. Winston, 1978: Earth-atmosphere radiative heating based on NOAA scanning radiometer measurements. Bull. Amer. Meteor. Soc . , 59, 1570-1573. Hartmann, D.L. , and D.A. Short, 198O: On the use of Earth radiation budget statistics for studies of clouds and climate. J. Atmos. Sci . , 37, 1237- 1250. -19- Hummel, J.R. , and R.A. Reck, 1979: A global surface albedo model. J. Appl . Meteor . , 18 , 3, 239-253. Lacis, A. A., and J.E. Hansen, 197^+: A parameterization for the absorption of solar radiation in the earth's atmosphere. J. Atmos. Sci. , 31, 118-133. London, J., 1957: A study of the atmosphere heat balance. Report Contract AF 19 (l22)-l65, College of Engineering, New York University, 99pp. (NTIS PB 115626. ) Ohring, G. , and P. Clapp, I98O: The effect of changes in cloud amount on the net radiation at the top of the atmosphere. J. Atmos. Sci. , 37, ^7-^-5^ ■ Ohring, G. , and P.F. Clapp, T.R. Heddinghaus, and A.F. Krueger, 198I: The quasi-global distribution of the sensitivity of the Earth-atmosphere radiation budget to clouds. J. Atmos. Sci. , 38, 2539-25^+1. Otterman, J., and R.S. Fraser, 1976: Earth-atmosphere system and surface reflectivities in arid regions from Landsat multispectral scanner measurements. Remote Sensing of Environment , 5, 2^7-266. Preuss, H. J. , and J.F. Geleyn, 1980: Surface albedos derived from satellite data and their impact on forecast models. Arch. Met. Geoph. Biokl . , Seo, A, 29, 3^5-356. Ramanathan, V., 1977: Interactions between ice-albedo, lapse-rate, and cloud- top feedback mechanisms: An analysis of the non-linear response of a GCM-climate model. J. Atmos. Sci. , 3k , 1885-1897- Robock, A. , 1980: The seasonal cycle of snow cover, sea ice and surface albedo. Monthly Weather Review , 108, 3, 267-285. Schneider, S.H., 1972: Cloudiness as a global climatic feedback mechanism: The effects on the radiation balance and surface temperature of variations in cloudiness. J. Atmos. Sci. , 29, 1^13-1^22. -20- Simmonds, I. , and C. Chidzey, 1982: The parameterization of longwave flux in Energy "balance climate models. J. Atmos. Sci . , 39, 21^U-2151. Warren, S.G. , and S.H. Schneider, 1979 : Seasonal simulation as a test for uncertainties in the parameterizations of a Budyko-Sellers zonal climate Model. J. Atmos. Sci. , 36, 1377-1391- -21- UNIVERSrtY OF ILLINOIS-URBANA NOAA SCIENTIFIC AND TECHNICAL PUBLIC/ 3 0112 101860150 Thi National Oceanic and Atmospheric Administration was established as part of the Department of Commerce on October 3, 1 970. The mission responsibilities of NOAA are to assess the socioeconomic impact of natural and technological changes in the environment and to monitor and predict the state of the solid Earth, the oceans and their living resources, the atmosphere, and the space environment of the Earth. The major components of NOAA regularly produce various types of scientific and technical informa- tion in the following kinds of publications: PROFESSIONAL PAPERS— Important defini- tive research results, major techniques, and special investigations. 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