Reprinted from the preprint volume of the Seventh NASA-CR-204604 Symposium onGlobal Change Studies, 28 January - 2 February 1996, Atlanta, GA by the American Meteorological Society, Boston, MA SOLAR ABSORPTION IN CLOUDY ATMOSPHERES l/,_ ,Z_ 5.2 Harshvardhan 1 William Ridgway 2 V. Ramaswamy 3 ....-, -7." ....... S.M. Freidenreich3 Michael Batey 1 IDept. of Earth & Atmospheric Sciences, Purdue University, West Lafayette, IN 2Applied Research Corporation, Landover, MD 3NOAA Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey 1. INTRODUCTION continue to be reported. Cess et al. (1995) analyzed top-of-the-atmosphere and surface broadband short- Water in all three phases absorbs a significant wave radiation budgets to show that the atmosphere, in amount of solar energy in the near-infrared at the global mean, absorbs 25 Wm -2more solar radiation wavenumbers less than about 18,000 cm -_. Vapor than is currently modeled based on theory. absorption is thought to be well quantified (Rothman et Ramanathan et al. (1995) have shown that an additional al. 1983), at least as far as absorption lines are con- contribution by clouds to atmospheric absorption is cerned. There may, however, be some as yet uncertain necessary to balance the energy budget in the Pacific continuum absorption (Stephens and Tsay 1990). The Ocean warm pool region. Pilewskie and Valero (1995) bulk absorption properties of liquid water are also inferred cloud absorption from identical broad band thought to be reasonably certain (Irvine and Pollack instruments flown on aircraft flying in a stacked forma- 1968, Hale and Querry 1973, Palmer and Williams tion above and below cloud layers during TOGA- COARE and CEPEX (both Pacific Ocean experi- 1974, Downing and Williams 1975). Standard Mie the- ory then provides the single scattering properties of liq- ments). Their conclusion was also that cloudy layers uid water clouds of a prescribed size distribution (King absorb more radiation than is anticipated by theory. These last three studies have expressed cloudy sky et al. 1990). With the above information on vapor and droplet absorption in terms of the cloud radiative forcing of the absorption, it is then possible to obtain theoretical esti- atmosphere which is the contribution due to the clouds mates of the spectral and band averaged radiative prop- alone (Charlock and Ramanathan 1985) and have all erties of cloud layers and atmospheric columns contain- used broadband measurements. Earlier spectral mea- surements (Twomey and Cocks 1982, Stephens and ing clouds, at least under the assumption that the clouds Platt 1987, Foot 1988) have also led to the conclusion are plane parallel and homogeneous. However, there is that theoretical reflectances are much higher than a long history of apparent discrepancies between theo- observed values in the near-infrared windows where retically obtained cloud radiative properties in the near- infrared and values inferred from measurements cloud properties dominate column reflectance and (Twomey and Cocks 1982, Stephens and Tsay 1990). absorption. In light of this accumulating evidence that inferred cloud absorption, based on both spectral and Invariably, the measurements have implied that clouds, broadband measurements, differs significantly from or cloudy atmospheres, absorb more solar radiation than indicated by computations based on the known theory, it is perhaps appropriate to revisit the problem of spectral absorption of solar radiation in cloudy properties. Recent results have piqued renewed interest in this atmospheres. The theoretical computations that have been used to compute spectral absorption are discussed problem. King et al. (1990) have made in situ measure- ments of the radiation field within thick cloud layers in Section 2. Radiative properties relevant to the cloud and inferred the single scattering albedos of water absorption problem are presented in Section 3 and are clouds in the near-infrared water vapor windows. Their placed in the context of radiative forcing in Section 4. measurements agree quite well with theoretical calcula- Implications for future measuring programs and the effect of horizontal inhomogeneities are discussed in tions. It is, therefore, quite surprising that instances of the summary Section 5. solar absorption well in excess of theory iCorresponding author address: Harshvardhan Dept. of Earth & Atmos. Sci., Purdue University West Lafayette, IN 47907-1397 7TMSYMPONGLOBALCHANGESTUDIES 127 2. THEORETICAL COMPUTATIONS 3. SPECTRAL COLUMN RADIATIVE HEATING Water vapor and liquid do not absorb at visible Although computations for several combinations wavelengths and measurements have shown that there of cloud type, optical depth, solar zenith angle and is no indication of an inordinate amount of foreign cloud location are available, here we will show a selec- absorption (aerosols, say) at shorter wavelengths tion of results that illustrate the main features of solar (Twomey and Cocks 1982, Stephens and Platt 1987). near-infrared radiative properties of cloudy columns. In any case, it is unlikely that any foreign matter would The results shown will be for an optical depth of 10. be pervasive and present in all clouds at all levels. Conclusions drawn from this set are mostly valid for Interest is therefore focused on the solar near-infrared. the thinner and thicker cases but exceptions will be noted as warranted. In this spectral region, the atmospheric column absorp- tion in the presence of clouds is dictated by a subtle The analyses of Cess et al. (1995) and Ramanathan interplay between vapor and liquid absorption and scat- et al. (1995) show that the column absorption in the tering. Although both vapor and liquid absorb at these presence of clouds is in excess of theoretical expecta- wavelengths, there are highly transparent windows in tions. We will therefore examine column properties and ultimately frame the results in terms of a cloud the vapor absorption spectrum whereas the liquid absorption is quite smeared out with only local maxima forcing of the entire atmospheric column. and minima. Moreover, the water vapor band centers The total spectral absorption in the atmospheric column for clear skies is dominated by the various are so optically thick that a significant portion of the spectrum can become completely saturated with only near-infrared water vapor bands. The addition of a modest water vapor path lengths. A result of these cloud layer modifies the column heating but in a man- characteristics is that column absorption is sensitive to ner that depends on the cloud properties and more the placement of the cloud in the atmosphere (Chou importantly on the location of the cloud layer. Figs. 1989, Schmetz 1993). l(a)-(d) show the incident, clear sky and cloudy sky A very thorough investigation of spectral solar column absorption for the four cases identified in the absorption was carried out by Davies et al. (1984) who showed the importance of above cloud vapor and the distribution of column absorption among cloud water MLS+CS;180-200 mb;t=lO; 0-o=30° MLS+CS;_ rob;I;=10;0-_3_ (a) {b) vapor, cloud droplets, and column vapor. In particular, they showed that for low clouds, vapor absorption within the cloud where scattering is expected to increase the effective path length, is negligible at low wavenumbers due to strong absorption above the cloud and becomes significant at the higher wavenumbers. c- Since that study, there have been several calcula- _os MLS+CL;180-200 rob;¢=10;0o=30_ MLS+CL;800-1100rob;x=lO;0_3_o tions of radiative fluxes in cloudy and clear atmos- (c) (d) _e pheres under the aegis of the Intercomparison of Radiation Codes in Climate Models (ICRCCM). The 4 shortwave portion of this effort has been summarized in Fouquart et al. (1991). Here we report on an extensive 2 set of near-exact computations carried out for ICRCCM • ...... by Ramaswamy and Freidenreich (1991). Two cloud 0 5 10 15 20 5 10 15 20 types were used, CS and CL, the main difference being Wavenumber I000 cm "1) the larger size drops in the CL distribution. The CL clouds are therefore more absorbing than the CS Figure I. Column absorption for the standard midlati- clouds. Optical depths of 1, 10, and 100 were used and tude summer atmosphere and embedded (a) CS cloud two solar zenith angles, 30° and 75.7 °. A high cloud between 180-200 mb, (b) CS cloud between 800-900 mb, (c) CL cloud between 180-200 rob, (d) CL cloud layer from 180-200 mb and a low layer from 800-900 mb were inserted in a standard midlatitude summer between 800-900 rob. Optical depth is 10.0 for all cases and the solar zenith angle is 30 o. atmospheric profile (McClatchey et al. 1972). The water vapor mixing ratio was increased to the saturated value in the cloud layers. No other gases apart from figures. The results are 100 cm-1degraded resolution water vapor were included. Therefore the effects of 03, plots based on the near-exact calculations mentioned 02 and COz are not considered. This is not a serious previously for an optical depth of 10 and solar zenith shortcoming since we shall be concentrating on spectral angle of 30°. The same incident and clear sky absorp- features outside the range of these gases. The surface tion are shown in the four panels. The strong vapor is assumed to be perfectly absorbing. absorption features and well defined windows are evi- dent in the clear sky results. For the mid-latitude sum- 128 AMERICANMETEOROLOGICASLOCIETY mer atmosphere used here, some of the band centers are 4 i i t High Cloud, CS vs CL; 1;=10; 0o=30o completely saturated but an important point to note is that the windows are exceedingly transparent, even at 2 fi ... 'T, the smallest wavenumbers that contain appreciable solar energy. This feature has important implications I A:__ii ' (a) for the cloud forcing. The insertion of a moderately thick cloud at high altitudes has two effects as seen from Figs. l(a) and vi,,---, l(c). The column absorption in the vapor bands is diminished considerably because of the reflection of solar energy at these wavenumbers since solar energy is I- CS Sum =-36.9 eL Sum =26.2 reflected above the regions of substantial water vapor, e_ -4 0// .... 5, , , . ...1...0..... 15 20 this energy is not available for absorption by the vapor t_ 4 O .... , i i bands. Also the absorption in the vapor windows Low Cloud, CS vs CL; 1;=10;00=30° increases since droplets absorb in a continuum manner ,< (b) across the spectrum. When the same cloud is inserted 2 at a low level in the atmosphere, the response is decid- edly different. There is still an increase in absorption O 0 in the windows of roughly comparable magnitude but "O there is no compensating decrease in band center o absorption. In fact, at the larger wavenumbers in the ¢_ -2 unsaturated bands, there is an increase in absorption resulting from enhanced within-cloud absorption and CS Sum =47.9 CL Su = . also absorption of reflected solar energy by overlying vapor. Comparison of the corresponding CS and CL -4 0 .... 5J ' , , 1i0 15 20 cases indicates that the primary effect of enhanced Wavenumber (1000 cm"1) droplet absorption is a significant increase in window absorption for both the low and high cloud cases. The Figure 2. The difference in column absorption between absorption in the band center regions is essentially overcast and clear conditions for (a) CS and CL cloud unchanged. placed between 180-200 mb and (b) CS and CL cloud The net effect of placing a cloud layer for the placed between 800-900 mb. The integrated difference entire near-infrared spectrum, both spectrally and inte- from 0-18,000 cm1for both CS and CL clouds is also grated over the 0-18,000 cm-1region is shown in Figs. marked on thefigure. 2(a)-(b) which are difference plots corresponding to Figs. l(a)-(d). The quantity plotted is the column spec- al. 1995, Ramanathan et al. 1995). Here we present the tral cloud radiative forcing for complete overcast. Figs. cloud forcing for overcast conditions, i.e. the difference 2(a) and (b) separately now show the influence of between clear and overcast net fluxes. The situation is droplet absorption. For the high cloud, positive differ- shown schematically in Fig. 3 in which the net down- ences correspond to enhanced window absorption and ward fluxes at the top of the atmosphere are negative differences to diminished band center absorp- tion. Overall, for the CS cloud, the integrated effect is FNLTOA= FDLTOA- FULToA (1) a reduction of column absorption whereas for the CL cloud there is an increase. For the low cloud, the situa- for clear sky conditions and tion is quite different. There is enhanced absorption in the windows but no corresponding decrease in the band FNcTOA= FDcTOA--FOCToA (2) centers. The integrated forcing is positive although the magnitude does depend on the droplet absorption. for overcast conditions where suffixes U, D and N stand for upward, downward and net fluxes respective- 4. CLOUD RADIATIVE FORCING ly and suffixes L and C stand for clear and overcast conditions. The cloud forcing at TOA is then As mentioned earlier, the renewed interest in cloud absorption is driven to some extent by the inferred cloud forcing based on recent analyses (Cess et CFrOA = FNcTOA- FNLTOA (3) There is a corresponding set of relations for the surface quantities. As our calculations are for zero surface 7TMSYMPONGLOBALCHANGESTUDIES 129 albedo and the downward flux at the top is the insola- 0 MLS+CS;180-200 rob;¢=10;0*---30° lM'LtS+tC S;l80l0-,900 rob;_=10;00=30° <"> tion, it follows that -1 CFrOA = - Fuc TM (4) and CFSW = FDcsW - FDLs_ (5) MLS+CL;180-200mb;1:=10;00--30° MLS+CL _ rob;"_=10;00--_11_ _o • (d) i 't_ -1 F:O, l- o, "D FUL FDC FUC O -2 ;7 ! c, TOA -3- i:i:i:i:i:i:i:i:i:i:i:i:i:i:i:!:i:i:i:i:i:i:i: .4i•0 5 10 15 20 0 5 10 15 2O SRF -- SRF Wavenumber (1000 cm-1) FD_RF I FusRF FDC 1_Fuc SRF F___ __/U//,/,////., f/.,f,2"/Z/.///., f4 Figure 4. Spectral cloud forcing for overcast condi- tions at both the surface (solid) and top-of-the-atmos- Figure 3. Schematic identifying the various upward phere (dashed). The cloud conditions are as in Fig. 1. and downward fluxes for clear and overcast conditions. For low clouds, the forcing is primarily confined to CFS_ is then simply the change in transmittance to the windows and the region of weak absorption at the surface with the addition of the cloud layer and wavenumbers larger than 12,000 cm-1. In the win- FtJcTM is the flux reflected to space by the cloud (recall dows, as for high clouds, the surface forcing is more that the surface is non-reflecting). Both CFTM and negative and this is also true for the band centers of the CF s_ are negative. It may also be shown that weaker bands. In these spectral regions, there is droplet absorption and enhanced vapor absorption CFSW = CF rOAq- AL - Ac (6) through the increase in path length within the cloud and the absorption of reflected energy by vapor above the where Ae and Ac are, respectively, clear sky and cloud. The strong band centers are saturated so both cloudy sky column absorption shown in Figs. l(a)-(d). the surface and TOA forcing are essentially zero. This When cloudy sky atmospheric absorption exceeds the is a major difference between high and low clouds. clear sky value, CFS_ is more negative than CF TM and Whereas for high clouds there is a reduction in column when the cloudy sky absorption is less than the clear absorption in the band centers, this is not so for low sky value, CF sRF is less negative. When CF sRF = clouds, and in all spectral regions, the surface forcing is CF TM, the presence of the cloud layer does not alter more negative than the TOA forcing. the column absorption. The relative magnitudes of CF SRFand CF roA are Figs. 4(a)-(d) show the surface and TOA forcing best illustrated by presenting the ratio for overcast conditions. Comparison of Figs. 4(a) and 4(b) for high and low clouds, respectively shows the R = CFSRF/CFTM. (7) extreme sensitivity of CF TM to cloud height. The sur- face forcing is much less sensitive. The spectral Cess et al. (1995) have used the spectrally integrated response is quite different in the vapor windows and value of R to examine cloud absorption. Here we pre- the band centers. sent the spectral variation of R in Figs. 5(a)-(d). From For high clouds, there is a substantial forcing at the Eq. (6) it is evident that R = 1.0 implies no change in top of the atmosphere in the band center region as well column absorption with the addition of a cloud layer. as the windows, i.e., the reflection by the cloud layer Values of R > 1.0 indicate an increase in atmospheric affects the entire spectrum. The surface forcing in the absorption and R < 1.0 indicates a loss. Also marked windows is more negative as a result of droplet absorp- on the plots is the spectrally integrated value of R inte- tion. However, in the band centers, the surface forcing grated from 0-18,000 cm -1. The integrated value is not is less negative implying a decrease in column absorp- directly comparable to the values quoted in Cess et al. tion. This is because energy that would have been (1995) since it does not include the effect of ozone absorbed in the lower troposphere is now reflected back absorption at larger wavenumbers. However, it does to space. indicate the change in column absorption in the near- infrared. 130 AMERICANMETEOROLOGICALSOCIETY the cloud but also an enhancement in the vapor absorp- 3 'l 1 ' I _ RI '1 1 ' I I MLS+CS;180-200 mb; i:=10;0o--30_ MLS+CS;800-900 mb;_=I0;00==30° tion above the cloud. This is the absorption of reflected energy at wavenumbers that still carry sufficient energy down to the level of the cloud and in which there is some vapor absorption. These are the weaker water I I" " " vapor bands at larger wavenumbers. There is a deple- I,I. R=1.14 tion in below cloud absorption but the integrated effect is one of enhanced column absorption as evident from 0 the value of R. I I i I I <c) (.) The effect of increased droplet absorption is felt only within the cloud. The heating rate of the cloud layer itself increases with an increase in droplet absorp- tion. This results in a greater overall absorption and a higher value of R. ; R=1.31 04 ' 6 8 1'01'2 14 1'6' '18 10 12 14 16 18 5. DISCUSSION Wavenumber (1000 cm"1) The results presented here suggest that a program Figure 5. Ratio of the cloud forcing at the surface and directed towards the measurement of spectral cloud top-of-the-atmosphere. MODIS channels are marked for reference. The cloud conditions are as in Fig. 1. radiative forcing could help resolve some of the uncer- The cloud forcing ratio integrated from 0-18,000 cml tainty in cloud absorption. Of course, these results are is also marked on the figures. for horizontally homogeneous plane parallel clouds and so there will still be a degree of ambiguity in any analy- The influence of cloud height is now dramatically sis of measurements. Near-infrared reflectance measurements have been evident. For high clouds, R is much less than 1.0 in the band centers and somewhat greater than 1.0 in the made over clouds by Twomey and Cocks (1982), window regions. It is close to 1.0 at wavenumbers Stephens and Platt (1987), Foot (1988) and others. Reflectance measurements in the vapor windows were larger than 12,000 cm -1 where droplet absorption is found to be inconsistent with plane parallel theory quite modest. The spectrally integrated value shows when the relative reflectance at several channels was this compensation and the net effect is close to 1.0 considered (Twomey and Cocks 1982). They pointed implying little change in column absorption in the pres- to reduced reflectance or, by inference, increased ence of the cloud layer. On the other hand, for low clouds, R > 1.0 absorption when compared to theory. However, King et al. (1990) have shown that window single scattering throughout the spectrum and the integrated value of the ratio exceeds 1.0. For the more absorbing cloud, this albedos of water cloud droplets agree with single scat- ratio is of the same order of magnitude as that present- tering theory. The prevalent explanation for the dis- ed by Cess et al. (1995) and Ramanathan et al. (1995). crepancy has been that plane parallel theory should not The significance of the spectral nature of R for mea- be expected to work for the typically inhomogeneous and structured clouds over which measurements were surement programs will be discussed in the next sec- tion. made. But the analysis of Cess et al. (1995) is still The integrated effect of the spectral forcing results intriguing because it suggests that the integrated broad band absorption of cloudy columns exceeds theoretical in a forcing through the atmospheric column that estimates. The field of view of the measurements is changes the heating rate profile. For high clouds, the reflection of energy high in the atmosphere results in a quite extensive (several kilometers), so the implication is that areal mean absorption is in excess of theory. uniform depletion of absorbed energy below the cloud. There is, of course, additional absorption within the One way to resolve the ambiguity to some extent is to consider simultaneous reflectance and transmission cloud layer. The degree of compensation is given by measurements such as by stacked aircraft flying above the integrated value of R. If R < 1.0, the increase in and below a cloud deck. These have recently been cloud layer absorption is less than the decreased made by Pilewskie and Valero (1995) who again find absorption below the cloud layer as is the case for the cloud layers absorbing more than the theoretically high CS cloud of optical depth 10.0. When the zenith expected broad band value. However, they do find that angle is greater, reflection is enhanced, and the net effect is a sharper decrease in column absorption. For the discrepancy is least when clouds are more homoge- neous. If such work is extended to encompass spectral instance, when the zenith angle is increased to 75.7 °, measurements, then it may be possible to isolate the the integrated R factor for the high CS cloud is 0.76 source of the discrepancy. In a similar experiment, compared to R = 0.91 for a zenith angle of 30°. When the cloud layer is placed low in the atmos- Hayasaka et al. (1995) were able to make measure- ments of total solar (0.3-3.0 gm) and near-infrared (0.7- phere, there is not only significant absorption within 7TMSYMPONGLOBALCHANGESTUDIES 131 3.0 _tm) radiation separately. They also found excess cloud is uniform and the domain is cyclic so there are absorption in the near-infrared but also unrealistic no edge effects. The computations shown were carried radiative properties. They attributed this to reflection out using the Monte Carlo method for a mean optical from cloud sides and other geometrical effects, and, in depth of 10.0 and solar zenith angle of 60°. Four single fact were able to correct for these effects by ratioing scattering albedos are presented encompassing the visible and near-infrared measurements using the range encountered in the solar near-infrared. Note that method of Ackerman and Cox (1981). A similar study the areal mean transmittance increases at the expense of by Rawlins (1989) for a field of broken clouds showed both reflectance and absorptance as the cloud layer that areal mean absorption for such inhomogeneous becomes more inhomogeneous. cloud layers ranges from the clear sky value to the expected layered cloud value. luReflectance _3Transmittance Absorptance I If the spectral cloud radiative forcing can be esti- c 1.o-r-x--cr-o-r_=r1--r.q0 I r-'r-'r_-r-=T"_0l_ i T'r-r'-(co_=--_0.95 mated by surface and TOA measurements, the sensitiv- ity of the cloud forcing and the spectral ratio, R, shown _ 0.8- _ ,. • i in Figs. 5(a)-(d) can be compared with theory. Possible measurement programs in the future could involve o.6 MODIS being developed for the Earth Observing System (King et al. 1992). The R factor plot shown 0.4 here (Fig. 5) also includes five selected channels from I-- MODIS which is a 36 channel instrument. There is the potential for measuring R in the windows and band centers using channels such as shown here. For pur- poses of illustration, we have chosen four window _" o.o 1 2 4 e 1tt:_ channels centered at 4695, 6098, 8065 and 11,655 cm-1 Number ofpixels onaside and one channel centered on a vapor band at 10,638 cm-L The spectral R factor and column absorption can Figure 6. Areal mean transmission, reflection and be estimated by simultaneous TOA and surface mea- absorption for three different single scattering albedos, surements. This would essentially parallel the Cess et 09,for a two-dimensional cascade model of cloud inho- al. (1995) effort but will be more informative since mogeneity. The mean optical depth is 10.0 and solar spectral quantities will be measured. zenith angle is 60 °. Each cascade creates two unequal Currently, there is the opportunity to use the optical depths in adjacent cells in each horizontal MODIS Airborne Simulator (MAS) which is a scan- dimension. ning spectrometer flown on a NASA ER-2 (Platnick et al. 1994). This instrument mimics MODIS in that it The results can be framed in terms of the cloud carries similar channels. Corresponding transmission forcing ratio, R, defined by Eq. (7). Table 1shows the measurements at the surface need to be made at the values of RN, N = 1,2,...32, for different values of the same near-infrared frequencies. The results presented single scattering albedo, co, where N is the number of in Figs. 5(a)-(d) could act as a guide for interpreting the pixels on a side. Rl corresponds to the forcing ratio for cloud forcing. For example, the difference in forcing the homogeneous case (1 pixel on a side). It is evident ratio, R, between windows and band centers could be that for this simple model, in which there are no edge effects, the R factor for areal mean radiative forcing is exploited. It will still be very difficult to isolate cloud inho- not appreciably affected by the degree of inhomogene- mogeneities as the source of the absorption discrepan- ity. There is actually a tendency for R to decrease somewhat for the more absorbing cases. cy. However, Davies et al. (1984) and Stephens (1988a,b) have shown that inhomogeneities and finite cloud effects reduce absorption and not increase it, as is Table 1. The ratio of the cloud radiative forcing at the required to explain the discrepancy. In the presence of surface to that at the top of the atmosphere. inhomogeneities, the transmission increases at the expense of both reflectance and absorption. This is illustrated in Fig. 6 for a geometrically plane parallel R1 R2 R4 R8 R16 R32 but inhomogeneous cascade model of a stratocumulus cloud (Cahalan et al. 1994, Marshak et al. 1995). In 1.00 1.00 1.00 1.00 1.00 1.00 1.00 this model, a homogeneous cloud is divided into two in 0.995 1.17 1.17 1.17 1.18 1.18 1.18 each horizontal dimension and a fraction of liquid 0.99 1.32 1.34 1.34 1.35 1.35 1.35 water moved from one side to the other while conserv- 0.95 2.70 2.65 2.63 2.64 2.65 2.66 ing total liquid water. This process is carried out for 0.9 4.40 4.38 4.34 4.35 4.38 4.39 the sub-portions until a two-dimensional inhomoge- 0.8 8.81 8.59 8.52 8.54 8.58 8.62 neous distribution of liquid water is obtained which has statistical properties similar to observed stratus in FIRE (Cahalan et al. 1994). The geometrical thickness of the 132 AMERICANMETEOROLOGICALSOCIETY Although the results presented here cannot address Irvine, W. M., and J. B. 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