Atmospheric Window and TOA Net CRE
This chapter deals with some features regarding the longwave and the net CRE, makes explicit an expectation about TSI (menationed already above), and places a non-observable (only computable) energy flow component, atmospheric window radiation, into the integer system.
On this page:
LWCRE
My approach once received a critical comment saying that I use the same LWCRE at TOA and at the surface; and while it is evident that their values are close, there is no theoretical reason why they should be identical.
Well, here is a reason.
Atmospheric LW cooling is defined as: "the infrared radiative energy entering the atmospheric column from below less that leaving it above and below".
ATM LW Cooling = ULW – OLR – DLR. With all-sky data, CERES EBAF Ed4.1 has –186.5 Wm-2; my theoretical value is 15 – 9 – 13 = –7 units = –186.76 Wm-2 with Unit = 26.68 Wm-2.
ATM LW Cooling (clear-sky) = ULW – OLR(clear-sky) – DLR(clear-sky); ULW is regarded the same.
OLR (clear-sky) = OLR(all-sky) + LWCRE at TOA,
DLR (clear-sky) = DLR(all-sky) – LWCRE at the surface.
If LWCRE at TOA = LWCRE at the surface, ATM LW cooling is the same in all-sky and clear-sky. But if not, that would introduce a serious inherent instability between the clear and cloudy regions, destabilizing the system immediately.
Stephens et al. (2012) have 26.7 ± 4 Wm-2 at TOA and 26.6 ± 5 Wm-2 at the surface.
CERES EBAF Ed4.1 has 27.61 Wm-2 at the surface and 25.77 Wm-2 at TOA, with a mean value of 26.69 Wm-2.
L'Ecuyer et al. (2019) have the higher value at TOA, 27.1 ± 3.7 Wm-2, and 26.3 ± 3.8 Wm-2 at the surface, with a mean value of 26.7 Wm-2.
Since the best fit of the unit for our four equations on the 22 running years of CERES observations is 26.68 ± 0.01 Wm-2, we regard this value as the most accurate estimate for the common LWCRE, and utilize it throughout our work.
TOA Net CRE
IPCC First Assessment Report 1990):
"The presence of clouds heats the climate system by 31 Wm-2 through reducing the TOA infrared emission. They also produce a cooling through the reflection of solar radiation. As demonstrated in Table 3.1 the latter process dominates over the former, so that the net effect of clouds on the annual global climate system is a 13 Wm-2 radiative cooling. Cloud radiative forcing is an integrated effect governed by cloud amount, cloud vertical distribution cloud optical depth and possibly the cloud droplet distribution"
Wild et al. (2018):
TOA net CRE = SW CRE + LW CRE =
RSR(clear) – RSR(all ) + OLR(clear) – OLR(all) =
[ ISR – ASR(clear ) ] –– [ ISR – ASR(all ) ] + OLR(clear) – OLR(all) =
ASR(all) – ASR(clear ) + OLR(clear) – OLR(all) =
[ OLR(clear ) – ASR(clear) ] + [ ASR(all) – OLR(all) ] =
TOA net IMB (all – clear) = EEI(all) – EEI(clear).
In summary, Net cloud radiative forcing is not an integrated effect governed by cloud amount, cloud vertical distribution, cloud optical depth, cloud reflectivity and cloud droplet distribution.
In principle , the fenomenon of TOA Net CRE can be understood, and its magnitude can be determined without any reference to clouds, solely from clear sky fluxes: reflected or absorbed solar radiation (clear) and emitted LW radiation (clear). This identity is not a numerical coincidence but the inherent physical nature of TOA Net CRE.
original: Wild et al. (2018)
TSI
Let us recall that the best fit for the unit of the solution to the four equtions is one unit = 26.68 ± 0.01 Wm-2, without direct reference to incoming solar radiation, since TOA solar fluxes are not involved in the equations. The extended integer system in the clear-sky includes TOA SW up (clear-sky) = 8/4 units, Absorbed solar radiation = 43/4 units, TOA Net Clear-sky imbalance = 3/4 unit, outgoing LW radiation = 40/4 units; and in the all-sky, Absorbed solar= 36/4 units, reflected solar = 15/4 units, outgoing LW = 36/4 units. These data point to a Total Solar Irradiance of 51 units, if the spherical weighting 4 is used, but CERES is quite explicit that they utilize a geodetic weighting factor of 4.0034. This way we can infer that the required external energy source to maintain the observed system of Earth's energy flows is
The mean value for TSIS TSI from January 11, 2018 to August 12, 2023 Level 3 data is 1361.77 Wm-2.
My approach once received a critical comment saying that I use the same LWCRE at TOA and at the surface; and while it is evident that their values are close, there is no theoretical reason why they should be identical.
Well, here is a reason.
Atmospheric LW cooling is defined as: "the infrared radiative energy entering the atmospheric column from below less that leaving it above and below".
ATM LW Cooling = ULW – OLR – DLR. With all-sky data, CERES EBAF Ed4.1 has –186.5 Wm-2; my theoretical value is 15 – 9 – 13 = –7 units = –186.76 Wm-2 with Unit = 26.68 Wm-2.
ATM LW Cooling (clear-sky) = ULW – OLR(clear-sky) – DLR(clear-sky); ULW is regarded the same.
OLR (clear-sky) = OLR(all-sky) + LWCRE at TOA,
DLR (clear-sky) = DLR(all-sky) – LWCRE at the surface.
If LWCRE at TOA = LWCRE at the surface, ATM LW cooling is the same in all-sky and clear-sky. But if not, that would introduce a serious inherent instability between the clear and cloudy regions, destabilizing the system immediately.
Stephens et al. (2012) have 26.7 ± 4 Wm-2 at TOA and 26.6 ± 5 Wm-2 at the surface.
CERES EBAF Ed4.1 has 27.61 Wm-2 at the surface and 25.77 Wm-2 at TOA, with a mean value of 26.69 Wm-2.
L'Ecuyer et al. (2019) have the higher value at TOA, 27.1 ± 3.7 Wm-2, and 26.3 ± 3.8 Wm-2 at the surface, with a mean value of 26.7 Wm-2.
Since the best fit of the unit for our four equations on the 22 running years of CERES observations is 26.68 ± 0.01 Wm-2, we regard this value as the most accurate estimate for the common LWCRE, and utilize it throughout our work.
TOA Net CRE
IPCC First Assessment Report 1990):
"The presence of clouds heats the climate system by 31 Wm-2 through reducing the TOA infrared emission. They also produce a cooling through the reflection of solar radiation. As demonstrated in Table 3.1 the latter process dominates over the former, so that the net effect of clouds on the annual global climate system is a 13 Wm-2 radiative cooling. Cloud radiative forcing is an integrated effect governed by cloud amount, cloud vertical distribution cloud optical depth and possibly the cloud droplet distribution"
- The TOA shortwave absorption under all sky and clear sky conditions suggests that the overall effect of clouds is to reduce the absorption of shortwave radiation in the climate system by 47 Wm-2 TOA shortwave cloud radiative effect.
- Accordingly the longwave cloud radiative effect at the TOA as the difference between the outgoing longwave radiation under all sky and clear sky conditions becomes positive at 28 Wm-2.-
- The net (shortwave and longwave combined cloud radiative effect at the TOA results in an overall energy loss of 19 Wm-2.
TOA net CRE = SW CRE + LW CRE =
RSR(clear) – RSR(all ) + OLR(clear) – OLR(all) =
[ ISR – ASR(clear ) ] –– [ ISR – ASR(all ) ] + OLR(clear) – OLR(all) =
ASR(all) – ASR(clear ) + OLR(clear) – OLR(all) =
[ OLR(clear ) – ASR(clear) ] + [ ASR(all) – OLR(all) ] =
TOA net IMB (all – clear) = EEI(all) – EEI(clear).
In summary, Net cloud radiative forcing is not an integrated effect governed by cloud amount, cloud vertical distribution, cloud optical depth, cloud reflectivity and cloud droplet distribution.
In principle , the fenomenon of TOA Net CRE can be understood, and its magnitude can be determined without any reference to clouds, solely from clear sky fluxes: reflected or absorbed solar radiation (clear) and emitted LW radiation (clear). This identity is not a numerical coincidence but the inherent physical nature of TOA Net CRE.
original: Wild et al. (2018)
TSI
Let us recall that the best fit for the unit of the solution to the four equtions is one unit = 26.68 ± 0.01 Wm-2, without direct reference to incoming solar radiation, since TOA solar fluxes are not involved in the equations. The extended integer system in the clear-sky includes TOA SW up (clear-sky) = 8/4 units, Absorbed solar radiation = 43/4 units, TOA Net Clear-sky imbalance = 3/4 unit, outgoing LW radiation = 40/4 units; and in the all-sky, Absorbed solar= 36/4 units, reflected solar = 15/4 units, outgoing LW = 36/4 units. These data point to a Total Solar Irradiance of 51 units, if the spherical weighting 4 is used, but CERES is quite explicit that they utilize a geodetic weighting factor of 4.0034. This way we can infer that the required external energy source to maintain the observed system of Earth's energy flows is
TSI = 51 × (4.0034/4) × 26.68 ± 0.01 Wm-2 = 1361.84 ± 0.5 Wm-2.
The mean value for TSIS TSI from January 11, 2018 to August 12, 2023 Level 3 data is 1361.77 Wm-2.
[Kopp, G. (2020), TSIS TIM Level 3 Total Solar Irradiance 24-hour Means, version 03,
Greenbelt, MD, USA: NASA Goddard Earth Science Data and Information Services Center (GES DISC),
Accessed <August 11, 2023 at https://doi.org/10.5067/TSIS/TIM/DATA306]
Costa and Shine (2012) performed LBL-computation of the global mean clear-sky atmospheric window radiation (STI, surface transmitted irradiance, without assumption on the wavelengths), and found it as 65 Wm-2, with regard to their model-OLR = 259 Wm-2. With proportionality, using our theoretical OLR(clear) = 266.8 Wm-2, this would result in WIN(clear) = 66.96 Wm-2.
Notice that 66.70 Wm-2 is an integer position = 10/4 units (with 51/4 incoming, 8/4 reflected, 40/4 LW-emitted and 3/4 clear-sky TOA net imbalance). This means that on the disk, 40 units outgoing LW is the sum of 10 units window radiation and 30 units atmospheric upward emission. Surface upward LW (ULW) on the sphere is 15 units, that is, 60 units on the disk. ATM up = ULW/2.
This of course reinforces the Clear-sky net imbalance at TOA = 3/4 units = 20.01 Wm-2 we were using in TSI calibration in the Geometric deduction.
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