# LONG WAVE RADIATION AT SEA SURFACE We will consider the NET long wave (LWnet  ) radiation at sea surface which represents the difference between the.

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LONG WAVE RADIATION AT SEA SURFACE We will consider the NET long wave (LWnet  ) radiation at sea surface which represents the difference between the upward infrared radiation emitted by the ocean surface (LWs  ) and downward infrared radiation from the atmosphere (LWa  ): LW net  = LW s  - LW a  (1) The long wave radiation is the radiation emitted by the ocean surface at wavelengths greater than those of the visible light (at about 800 nanometres (nm)) but shorter than those of microwaves (at about 800,000 nm). Infrared radiation is associated with heat energy and not with visible light.

Net LW radiation at sea surface comes out as a result of many complex processes LW net  =???

The ocean surface irradiance consists of the emitted LW radiation from the sea surface and reflected atmospheric LW irradiance: LW s  = LW s0  +  L LW a  (2) where LW s0  is LW irradiance of ocean surface  L is surface long wave albedo Thus, the net LW radiation at sea surface can be expressed as: LW net  = LW s0  - (1-  L )LW a  (3)

Two industrial workers go for a lunch: They take (besides the meals) each cup of tea simultaneously. The first worker puts sugar into the cup immediately and starts to eat the main dish. The second worker first starts to eat and puts the sugar into the cup just before the drinking. Whose tea will be hotter at the moment of drinking? They start to drink their tea simultaneously

Upward long wave irradiance from sea surface This is the major component of longwave exitance!!!! For this part the physics is a simple blackbody radiation LW s0  =  T s 4 (4) where  is the Stefan-Boltzmann constant (5.67  10-8  W  m-2  K -4 ) T s is the sea surface !!!skin!!! temperature in degrees Kelvin  is the emissivity of the sea surface Emissivity of the sea surface  in a general case depends on the sea state and optical properties of the sea water. For the fresh water  = 0.92 and varies from 0.89 to 0.98 for different conditions.

Sea surface skin temperature Ts is not equivalent to SST, measured at ships by buckets or engine intakes, it is the temperature of very thin (several to several hundreds  ) surface skin layer, namely skin temperature. Longwave absorption and emission both take place in just about the top 0.5 mm of water, depending on wavelength. Back to the skin temperature issue - later Downward amospheric long wave irradiance Downwelling longwave radiation (longwave irradiance) originates from the emission by atmospheric gases (mainly water vapor, carbon dioxide and ozone), aerosols and clouds. Long-wave albedo is also poorly known and depends on the sea state and cloud conditions. Downwelling LW is the smallest, but the most uncertain term in the net LW radiation (longwave exitance).

MeasurementsModelling - RTMsParameterization Determining surface net long wave radiation

Measurements of LW radiation: The pyrgeometer is of a similar construction to the pyranometer, but the single dome is made from silicon or similar material transparent to the longwave band, coated on the inside with an interference filter to block shortwave radiation. The longwave irradiance passing through the dome, which we wish to determine, is only one component of the thermal balance of the thermopile. The remaining components come from various parts of the instrument. To isolate the geophysical component, the manufacturers provide the correction equations.

Modelling of the long wave radiation (RTMs) The radiative transfer equation (RTE) states that the energy radiated by a parcel of material in a particular frequency range and particular direction (denoted by an increment of solid angle around the direction) is the sum of energy transmitted through the parcel and the energy emitted from within the parcel, in that frequency interval and direction. RTE evaluates the effect of changes in temperature, humidity, cloud, aerosols, and chemical composition. Calculation of LW radiation should include all the major absorption bands of CO2, H2O, and O3, as well the weaker bands of CO2, N2O and CH4. Atmospheric column consists of N plane parallel layers, n=1,2,…,N. Temperatures T n, n=0,1,….,N are denoted at layer edges. The mean optical thickness of the nth layer at a particular frequency is  n. Structure of a simple RTM

At frequency and beam angle  the upward IR irradiance U,n and the downward IR irradiance D,n at the edges of the layer n are: where  = cos . In (5,6): the first terms are the transmitted IR irradiances given by Lambert’s law, and the second terms are the IR irradiances emitted in the layer: where B,n is the Planck function at frequency and temperature T n. Boundary conditions: (5.6) (7,8) (9,10)  is the albedo,  =1-  is the emissivity of the ocean surface. Equation (9): no downward IR flux at the top of the atmosphere. Equation (10): the upflux at the ocean surface is given by the sum of emission from the ocean plus the reflection of the downward flux.

For the frequency range [ a, b ] the total upward U n and downward D n IR fluxes result from integrating U,n and U,n overall frequencies in [ a, b ] and beam angles: 9,10 Problems: Numerical solution of (5)-(12) is difficult and expensive due to:  The spectral complexity of the atmospheric constituents  Vertical inhomogeneity of the chemical composition of the atmosphere There is a lack of measurements of basic parameters in the atmospheric column

Short summary: Most exact are the Line-By-Line Radiative Transfer Models (LBLRTM) which compute transfer of each constituent for each emission and absorption spectral line at many levels throughout the profile. Their computational burden is therefore large, which makes them unsuitable for routine use in numerical models. Over the years therefore, many broadband RTM's have been developed, increasing in accuracy and efficiency with improved parameterizations and increased computer power. Such models are widely applied in climate modelling, and in flux retrieval from direct and remotely sensed atmospheric variables. The computation of LW flux with the best high spectral resolution codes under clear conditions is at an advanced state. For cloudy sky conditions, however, RTM's are not well validated. The calculation of the downwelling longwave flux under a cloud requires knowledge of both cloud base height and emissivity.

Parameterization of LW radiation: LW net  = LW s0  - (1-  L )LW a  What do we measure? SST Ta, q, C (Cn, Cl) 1. No problem to parameterize the LW s0 , if we have SST and the emissivity of the sea surface: LW s0  =  T s 4 However, you have to remember that is T s 4 a skin temperature and is not equal to the bulk SST (LATER!)

2. LW albedo is more poorly known that a SW albedo. Some very tentative estimates give values in the range of 0.04-0.05 (e.g. Clark et al. 1974). Since  the value [ 1-LW albedo ] is close (at least of the same order as) to the emmissivity of sea surface [  ]  the accuracy of  L and  is approximately the same there is an approach to establish an effective emissivity and to re-write the equation for the net LW as follows: LW net  =  T s 4  - (1-  L )LW a  LW net  =  (  T s 4  - LW a  ) (13) where  is an effective emissivity and should not be understood as an emissivity of the sea surface (typical mistake). From (2), (4), (13):  =(LW s0  - LW a  )/ (  T s 4  - LWa  ) (14) Important:    = LW s0  /  T s 4 

T air, q, C n, C l 3. Parameterization of downwelling atmospheric LW radiation LW net  =  (  T s 4  - LW a  ) However, this approach results in very uncertain dependencies due to very different optical properties of clear sky and cloudy atmosphere. Air temperature blackbody radiation shows significant differences for clear skies and cloudy skies. The simplest approach is to measure downwelling LW radiation and to compare it with different combinations of surface parameters:

! separate analysis should be performed for atmospheric LW under clear sky and clouds Cloudy conditions Clear sky Guest (1998) – 2 months of direct LW measurements in Weddell Sea: Processes are quite different under clear skies and clouds

Bignami et al. (1995) using results from direct observations in seven cruises in Mediterranean Sea, found close relationship between surface water vapor pressure and the ratio between atmospheric downwelling LW and air temperature blackbody radiation: LW a  =  T a 4 (a+be  ) where a=0.684, b=0.0056,  =0.75 1. Downwelling long wave radiation under clear skies Since information about atmospheric gases and aerosols is generally unavailable in routine observational practice, major efforts of researchers were concentrated on studying relationships between the clear sky downwelling atmospheric LW on  Surface humidity  Surface air temperature Theoretically, from a physical view point, surface humidity should have a closer link with surface humidity.

However, in practice much better relationships are observed for surface air temperature. Reasons:  more easily available (more observations)  measurements are more accurate Swinbank (1963) from Indian Ocean and lake observations: LW a  =  T a 4 (a+bT a  ) (14a) or ln(LW a  /  T a 4 ) =a+  ln(T a ) (14b) where a=-15.75,  =0.75 Guest (1998) tested many formulations of clear sky atmospheric LW.  No evidence of a better approximation for humidity than for air temperature.

Guest (1998) results (for your files):

Malevsky et al (1992) from a very big data set collected in different World Ocean regions (incl. tropics and mid-latitudes) found the following relationship between the downwelling atmospheric LW and humidity (water vapor pressure): LW a  =  T a 4 (0.60+0.049  e) (16) Similar dependency for air temperature was: LW a  = 1.026T a 2  10-5 –0.541 (17) There has been found considerably lesser scatter for (17) than for (16) and a smaller RMS error. INTERESTING: equation (17) looks physically less reasonable than those which include  T a 4. However, analysis of empirical data shows that formula (17) works well in most conditions.

Effective emissivity of sea surface (accounts for the LW albedo and skin effect)   !!! Sea surface !skin! temperature blackbody radiation. Since we do not have normally “skin” estimate, we account for the bulk effect in  Atmospheric downwelling LW under clear skies: Parameterized as a function of either surface humidity or surface temperature Relationships with temperature give better results! Function of cloud cover – Should account for the effect of clouds ? Thus, now we assume the following form of parameterization of the net LW radiation: LW net  =  [  T s 4  - ( LW a0   F(c) )]

We DO NOT know (measure) We come actually to another RTM! 2. Downwelling long wave radiation under clouds – the cloud modification of LW a . What should be parameterized from a theoretical view point is a cloud temperature blackbody radiation:  T cl 4  LW c  (2) = n(2)  (2)  T cl (2) 4 + [1-n(2)] LW c  (3) LW c  (1) = n(1)  (1)  T cl (1) 4 + [1-n(1)] LW c  (2) LW c  (tot) = (1-  (0)) LW c  (1) + + LW a  (sky) +  (0)  T 0 (1) 4 Lind and Katsaros (1982): n is fractional cloud cover of the subscribed cloud layer T cl is cloud base temperature of the subscribed cloud layer  is effective emittance of the subscribed cloud layer  (0) is emittance of layer from the surface to lowest cloud base T cl is equivalent radiative temperature of the lower layer

Paramete- rization of F(n) The only available parameter is the total fractional cloud cover and sometimes is the fractional cover of the low-level cloudiness. Typical approach: to make measurements under the known cloud conditions and to compare clear sky atmospheric LW with that measured under the cloudy sky. LW a  + LW cl  LW a  This effect has to be parameterized Typical expression is 1  ac  for the total cloud cover Bignami et al. (1995): F(n) = 1+0.1762c 2 (Mediterranean Sea) Clark et al. (1974): F(n) = 1-0.69c 2 (Pacific Ocean) Efimova (1962): F(n) = 1-0.80c (land data)

Malevsky et al. (1992) from his collection of field measurements for the total cloud cover found: LWcl+a  = 0.928Ta2  10-5 –0.397 (18) He assumed that LWcl+a  = LWa  (1+ktnt2) (19) Coefficient k t can be derived from (19) under n t =1: k t = (LW cl+a  + LW a  ) / (LW a  ) (20) where: LW a  = 1.026T a 2  10 -5 –0.541) Not surprisingly, in this formulation k t becomes dependent on the air temperature, since both LW cl+a  and LW a  are the functions of air temperature.

Computation of the k t from a simple RTM: k t = (1/LW a  ) [  cl  a T cl 4 + +LW a  (0)(4  h/T a )-1]  cl – emissivity of the cloud base  cl – temperature of the cloud base LW a  (0) – irradiance below the cloud layer  cl – surface temperature  - temperature gradient in the undercloud layer h – cloud layer height Thus, for the total cloud cover only: LW a  = [LW a0   F(c)]=(1.026T a 2 10 -5 -0.541)(1+k t n t 2 ) k t = (-0.098T a 2  10 -5 + 0.144) / (1.026T a 2 10 -5 -0.541)

Malevsky et al. (1992) first considered the effect of cloudiness for three different layers (low cloudiness, mid-level cloudiness and upper layer cloudiness). For upper layer: LW clu+a  = 0.995T a 2  10 -5 –0.496 (21) For mid-level: LW clm+a  = 0.932T a 2  10 -5 –0.401 (22) For lower layer: LW cll+a  = 0.921T a 2  10 -5 –0.385 (23) For upper layer: k u = (LW clu+a  +LW a  )/(LW a  ) (24) For mid-level: k m = (LW clm+a  +LW a  )/(LW a  ) (25) For lower layer: k l = (LW cll+a  +LW a  )/(LW a  ) (26) For the cloud coefficients:

However, normally we have observations only for the fractional cloud cover of total and low-layer cloudiness. Thus, this 3-layer formulation has been simplified for the consideration of the total and low-layer cloudiness: LW a  = (1.026T a 2 10 -5 -0.541)(1+k l n l 2 )(1+k u+m (n t 2 -n l 2 ) (27) k l = (LW cll+a  +LW a  )/(LW a  ) (28) k u+m = (k t n t 2 - k l n l 2 ) / [(1+k t n t 2 )(n t 2 –n l 2 )] (29) k u+m is the coeeficient accounting for the total effect of the mid and upper layer cloudiness, which can be derived from the coefficients for the total and low-level cloudiness: Now we can finally derive the parameterization of the net long-wave radiation at ocean surface in a general form: LW net  =  [  T s 4  - (LW a0   F(c))]

Summary:  History is very long  The number of parameterizations approaches several tens  Formulations are similar  Differences are large Brunt (1932) LW=  T s 4 (0.39-0.05e z 1/2 )(1-0.8n d ),  =0.98, d=1 Berliand and Berliand (1952) LW=  T s 4 (0.39-0.05e z 1/2 )(1-0.8n d )+4  T a 3 (T s -T a ),  =0.98, d=1 Anderson (1952) LW=  [T s 4 -T a 4 (0.74+0.0049e z )](1-0.8 n d ),  =0.98, d=1 Efimova (1961) LW=  T a 4 (0.254-0.00495e z )(1-cn d )+4  T a 3 (T s -T a ),  =0.96, d=1 Swinbank (1963) LW=  [T s 4 -9.36  10 -6 T a 6 ](1-0.8 n d ),  =0.98, d=1 Clark et al. (1974) LW=  T s 4 (0.39-0.05e z 1/2 )(1-cn d )+4  T a 3 (T s -T a ),  =0.98, d=2 Bunker (1976) LW=0.022[  T a 4 (11.7-0.23e z )(1-0.68n d )+4  T a 3 (T s -T a ),  =0.96, d=1 Hastenrath and Lamb (1978) LW=  T s 4 (0.39-0.056q 1/2 )(1-0.53n d )+4  T a 3 (T s -T a ),  =0.98, d=2 Malevsky et al. (1992b) LW=  (  T s 4 -(1.026T a 2 10 -5 -0.541)(1+cn d )),  =0.91, d=2 Bignami et al. (1995) LW=  T s 4 -[  T a 4 (0.653+0.00535 e z )(1+0.1762n d )),  =0.98, d=2 Josey et al. (2001) LW=  T s 4 -(1-  L )  [T a +an 2 +bn +c +0.84(D+4.01)] 4,  =0.98, a, b, c, D = empirical coefficients,  L = 0.045

Variations in short-wave radiation and long-wave radiation due to the parameterizations (North Atlnatic SW and LW radiation budget)

Summary of LW radiation parameterizations:  Under clear sky and small cloudiness the accuracy is normally better than 15 W/m 2  Higher uncertainties occur under the moderate and high cloud cover  Uncertainties in the tropics are typically higher than in mid and high latitudes and are primarily associated with atmospheric clear sky IR irraidance  “Hot issues” of all parameterizations are “skin temperature” and representation of the multi-layer cloudiness of different types by fractional [total] cloud cover

Recommendations:  Do not hesitate to use “old” parameterizations  Try to avoid the use of parameterizations based on water vapor pressure and humidity  Do not use Bignami et al. (1995) except for Mediterranean sea  Be careful with the choice of emissivity value. Always remember – it is effective emissivity and not the emissivity of surface

Radiation balance of the ocean RB = SW  (1-  ) - LW net  (30) At the ocean surface: defcit surplus Incoming radiation Outgoing radiation At the top of atmosphere Winter Spring Summer Fall SW LW

SW LW RB

Variations of SW and LW radiation due to different parameterizations

/helios/u2/gulev/handout/ longwave1.f – collection of LW radiation F77 codes  RIZL – Malevsky et al. (1992) scheme  RLWISI – Efimova (1961) as modified by Isemer et al (1989)  RLW_CLA – Clark et al. (1974)  RLW_BIG – Bignami et al. (1995) Try to compare Malevsky, Efimova, Bignami and Clark schemes: For Ts = 12C:  Clear sky, dependence on temperature, humidity  Cloud cover octa=4, dependence on temperature  Tair = 15C, dependence on cloud cover (in octas)

/helios/u2/gulev/handout/ swm_test.f – program to compute instantaneous values of SW radiation, using Malevsky et al. (1992) and Dobson and Simth (1988) schemes. Compilation: f77 –o swm_test swm_test.f radiation.f Results: sw.res swr_test.f – program to compute daily values of SW radiation, using Reed (1977) scheme. Compilation: f77 –o swr_test swr_test.f radiation1.f Results: swr.res lw_test.f – program to compute values of LW radiation, using Malevsky et al. (1992), Clark et al. (1974), Bignami et al. (1995) and Emivova (1962) schemes. Compilation: f77 –o lw_test lw_test.f longwave1.f Results: lw.res

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