MODULE data_parameters !------------------------------------------------------------------------------- ! ! Description: ! Global parameters for the program are defined. ! ! Current Code Owner: DWD, Ulrich Schaettler ! phone: +49 69 8062 2739 ! fax: +49 69 8236 1493 ! email: uschaettler@dwd.d400.de ! ! History: ! Version Date Name ! ---------- ---------- ---- ! 1.1 1998/03/11 Ulrich Schaettler ! Initial release ! 1.8 1998/08/03 Ulrich Schaettler ! Eliminated intgribf, intgribc, irealgrib, iwlength and put it to data_io. ! 1.10 1998/09/29 Ulrich Schaettler ! Eliminated parameters for grid point and diagnostic calculations. ! !VERSION! !DATE! ! ! ! Code Description: ! Language: Fortran 90. ! Software Standards: "European Standards for Writing and ! Documenting Exchangeable Fortran 90 Code". !======================================================================= ! ! Declarations: ! ! Modules used: !======================================================================= IMPLICIT NONE !======================================================================= ! Global (i.e. public) Declarations: ! Parameters for the Program: INTEGER, PARAMETER :: & ireals = SELECTED_REAL_KIND (12,200), & ! number of desired significant digits for ! real variables ! corresponds to 8 byte real variables iintegers = KIND (1) ! kind-type parameter of the integer values ! corresponds to the default integers !======================================================================= END MODULE data_parameters MODULE flake_derivedtypes !------------------------------------------------------------------------------ ! ! Description: ! ! Derived type(s) is(are) defined. ! ! ! Current Code Owner: DWD, Dmitrii Mironov ! Phone: +49-69-8062 2705 ! Fax: +49-69-8062 3721 ! E-mail: dmitrii.mironov@dwd.de ! ! History: ! Version Date Name ! ---------- ---------- ---- ! 1.00 2005/11/17 Dmitrii Mironov ! Initial release ! !VERSION! !DATE! ! ! ! Code Description: ! Language: Fortran 90. ! Software Standards: "European Standards for Writing and ! Documenting Exchangeable Fortran 90 Code". !============================================================================== ! ! Declarations: ! ! Modules used: USE data_parameters , ONLY : & ireals , & ! KIND-type parameter for real variables iintegers ! KIND-type parameter for "normal" integer variables !============================================================================== IMPLICIT NONE !============================================================================== ! ! Declarations ! Maximum value of the wave-length bands ! in the exponential decay law for the radiation flux. ! A storage for a ten-band approximation is allocated, ! although a smaller number of bands is actually used. INTEGER (KIND = iintegers), PARAMETER :: & nband_optic_max = 10_iintegers ! Define TYPE "opticpar_medium" TYPE opticpar_medium INTEGER (KIND = iintegers) :: & nband_optic ! Number of wave-length bands REAL (KIND = ireals), DIMENSION (nband_optic_max) :: & frac_optic , & ! Fractions of total radiation flux extincoef_optic ! Extinction coefficients END TYPE opticpar_medium !============================================================================== END MODULE flake_derivedtypes ! File %M% from Library %Q% ! Version %I% from %G% extracted: %H% !------------------------------------------------------------------------------ SUBROUTINE flake_interface ( dMsnowdt_in, I_atm_in, Q_atm_lw_in, height_u_in, height_tq_in, & U_a_in, T_a_in, q_a_in, P_a_in, & depth_w, fetch, depth_bs, T_bs, par_Coriolis, del_time, & T_snow_in, T_ice_in, T_mnw_in, T_wML_in, T_bot_in, T_B1_in, & C_T_in, h_snow_in, h_ice_in, h_ML_in, H_B1_in, T_sfc_p, & albedo_water, albedo_ice, albedo_snow, & opticpar_water, opticpar_ice, opticpar_snow, & T_snow_out, T_ice_out, T_mnw_out, T_wML_out, T_bot_out, T_B1_out, & C_T_out, h_snow_out, h_ice_out, h_ML_out, H_B1_out, T_sfc_n,Q_sensible,Q_latent,Q_momentum) ! Modules used: USE data_parameters , ONLY : & ireals, & ! KIND-type parameter for real variables iintegers ! KIND-type parameter for "normal" integer variables USE flake_derivedtypes ! Definitions of several derived TYPEs USE flake_parameters , ONLY : & tpl_T_f , & ! Fresh water freezing point [K] tpl_rho_w_r , & ! Maximum density of fresh water [kg m^{-3}] h_Snow_min_flk , & ! Minimum snow thickness [m] h_Ice_min_flk ! Minimum ice thickness [m] USE flake_paramoptic_ref ! Reference values of the optical characteristics ! of the lake water, lake ice and snow USE flake_albedo_ref ! Reference values the albedo for the lake water, lake ice and snow USE flake , ONLY : & flake_driver , & ! Subroutine, FLake driver flake_radflux , & ! Subroutine, computes radiation fluxes at various depths ! T_snow_p_flk, T_snow_n_flk , & ! Temperature at the air-snow interface [K] T_ice_p_flk, T_ice_n_flk , & ! Temperature at the snow-ice or air-ice interface [K] T_mnw_p_flk, T_mnw_n_flk , & ! Mean temperature of the water column [K] T_wML_p_flk, T_wML_n_flk , & ! Mixed-layer temperature [K] T_bot_p_flk, T_bot_n_flk , & ! Temperature at the water-bottom sediment interface [K] T_B1_p_flk, T_B1_n_flk , & ! Temperature at the bottom of the upper layer of the sediments [K] C_T_p_flk, C_T_n_flk , & ! Shape factor (thermocline) h_snow_p_flk, h_snow_n_flk , & ! Snow thickness [m] h_ice_p_flk, h_ice_n_flk , & ! Ice thickness [m] h_ML_p_flk, h_ML_n_flk , & ! Thickness of the mixed-layer [m] H_B1_p_flk, H_B1_n_flk , & ! Thickness of the upper layer of bottom sediments [m] ! Q_snow_flk , & ! Heat flux through the air-snow interface [W m^{-2}] Q_ice_flk , & ! Heat flux through the snow-ice or air-ice interface [W m^{-2}] Q_w_flk , & ! Heat flux through the ice-water or air-water interface [W m^{-2}] Q_bot_flk , & ! Heat flux through the water-bottom sediment interface [W m^{-2}] I_atm_flk , & ! Radiation flux at the lower boundary of the atmosphere [W m^{-2}], ! i.e. the incident radiation flux with no regard for the surface albedo I_snow_flk , & ! Radiation flux through the air-snow interface [W m^{-2}] I_ice_flk , & ! Radiation flux through the snow-ice or air-ice interface [W m^{-2}] I_w_flk , & ! Radiation flux through the ice-water or air-water interface [W m^{-2}] I_h_flk , & ! Radiation flux through the mixed-layer-thermocline interface [W m^{-2}] I_bot_flk , & ! Radiation flux through the water-bottom sediment interface [W m^{-2}] I_intm_0_h_flk , & ! Mean radiation flux over the mixed layer [W m^{-1}] I_intm_h_D_flk , & ! Mean radiation flux over the thermocline [W m^{-1}] Q_star_flk , & ! A generalized heat flux scale [W m^{-2}] u_star_w_flk , & ! Friction velocity in the surface layer of lake water [m s^{-1}] w_star_sfc_flk , & ! Convective velocity scale, using a generalized heat flux scale [m s^{-1}] dMsnowdt_flk ! The rate of snow accumulation [kg m^{-2} s^{-1}] USE SfcFlx , ONLY : & SfcFlx_lwradwsfc , & ! Function, returns the surface long-wave radiation flux SfcFlx_momsenlat ! Subroutine, computes fluxes of momentum and of sensible and latent heat !============================================================================== IMPLICIT NONE !============================================================================== ! ! Declarations ! Input (procedure arguments) REAL (KIND = ireals), INTENT(IN) :: & dMsnowdt_in , & ! The rate of snow accumulation [kg m^{-2} s^{-1}] I_atm_in , & ! Solar radiation flux at the surface [W m^{-2}] Q_atm_lw_in , & ! Long-wave radiation flux from the atmosphere [W m^{-2}] height_u_in , & ! Height above the lake surface where the wind speed is measured [m] height_tq_in , & ! Height where temperature and humidity are measured [m] U_a_in , & ! Wind speed at z=height_u_in [m s^{-1}] T_a_in , & ! Air temperature at z=height_tq_in [K] q_a_in , & ! Air specific humidity at z=height_tq_in P_a_in ! Surface air pressure [N m^{-2} = kg m^{-1} s^{-2}] REAL (KIND = ireals), INTENT(IN) :: & depth_w , & ! The lake depth [m] fetch , & ! Typical wind fetch [m] depth_bs , & ! Depth of the thermally active layer of the bottom sediments [m] T_bs , & ! Temperature at the outer edge of ! the thermally active layer of the bottom sediments [K] par_Coriolis , & ! The Coriolis parameter [s^{-1}] del_time ! The model time step [s] REAL (KIND = ireals), INTENT(IN) :: & T_snow_in , & ! Temperature at the air-snow interface [K] T_ice_in , & ! Temperature at the snow-ice or air-ice interface [K] T_mnw_in , & ! Mean temperature of the water column [K] T_wML_in , & ! Mixed-layer temperature [K] T_bot_in , & ! Temperature at the water-bottom sediment interface [K] T_B1_in , & ! Temperature at the bottom of the upper layer of the sediments [K] C_T_in , & ! Shape factor (thermocline) h_snow_in , & ! Snow thickness [m] h_ice_in , & ! Ice thickness [m] h_ML_in , & ! Thickness of the mixed-layer [m] H_B1_in , & ! Thickness of the upper layer of bottom sediments [m] T_sfc_p ! Surface temperature at the previous time step [K] ! Input/Output (procedure arguments) REAL (KIND = ireals), INTENT(INOUT) :: & albedo_water , & ! Water surface albedo with respect to the solar radiation albedo_ice , & ! Ice surface albedo with respect to the solar radiation albedo_snow ! Snow surface albedo with respect to the solar radiation TYPE (opticpar_medium), INTENT(INOUT) :: & opticpar_water , & ! Optical characteristics of water opticpar_ice , & ! Optical characteristics of ice opticpar_snow ! Optical characteristics of snow ! Output (procedure arguments) REAL (KIND = ireals), INTENT(OUT) :: & T_snow_out , & ! Temperature at the air-snow interface [K] T_ice_out , & ! Temperature at the snow-ice or air-ice interface [K] T_mnw_out , & ! Mean temperature of the water column [K] T_wML_out , & ! Mixed-layer temperature [K] T_bot_out , & ! Temperature at the water-bottom sediment interface [K] T_B1_out , & ! Temperature at the bottom of the upper layer of the sediments [K] C_T_out , & ! Shape factor (thermocline) h_snow_out , & ! Snow thickness [m] h_ice_out , & ! Ice thickness [m] h_ML_out , & ! Thickness of the mixed-layer [m] H_B1_out , & ! Thickness of the upper layer of bottom sediments [m] T_sfc_n ! Updated surface temperature [K] ! Local variables of type REAL REAL (KIND = ireals) :: & Q_momentum , & ! Momentum flux [N m^{-2}] Q_sensible , & ! Sensible heat flux [W m^{-2}] Q_latent , & ! Latent heat flux [W m^{-2}] Q_watvap ! Flux of water vapour [kg m^{-2} s^{-1}] !============================================================================== ! Start calculations !------------------------------------------------------------------------------ !------------------------------------------------------------------------------ ! Set albedos of the lake water, lake ice and snow !------------------------------------------------------------------------------ ! Use default value albedo_water = albedo_water_ref ! Use empirical formulation proposed by Mironov and Ritter (2004) for GME !_nu albedo_ice = albedo_whiteice_ref albedo_ice = EXP(-c_albice_MR*(tpl_T_f-T_sfc_p)/tpl_T_f) albedo_ice = albedo_whiteice_ref*(1._ireals-albedo_ice) + albedo_blueice_ref*albedo_ice ! Snow is not considered albedo_snow = albedo_ice !------------------------------------------------------------------------------ ! Set optical characteristics of the lake water, lake ice and snow !------------------------------------------------------------------------------ ! Use default values opticpar_water = opticpar_water_ref opticpar_ice = opticpar_ice_opaque ! Opaque ice opticpar_snow = opticpar_snow_opaque ! Opaque snow !------------------------------------------------------------------------------ ! Set initial values !------------------------------------------------------------------------------ T_snow_p_flk = T_snow_in T_ice_p_flk = T_ice_in T_mnw_p_flk = T_mnw_in T_wML_p_flk = T_wML_in T_bot_p_flk = T_bot_in T_B1_p_flk = T_B1_in C_T_p_flk = C_T_in h_snow_p_flk = h_snow_in h_ice_p_flk = h_ice_in h_ML_p_flk = h_ML_in H_B1_p_flk = H_B1_in !------------------------------------------------------------------------------ ! Set the rate of snow accumulation !------------------------------------------------------------------------------ dMsnowdt_flk = dMsnowdt_in !------------------------------------------------------------------------------ ! Compute solar radiation fluxes (positive downward) !------------------------------------------------------------------------------ I_atm_flk = I_atm_in CALL flake_radflux ( depth_w, albedo_water, albedo_ice, albedo_snow, & opticpar_water, opticpar_ice, opticpar_snow ) !------------------------------------------------------------------------------ ! Compute long-wave radiation fluxes (positive downward) !------------------------------------------------------------------------------ Q_w_flk = Q_atm_lw_in ! Radiation of the atmosphere Q_w_flk = Q_w_flk - SfcFlx_lwradwsfc(T_sfc_p) ! Radiation of the surface (notice the sign) !------------------------------------------------------------------------------ ! Compute the surface friction velocity and fluxes of sensible and latent heat !------------------------------------------------------------------------------ ! write(*,*)'print1',height_u_in, height_tq_in, fetch,U_a_in, T_a_in, q_a_in, T_sfc_p, P_a_in, h_ice_p_flk,Q_momentum, Q_sensible, Q_latent, Q_watvap CALL SfcFlx_momsenlat ( height_u_in, height_tq_in, fetch, & U_a_in, T_a_in, q_a_in, T_sfc_p, P_a_in, h_ice_p_flk, & Q_momentum, Q_sensible, Q_latent, Q_watvap ) u_star_w_flk = SQRT(-Q_momentum/tpl_rho_w_r) ! write(*,*)'print2',height_u_in, height_tq_in, fetch,U_a_in, T_a_in, q_a_in, T_sfc_p, P_a_in, h_ice_p_flk,Q_momentum, Q_sensible, Q_latent, Q_watvap !------------------------------------------------------------------------------ ! Compute heat fluxes Q_snow_flk, Q_ice_flk, Q_w_flk !------------------------------------------------------------------------------ Q_w_flk = Q_w_flk - Q_sensible - Q_latent ! Add sensible and latent heat fluxes (notice the signs) IF(h_ice_p_flk.GE.h_Ice_min_flk) THEN ! Ice exists IF(h_snow_p_flk.GE.h_Snow_min_flk) THEN ! There is snow above the ice Q_snow_flk = Q_w_flk Q_ice_flk = 0._ireals Q_w_flk = 0._ireals ELSE ! No snow above the ice Q_snow_flk = 0._ireals Q_ice_flk = Q_w_flk Q_w_flk = 0._ireals END IF ELSE ! No ice-snow cover Q_snow_flk = 0._ireals Q_ice_flk = 0._ireals END IF !------------------------------------------------------------------------------ ! Advance FLake variables !------------------------------------------------------------------------------ CALL flake_driver ( depth_w, depth_bs, T_bs, par_Coriolis, & opticpar_water%extincoef_optic(1), & del_time, T_sfc_p, T_sfc_n ) !------------------------------------------------------------------------------ ! Set output values !------------------------------------------------------------------------------ T_snow_out = T_snow_n_flk T_ice_out = T_ice_n_flk T_mnw_out = T_mnw_n_flk T_wML_out = T_wML_n_flk T_bot_out = T_bot_n_flk T_B1_out = T_B1_n_flk C_T_out = C_T_n_flk h_snow_out = h_snow_n_flk h_ice_out = h_ice_n_flk h_ML_out = h_ML_n_flk H_B1_out = H_B1_n_flk ! write(*,*)'printEND',height_u_in, height_tq_in, fetch,U_a_in, T_a_in, q_a_in, T_sfc_p, P_a_in, h_ice_p_flk,Q_momentum, Q_sensible, Q_latent, Q_watvap !------------------------------------------------------------------------------ ! End calculations !============================================================================== END SUBROUTINE flake_interface SUBROUTINE eta_flake (I_atm, Q_atm_lw_in, U10, V10, & !Inserir só as variáveis do Eta. T_a_in, q_a_in, P_a_in) USE data_parameters , ONLY : & ireals, & ! KIND-type parameter for real variables iintegers ! KIND-type parameter for "normal" integer variables USE flake_derivedtypes ! Definitions of several derived TYPEs IMPLICIT NONE ! Input (procedure arguments) !REAL (KIND = ireals), INTENT(IN) :: & REAL (KIND = ireals) :: dMsnowdt_in ! The rate of snow accumulation [kg m^{-2} s^{-1}] REAL (KIND = ireals) :: I_atm_in ! Solar radiation flux at the surface [W m^{-2}] REAL (KIND = ireals) :: Q_atm_lw_in ! Long-wave radiation flux from the atmosphere [W m^{-2}] REAL (KIND = ireals) :: height_u_in ! Height above the lake surface where the wind speed is measured [m] REAL (KIND = ireals) :: height_tq_in! Height where temperature and humidity are measured [m] REAL (KIND = ireals) :: U10 REAL (KIND = ireals) :: V10 REAL (KIND = ireals) :: U_a_in ! Wind speed at z=height_u_in [m s^{-1}] REAL (KIND = ireals) :: T_a_in ! Air temperature at z=height_tq_in [K] REAL (KIND = ireals) :: q_a_in ! Air specific humidity at z=height_tq_in REAL (KIND = ireals) :: P_a_in ! Surface air pressure [N m^{-2} = kg m^{-1} s^{-2}] !INTEGER (KIND = iintegers) :: & INTEGER (KIND = iintegers) :: nelem ! EA: Número de elemento !INTEGER (KIND = iintegers) :: hora ! EA: hora !REAL (KIND = ireals), INTENT(IN) :: & REAL (KIND = ireals) :: depth_w ! The lake depth [m] REAL (KIND = ireals) :: fetch ! Typical wind fetch [m] REAL (KIND = ireals) :: depth_bs ! Depth of the thermally active layer of the bottom sediments [m] REAL (KIND = ireals) :: T_bs ! Temperature at the outer edge of ! the thermally active layer of the bottom sediments [K] REAL (KIND = ireals) :: par_Coriolis ! The Coriolis parameter [s^{-1}] REAL (KIND = ireals) :: del_time ! The model time step [s] !REAL (KIND = ireals), INTENT(IN) :: & REAL (KIND = ireals) :: T_snow_in ! Temperature at the air-snow interface [K] REAL (KIND = ireals) :: T_ice_in ! Temperature at the snow-ice or air-ice interface [K] REAL (KIND = ireals) :: T_mnw_in ! Mean temperature of the water column [K] REAL (KIND = ireals) :: T_wML_in ! Mixed-layer temperature [K] REAL (KIND = ireals) :: T_bot_in ! Temperature at the water-bottom sediment interface [K] REAL (KIND = ireals) :: T_B1_in ! Temperature at the bottom of the upper layer of the sediments [K] REAL (KIND = ireals) :: C_T_in ! Shape factor (thermocline) REAL (KIND = ireals) :: h_snow_in ! Snow thickness [m] REAL (KIND = ireals) :: h_ice_in ! Ice thickness [m] REAL (KIND = ireals) :: h_ML_in ! Thickness of the mixed-layer [m] REAL (KIND = ireals) :: H_B1_in ! Thickness of the upper layer of bottom sediments [m] REAL (KIND = ireals) :: T_sfc_p ! Surface temperature at the previous time step [K] REAL (KIND = ireals) :: I_atm ! EA:Radiação incidente REAL (KIND = ireals) :: Tmp_a REAL (KIND = ireals) :: u_a ! EA: Vento !REAL (KIND = ireals) :: dMsnowdt_in !REAL (KIND = ireals) :: Q_a !REAL (KIND = ireals) :: hora REAL (KIND = ireals) :: dia ! Input/Output (procedure arguments) !REAL (KIND = ireals), INTENT(INOUT) :: & REAL (KIND = ireals) :: albedo_water ! Water surface albedo with respect to the solar radiation REAL (KIND = ireals) :: albedo_ice ! Ice surface albedo with respect to the solar radiation REAL (KIND = ireals) :: albedo_snow ! Snow surface albedo with respect to the solar radiation TYPE (opticpar_medium) :: & opticpar_water , & ! Optical characteristics of water opticpar_ice , & ! Optical characteristics of ice opticpar_snow ! Optical characteristics of snow ! Output (procedure arguments) !REAL (KIND = ireals), INTENT(OUT) :: & REAL (KIND = ireals) :: T_snow_out ! Temperature at the air-snow interface [K] REAL (KIND = ireals) :: T_ice_out ! Temperature at the snow-ice or air-ice interface [K] REAL (KIND = ireals) :: T_mnw_out ! Mean temperature of the water column [K] REAL (KIND = ireals) :: T_wML_out ! Mixed-layer temperature [K] REAL (KIND = ireals) :: T_bot_out ! Temperature at the water-bottom sediment interface [K] REAL (KIND = ireals) :: T_B1_out ! Temperature at the bottom of the upper layer of the sediments [K] REAL (KIND = ireals) :: C_T_out ! Shape factor (thermocline) REAL (KIND = ireals) :: h_snow_out ! Snow thickness [m] REAL (KIND = ireals) :: h_ice_out ! Ice thickness [m] REAL (KIND = ireals) :: h_ML_out ! Thickness of the mixed-layer [m] REAL (KIND = ireals) :: H_B1_out ! Thickness of the upper layer of bottom sediments [m] REAL (KIND = ireals) :: T_sfc_n ! Updated surface temperature [K] REAL (KIND = ireals) :: Q_sensible REAL (KIND = ireals) :: Q_latent REAL (KIND = ireals) :: Q_momentum REAL (KIND = ireals) :: u_star_st ! DECLARE NAMELISTS. !------------------- NAMELIST /ETAFLAKENML/ & & height_u_in,height_tq_in,depth_w ,fetch, depth_bs,T_bs, & & par_Coriolis,del_time,u_star_st,T_snow_in,T_ice_in,T_mnw_in, & & T_wML_in,T_bot_in,T_B1_in, C_T_in,h_snow_in,h_ice_in,h_ML_in, & & H_B1_in ,T_sfc_p,albedo_water ,albedo_ice ,albedo_snow OPEN(1, FILE='ETAFLAKE.nml', STATUS='OLD') REWIND 1 READ(1, ETAFLAKENML) CLOSE(1) U_a_in = sqrt(U10*U10+V10*V10) write(*,*)'T_snow_out T_ice_out T_mnw_out T_wML_out T_bot_out T_B1_out T_sfc_n albedo_water Q_sensible Q_latent Q_momentum C_T_out h_ML_out H_B1_out' write(2,*)'Time_step;T_sfc_n;T_wML_out;T_mnw_out;T_bot_out;T_B1_out;Q_sensible;Q_latent;Q_momentum;albedo_water;C_T_out;h_ML_out;H_B1_out' CALL flake_interface ( dMsnowdt_in, I_atm_in, Q_atm_lw_in, height_u_in, height_tq_in, & U_a_in, T_a_in, q_a_in, P_a_in, & depth_w, fetch, depth_bs, T_bs, par_Coriolis, del_time, & T_snow_in, T_ice_in, T_mnw_in, T_wML_in, T_bot_in, T_B1_in, & C_T_in, h_snow_in, h_ice_in, h_ML_in, H_B1_in, T_sfc_p, & albedo_water, albedo_ice, albedo_snow, & opticpar_water, opticpar_ice, opticpar_snow, & T_snow_out, T_ice_out, T_mnw_out, T_wML_out, T_bot_out, T_B1_out, & C_T_out, h_snow_out, h_ice_out, h_ML_out, H_B1_out, T_sfc_n,Q_sensible,Q_latent,Q_momentum) write(*,100)T_snow_out,T_ice_out,T_mnw_out,T_wML_out,T_bot_out ,T_B1_out ,T_sfc_n,albedo_water,Q_sensible ,Q_latent, Q_momentum,C_T_out,h_ML_out,H_B1_out 100 format(i4,7(3x,f7.2),5x,f4.2,7x,f6.2,5x,f6.2,2x,f19.16,2x,f4.2,2(4x,f4.2)) write(2,*)T_sfc_n,';',T_wML_out,';',T_mnw_out,';',T_bot_out,';',T_B1_out,';',Q_sensible,';',Q_latent,';',Q_momentum,';',albedo_water,';',C_T_out,';',h_ML_out,';',H_B1_out END SUBROUTINE eta_flake