! File %M% from Library %Q% ! Version %I% from %G% extracted: %H% !------------------------------------------------------------------------------ MODULE flake !------------------------------------------------------------------------------ ! ! Description: ! ! The main program unit of the lake model FLake, ! containing most of the FLake procedures. ! Most FLake variables and local parameters are declared. ! ! FLake (Fresh-water Lake) is a lake model capable of predicting the surface temperature ! in lakes of various depth on the time scales from a few hours to a year. ! The model is based on a two-layer parametric representation of ! the evolving temperature profile, where the structure of the stratified layer between the ! upper mixed layer and the basin bottom, the lake thermocline, ! is described using the concept of self-similarity of the temperature-depth curve. ! The concept was put forward by Kitaigorodskii and Miropolsky (1970) ! to describe the vertical temperature structure of the oceanic seasonal thermocline. ! It has since been successfully used in geophysical applications. ! The concept of self-similarity of the evolving temperature profile ! is also used to describe the vertical structure of the thermally active upper layer ! of bottom sediments and of the ice and snow cover. ! ! The lake model incorporates the heat budget equations ! for the four layers in question, viz., snow, ice, water and bottom sediments, ! developed with due regard for the vertically distributed character ! of solar radiation heating. ! The entrainment equation that incorporates the Zilitinkevich (1975) spin-up term ! is used to compute the depth of a convectively-mixed layer. ! A relaxation-type equation is used ! to compute the wind-mixed layer depth in stable and neutral stratification, ! where a multi-limit formulation for the equilibrium mixed-layer depth ! proposed by Zilitinkevich and Mironov (1996) ! accounts for the effects of the earth's rotation, of the surface buoyancy flux ! and of the static stability in the thermocline. ! The equations for the mixed-layer depth are developed with due regard for ! the volumetric character of the radiation heating. ! Simple thermodynamic arguments are invoked to develop ! the evolution equations for the ice thickness and for the snow thickness. ! The heat flux through the water-bottom sediment interface is computed, ! using a parameterization proposed by Golosov et al. (1998). ! The heat flux trough the air-water interface ! (or through the air-ice or air-snow interface) ! is provided by the driving atmospheric model. ! ! Empirical constants and parameters of the lake model ! are estimated, using independent empirical and numerical data. ! They should not be re-evaluated when the model is applied to a particular lake. ! The only lake-specific parameters are the lake depth, ! the optical characteristics of lake water, ! the temperature at the bottom of the thermally active layer ! of bottom sediments and the depth of that layer. ! ! A detailed description of the lake model is given in ! Mironov, D. V., 2005: ! Parameterization of Lakes in Numerical Weather Prediction. ! Part 1: Description of a Lake Model. ! Manuscript is available from the author. ! Dmitrii Mironov ! German Weather Service, Kaiserleistr. 29/35, D-63067 Offenbach am Main, Germany. ! dmitrii.mironov@dwd.de ! ! Lines embraced with "!_tmp" contain temporary parts of the code. ! Lines embraced/marked with "!_dev" may be replaced ! as improved parameterizations are developed and tested. ! Lines embraced/marked with "!_dm" are DM's comments ! that may be helpful to a user. ! Lines embraced/marked with "!_dbg" are used ! for debugging purposes only. ! ! ! 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 ! ! The variables declared below ! are accessible to all program units of the MODULE flake. ! Some of them should be USEd by the driving routines that call flake routines. ! These are basically the quantities computed by FLake. ! All variables declared below have a suffix "flk". ! FLake variables of type REAL ! Temperatures at the previous time step ("p") and the updated temperatures ("n") REAL (KIND = ireals) :: & T_mnw_p_flk, T_mnw_n_flk , & ! Mean temperature of the water column [K] 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_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] ! Thickness of various layers at the previous time step ("p") and the updated values ("n") REAL (KIND = ireals) :: & 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] ! The shape factor(s) at the previous time step ("p") and the updated value(s) ("n") REAL (KIND = ireals) :: & C_T_p_flk, C_T_n_flk , & ! Shape factor (thermocline) C_TT_flk , & ! Dimensionless parameter (thermocline) C_Q_flk , & ! Shape factor with respect to the heat flux (thermocline) C_I_flk , & ! Shape factor (ice) C_S_flk ! Shape factor (snow) ! Derivatives of the shape functions REAL (KIND = ireals) :: & Phi_T_pr0_flk , & ! d\Phi_T(0)/d\zeta (thermocline) Phi_I_pr0_flk , & ! d\Phi_I(0)/d\zeta_I (ice) Phi_I_pr1_flk , & ! d\Phi_I(1)/d\zeta_I (ice) Phi_S_pr0_flk ! d\Phi_S(0)/d\zeta_S (snow) ! Heat and radiation fluxes REAL (KIND = ireals) :: & 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}] ! Velocity scales REAL (KIND = ireals) :: & 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}] ! The rate of snow accumulation REAL (KIND = ireals) :: & dMsnowdt_flk ! The rate of snow accumulation [kg m^{-2} s^{-1}] !============================================================================== ! Procedures !============================================================================== CONTAINS !============================================================================== ! The codes of the FLake procedures are stored in separate "*.incf" files ! and are included below. !------------------------------------------------------------------------------ !============================================================================== include 'flake_radflux.incf' !============================================================================== !============================================================================== include 'flake_driver.incf' !============================================================================== !============================================================================== include 'flake_buoypar.incf' !============================================================================== !============================================================================== include 'flake_snowdensity.incf' !============================================================================== !============================================================================== include 'flake_snowheatconduct.incf' !============================================================================== END MODULE flake