## Max-Planck-Institut für Meteorologie: Model MPI ECHAM4 (T42 L19) 1996

### Model Designation

MPI ECHAM4 (T42 L19) 1996

### Model Lineage

Model MPI ECHAM4 (T42 L19) 1996 is the fourth in a series of models developed at MPI that originally derive from cycle 17 of the European Centre for Medium-Range Weather Forecasts (ECMWF) model. The ECHAM4 model's immediate predecessor is AMIP baseline model MPI ECHAM3 (T42 L19) 1992. The ECHAM4 model differs most sharply from its predecessor in its treatment of transport and diffusion, of chemistry and radiation, and of the planetary boundary layer (PBL). The parameterizatons of convection, cloud formation, and land surface characteristics also have been modified.

### Model Documentation

Much of the literature on the baseline model remains relevant. Overall documentation of the ECHAM4 model is provided by Roeckner et al. (1996)[52]. Details of the new semi-Lagrangian transport scheme are given by Williamson and Rasch (1994)[57] and Hack et al. (1993)[58]. The radiation scheme is documented by Fouquart and Bonnel (1980)[63], Morcrette (1991)[64], Giorgetta and Wild (1995)[68], and Rockel et al. (1991)[17]. The reformulation of the PBL is after Brinkop and Roeckner (1995)[59]. Modification of the convection scheme follows Nordeng (1996)[72], and changes in cloud formation are after Sundqvist et al. (1989)[73] and Slingo (1987)[74]. The new land surface characteristics are described by Claussen et al. (1994)[76], Patterson (1990)[79], and Zobler (1986)[80]. Validation of various aspects of the ECHAM4 model is provided by Chen and Roeckner (1996)[53], Chen et al. (1996)[54], Lohmann et al. (1995)[55], and Wild et al. (1996)[56].

## Numerical/Computational Properties

### Horizontal Representation

The horizontal representation is as in the baseline model, except that horizontal advection of water vapor and cloud water are treated by the shape-preserving semi-Lagrangian transport (SLT) scheme of Williamson and Rasch (1994)[57], with further details supplied by Hack et al. (1993)[58]. Because the SLT scheme is not inherently conservative, mass conservation is enforced at every time step through a variational adjustment of the advected variable field which weights the amplitude of the adjustment in proportion to the advection tendencies and the field itself.

### Vertical Representation

The vertical representation is as in the baseline model, except that vertical advection of positive definite quantities is treated by the SLT scheme.

### Computer/Operating System

The AMIP simulation was run on a Cray C90 computer using 4 processors in the UNICOS environment.

### Computational Performance

About 3.5 minutes of Cray C90 computation time per simulated day.

### Smoothing/Filling

Smoothing and filling procedures are the same as for the baseline model, except that filling of spurious negative atmospheric moisture values is obviated by the use of the SLT scheme.

## Dynamical/Physical Properties

### Diffusion

- In contrast to the baseline model, linear tenth-order (del^10) horizontal diffusion is applied to all prognostic variables below about 150 hPa. In the model stratosphere, the order of the scheme is reduced incrementally to second-order (del^2) at the upper two model levels. The horizontal diffusion coefficient is consistent with a height-invariant damping time scale of 9 hours for the highest resolvable wave number (n=42).
- In a departure from the K-theory approach of the baseline model, a higher-order closure scheme after Brinkop and Roeckner (1995) [59] is used to compute the vertical diffusion of momentum, heat, moisture, and cloud water. The eddy diffusion coefficients are calculated as functions of the square root of the prognostic turbulence kinetic energy (TKE) and a mixing length which is a function of both stability and height. Above the PBL, the asymptotic value of the mixing length (cf. Blackadar 1962[60]) is assumed to decrease exponentially with height, from ~ 300 m to ~ 30 m following Holtslag and Boville 1993[61]). See also Planetary Boundary Layer and Surface Fluxes.

### Chemistry

Trace constituents including methane, nitrous oxide, and 16 different CFC's are added to the chemistry of the baseline model.

### Radiation

The radiation scheme of the baseline model is replaced. Instead, shortwave radiation is treated by the two-stream method of Fouquart and Bonnell (1980)[63], and longwave radiation by the method of Morcrette (1991)[64]. In addition, further changes are made in the treatment of other gaseous absorbers, continuum absorption by water vapor, and cloud-radiative interactions.

- For clear-sky conditions, shortwave radiation is modeled by a two-stream formulation in spectral wavelength intervals 0.25-0.68 micron and 0.68-4.0 microns using a photon path distribution method to separate the effects of scattering and absorption processes. Shortwave absorption by water vapor, ozone, oxygen, carbon dioxide,methane, and nitrous oxide is included. Rayleigh scattering by gases and Mie scattering/absorption by aerosols also are treated. Cf. Fouquart and Bonnell (1980)[63] and Morcrette (1991)[64] for further details.
- The clear-sky longwave scheme employs a broad-band flux emissivity method in six spectral intervals from wavenumbers 0 to 2.820 x 10^5 m^-1. The Morcrette (1991)[64] code is extended to include additional greenhouse gases (i.e., methane, nitrous oxide, and 16 types of CFC's, as well as the 14.6 micron band of ozone (see Chemistry). The respective absorption coefficients are fitted from AFGL[65], HITRAN91[66], and GEISA[67] spectroscopic data. Based on calculations by Ma and Tipping (1991)[69], 1992a[70], 1992b[71]), the formulation of the water vapor continuum has been revised to include temperature-weighted band averages of e-type absorption and a band-dependent ratio of (p-e)-type to e-type continuum absorption (cf. Giorgetta and Wild 1995[68]).
- For cloud-radiative interactions, single-scattering properties are
calculated following Rockel et al. (1991)[17],
a method that entails high-resolution Mie calculations using idealized
size distributions for both cloud droplets and ice crystals. The averaging
over the required wide spectral ranges is done by weighting with the Planck
function. The single-scattering parameters are expressed as functions of
effective radius
**r**by polynomial fitting of the results for different**r**. To account for the non-sphericity of ice crystals the associated asymmetry factor is reduced to ~ 0.80 for a wide range of**r**. The**r**values of both cloud droplets and ice crystals are parameterized in terms of prognostic liquid and ice water content (see Cloud Formation). As in the baseline model, radiative fluxes are calculated assuming that clouds of different types are randomly overlapped in the vertical, while convective cloud and nonconvective cloud of the same type in adjacent layers are treated as fully overlapped.

### Convection

The Tiedtke (1989)[22] convection scheme of the baseline model still is utilized, but with modifications introduced after Nordeng (1996)[72]. Organized entrainment depends on local buoyancy and organized detrainment is derived for a spectrum of clouds. The detrained cloud water, as well as that present in shallow non-precipitating cumulus clouds, is made a source term in the stratiform cloud water transport equation (see Cloud Formation), and buoyancy in updrafts is controlled by the water loading. The closure assumption of the baseline model also is modified: cloud-base mass flux is linked to convective instability instead of moisture convergence.

### Cloud Formation

The prognostic cloud-formation scheme of the baseline model is modified. Fractional cloudiness is determined as a nonlinear function of relative humidity excess above a threshold value, following Sundqvist et al. (1989)[73]. Threshold values decrease exponentially with height (between 99% at the surface to 60% in the upper troposphere) after Xu and Krueger (1991)[28]. The formation of marine stratocumulus clouds is linked to the existence of a low-level inversion following Slingo (1987)[74]. Cloud water from convective detrainment as well as that contained in non-precipitating shallow cumulus clouds (see Convection) is a source term for prognostic stratiform cloud formation . The transport and turbulent diffusion of cloud water also are treated by the SLT and TKE schemes (see Horizontal Representation, Diffusion, and Planetary Boundary Layer). See also Radiation for treatment of cloud optical properties.

### Planetary Boundary Layer

The baseline model's PBL representation is replaced by a higher-order closure scheme that computes the turbulent transfer of momentum, heat, moisture, and cloud water (cf. Brinkop and Roeckner (1995)[59]). The eddy diffusion coefficients are calculated as functions of the square root of the prognostic turbulence kinetic energy (TKE) and a mixing length which is a function of both stability and height. The TKE is calculated from rate equations for the respective variables which include buoyancy, dissipation, wind shear, and vertical diffusion terms, but which neglect TKE advection. The buoyancy flux is formulated in terms of cloud-conservative variables (see Cloud Formation in the baseline model). The boundary condition is expressed as a function of friction velocity and convective length scale. The asymptotic value of the mixing length (cf. Blackadar 1962[60]) is 300 m within the PBL, following Holtslag and Boville 1993[61]). See also Diffusion and Surface Fluxes.

### Surface Characteristics

Vegetation parameters, albedos, and roughness lengths differ from those of the baseline model:

- Fields of leaf area index (LAI), fractional vegetation cover, and forest ratio are constructed by allocating these parameters according to major ecosystem complexes identified by Olson et al. (1983)[78]. The albedos of snow-free land are derived by blending the albedos of these biome distributions with those obtained from Earth Radiation Budget Experiment (ERBE) satellite data and from the estimates of Dorman and Sellers (1989)[75]. The roughness lengths over land are recalculated to include the new vegetation and forest covers as well as the effects of subgrid-scale orography and urbanization, as in the baseline model. Cf. Claussen et al. (1994)[76] for further details. See also Land Surface Processes.
- In addition, the roughness lengths for computing surface fluxes of heat and moisture over oceans are decreased from those of the baseline model in accordance with experimental data of Large and Pond (1982)[77].

### Surface Fluxes

As in the baseline model, the turbulent surface fluxes are formulated as functions of roughness length and moist bulk Richardson number, but with decreased ocean roughness lengths used for calculating the heat and moisture fluxes (see Surface Characteristics).

### Land Surface Processes

The treatment of land surface processes is the same as in the baseline model, except that the heat capacity, thermal conductivity, and field capacity for soil moisture are prescribed according to geographically varying values derived from Food and Agriculture Organization (FAO) soil type distributions (cf. Patterson (1990)[79], and Zobler (1986)[80]).

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Last update May 12, 1998. For further information, contact: Tom Phillips ( phillips@tworks.llnl.gov )

UCRL-ID-116384