# ARTS built-in documentation server

## Workspace Method surfaceLambertianSimple

### Description

Creates variables to mimic a Lambertian surface. A Lambertian surface can be characterised solely by its reflectivity, here taken from surface_scalar_reflectivity. The down-welling radiation field is estimated by making calculations for *lambertian_nza* directions. The range of zenith angles ([0,90]) is divided in an equidistant manner for 1D. For 2D and 3D see below. The values for surface_rmatrix are assuming a constant radiance over each zenith angle range. See AUG. Default is to select the zenith angles for sensor_los to be placed centrally in the grid ranges. For example, if *lambertian_nza* is set to 9, down-welling radiation will be calculated for zenith angles = 5, 15, ..., 85. The position of these angles can be shifted by *za_pos*. This variable specifies the fractional distance inside the ranges. For example, a *za_pos* of 0.7 (np still 9) gives the angles 7, 17, ..., 87. Only upper-left diagonal element of the surface_rmatrix is non-zero. That is, the upwelling radiation is always unpolarised. Local thermodynamic equilibrium is assumed, which corresponds to that the reflection and emission coefficients "add up to 1". For 2D and 3D, the down-welling directions are placed along the the viewing direction, e.g. for 3D the azimuth angle is kept constant. In 2D and 3D surface topography can exist, and to avoid getting views going directly into the surface, angels are not distributed over 90 deg, but 90-abs(surface_normal[0]).

**Authors: **Patrick Eriksson

### Synopsis

surfaceLambertianSimple( | surface_los, surface_rmatrix, surface_emission, f_grid, stokes_dim, atmosphere_dim, rtp_pos, rtp_los, surface_normal, surface_skin_t, surface_scalar_reflectivity, lambertian_nza, za_pos ) |

### Variables

OUT | surface_los | (Matrix) | Downwelling radiation directions to consider in surface reflection. |

OUT | surface_rmatrix | (Tensor4) | The reflection coefficients for the directions given by surface_los to the direction of interest. |

OUT | surface_emission | (Matrix) | The emission from the surface. |

IN | f_grid | (Vector) | The frequency grid for monochromatic pencil beam calculations. |

IN | stokes_dim | (Index) | The dimensionality of the Stokes vector (1-4). |

IN | atmosphere_dim | (Index) | The atmospheric dimensionality (1-3). |

IN | rtp_pos | (Vector) | Position of a radiative transfer point. |

IN | rtp_los | (Vector) | Line-of-sight at a radiative transfer point. |

IN | surface_normal | (Vector) | The normal vector for a point at the surface. |

IN | surface_skin_t | (Numeric) | Surface skin temperature. |

IN | surface_scalar_reflectivity | (Vector) | Surface reflectivity, assuming it can be described as a scalar value. |

GIN | lambertian_nza | (Index, Default: 9) | Number of downwelling streams. |

GIN | za_pos | (Numeric, Default: 0.5) | Position of angle in surface_los inside ranges of zenith angle grid. See above. |