# ARTS built-in documentation server

## Workspace Method iySurfaceLambertian

### Description

This method calculates upwelling radiation for a lambertian surface due to the scattering of the downgoing diffuse radiation and emission from the surface. This method works only for 1D or 3D atmospheres. For the integration over the zenith angles a gaussian quadrature with N_za angles is used. For 1D atmospheres N_aa is ignored. For 3D atmospheres without clouds azimuthal dependency can be neglected. N_aa = 1 is sufficient. For 3D atmospheres with cloudbox on azimuthal dependency needs to be accounted. In that case the number of azimuth angles N_aa as a rule ofthumb should be set to 4*N_za. For the 1D case N_za downwelling streams and 3D case N_za*N_aa downwelling streams are calculated. This method is designed to be part of iy_surface_agenda Important this method calculates only the scattering of the diffuse downward radiation. No direct incoming radiation is considered Jacobian is supported only for Skin temperature

**Authors: **Manfred Brath

### Synopsis

iySurfaceLambertian( | iy, diy_dx, iy_transmittance, iy_id, jacobian_do, stars_do, atmosphere_dim, nlte_field, cloudbox_on, stokes_dim, f_grid, lat_grid, lon_grid, z_surface, refellipsoid, rtp_pos, rtp_los, rte_pos2, iy_unit, surface_scalar_reflectivity, surface_props_data, surface_props_names, dsurface_names, jacobian_quantities, iy_main_agenda, N_za, N_aa ) |

### Variables

OUT+IN | iy | (Matrix) | Monochromatic pencil beam radiance spectrum. |

OUT+IN | diy_dx | (ArrayOfTensor3) | Derivative of iy with respect to retrieval quantities. |

IN | iy_transmittance | (Tensor3) | Transmittance to be included in iy. |

IN | iy_id | (Index) | Identification number of iy. |

IN | jacobian_do | (Index) | Flag to activate (clear-sky) Jacobian calculations. |

IN | stars_do | (Index) | Flag to activate the star(s). |

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

IN | nlte_field | (EnergyLevelMap) | The field of NLTE temperatures and/or ratios. |

IN | cloudbox_on | (Index) | Flag to activate the cloud box. |

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

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

IN | lat_grid | (Vector) | The latitude grid. |

IN | lon_grid | (Vector) | The longitude grid. |

IN | z_surface | (Matrix) | The surface altitude. |

IN | refellipsoid | (Vector) | Reference ellipsoid. |

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

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

IN | rte_pos2 | (Vector) | A second geographical position to define the geometry for radiative transfer calculations. |

IN | iy_unit | (String) | Selection of output unit for radiative transfer methods. |

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

IN | surface_props_data | (Tensor3) | Various surface properties. |

IN | surface_props_names | (ArrayOfString) | Name on surface properties found in surface_props_data. |

IN | dsurface_names | (ArrayOfString) | Name of surface retrieval quantities. |

IN | jacobian_quantities | (ArrayOfRetrievalQuantity) | The retrieval quantities in the Jacobian matrix. |

IN | iy_main_agenda | (Agenda) | Agenda calculating the single monochromatic pencil beam spectrum. |

GIN | N_za | (Index, Default: 3) | Number of zenith angles. |

GIN | N_aa | (Index, Default: 1) | Number of azimuth angles |