Emission Models 
===============

emiproc can also genereate emissions using various well known methods 


.. _vprm:

VPRM 
---- 

The VPRM simulates the vegetation respiration and photosynthesis using the following 
inputs:

* temperature
* radiation
* satellite data
* vegetation parameters


There are 4 implementation of the VPRM model:

- standard (Mahadevan et al., 2008)
- urban  (Hardiman et al., 2017)
- urban winbourne (Winbourne et al., 2021)
- modified (Gourdij et al., 2021)

see :py:mod:`emiproc.profiles.vprm`

Standard VPRM
^^^^^^^^^^^^^

PAR (Photosynthetically Active Radiation) is calculated from the shortwave radiation:

.. math::
    \mathrm{PAR} = \frac{\mathrm{RAD}}{0.505}

Respiration is calculated from the temperature:

.. math::
    \mathrm{Resp} = \alpha * T + \beta

The Gross Ecosystem Exchange (GEE) is calculated from the temperature, PAR and the vegetation indices:

.. math::
    \mathrm{GEE} = - \lambda * T_{scale} * P_{scale} * W_{scale} * \mathrm{EVI} * \frac{ \mathrm{PAR} }{1 + \frac{\mathrm{PAR}}{PAR0}}

where the different scales are:

- :math:`T_{scale}`: Temperature scale

.. math::
    T_{scale} = \frac{(T - T_{\text{min}}) \cdot (T - T_{\text{max}})}{(T - T_{\text{min}}) \cdot (T - T_{\text{max}}) + (T - T_{\text{opt}})^2} \text{if } T \geq T_{\text{min}} \text{ else } 0

- :math:`P_{scale}`: Photosynthesis scale

.. math::
    P_{scale} = \frac{1 + \mathrm{LSWI}}{2}

- :math:`W_{scale}`: Water scale

.. math::
    W_{scale} = \frac{1 + \mathrm{LSWI}}{1 + \mathrm{LSWI}_{max}}

The Net Ecosystem Exchange (NEE) is calculated from the respiration and GEE.

.. math::
    \mathrm{NEE} = \mathrm{Resp} + \mathrm{GEE}


Units for all fluxes (NEE, GEE, Resp, ...) are

.. math::
    \frac{\mu mol_{\mathrm{CO2}}}{m^2 * s}

Urban VPRM
^^^^^^^^^^

The VPRM model can be extended to urban areas according to [Urban_VPRM_Hardiman_2017]_.

- A "urban temperature" is used instead of the global temperature to represent
    the urban heat island phenomenon.
- The formula for :math:`P_{scale}` is modified to

.. math::
    P_{scale} = \frac{\mathrm{EVI} - \mathrm{EVI}_{min}}{\mathrm{EVI}_{max} - \mathrm{EVI}_{min}}

- The respiration is calculated differently

.. math::
    \mathrm{Resp} = \frac{\mathrm{Resp_{e-init}}}{2} * (1 - \mathrm{ISA}) + \frac{\mathrm{EVI} + \mathrm{EVI}_{min} * \mathrm{ISA}}{\mathrm{EVI}_{ref}} * \frac{\mathrm{Resp_{e-init}}}{2}

where :math:`\mathrm{Resp_{e-init}}` is the basic vprm respiration and :math:`\mathrm{ISA}` is the impervious surface area at the vegetation location.


Urban VPRM with winbourne
^^^^^^^^^^^^^^^^^^^^^^^^^^

This is a variant of the urban VPRM model that uses a different formulation for :math:`T_{scale}`:

.. math::
    T_{scale} = \begin{cases}
    \frac{(T - 0) \cdot (T - 40)}{(T - 0) \cdot (T - 40) + (T - 20)^2} & \text{if } T \leq 20 \\
    1 & \text{if } 20 < T < 30 \\
    \frac{(T - 0) \cdot (T - 40)}{(T - 0) \cdot (T - 40) + (T - 30)^2} & \text{if } T \geq 30
    \end{cases}



modified-VPRM
^^^^^^^^^^^^^

The modified-VPRM model follows the standard VPRM for GEE and has a different model
for the estimate of respiration: for more details see [VPRM_modified_groudji_2022]_.


Heating Degree Days (HDD)
-------------------------


Calculates the demand of heating based on the temperature.

see :py:mod:`emiproc.profiles.hdd`


Human Respiration
-----------------

Human respirations can be generated using maps of population density and 
emission factors per person.

see :py:mod:`emiproc.human_respiration`