# Senescence



## Leaf number senescence


The leaf senescence phase begins 40\% between floral initiation and
end of juvenile, and ends at harvest ripe (Fig. \@ref(fig:PhenologWheatModule)),
at which stage, all green leaves are dead. During leaf senescence
phase (Fig. \@ref(fig:PhenologWheatModule)), leaf number senescence
is calculated by daily thermal time ($\Delta TT$, Equation \@ref(eq:thermaltime))
as follows:

\begin{equation}

\Delta N_{d,\,sen}=\Delta TT\times\frac{f_{sen,\,l}\times N_{d}}{r_{sen,\,l}}

\end{equation}

where $N_{d}$ is the total leaf number; $f_{sen,\,l}$ is the fraction
of the total leaf number senescing per main stem node and specified
by `fr_lf_sen_rate` in wheat.xml (default value 0.035);
$r_{sen,\,l}$ is the rate of node senescence on main stem and specified
by `node_sen_rate` in wheat.xml (default value 60.0 $^{\circ}$Cd
node\textsuperscript{-1}). 


## Leaf area senescence


There are five causes of leaf senescence: age ($\text{\ensuremath{\Delta}LAI}_{sen,\,age}$),
water stress ($\text{\ensuremath{\Delta}LAI}_{sen,\,sw}$), light
intensity ($\text{\ensuremath{\Delta}LAI}_{sen,\,light}$), frost
($\text{\ensuremath{\Delta}LAI}_{sen,\,frost}$) and heat ($\text{\ensuremath{\Delta}LAI}_{sen,\,heat}$).
The maximum of these causes is the day's total leaf area index senescence.

\begin{equation}

\text{\ensuremath{\Delta}LAI}_{sen}=\max(\text{\ensuremath{\Delta}LAI}_{sen,\,age},\;\text{\ensuremath{\Delta}LAI}_{sen,\,sw},\;\Delta\text{LAI}_{sen,\,light},\;\text{\ensuremath{\Delta}LAI}_{sen,\,frost},\;\text{\ensuremath{\Delta}LAI}_{sen,\,heat})

\end{equation}


Leaf area senescence caused by age corresponds to the leaf area of
the number of leaves senesced ($\Delta N_{d,\,sen}$) from the lowest
leaf position.

Leaf area senescence caused by soil water ($\text{\ensuremath{\Delta}LAI}_{sen,\,sw}$)
is calculated as follows.


\begin{equation}

\text{\ensuremath{\Delta}LAI}_{sen,\,sw}=k_{sen,\,sw}\times(1-f_{sw,\,photo})\times\text{LAI}

\end{equation}

where $k_{sen,\,sw}$ is the slope of the linear equation relating
to soil water stress to leaf senescence rate and is specified by `sen_rate_water`
in wheat.xml (default value 0.10); $f_{sw,\,photo}$ is soil water
stress for photosynthesis (Equation \@ref(eq:swstressphoto)); LAI is the
leaf area index.

Leaf area senescence caused by light intensity ($\text{\ensuremath{\Delta}LAI}_{sen,\,light}$)
is calculated as follows:


\begin{equation}

\text{\ensuremath{\Delta}LAI}_{sen,\,light}=k_{sen,\,light}\times(\text{LAI}-\text{LAI}_{c,\,light})\times\text{LAI}\quad\text{LAI}>\text{LAI}_{c,\,light} (\#eq:SensLight)

\end{equation}

where $k_{sen,\,light}$ is sensitivity of leaf area senescence to
shading and is specified by `sen_light_slope` in wheat.xml
(default value 0.002); $\text{LAI}_{c,\,light}$ is the critical LAI
when shading is starting to cause leaf area senescence and is specified
by `lai_sen_light` in wheat.xml (default value 7).

The leaf area senescence caused by frost is a ratio of LAI.


\begin{equation}

\text{\ensuremath{\Delta}LAI}_{sen,\,frost}=k_{sen,\,frost}\text{\ensuremath{\times}LAI} (\#eq:SensFrost)

\end{equation}

where $k_{sen,\,frost}$ is a function of daily minimum temperature
and is defined by parameters `x_temp_senescence` and `y_senescence_fac`
in wheat.xml, which are linearly interpolated by APSIM. The default
value of $k_{sen,\,frost}$ is zero, i.e. there is no frost stress
in leaf area in the current APSIM-Wheat module.

Senescence by heat calculation has been added in APSIM 7.5. The leaf
area senescence by heat is a ratio of LAI \citep{asseng2011theimpact}.


\begin{equation}

\text{\ensuremath{\Delta}LAI}_{sen,\,heat}=k_{sen,\,heat}\times\text{LAI} (\#eq:SensHeat)

\end{equation}


where $k_{sen,\,heat}$ is a function of daily maximum temperature
which is defined by parameters `x_maxt_senescence` and `y_heatsenescence_fac`
in wheat.xml which are linearly interpolated by APSIM. 


```{r wdHeatSenescence,fig.cap='Fraction of senescence of leaf area index ($k_{sen,\\,heat}$) in response to maximum temperature.' }  

p <- wdVisXY(wheat_xml, 
		"x_maxt_senescence", "y_heatsenescence_fac",
		xlab = expression(paste("Maximum temperature", ~"("*degree*"C)")),
		ylab = "Senescence fraction of LAI")
print(p)

```


The total leaf area of plant must be more than the minimum plant area
(`min_tpla`), which has default value 5 mm$^{\text{2}}$ plant$^{\text{-1}}$.
When some leaves are senesced, only a small amount of nitrogen is
retained in the senesced leaf, the rest is made available for re-translocation
included into the `Stem` N pool ( Section @ref(NitrogenPartitioningAndRetranslocation)).
The concentration of nitrogen in senesced material is specified in
wheat.xml.


## Biomass senescence


Leaf biomass senescence $\Delta Q_{sl}$ is the ratio of leaf area
senescence ($\text{\ensuremath{\Delta}LAI}_{sen}$) with total the
green LAI at the time considered (LAI). 

\begin{equation}

\Delta Q_{sl}=\Delta Q_{l}\frac{\text{\ensuremath{\text{\ensuremath{\Delta}LAI}_{sen}}}}{\text{LAI}}

\end{equation}

where $\Delta Q_{l}$ is the daily increase of leaf biomass.


## Root senescence


A rate of 0.5\% of root biomass and root length is senesced each day
and detaches immediately being sent to the soil nitrogen module and
distributed as fresh organic matter in the profile.


\begin{equation}

\Delta Q_{sen,\,root}=\Delta Q_{root}\times f_{sen,\,root}

\end{equation}

where $\Delta Q_{sen,\,root}$ is the daily `Root` senesced
biomass, and $f_{sen,\,root}$ is the fraction of senesced root biomass,
which is defined in `x_dm_sen_frac_root` and `y_dm_sen_frac_root`
in wheat.xml (Fig. \@ref(fig:wdRootSens))


```{r wdRootSens,fig.cap='Fraction of senescence of root biomass.' }  

p <- wdVisXY(wheat_xml, 
		"x_dm_sen_frac_root", "y_dm_sen_frac_root",
		xlab = 'Fraction of material senescence',
		ylab = "Senescence fraction of Root biomass")
print(p)

```



\begin{equation}

\Delta L_{sen,\,root}=\Delta Q_{sen,\,root}\times\text{SRL}

\end{equation}

where $\Delta L_{sen,\,root}$ is the daily root length senescence,
and SRL is the specific root length. 

Root senescence occurs in each of the soil layers where roots are
present, as a proportion of the total root length.

\begin{equation}

\Delta L_{sen,\,root}(i)=\Delta L_{sen,\,root}\times\frac{L_{r}(i)}{\sum_{j=1}^{i}L_{r}(j)}

\end{equation}

where $L_{sen,\,root}(i)$ is the root length senescence in soil layer
$i$, $L_{r}(i)$ is root length in layer $i$, and $\sum_{j=1}^{i}L_{r}(j)$is
the total root length for all the layers where root are present.