.. _rst_Crops and Irrigation:

Crops and Irrigation
========================

.. _Summary of CLM5.0 updates relative to the CLM4.5:

Summary of CLM5.0 updates relative to the CLM4.5
-----------------------------------------------------

We describe here the complete crop and irrigation parameterizations that
appear in CLM5.0. Corresponding information for CLM4.5 appeared in the
CLM4.5 Technical Note (:ref:`Oleson et al. 2013 <Olesonetal2013>`). 

CLM5.0 includes the following new updates to the CROP option, where CROP
refers to the interactive crop management model and is included as an option with the BGC configuration:

- New crop functional types

- All crop areas are actively managed

- Fertilization rates updated based on crop type and geographic region

- New Irrigation triggers

- Phenological triggers vary by latitude for some crop types

- Ability to simulate transient crop management

- Adjustments to allocation and phenological parameters

- Crops reaching their maximum LAI triggers the grain fill phase

- Grain C and N pools are included in a 1-year product pool

- C for annual crop seeding comes from the grain C pool

- Initial seed C for planting is increased from 1 to 3 g C/m^2 

These updates appear in detail in the sections below. Many also appear in
:ref:`Levis et al. (2016) <Levisetal2016>`.

.. _The crop model:

The crop model
-------------------

Introduction
^^^^^^^^^^^^^^^^^^^

Groups developing Earth System Models generally account for the human
footprint on the landscape in simulations of historical and future
climates. Traditionally we have represented this footprint with natural
vegetation types and particularly grasses because they resemble many
common crops. Most modeling efforts have not incorporated more explicit
representations of land management such as crop type, planting,
harvesting, tillage, fertilization, and irrigation, because global scale
datasets of these factors have lagged behind vegetation mapping. As this
begins to change, we increasingly find models that will simulate the
biogeophysical and biogeochemical effects not only of natural but also
human-managed land cover.

AgroIBIS is a state-of-the-art land surface model with options to
simulate dynamic vegetation (:ref:`Kucharik et al. 2000 <Kuchariketal2000>`) and interactive
crop management (:ref:`Kucharik and Brye 2003 <KucharikBrye2003>`). The interactive crop
management parameterizations from AgroIBIS (March 2003 version) were
coupled as a proof-of-concept to the Community Land Model version 3
[CLM3.0, :ref:`Oleson et al. (2004) <Olesonetal2004>` ] (not published), then coupled to the
CLM3.5 (:ref:`Levis et al. 2009 <Levisetal2009>`) and later released to the community with
CLM4CN (:ref:`Levis et al. 2012 <Levisetal2012>`), and CLM4.5BGC. Additional updates after the
release of CLM4.5 were available by request (:ref:`Levis et al. 2016 <Levisetal2016>`), 
and those are now incorporated into CLM5.

With interactive crop management and, therefore, a more accurate
representation of agricultural landscapes, we hope to improve the CLM’s
simulated biogeophysics and biogeochemistry. These advances may improve
fully coupled simulations with the Community Earth System Model (CESM),
while helping human societies answer questions about changing food,
energy, and water resources in response to climate, environmental, land
use, and land management change (e.g., :ref:`Kucharik and Brye 2003 <KucharikBrye2003>`; :ref:`Lobell et al. 2006 <Lobelletal2006>`).
As implemented here, the crop model uses the same physiology as the
natural vegetation, though uses different crop-specific parameter values,
phenology, and allocation, as well as fertilizer and irrigation management.

.. _Crop plant functional types:

Crop plant functional types
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

To allow crops to coexist with natural vegetation in a grid cell, the 
vegetated land unit is separated into a naturally vegetated land unit and
a managed crop land unit. Unlike the plant functional types (pfts) in the
naturally vegetated land unit, the managed crop pfts in the managed crop 
land unit do not share soil columns and thus permit for differences in the 
land management between crops. Each crop type has a rainfed and an irrigated 
pft that are on independent soil columns. Crop grid cell coverage is assigned from 
satellite data (similar to all natural pfts), and the managed crop type
proportions within the crop area is based on the dataset created by
:ref:`Portmann et al. (2010)<Portmannetal2010>` for present day. New in CLM5, crop area is
extrapolated through time using the dataset provided by Land Use Model 
Intercomparison Project (LUMIP), which is part of CMIP6 Land use timeseries 
(:ref:`Lawrence et al. 2016 <Lawrenceetal2016>`). For more details about how
crop distributions are determined, see Chapter :numref:`rst_Transient Landcover Change`. 

CLM5 includes eight actively managed crop types
(temperate soybean, tropical soybean, temperate corn, tropical 
corn, spring wheat, cotton, rice, and sugarcane) that are chosen 
based on the availability of corresponding algorithms in AgroIBIS and as 
developed by :ref:`Badger and Dirmeyer (2015)<BadgerandDirmeyer2015>` and
described by :ref:`Levis et al. (2016)<Levisetal2016>`. The representations of
sugarcane, rice, cotton, tropical corn, and tropical soy are new in CLM5.
Sugarcane and tropical corn are both C4 plants and are therefore represented
using the temperate corn functional form. Tropical soybean uses the temperate
soybean functional form, while rice and cotton use the wheat functional form.
In tropical regions, parameter values were developed for the Amazon Basin, and planting
date window is shifted by six months relative to the Northern Hemisphere. 

In addition, CLM’s default list of plant functional types (pfts) includes an
irrigated and unirrigated unmanaged C3 crop (:numref:`Table Crop plant functional types`) treated as a second C3 grass.
The unmanaged C3 crop is only used when the crop model is not active and 
has grid cell coverage assigned from satellite data, and 
the unmanaged C3 irrigated crop type is currently not used 
since irrigation requires the crop model to be active.
The default list of pfts also includes twenty-three inactive crop pfts 
that do not yet have associated parameters required for active management. 
Each of the inactive crop types is simulated using the parameters of the 
spatially closest associated crop type that is most similar to the functional type (e.g., C3 or C4), 
which is required to maintain similar phenological parameters based on temperature thresholds.
Information detailing which parameters are used for each crop type is 
included in :numref:`Table Crop plant functional types`. It should be noted that pft-level history output merges
all crop types into the actively managed crop type, so analysis 
of crop-specific output will require use of the land surface dataset to 
remap the yields of each actively and inactively managed crop type. Otherwise, the 
actively managed crop type will include yields for that crop type and all inactively
managed crop types that are using the same parameter set.

.. _Table Crop plant functional types:

.. table:: Crop plant functional types (pfts) included in CLM5BGCCROP.

 ===  ===========================  ================  ===========================
 IVT  Plant function types (PFTs)  Management Class  Crop Parameters Used
 ===  ===========================  ================  ===========================
  15  c3 unmanaged rainfed crop    none              not applicable             
  16  c3 unmanaged irrigated crop  none              not applicable             
  17  rainfed temperate corn       active            rainfed temperate corn     
  18  irrigated temperate corn     active            irrigated temperate corn   
  19  rainfed spring wheat         active            rainfed spring wheat       
  20  irrigated spring wheat       active            irrigated spring wheat     
  21  rainfed winter wheat         inactive          rainfed spring wheat       
  22  irrigated winter wheat       inactive          irrigated spring wheat     
  23  rainfed temperate soybean    active            rainfed temperate soybean  
  24  irrigated temperate soybean  active            irrigated temperate soybean
  25  rainfed barley               inactive          rainfed spring wheat       
  26  irrigated barley             inactive          irrigated spring wheat     
  27  rainfed winter barley        inactive          rainfed spring wheat       
  28  irrigated winter barley      inactive          irrigated spring wheat     
  29  rainfed rye                  inactive          rainfed spring wheat       
  30  irrigated rye                inactive          irrigated spring wheat     
  31  rainfed winter rye           inactive          rainfed spring wheat       
  32  irrigated winter rye         inactive          irrigated spring wheat     
  33  rainfed cassava              inactive          rainfed rice               
  34  irrigated cassava            inactive          irrigated rice             
  35  rainfed citrus               inactive          rainfed spring wheat       
  36  irrigated citrus             inactive          irrigated spring wheat     
  37  rainfed cocoa                inactive          rainfed rice               
  38  irrigated cocoa              inactive          irrigated rice             
  39  rainfed coffee               inactive          rainfed rice               
  40  irrigated coffee             inactive          irrigated rice             
  41  rainfed cotton               active            rainfed cotton             
  42  irrigated cotton             active            irrigated cotton           
  43  rainfed datepalm             inactive          rainfed cotton             
  44  irrigated datepalm           inactive          irrigated cotton           
  45  rainfed foddergrass          inactive          rainfed spring wheat       
  46  irrigated foddergrass        inactive          irrigated spring wheat     
  47  rainfed grapes               inactive          rainfed spring wheat       
  48  irrigated grapes             inactive          irrigated spring wheat     
  49  rainfed groundnuts           inactive          rainfed rice               
  50  irrigated groundnuts         inactive          irrigated rice             
  51  rainfed millet               inactive          rainfed tropical corn      
  52  irrigated millet             inactive          irrigated tropical corn    
  53  rainfed oilpalm              inactive          rainfed rice               
  54  irrigated oilpalm            inactive          irrigated rice             
  55  rainfed potatoes             inactive          rainfed spring wheat       
  56  irrigated potatoes           inactive          irrigated spring wheat     
  57  rainfed pulses               inactive          rainfed spring wheat       
  58  irrigated pulses             inactive          irrigated spring wheat     
  59  rainfed rapeseed             inactive          rainfed spring wheat       
  60  irrigated rapeseed           inactive          irrigated spring wheat     
  61  rainfed rice                 active            rainfed rice               
  62  irrigated rice               active            irrigated rice             
  63  rainfed sorghum              inactive          rainfed tropical corn      
  64  irrigated sorghum            inactive          irrigated tropical corn    
  65  rainfed sugarbeet            inactive          rainfed spring wheat       
  66  irrigated sugarbeet          inactive          irrigated spring wheat     
  67  rainfed sugarcane            active            rainfed sugarcane          
  68  irrigated sugarcane          active            irrigated sugarcane        
  69  rainfed sunflower            inactive          rainfed spring wheat       
  70  irrigated sunflower          inactive          irrigated spring wheat     
  71  rainfed miscanthus           inactive          rainfed tropical corn      
  72  irrigated miscanthus         inactive          irrigated tropical corn    
  73  rainfed switchgrass          inactive          rainfed tropical corn      
  74  irrigated switchgrass        inactive          irrigated tropical corn    
  75  rainfed tropical corn        active            rainfed tropical corn      
  76  irrigated tropical corn      active            irrigated tropical corn    
  77  rainfed tropical soybean     active            rainfed tropical soybean   
  78  irrigated tropical soybean   active            irrigated tropical soybean 
 ===  ===========================  ================  ===========================



.. _Phenology:

Phenology
^^^^^^^^^^^^^^^^

CLM5-BGC includes evergreen, seasonally deciduous (responding to changes
in day length), and stress deciduous (responding to changes in
temperature and/or soil moisture) phenology algorithms (Chapter :numref:`rst_Vegetation Phenology and Turnover`). 
CLM5-BGC-crop uses the AgroIBIS crop phenology algorithm,
consisting of three distinct phases.

Phase 1 starts at planting and ends with leaf emergence, phase 2
continues from leaf emergence to the beginning of grain fill, and phase
3 starts from the beginning of grain fill and ends with physiological
maturity and harvest.

.. _Planting:

Planting
'''''''''''''''''

All crops must meet the following requirements between the minimum planting date and the maximum
planting date (for the northern hemisphere) in :numref:`Table Crop phenology parameters`:

.. math::
   :label: 25.1

   \begin{array}{c} 
   {T_{10d} >T_{p} } \\ 
   {T_{10d}^{\min } >T_{p}^{\min } }  \\ 
   {GDD_{8} \ge GDD_{\min } } 
   \end{array}

where :math:`{T}_{10d}` is the 10-day running mean of :math:`{T}_{2m}`, (the simulated 2-m air
temperature during each model time step) and :math:`T_{10d}^{\min}`  is
the 10-day running mean of :math:`T_{2m}^{\min }`  (the daily minimum of
:math:`{T}_{2m}`). :math:`{T}_{p}` and :math:`T_{p}^{\min }`  are crop-specific coldest planting temperatures
(:numref:`Table Crop phenology parameters`), :math:`{GDD}_{8}` is the 20-year running mean growing
degree-days (units are degree-days or :sup:`o` days) tracked
from April through September (NH) above 8\ :sup:`o` C with
maximum daily increments of 30\ :sup:`o` days (see equation :eq:`25.3`), and
:math:`{GDD}_{min }`\ is the minimum growing degree day requirement
(:numref:`Table Crop phenology parameters`). :math:`{GDD}_{8}` does not change as quickly as :math:`{T}_{10d}` and :math:`T_{10d}^{\min }`, so
it determines whether it is warm enough for the crop to be planted in a grid cell, while the
2-m air temperature variables determine the day when the crop may be planted if the :math:`{GDD}_{8}` threshold is met.
If the requirements in equation :eq:`25.1` are not met by the maximum planting date, 
crops are still planted on the maximum planting date as long as  :math:`{GDD}_{8} > 0`. In
the southern hemisphere (SH) the NH requirements apply 6 months later.

At planting, each crop seed pool is assigned 3 gC m\ :sup:`-2` from its 
grain product pool. The seed carbon is transferred to the leaves upon leaf emergence. An
equivalent amount of seed leaf N is assigned given the pft’s C to N
ratio for leaves (:math:`{CN}_{leaf}` in :numref:`Table Crop allocation parameters`; this differs from AgroIBIS,
which uses a seed leaf area index instead of seed C). The model updates the average growing degree-days necessary
for the crop to reach vegetative and physiological maturity,
:math:`{GDD}_{mat}`, according to the following AgroIBIS rules:

.. math::
   :label: 25.2

   \begin{array}{lll} 
   GDD_{{\rm mat}}^{{\rm corn,sugarcane}} =0.85 GDD_{{\rm 8}} & {\rm \; \; \; and\; \; \; }& 950 <GDD_{{\rm mat}}^{{\rm corn,sugarcane}} <1850{}^\circ {\rm days} \\ 
   GDD_{{\rm mat}}^{{\rm spring\ wheat,cotton}} =GDD_{{\rm 0}} & {\rm \; \; \; and\; \; \; } & GDD_{{\rm mat}}^{{\rm spring\ wheat,cotton}} <1700{}^\circ {\rm days} \\ 
   GDD_{{\rm mat}}^{{\rm temp.soy}} =GDD_{{\rm 10}} & {\rm \; \; \; and\; \; \; } & GDD_{{\rm mat}}^{{\rm temp.soy}} <1900{}^\circ {\rm days} \\ 
   GDD_{{\rm mat}}^{{\rm rice}} =GDD_{{\rm 0}} & {\rm \; \; \; and\; \; \; } & GDD_{{\rm mat}}^{{\rm rice}} <2100{}^\circ {\rm days} \\ 
   GDD_{{\rm mat}}^{{\rm trop.soy}} =GDD_{{\rm 10}} & {\rm \; \; \; and\; \; \; } & GDD_{{\rm mat}}^{{\rm trop.soy}} <2100{}^\circ {\rm days}
   \end{array}

where :math:`{GDD}_{0}`, :math:`{GDD}_{8}`, and :math:`{GDD}_{10}` are the 20-year running mean growing
degree-days tracked from April through September (NH) over 0\ :sup:`o`\C, 8\ :sup:`o`\C, and
10\ :sup:`o`\C, respectively, with maximum daily increments of
26\ :sup:`o`\days (for :math:`{GDD}_{0}`) or 30\ :sup:`o`\days (for :math:`{GDD}_{8}` and :math:`{GDD}_{10}`). Equation :eq:`25.3` shows how we calculate
:math:`{GDD}_{0}`, :math:`{GDD}_{8}`, and :math:`{GDD}_{10}` for each model timestep:

.. math::
   :label: 25.3

   \begin{array}{lll} 
   GDD_{{\rm 0}} =GDD_{0} +T_{2{\rm m}} -T_{f} & \quad {\rm \; \; \; where\; \; \; } & 0 \le T_{2{\rm m}} -T_{f} \le 26{}^\circ {\rm days} \\ 
   GDD_{{\rm 8}} =GDD_{8} +T_{2{\rm m}} -T_{f} -8 & \quad {\rm \; \; \; where\; \; \; } & 0 \le T_{2{\rm m}} -T_{f} -8\le 30{}^\circ {\rm days} \\ 
   GDD_{{\rm 10}} =GDD_{10} +T_{2{\rm m}} -T_{f} -10 & \quad {\rm \; \; \; where\; \; \; } & 0 \le T_{2{\rm m}} -T_{f} -10\le 30{}^\circ {\rm days} 
   \end{array}

where, if :math:`{T}_{2m}` -  :math:`{T}_{f}` takes on values
outside the above ranges within a day, then it equals the minimum or maximum value in
the range for that day. :math:`{T}_{f}` is the freezing temperature of water and equals 273.15 K,
:math:`{T}_{2m}` is the 2-m air temperature in units of K, and *GDD* is in units of ºdays.

.. _Leaf emergence:

Leaf emergence
'''''''''''''''''''''''

According to AgroIBIS, leaves may emerge when the growing degree-days of
soil temperature to 0.05 m depth (:math:`GDD_{T_{soi} }` ), which is tracked since planting,
reaches 1 to 5% of :math:`{GDD}_{mat}`
(see Phase 2 % :math:`{GDD}_{mat}` in :numref:`Table Crop phenology parameters`). The base temperature threshold values for :math:`GDD_{T_{soi} }` 
are listed in :numref:`Table Crop phenology parameters` (the same base temperature threshold values are also used for 
:math:`GDD_{T_{{\rm 2m}} }` in section :numref:`Grain Fill`), and leaf emergence (crop phenology phase 2) 
starts when this threshold is met. Leaf onset occurs in the first
time step of phase 2, at which moment all seed C is transferred to leaf
C. Subsequently, the leaf area index generally increases throughout phase 2 until it reaches
a predetermined maximum value. Stem and root C also increase throughout phase 2 based on
the carbon allocation algorithm in section :numref:`Leaf emergence to grain fill`.

.. _Grain fill:

Grain fill
'''''''''''''''''''

The grain fill phase (phase 3) begins in one of two ways. The first potential trigger is based on temperature, similar to phase 2. A variable tracked since
planting, similar to :math:`GDD_{T_{soi} }`  but for 2-m air temperature,
:math:`GDD_{T_{{\rm 2m}} }`, must reach a heat unit threshold, *h*, of
of 40 to 65% of  :math:`{GDD}_{mat}` (see Phase 3 % :math:`{GDD}_{mat}` in :numref:`Table Crop phenology parameters`). 
For crops with the C4 photosynthetic pathway (temperate and tropical corn, sugarcane),
the :math:`{GDD}_{mat}` is based on an empirical function and ranges between 950 and 1850.
The second potential trigger for phase 3 is based on leaf area index. 
When the maximum value of leaf area index is reached in phase 2 (:numref:`Table Crop allocation parameters`), phase 3 begins. 
In phase 3, the leaf area index begins to decline in
response to a background litterfall rate calculated as the inverse of
leaf longevity for the pft as done in the BGC part of the model.

.. _Harvest:

Harvest
''''''''''''''''

Harvest is assumed to occur as soon as the crop reaches maturity. When
:math:`GDD_{T_{{\rm 2m}} }` reaches 100% of :math:`{GDD}_{mat}` or
the number of days past planting reaches a crop-specific maximum 
(:numref:`Table Crop phenology parameters`), then the crop is harvested. 
Harvest occurs in one time step using the BGC leaf offset algorithm. 


.. _Table Crop phenology parameters:

.. table:: Crop phenology and morphology parameters for the active crop plant functional types (pfts) in CLM5BGCCROP. Numbers in the first row correspond to the list of pfts in :numref:`Table Crop plant functional types`.

 ===================================  =========================  ==========================  ==========================  ==========================  ==========================  =========================  =========================  ==========================
 \                                    temperate corn             spring wheat                temperate soybean           cotton                      rice                        sugarcane                  tropical corn              tropical soybean
 ===================================  =========================  ==========================  ==========================  ==========================  ==========================  =========================  =========================  ==========================
 IVT                                  17, 18                     19, 20                      23, 24                      41, 42                      61, 62                      67, 68                     75, 76                     77, 78                    
 :math:`Date_{planting}^{min}`        April 1                    April 1                     May 1                       April 1                     Janurary 1                  Janurary 1                 March 20                   April 15                      
 :math:`Date_{planting}^{max}`        June 15                    June  15                    June 15                     May 31                      Feburary 28                 March 31                   April 15                   June 31                      
 :math:`T_{p}`\(K)                    283.15                     280.15                      286.15                      294.15                      294.15                      294.15                     294.15                     294.15                    
 :math:`T_{p}^{ min }`\(K)            279.15                     272.15                      279.15                      283.15                      283.15                      283.15                     283.15                     283.15                    
 :math:`{GDD}_{min}`\(ºdays)          50                         50                          50                          50                          50                          50                         50                         50                        
 base temperature for GDD (ºC)        8                          0                           10                          10                          10                          10                         10                         10                        
 :math:`{GDD}_{mat}`\(ºdays)          950-1850                   :math:`\mathrm{\le}`\ 1700  :math:`\mathrm{\le}`\ 1900  :math:`\mathrm{\le}`\ 1700  :math:`\mathrm{\le}`\ 2100  950-1850                   950-1850                   :math:`\mathrm{\le}`\ 2100
 Phase 2 % :math:`{GDD}_{mat}`        0.03                       0.05                        0.03                        0.03                        0.01                        0.03                       0.03                       0.03                      
 Phase 3 % :math:`{GDD}_{mat}`        0.65                       0.6                         0.5                         0.5                         0.4                         0.65                       0.5                        0.5                       
 Harvest: days past planting          :math:`\mathrm{\le}`\ 165  :math:`\mathrm{\le}`\ 150   :math:`\mathrm{\le}`\ 150   :math:`\mathrm{\le}`\ 160   :math:`\mathrm{\le}`\ 150   :math:`\mathrm{\le}`\ 300  :math:`\mathrm{\le}`\ 160  :math:`\mathrm{\le}`\ 150 
 :math:`z_{top}^{\max }` (m)          2.5                        1.2                         0.75                        1.5                         1.8                         4                          2.5                        1                         
 SLA (m :sup:`2` leaf g :sup:`-1` C)  0.05                       0.035                       0.035                       0.035                       0.035                       0.05                       0.05                       0.035                     
 :math:`\chi _{L}` index              -0.5                       -0.5                        -0.5                        -0.5                        -0.5                        -0.5                       -0.5                       -0.5                      
 grperc                               0.11                       0.11                        0.11                        0.11                        0.11                        0.11                       0.11                       0.11                      
 flnr                                 0.293                      0.41                        0.41                        0.41                        0.41                        0.293                      0.293                      0.41                      
 fcur                                 1                          1                           1                           1                           1                           1                          1                          1                         
 ===================================  =========================  ==========================  ==========================  ==========================  ==========================  =========================  =========================  ==========================

Notes: :math:`Date_{planting}^{min}` and :math:`Date_{planting}^{max}` are
the minimum and maximum planting date in the Northern Hemisphere, the corresponding dates
in the Southern Hemisphere apply 6 months later.
:math:`T_{p}` and :math:`T_{p}^{ min }` are crop-specific average and coldest planting temperatures, respectively.
:math:`{GDD}_{min}` is the lowest (for planting) 20-year running mean growing degree-days based 
on the base temperature threshold in the 7\ :sup:`th` row, tracked from April to September (NH).
:math:`{GDD}_{mat}` is a crop’s 20-year running mean growing
degree-days needed for vegetative and physiological maturity. Harvest
occurs at 100%\ :math:`{GDD}_{mat}` or when the days past planting
reach the number in the 11\ :sup:`th` row. Crop growth phases
are described in the text. :math:`z_{top}^{\max }`  is the maximum
top-of-canopy height of a crop, *SLA* is specific leaf area. :math:`\chi _{L}` is the leaf
orientation index, equals -1 for vertical, 0 for
random, and 1 for horizontal leaf orientation.
grperc is the growth respiration factor. flnr is the fraction of leaf N in the Rubisco enzyme.
fcur is the fraction of allocation that goes to currently displayed growth.

.. _Allocation:

Allocation
^^^^^^^^^^^^^^^^^

Allocation changes based on the crop phenology phases phenology (section :numref:`Phenology`).
Simulated C assimilation begins every year upon leaf emergence in phase
2 and ends with harvest at the end of phase 3; therefore, so does the
allocation of such C to the crop’s leaf, live stem, fine root, and
reproductive pools.

Typically, C:N ratios in plant tissue vary throughout the growing season and
tend to be lower during early growth stages and higher in later growth stages.
In order to account for this seasonal change, two sets of C:N
ratios are established in CLM for the leaf, stem, and fine root of
crops: one during the leaf emergence phase (phenology phase 2), and a second during 
grain fill phase (phenology phase 3). This modified C:N ratio approach accounts for the nitrogen
retranslocation that occurs during the grain fill phase (phase 3) of crop growth. Leaf, stem, and root
C:N ratios for phase 2 are calculated
using the new CLM5 carbon and nitrogen allocation scheme
(Chapter :numref:`rst_CN Allocation`), which provides a target C:N value
(:numref:`Table Crop allocation parameters`) and allows C:N to vary through time.
During grain fill (phase 3) of the crop growth cycle, a portion of the
nitrogen in the plant tissues is moved to a storage pool to fulfill
nitrogen demands of organ (reproductive pool) development, such that the
resulting C:N ratio of the plant tissue is reflective of measurements at
harvest. All C:N ratios were determined by calibration process, through
comparisons of model output versus observations of plant carbon
throughout the growing season.

The BGC part of the model keeps track of a term representing excess
maintenance respiration, which supplies the carbon required for maintenance respiration during periods of
low photosynthesis (Chapter :numref:`rst_Plant Respiration`).
Carbon supply for excess maintenance respiration 
cannot continue to happen after harvest for annual crops, so at harvest
the excess respiration pool is turned into a flux that extracts
CO\ :sub:`2` directly from the atmosphere. This way 
any excess maintenance respiration remaining at harvest is eliminated as if such
respiration had not taken place.


.. _Leaf emergence to grain fill:

Leaf emergence 
'''''''''''''''''''''''''''''''''''''

During phase 2, the allocation coefficients (fraction of available C) to
each C pool are defined as:

.. math::
   :label: 25.4

   \begin{array}{l} {a_{repr} =0} \\ {a_{froot} =a_{froot}^{i} -(a_{froot}^{i} -a_{froot}^{f} )\frac{GDD_{T_{{\rm 2m}} } }{GDD_{{\rm mat}} } {\rm \; \; \; where\; \; \; }\frac{GDD_{T_{{\rm 2m}} } }{GDD_{{\rm mat}} } \le 1} \\ {a_{leaf} =(1-a_{froot} )\cdot \frac{a_{leaf}^{i} (e^{-b} -e^{-b\frac{GDD_{T_{{\rm 2m}} } }{h} } )}{e^{-b} -1} {\rm \; \; \; where\; \; \; }b=0.1} \\ {a_{livestem} =1-a_{repr} -a_{froot} -a_{leaf} } \end{array}

where :math:`a_{leaf}^{i}` , :math:`a_{froot}^{i}` , and
:math:`a_{froot}^{f}`  are initial and final values of these
coefficients (:numref:`Table Crop allocation parameters`), and *h* is a heat unit threshold defined in
section :numref:`Grain fill`. At a crop-specific maximum leaf area index,
:math:`{L}_{max}` (:numref:`Table Crop allocation parameters`), carbon allocation is directed
exclusively to the fine roots.

.. _Grain fill to harvest:

Grain fill 
''''''''''''''''''''''''''''''

The calculation of :math:`a_{froot}`  remains the same from phase 2 to
phase 3. During grain fill (phase 3), other allocation coefficients change to:

.. math::
   :label: 25.5

   \begin{array}{ll} 
   a_{leaf} =a_{leaf}^{i,3} & {\rm when} \quad a_{leaf}^{i,3} \le a_{leaf}^{f} \quad {\rm else} \\ 
   a_{leaf} =a_{leaf} \left(1-\frac{GDD_{T_{{\rm 2m}} } -h}{GDD_{{\rm mat}} d_{L} -h} \right)^{d_{alloc}^{leaf} } \ge a_{leaf}^{f} & {\rm where} \quad \frac{GDD_{T_{{\rm 2m}} } -h}{GDD_{{\rm mat}} d_{L} -h} \le 1 \\ 
    \\ 
   a_{livestem} =a_{livestem}^{i,3} & {\rm when} \quad a_{livestem}^{i,3} \le a_{livestem}^{f} \quad {\rm else} \\ 
   a_{livestem} =a_{livestem} \left(1-\frac{GDD_{T_{{\rm 2m}} } -h}{GDD_{{\rm mat}} d_{L} -h} \right)^{d_{alloc}^{stem} } \ge a_{livestem}^{f} & {\rm where} \quad \frac{GDD_{T_{{\rm 2m}} } -h}{GDD_{{\rm mat}} d_{L} -h} \le 1 \\ 
    \\ 
   a_{repr} =1-a_{froot} -a_{livestem} -a_{leaf} 
   \end{array}

where :math:`a_{leaf}^{i,3}`  and :math:`a_{livestem}^{i,3}`  (initial
values) equal the last :math:`a_{leaf}`  and :math:`a_{livestem}` 
calculated in phase 2, :math:`d_{L}` , :math:`d_{alloc}^{leaf}`  and
:math:`d_{alloc}^{stem}`  are leaf area index and leaf and stem
allocation decline factors, and :math:`a_{leaf}^{f}`  and
:math:`a_{livestem}^{f}`  are final values of these allocation
coefficients (:numref:`Table Crop allocation parameters`).

.. _Nitrogen retranslocation for crops:

Nitrogen retranslocation for crops
''''''''''''''''''''''''''''''''''''''

Nitrogen retranslocation in crops occurs when nitrogen that was used for
tissue growth of leaves, stems, and fine roots during the early growth
season is remobilized and used for grain development (:ref:`Pollmer et al. 1979 
<Pollmeretal1979>`, :ref:`Crawford et al. 1982 <Crawfordetal1982>`, :ref:`Simpson et al. 1983 
<Simpsonetal1983>`, :ref:`Ta and Weiland 1992 <TaWeiland1992>`, :ref:`Barbottin et al. 2005 <Barbottinetal2005>`,
:ref:`Gallais et al. 2006 <Gallaisetal2006>`, :ref:`Gallais et al. 2007 <Gallaisetal2007>`). Nitrogen allocation
for crops follows that of natural vegetation, is supplied in CLM by the
soil mineral nitrogen pool, and depends on C:N ratios for leaves, stems,
roots, and organs. Nitrogen demand during organ development is fulfilled
through retranslocation from leaves, stems, and roots. Nitrogen
retranslocation is initiated at the beginning of the grain fill stage
for all crops except soybean, for which retranslocation is after LAI decline.
Nitrogen stored in the leaf and stem is moved into a storage
retranslocation pool for all crops, and for wheat and rice, nitrogen in roots is also
released into the retranslocation storage pool. The quantity of nitrogen
mobilized depends on the C:N ratio of the plant tissue, and is
calculated as

.. math::
   :label: 25.6

   leaf\_ to\_ retransn=N_{leaf} -\frac{C_{leaf} }{CN_{leaf}^{f} }

.. math::
   :label: 25.7

   stemn\_ to\_ retransn=N_{stem} -\frac{C_{stem} }{CN_{stem}^{f} }

.. math::
   :label: 25.8

   frootn\_ to\_ retransn=N_{froot} -\frac{C_{froot} }{CN_{froot}^{f} }

where :math:`{C}_{leaf}`, :math:`{C}_{stem}`, and :math:`{C}_{froot}` is the carbon in the plant leaf, stem, and fine
root, respectively, :math:`{N}_{leaf}`, :math:`{N}_{stem}`, and :math:`{N}_{froot}`
is the nitrogen in the plant leaf, stem, and fine root, respectively, and :math:`CN^f_{leaf}`,
:math:`CN^f_{stem}`, and :math:`CN^f_{froot}` is the post-grain fill C:N
ratio of the leaf, stem, and fine root respectively (:numref:`Table Crop allocation parameters`). Since
C:N measurements are often taken from mature crops, pre-grain development C:N
ratios for leaves, stems, and roots in the model are optimized to allow maximum
nitrogen accumulation for later use during organ development, and post-grain
fill C:N ratios are assigned the same as crop residue. After 
nitrogen is moved into the retranslocated pool, 
the nitrogen in this pool is used to meet plant
nitrogen demand by assigning the available nitrogen from the
retranslocated pool equal to the plant nitrogen demand for each organ (:math:`{CN_{[organ]}^{f} }` in :numref:`Table Crop allocation parameters`). Once the
retranslocation pool is depleted, soil mineral nitrogen pool is used to
fulfill plant nitrogen demands.

.. _Harvest to food and seed:

Harvest
''''''''''''''''''''''''''''''

Variables track the flow of grain C and
N to food and of all other plant pools, including live stem C and N, to litter. Putting live
stem C and N into the litter pool is in contrast to the approach for unmanaged PFTs which
puts live stem C and N into dead stem pools first. Leaf and root C and N pools
are routed to the litter pools in the same manner as natural vegetation. Whereas food C and N
was formerly transferred to the litter pool, CLM5 routes food C and N
to a grain product pool where the C and N decay to the atmosphere over one year,
similar in structure to the wood product pools. 
Additionally, CLM5 accounts for the C and N required for crop seeding by removing the seed C and N from the grain
product pool during harvest. The crop seed pool is then used to seed crops in the subsequent year. 
Calcuating the crop yields (Equation :eq:`25.9`) requires that you sum the GRAINC_TO_FOOD variable 
for each year, and must account for the proportion of C in the dry crop weight. 
Here, we assume that grain C is 45% of the total dry weight. Additionally, harvest is not typically 100% efficient, so
analysis needs to assume that harvest efficiency is less. We assume a harvest 
efficiency of 85%.

.. math::
   :label: 25.9

     Grain\ yield(g.m^{-2})=\frac{\sum(GRAINC\_ TO\_ FOOD)*0.85}{0.45}


.. _Table Crop allocation parameters:

.. table:: Crop allocation parameters for the active crop plant functional types (pfts) in CLM5BGCCROP. Numbers in the first row correspond to the list of pfts in :numref:`Table Crop plant functional types`.

 ===========================================  ==============  ============  ==================  ======  ======  =========  =============  ================
 \                                            temperate corn  spring wheat  temperatue soybean  cotton  rice    sugarcane  tropical corn  tropical soybean
 ===========================================  ==============  ============  ==================  ======  ======  =========  =============  ================
 IVT                                          17, 18          19, 20        23, 24              41, 42  61, 62  67, 68     75, 76         77, 78          
 :math:`a_{leaf}^{i}`                         0.6             0.9           0.85                0.85    0.75    0.6        0.6            0.85            
 :math:`{L}_{max}` (m :sup:`2`  m :sup:`-2`)  5               7             6                   6       7       5          5              6               
 :math:`a_{froot}^{i}`                        0.1             0.05          0.2                 0.2     0.1     0.1        0.1            0.2             
 :math:`a_{froot}^{f}`                        0.05            0             0.2                 0.2     0       0.05       0.05           0.2             
 :math:`a_{leaf}^{f}`                         0               0             0                   0       0       0          0              0               
 :math:`a_{livestem}^{f}`                     0               0.05          0.3                 0.3     0.05    0          0              0.3             
 :math:`d_{L}`                                1.05            1.05          1.05                1.05    1.05    1.05       1.05           1.05            
 :math:`d_{alloc}^{stem}`                     2               1             5                   5       1       2          2              5               
 :math:`d_{alloc}^{leaf}`                     5               3             2                   2       3       5          5              2               
 :math:`{CN}_{leaf}`                          25              20            20                  20      20      25         25             20              
 :math:`{CN}_{stem}`                          50              50            50                  50      50      50         50             50              
 :math:`{CN}_{froot}`                         42              42            42                  42      42      42         42             42              
 :math:`CN^f_{leaf}`                          65              65            65                  65      65      65         65             65              
 :math:`CN^f_{stem}`                          120             100           130                 130     100     120        120            130             
 :math:`CN^f_{froot}`                         0               40            0                   0       40      0          0              0               
 :math:`{CN}_{grain}`                         50              50            50                  50      50      50         50             50              
 ===========================================  ==============  ============  ==================  ======  ======  =========  =============  ================

Notes: Crop growth phases and corresponding variables are described throughout
the text. :math:`{CN}_{leaf}`, :math:`{CN}_{stem}`, and :math:`{CN}_{froot}` are
the target C:N ratios used during the leaf emergence phase (phase 2).


.. _Other Features:

Other Features
^^^^^^^^^^^^^^^^^^^^^^^

.. _Physical Crop Characteristics:

Physical Crop Characteristics
''''''''''''''''''''''''''''''
Leaf area index (*L*) is calculated as a function of specific leaf area  
(SLA, :numref:`Table Crop phenology parameters`) and leaf C. 
Stem area index (*S*) is equal to 0.1\ *L* for temperate and tropical corn and sugarcane and 0.2\ *L* for
other crops, as in AgroIBIS. All live
C and N pools go to 0 after crop harvest, but the *S* is kept at 0.25 to
simulate a post-harvest “stubble” on the ground.

Crop heights at the top and bottom of the canopy, :math:`{z}_{top}`
and :math:`{z}_{bot}` (m), come from the AgroIBIS formulation:


.. math::
   :label: 25.10

   \begin{array}{l} 
   {z_{top} =z_{top}^{\max } \left(\frac{L}{L_{\max } -1} \right)^{2} \ge 0.05{\rm \; where\; }\frac{L}{L_{\max } -1} \le 1} \\ 
   {z_{bot} =0.02{\rm m}} 
   \end{array}

where :math:`z_{top}^{\max }` is the maximum top-of-canopy height of the crop (:numref:`Table Crop phenology parameters`)
and :math:`L_{\max }` is the maximum leaf area index (:numref:`Table Crop allocation parameters`).

.. _Interactive fertilization:

Interactive Fertilization 
''''''''''''''''''''''''''''''
CLM simulates fertilization by adding nitrogen directly to the soil mineral nitrogen pool to meet
crop nitrogen demands using both industrial fertilizer and manure application. CLM’s separate crop land unit ensures that
natural vegetation will not access the fertilizer applied to crops.
Fertilizer in CLM5BGCCROP is prescribed by crop functional types and varies spatially
for each year based on the LUMIP land use and land cover change
time series (LUH2 for historical and SSPs for future) (:ref:`Lawrence et al. 2016 <Lawrenceetal2016>`).
One of two fields is used to prescribe industrial fertilizer based on the type of simulation.
For non-transient simulations, annual fertilizer application in g N/m\ :sup:`2`/yr 
is specified on the land surface data set by the field CONST_FERTNITRO_CFT. 
In transient simulations, annual fertilizer application is specified on the land use time series
file by the field FERTNITRO_CFT, which is also in g N/m\ :sup:`2`/yr.
The values for both of these fields come from the LUMIP time series for each year.
In addition to the industrial fertilizer, background manure fertilizer is specified
on the parameter file by the field 'manunitro'. For the current CLM5BGCCROP,
manure N is applied at a rate of 0.002 kg N/m\ :sup:`2`/yr. Because previous versions 
of CLM (e.g., CLM4) had rapid denitrification rates, fertilizer is applied slowly
to minimize N loss (primarily through denitrification) and maximize plant uptake. 
The current implementation of CLM5 inherits this legacy, although denitrification rates
are slower in the current version of the model (:ref:`Koven et al. 2013 <Kovenetal2013>`). As such,
fertilizer application begins during the leaf emergence phase of crop
development (phase 2) and continues for 20 days, which helps reduce large losses
of nitrogen from leaching and denitrification during the early stage of
crop development. The 20-day period is chosen as an optimization to
limit fertilizer application to the emergence stage. A fertilizer
counter in seconds, *f*, is set as soon as the leaf emergence phase for crops
initiates:

.. math::
   :label: 25.11

    f = n \times 86400 

where *n* is set to 20 fertilizer application days and 86400 is the number of seconds per day. When the crop enters
phase 2 (leaf emergence) of its growth
cycle, fertilizer application begins by initializing fertilizer amount
to the total fertilizer at each column within the grid cell divided by the initialized *f*.
Fertilizer is applied and *f* is decremented each time step until a zero balance on
the counter is reached.


.. _Biological nitrogen fixation for soybeans:

Biological nitrogen fixation for soybeans
''''''''''''''''''''''''''''''''''''''''''
Biological N fixation for soybeans is calculated by the fixation and uptake of
nitrogen module (Chapter :numref:`rst_FUN`) and is the same as N fixation in natural vegetation. Unlike natural
vegetation, where a fraction of each pft are N fixers, all soybeans
are treated as N fixers.

.. _Latitude vary base tempereature for growing degree days:

Latitudinal variation in base growth tempereature 
''''''''''''''''''''''''''''''''''''''''''''''''''''''''
For most crops, :math:`GDD_{T_{{\rm 2m}} }` (growing degree days since planting) 
is the same in all locations. However,
the for both rainfed and irrigated spring wheat and sugarcane, the calculation of 
:math:`GDD_{T_{{\rm 2m}} }` allows for latitudinal variation:

.. math::
   :label: 25.12

   latitudinal\ variation\ in\ base\ T = \left\{
   \begin{array}{lr}    
   baset +12 - 0.4 \times latitude &\qquad 0 \le latitude \le 30 \\
   baset +12 + 0.4 \times latitude &\qquad -30 \le latitude \le 0    
   \end{array} \right\}

where :math:`baset` is the *base temperature for GDD* (7\ :sup:`th` row) in :numref:`Table Crop phenology parameters`.
Such latitudinal variation in base growth temperature could increase the base temperature, slow down :math:`GDD_{T_{{\rm 2m}} }`
accumulation, and extend the growing season for regions within 30ºS to 30ºN for spring wheat
and sugarcane.

.. _Separate reproductive pool:

Separate reproductive pool
''''''''''''''''''''''''''''''
One notable difference between natural vegetation and crops is the
presence of reproductive carbon and nitrogen pools. Accounting
for the reproductive pools helps determine whether crops are performing
reasonably through yield calculations.
The reproductive pool is maintained similarly to the leaf, stem,
and fine root pools, but allocation of carbon and nitrogen does not
begin until the grain fill stage of crop development. Equation :eq:`25.5` describes the
carbon and nitrogen allocation coefficients to the reproductive pool.
In CLM5BGCCROP, as allocation declines in stem, leaf, and root pools (see section :numref:`Grain fill to harvest`)
during the grain fill stage of growth, increasing amounts of carbon and
nitrogen are available for grain development.


.. _The irrigation model:

The irrigation model
-------------------------

The CLM includes the option to irrigate cropland areas that are equipped
for irrigation. The application of irrigation responds dynamically to
the soil moisture conditions simulated by the CLM. This irrigation
algorithm is based loosely on the implementation of 
:ref:`Ozdogan et al. (2010) <Ozdoganetal2010>`.

When irrigation is enabled, the crop areas of each grid cell are divided
into irrigated and rainfed fractions according to a dataset of areas
equipped for irrigation (:ref:`Portmann et al. 2010 <Portmannetal2010>`). 
Irrigated and rainfed crops are placed on separate soil columns, so that 
irrigation is only applied to the soil beneath irrigated crops.

In irrigated croplands, a check is made once per day to determine
whether irrigation is required on that day. This check is made in the
first time step after 6 AM local time. Irrigation is required if crop
leaf area :math:`>` 0, and the available soil water is below a specified 
threshold.

The soil moisture deficit :math:`D_{irrig}` is 

.. math::
   :label: 25.61

   D_{irrig} = \left\{
   \begin{array}{lr}    
   w_{thresh} - w_{avail} &\qquad w_{thresh} > w_{avail} \\
   0 &\qquad w_{thresh} \le w_{avail}    
   \end{array} \right\}

where :math:`w_{thresh}` is the irrigation moisture threshold (mm) and 
:math:`w_{avail}` is the available moisture (mm).  The moisture threshold 
is

.. math::
   :label: 25.62

   w_{thresh} = f_{thresh} \left(w_{target} - w_{wilt}\right) + w_{wilt}

where :math:`w_{target}` is the irrigation target soil moisture (mm) 

.. math::
   :label: 25.63

   w_{target} = \sum_{j=1}^{N_{irr}} \theta_{target} \Delta z_{j} \ ,

:math:`w_{wilt}` is the wilting point soil moisture (mm) 

.. math::
   :label: 25.64

   w_{wilt} = \sum_{j=1}^{N_{irr}} \theta_{wilt} \Delta z_{j} \ ,

and :math:`f_{thresh}` is a tuning parameter.  The available moisture in 
the soil is 

.. math::
   :label: 25.65

   w_{avail} = \sum_{j=1}^{N_{irr}} \theta_{j} \Delta z_{j} \ ,

:math:`N_{irr}` is the index of the soil layer corresponding to a specified 
depth :math:`z_{irrig}` (:numref:`Table Irrigation parameters`) and 
:math:`\Delta z_{j}` is the thickness of the soil layer in layer :math:`j` (section 
:numref:`Vertical Discretization`).  :math:`\theta_{j}` is the 
volumetric soil moisture in layer :math:`j` (section :numref:`Soil Water`).
:math:`\theta_{target}` and 
:math:`\theta_{wilt}` are the target and wilting point volumetric 
soil moisture values, respectively, and are determined by inverting 
:eq:`7.94` using soil matric 
potential parameters :math:`\Psi_{target}` and :math:`\Psi_{wilt}` 
(:numref:`Table Irrigation parameters`). After the soil moisture deficit 
:math:`D_{irrig}` is calculated, irrigation in an amount equal to 
:math:`\frac{D_{irrig}}{T_{irrig}}` (mm/s) is applied uniformly over 
the irrigation period :math:`T_{irrig}` (s).  Irrigation water is applied
directly to the ground surface, bypassing canopy interception (i.e.,
added to  :math:`{q}_{grnd,liq}`: section :numref:`Canopy Water`). 

To conserve mass, irrigation is removed from river water storage (Chapter :numref:`rst_River Transport Model (RTM)`).  
When river water storage is inadequate to meet irrigation demand, 
there are two options: 1) the additional water can be removed from the 
ocean model, or 2) the irrigation demand can be reduced such that 
river water storage is maintained above a specified threshold.  

.. _Table Irrigation parameters:

.. table:: Irrigation parameters

 +--------------------------------------+-------------+
 | Parameter                            |             |
 +======================================+=============+
 | :math:`f_{thresh}`                   |  1.0        |
 +--------------------------------------+-------------+
 | :math:`z_{irrig}`       (m)          |  0.6        |
 +--------------------------------------+-------------+
 | :math:`\Psi_{target}`   (mm)         | -3400       |
 +--------------------------------------+-------------+
 | :math:`\Psi_{wilt}`     (mm)         | -150000     |
 +--------------------------------------+-------------+

.. add a reference to surface data in chapter2
  To accomplish this we downloaded
  data of percent irrigated and percent rainfed corn, soybean, and
  temperate cereals (wheat, barley, and rye) (:ref:`Portmann et al. 2010 <Portmannetal2010>`),
  available online from
  *ftp://ftp.rz.uni-frankfurt.de/pub/uni-frankfurt/physische\_geographie/hydrologie/public/data/MIRCA2000/harvested\_area\_grids.*