.. # with overline, for parts * with overline, for chapters =, for sections -, for subsections ^, for subsubsections ", for paragraphs #################### Calibration #################### *************************************** What is calibration for ``dvmdostem``? *************************************** Calibration is defined as the estimation and adjustment of model parameters and constants to improve the agreement between model output and a data set. [Rykiel_1996]_ Being originally a biogeochemical model, ``dvmdostem`` calibration is mainly focused on the carbon (C) and nitrogen (N) cycle. Rate-limiting parameters for various processes are adjusted until model values of C and N fluxes and stocks match field-based estimates or observations, which we refer to as "target values". Below is a table of variables or processes and their corresponding rate limiting parameters: ================================= ============================================== Gross Primary Productivity (GPP) Cmax Autotrophic Respiration (Ra) Kr Heterotrophic Respiration (Rh) Kd maximum plant N uptake Nmax C and N litter production Cfall, Nfall soil C and N immobilization micbnup, kdcrawc, kdscoma, kdcsomapr, kdcsomcr ================================= ============================================== For this reason, calibrations are conducted at the site level, using sentinel sites representing typical mature ecosystems, well characterized and monitored over long periods of time. The selection of parameters for calibration is based on: 1. The sensitivity of the model carbon and nitrogen stocks and fluxes to these parameters. 2. The uncertainty of the parameter values. .. raw:: html ****************************** When to conduct a calibration? ****************************** Calibrations are typically conducted for every vegetation community type the model is parameterized for. However, recent studies have shown that parameter uncertainty may not only vary between community type, but also in space within the same community type [Euskirchen_2021]_. Therefore, multiple calibrations can be developed for the same community type but different eco-climatic regions. ***************************** How to conduct a calibration? ***************************** The comparison between model outputs and target values are done at equilibrium, i.e. a simulation under constant environment (climate, atmospheric CO2, and vegetation), when all fluxes and stocks have reach a steady state. Calibration targets =================== As mentioned above, target values are based on field observations for the main carbon and nitrogen fluxes and stocks targeted for the calibration. Target values are representing the “typical” state of a mature ecosystem for the vegetation community for which the calibration is developed. For this reason, as often as possible, target values are computed from observations collected across multiple years, at the sentinel site where the calibration is developed. In this case, a target value will be computed as the mean of a multi-year time series. The standard deviation is also important to compute and store as it can inform a subsequent uncertainty analysis at the sentinel site. Target values are stored in the text file named `calibration_targets.py` in the calibration directory. Vegetation Targets ------------------ **INGPP, INNPP** are target values for gross and net primary productivity reached by vegetation not limited by nutrient availability. These target values are typically assessed from fertilization experiments. When fertilization experiment is not available at the sentinel site where calibration is developed, fertilization factor can be calculated from literature review of fertilization experiment in similar ecosystem. This fertilization factor is computed as the ratio between GPP or NPP in control and fertilized plots. These two variables should have target values for every PFT. **GPP, NPP** are target values for gross and net primary productivity reached by mature vegetation under natural conditions. When data is available, these target values are averaged across multi-year observations. These two variables should have target values for every PFT. Partitioning between PFT can be done based on aboveground NPP estimated from biomass quantification. **NUPTAKE** is the rate of nitrogen uptake by the vegetation. As for the carbon fluxes, this flux should be partitioned by plant functional type. This target value is usually set from literature review. **VEGC** is the target value for vegetation carbon pools. VEGC should be indicated for every compartment (i.e. leaf, stem, and root) of every plant functional type. Target values are based on biomass estimations. If biomass estimates are not available for all compartments (e.g. root) or all PFT (e.g. green mosses), partitioning information should be estimated from literature review. **VEGN** is the target value for vegetation nitrogen pools. VEGN should be indicated for every compartment (i.e. leaf, stem, and root) of every plant functional type. Target values are based on biomass estimations and C:N ratios. If biomass or C:N estimates are not available for all compartments (e.g. root) or all PFT (e.g. green mosses), partitioning information should be estimated from literature review. Soil Targets ------------ **SOILC** is the target value for soil carbon pools. It is estimated separately for the fibric layer, the humic layer and the top 1 meter of the mineral layer. **ORGN** is the target value of the soil nitrogen pool. In contract to SOILC, ORGN is estimated for the organic layer *and* the top 1 meter mineral soil. It is usually estimated from the soil carbons pools and estimated C:N ratios. **AVLN** is the target value for soil available nitrogen. By definition, this pool is estimated across the rooting depth only (indicated in the parameter file cmt\_dimvegetation.txt). Calibration parameters ====================== Calibrated parameters are stored in the text file named `cmt\_calparbgc.txt` in the parameter directory. Vegetation parameters --------------------- **Cmax** is the maximum rate of carbon assimilation. It is defined by plant functional type. Maximum assimilation is reached when plants are exposed to no significant limitation in nutrient availability. For this reason, Cmax is calibrated with nitrogen feedback off. Cmax is adjusted so that model GPP is equal to observed GPP estimates from fertilization experiments. When fertilization experiments are not available for the community/region of interest, it is estimated by applying a multiplicative factor to observed GPP in control (not manipulated) plots. Based on literature, this fertilization factor can vary from 1.25 to 1.5. **Kr** is the limiting rate of maintenance respiration (Rm) at :math:`0^oC`: .. math:: Rm = Kr * VEGC where VEGC is vegetation carbon pool. Kr is itself a function of vegetation carbon pool: .. math:: Kr = e^{(Kr_a * VEGC) + Kr_b} .. Alternate formulation... .. .. math:: Kr = \exp{([Kr_a * VEGC] + Kr_b)} :math:`Kr_a` is usually set to :math:`-8.06e10^5`, and :math:`Kr_b` is calibrated for every vegetation compartment: leaf, stem and root. Because the relationship between biomass and maintenance respiration is not linear and decreases as biomass increases, :math:`Kr_b` should be negative. **Cfall** is the limiting rate of carbon litterfall (Cltr): .. math:: Cltr = Cfall * VEGC where VEGC is the vegetation carbon pool. Cfall is calibrated for every vegetation compartment: leaf, stem and root. **Nmax** is the maximum rate of plant nitrogen uptake. Maximum vegetation nitrogen uptake is reached when plants productivity is at its maximum, and there are no significant limitation from low temperature. **Nfall** is the limiting rate of nitrogen litterfall (Nltr): .. math:: Nltr = Nfall * VEGN where VEGN is the vegetation nitrogen pool. Nfall is calibrated for every vegetation compartment: leaf, stem and root. Soil parameters --------------- .. **:math:`Nup_{mic}`** reStructuredText can't do super/sub inside bold. :math:`Nup_{mic}` is the limiting rate of microbial nitrogen uptake per unit of detrital carbon respired (g/g). :math:`Nup_{mic}` directly influences nitrogen immobilization by decomposers, and net mineralization which is the amount of inorganic nitrogen produced during the decomposition of the soil organic matter minus that immobilized by decomposers. **Kdc** is the limiting rate of soil carbon decomposition. Kdc is calibrated for the four soil carbon pools: litter/raw pool, active, physically and chemically resistant pools. The higher the value of this rate is, the faster the turnover is. Therefore: .. math:: Kdc_{raw} > Kdc_{active} > Kdc_{pr} > Kdc_{cr} ************************************** Calibration Process - Conceptual ************************************** This is a general descrpiption of the modeling steps that have been most successfully used for finding optimal parameter sets (calibration in other words). For technical specifics of using various software tools to carry out the process see the examples for :ref:`manual calibration ` and :ref:`MADS assisted calibration `. Calibration is done in equilibrium simulation and in calibration mode. Because biogeochemical turn-overs in the vegetation are faster than in the soil, vegetation-related variables reach equilibrium sooner than soil-related variables. Therefore, the length of the equilibrium run can be set to shorter time when vegetation-related parameters are calibrated (e.g. 200 to 500 years), whereas soil calibration typically requires several thousand years to reach equilibrium. Calibrate vegetation parameters **without** N limitation ======================================================== #. Set ``NFEED=OFF`` and ``AVLN=OFF``. #. Adjust Cmax until INGPP (GPP without N limitation) matches target for every plant functional type. Increasing Cmax increases GPP. Calibrate vegetation parameters **with** N limitation ===================================================== #. Set ``NFEED=ON`` and ``AVLN=ON``. #. Set the level of N limitation with Nmax and Nup\ :sub:`mic` so that actual GPP, and AVLN match the target values. Increasing Nmax should increase GPP, and increasing Nup\ :sub:`mic` should decrease both GPP and AVLN. #. Set the ratio between GPP and NPP with Krb. Krb influences maintenance respiration, and it will also affect the ratio between GPP and NPP. Increasing Krb will increase respiration and decrease NPP. Krb should therefore be calibrated targeting NPP. #. Calibrate Cfall targeting VEGC. Change in vegetation is a result of NPP (input) and Litterfall (output). Therefore, VEGC pools will be influenced both by Krb and Cfall parameters. Because Krb has been adjusted in step 3, the focus here should be on adjusting Cfall with minimal adjustment to Krb. #. Calibrate Nfall targeting VEGN. Vegetation nitrogen pool is a result of vegetation nitrogen uptake (input) and litterfall (output). Calibrate soil parameters ========================= #. Calibrate decomposition rate limiting parameters targeting soil carbon stocks. The fibric layer is dominated by raw and active carbon pools. The humic layer is dominated by active and physically resistant pools. Finally, the mineral layer is dominated by pools of slower turnover. Therefore, Kdc for the raw material should be adjusted targeting soil C stock in the fibric layer. Kdc for the active organic matter will affect primarily fibric and humic carbon pools. Kdc for the physically resistant pool will affect primarily the humic and mineral pools. *********** Reference *********** .. [Euskirchen_2021] Euskirchen, Eugénie S. et al. 2021 Assessing dynamic vegetation model parameter uncertainty across Alaskan arctic tundra plant communities. *Ecological Applications* 32 : n. pag. .. [Rykiel_1996] Rykiel, E. J., Jr. 1996. Testing ecological models: the meaning of validation. *Ecological Modeling*, 90: 229–244. https://doi.org/10.1016/0304-3800(95)00152-2