# Land and ocean components of the global carbon cycle

## Overview

This recipe reproduces most of the figures of Anav et al. (2013):

• Timeseries plot for different regions

• Seasonal cycle plot for different regions

• Errorbar plot for different regions showing mean and standard deviation

• Scatterplot for different regions showing mean vs. interannual variability

• 3D-scatterplot for different regions showing mean vs. linear trend and the model variability index (MVI) as a third dimension (color coded)

• Scatterplot for different regions comparing two variable against each other (cSoil vs. cVeg)

In addition, performance metrics are calculated for all variables using the performance metric diagnostics (see details in Performance metrics for essential climate parameters).

## MVI calculation

The Model variability index (MVI) on a single grid point (calculated in carbon_cycle/mvi.ncl is defined as

$MVI = \left( \frac{s^M}{s^O} - \frac{s^O}{s^M} \right)^2$

where $$s^M$$ and $$s^O$$ are the standard deviations of the annual time series on a single grid point of a climate model $$M$$ and the reference observation $$O$$. In order to get a global or regional result, this index is simple averaged over the respective domain.

In its given form, this equation is prone to small standard deviations close to zero. For example, values of $$s^M = 10^{-5} \mu$$ and $$s^O = 10^{-7} \mu$$ (where $$\mu$$ is the mean of $$s^O$$ over all grid cells) results in a MVI of the order of $$10^4$$ for this single grid cell even though the two standard deviations are close to zero and negligible compared to other grid cells. Due to the use of the arithmetic mean, a single high value is able to distort the overall MVI.

In the original publication, the maximum MVI is in the order of 10 (for the variable gpp). However, a naive application of the MVI definition yields values over $$10^9$$ for some models. Unfortunately, Anav et al. (2013) do not provide an explanation on how to deal with this problem. Nevertheless, this script provides two configuration options to avoid high MVI values, but they are not related to the original paper or any other peer-revied study and should be used with great caution (see User settings in recipe).

## Available recipes and diagnostics

Recipes are stored in recipes/

• recipe_anav13jclim.yml

Diagnostics are stored in diag_scripts/

• carbon_cycle/main.ncl

• carbon_cycle/mvi.ncl

• carbon_cycle/two_variables.ncl

• perfmetrics/main.ncl

• perfmetrics/collect.ncl

## User settings in recipe

1. Preprocessor

• mask_fillvalues: Mask common missing values on different datasets.

• mask_landsea: Mask land/ocean.

• regrid: Regridding.

• weighting_landsea_fraction: Land/ocean fraction weighting.

2. Script carbon_cycle/main.ncl

• region, str: Region to be averaged.

• legend_outside, bool: Plot legend in a separate file (does not affect errorbar plot and evolution plot)

• seasonal_cycle_plot, bool: Draw seasonal cycle plot.

• errorbar_plot, bool: Draw errorbar plot.

• mean_IAV_plot, bool: Draw Mean (x-axis), IAV (y-axis) plot.

• evolution_plot, bool: Draw time evolution of a variable comparing a reference dataset to multi-dataset mean; requires ref_dataset in recipe.

• sort, bool, optional (default: False): Sort dataset in alphabetical order.

• anav_month, bool, optional (default: False): Conversion of y-axis to PgC/month instead of /year.

• evolution_plot_ref_dataset, str, optional: Reference dataset for evolution_plot. Required when evolution_plot is True.

• evolution_plot_anomaly, str, optional (default: False): Plot anomalies in evolution plot.

• evolution_plot_ignore, list, optional: Datasets to ignore in evolution plot.

• evolution_plot_volcanoes, bool, optional (default: False): Turns on/off lines of volcano eruptions in evolution plot.

• evolution_plot_color, int, optional (default: 0): Hue of the contours in the evolution plot.

• ensemble_name, string, optional: Name of ensemble for use in evolution plot legend

3. Script carbon_cycle/mvi.ncl

• region, str: Region to be averaged.

• reference_dataset, str: Reference dataset for the MVI calculation specified for each variable seperately.

• mean_time_range, list, optional: Time period over which the mean is calculated (if not given, use whole time span).

• trend_time_range, list, optional: Time period over which the trend is calculated (if not given, use whole time span).

• mvi_time_range, list, optional: Time period over which the MVI is calculated (if not given, use whole time span).

• stddev_threshold, float, optional (default: 1e-2): Threshold to ignore low standard deviations (relative to the mean) in the MVI calculations. See also MVI calculation.

• mask_below, float, optional: Threshold to mask low absolute values (relative to the mean) in the input data (not used by default). See also MVI calculation.

4. Script carbon_cycle/two_variables.ncl

• region, str: Region to be averaged.

5. Script perfmetrics/main.ncl

6. Script perfmetrics/collect.ncl

## Variables

• tas (atmos, monthly, longitude, latitude, time)

• pr (atmos, monthly, longitude, latitude, time)

• nbp (land, monthly, longitude, latitude, time)

• gpp (land, monthly, longitude, latitude, time)

• lai (land, monthly, longitude, latitude, time)

• cveg (land, monthly, longitude, latitude, time)

• csoil (land, monthly, longitude, latitude, time)

• tos (ocean, monthly, longitude, latitude, time)

• fgco2 (ocean, monthly, longitude, latitude, time)

## Observations and reformat scripts

• CRU (tas, pr)

• JMA-TRANSCOM (nbp, fgco2)

• MTE (gpp)

• LAI3g (lai)

• NDP (cveg)

• HWSD (csoil)