Matrix approach to facilitate land carbon modeling:Case studies with CLM45 and ORCHIDEE-MICT

Yuanyuan Huang1,2,3, Xingjie Lu1,2, Zheng Shi1,2, David Lawrence4, Charles Koven5, Jianyang Xia6,7, Philippe ciais3, Yiqi Luo1,2,8

Contact: yuanyuan.huang@lsce.ipsl.fr

Introduction

S0 S1 S2 S3 S4 S5

I I0 Ie Ie Ie Ie Ie

B B0 B0 Be Be Be Be

N N0 N0 N0 Ne Ne Ne

ɛ ɛ0 ɛ0 ɛ0 ɛ0 ɛe ɛe

V V0 V0 V0 V0 V0 Ve

Matrix Simulations Using MATLAB

CLM Default Run 2eCO2(560ppm)

CLM Default Run 1CO2(280ppm)

The terrestrial carbon (C) cycle has been commonly

represented by a series of C balance equations to track C

influxes into and effluxes out of individual pools in earth

system models (ESMs). This representation matches our

understanding of C cycle processes well but makes it difficult

to track model behaviors. It is also computationally

expensive, especially for soil organic carbon (SOC) spin-up.

To overcome these challenges, we have developed a matrix

approach, which reorganizes C balance equations in the

original ESM into one matrix equation without changing any

modeled C cycle processes. We applied the matrix approach

to the Community Land Model (CLM4.5) and ORCHIDEE-

MICT with vertically resolved biogeochemistry.

1. The matrix equation exactly reproduces litter and SOC of the standard CLM45 and

SOC of ORCHIDEE-MICT.

2. The matrix analytical solution can potentially accelerate model spin-up and alleviate

the constraint from high computational requirement.

3. Easy diagnosis of system properties such as C residence time and C storage potential,

and traceability analysis.

4. Broad scientific applications through effective manipulation of matrix components

such as attribution of global change impacts.

𝑿 : 70x1I : 70x1 𝑨 : 70x70

𝑿 : 100x1I : 100x1𝑨 : 100x100

𝜺 : 70x70 𝒌 : 70x70𝑽 : 70x70

𝜺 : 100x100 𝒌 : 100x100 𝑽 : 100x100

ORCHIDEE-MICT

CLM45Figure 1. The matrix equation (up) and structure of ORCHIDEE-MICT

(left), CLM45 (right) litter and SOC processes.

Figure 2. C pools simulated

from the matrix equation (left

column) and the 1:1 line

spanned by matrix vs. default

CLM45 simulations at a Brazil

site.

Figure 3. C pools simulated from the

matrix equation (left column) and

the difference between the matrix

and default CLM45 after 10 years

simulation starting from 1850.

Figure 4. The same as Figure

2, but for ORCHIDEE-MICT

at a high latitude site.

Figure 5. The same as Figure 3, but

for ORCHIDEE-MICT after 150

years simulation starting from cold

start.

CLM45

ORCHIDEE-MICT

Figure 6. C storages (fast, slow and passive ) after

150 + 200,000+100 years default ORCHIDEE-MICT

simulation (left column) and C storage capacity

diagnosed from 398 years matrix calculation (right

column).

Figure 7. Ecosystem C residence time (a), C input (b) and C storages (c) diagnosed from the

CLM45 matrix simulation at an Alaska site.

3-dimentional parameter space:

Ecosystem C input

Ecosystem C residence time

Ecosystem C storage potential

1. C storage capacity captures the

maximum C an ecosystem can store (C

input x C residence time).

2. C storage potential tracks transient C

dynamics and is the difference between

C storage capacity and storage.

3. C residence time diagnosed from the

matrix equation is different from the

common practice of dividing stocks by

fluxes at non-steady state conditions.

CO2 fertilization affects litter and

SOC through C input, allocation

of external C into different C

pools, nitrogen regulation, altered

soil environmental conditions, and

vertical mixing along the soil

profile in CLM45.

Figure 8. Simulation protocol.

Figure 9. Total CO2 fertilization effect (topleft) and relative contributions from various processes.

1. Center for Ecosystem Science and Society, Northern Arizona University, Flagstaff, AZ, USA

2. Department of Microbiology and Plant Biology, University of Oklahoma, Norman, Oklahoma, USA

3. Laboratoire des Sciences du Climat et de l’Environnement, 91191 Gif-sur-Yvette, France

4. Climate and Global Dynamics Division, National Center for Atmospheric Research, Boulder, CO, USA

5. Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

6. Tiantong National Forest Ecosystem Observation and Research Station, School of Ecological and Environmental Sciences, East China Normal University, Shanghai 200062, China.

7. Research Center for Global Change and Ecological Forecasting, East China Normal University, Shanghai 200062

8. Department of Earth System Science, Tsinghua University, Beijing, China,

Model Structure and the Matrix Equation

Application 1: Model Spin-up

Application 2: 3-dimentional diagnostics

Summary

Authors and Reference

Luo Y, Shi Z, Lu X et al. (2017) Transient dynamics of terrestrial carbon storage: mathematical foundation and its applications. Biogeosciences, 14, 145-161.

Application 3: Attribution of Response to Global Change

The relative contribution from each of

these processes are quantified through a

series of matrix simulations which

sequentially plug in relevant factors

under 580 ppm CO2 conditions

compared to 280 ppm CO2. As shown in

Figure 9, the largest contribution comes

from altered litter input.

Matrix vs. Default Simulations

Global Total SOC

ORCHIDEE-MICT Default: 3328 GtCORCHIDEE-MICT Matrix: 3304 GtC