One Dimensional Analytical Land-Vegetation-Atmosphere
coupled model to investigate soil moisture bimodality.
Abhinav Dengri, Graduate School of Engineering, Hokkaido UniversityTomohito J. Yamada, Faculty of Engineering, Hokkaido University

1. INTRODUCTION

representing cropland.
∂θ𝑎𝑄𝑠ϵ𝑎 ϵ𝑠 σ𝑇𝑠4 ∂Δθ̃𝑎 θ𝑎∗ − θ𝑎=+−+∂𝑡ρ𝑐𝑝 ℎ𝑎ρ𝑐𝑝 ℎ𝑎∂𝑡τ∂𝑞𝑎∂Δ𝑞̃𝑎ρℎ𝑎= 𝐸 − ρℎ𝑎+ 𝐹𝑞∂𝑡∂𝑡∂𝑇𝑠ρ𝑠 𝑐𝑝𝑠 ℎ𝑠= (1 − 𝐴𝑠 )𝐹𝑟𝑎𝑑 − 𝑄𝑠 − 𝐿𝑒 (𝐸)∂𝑡− ϵ𝑠 σ𝑇𝑠4∂𝑞𝑠𝑤𝑜 ℎ𝑠= 𝑃 − 𝐸 − 𝐿(𝑞𝑠 )∂𝑡Surface vegetation through transpiration influences theexchange of moisture and energy between the land
surface and atmosphere1. Transpiration throughstomatal opening is greatly controlled by soil water
potential, i.e., soil moisture2. The Global LandAtmosphere coupling Experiment (GLACE) identified
regions with strong land-atmosphere interaction to belocated in transition and irrigated regions whereevapotranspiration is strongly influenced by soil
moisture3. The strength of land-atmosphere coupling
can be largely impacted by irrigation activities4. For
Illinois, the United States, the region with strong landatmosphere interaction, D'Odorico and Porporato, 2004
found the probability distribution of twenty years ofsummer soil moisture displayed two distinct peaks andtermed this distribution as soil moisture bimodality.
The Analysis of AMSRE satellite soil moisture data
showed global soil moisture bimodality, whichcoincided with transition region6. D'Andrea et al. 2006,
through a one-dimensional continental-scale idealized
coupled land-atmosphere model, highlighted theimportance of spring soil moisture for causing soilmoisture bimodality. In the present study, wedeveloped a simple box model for soil-vegetationatmosphere dynamics for the mid-latitude region. Our
objective is to examine the robustness of the multiple
equilibria in the soil-vegetation-atmosphere systemwith the inclusion of the dynamic response ofvegetation.

(1)
(2)
(3)
(4)

The equation (5) represents dynamics LAI scheme
is based on Törnros and Menzel 2014, where LAI is afunction of accumulated precipitation over the last fivemonths (𝑝𝑎𝑐𝑐 ).
Λ𝑑𝑦𝑛𝑎𝑚𝑖𝑐=𝛽𝑜+𝛽1𝑝𝑎𝑐𝑐
𝑏 = 0.45𝐿𝐴𝐼 0.36

(5)(6)Figure 1: Schematic of land-vegetation-atmosphere coupled model.

2. METHODOLOGY

Evapotranspiration ( 𝐸𝑇 ) is partitioned into soil
evaporation ( 𝐸𝑠 ) and plant transpiration ( 𝑇 ). Theequation (6), based on Wei et al. 2018 describes theratio of transpiration to evapotranspiration ( 𝑏 ) forcropland.

The figure (1) shows the schematic of the landvegetation-atmosphere coupled model. The equations(1)-(4) gives the temporal dynamics of four prognostic
variables, i.e., average Potential temperature (𝜃𝑎 ) andaverage relative humidity (𝑞𝑎 ) of the PBL, averagetemperature (𝑇𝑠 ) and average relative humidity of thesoil layer. The study employs two different model. First,
without explicit vegetation model (Control Model,CM). The second model considers vegetation module
which includes two different LAI schemes. i.e., static(representing broadleaf evergreen forest and bare soil)
based on Koster and Suarez 1996 and dynamic LAI

3. RESULTS
The CM without the explicit vegetation gave twostable equilibria, i.e., dry, steady-state, and wet steadystate (fig. 2A), depending on early summer soilmoisture. For the fixed incoming lateral moisture flux,summer with low early summer soil moisture will end
up in a dry and hot state compared to those starting with4

the high summer soil moisture. The dynamic crop
vegetation maintains the two stable equilibria, ‘dry/hot’and ‘wet/cool’ as CM but requires higher initial soil
moisture to showcase a wet/cool state. On the other
hand, fig 2B shows that both forest land and barren land
have only one stable equilibrium, i.e., wet, and dry
respectively.
We also simulated the synoptic flow variability
by stochastically varying the lateral moisture
convergence flux (Fq). Figure (2) shows the soil
moisture histogram for the three different vegetation
cover obtained from the time series of the data. Thecropland with dynamic LAI and shows a stronger
bimodal mode compared to the CM. For static LAI, thesoil moisture histogram for both the constant forcing isunimodal but with peaks at different soil moisturevalues. The high LAI region has a greater probabilityof always remaining in the wet stable state, whereas thebare soil has peaked at dry soil moisture value.

temperature and humidity.

Figure 3: Time evolution of soil moisture in case of synoptic forcing
for different vegetation cover.

Acknowledgements
This study is supported by ArCS II (Arctic Challenge for
Sustainability). We would like to express our sincere gratitude.

5. REFERENCES
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Figure 2: Preferential equilibrium states for different vegetation
cover for initial soil moisture.

4. DISCUSSION
It also concludes the importance of landscapevegetation type, in addition to early summer moisture,
in increasing the seasonal forecast of the mid-latitude
summer season. Change from natural vegetation tocultivated vegetation increases the probability of adry/hot state. The model, although simple, provides
valuable insights into the soil-vegetation-atmosphereinteraction process and leads to realistic values for the5