Water balance modelling

How is this defined?

Modeling the water balance is the translation of the biophysical processes (e.g. tree transpiration, interception of precipitation) in a set of equations. These equations are based on measurements taken from a large number of forest stands of a wide variety of species under different climatic and soil conditions, ages and management techniques. The Biljou© model operates on a daily time interval. This calculated interval represents a compromise between:

• A brief interval (by the hour), which presents the problem of meteorological data availability and makes difficult to represent accurately some transient phenomena, and
• A longer interval (by month or by decade) not allows to break down of a number of processes, notably inability to represent properly the phenomena occurring at short term such as the regulation of tree transpiration.

What are the different functions?

The water balance page describes the general organization of water fluxes exchanged in a forests ecosystem. In the Biljou© model each water flux is represented by one or more equations, with the exception of drainage, which are calculated by their differences.

Variation in leaf area index

Evergreen species, which include coniferous trees, generally have a constant leaf area index (LAI) throughout the year. For deciduous species (broadleaved and larch), the model requires two parameters: the date of bud burst and the date when the full leaves or needles fall. From the date of bud burst, LAI increases linearly for 30 days to the maximum value. Similarly, 30 days before full leaf fall, LAI decreases for 30 days until it reaches 0. Regardless of the type canopy, maximum leaf area index is a required parameter.

Tree transpiration and its regulation (T)

Daily transpiration levels are calculated as a function of the ETP and the leaf area index. Taken from extensive data from our own experiments and from published studies, the maximum T / PET is 0.75 (see Granier et al., 1995) in conditions of high LAI ( > 6) and in the absence of water stress. When the LAI is lower than 6, transpiration, and effectively T / PET, will decrease proportionally to decreasing LAI. While the soil is drying, transpiration is limited by stomatal regulation when the relative extractable soil water (REW) drops below the threshold of 0.4. The opposite figure shows all of these variations (see the page transpiration and regulation).

Precipitation interception (In)

From numerous measurements taken in conifer and deciduous stands, we have established a function which gives the ratio of interception to incident rainfall: i) below a threshold called the canopy storage capacity (typically ranging between 1 and 3 mm), 100% of rain is intercepted, which threshold is depending on LAI, ii) beyond the canopy storage capacity, when increasing rainfall, relative interception decreases following an hyperbolic function (see opposite figure). Furthermore, for a given rainfall event, In increases when increasing LAI.
Rain that reaches the ground level (i.e. throughfall) is calculated as being the difference between incident rainfall and interception (see the provided graph and the page precipitation interception).

Soil and understory evapotranspiration (ETu)

This water flux is directly dependent on the radiative energy that reaches the soil surface of this ecosystem: depending on, incidental radiation and the LAI (in the absence of leaves, the WAI or wood area index; see the page transpiration and regulation).

Drainage (Dr)

It is calculated as the difference between the water input and losses through the equation : Dr = Pi – In – T - ETu (see the web page Drainage).

Soil moisture measurements show that after rain has reached dry soil, rehydration dynamics is slower than expected. In effect, the macroporosity will allow for rapid water flow, even if the soil moisture has not reached field capacity. This phenomenon of preferential water flow is even more pronounced in soils with visible cracks as a result of their drying. The Biljou© model takes into account this phenomenon; for each soil layer, drainage is calculated as follows:

• if the soil layer is at field capacity, additional water input is removed by drainage,
• if soil is drier, a part of water input is drained following macroporosity, while the remaining part moistens the soil layer.

The figure below shows the difference between two simulations of relative extractable soil water (REW) for two cases and considers the presence or absence of rapid fluxes through the macroporosity.

General Organization Model

The model uses daily weather data (see the page Meteorology) :

• precipitation
• air temperature
• relative humidity, water vapour pressure or air vapour pressure deficit
• wind speed
• global radiation

Certain parameters characterizing the soil and the stand are necessary to run the model:

• stand type : deciduous or evergreen
• dates of bud burst and full leaf fall for deciduous stands
• the maximum leaf area index of the canopy
• the hydrodynamical and soil physical characteristics and the proportion of fine roots in each soil layer ( 2 or 3 layers)

The model will run the following calculation loop each day:

1. Calculation of PET, using the meteorological variables
2. Calculation of the rainfall interception and of throughfall
3. Calculation of the sub-layer evapotranspiration
4. Calculation of transpiration, possibly limited when REW is less than 0.4
5. Addition of thoughfall to the soil reserves. For each soil layer at the site, a part of the throughfall rehydrates this layer, the remainder will migrate via drainage into the next layer. The final drainage is what comes from the deeper soil layer.
6. Subtraction of sub layer evapotranspiration from the surface layer
7. Subtraction of transpiration from the different soil layers
8. Calculation of the new soil water content and the REW
9. End of daily loop

At the end of each year, the balance of the various fluxes and drought indices (duration, intensity, area) are calculated over one full year for evergreen stands or over the period between bud burst and leaf fall for deciduous stands.

Useful reference

Granier A, Badeau V, Bréda N (1995) Modélisation du bilan hydrique des peuplements forestiers. Revue Forestière Française, XLVII, 59-68.

Badeau V, Bréda N (2008) Modélisation du bilan hydrique : étape clé de la détermination des paramètres et des variables d’entrée. RDV techniques hors-série n°4 – ONF.

Granier A, Breda N, Biron P, Villette S (1999) A lumped water balance model to evaluate duration and intensity of drought constraints in forest stands. Ecological Modelling 116: 269-283.

Courbet F, Doussan C, Limousin J-M, Martin-St Paul N, Simioni G (2022) Forêt et changement climatique - Comprendre et modéliser le fonctionnement hydrique des arbres. Editions Quae, collection Synthèses, 144 p.