A lumped water balance model to evaluate duration and intensity of drought constraints in forest stands
Introduction
The literature describes a wide variety of water balance models (mainly for agricultural and hydrological applications), that differ in their objectives, input data, complexity, spatial and temporal resolution. The main purpose of a water balance model is to predict temporal variations in soil water content, and to assess the water stress conditions actually experienced by a crop or a forest stand.
There is an increasing demand for large scale (region, continent) and for long term studies on forest–site–climate interactions, as much for hydrological as for forest management purposes. Such extensive applications require robust water balance models using simple soil and stand parameters and basic climatic data, in order to run simulations over many years. We developed a simple and lumped water balance model aimed basically at quantifying drought intensity and duration in forest stands. It uses a small set of parameters and standard daily meteorological data (potential evapotranspiration and precipitation). Evapotranspiration, which is generally the largest flux component, besides throughfall, is estimated here from ecophysiological relationships at stand scale. These relationships are driving by maximum leaf area index (LAI) to calculate canopy transpiration, understorey evapotranspiration and rainfall intercepted by tree canopies. It can be used for different sites and purposes, like long term (several years) or short term studies on the impact of drought on forest stands.
This model estimates the main terms of the hydrological cycle in forest stands: soil water content, stand transpiration and interception, drainage. It allows also to compute seasonal and annual integrated water stress indices to characterise drought events affecting physiological processes and growth of trees from various species, over long term periods.
This model was used for a retrospective analysis of the effects of drought on radial tree growth, and on crown conditions. It helped also to relate the effects of soil drought and tree physiology (Bréda, 1994), or nutrient dynamics in forest stands (Marques et al., 1996). It has also been used for predictive applications, e.g. to simulate the consequences of various sylvicultural management scenari (thinning intensity) or to quantify the consequences of global climate changes using data from the global climate model (GCM).
This paper describes the functions used in the model and its validation in various forest stands. Examples of annual variations in soil water content are shown for coniferous and broad-leaved stands growing on different soil types and under various climatic conditions. An example of long term analysis of the effects of water stress on radial growth of forest trees is also presented. Finally, a map of average water stress intensity in France is also shown.
Section snippets
List of symbols and abbreviations
Water fluxes and soil water content are expressed in mm H2O that is 10−3 m3 per m2 of ground area.P rainfall Th throughfall In rainfall interception Is water stress index T tree transpiration Eu evaporation from understorey plus soil PET potential evapotranspiration (Penman formula) ET actual evapotranspiration=T+Eu+In W available soil water Wm minimum soil water (i.e. lower limit of water availability) WF soil water content at field capacity EW extractable water=W−Wm EWM maximum extractable water=WF−Wm REW relative
Model description
This model is iterative and the variation in soil water content are calculated at a daily pace as:where ΔW is the change in soil water content between two successive days.
Comparison between hourly and daily models
We checked that: (i) the validity of using the Penman equation to estimate tree and overstorey transpiration; and (ii) the influence of hourly or daily time pace on the simulated soil water content. We compared the daily model to a hourly version which was based on the Penman–Monteith equation to estimate tree transpiration, and on equations of Rutter et al. (1971) for rainfall interception. The modelled variations of soil water content were tested with the two models over a 3-year period,
Validation
Validation of the model was done by comparing simulated and measured soil water, using weekly measurements with a neutron probe in various forest stands differing in structure, species composition, climate and soil conditions.
The first stand was a 30-year-old oak (Quercus petraea) plain forest, which was extensively described by Bréda et al. (1993). A second stand was a 30-year-old spruce (Picea abies) forest (Biron, 1994) located in the Vosges mountain, at 1000 m elevation. In both stands,
Examples of seasonal pattern of REW
Three simulations of the time course of REW during 4 contrasted years are shown in Fig. 10. The first one corresponds to a coniferous stand growing on a deep soil (EWM=180 mm), the two others to broad-leaved stands growing on a deep (EWM=185 mm), and on a shallow (EWM=72 mm) soil, respectively. Due to differences in phenology, water reserve under the coniferous was depleted earlier during spring and early summer, while full recovery of field capacity during autumn occurred at the same time for
Example of use of water stress index
In a regional dendroclimatological study (Badeau, 1995), inter-annual variations of radial growth in plain stands of beech (Fagus sylvatica) were analysed in relation to climate. Water balance simulation was made on a 42 year (1950–1991) climatic time-series in order to calculate the seasonal stress index (Is) (from budburst to the end of August). The influence of water deficits on tree growth has to be analysed without confusing factors, especially the effect of age has to be removed from the
Example of drought diagnosis at a regional scale
Analysis of spatial and temporal variation in soil water availability and prediction of regional drought risks are of major interest for forest management. To characterise annual (average) local water stress conditions in forests or quantification of exceptional droughts, relevant variables are the mean drought duration and the maximal drought intensity. As an example, the model was run for a ‘standard’ broad-leaved stand, growing on a soil with an extractable water of 140 mm in different
Discussion
The main advantage of the model presented here is that it uses in its basic version only two parameters, leaf area index and maximum extractable water in the soil, which can be easily measured or estimated. Maximum extractable water can be calculated from simple field measurements (depth, texture, porosity). This allows simulations to be performed over a wide range of soil types and tree species.
To simulate water transfer in the soil, we decided not to use hydraulic parameters like hydraulic
References (47)
- et al.
Simulated and measured water uptake by Picea abies under non limiting soil water conditions
Agric. For. Meteorol.
(1994) - et al.
Comparison of two methods for estimating the evaporation of a Pinus pinaster (Ait.) stand: sap flow and energy balance with sensible heat flux measurements by an eddy covariance method
Agric. For. Meteorol.
(1991) - et al.
The development and proving of models of large scale evapotranspiration: an Australian study
- et al.
Vapour flux density and transpiration rate comparisons in a stand of Maritime Pine (Pinus pinaster Ait.) in Les Landes forest
Agric. For. Meteorol.
(1990) - et al.
Transpiration of natural rain forest and its dependence on climatic factors
Agric. For. Meteorol.
(1996) - et al.
Stomatal control of transpiration: Scaling up from leaf to region
- et al.
Partitioning evapotranspiration into tree and understorey components in two young Pinus radiata D. Don stands
Agric. For. Meteorol.
(1990) - et al.
A predictive model of rainfall interception in forests. I. Derivation of the model from observations in a plantation of Corsican pine
Agric. Meteorol.
(1971) - et al.
Sampling strategies for measurement of soil hydraulic properties to predict rice yield using simulation models
Geoderma
(1993) Interception des précipitations par le couvert forestier
Ann. Sci. For.
(1968)