Design concepts

Design concepts of the MEDFATE model

Environmental effects in MEDFATE

MEDFATE operates environmental effects in different ways for seedlings and established plants. Some climatic factors, such as winter temperature, may operate directly on vegetation by restricting seedling establishment but without affecting already established plants. This kind of design may lead to substantial temporal lags between climatic changes and simulated vegetation responses. The other kind of climatic effects are perturbations that affect the survival of established plants (immature and mature plant cohorts) or seed cohorts. In the current version of the model, Mediterranean summer drought and wildfires are implemented in this way.

Temperature limitations to seedling establishment

The ability of seedlings to survive the first year and establish successfully is a critical factor of species distributions, because it is assumed that older plants have more resources to withstand climatic variations. The design of MEDFATE assumes that both temperature and precipitation patterns (other meteorological factors like wind strength are excluded) limit the distribution of plants. However, the effects of high temperature and low precipitation (i.e. drought) are implemented at the level of established plants (either immature and mature cohorts). Since the ‘seedling’ stage lasts for less than one year in MEDFATE, drought-effects on very young plants are dealt one year after establishment. In contrast, the effects of low winter temperatures, which may lead to frost and damage the vascular system of plants, are implemented when determining seedling establishment (layer temperature of the coldest month). Other variables, like elevation, are present in the model but are not used because they are considered proxies for temperature.

Drought-driven mortality of established plants

In water-limited areas, such as in the Mediterranean basin, the main effects of climatic changes are likely to operate through modifications of the water balance, by reducing plant growth and occasionally leading to increased mortality rates and episodes of forest dieback. Drought-driven mortality in plants is originated from a decrease in soil water availability, which in turn depends on a broad range of factors acting at different scales (Western et al. 2002). At small spatial scales, water availability in the soil depends on the balance between net rainfall, relief and evapotranspiration as well as on the capacity of soil to retain water. All these effects are dealt externally to MEDFATE, when calculating the layer that represents cumulative summer water deficit. Another factor that modulates drought effects is plant competition. In densely-populated stands competition for water increases and thus drought-effects can be greater than in sparse stands. As this factor depends on vegetation itself, the modulation of drought depending on stand density is implemented in the Drought effects sub-model.

Climate changes and fire regime

Climate is a major driver of fire regimes in Mediterranean-type ecosystems. Moreover, among the potential drivers of fires at regional scale only climatic factors have a large inter-annual variability. Despite its importance, to predict climatic fire regime changes in regions with Mediterranean-type climate still remains a challenge. One of the reasons is because large and convective wildfires are often the result of extremely dry and hot weather conditions whose temporal pattern of occurrence is difficult to predict. Whereas heat waves are expected to increase their frequency in the future (Fischer & Schär 2010), their specific spatial and temporal pattern is indeed more complex than simple shifts of the whole temperature distribution to increased values (Hertig et al. 2010). Moreover, rainfall predictions provided by general circulation models have a lot of uncertainty in their local seasonality, which hinders accurately predicting the length of dry periods that are crucial to fuel moisture conditions. In addition to these difficulties in predicting extreme climatic conditions, predictions of fire regime changes in Mediterranean-type climates must take into account that fire regimes are also strongly affected by fuel structure, which can sometimes be even more important than climatic conditions (Pausas & Paula 2012). Indeed, the western Mediterranean basin has been classified as a region where both fuel moisture and fuel structure can have a role in shaping fire regimes (Pausas & Fernández-Muñoz 2011). Given the difficulties mentioned above, in MEDFATE we adopted a very simple approach to model and project the relationship between climate and fire regimes. We took historic trends in climatic conditions conducive to large wildfires by identifying those years were severe climatic conditions had occurred. Recent fire regime characteristics in the Western Mediterranean have been correlated with summer precipitation and summer maximum temperatures (Turco et al. 2013). Therefore, we used the cumulative soil water deficit index to define when a year is considered severe. Cumulative soil water deficit values calculated using historic data were used to classify past years as ‘severe’ or ‘normal’ and derive input distributions for the amount area burned and the size of fires (assuming a potential fire regime that is not fuel limited nor influenced by anthropogenic factors such as fire suppression). By calculating these average values on expected future climatic conditions we can determine whether a given year will have severe climatic conditions according to a given climatic scenario. In short, our approach is to simulate different temporal trends in the frequency of severe years.

Succession sub-model

The succession sub-model of MEDFATE follows mainly the FATE succession model created by Moore & Noble (Moore & Noble 1990), although it adopts some of the modificatons introduced in FATELAND (Pausas & Ramos 2006) as well as additional idiosincratic development. The succession model is deterministic and simulates cohorts of plants that go through a series of discrete life stages: seeds (propagules), seedlings, immature plants and mature plants. The FATE model manages the transitions through life stages, based on fecundity, germination and establishments parameters, maturation and lifespan parameters and the response to perturbations, which includes resprouting as plants of a former life stage (see Fig. 1). Propagules can be seeds and vegetative reproductive structures with or without dormancy (e.g. serotinous cones). Germination of propagules is enforced depending on the environmental conditions and the germination requirements of the species. The seedling stage is assumed to last less than one time step (a year) and cohorts at this life stage are not stored. Once established, immature plants are capable of self-supporting and avoid short-term environmental fluctuations but are not able to reproduce.

Plant abundance in MEDFATE represents the percentage of the stand covered by plants in the cohort calculated by projecting their crowns to the ground. Transitions to maturity and senescence of plant cohorts are determined by maturation time and life span of the species, respectively. (Effective) age is stored in the model a surrogate of plant height, because height is calculated using the deterministic growth function. Plant growth is modelled in three phases (Fig. 2): a first growth rate for immature cohorts, a second growth rate for mature cohorts younger than a pre-specified age, and zero growth for older cohorts. Therefore, plant growth is not related to environmental conditions; it simply follows the age of the plant cohort. However, species can have different growth speed and therefore compete for light with different abilities.

A dominant environmental influence on survival of plants in FATE is assumed to be the availability of light, which allows considering competition among plant cohorts (either intra- or interspecific). The amount of light reaching each plant cohort stand determines survival of its individuals and is calculated from the cumulative abundance of plants above it. Thus, shade-tolerant species may be allowed to survive under low levels of light in the understory, whereas seedlings or saplings of other species may die of starvation. While light limitations causing plant starvation are implemented in the Succesion sub-model, the responses of plants to perturbations are modelled in other sub-modules. Being designed to model vegetation changes in regions with Mediterranean climate, MEDFATE explicitly includes the effects of wildfires and summer drought on the survival of plant cohorts (see Drought effects and Fire regime sub-models). The effects of other environmental factors, such as temperature, are lumped into the bioclimatic model that imposes limits to seedling establishment using a set of bioclimatic variables (currently as the sole function of temperature of the coldest month).

Reproduction & dispersal sub-model

The original FATE model (Moore & Noble 1990) was not spatially explicit and dispersal of propagules was accounted for in a very simplistic way (i.e., plants were assumed to be either widely-dispersed or only locally dispersed). The FATE model assumes that any species with mature cohorts present in the stand will produce sufficient propagules to provide maximum (i.e., high) seed abundance in the corresponding seed cohort. More recent implementations of the FATE model, like FATELAND (Pausas 2006; Pausas & Ramos 2006) or LAMOS (Cousins et al. 2003), include seed dispersal sub-models, which are responsible for distributing seed among cells. MEDFATE currently tries to mimic the approach implemented in FATELAND, but it is simpler than the former. Mature plant cohorts are assumed to provide enough seeds to maintain the local seed bank at high level. Additionally, mature plant cohorts of a given species produce an integer number of ‘dispersers’ that are moved to other cells. The number of ‘dispersers’ is determined by the fecundity of species and the total abundance of mature cohorts in the source cell. The location reached by each disperser is chosen using a negative exponential kernel. If the sink location is on a wildland cell, then its seed bank for the corresponding species will be set to high level. Otherwise, the disperser will be lost.

Drought effects sub-model

Whereas drought effects may in reality span several years (e.g.)(Bigler et al. 2006), in MEDFATE, drought-driven mortality events are assumed to occur within the summer season (although the cumulative soil water deficit index averages the deficit of two years). In MEDFATE, the level of drought in a given cell depends on climatic balance and the topography of the area. However, drought-driven mortality is not only the result of a deficit in soil water. Rather, it may be enhanced by predisposing factors and, after the drought event, be modulated by other factors (Galiano et al. 2010). MEDFATE assumes that high stand density can be a predisposing factor leading to enhanced mortality. Specifically, the level of summer drought calculated for the cell may be increased for those strata that have a high density of stands. Thus, it is assumed that plants of the same stratum compete for the same water resources below ground, but do not compete with plants of other strata. Plants in a cohort may be unaffected by drought, they may be killed outright, or they may survive to resprout after losing part of their aboveground somatic tissue (in which case its effective age will decrease). All resprouting plants in a life stage are assumed to be set back to a single effective age. In MEDFATE, the use of terms “unaffected” and “resprout” is not exactly the usual one. A plant that suffers minor damage or that resprouts vigorously is unaffected as far as the model is concerned. The response to a drought event can be different depending on the species identity, the plant cohort’s current life stage (immature or mature) and the intensity of drought (four drought levels are considered). Both killed and resprouting plants contribute to the amount of dead fine fuels. Unlike with fire perturbations (see below), seed cohorts are unaffected by drought.

Fuel type sub-model

The amount, flammability and distribution (vertically or horizontally) of fuel are critical factors modulating fire behaviour and fire effects. Since MEDFATE does not model fire behaviour mechanistically, it does not account for all characteristics of fuel. Nevertheless, the cells in MEDFATE can be classified into three categories of vulnerability to suffer crown fires, according to the vertical distribution of fuels across the stand. This fuel typology currently follows the procedures of Piqué et al. (2011), a set of guidelines for the management of vertical continuity of forest fuels developed with the help of fire experts. Fuel type for any cell is calculated using the state base variables of MEDFATE (i.e. the abundance and age of plant cohorts) and following the protocols defined in Beltrán (2012). Dead fine fuels are taken into account when calculating fuel type. In MEDFATE, the fuel type is used to determine the rate of fire spread and, ultimately, whether the fire that impacted the cell was a surface fire or a crown fire (see below).

Fire regime sub-model

The fire regime sub-model closely resembles the MEDFIRE model (Brotons et al. 2013) and inherits most of its design concepts. The fire regime sub-model is designed to allow the fire spread rate to partially depend on the main factors determining fire shapes in real landscapes (Rothermel 1972). Specifically, fire spread rate is calculated as function of fuel load, topography and wind direction. Therefore, the shape of a fire arises as a result of distinct rates of fire spread from one cell to the other. In contrast, fire size is primarily determined by applying a top-down approach in which the area potentially burnt by each fire is selected from an input distribution of fire sizes. Potential fire size distribution depends on the climatic severity of the year. Adverse years are characterized by a high number of weather risk days (Piñol et al. 1998). Therefore, the statistical distribution of fire sizes in adverse years has a higher probability of large wildfires compared to normal (non-adverse) years. Total area burnt per year is also drawn annually from a statistical distribution that differs in adverse compared to normal years. Fire intensity levels are mostly related to the rate of spread in the cell. Thus, the model assumes that faster fires burn with higher intensity. Whether the fire is a surface fire or a crown fire is determined on the basis of the rate of spread (i.e. intensity) and the vulnerability of the stand to burn as a crown fire (i.e. the fuel type).

The explicit inclusion of processes leading to fire extinction may help gaining insight on the factors determining fire size distributions (Loepfe et al. 2011). Two distinct fire suppression strategies are implemented in MEDFIRE (Brotons et al. 2013). Both strategies are related to the concept of fire fighting opportunity, which is defined as instances in which low fire intensity allows fire fighters to control and extinguish it, and leading to an effective fire size smaller than the potential fire size. As a consequence, effective area burnt is an emergent property of the model and allows assessing the role of climatic variability (i.e. proportion of climatic adverse years) and fire suppression in the determining fire impact and fire size distributions.

Fire effects sub-model

Established plant cohorts (i.e. immature and mature cohorts) can have three fates when a disturbance occurs in its cell, as in the original FATE model (Moore & Noble 1990). As with drought perturbations, a plants may be unaffected by fire disturbances, they may be killed outright, or they may survive to resprout after losing some of its somatic tissue (in which case its effective age will decrease). The seed bank of a species (both dormant and active) may also suffer abundance reduction as a result of a fire disturbance. Alternatively, the dormancy of part of the dormant seed pool may be broken. These seeds will be moved to the active seed pool and may germinate after the fire event. In the original FATE model one could implement several disturbances (or levels of disturbance). The current implementation of MEDFATE allows for two types of fire disturbance: surface fires and crown fires; thus, fire effects on established plants and on seed cohorts have to be specified for each fire type. Fire disturbances also burn dead fine fuels. In this case, however, the only distinction to make between surface and crown fires is the height beyond which fine fuels are not consumed.