On the sources of vegetation activity variation, and their
Transcript Of On the sources of vegetation activity variation, and their
On the sources of vegetation activity variation, and their relation with water balance in Mexico
F. MORA
Center for Advanced Land Management Information Technologies; University of Nebraska-Lincoln, 113 Ncbraska Hall, Lincoln, Nebraska 68588-0157, USA; email: [email protected]~i
L. R. IVERSON
USDA Forest Service, 359 Main Road, Delaware, Ohio 43015: USA
(Received 13 A~lglrst1996; 117 ~ I I I Nfo/ j.1)~18 JLL/!1. 9 9 7 )
Abstract. Natural landscape surface proccsses are largely controlled by the relationship between climate and vcgetation. Water balance integrates the effects of climate on patterns of vegetation distribution and productivity, and lor that season, functional rclalionships can be established using watcr balance variables as predictors of vegetation response. In this study, we evaluate, at the country and ccoregion level of analysis, thc relationships between indicators of vcgetation productivity and seasonality with several water balance variables. Vegetation indicators were derived from rnultitcmporal analysis of satellite images, and water balance variables were obtained from ground meteorological station data. Spatial and temporal variation of climate and vegetation were evaluated with remote sensing and G I s tcchnology, and empirical relationships were evaluated statistically via rcgrcssion models. Significant non-linear relationships were established for vegetation productivity, precipitation, and actual evapotranspiration at the country levcl in Mexico, where the landscape is reprcsented by a wjde diversity of ccosysterns. Variation of vegetation patterns of productivity and seasonality is explained less at the ecoregion scale relative to the country level, but water balance variables still account for -50% of variation in vegetation.
1. Introduction Land surface processes, such as primary productivity, energy balances (e.g.,
evapotranspiration processes), and biogeocl~emicalcycles, are largely controlled at landscape scales by the interaction of climate with terrestrial vegetation. For that reason, vegetation disturbances can greatly modify landscape ecological processes. Presently, there is great concern that high rates of land surface modification: and therefore modification of ecological processes, are occurring due to anthropogenic causes such as deforestation and other land-use changes.
Modifications of landscape processes at the regional level are particularly important in developing countries where high rates of deforestation are occurring. Ten major fronts of active deforestation of tropical vegetation have been identified for the globe, five of which are located in Latin American countries, with Mexico ranking near the top (Myers 1993). According to Mexican oficials, land-use modification in Mexico is occurring at more than 1% per year considering all vegetation types, increasing in recent years. During the last 30 years, more than 25% of the forested cover has been lost (Inventario Nacional Forestal [INF] 1985, 1991).
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F. Mora and L.R. Iverson
Long- and short-term evaluation methods are needed to monitor landscape processes and modifications under such situations. Some national and international efforts are beginning to better monitor conditions over iandscapes susceptible to high rates of change, but a large scale efrort is still needed to gather observations that can be used to evaluate functional relationships. In general, the current availability of data in developing countries (as in Mexico) is poor, which in turn, largely restricts the functional analysis of land-surface processes. Due to these limitations, remotely sensed data currently provides the most appropriate tool for the evaluation of landscape processes at regional scales in these countries.
The general objective in this study is to evaluate the value of remotely sensed data linked to statistical modelling to provide a tool for the analysis of ecological processes at landscape scale. The evaluation is based on the analyses of empirical relationships between integrated and seasonal measures of remotely sensed vegetation indexes with annual water balance variables that can be estimated from ground observations. First, different sources of variation in vegetation activity are analysed as a response of different scales of observation and explanatory variables. Later, a series of empirical models are fitted to explain such variation. The relationships between seasonal variations of vegetation and water balance can help elucidate those mechanisms that regulate vegetation-climate surface processes in the landscape of Mexico.
1.1. Background Evidence continues to mount as to the value of remotely sensed imagery for the
assessment of landscape processes. For example, land-surface processes at continental and regional scales have been related to the normalized difference vegetation index (NDVI), derived from satellite imagery. Net primary productivity, potential and actual evapotranspiration and atmospheric CO, dynamics have been correlated with NDVI at several scales and in different parts of the globe (Box et nl. 1989, Chong et al. 1993, Choudhury 1987, Fung et al. 1987, Goward et al. 1985, 1987, Maisongrande et al. 1995, Running 1986, Running and Nemani 1988, Running et a/. 1989, Tucker and Sellers 1986, Tucker et al. 1986). In addition, seasonal patterns of vegetation indexes can also be used to estimate climatic variability (Gallo 1989, 1990).
Direct estimation of variables associated with regional water balance is potentially a major constraint to functionally linking land surface processes for regions where data are scarce. Actual evapotranspiration and soil moisture are extremely dificult variables to estimate without making several, and sometimes very general, assumptions. Although, estimates of water balance variables can be obtained using several methods that include the use of satellite imagery along with simulation modelling, they are yet to be adequately calibrated with ground observations (Pinker 1990).
At present, water balance variables estimated via empirical methods give regional values based on a few climatic variables that are more readily available from meteorological stations, i.e., temperature, precipitation, direction and speed of wind, and relative humidity (Thornthwaite and Mather 1957, Eaglernan 1980). Measurements of air temperature and precipitation are the only meteorological variables used in water balance calculations currently being gathered at most Mexican weather stations. For that reason, the Thornthwaite and Mather (1957) approach for water balance was used because other accurate formulae require data such as wind speed which is not available. Therefore, among all possible methods
Vegetation activity and water balance
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to use, the Thornthwaite and Mather method was the most suitable procedure for estimating water balance in this study.
Empirical functional relationships between remotely sensed vegetation parameters and water balance variables have previously been established using integrated NDVI (iNDVI) or a similar measure from the Advanced Very High Resolution Radiometer (AVHRR) sensor that can biologically interpreted. NDVI measures have been highly correlated with water balance variables, specifically with actual evapotranspiration, soil moisture, and precipitation (Davenport and Nicholson 1993, Farrar et al. 1994, Kustas et al. 1994, Di et al. 1994, Malo and Nicholson 1990, Nicholson and Farrar 1994, Sandholt and Andersen 1993, Seevers and Ottmann 1994).
Integrated annual and seasonal NDVI measures (which in turn, are related to vegetation activity) can be obtained by applying principal component analysis to monthly derived NDVI indexes from AVHRR data. Principal component analysis resulted in several NDVI measures that capture the seasonality in the Mexican landscape (Mora and Iverson 1997). Such components can be used as response variables in water balance processes. Integrated annual measures of NDVI can be correlated to annual variations of potential and actual evapotranspiration, soil moisture, precipitation, and the surplus or deficit of water. It is more difficult, however, to correlate seasonal NDVI measures with seasonal variations of water balance, because they vary according to specific vegetation types. Empirical relationships of seasonal patterns are therefore harder to evaluate (Chong et al. 1993). In such cases, the scale at which seasonal water balance controls the vegetation distribution appears to be different from the scale at which the annual water balance variation produces its effects.
When an empirical relationship between vegetation activity and water balance is found, spatial autocorrelation effects among such processes should also be considered. This analysis is particularly important because such landscape processes can be significantly correlated if they share a common spatial structure. It is therefore necessary to identify the sources of environmental variation by 'partialling out' the spatial component in correlation analysis, especially if linear regression models are used.
There are four major components of landscape variation when analysing spatially referenced data (Legendre 1993, Bocard et al. 1992): (1) non-spatial environmental variation; (2) spatially structured environmental variation; (3) spatial variation of the process under consideration; and (4) the unexplained, non-spatial variation. These components of variation can be identified using partial regression analysis, after empirical relationships between water balance variables and vegetation activity are established. Partial regression analysis involves the use of multiple regression models that include 'space' as an explanatory variable along with the environmental variables.
2. Methodology The overall procedure used to evaluate the relationships between measures of
NDVI and water balance in Mexico considers two scales of analysis, the country scale and the ecoregion scale. At the country scale, variability among ecosystems permits the evaluation of NDVI variations over a complete set of different ecological situations, e.g., deserts, semideserts, conifers, dry deciduous selvas (we use the term selva here, which can loosely be translated as 'tropical forest'), savannas, and perennial
F. Mora and L.R. lverson
selvas. At the ecoregion scale, the variability in NDVI and water balance is largely attributed to more subtle differences among ecosystems within ecoregions.
The possible relationships at the two scales of analysis were explored through correlation, multiple regression, and non-linear regression analysis. Initially, the correlation between NDVI measures and water balance variables served to identify the variables to use in model fitting. Afterwards, non-linear regression analysis, using a previous model structure (Box et al. 1989) was used to fit the relationship between the most significant variables that explained vegetation indicators without considering spatial effects in water balance. Finally, partial correlation analysis (Legendre 1993) is used to explore the effects of spatial autocorrelation in the models and to identify the spatial structure of both dependent and independent variables. The models used to explore the combined effects of water balance variables over vegetation activity indicators were evaluated via multiple regression analysis.
2.1. Integrated and seasonal NDV1 measures In an earlier study, annual integrated and seasonal NDVI measures were obtained
from principal component analysis (PCA) of the Global Vegetation Index (GVI) data produced by the National Oceanic and Atmospheric Administration (NOAA) AVHRR (Mora and Iverson 1997). The first five principal components obtained, captured more than 95% of the monthly GVI variation in Mexican data. Integrated annual vegetation activity was highly related to the first principal component which can therefore be interpreted as another measure of annual integrated NDVI (iNDVI). Seasonal variations in natural vegetation, which key on the temporal variability of chlorophyll (e.g. the July-August NDVI monthly values normally mark the peak of greenness), were mostly captured by the second principal component (sNDVI). Thus, sNDVI was a measure of natural vegetation that followed a strong seasonal pattern in Mexico. The other three components were associated with irrigated agricultural vegetation, and were not considered further in this study.
2.2. Water balance data Direct observations of water balance variables in Mexico are not currently
available. Climatic data is gathered in a national network of weather stations where observations of precipitation and air temperature are recorded (INEGI 1980). Water balance was estimated from these records. Potential relationships between water balance and vegetation activity were established using data for 2214 weather stations, which provided long-term monthly means (-25 years) of temperature data and precipitation. The long-term temporal variation was therefore captured. Since additional parameters such as the direction of wind and relative humidity were not available for all stations, estimates of several water balance variables (potential and actual evapotranspiration, soil moisture; water deficit and surplus) were empirically obtained according to Thornthwaite and Mather methodology (Thornthwaite and Mather 1955).
2.2.1. Water balance estimation according to the Thornthwaite and Mather approach Thornthwaite and Mather's approach for water balance modelling has been
implemented and used for more than 40 years. Even though it has been criticized due to its empirical approach, this method represents about the only way to estimate the water balance for places where only records of air temperature and precipitation exist. Modelling algorithms which use their equations (e.g., WATBUG, from Willmot
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1977) are available to give water balance estimates from inputs of mean monthly air temperature, mean monthly precipitation, and some indication of water holding capacity for the location. Formulas described in WATBUG were used here to implement a cartographic G I s model of water balance. Five water balance (WB) variables were calculated from records on precipitation (P), air temperature (T), latitude, and duration of daylight. These include soil moisture (SIM),potential evapotranspiration (PE), actual evapotranspiration (AE), water deficit (WD), and water surplus (WS). Since the water balance approach used here integrates the effects of several factors, estimates of water balance variables, except for P and PE, contain somc dependency on vegetation types through the soil moisture storage (figure 1).
Soil moisture (SiM)is the amount of water that is stored in the soil, and is available for plant growth. By definition, soil moisture is stored only when precipitation exceeds the potential evaporative demand (PE) of the atmosphere, otherwise the precipitation is evaporated. The maximum amount of soil moisture that can be available for plant growth on a specific site is a direct function of the water-holding capacity on that site (primarily soil structure but also rooting depth of the vegetation layer), as modified over time by the existing vegetation and PE. Soil maps with sufficient detail on water-holding capacities, and sufficient extent to cover all Mexico were not available. As such, inaccuracies of SIMwill occur at the fine scale. However, when calculating soil moisture here, we can assume that large-scale and long-term effects of precipitation and potential evapotranspiration will generally overwhelm the eflect of variations in water-holding capacity among soil types.
Evapotranspiration is the process of water transfer from vegetated land surfaces
Adjusted Potential Evapotranspiration [mm/year]
Figure 1. Exponential relationship for soil moisture retention data reported in Thorntliwaite and Mather (1955). Soil moisture storage is plotted as a f~~nctioonf adjusted potential evapotranspiration using different vegetation types which, in turn, have various rooting zone depths.
F. Mora and L.R. Iverson
into the atmosphere due to soil evaporation and plant transpiration (Rosenberg et al. 1983). In the Thornthwaite and Mather approach, evapotranspiration is mainly a direct function of air temperature, by being directly related to the amount of energy available at the soil-plant surface. As defined by Thornthwaite, potential evapotranspiration (PE) can be expressed as the evaporative water loss from a site covered by vegetation that receives unlimited amounts of water (Thornthwaite 1948). As it is directly related to both heat and radiation, PE is modified by humidity and wind speed (Stephenson 1990), but over wide geographic areas, substantially more modification results due to changes in latitude and duration of daylight (Willmott 1977). According to Thornthwaite's approach, PE is calculated here as a direct function of air temperature and heat index, and adjusted by latitude and duration of day (Willmott 1977).
Actual evapotranspiration (AE), on the other hand, is the actual water transferred from the surface to the atmosphere in accordance with present meterological, plant, and soil conditions, and depending upon available water. In an ecological context, AE can be defined as the biologically usable energy and water used by plants (Stephenson 1990). It is expressed as the amount of evaporative water loss in relation to its present availability. According to the Thornthwaite method, AE is estimated from available soil moisture (SM) and precipitation (P). When there is a water deficit in the soil (i.e., P E > S M ) AE equals PE, otherwise AE is equal to the amount of precipitation ( P ) plus the moisture accumulated in the soil (SM).
Estimates of actual evapotranspiration require soil moisture (SM) estimates in advance. Unfortunately, soil water-holding capacity, a variable required for soil moisture estimation, was not available. Alternatively, an approach that used information related to the water that is retained in the soil from a series of soil moisture retention tables (Thornthwaite and Mather 1957) was used. These soil moisture retention tables were used together with land cover type information to estimate soil moisture. The soil moisture retention tables assumed that moisture accumulated in the soil is depleted exponentially as a function of PE, and varies according to the depth at which the water is held in the rooting zone. As water-holding capacity is a function of soil structure and rooting depth, there is a relationship between waterholding capacity and vegetation type (e.g., mature forests have a much deeper rooting zone, and therefore a higher water-holding capacity, than shallow-rooted crops, regardless of the soil texture). Empirical relationships like these permit the estimation of soil moisture storage, directly from soil moisture retention tables, for different dominant vegetation types within ecoregions, and for different depths of the rooting zone.
Thornthwaite and Mather (1957) previously published several soil moisture retention tables for different vegetation types and depths of the rooting system for crops and natural vegetation. From the data published in the tables, several logtransformed regression equations were fitted to describe how soil moisture is depleted by vegetation according to PE at different depths of rooting zones (see figure 1). These parameters were used to estimate the soil moisture in the different ecoregions according to dominant vegetation. Curves for water-holding capacities of 50 mm in the rooting zone were used for 'deserts', 75 mm for 'semideserts', 100 for 'deciduous selvas', 125 for 'subtropical matorrals', 150mm for 'selvas' and 250 mm for 'conifer forests'. Obviously, if an adequate soil map was available, the use of that map in conjunction with a vegetation map could provide an improvement to the method employed here to estimate soil moisture.
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A water deficit (WD) is present when water availability does not meet the vegetation evaporative demands. By definition it is the difference between monthly PE and AE (Stephenson 1990). On the other hand, a water. surplus (WS) is an excess of water in the environment, and is obtained when precipitation exceeds PE, minus the water that is retained in the soil. Precipitation (P) is the amount of water that is received as rainfall.
2.3. GIS irnplernerttariorz A cartographic model, which included several NDVI measures, a map of vegeta-
tion types derived from remotely sensed images (covering the whole country with a 16km pixel size), and the water balance database for 2214 weather stations in Mexico, was implemented in Arc/Info CIS (ESRI 1995) and used to explore the climate-vegetation relationships. The implementation of a CIS cartographic model permitted the evaluation of the relationship between NDVI measures and water balance variables at two scales of analysis: ( 1 ) the country scale; and (2) the ecoregions scale.
The classification of the country into different ecoregions (figure 2) was used as a stratification criterion for the two levels of analysis. A subset of 1162 weather stations was obtained by masking their location with six 'natural' ecoregions (occupying 69% of the Mexican landscape, not including irrigation and agriculture from figure 2). A data set was thus created that included the six annual water balance variables, annual integrated and seasonal NDVI measures, ecoregions, and the geographic location of weather stations used in the analysis. These data were then used to fit linear and non-linear models.
Two special advantages are gained when seasonal water balance variables are calculated with the aid of CIS. First, potential evapotranspiration can be adjusted by latitude and duration of daylight to produce adjusted potential evapotranspiration (ADPE). Secondly, soil moisture can be estimated from PE, using the parameters of soil moisture retention tables associated with the dominant vegetation within ecoregions (figure 1). The temporal variation of water balance can thus be associated with qualitative differences in vegetation types ('natural' vs. 'non-natural'), when using a cartographic model that includes such characteristics in vegetation types.
Although the water balance-vegetation relationships were statistically assessed on a point basis for each of the weather stations, the CIS implementation also allowed the point data to be interpolated using spherical kriging models in Arc/Info (ESRI 1995). This resulted in country-level maps for each of the six variables, and allowed the exploration of their scales and forms of variation. Maps of the predicted results of the regression models permitted a visual evaluation of the forms of variation over the country.
2.4. Statistical exploratory analysis Exploratory analysis was conducted on the data in order to establish potential
relationships. Possible climate-vegetation relationships were established based on graphical analysis (scattergrams) and by using Pearson's product-moment correlation coefficients evaluated at p =0.05.
2.5. Mode fitting Non-linear relationships were tested using the model proposed by Box et a/.
(1989). Even though the model could be fitted by transformed linear regression, the
F. Mora and L.R. Iversoi~
a Deserts
nSemideserts
Conifer Forest
Deciduous Selvas
Subtropical Deciduous Selvas
I~elvas
Irrigation
Agriculture
Figure 3
Wather Stations
Distribution of wcather stations within ccoregions in Mcxico. The classilication into ccoregions is described in Mora and lverson (1997).
non-linear approach was used in order lo prevent autocorrelation eiTects in the model parameters. The model has strong ~hcoreticalsupport, and its use permits a direct comparison between the parameters obtained here and those obtained by Box et (11. (1989). Box's model that describes the relationship between NDVI measures and water balance variables has the following form:
where iNDVI=integrated annual variation of NDVI, as produced via principal component analysis for the period of 1985-1989 (the iNDVI is scaled to a 0-1
range); 2 =asymptote or highest iNDVI value; b= slope or iNDVI rate of change as
a function of A E or P (WB units in m~n/yearI ) ; and WB=water balance variable.
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In the following models WB = AE when actual evapotranspiration (mmIyear-') is used; and WB = P when precipitation (mmlyear-') is used.
The model was fitted using a loss non-linear function, which minimizes the residual variance (sum of squared deviations) around the regression line, using a quasi-Newton minimization method (first order and second order derivative of the function).
Linear regression analysis was performed using the least squares method. In both non-linear and linear regression methods, the plot of observed vs. predicted values, normal and half-normal probability plots of residuals, and the proportion of variance explained were used to evaluate the model fit.
2.6. Multivariate regression analysis Multiple regression analysis was used to test the interaction between water
balance variables and spatial autocorrelation, in explaining the variation of both iNDVI and the sNDVI at the country scale. Subsequently, the combined effect of water balance variables over vegetation indicators included the water balance spatial structures. At the ecoregion scale, only environmental variation (without partialling out the spatial component) was tested in the regression models. The Durbin-Watson test, histograms, normal probability, and standard residuals vs. predicted plots were used in residual analysis. Tolerance and variance inflation factor (VIF) values were used in multicollinearity diagnostics for all regression models.
2.6.1. Partial correlation analysis At the country scale, stepwise multiple regression analyses was used to identify
four sources of iNDVI and sNDVI variation (a,b, c, ~ is;ee table 1). First, nine spatial variables that define the spatial component in the analysis were regressed on each water balance variable to determine their correspondent spatial structure. The nine spatial variables were obtained when a matrix of two-dimensional geographical co-ordinates (x =longitude and y =latitude) was completed by adding all terms for a cubic trend regression surface of the form:
This cubic form of geographic co-ordinates accounts not only for linear gradient patterns, but also complex features such as patches or gaps (Bocard et al. 1992).
Table 1. Sources of iNDVl and sNDVl variation.
Components of variation in NDVI-space
Equations and regression models
Non-spatial WB variation [a]
Spatially structured WB variation
Cbl iNDVI spatial variation independent
of WB [c]
+ WB (environmental) va3ance [a+ h]
Spatial structure [h c]
+ + Environmental-spatial combincd [a h c]
variation
Unexplained variance [dl
iNDVl = [AEres, PEres, Pres, SMres, WDres, WSres]
iNDVI = [AE, PE, P, SM, WD, WS]-[a]
iNDV1 = [ A E , PE, P, SIM, WD, WS]
iNDVl = [JY LONG, LAT)]
iNDV1 = [AE, PE, P, SIM, WD, WS, LONG, LAT]
[dl = 1-[a]- [b] -[c]
1852
F. M o m and L.R. Iuerson
F. MORA
Center for Advanced Land Management Information Technologies; University of Nebraska-Lincoln, 113 Ncbraska Hall, Lincoln, Nebraska 68588-0157, USA; email: [email protected]~i
L. R. IVERSON
USDA Forest Service, 359 Main Road, Delaware, Ohio 43015: USA
(Received 13 A~lglrst1996; 117 ~ I I I Nfo/ j.1)~18 JLL/!1. 9 9 7 )
Abstract. Natural landscape surface proccsses are largely controlled by the relationship between climate and vcgetation. Water balance integrates the effects of climate on patterns of vegetation distribution and productivity, and lor that season, functional rclalionships can be established using watcr balance variables as predictors of vegetation response. In this study, we evaluate, at the country and ccoregion level of analysis, thc relationships between indicators of vcgetation productivity and seasonality with several water balance variables. Vegetation indicators were derived from rnultitcmporal analysis of satellite images, and water balance variables were obtained from ground meteorological station data. Spatial and temporal variation of climate and vegetation were evaluated with remote sensing and G I s tcchnology, and empirical relationships were evaluated statistically via rcgrcssion models. Significant non-linear relationships were established for vegetation productivity, precipitation, and actual evapotranspiration at the country levcl in Mexico, where the landscape is reprcsented by a wjde diversity of ccosysterns. Variation of vegetation patterns of productivity and seasonality is explained less at the ecoregion scale relative to the country level, but water balance variables still account for -50% of variation in vegetation.
1. Introduction Land surface processes, such as primary productivity, energy balances (e.g.,
evapotranspiration processes), and biogeocl~emicalcycles, are largely controlled at landscape scales by the interaction of climate with terrestrial vegetation. For that reason, vegetation disturbances can greatly modify landscape ecological processes. Presently, there is great concern that high rates of land surface modification: and therefore modification of ecological processes, are occurring due to anthropogenic causes such as deforestation and other land-use changes.
Modifications of landscape processes at the regional level are particularly important in developing countries where high rates of deforestation are occurring. Ten major fronts of active deforestation of tropical vegetation have been identified for the globe, five of which are located in Latin American countries, with Mexico ranking near the top (Myers 1993). According to Mexican oficials, land-use modification in Mexico is occurring at more than 1% per year considering all vegetation types, increasing in recent years. During the last 30 years, more than 25% of the forested cover has been lost (Inventario Nacional Forestal [INF] 1985, 1991).
01431161/98 $12.00 f:) I998 Taylor & Francis Lld
1844
F. Mora and L.R. Iverson
Long- and short-term evaluation methods are needed to monitor landscape processes and modifications under such situations. Some national and international efforts are beginning to better monitor conditions over iandscapes susceptible to high rates of change, but a large scale efrort is still needed to gather observations that can be used to evaluate functional relationships. In general, the current availability of data in developing countries (as in Mexico) is poor, which in turn, largely restricts the functional analysis of land-surface processes. Due to these limitations, remotely sensed data currently provides the most appropriate tool for the evaluation of landscape processes at regional scales in these countries.
The general objective in this study is to evaluate the value of remotely sensed data linked to statistical modelling to provide a tool for the analysis of ecological processes at landscape scale. The evaluation is based on the analyses of empirical relationships between integrated and seasonal measures of remotely sensed vegetation indexes with annual water balance variables that can be estimated from ground observations. First, different sources of variation in vegetation activity are analysed as a response of different scales of observation and explanatory variables. Later, a series of empirical models are fitted to explain such variation. The relationships between seasonal variations of vegetation and water balance can help elucidate those mechanisms that regulate vegetation-climate surface processes in the landscape of Mexico.
1.1. Background Evidence continues to mount as to the value of remotely sensed imagery for the
assessment of landscape processes. For example, land-surface processes at continental and regional scales have been related to the normalized difference vegetation index (NDVI), derived from satellite imagery. Net primary productivity, potential and actual evapotranspiration and atmospheric CO, dynamics have been correlated with NDVI at several scales and in different parts of the globe (Box et nl. 1989, Chong et al. 1993, Choudhury 1987, Fung et al. 1987, Goward et al. 1985, 1987, Maisongrande et al. 1995, Running 1986, Running and Nemani 1988, Running et a/. 1989, Tucker and Sellers 1986, Tucker et al. 1986). In addition, seasonal patterns of vegetation indexes can also be used to estimate climatic variability (Gallo 1989, 1990).
Direct estimation of variables associated with regional water balance is potentially a major constraint to functionally linking land surface processes for regions where data are scarce. Actual evapotranspiration and soil moisture are extremely dificult variables to estimate without making several, and sometimes very general, assumptions. Although, estimates of water balance variables can be obtained using several methods that include the use of satellite imagery along with simulation modelling, they are yet to be adequately calibrated with ground observations (Pinker 1990).
At present, water balance variables estimated via empirical methods give regional values based on a few climatic variables that are more readily available from meteorological stations, i.e., temperature, precipitation, direction and speed of wind, and relative humidity (Thornthwaite and Mather 1957, Eaglernan 1980). Measurements of air temperature and precipitation are the only meteorological variables used in water balance calculations currently being gathered at most Mexican weather stations. For that reason, the Thornthwaite and Mather (1957) approach for water balance was used because other accurate formulae require data such as wind speed which is not available. Therefore, among all possible methods
Vegetation activity and water balance
1845
to use, the Thornthwaite and Mather method was the most suitable procedure for estimating water balance in this study.
Empirical functional relationships between remotely sensed vegetation parameters and water balance variables have previously been established using integrated NDVI (iNDVI) or a similar measure from the Advanced Very High Resolution Radiometer (AVHRR) sensor that can biologically interpreted. NDVI measures have been highly correlated with water balance variables, specifically with actual evapotranspiration, soil moisture, and precipitation (Davenport and Nicholson 1993, Farrar et al. 1994, Kustas et al. 1994, Di et al. 1994, Malo and Nicholson 1990, Nicholson and Farrar 1994, Sandholt and Andersen 1993, Seevers and Ottmann 1994).
Integrated annual and seasonal NDVI measures (which in turn, are related to vegetation activity) can be obtained by applying principal component analysis to monthly derived NDVI indexes from AVHRR data. Principal component analysis resulted in several NDVI measures that capture the seasonality in the Mexican landscape (Mora and Iverson 1997). Such components can be used as response variables in water balance processes. Integrated annual measures of NDVI can be correlated to annual variations of potential and actual evapotranspiration, soil moisture, precipitation, and the surplus or deficit of water. It is more difficult, however, to correlate seasonal NDVI measures with seasonal variations of water balance, because they vary according to specific vegetation types. Empirical relationships of seasonal patterns are therefore harder to evaluate (Chong et al. 1993). In such cases, the scale at which seasonal water balance controls the vegetation distribution appears to be different from the scale at which the annual water balance variation produces its effects.
When an empirical relationship between vegetation activity and water balance is found, spatial autocorrelation effects among such processes should also be considered. This analysis is particularly important because such landscape processes can be significantly correlated if they share a common spatial structure. It is therefore necessary to identify the sources of environmental variation by 'partialling out' the spatial component in correlation analysis, especially if linear regression models are used.
There are four major components of landscape variation when analysing spatially referenced data (Legendre 1993, Bocard et al. 1992): (1) non-spatial environmental variation; (2) spatially structured environmental variation; (3) spatial variation of the process under consideration; and (4) the unexplained, non-spatial variation. These components of variation can be identified using partial regression analysis, after empirical relationships between water balance variables and vegetation activity are established. Partial regression analysis involves the use of multiple regression models that include 'space' as an explanatory variable along with the environmental variables.
2. Methodology The overall procedure used to evaluate the relationships between measures of
NDVI and water balance in Mexico considers two scales of analysis, the country scale and the ecoregion scale. At the country scale, variability among ecosystems permits the evaluation of NDVI variations over a complete set of different ecological situations, e.g., deserts, semideserts, conifers, dry deciduous selvas (we use the term selva here, which can loosely be translated as 'tropical forest'), savannas, and perennial
F. Mora and L.R. lverson
selvas. At the ecoregion scale, the variability in NDVI and water balance is largely attributed to more subtle differences among ecosystems within ecoregions.
The possible relationships at the two scales of analysis were explored through correlation, multiple regression, and non-linear regression analysis. Initially, the correlation between NDVI measures and water balance variables served to identify the variables to use in model fitting. Afterwards, non-linear regression analysis, using a previous model structure (Box et al. 1989) was used to fit the relationship between the most significant variables that explained vegetation indicators without considering spatial effects in water balance. Finally, partial correlation analysis (Legendre 1993) is used to explore the effects of spatial autocorrelation in the models and to identify the spatial structure of both dependent and independent variables. The models used to explore the combined effects of water balance variables over vegetation activity indicators were evaluated via multiple regression analysis.
2.1. Integrated and seasonal NDV1 measures In an earlier study, annual integrated and seasonal NDVI measures were obtained
from principal component analysis (PCA) of the Global Vegetation Index (GVI) data produced by the National Oceanic and Atmospheric Administration (NOAA) AVHRR (Mora and Iverson 1997). The first five principal components obtained, captured more than 95% of the monthly GVI variation in Mexican data. Integrated annual vegetation activity was highly related to the first principal component which can therefore be interpreted as another measure of annual integrated NDVI (iNDVI). Seasonal variations in natural vegetation, which key on the temporal variability of chlorophyll (e.g. the July-August NDVI monthly values normally mark the peak of greenness), were mostly captured by the second principal component (sNDVI). Thus, sNDVI was a measure of natural vegetation that followed a strong seasonal pattern in Mexico. The other three components were associated with irrigated agricultural vegetation, and were not considered further in this study.
2.2. Water balance data Direct observations of water balance variables in Mexico are not currently
available. Climatic data is gathered in a national network of weather stations where observations of precipitation and air temperature are recorded (INEGI 1980). Water balance was estimated from these records. Potential relationships between water balance and vegetation activity were established using data for 2214 weather stations, which provided long-term monthly means (-25 years) of temperature data and precipitation. The long-term temporal variation was therefore captured. Since additional parameters such as the direction of wind and relative humidity were not available for all stations, estimates of several water balance variables (potential and actual evapotranspiration, soil moisture; water deficit and surplus) were empirically obtained according to Thornthwaite and Mather methodology (Thornthwaite and Mather 1955).
2.2.1. Water balance estimation according to the Thornthwaite and Mather approach Thornthwaite and Mather's approach for water balance modelling has been
implemented and used for more than 40 years. Even though it has been criticized due to its empirical approach, this method represents about the only way to estimate the water balance for places where only records of air temperature and precipitation exist. Modelling algorithms which use their equations (e.g., WATBUG, from Willmot
Vegetation activity and water balance
1847
1977) are available to give water balance estimates from inputs of mean monthly air temperature, mean monthly precipitation, and some indication of water holding capacity for the location. Formulas described in WATBUG were used here to implement a cartographic G I s model of water balance. Five water balance (WB) variables were calculated from records on precipitation (P), air temperature (T), latitude, and duration of daylight. These include soil moisture (SIM),potential evapotranspiration (PE), actual evapotranspiration (AE), water deficit (WD), and water surplus (WS). Since the water balance approach used here integrates the effects of several factors, estimates of water balance variables, except for P and PE, contain somc dependency on vegetation types through the soil moisture storage (figure 1).
Soil moisture (SiM)is the amount of water that is stored in the soil, and is available for plant growth. By definition, soil moisture is stored only when precipitation exceeds the potential evaporative demand (PE) of the atmosphere, otherwise the precipitation is evaporated. The maximum amount of soil moisture that can be available for plant growth on a specific site is a direct function of the water-holding capacity on that site (primarily soil structure but also rooting depth of the vegetation layer), as modified over time by the existing vegetation and PE. Soil maps with sufficient detail on water-holding capacities, and sufficient extent to cover all Mexico were not available. As such, inaccuracies of SIMwill occur at the fine scale. However, when calculating soil moisture here, we can assume that large-scale and long-term effects of precipitation and potential evapotranspiration will generally overwhelm the eflect of variations in water-holding capacity among soil types.
Evapotranspiration is the process of water transfer from vegetated land surfaces
Adjusted Potential Evapotranspiration [mm/year]
Figure 1. Exponential relationship for soil moisture retention data reported in Thorntliwaite and Mather (1955). Soil moisture storage is plotted as a f~~nctioonf adjusted potential evapotranspiration using different vegetation types which, in turn, have various rooting zone depths.
F. Mora and L.R. Iverson
into the atmosphere due to soil evaporation and plant transpiration (Rosenberg et al. 1983). In the Thornthwaite and Mather approach, evapotranspiration is mainly a direct function of air temperature, by being directly related to the amount of energy available at the soil-plant surface. As defined by Thornthwaite, potential evapotranspiration (PE) can be expressed as the evaporative water loss from a site covered by vegetation that receives unlimited amounts of water (Thornthwaite 1948). As it is directly related to both heat and radiation, PE is modified by humidity and wind speed (Stephenson 1990), but over wide geographic areas, substantially more modification results due to changes in latitude and duration of daylight (Willmott 1977). According to Thornthwaite's approach, PE is calculated here as a direct function of air temperature and heat index, and adjusted by latitude and duration of day (Willmott 1977).
Actual evapotranspiration (AE), on the other hand, is the actual water transferred from the surface to the atmosphere in accordance with present meterological, plant, and soil conditions, and depending upon available water. In an ecological context, AE can be defined as the biologically usable energy and water used by plants (Stephenson 1990). It is expressed as the amount of evaporative water loss in relation to its present availability. According to the Thornthwaite method, AE is estimated from available soil moisture (SM) and precipitation (P). When there is a water deficit in the soil (i.e., P E > S M ) AE equals PE, otherwise AE is equal to the amount of precipitation ( P ) plus the moisture accumulated in the soil (SM).
Estimates of actual evapotranspiration require soil moisture (SM) estimates in advance. Unfortunately, soil water-holding capacity, a variable required for soil moisture estimation, was not available. Alternatively, an approach that used information related to the water that is retained in the soil from a series of soil moisture retention tables (Thornthwaite and Mather 1957) was used. These soil moisture retention tables were used together with land cover type information to estimate soil moisture. The soil moisture retention tables assumed that moisture accumulated in the soil is depleted exponentially as a function of PE, and varies according to the depth at which the water is held in the rooting zone. As water-holding capacity is a function of soil structure and rooting depth, there is a relationship between waterholding capacity and vegetation type (e.g., mature forests have a much deeper rooting zone, and therefore a higher water-holding capacity, than shallow-rooted crops, regardless of the soil texture). Empirical relationships like these permit the estimation of soil moisture storage, directly from soil moisture retention tables, for different dominant vegetation types within ecoregions, and for different depths of the rooting zone.
Thornthwaite and Mather (1957) previously published several soil moisture retention tables for different vegetation types and depths of the rooting system for crops and natural vegetation. From the data published in the tables, several logtransformed regression equations were fitted to describe how soil moisture is depleted by vegetation according to PE at different depths of rooting zones (see figure 1). These parameters were used to estimate the soil moisture in the different ecoregions according to dominant vegetation. Curves for water-holding capacities of 50 mm in the rooting zone were used for 'deserts', 75 mm for 'semideserts', 100 for 'deciduous selvas', 125 for 'subtropical matorrals', 150mm for 'selvas' and 250 mm for 'conifer forests'. Obviously, if an adequate soil map was available, the use of that map in conjunction with a vegetation map could provide an improvement to the method employed here to estimate soil moisture.
Vegetation ucticity and water balance
1849
A water deficit (WD) is present when water availability does not meet the vegetation evaporative demands. By definition it is the difference between monthly PE and AE (Stephenson 1990). On the other hand, a water. surplus (WS) is an excess of water in the environment, and is obtained when precipitation exceeds PE, minus the water that is retained in the soil. Precipitation (P) is the amount of water that is received as rainfall.
2.3. GIS irnplernerttariorz A cartographic model, which included several NDVI measures, a map of vegeta-
tion types derived from remotely sensed images (covering the whole country with a 16km pixel size), and the water balance database for 2214 weather stations in Mexico, was implemented in Arc/Info CIS (ESRI 1995) and used to explore the climate-vegetation relationships. The implementation of a CIS cartographic model permitted the evaluation of the relationship between NDVI measures and water balance variables at two scales of analysis: ( 1 ) the country scale; and (2) the ecoregions scale.
The classification of the country into different ecoregions (figure 2) was used as a stratification criterion for the two levels of analysis. A subset of 1162 weather stations was obtained by masking their location with six 'natural' ecoregions (occupying 69% of the Mexican landscape, not including irrigation and agriculture from figure 2). A data set was thus created that included the six annual water balance variables, annual integrated and seasonal NDVI measures, ecoregions, and the geographic location of weather stations used in the analysis. These data were then used to fit linear and non-linear models.
Two special advantages are gained when seasonal water balance variables are calculated with the aid of CIS. First, potential evapotranspiration can be adjusted by latitude and duration of daylight to produce adjusted potential evapotranspiration (ADPE). Secondly, soil moisture can be estimated from PE, using the parameters of soil moisture retention tables associated with the dominant vegetation within ecoregions (figure 1). The temporal variation of water balance can thus be associated with qualitative differences in vegetation types ('natural' vs. 'non-natural'), when using a cartographic model that includes such characteristics in vegetation types.
Although the water balance-vegetation relationships were statistically assessed on a point basis for each of the weather stations, the CIS implementation also allowed the point data to be interpolated using spherical kriging models in Arc/Info (ESRI 1995). This resulted in country-level maps for each of the six variables, and allowed the exploration of their scales and forms of variation. Maps of the predicted results of the regression models permitted a visual evaluation of the forms of variation over the country.
2.4. Statistical exploratory analysis Exploratory analysis was conducted on the data in order to establish potential
relationships. Possible climate-vegetation relationships were established based on graphical analysis (scattergrams) and by using Pearson's product-moment correlation coefficients evaluated at p =0.05.
2.5. Mode fitting Non-linear relationships were tested using the model proposed by Box et a/.
(1989). Even though the model could be fitted by transformed linear regression, the
F. Mora and L.R. Iversoi~
a Deserts
nSemideserts
Conifer Forest
Deciduous Selvas
Subtropical Deciduous Selvas
I~elvas
Irrigation
Agriculture
Figure 3
Wather Stations
Distribution of wcather stations within ccoregions in Mcxico. The classilication into ccoregions is described in Mora and lverson (1997).
non-linear approach was used in order lo prevent autocorrelation eiTects in the model parameters. The model has strong ~hcoreticalsupport, and its use permits a direct comparison between the parameters obtained here and those obtained by Box et (11. (1989). Box's model that describes the relationship between NDVI measures and water balance variables has the following form:
where iNDVI=integrated annual variation of NDVI, as produced via principal component analysis for the period of 1985-1989 (the iNDVI is scaled to a 0-1
range); 2 =asymptote or highest iNDVI value; b= slope or iNDVI rate of change as
a function of A E or P (WB units in m~n/yearI ) ; and WB=water balance variable.
Vegetation actiziity and water balance
1851
In the following models WB = AE when actual evapotranspiration (mmIyear-') is used; and WB = P when precipitation (mmlyear-') is used.
The model was fitted using a loss non-linear function, which minimizes the residual variance (sum of squared deviations) around the regression line, using a quasi-Newton minimization method (first order and second order derivative of the function).
Linear regression analysis was performed using the least squares method. In both non-linear and linear regression methods, the plot of observed vs. predicted values, normal and half-normal probability plots of residuals, and the proportion of variance explained were used to evaluate the model fit.
2.6. Multivariate regression analysis Multiple regression analysis was used to test the interaction between water
balance variables and spatial autocorrelation, in explaining the variation of both iNDVI and the sNDVI at the country scale. Subsequently, the combined effect of water balance variables over vegetation indicators included the water balance spatial structures. At the ecoregion scale, only environmental variation (without partialling out the spatial component) was tested in the regression models. The Durbin-Watson test, histograms, normal probability, and standard residuals vs. predicted plots were used in residual analysis. Tolerance and variance inflation factor (VIF) values were used in multicollinearity diagnostics for all regression models.
2.6.1. Partial correlation analysis At the country scale, stepwise multiple regression analyses was used to identify
four sources of iNDVI and sNDVI variation (a,b, c, ~ is;ee table 1). First, nine spatial variables that define the spatial component in the analysis were regressed on each water balance variable to determine their correspondent spatial structure. The nine spatial variables were obtained when a matrix of two-dimensional geographical co-ordinates (x =longitude and y =latitude) was completed by adding all terms for a cubic trend regression surface of the form:
This cubic form of geographic co-ordinates accounts not only for linear gradient patterns, but also complex features such as patches or gaps (Bocard et al. 1992).
Table 1. Sources of iNDVl and sNDVl variation.
Components of variation in NDVI-space
Equations and regression models
Non-spatial WB variation [a]
Spatially structured WB variation
Cbl iNDVI spatial variation independent
of WB [c]
+ WB (environmental) va3ance [a+ h]
Spatial structure [h c]
+ + Environmental-spatial combincd [a h c]
variation
Unexplained variance [dl
iNDVl = [AEres, PEres, Pres, SMres, WDres, WSres]
iNDVI = [AE, PE, P, SM, WD, WS]-[a]
iNDV1 = [ A E , PE, P, SIM, WD, WS]
iNDVl = [JY LONG, LAT)]
iNDV1 = [AE, PE, P, SIM, WD, WS, LONG, LAT]
[dl = 1-[a]- [b] -[c]
1852
F. M o m and L.R. Iuerson