Introduction

The single major function of an ecosystem is the maintenance of a long-term, balanced material cycle (i.e. C, N, P and hydrology cycles). In natural ecosystem, plant communities adjust to environment to maximize the use of resources while maintain this function. However, human-modified ecosystems fail to perform such functions, hence huge environment problems result, such as environment pollution and global warming. Through evolution, each member of a system adapts to the physical environment and to other organisms so as to achieve more efficient resource exploitation over time while still balancing the material cycle. It is the behaviors of the plant community (e.g. productivity, competition and evolution), which are determined by the characteristics of a plant itself and the physical environment, that ultimately support this important ecosystem function. To achieve a sustainable relationship between humans and nature, we need to understand how the interaction of the characteristics of biotic components and the physical environment affect the behavior of the plants in a natural ecosystem. In this project, I will exam only productivity, as it is the process we are most interested in.

Environmental factors affect the productivity of plants in different ways and can be recognized as slow variables and quick variables. Slow variables are those physical factors affecting plant growth that do not have seasonal variations and tend to be consistent over extended periods of time, decades at least. Quick variables are the climatic factors that have seasonal variations, such as precipitation and temperature. Plants respond to the variation of quick variables during the year. However, at different locations, plants respond to quick variables in different ways due to the difference in slow variables. For example, where soil is thick, plants may have a slow response to reduced precipitation as the large soil water storage keeps supplying water to plants, while where soil is thin, the growth of plants may be reduced more quickly with reduced precipitation because of the low storage of soil water.

The Serengeti ecosystem is perhaps the ecosystem that is most close to a natural state, and covers a wide range of geological, biological and climatic variations. Precipitation is the major constraint factor affecting the plant community there. Remotely sensed data provide continuous and accurate information of the biosphere with wide regional coverage. The overall objective of this project is to use remotely sensed data and a geographic information system (GIS) to characterize the temporal and spatial variations of precipitation and primary productivity, as well as spatial variations of physical factors and vegetation types in order to understand how productivity changes with precipitation at different locations and how physical factors and vegetation type affects the way by which productivity changes with precipitation.

The specific objectives of this study are to: 1) describe the spatial variation of the relationship between precipitation (and temperature) and productivity; 2) identify the factors, such as soil properties, topography, vegetation and disturbance (fire and grazing), that account for the spatial variation of this relationship and 3) to determine if the 8kmx8km low resolution images are sufficient to detect the spatial variation of the precipitation-productivity relationship and the effects of soil, topography and vegetation on that relationship.

Method

I use monthly precipitation and NDVI to generate a regression model for the correlation between monthly precipitation and NDVI for each grid. Then, I apply geographically weighted regression (GWR) analysis to each parameter and regression correlation of the precipitation ~ NDVI regression model as a dependent variable. Finally, I use soil properties, topography, vegetation cover, animal density and fire frequency as independent variables to identify the major factors that affect each regression parameter as well as the spatial variation of the significance and the way that each independent variable affects the parameters of the regression model.

Study area

The Serengeti-Mare ecosystem (map 1), an area of about 25000 km² on the board of Tanzania and Kenya, east Africa (34⁰ to 36⁰ E, 1⁰ to 3⁰ 30’ S), is functionally defined by the seasonal migration of 1.2 million wildebeest and is comprised by Serengeti National park and string of game reserve areas which buffer the core protected area from areas of unrestricted land use and intense human settlement. The ecosystem itself is defined by two major habitat types, short grass plains and the savanna woodlands.

Map 1. The Serengeti ecosystem and its major landscape features

The climate of the Serengeti ecosystem is both varied and varying; varied, because it ranges from true grasslands (<550 mm mean annual precipitation) in the southeast to broadleaf miombo woodlands in the northern extension (precip <900mm) over a relatively short spatial scale (200 km) (Map 1). Spatially, landform influences the local weather system by producing a rainfall gradient via two landscape features: the Crater highlands and Meru-Kilimanjaro mountain range to the east, and Lake Victoria to the west. Prevailing winds from the east carry moisture originating from the Indian Ocean and release it in the form of precipitation as they cross the highlands. In contrast, winds originating from the west carry moisture inland from Lake Victoria, counteracting this rain shadow effect from the east, leading to the rainfall gradient. Precipitation is also varying because the climate exhibits temporal variability, particularly with regard to rainfall. Inter-annual rainfall variability in East Africa, the El Niño/Southern Oscillation (ENSO), is one of the more important controlling factors (Janowiak, 1988; Ropelewski and Halpert, 1987; 1989; 1996).

The Serengeti is part of the high interior plateau of East Africa. It slopes from its highest part (1,850 01m) on the eastern plains near the Gol Mountains toward Speke Gulf (9,2001m). West of a line going through Seronera, the underlying geology consists of very old Precambrian (2500 m) volcanic rock and banded ironstone. Soils on the eastern plains are highly saline and alkaline, and are also shallow as a result of their recent volcanic origins. The soils become progressively deeper and less alkaline toward the northwestern plains and into the woodlands. The soil catena, which is the gradient of soil types from ridge top to drainage sump, is characterized by shallow, sandy, well-drained soil at the top, changing to deep, silty, poorly drained soil at the bottom (Sinclair, 1995).

Description of the relationship between precipitation and productivity

There is a strong correlation between the normalized difference vegetation index (NDVI) and the leaf area index, which is used to calculate productivity. In this study, I use monthly NDVI of a 8kmx8km resolution, from 2000 to 2006, to represent the temporal variations of productivity. Monthly precipitation maps in 1kmx1km resolution for the same period are created using software PPTmap4 based on station measurement. These precipitation data sets are rescaled by mean to 8kmx8km grids; then, for each 8kmx8km grid, the time series of monthly precipitation and NDVI are plotted, from which I identify a one month lag of the response of NDVI to precipitation. I test different regression models including linear regression, polynomial regressions, exponential and logarithm regressions for each grid using the previous month’s precipitation and the current month’s NDVI. Then I choose the one that has the overall high AIC value and is also more ecologically meaningful to describe the relationship between precipitation and productivity. Then I create a raster layer for each parameter, as well for the regression correlation (R²). The spatial variation of the parameters and R² represent the spatial variation of the response of productivity to annual variations of precipitation.

Determining the factors that affect the PPT~NDVI correlation using GWR

I create a topographic convergence index (TCI) using a 30mx30m digital elevation model, and then calculate the average TCI for each 8kmx8km grid. The Africover vegetation map is used to characterize the dominant vegetation at each grid. The fire frequency map (2000 – 2006, 10kmx10km) and animal density (number of animals per month) calculated from a one-year flight record (Dec 1970 – Nov 1971) are used to describe the disturbance. I use soil water holding capacity (WHC) to represent the impact of soil on the PPT~NDVI correlation, as this soil property determines the capacity of the soil to store water, and is hence the one factor with the greatest impact on PPT~NDVI correlation among those soil properties.

Next, I run the geographically weighted regression model (GWR) with each individual independent variable and each parameter of the PPT~NDVI regression model. If the overall local R² of the GWR is larger than 0.15, I analyze each individual independent variable against the local R² and the slope of the GWR output of the given independent variable and the parameter of the PPT~NDVI regression to identify the factors that can explain the spatial variation of the local R²s and the slopes.

Results and discussion

1. Regression model of the correlation between monthly precipitation and NDVI (PPT~NDVI regression model)

Overall, the AIC values are the highest of quadratic models for all the grids. Also, the way that the regression equation is written represents the mechanism by which precipitation affects productivity. Therefore, I choose the quadratic regression model to describe the correlation between monthly precipitation and NDVI. I rewrite the equation into the following format:

NDVI_(x,y) = a_(x,y) + b_(x,y)*PPT_(x,y)* (c_(x,y) – PPT_(x,y))

a(x,y), b(x,y) and c(x,y) are the parameters of the regression model at location (x,y); PPT(x,y) is the previous month’s precipitation at location (x,y). In the rest of the paper, I refer to the quadratic regression parameters as ‘a’, ‘b’ and ‘c’, and to the regression correlation as ‘R²’. By rewriting the equation in this way, I am able to identify the biological meaning of the quadratic regression model.

The biological meaning of parameter ‘a’

The parameter ‘a’ is the minimum biomass on the ground over the year, and it is affected by vegetation type and amount of precipitation. For example, if there is no growth (e.g. when it is very dry), grass will die off, but trees still has roots and branches above the ground; therefore, ‘a’ will be lower for grass than trees. Also, if two areas are both covered by trees, one area is much drier than the other area, and the minimum productivity at a dry area will be lower than in a wet area as the minimum available water that can support the amount of biomass is lower in dry areas.

The biological meaning of b*PPT*(c-PPT)

This part of the equation represents how precipitation affects the growth of plants. There are both positive and negative effects associated with a given amount of water on the productivity of plants. On one hand, water as a resource directly supports the growth of plants (positive effect). The ‘b*PPT’ then represents this positive force. On the other hand, it is not just water alone that supports plant growth. Plant growth is supported by other resources, such as nutrients, and is also constrained by environment stresses such as disturbances. The negative effect associated with a given amount of available water comes from the constraint of other factors. We know plants consume resources at given ration, known as optimal foraging ratio. When the relative proportion of a given resource is below this ratio, it becomes the major constraint of productivity. Assuming other resources remain constant, there will be a maximum value of available water at which water is no longer the constraining factor, and furthermore, over that point, extra water that cannot be absorbed by plants can cause water logging and reduce plant growth. How great the negative force may be is determined by how close the availability of water is to this maximum point. ‘c – PPT’ represents this negative force, and it is the positive and negative effects together that determine the productivity of plants.

The multiple of ‘b*PPT’ and ‘c-PPT’ represents such a combination of the positive and negative effects, and how the combined impact changes with the amount of available water. When available water is low, the positive effect has a more significant effect on plant growth, while when increasing available water, the negative effect become more significant. In addition, ‘c/2’ is that maximum point at which the negative effect becomes more significant than the positive effect associated with available water.

Map 2 shows the spatial variation of the parameters and regression correlation of the quadratic regression model. What factors responses are and how they affect such variation are discussed in the next section – “The results of GWR analysis.”

Map 2a. R^2 of quadratic regression	Map 2b. parameter ‘a’ of quadratic regression
Map 2c. parameter ‘b’ of quadratic regression	Map 2d. parameter ‘c’ of quadratic regression

2. The results of GWR analysis

When running GWR with individual independent variables, the local R² indicates how significant the impact of the independent variable is on the dependent variable, and the slope indicates the way by which the independent variable impacts the dependent variable. In the rest of the paper, I mention the results from GWR analysis in such a way: local R² and/or slope of GWR (independent variable ~ dependent variable). The following are the outcomes of GWR analysis. Because parameter ‘b’ is assumed to be determined by the type of the species of the plant, it is not discussed here.

Regression correlation (R²) of the PPT~NDVI regression model

Through GWR analysis, I found that annual precipitation, topographical convergence index (TCI) and soil water holding capacity (WHC) have impacts on the ‘R²’ of PPT~NDVI quadratic regression correlation.

	Annual PPT	TCI	WHC
Local R^2 of GWR	0.12 – 0.93	0.064 – 0.92	0.040 – 0.91
Table 1. Local R^2 of GWR analysis for ‘R^2’ of quadratic regression

Annual precipitation is identified as the most significant factor that impacts the ‘R²’ of the quadratic regression. However, the ‘R²’ changes with annual precipitation in different ways according to the amount of annual precipitation. For example, the ‘R²’ is low when annual precipitation is either too low or too high (Graph 1). Generally, the ‘R²’ increases with annual precipitation where annual precipitation is low (blue area in Graph 3), and decreases with annual precipitation where annual precipitation is high (red area in Graph 3). Graph 3 is the slope of GWR (annual precipitation ~ ‘R²’). The positive value of the slope indicates that the ‘R²’ increases with annual precipitation at that location, while the negative value indicates that the ‘R²’ decreases with annual precipitation. We can see that overall, the annual precipitation and ‘R²’ are negatively correlated in the northern area and positively associated in the south.

Graph 1. Impact of annual precipitation on the R^2 of PPT~NDVI quadratic regression (the color of the dots correspond to the color of the area in Graph 2)
Graph 2. Spatial variation of annual precipitation	Graph 3. The slope of GWR (annual precipitation ~ ‘R^2’)

In the south, where annual precipitation is low, during the dry season there will be a great soil water deficit. Therefore, increased precipitation after the dry season will first recharge the soil water, and a small amount of that precipitation will be used by plants, but later on, when the soil water pool recovers, most of the precipitation will then be used by plants. Thus, although the area receives the same amount of precipitation, at different times, according to the previous soil moisture content, the precipitation can result in a great difference in plant growth. Towards the northwest, increasing annual precipitation causes less and less soil water deficits during the dry season; thus, less precipitation is needed to recharge the soil water pool after the dry season, and consequently, a greater proportion of precipitation is used by plants, which ultimately results in a high correlation between monthly precipitation and NDVI. Thus, the strength of the correlation between precipitation and NDVI is affected by previous precipitation and soil moisture conditions.

In the northern area, the annual precipitation is high, and two mechanisms may result in a low R². First, when precipitation is high, runoff could happen. This loss of received precipitation through runoff results in a relatively small proportion of that precipitation being used by plants. Second, while water is abundant, the constraints of other factors on plants growth are more significant. The spatial variation of these factors results in the low correlation between monthly precipitation and NDVI.

In the areas in between, where the precipitation is neither too high nor too low, most of the precipitation received is used to support plant growth, so the ‘R²’ is maximized.

Graph 4. The slope of GWR (TCI ~ ‘R^2’)

Graph 5. The slope of GWR (WHC ~ ‘R^2’)

TCI is used to measure soil moisture, and high soil moisture is associated with high TCI while low soil moisture is associated with low TCI. At the western corridor and eastern side, the slopes of GWR (TCI~R²) are negative, which means the ‘R²’ decreases with increasing soil moisture in those areas, and at the Serengeti plain and northern part of the park, the slopes of GWR (TCI~R²) are positive, which means the ‘R²’ increases with increasing soil moisture in these locations (Graph 4).

WHC measures the capacity of soil to hold water that is readily available for uptake by plants (Graph 5). In most areas of the park, WHC does not impact the ‘R²’ (green areas). In the western corridor, the center of the plain and the northeast and southeast boundaries of the park, WHC has a negative impact on the ‘R²’ (Graph 5). This means if the soil can hold more water, there is less correlation between precipitation and NDVI.

Parameter ‘a’ of the PPT~NDVI regression model

The GWR analysis identifies that the annual precipitation and %tree cover are the factors having a significant impact on the parameter ‘a.’ Graph 6 shows the spatial variation of the greatness of the impact of annual precipitation and % tree cover on the constant above-ground biomass ‘a’, as well the way they affect it. The significance of the impact of mean annual precipitation and % tree cover varies in spaces in different ways. The map below and to the left is the spatial variation of the local R² of GWR for mean annual precipitation and ‘a,’ while the right map below is the spatial variation of the local R² of GWR for % tree cover and ‘a.’ Both annual precipitation and % tree cover have a greater impact on ‘a’ in the northern area. Annual precipitation also has a significant impact on ‘a’ at the west-east boundary of the park.

1a. Local R^2 of GWR for mean annual precipitation and parameter ‘a’	1b. Local R2 of GWR for % tree cover and parameter ‘a’
1c. Slope of GWR (annual precipitation ~ ‘a’)		1d. Slope of GWR (% tree cover ~ ‘a’)
Graph 6. The spatial variation of the significance of the impact and means of impact of annual precipitation and % tree cover on parameter ‘a.’

The parameter ‘a’ increases with both mean annual precipitation and % tree cover, but in different ways. The parameter ‘a’ has a slight increase with annual precipitation when annual precipitation is below 70cm, then increases much faster with annual precipitation above 70cm. In contrast, parameter ‘a’ shows an overall increasing trend with % tree cover.

Fig1. Impact of annual precipitation on parameter ‘a’

Fig2. Impact of % tree cover on parameter ‘a’

Soil nitrogen and % herb cover also impact the local R² of GWR for ‘a,’ annual precipitation and % tree cover within the park, while soil nitrogen and soil water holding capacity impact the local R² of GWR for ‘a’ and % tree cover. Local R²s of both GWR (annual precipitation ~ ‘a’) and GWR (% tree cover ~ ‘a’) decrease with soil nitrogen (Fig 3 and 4). This indicates that increasing soil nitrogen reduces the significance of the impact of annual precipitation and % tree cover on parameter ‘a.’ % herb cover decreases the significance of the impact of annual precipitation on parameter ‘a.’ Soil water holding capacity (WHC) also has a negative impact on the significance of the correlation between % tree cover and parameter ‘a.’

When the whole area is included, no factor is found that accounts for the spatial variation of the local R². This may indicate that without human impact, the plant community tends to adapt to physical environment factors.

Fig 3. Impact of soil nitrogen on local R^2 of GWR (annual precipitation ~ ‘ a’) of natural land	Fig 4. Impact of soil nitrogen on local R^2 of GWR (%tree cover ~ ‘a’) of naural land
Fig 5. Impact of % herb on the local R^2 of GWR (annual precipitation ~ ‘a’) of natural land	Fig 6. Impact of soil water holding capacity on local R^2 of GWR (annual precipitation ~ ‘a’)

Parameter ‘c’ of the PPT~NDVI regression model

Graph 7. Spatial distribution of parameter ‘c’ (left) and % tree cover (right)

The total number of animals, soil nitrogen, fire frequency and % tree cover are supposed to affect the parameter ‘c.’ There is a spatial pattern of the parameter ‘c,’ but none of these factors has significant local R²s of GWR analysis.

By comparing the spatial distribution of parameter ‘c’ with the spatial distribution of the above factors, I found that the spatial pattern of ‘c’ is somehow correlated to % tree cover (Graph 7). The low local R² values of GWR may be due to the non-linear correlation between % tree cover and parameter ‘c,’ and the poor spatial resolution of soil nitrogen and fire frequency data may be the reason for low local R²s of these two factors. Furthermore, soil nitrogen also varies throughout the year, and the soil nitrogen data was taken only once. This may also explain why there is no correlation found between soil nitrogen and parameter ‘c.’

Conclusion

In conclusion, using 8km x 8km resolution data I am able to identify the spatial pattern of the ‘R²’ and regression parameters of the quadratic regression model of the correlation between monthly precipitation and NDVI. Annual precipitation and vegetation type are the two factors identified as having the greatest impact on the ‘R²’ and parameter ‘a’ of the correlation between monthly precipitation and NDVI over the whole region. Soil nitrogen, TCI and WHC are identified to impact ‘R²’ and parameter ‘a,’ but only within the park. Parameter ‘c’ does show a spatial pattern, but no factors can explain this spatial pattern based on GWR analysis. Furthermore, temperature, one of the most important factors that determine plant growth, is not included here because of the lack of good spatial data. Thus, finer spatial resolution data and the temporal variations of temperature and soil nutrient contents will be required to fully explore the impact of environmental factors on the response of NDVI to precipitation.

Reference

Janowiak, J. 1988: An investigation of Interannual Rainfall Variability in Africa. J. Climate, 1, 240-255.

Ropelewski, C.F. and M.S. Halpert, 1987. Global and regional scale precipitation patterns associated with El Niño/Southern Oscillation, Mon. Wea. Rev. 115:1606-1626.

Ropelewski, C.F. and M.S. Halpert, 1989. Precipitation patterns associated with high index phase of Southern Oscillation, J. Climate, 2:268-284.

Ropelewski, C. F., and M. S. Halpert, 1996: Quantifying Southern Oscillation–precipitation relationships. J. Climate,9, 1043–1059.

Sinclair A.R.E., 1995, Serengeti II: Dynamics, Management, and Conservation of an Ecosystem