Spatial Uncertainty Handling in Lake Extent Trend Analysis Using Remote Sensing and GIS Tools: The Case of Lake Naivasha ()
1. Introduction
Mapping the surface area of spatial objects on the surface of the Earth requires the handling of spatial uncertainty. This spatial uncertainty may originate from the definition of the spatial object within a class, the type of boundary (crisp or fuzzy), the accuracy with which it can be detected and the time and scale of observation. In studies of trends, such as change of size of glaciers as a result of climate change, or the shrinking of a lake due to increasing water extraction for irrigation, it is important to include the spatial distribution of uncertainty regarding the mapped feature for each date [1]. If both spatial and temporal uncertainties are known, a more reliable assessment of the trend can be made.
This paper presents an approach to include uncertainty of the mapped feature into multi-temporal analysis. The approach uses membership ml to the class “lake” as a measure of certainty for that class. The underlying assumption is that the combined uncertainty as a result of class definition, mixed pixels, gradual transitions, sensor characteristics and the classification is directly reflected in a decrease in membership for the class of interest. The uncertainty for lake, ul, is defined as in Equations (1) and (2) below
(1)
for all memberships mi for class i in a pixel and
and 
(2)
To demonstrate the approach, a series of Landsat 7 ETM+ images of Lake Naivasha, Kenya (Table 1) was used. Over the past decade, water levels and surface area of the lake have dropped, presumably because of larger water consumption by the people and agricultural activities along the shore as well as climatic changes [2]. The North-western part of the lake is surrounded by steep slopes, providing a relatively crisp boundary. In other areas the boundaries of the lake are gradual and include various types of marshes. Whether the marshes belong to the lake or the land is a matter of definition, as definitions depend on the type of vegetation and the length of time the marsh is actually flooded each year. Added vagueness comes from green algae and from free floating vegetation, which moves around the lake depending on the wind direction. The algae and floating vegetation increase the spectral confusion between the lake area and the surrounding vegetation classes [1].
2. Methods
2.1. Study Area Description
Lake Naivasha in Kenya has been used in this study (Figure 1). The lake is located at approximately 00˚45'00''S, 36˚21'00''E. It is situated in the West of Naivasha town in Kakuru District within Rift Valley Province. It is a shallow (mean depth of 6 m, endorheic, freshwater lake in warm and semiarid conditions in the eastern Rift Valley of Kenya, lying within an enclosed basin at an altitude of 1886 m above mean sea level with surface area fluctuating between 100 and 150 km2. It is world famous for its high biodiversity, especially for birds (more than 350 bird species) [3]. In the year 1995, Lake Naivasha was declared as Ramsar site (Wetland of International Importance) because of its diverse acquatic and terrestrial ecosystems.
The climate of this wetland area is hot and dry with a high potential evaporation exceeding the rainfall by around three times [4]. The area receives rainfall between April to June and October to December each year. The
Table 1. Landsat ETM+ images of Lake Naivasha.
Figure 1. Location of study area and corresponding Landsat7 ETM+ image acquired on the 15 October 2002.
rest of the year is dry season.
The lake system has fringing swamps dominated by papyrus and submerged vegetation and an attendant riverine floodplain with a delta into the lake. These swamps vary in size especially during the rainy season resulting into uncertainty in lake/water boundary. In addition, there are acquatic plants (water hyacinth) that live and reproduce freely on the surface of fresh water or can be anchored in mud. There are also other submerged vegetation species. The presence of these types of vegetation makes the delineation of water/land boundary difficult especially when they are submerged due to water level rise.
2.2. Spatial and Temporal Quality of Datasets Used
In this study, time series images from ETM+ were used. The selection was based on free availability of these images and prior knowledge of the study area via literature. Since the study area lies within equatorial zone, where cloud cover is a serious problem for remote sensing studies, images with less than 2% cloud cover were used. In most of these images, the lake was cloud free. Table 1 shows a combination of images used in this study
2.3. Characteristics of Data Used
ETM+ is an imaging instrument onboard NASA’s Landsat7 satellite launched in April 1999. It collects information in eight bands of the electromagnetic spectrum. Seven of these bands are reflective while band 6 is emissive. The sensor has large spectral coverage within the reflective and infrared portion of the spectrum. Table 2 gives a summary of spectral, spatial and radiometric characteristics of ETM+ sensor while Table 3 describes the general characteristics of the sensor/platform system.
2.4. Image Analysis and Understanding
Object-oriented and fuzzy approaches to mapping are now increasingly applied to change detection and monitoring based on remotely sensed images [5-7]. In this approach, we firstly created image objects through seg-
Table 2. 7 Spectral bands of ETM+ (Reflective).
Table 3. Sensor/platform characteristics: ETM+.
mentation and object-based classification. While we used a multi-resolution segmentation algorithm to transform a discrete image into homogeneous regions whose size was equal or greater than the spatial resolution of the sensor, the fuzzy object rule-based classification was used to assign the class labels. The multi-resolution segmentation algorithm applies the principle of minimizing variability among pixel values contained in the scale parameter selected. Different parameters were tested. The starting parameter was the spatial resolution of the ETM+ sensor which resulted into 166 image objects. Changing the scale parameter to 60 resulted into 153 image objects. The resulting image objects with this parameter were larger compared to the 30 parameter. The following sequence of scale parameters was tested: 30, 60, 90, 120, 150, 180, 210 and 240. Figure 2 shows the trend of image objects for the applied scale parameters in that sequence. Apart from the decrease in number of image objects as a result of increase in scale parameter, the total size of the lake changed as well. This implies that seasonal variations in water levels influence the estimation of the lake extent at point in time.
Figure 2 shows that at the pixel level, the lake extent is more uncertain. This is due to limitation of sensor spatial and spectral resolution in space, ambiguity due to the point spread function (PSF) at pixel during the sensor re-