VOXEL-BASED ANALYSIS AND VISUALIZATION OF RAINFALL DATA

Shalini Venkataraman Staff Researcher, Scientific Visualization Center for Computation and Technology Louisiana State University [email protected]

Kwabena O. Asante, PhD Environmental Scientist SAIC USGS EROS 47914 252nd Street Sioux Falls, SD 57198 [email protected]

ABSTRACT

The remote sensing of hydrologic variables such as rainfall, soil moisture and streamflow is becoming increasingly more important as we strive to improve our understanding of the earth’s climate. Because these variables change more rapidly than other land cover characteristics, a high frequency of image acquisition is required. This in turn results in a large volume of data that must be compared to detect changes and trends in moisture flux. Traditional remote sensing tools are not well suited to this analysis because of the large number of scenes involved. In this paper, we explore the use of 3D geovisualization techniques to analyze a large time series of satellite imagery. We take advantage of the 3 dimensional voxel data structure to transform the image collection in a space-time cube. We employ 3D voxel-based visualization methods also known as volume visualization to perform feature analysis, change detection and segmentation of this large spatio-temporal dataset. We demonstrate that the use of the space- time cube offers even those hydrometeorologists that prefer to look at 2D maps and graphs with improved access to the time series data through software tools for dynamic graphing and slicing. In a practical application, we use the space-time cube to present the evolution of the annual rainfall cycle over Africa as a single visual image.

INTRODUCTION

Hydrometeorologists involved in the study of hydrologic variables such as rainfall, soil moisture and streamflow have traditionally relied on point measurements to characterize these parameters. Two-dimensional graphs have remained the main tools for characterizing the temporal variations of these parameters, while surface fitting techniques such as kriging, spline and inverse distance weight interpolation have been relied on to produce spatially uniform representations of the parameters. Under the operational geostationary weather satellite systems GOES and Meteosat, hydrometeorological events are monitored on a near real time basis. The primary objective of these operational meteorological systems is the provision of timely information to support early warning and emergency operations. Accuracy and internal consistency are often sacrificed in favor of timeliness of data delivery. As a result, little attention has been paid to temporal patterns in the datasets. The Tropical Rainfall Measurement Mission (TRMM) marked the first research mission dedicated to the remote sensing of moisture fluxes. The Gravity Recovery and Climate Experiment (GRACE), the Global Precipitation Measurement (GPM) mission, the soil moisture mission (HYDROS) and the proposed Water Elevation Recovery (WaTER) mission are all expected to produce internally consistent time series datasets from which the characterization of temporal patterns will assume greater importance. Existing analytical tools used within the hydrologic sciences are not well suited to handling such time series analysis. The use of Geographic Information System (GIS) and remote sensing software for analyzing spatially distributed datasets is just beginning to become routine within the field, and most hydrologists still rely on spreadsheets for time series analysis. GIS software has evolved out of the work of the geographic science community and is therefore well equipped for spatial analysis tasks but not temporal analysis. Time series analysis of land cover change occurring over periods of several years remains the main thrust in this field. Moisture fluxes,

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota on the other hand evolve at time scales on the order of several minutes to days, resulting in a huge volume of data with rapidly changing signatures which pose a major challenge to existing GIS and remote sensing software. By contrast, the field of scientific visualization has always dealt with large datasets mostly occurring in two fields: imaging and computational science. 3D imaging devices continue to increase the resolution of their sampled volumes with the current generation approaching a giga-voxel. Similarly, computational science such as fluid dynamics continues to increase the mesh resolution for large scale simulations thereby increasing the size of data to be visualized. This has led to the development of efficient algorithms to read, analyze and visualize very large datasets in real-time. Specifically, a class of techniques known as volume visualization has been proven very effective to understand 3D data as is without resorting to intermediate polygonal representation. Within the earth sciences, 3D visualization tools have long been employed in the geological science to visualize subsurface phenomena such as reservoir formations and aquifers. These technologies have recently been adopted by the meteorological community for studying the vertical profile of atmospheric parameters such as temperature and atmospheric moisture. However, there has been very little work in the application of volume visualization techniques for spatio-temporal analysis of time-varying maps. In this paper, we present a novel application of volume visualization algorithms to analyze time-varying satellite precipitation maps. We “stack” the time varying 2D images to produce a 3D volume known as space-time cube. This data cube is then rendered to a 2D image using a volume rendering technique known as raycasting. This technique allows us to display spatial dynamics as well as changes occurring over time, simultaneously, and to perform data analysis functions on the entire data cube. We present a background study of current methods in spatio- temporal analysis and representation. Subsequently, we describe the volume rendering algorithm used to load and display data in the space-time cube. This is followed a presentation of various tools available for manipulating and analyzing the space-time cube. We conclude with a sample application visualizing the annual rainfall cycle over Africa.

BACKGROUND WORK

Time series of hydrometeorological events can be viewed from two perspectives. Events can be viewed as they evolve through a fixed frame of reference, referred to as the Eularian view of motion. It is the most commonly used to monitor the progress of an event as it moves through a fixed Cartesian space or to study the passage of events over a fixed location. Examples of events viewed from the Eularian perspective include the distribution of rainfall events at a rain gauge or a trace of the track of a cyclone on a geographic map. Conversely, the Lagrangian view of motion studies the evolution of the event through a frame of reference that moves with the event. The use of a dynamic frame of reference shifts the focus away from tracking the location of the event to tracking the relative position and condition of particles within the moving event. In hydrometeorology, the Lagrangian view of motion is most commonly used to study the condition of rainfall and wind fields around a cyclone or dispersion of chemical plumes in a fluid. By combining a time series of spatially distributed grids in a space-time cube, we enable the user to track the evolution of events in time both in terms of the physical location of the event and the relative condition of particles within the moving event. The space-time cube can consequently be viewed as combining the Eularian and Lagrangian perspective of an event into a single picture. Within hydrometeorology, the most common approach for combining time and space is the Hovmuller diagram. The diagram is a plot showing the variations in intensity of a parameter with changing latitude (or longitude) on one axis and time on the other. It is most commonly used to study climate phenomena that move north and south during the course of a year. Combining time and space in this manner provides the some insight into events that move orthogonally along the Cartesian axes. However, Hovmuller diagrams are of limited utility for events that move at oblique angles to the lines of latitude and longitude, and they do not provide much information of the shape of the event along its path of motion. Modern Geographic Information Systems (GIS) provide rich facilities to interact and visualize data on maps in two or even three dimensions. In GIS, the temporal data is commonly visualized by means of animations, which represent changes in the data. For example, the scientific visualization studio at the NASA Goddard Space Flight Center uses image animations to display TRMM rainfall maps that are generated several times a day. By using animations, the evolution of time series data produced at a high temporal frequency can be conveyed efficiently. However, detailed data analysis is hardly possible when using animations, and users are required to rely on their memory of the previous scenes of the animation to construct a mental image of the evolution of the event. What is required is a medium that enables all slices of the animation to be frozen in a three dimensional space.

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota According to Hedley (1999), Hagerstrand first introduced the space-time cube during the late 1960’s. In its basic appearance, the cube has on its base a representation of the geography (along the x- and y-axis), while the cube’s height represents time (z-axis). However, when the concept was introduced the options to create the graphics were limited to manual methods and the user could only experience one view created by the draftperson. Today, software and graphics have been developed where it is possible to view, manipulate and query this data in real-time. Kraak (2003) explains this approach from a geovisualization perspective specifically in analysis of multi-variate and multi-resolution discrete event data such as path of buses in time using GPS. In this paper, we extend the space-time cube concept to represent time-varying 2D images of daily and monthly precipitation data. We use state-of-art rendering techniques in scientific visualization of volumes to interact, display and analyze the data in the cube. Visualization deals with the use of graphical models to represent data, coupled with suitable interaction operations that support an active user exploration of data representations. In particular, the field of scientific visualization has given the word “visualization” an enhanced meaning (McCormick, 1987). Visualization refers to specific ways in which modern computer technology can be used to make data visible in real-time in order to understand data. Visualization techniques can greatly enhance knowledge discovery processes involving geo- referenced data, and a new field called geovisualization has evolved to study ways of displaying geographic information with spatial and temporal attributes (MacEachren, 2001). In particular, volume visualization plays a great role in exposing structures in 3D datasets that can consequently be explored using before conventional statistical methods or data mining techniques. Volume visualization, once confined to the realm of supercomputing, is now widely implemented on commodity hardware. Examples of volume visualization include Display 3- Dimensional (D3D) (McCaslin, 2000) developed at the NOAA Forecast Systems Laboratory (FSL). D3D includes tools for producing isosurfaces and cross-sections from the 3D data. It has also being used to view 3D data of atmospheric fields such as air trajectories, wind velocity and temperature in at different heights in the atmosphere. Another example of geovisualization software is GeoVista Studio from Pennsylvania State Unversity (Takatsuka, 2002) that uses dynamically linked visual representations such as maps, scatterplot matrices and parallel coordinate visualization for exploration and analysis.

OVERVIEW OF VOLUME VISUALIZATION

Volume visualization is concerned with the representation, manipulation and display of volumetric data, typically represented by a 3D grid of scalar values also known as voxels. Volume rendering is the process of projecting this 3D grid onto a 2D image plane to gain understanding of the structure contained within the data. The raycasting algorithm computes the light transport by casting rays into the volume along the viewing direction and sampling the voxels along the path at fixed intervals. The final pixel in the image is the integration of attenuated colors (light emission) and extinction coefficients (light absorption) for the samples along each viewing ray. The contribution of each volume sample or voxel to the final image is explicitly computed, and the net effect is aggregated and presented in the final display. As shown in Figure 1, the number of samples along the rays directly affects the image quality.

Figure 1. A voxel cube showing the application of optical model for viewing objects in three dimensions. The number of samples are increased to show progression in image quality. Image reproduced from Siggraph 2002 course notes (www.siggraph.org)

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota The voxel value at any sample point is mapped to physical quantities such as color and transparency that define the light emission and absorption. A transfer function defines the exact mapping from scalar voxel values to color and transparency and can be changed at run-time to reveal or occlude voxels. Analytically, the volume rendering integral, I is approximated by

where n is the number of samples, i and Ci are the transparency and color values respectively at sample point i. As shown in Figure 2, the advantage gained by a volumetric representation is that objects have information inside them. This allows us to render amorphous phenomena or structures that are impossible to identify geometrically. Traditionally, volume rendering has been used in medical reconstruction where the 2D cross sectional images would be stacked on top of each other to form a volume dataset. Our application visualizes the GOES-based satellite rainfall estimates (RFE) from NOAA’s Climate Prediction Center (Xie, 1997). The NOAA RFE data are converted to grayscale tiff images using the GIS software, ArcView. Each data scene had a resolution of 874x919 giving us approximately 300 million voxels for a year of daily rainfall data. For visualization, the time-varying stacks of the gray scale tiff images are loaded and stacked into Amira (amira.zib.de) and Vol-a-Tile (Venkataraman, 2004). Amira is a commercial visualization software with powerful analytical, feature extraction and segmentation functionalities that is widely used in imaging applications. Vol-a-tile is an open source volume visualizer written in C++ and OpenGL. It has in-built capabilities of integrating color and transparency through voxel cells. Both these software use hardware accelerated 3D texture mapping for improved interactive rendering rates.

Stacks of 2D Daily Rainfall Values 3D Space-time cube

Figure 2. An example of 3D image composition from component rainfall data slices

DISPLAY, MANIPULATION AND ANALYSIS

Application of Transfer Functions For display purposes, all materials present in the dataset need to have visual properties such as color and opacity (or translucency) associated with them. The map used to compute visual properties from a material type is called a transfer function. The color table is used to map data values to meaningful colors. The opacity table is used to expose the part of the volume most interesting to the user and to make transparent the uninteresting parts. Each element in a volume contributes both color and opacity and the final pixel value is determined as the sum of all the values. The setting of the color and opacity tables can be a time consuming process involving several trial-and-error iterations and subjective judgments of what parameters need to be altered. The user may use the range and

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota distribution of data values within the data cube as a guide in setting up the transfer functions. The tables are then modified interactively until a satisfactory image is obtained. The data cube can be rendered to the screen in a variety of ways. A common approach is to sample the dataset along rays at increasing distances from the viewer, and to blend colors to derive pixel intensities. The color at each sample point is acquired by extracting the rainfall value from the dataset, then looking up the color of that value using the transfer function. Our approach exploits commodity graphics hardware to implement this process. Thus, the time it consumes decreases considerably compared to a software implementation resulting in interactive frame rates. Transfer functions are fundamental to direct volume rendering because their role is essentially to make the data visible. By assigning optical properties like color and opacity to the voxel data, the volume can be rendered with traditional computer graphics methods. Good transfer functions reveal important structures in the data without obscuring them with unimportant regions. By altering the transfer functions, different images of the same dataset can be achieved. This is especially useful because some images might convey more information than others. Although polygonal surface extraction techniques such as triangulation can be used, the volume rendered image has the advantage of allowing wispy features which would otherwise be too faint to be recognized by the surface extraction algorithm to be displayed if the net effect of such features is significant.

Figure 3. A space-time cube of daily rainfall values across Africa during the year 2000.

The image in Figure 3 shows the spatio-temporal distribution of daily rainfall totals across Africa during the year 2000. Different magnitudes of storms are emphasized by adjusting the color map. Storms resulting in daily rainfall values of between 20 and 30 mm per day are shown as shades of green while storms with greater than 30 mm/day of rainfall are shown in red. The use of this color map coupled with low transparency allows the viewer to see the series of cyclonic systems that dumped huge quantities of rainfall over southern Africa resulting in record floods (Christie and Hanlon, 2001).

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota

Figure 4. Views of a space-time cube of rainfall using the same color map with different transparencies. At higher transparencies, only storms with higher rainfall values are visible because they tend to be more persistent.

The two images shown in Figure 4 are integrated views of rainfall in 2000 as seen from southern Africa with January 1st at the top and December 31st at the bottom of the stack. The same color map is used for all the images. However, the use of different image transparencies allows us to emphasize different features in the data. The first image has the lowest transparency, and it is useful for identifying areas where little or no rainfall occurred across Africa from south to north along the meridian at a given time of the year. By comparison, the second image has high transparency, and it is useful for highlight areas of the continent that received high rainfall amounts during the year.

Subsetting An important capability in 3D visualization is the ability to reduce the dataset to a subset of the original in all three dimensions. Subsetting is employed to allow a particular event(s) or feature in the dataset to be studied in more detail by optimizing the color map and transparency locally. The internal structure of the volumetric data is often obscured in the volume rendering process. Clipping planes can be used to remove regions that occlude and reveal more information. Since the full dataset is in memory, this region of interest can be specified and manipulated in real-time. Figure 5 shows the data clipped to a window covering southern Africa between January and March, 2000 when the cyclonic storms were impacting the region. The high rainfall values associated with the storms can be emphasized in the subset view to study features such as the disintegration of the storms overland.

Figure 5. A subset of the African rainfall dataset showing high rainfall associated with cyclonic systems in southern Africa in early 2000.

Slicing Another important feature is the ability to make cross-sections through the data using one or more planes parallel to the Cartesian axes as shown in Figure 6. In the context of hydrometeorology, this feature is useful for studying the evolution of rainfall patterns along the track of a major storm or hurricane. A two-dimensional slice is taken through the data either parallel to the coordinate planes or in user-controlled arbitrary orientation to probe the voxels along the plane. We can sweep the slice plane through the data along the Z-axis to see the temporal change in data on along the X and Y-axis thereby producing a Hovmuller diagram. Although slicing limits data use to a 2D

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota visualization space, it remains a very valuable technique for those users who are better able to comprehend 2D information than 3D.

Figure 6. Slices of the African rainfall dataset using three planes parallel to the Cartesian axes.

Dynamic Graphing For those hydrometeorologists who would still like to be able to see graphs of moisture fluxes, the presentation of space-time cube in a 3D visualization environment enables graphing to be done interactively through any location in the data as shown in Figure 7. As with slicing, graphing can be done along any line parallel to the three axes or at any oblique angle in the three dimensional space. This feature alone presents a compelling reason why users of spatially distributed time series data would want to load their data into space-time cube. Hydrometeorologists in operational agencies often need to review to trends in datasets to justify forecasting decisions or hazard assessments. The ability to dynamically produce graphs of time series data by simply moving a point around is extremely valuable in such settings.

Figure 7. The use of a line probe to produce a graph of events within the space-time cube. The line probe can also be applied at oblique angles.

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota In summary, by loading spatially distributed time series into a space-time cube using voxel-based visualization software, we are able to study spatio-temporal structures in the data. We can visualize different structures in the data by applying transfer functions consisting of color maps and transparency settings to the data. We are also able to query the data using a variety of data reduction and display tools such as subsetting, slicing and graphing. The methods described in this paper are generic and can be applied to a wide variety of remotely sensed time series data.

ANNUAL AFRICAN RAINFALL CYCLE

One of the most significant advantages of presenting data in a space-time cube is that it allows the user to freeze time and observe events as they evolve over time. The annual rainfall cycle over Africa is one such interesting cycle. Because the continent extends almost evenly across the two sides of the equator, the zone of highest rainfall over Africa at any point in time is largely determined by the position of the Inter-Tropical Convergence Zone (ITCZ). In early January, the ITCZ begins its northward journey from southern Africa. It crosses the equator in April and continues north reaching its most northward position in late July or early August. It then reverses course and migrates back south, arriving in southern Africa again in the latter part of the year.

Figure 8. A space-time view of the annual rainfall cycle over Africa

Figure 8 shows a perspective view of a space time cube of the African rainfall cycle as determined from the median monthly rainfall total from the NOAA RFE data. Areas of transparency during any given month received less than 100 mm of water while areas shown in red received more than 200 mm for the month. All other areas with between 100 and 200 mm are shown in blue. Some regions appear as varying combinations of red and blue indicating the integration of the two colors over several adjacent cells. Areas of modal rainfall peaks in the Greater Horn and south-central regions of the continent can clearly be seen. Winter rainfall over the Mediterranean region of North Africa is also clearly visible. Perhaps the most striking feature of the whole data set is the gapping hole in the middle of the continent which coincides with the mid-year drought occurring during the winter in the Southern Hemisphere. Features like these are difficult to explain without an image, and it is expected that continued geovisualization of these time series data will provided additional insight in interannual variations of the dimensions and location of this hole in the data.

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota CONCLUSIONS AND FUTURE WORK

In this paper, we have demonstrated that volume visualization technology commonly applied for medical imaging and numerical simulation can be successfully applied for visualizing satellite-derived rainfall data as well as other spatially distributed time series data. The use of the space-time cube allowed us to discern spatial and temporal patterns in a dataset containing close to 300 million individual values. It also allows us to apply different color maps and transparencies and perform queries on the data. We are also able to dynamically generate graphs along lines orthogonal to any axis and at oblique angles. Data reduction functions such as slicing through different planes and subsetting to allow for more focused study of any region of the space-time cube were also demonstrated. Potential applications of this volume visualization technique cuts across all areas of remote sensing in which time series data are produced. We plan to continue exploring trends in these and other remotely sensed data by building analytical functions that operate on the data values within the space-time cube. The application of glyphs that have been used in other fields of information visualization can be combined with maps to show multiple data attributes as well as linear or cyclical structures in the data. We will employ these methods to allow us to visualize multivariate data such as the multiple bands of a Landsat image in the future.

ACKNOWLEDGEMENTS

We would like to acknowledge the contributions of FEWS NET partners at USAID, NOAA, and USGS who facilitate the processing and distribution of the daily rainfall time series used in this paper. We would also like to thank our colleagues at the Center for Computation and Technology, Louisiana State University for supporting this research and providing access to high-end graphics workstations and software for the visualization.

REFERENCES

Cabral, B., N. Cam and J. Foran (1994). Accelerated volume rendering and tomographic reconstruction using texture mapping hardware. Symposium on Volume Visualization, pp 91-98. Christie, F., Hanlon, J., (2001). Mozambique and the Great Flood of 2000. Indiana University Press, Bloomington, Indiana. Hedley, N.R., Drew, C.H., Arfin, E. and Lee, A. (1999). Hagerstrand Revisited: Interactive Space-Time Visualizations of Complex Spatial Data. Informatica, 23(4), 155-168. Kraak, M.-J. (2003). The space-time cube revisited from a geovisualization perspective. Proc. of the 21st ICA Conference, Durban, South-Africa, 8 pages. Lichtenbelt, B., R. Crane and S. Naqvi.(1998). Introduction to Volume Rendering. Prentice Hall, 1st edition. MacEachren, A.M. and M.J. Kraak (2001). Research Challenges in Geovisualization. Cartography and Geographic Information Systems. Vol No 1:3-12. McCaslin, P., T. Philip, A. McDonald and E.J. Szoke (2000). 3D Visualization Development at NOAA Forecast Systems Laboratory. ACM SIGGRAPH Computer Graphics, Vol. 34 no. 1, pp 41-44. McCormick, B., T.A. DeFanti and M.D. Brown (1987). Visualization in Scientific Computing. Computer Graphics, l, 6. Takatsuka, M. and M.Gahegan (2002). GeoVista Studio: A codeless visual programming environment for geoscientific data analysis and visualization. Journal of Computers & Geosciences, 28:1131-1144. Xie, P. and P.A. Arkin (1997). A 17-year monthly analysis based on gauge observations, satellite estimates, and numerical model outputs. Bulletin of the American Meteorological Society 78(11): 2539-58. Venkataraman, S. (2004). Volume Rendering of Large Data for Scalable Displays Using Photonic Switching. Master’s Project, University of Illinois at Chicago.

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota