1. with contributions from Steve Kopp, Steve Grise, and Tim Whiteaker
Space and Time
By David R. Maidment
with contributions from Steve Kopp, Steve Grise, and Tim Whiteaker

2. Space and Time Introductory concepts
Discrete space-time model – Arc Hydro
Temporal Geoprocessing
Continuous space-time model – netCDF
Tracking Analyst

3. Space and Time Introductory concepts
Discrete space-time model – Arc Hydro
Temporal Geoprocessing
Continuous space-time model – netCDF
Tracking Analyst

4. Linking GIS and Water Resources
Water Environment
(Watersheds, gages, streams)
Water Conditions
(Flow, head, concentration)

5. Data Cube A simple data model Time, T “When” D “Where” Space, L
Variables, V
“What”

6. Discrete Space-Time Data Model ArcHydro
Time, TSDateTime
TSValue
Space, FeatureID
Variables, TSTypeID

7. Continuous Space-Time Model – NetCDF (Unidata)
Time, T
Coordinate
dimensions
{X} D
Space, L
Variable dimensions
{Y}
Variables, V

8. CUAHSI Observations Data Model
A relational database at the single observation level (atomic model)
Stores observation data made at points
Metadata for unambiguous interpretation
Traceable heritage from raw measurements to usable information
Streamflow
Groundwater
levels
Precipitation
& Climate
Soil
moisture
data
Water Quality
Flux tower
data

9. ODM and HIS in an Observatory Setting e. g. http://www. bearriverinfo
Pre Conference Seminar

10. Space, Time, Variables and Observations
An observations data model archives values of variables at
particular spatial locations and points in time
Observations Data Model
Data from sensors (regular time series)
Data from field sampling (irregular time points)
Variables (VariableID)
Space (HydroID)
Time

11. Space, Time, Variables and Visualization
A visualization is a set of maps, graphs and animations that display the variation of a phenomenon in space and time
Vizualization
Map – Spatial distribution for a time point or interval
Graph – Temporal distribution for a space point or region
Animation – Time-sequenced maps
Variables (VariableID)
Space (HydroID)
Time

12. Space, Time, Variables and Simulation
A process simulaton model computes values of sets of variables at
particular spatial locations at regular intervals of time
Process Simulation Model
A space-time point is unique
At each point there is a set of variables
Variables (VariableID)
Space (HydroID)
Time

13. Space, Time, Variables and Geoprocessing
Geoprocessing is the application of GIS tools to transform spatial data and create new data products
Geoprocessing
Interpolation – Create a surface from point values
Overlay – Values of a surface laid over discrete features
Temporal – Geoprocessing with time steps
Variables (VariableID)
Space (HydroID)
Time

14. Space, Time, Variables and Statistics
A statistical distribution is defined for a particular variable defined over a particular space and time domain
Statistical distribution
Represented as {probability, value}
Summarized by statistics (mean, variance, standard deviation)
Variables (VariableID)
Space (HydroID)
Time

15. Space, Time, Variables and Statistical Analysis
A statistical analysis summarizes the variation of a set of variables over a particular domain of space and time
Statistical analysis
Multivariate analysis – correlation of a set of variables
Geostatistics – correlation space
Time Series Analysis – correlation in time
Variables (VariableID)
Space (HydroID)
Time

16. From Robert Vertessy, CSIRO, Australia
Space-Time Datasets
CUAHSI Observations Data Model
Sensor and laboratory databases
Pre Conference Seminar
From Robert Vertessy, CSIRO, Australia

17. Space and Time Introductory concepts
Discrete space-time model – Arc Hydro
Temporal Geoprocessing
Continuous space-time model – netCDF
Tracking Analyst

18. Space-Time Cube Time TSDateTime Data Value TSValue FeatureID Space
Variable
TSTypeID

19. Time Series Data

20. Time Series of a Particular Type

21. A time series for a particular feature

22. A particular time series for a particular feature

23. All values for a particular time

24. MonitoringPointHasTimeSeries Relationship

25. TSTypeHasTimeSeries

26. Arc Hydro TSType Table Arc Hydro has 6 Time Series DataTypes Units of
measure
Regular or
Irregular
Time
interval
Type Of
Time
Series
Info
Recorded or
Generated
Type
Index
Variable
Name
Arc Hydro has 6 Time Series DataTypes
Instantaneous
Cumulative
Incremental
Average
Maximum
Minimum

27. Time Series Types Instantaneous Incremental Average Cumulative Minimum
Maximum

28. A Theme Layer
Synthesis over all data sources of observations of a particular variable e.g. Salinity

29. Texas Salinity Theme 7900 series 347,000 data 7900 series TPWD 3400
TCEQ 3350
TWDB 150

30. Copano and Aransas Bay Salinity
Number of Data
0 – 50
50 – 150
150 – 400
400 – 1000
1000 – 3000
Copano Bay
Aransas Bay

31. Texas Daily Streamflow Theme
USGS Data
1138 sites
(400 active)

32. Austin – Travis Lakes Streamflow
Years of Data
0 – 10
10 – 20
20 – 40
40 – 60
60 – 110

33. Texas Water Temperature Theme
22,700 series
966,000 data

34. Austin – Travis Lakes Water Temperature
Number of Data
0 – 50
50 – 150
150 – 400
400 – 1000
1000 – 5000

36. Data from Individual Sites

37. HydroPortal to access Themes

38. Space and Time Introductory concepts
Discrete space-time model – Arc Hydro
Temporal Geoprocessing
Continuous space-time model – netCDF
Tracking Analyst

39. Four Panel Diagram Time Series {value, time} Feature Series
{shape,value, time}
Four Panel
Diagram
Raster Series
{raster, time}
Attribute Series
{featureID, value, time}

40. Time series from gages in Kissimmee Flood Plain
21 gages measuring water surface elevation
Data telemetered to central site using SCADA system
Edited and compiled daily stage data stored in corporate time series database called dbHydro
Each time series for each gage in dbHydro has a unique dbkey (e.g. ahrty, tyghj, ecdfw, ….)

41. Compile Gage Time Series into an Attribute Series table

42. Hydraulic head Land surface h Mean sea level (datum)
Hydraulic head is the water surface elevation in a standpipe
anywhere in a water system, measured in feet above mean sea
level

43. Map of hydraulic head Z Hydraulic head, h h(x, y) x y X Y
A map of hydraulic head specifies the continuous spatial
distribution of hydraulic head at an instant of time

44. Time sequence of hydraulic head mapsz t3 t2 t1
Hydraulic head, h x y

45. Attribute Series to Raster Series

46. Inundation d h L Depth of inundation = d IF (h - L) > 0 then

47. Inundation Time Series
d(x,y,t) = h(x,y,t) – LT(x,y) h
(x,y,t)
LT(x,y)
d(x,y,t) t
Time

48. Ponded Water Depth
Kissimmee River
June 1, 2003

49. Depth Classification
Depth
Class 11 5
9-10 4
7-8 3
5-6 2
3-4 1
1-2 -1

50. Feature Series of Ponded Depth

51. Attribute Series for Habitat Zones

52. Space and Time Introductory concepts
Discrete space-time model – Arc Hydro
Temporal Geoprocessing
Continuous space-time model – netCDF
Tracking Analyst

53. Multidimensional Data
Data cube (3D) or hypercube (4D,5D…)
Temperature varying with time
Temperature varying with time and altitude T Y X

54. Multidimensional Data
Time = 3
Time = 2
Time = 1

55. Multidimensional Data
Time = 3
Time = 2
Time = 1

56. Multidimensional Data
Time = 1
Time = 2
Data Cube
Time = 3
Time Slices

57. Multidimensional Data
Includes variation in (x,y,z,t)

58. What is NetCDF? NetCDF (network Common Data Form)
A platform independent format for representing multi-dimensional array-orientated scientific data.
Self Describing - a netCDF file includes information about the data it contains.
Direct Access - a small subset of a large dataset may be accessed efficiently, without first reading through all the preceding data.
Sharable - one writer and multiple readers may simultaneously access the same netCDF file.
NetCDF is new to the GIS community but widely used by scientific communities for around many years

59. What is a NetCDF file? NetCDF is a binary file
A NetCDF file consists of:
Global Attributes: Describe the contents of the file
Dimensions: Define the structure of the data
(e.g Time, Depth, Latitude, Longitude)
Variables: Holds the data in arrays shaped by Dimensions
Variable Attributes: Describes the contents of each variable
CDL (network Common Data form Language) description takes the following form
netCDF name {
dimensions: ...
variables: ...
data: ... }

60. Storing Data in a netCDF File

61. NetCDF Data Sources
Community Climate Systems Model (CCSM) 
The CCSM is fully-coupled, global climate model that provides state-of-the-art computer simulations of the Earth's past, present, and future climate states.
100 yrs of climate change forecast data ( )
Control runs ( ) and scenario runs
Temperature, precipitation flux, surface snow thickness, snowfall flux, cloud water content, etc.
Program for Climate Model Diagnosis and Intercomparison (PCMDI)

62. NetCDF Data Sources
Vegetation and Ecosystem Modeling and Analysis Project (VEMAP)
VEMAP was a large, collaborative, multi-agency program to simulate and understand ecosystem dynamics for the continental United States.
The VEMAP Data Portal is a central collection of files maintained and serviced by the NCAR Data Group
Climate data interval: Annual, monthly, and daily.
Data type: Historical and model results
Data: Temperature, irradiance, precipitation, humidity, incident solar radiation, vapor pressure, elevation, land area, vegetation, water holding capacity of soil, etc.

63. NetCDF Data Sources
British Atmospheric Data Center (BADC)
The role of the BADC is to assist UK atmospheric researchers to locate, access and interpret atmospheric data.
Many datasets are publicly available but datasets marked with key symbol have restricted access.
Datasets are organized by projects or organizations.
Climatology Interdisciplinary Data Collection (CIDC) has monthly means of over 70 Climate Parameters.
Met Office - Historical Central England Temperature Data has the monthly series, which begins in 1659, is the longest available instrumental record of temperature in the world. The daily series begins in 1772.

64. NetCDF Data Sources
National Oceanic & Atmospheric Administration (NOAA)
National Digital Forecast Database (NDFD)
Radar Integrated Display with Geospatial Element (RIDGE)
Precipitation Analysis
Climate Diagnostics Center
NCDC THREDDS Catalog
NCDC NCEP Stage IV Radar Rainfall

65. NetCDF in ArcGIS NetCDF data is accessed as
Raster
Feature
Table
Direct read (no scratch file)
Exports GIS data to netCDF

66. Gridded Data
Raster
Point Features

67. NetCDF Tools Toolbox: Multidimension Tools Make NetCDF Raster Layer
Make NetCDF Feature Layer
Make NetCDF Table View
Raster to NetCDF
Feature to NetCDF
Table to NetCDF
Select by Dimension

68. Space and Time Introductory concepts
Discrete space-time model – Arc Hydro
Temporal Geoprocessing
Continuous space-time model – netCDF
Tracking Analyst

69. Tracking Analyst Simple Events Complex Event
1 feature class that describes What, When, Where
Complex Event
1 feature class and 1 table that describe What, When, Where
Arc Hydro

70. Simple Event ID Time Geometry Value 1 T1 X1,Y1 0.1 2 T2 X2,Y2 0.3 T3
0.7 T4
X4,Y4
0.4 3 T5
X5,Y5
0.5 T6
X6,Y6
0.2 4 T7
X7,Y7 T8
X8,Y8
0.8 T9
X9,Y9
Unique Identifier
for objects being
tracked through
time
Observation
Time of observation (in order)
Geometry of observation

71. Complex Event (stationary version)ID
Time
Value 1 T1
0.1 2 T2
0.3 T3
0.7 T4
0.4 3 T5
0.5 T6
0.2 4 T7 T8
0.8 T9 ID
Geometry 1
X1,Y1 2
X2,Y2 3
X3,Y3 4
X4,Y4
Cases 1, 2, 3, 4, 5
The object maintains its geometry (i.e. it is stationary)

72. Complex Event (dynamic version)ID
Geometry
Time
Value 1
X1,Y1 T1
0.1 2
X2,Y2 T2
0.3
X3,Y3 T3
0.7
X4,Y4 T4
0.4 3
X5,Y5 T5
0.5
X6,Y6 T6
0.2 4
X7,Y7 T7
X8,Y8 T8
0.8
X9,Y9 T9 ID
Gage Number 1
1001 2
1002 3
1003 4
1004
Cases 6 and 7
The object’s geometry can vary with time (i.e. it is dynamic)

73. Tracking Analyst Display

74. Feature Class and Time Series Table

75. Temporal Layer
Shape from feature class is joined to time series value from Time
Series table

76. Summary Concepts
Hydrologic variables are defined as a function of space and time
Although space and time seem alike as independent dimensions they are not:
Space can be discrete or continuous and is multidimensional
Time is one-dimensional
This leads to idea of spatially-referenced time series of data

77. Summary Concepts (II)
In Arc Hydro, discrete spatial features are associated with time series values through a HydroID-FeatureID relationship
Time series associated with individual features become Attribute Series associated with a Feature class
Attribute series can be transformed to Raster Series and Feature Series by temporal geoprocessing (Four panel diagram)

78. Summary Concepts (III)
ArcGIS explicitly supports time representations through
By allowing operations on netCDF files for spatially continuous fields
By allowing visualization of moving features using Tracking Analyst