space and time

Space and Time

By David R. Maidment

with contributions from Steve Kopp, Steve Grise, and Tim Whiteaker

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

GISWaterResources

Water EnvironmentWater Environment(Watersheds, gages, streams)(Watersheds, gages, streams)

Water ConditionsWater Conditions(Flow, head, concentration)(Flow, head, concentration)

Data Cube

Space, L

Time, T

Variables, V

D

“What”

“Where”

“When”

A simple data model

6

Space, FeatureID

Time, TSDateTime

Variables, TSTypeID

TSValue

Discrete Space-Time Data ModelArcHydro

Continuous Space-Time Model – NetCDF (Unidata)

Space, L

Time, T

Variables, V

D

Coordinate dimensions{X}

Variable dimensions{Y}

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

Flux towerdata

Precipitation& Climate

Groundwaterlevels

Water Quality

Soil moisturedata

Pre Conference Seminar

9

ODM and HIS in an Observatory Settinge.g. http://www.bearriverinfo.org

Space, Time, Variables and Observations

Variables (VariableID)Variables (VariableID)

Space (HydroID)Space (HydroID) TimeTime

Observations Data ModelObservations Data Model• Data fromData from sensors sensors (regular (regular time series)time series)• Data from Data from field sampling field sampling (irregular time points)(irregular time points)

An An observations data model observations data model archives values of variables at archives values of variables at particular spatial locations and points in timeparticular spatial locations and points in time

Space, Time, Variables and Visualization



VizualizationVizualization• MapMap – Spatial distribution for a time point or – Spatial distribution for a time point or intervalinterval• GraphGraph – Temporal distribution for a space – Temporal distribution for a space point or regionpoint or region• Animation Animation – Time-sequenced maps– Time-sequenced maps

A A visualizationvisualization is a set of maps, graphs and animations that display the is a set of maps, graphs and animations that display the variation of a phenomenon in space and timevariation of a phenomenon in space and time

Space, Time, Variables and Simulation



Process Simulation ModelProcess Simulation Model• A A space-time point space-time point is uniqueis unique• At each point there is a At each point there is a set of variablesset of variables

A A process simulaton model process simulaton model computes values of sets of variables at computes values of sets of variables at particular spatial locations at regular intervals of timeparticular spatial locations at regular intervals of time

Space, Time, Variables and Geoprocessing



GeoprocessingGeoprocessing• Interpolation Interpolation – Create a surface from point – Create a surface from point valuesvalues• OverlayOverlay – Values of a surface laid over – Values of a surface laid over discrete featuresdiscrete features• Temporal Temporal – Geoprocessing with time steps– Geoprocessing with time steps

Geoprocessing Geoprocessing is the application of GIS tools to transform spatial data and is the application of GIS tools to transform spatial data and create new data productscreate new data products

Space, Time, Variables and Statistics



Statistical distributionStatistical distribution• Represented as Represented as {probability, value}{probability, value}• Summarized by Summarized by statisticsstatistics (mean, variance, (mean, variance, standard deviation)standard deviation)

A A statistical distribution statistical distribution is defined for a particular variable defined over a is defined for a particular variable defined over a particular space and time domainparticular space and time domain

Space, Time, Variables and Statistical Analysis



Statistical analysisStatistical analysis• Multivariate analysis Multivariate analysis – correlation of a set – correlation of a set of variablesof variables• Geostatistics Geostatistics – correlation space– correlation space• Time Series Analysis Time Series Analysis – correlation in time– correlation in time

A A statistical analysis statistical analysis summarizes the variation of a set of variables over a summarizes the variation of a set of variables over a particular domain of space and timeparticular domain of space and time

Pre Conference Seminar

16

CUAHSI Observations Data Model

Space-Time Datasets

Sensor and laboratory databases

From Robert Vertessy, CSIRO, Australia

Space and Time






Space-Time Cube

TSDateTime

TSTypeID

TSValue

FeatureID

Time

Space

Variable

Data Value

Time Series Data

Time Series of a Particular Type

A time series for a particular feature

A particular time series for a particular feature

All values for a particular time

MonitoringPointHasTimeSeries Relationship

TSTypeHasTimeSeries

Arc Hydro TSType Table

TypeIndex

VariableName

TypeOf

TimeSeries

Info

Regular or

Irregular

Unitsof

measure

Timeinterval

Recordedor

Generated

Arc Hydro has 6 Time Series DataTypes1. Instantaneous2. Cumulative3. Incremental4. Average5. Maximum6. Minimum

Instantaneous

Cumulative

AverageIncremental

Maximum Minimum

Time Series Types

A Theme Layer

Synthesis over all data sources of observations of a particular variable e.g. Salinity

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Texas Salinity Theme

7900 series347,000 data

7900 seriesTPWD 3400TCEQ 3350TWDB 150

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Copano and Aransas Bay Salinity

Number of Data0 – 5050 – 150150 – 400400 – 10001000 – 3000

Copano Bay

Aransas Bay

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Texas Daily Streamflow Theme

USGS Data 1138 sites

(400 active)

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Austin – Travis Lakes Streamflow

Years of Data0 – 1010 – 2020 – 4040 – 6060 – 110

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Texas Water Temperature Theme

22,700 series966,000 data

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Austin – Travis Lakes Water Temperature

Number of Data0 – 5050 – 150150 – 400400 – 10001000 – 5000

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http://data.crwr.utexas.edu

Data from Individual Sites

HydroPortal to access Themes

Space and Time






Time Series{value, time}

Attribute Series{featureID, value, time}

Raster Series{raster, time}

Feature Series{shape,value, time}

Four Panel Diagram

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, ….)

Compile Gage Time Series into an Attribute Series table

Hydraulic head

Hydraulic head is the water surface elevation in a standpipeanywhere in a water system, measured in feet above mean sealevel

h

Land surface

Mean sea level(datum)

Map of hydraulic head

X

Y

Z

Hydraulic head, h

xy

h(x, y)

A map of hydraulic head specifies the continuous spatialdistribution of hydraulic head at an instant of time

Time sequence of hydraulic head maps

x

y

z

Hydraulic head, h

t1

t2

t3

Attribute Series to Raster Series

Inundation

hL

d

Depth of inundation = d IF (h - L) > 0 then d = h – LIF (h – L) < 0 thend = 0

Inundation Time Series

t

h(x,y,t)LT(x,y)

Time

d(x,y,t)

d(x,y,t) = h(x,y,t) – LT(x,y)

Ponded Water DepthKissimmee River

June 1, 2003

Depth Classification

Value_ From_ To_-1 -100 -0.00010 0 01 0.0001 0.52 0.5 13 1 1.54 1.5 25 2 2.56 2.5 37 3 3.58 3.5 49 4 4.5

10 4.5 511 5 100

0

5

4

3

2

1

Depth Class

11

9-10

7-8

5-6

3-4

1-20-1

Feature Series of Ponded Depth

Attribute Series for Habitat Zones

Space and Time






Multidimensional Data

Data cube (3D) or hypercube (4D,5D…)

• Temperature varying with time

• Temperature varying with time and altitude

XY

TZ

XY

T


Time = 1

Time = 2

Time = 3


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Y

X

TimeTime = 1

Time = 2

Time = 3

Data Cube

Time Slices

Multidimensional Data141 241 341

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Time = 1

Time = 2

Time = 3


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Y

X

Time

Altitude

Includes variation in (x,y,z,t)

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

What is a NetCDF file?NetCDF is a binary file

A NetCDF file consists of:Global Attributes: Describe the contents of the fileDimensions: Define the structure of the data

(e.g Time, Depth, Latitude, Longitude)Variables: Holds the data in arrays shaped

by DimensionsVariable Attributes: Describes the contents of

each variableCDL (network Common Data form Language) description takes the

following formnetCDF name {

dimensions: ... variables: ... data: ...

}

Storing Data in a netCDF File

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Y

X

Time

netcdf mynetcdf{dimensions:

X=4;Y=4;Time=UNLIMITED;

variables:float X(X);float Y(Y);int Time(Time);float Temperature(Time, Y, X);

data:X = 10, 20, 30, 40;Y = 110, 120, 130, 140;Time = 31, 59, 90;

}

NetCDF Data Sources

• Community Climate Systems Model (CCSM) http://www.ccsm.ucar.edu, https://www.earthsystemgrid.org/

• 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 (2000-2099)• Control runs (1870-1999) and scenario runs• Temperature, precipitation flux, surface snow thickness, snowfall

flux, cloud water content, etc.

• Program for Climate Model Diagnosis and Intercomparison (PCMDI) http://www-pcmdi.llnl.gov/

http://www.ccsm.ucar.edu/

https://www.earthsystemgrid.org/

http://www-pcmdi.llnl.gov/

NetCDF Data Sources

• Vegetation and Ecosystem Modeling and Analysis Project (VEMAP) http://dataportal.ucar.edu/vemap/main.html• 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.

http://dataportal.ucar.edu/vemap/main.html

NetCDF Data Sources

• British Atmospheric Data Center (BADC) http://badc.nerc.ac.uk/data/• 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.

http://badc.nerc.ac.uk/data/

NetCDF Data Sources

• National Oceanic & Atmospheric Administration (NOAA)• National Digital Forecast Database (NDFD)

http://www.nws.noaa.gov/ndfd/• Radar Integrated Display with Geospatial Element (RIDGE)

http://www.srh.weather.gov/ridge/• Precipitation Analysis

http://www.srh.noaa.gov/rfcshare/precip_download.php• Climate Diagnostics Center http://www.cdc.noaa.gov/• NCDC THREDDS Catalog

http://www.ncdc.noaa.gov/thredds/catalog.html • NCDC NCEP Stage IV Radar Rainfall

http://www.ncdc.noaa.gov/thredds/catalog/radar/StIV/catalog.html

http://www.nws.noaa.gov/ndfd/

http://www.srh.weather.gov/ridge/

http://www.srh.noaa.gov/rfcshare/precip_download.php

http://www.cdc.noaa.gov/

http://www.ncdc.noaa.gov/thredds/catalog.html

http://www.ncdc.noaa.gov/thredds/catalog/radar/StIV/catalog.html

NetCDF in ArcGISNetCDF data is accessed as

• Raster• Feature• Table

• Direct read (no scratch file)• Exports GIS data to netCDF

Gridded Data

Raster

Point Features

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

Space and Time






Tracking Analyst

• Simple Events – 1 feature class that describes What, When,

Where

• Complex Event– 1 feature class and 1 table that describe

What, When, Where

Arc Hydro

Simple EventID Time Geometry Value

1 T1 X1,Y1 0.1

2 T2 X2,Y2 0.3

1 T3 X3,Y3 0.7

2 T4 X4,Y4 0.4

3 T5 X5,Y5 0.5

2 T6 X6,Y6 0.2

4 T7 X7,Y7 0.1

1 T8 X8,Y8 0.8

1 T9 X9,Y9 0.3

Unique Identifier for objects being tracked throughtime

Time of observation (in order) Geometry of observation

Observation

Complex Event (stationary version)

ID Geometry

1 X1,Y1

2 X2,Y2

3 X3,Y3

4 X4,Y4

ID Time Value

1 T1 0.1

2 T2 0.3

1 T3 0.7

2 T4 0.4

3 T5 0.5

2 T6 0.2

4 T7 0.1

1 T8 0.8

1 T9 0.3

The object maintains its geometry (i.e. it is stationary)

Cases 1, 2, 3, 4, 5

Complex Event (dynamic version)

ID Gage Number

1 1001

2 1002

3 1003

4 1004

ID Geometry Time Value

1 X1,Y1 T1 0.1

2 X2,Y2 T2 0.3

1 X3,Y3 T3 0.7

2 X4,Y4 T4 0.4

3 X5,Y5 T5 0.5

2 X6,Y6 T6 0.2

4 X7,Y7 T7 0.1

1 X8,Y8 T8 0.8

1 X9,Y9 T9 0.3

The object’s geometry can vary with time (i.e. it is dynamic)

Cases 6 and 7

Tracking Analyst Display

Feature Class and Time Series Table

Temporal Layer

Shape from feature class is joined to time series value from TimeSeries table

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

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)

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

space and time

Documents

spatial data

time stepsgeoprocessing

time domainspace

spacetime point

space point

particular space

point values

new data productsspace