1. Space, Time and Variables in Hydrology
David R. Maidment
Feb 7, 2008

2. Hydrologic Cycle

3. Hydrologic System
Take a watershed and extrude it vertically into the atmosphere
and subsurface, Applied Hydrology, p.7- 8
A hydrologic system is “a structure or volume in space surrounded by a boundary, that accepts water and other inputs, operates on them internally, and produces them as outputs”

4. Reynolds Transport Theorem
Rate of change of B stored in the control volume
Total rate of change of B in the fluid system
Net outflow of B across the control surface

5. Geography

6. Geographic Things

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

8. ArcHydro Time Series

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

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

11. 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

12. 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

13. 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

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