Download Space, Time and Variables in Hydrology

Space, Time and Variables in
Hydrology
David R. Maidment
Feb 7, 2008
Hydrologic Cycle
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”
Reynolds Transport Theorem
dB
  d   v.dA
dt
cv
cs
Total rate of
change of B
in the fluid
system
Rate of change
of B stored in
the control
volume
Net outflow of B
across the
control surface
Geography
Geographic Things
Data Cube
A simple data model
Time, T
“When”
D
“Where”
Space, L
Variables, V “What”
ArcHydro Time Series
Continuous Space-Time Model –
NetCDF (Unidata)
Time, T
Coordinate
dimensions
{X}
D
Space, L
Variables, V
Variable dimensions
{Y}
Discrete Space-Time Data Model
ArcHydro
Time, TSDateTime
TSValue
Space, FeatureID
Variables, TSTypeID
CUAHSI Observations Data Model
• A relational database at
Streamflow
the single observation
level (atomic model)
• Stores observation data
Precipitation
made at points
& Climate
• Metadata for
unambiguous
interpretation
Water Quality
• Traceable heritage from
raw measurements to
usable information
Groundwater
levels
Soil
moisture
data
Flux tower
data
Space, Time, Variables and Observations
An observations data model archives values of variables at
particular spatial locations and points in time
Variables (VariableID)
Observations Data Model
• Data from sensors
(regular time series)
• Data from field sampling
(irregular time points)
Space (HydroID)
Time
Space, Time, Variables and Simulation
A process simulaton model computes values of sets of variables at
particular spatial locations at regular intervals of time
Variables (VariableID)
Space (HydroID)
Process Simulation Model
• A space-time point is unique
• At each point there is a set of
variables
Time
Space, Time, Variables and Statistics
A statistical distribution is defined for a particular variable
defined over a particular space and time domain
Variables (VariableID)
Space (HydroID)
Statistical distribution
• Represented as {probability, value}
• Summarized by statistics (mean,
variance, standard deviation)
Time