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 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

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 Variable dimensions {Y} Variables, V

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

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

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

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

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