Hydrology Modeling in Alaska: Modeling Overview 30 October 2009 International Arctic Research Center

Overview Characterizing Models Simulation basis Spatial representation Temporal representation Method of solution Considerations for Choosing an Appropriate Model Basic References

Characterizing Models Terms used to characterize hydrologic models From Dingman, 2002

Characterizing Models: Simulation Basis Physically based- uses equations derived from basic physics to simulate system response (e.g., flows and storages). Conceptual- uses “reasonable” a priori relationships. Ex Subsurface outflow modeled as a linear function of storage volume. Empirical/regression- uses observationally derived relationships. Statistical regression techniques often used to develop these relationships. Ex Snowmelt rate modeled as proportional to air temperature. Stochastic- employs time series analysis and/or probabilistic models to characterize the behavior of one or more system variables.

Characterizing Models: Spatial Representation Lumped- region or watershed represented as a point. Spatially varying inputs (soils, veg, topo, etc.) each characterized by single parameter that is a representative value. (Also called ‘0-dimensional’ models) Distributed- provides some representation of the spatial variability of the watershed. May be grid-based, involve dividing watersheds into sub-basins, or linking lumped models.

Characterizing Models: Temporal Representation Steady state- outputs represent long-term average or ultimate magnitude of a quantity. Ex Global average temperature. Steady state seasonal- outputs are long-term seasonal averages of a quantity. Ex Average monthly ET. Single event- simulates time-varying response of a system to an isolated event. Ex Streamflow response to specified design storm. Continuous- outputs are a continuous sequence of responses to a sequence of inputs over a specified period. Ex Hourly or daily streamflow response to one or more years of specified weather data.

Characterizing Models: Method of Solution 0-Dimensional- computations not based on formal coordinate system. Formal analytical- basic differential equations in coordinate system solved analytically. Formal numerical- basic differential equations solved by finite-difference or finite-element discretization schemes. Hybrid- 0-dimensional and formal solutions used for different processes within model. Ex a model may use a formal numerical solution for soil water movement, while ET estimates are made with a 0-dimensional method.

Considerations for Developing or Choosing an Appropriate Model Accuracy of model results is a function of Accuracy of input data Degree to which model structure represents hydrologic processes important to the problem Complex models… require complex data In general, model data requirements should be in tune with available data sources. Likewise, models of various hydrologic processes should be in balance What is the application? Predictive versus verifying historical water balance Water balance models may be constructed to quantify or confirm inflows, outflows, and storages in a system. Simulation models may be used to predict hydrologic response to specified forcing, such as primary inputs/outputs (P, T, Q, land use). Operational and short term forecast versus study of long-term change In one case statistical models may be most efficient for the application, while in the other, physically-based models may be necessary to capture important changes in hydrologic response

Basic References Physical Hydrology (Dingman, 2002) Introduction to Hydrology (Viessman & Lewis, 2003) Handbook of Hydrology (Maidment, 1993)