Document PIHM calibration using evolutionary algorithms

Overview

Automatic calibration of PIHM can be done a sensitivity-based parameter estimation method known as Partition Calibration Strategy (PCS) for efficient model parameter optimization. It uses an evolutionary algorithm. The approach is described in detail in:

Yu, X., G. Bhatt, C. Duffy, Y. Shi, 2013, Parameterization for Distributed Watershed Modeling 
Using National Data and Evolutionary Algorithm, Computers in Geoscience, Vol (58), p. 80-90.

The underlying model watershed model PIHM, is a physics-based, fully-coupled, distributed hydrologic code that simulates 2-D overland flow, 1-D unsaturated flow and 2-D groundwater flow and 1-D stream dynamics. PIHM and PHIMgis are open source codes (www.pihm.psu.edu) that are being widely applied to catchment research.

Ideally a multi-state optimization is performed such that the model is constrained by actual field data for streamflow, groundwater levels, soil moisture, LAI as time series at specific locations or as fields of geospatial data. The example below refers to a time series procedure.

Evolutionary Algorithm

The CMA-ES (Covariance Matrix Adaptation Evolution Strategy) is an evolutionary algorithm for difficult non-linear non-convex optimization problems in continuous domains. CMA-ES is a rank-based (η, λ) evolution strategy where the best of the offspring form the next parent generation. It generates a new population membership by sampling from a probability distribution that is constructed during the optimization process. This page provides a short overview of CMA-ES. [The CMA-ES source code is on line]. For a detailed description of the algorithm, the reader is referred to the tutorial by Hansen (2006):

Hansen, N., 2006. The CMA Evolution Strategy: A Comparing Review. Towards a New Evolutionary computation, 
pp. 75-102. http://dx.doi:10.1007/3-540- 32494-1_4.

Basic Steps

1. First assign a-priori model parameters to each element in the unstructured mesh in PIHM model. Typically we recommend that this would be done from National data, such as the data offered on-line as HUC-12 watersheds for Continental USA. The web service HydroTerre provides the essential geospatial/temporal data necessary for modeling at the HUC-12 scale anywhere in CONUS. The necessary geospatial tools are provided in PIHMgis for build the unstructured mesh and assign a-priori parameters. Model building from a-priori data is the subject of a separate Model Development Tutorial.
2. Next perform a parameter sensitivity using a Monte Carlo Sensitivity Analysis with the catchment model to establish characteristic time scales of important the processes operating in the catchment. The result of this step allows parameters to be partitioned with respect to characteristic time scales. Past experience tells us that we typically find 2 categories or partition groups (Yu, et al, 2013). “Event-scale” parameters, or those sensitive to rapid hydrologic change, and we refer to this group as the EG partition. A second group of parameters are less sensitive to short term events, but respond to seasonal or longer period hydro-climatic or biophysical processes. This group is defined as the seasonal-scale partition SG. Table 1 illustrates a typical grouping that works well in the northeast and mid-Atlantic region. Additional groups are possible but we will confine our analysis to EG-SG partitions. The purpose of this partition is to reduce the computational requirements of the parameter estimation problem by carrying out the optimization w/re to each partition separately.
3. The third step involves applying the CMA-ES to optimize the parameters for the EG partition while holding the SG partition parameters constant (e.g. a-priori parameters). The time period selected for the EG parameters is typically a flooding after low streamflow months when the initial condition of the watershed is dry and can be resolved by spin-up.
4. Finally, using the new set of EG parameters (step 3) to estimate for the seasonal low-streamflow and storage conditions. We found near linear responses of SG partition parameters that are dominated by seasonal and long-term changes. The calibration of SG partition parameters amounts to optimizing seasonal parameters such as those associated with ET. Our experience suggests that sequence of estimating the EG then the SG partition parameters works the best in many watersheds.

Table 1: Calibration parameters, corresponding hydrologic processes and their typical behavior as event-scale parameters group (EG) or seasonal-scale parameters group (SG)

Parameter	Hydrological processes	Partition group
Matrix conductivity (horizontal)	Subsurface flow	EG
Matrix conductivity (Vertical)	Subsurface flow	EG
Macropore conductivity (horizontal)	Subsurface flow	EG
Macropore conductivity (Vertical)	Subsurface flow	EG
Infiltration rate	Infiltration	EG
Macropore depth	Subsurface flow	EG
Porosity	Subsurface flow, Recharge	EG
Van Genuchten parameter α	Subsurface flow, recharge	EG
Van Genuchten parameter β	Subsurface flow, recharge	EG
River Manning’s roughness	Channel routing	EG
River bed conductivity (horizontal)	Channel routing	EG
River bed conductivity (vertical)	Channel routing	EG
Root zone depth	Transpiration and evaporation	SG
Vegetation fraction	Transpiration and evaporation	SG
Field capacity	Evaporation	SG
Wilting point	Evaporation	SG
Max. interception storage capacity	Interception loss factor	SG
Minimum canopy resistance	Transpiration	SG