Parameter transferability: Do structurally similar hydrological units also behave similar?
Abstract:
IntroductionThe functioning of a catchment is the result of the interplay between boundary conditions and internal feedbacks within the system. Geographically different areas, which are subject to similar boundary conditions, often show similar structures or pattern formation [Rietkerk and van de Koppel, 2008], such as the often observed clustered vegetation patterns in semi-arid areas. But not only in different parts of the world patterns are similar; it also occurs at completely different scales. For example, dendritic networks are visible as macropores at the meter scale, rills at the hillslope scale and rivers at the catchment scale.
This means that under similar initial conditions or sufficiently long time scales, areas that have encountered similar forcing (boundary conditions) should result in similar catchment structure and functioning. It is exactly this notion why the catchments can potentially being grouped with 'similar' catchments and subsequently being classified. However, the catchment classification initiative (see special issue on Catchment classification and PUB, 2011, Hydrol. Earth Syst. Sci., 15) still has several open questions: An important one is the question which variables, parameters or signatures should be used to compare different (sub) catchments [e.g. Reusser and Zehe, 2011]. While one avenue is to compare observations of states and fluxes within a catchment and fluxes across its boundaries, we will focus in this study on transferability of model parameters to test if model compartments that look structurally similar can also be described with the same model parameters. In this study we only look at the unsaturated zone.
This study is a first step towards the ultimate goal to model hydrological behavior at the mesoscale (~200 km2) with a physically based model. By transferring model parameters to other grid cells we aim to parameterize the full model domain without further calibration. In a next step, we will aim to reduce simulation time by also transferring simulation results from one grid cell to another. Furthermore, this detailed classification of grid cells or model compartments may also serve to guide future measuring campaigns.
Observations
For this study we use observations from an extensive monitoring network installed and analyzed within the DFG funded CAOS (Catchments As Organized Systems) framework. All observations are done in the Attert Basin in Luxembourg. Within this 288 km2basin three distinct geologies are present: the North is mainly schist, the South consists of sandstone and in between marls are found.
Spread over this basin, more than 40 sensor clusters have been installed, where each cluster spans an area of approximately 20 by 20 m (Fig.1a). Within each cluster, four piezometers, three soil moisture profiles (with each profile three or four sensors up to a depth of 80 cm) and a matrix potential profile (with three sensors at the same depths) have been installed. Furthermore, sap flow of four to five trees is measured; LAI observations are available for several cluster sites and a weather station observes incoming solar radiation, temperature, relative humidity and wind speed and direction. Surface density of macropores is observed in the vicinity of several clusters; several ERT and GPR measurements give some additional information about soil layering and depth to bedrock at few specific catenas, while many soil core samples have been analysed for their grain size distribution (>300) and soil water retention properties (>130).
This dense observation network provides forcing data and several model parameters to run the model as well as calibration data to tune some other model parameters.
Model description
In this study we use the newly developed CAOS model, which on the one hand strongly relies on the simplification of the landscape to multiple 1D dissipation gradients while being strictly physically based on the other hand, including mass and energy balancing. The model should ultimately be able to simulate water, solutes and energy at the lower mesoscale (up to ~200 km2). It has a hierarchical structure in which a catchment is subdivided into streams, hillslopes and riparian zones, where the latter two are subdivided into a fast (e.g. rapid subsurface flow) and slow (groundwater) lateral flow domain extending over the full length of the hillslope/riparian zone and several 'Elementary Functional Units' (EFU) describing flow in the unsaturated zone. To reduce computer simulation time, flow of water, solutes and energy is assumed to be 1-dimensional. Also bidirectional feedbacks between two objects are not taken into account: e.g. a water table rise in the saturated zone is thus not 'seen' in the unsaturated zone.
In the current study we only focus on the unsaturated zone in which only vertical fluxes are simulated. In such an EFU a double domain concept is implemented in which matrix flow is solved with the 'theta'-based (mass-conservative) Richards equation. Infiltration excess water is directed to the Macropore domain, which is simulated as a non-linear reservoir where the outgoing specific discharge is given by q=khb, where k and h are the reservoir constant and water level and bis a non-linearity factor. If the matrix becomes close to saturation at deeper layers, excess water is directed to the fast lateral flow domain (Fig. 1b).
Evaporation and transpiration is determined with the Penman-Monteith equation, in the same way as in the Catflow model [Zehe et al. 2001]. In this formulation, differences in soil evaporation, transpiration and evaporation from the canopy interception store are expressed in differences in empirical resistance terms depending on water availability, water vapour deficit and the turbulence of the boundary layer.
Calibration and parameter transferability
Several model parameters are observed in the field or in the lab: Van Genuchten parameters are obtained from lab-derived soil moisture retention curves of soil cores, the total depth of the EFU is obtained from maximum piezometer depths, soil layering is obtained from visual inspection of the drilling cores, the macropore density is obtained from small scale sprinkling experiments with dye tracer and LAI observations have been done in the field as well. However, several of these parameters have large uncertainties or have not been observed everywhere, while there are also some parameters that have not been observed in the field: for example, the numerical grid size of the top soil layer influences the amount of infiltration excess water.
Therefore we will perform sensitivity analyses on these model parameters and if the sensitivity is large in combination with a large uncertainty of the observation, we will use these parameters as calibration parameters. Calibration will be done by fitting the soil moisture data observed at different depths and by comparing the transpiration rate qualitatively with the sap flow measurements. This will be done for each cluster in the basin.
Once they are all calibrated, parameter sets of one cluster will be transferred to other clusters. With this cross-validation, similarity in hydrological functioning will be explored and linked to easy-to-observe parameters such as geology, slope, aspect, height above nearest drain or land use. This link between hydrological functioning and catchment structure, will make it possible to parameterize the model for the whole 288 km2Attert basin, without further calibration.
References
Reusser, D. E. & Zehe, E. Inferring model structural deficits by analyzing temporal dynamics of model performance and parameter sensitivity. Water Resour. Res., 2011, 47, doi:10.1029/2010WR009946
Rietkerk, M. & van de Koppel, J. Regular pattern formation in real ecosystems. Trends in Ecology & Evolution. 2008, 23 (3), 169 - 175, doi:http://dx.doi.org/10.1016/j.tree.2007.10.013.
Zehe, E.; Maurer, T.; Ihringer, J. & Plate, E. Modeling water flow and mass transport in a loess catchment. Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and Atmosphere , 2001, 26, 487 - 507, doi: http://dx.doi.org/10.1016/S1464-1909(01)00041-7
Figures caption
Figure 1: a) sketch of all sensors within a cluster site, b) Sketch of model setup of the unsaturated zone