Research paperThe value of simplified models for spin up of complex models with an application to subsurface hydrology
Introduction
Mathematical environmental models are affected by different sources of uncertainty (Beven, 2007; Refsgaard et al., 2007; Tartakovsky et al., 2012). Among others, setting the model initial conditions showed to be a significant source of ambiguity affecting model results and interpretations in many applications (Ajami et al., 2015; Berthet et al., 2009; Bruun and Jensen, 2002; Carvalhais et al., 2008; Noto et al., 2008; Rodell et al., 2005; Seck et al., 2015).
When possible, direct measurements are preferable to set up the initial conditions of a model (Baroni et al., 2010; D'Odorico et al., 2004; Erdal et al., 2014). However, observations are generally limited in their spatial resolution and coverage. For this reason, using direct measurements is unsuitable for many spatially distributed models. To overcome this limitation, regionalization approaches have been used (Ajami et al., 2014a; Kwon and Grunwald, 2015; Noto et al., 2008; Sivapalan et al., 1987; Weihermüller et al., 2013). For example, Sivapalan et al. (1987) used a topography-soil index to map the spatial distribution of the initial groundwater table for a subsurface-hydrological model. Similarly, Troch et al. (1993) estimated the groundwater distribution based on recession flow analysis. Ajami et al. (2014a) calibrated an empirical groundwater-level function based on preliminary spin-up tests. Weihermüller et al. (2013) used pedotransfer functions based on soil properties known at higher spatial resolution to obtain the initial values of the carbon pool for a land-surface model. However, the application of these approaches is often limited because the developed empirical functions are site-specific requiring adaptation when the method is used at other locations (Dimassi et al., 2018).
An alternative approach is to “spin up” a model in order to obtain feasible initial conditions for subsequent simulations. It is common practice to run the models with repeated forcings of a single year (or more) until they reach a dynamic steady state, that is, the temporal fluctuations are nearly identical from one simulation year to the next (Yang et al., 1995). To reach dynamic steady state may require simulations spanning tens of years for groundwater and land-surface models (Ajami et al., 2014b; Baroni et al., 2017; Cosgrove et al., 2003; Goderniaux et al., 2009; Jones et al., 2008; Rodell et al., 2005), and even hundreds to thousands of years in biogeochemical models (Law et al., 2001; Pietsch and Hasenauer, 2006).
Despite its wide use, the spin-up approach is limited by the computational resources when long simulation periods are necessary. For this reason, in several cases the number of simulated years may be defined more by the actual availability of computer power than by a proper definition of convergence criteria (Ajami et al., 2014b; Bruun and Jensen, 2002; Hashimoto et al., 2011; Shrestha and Houser, 2010). The problem is particularly relevant for complex integrated models based on partial differential equations describing processes in several compartments, or integrating different systems. Despite increasing computer power, these models routinely push available computing resources to their limit (Clark et al., 2017; Kollet et al., 2010). Because the actual capability to run long time series with these types of models is precluded, proper spin-up of these models is often limited.
In this study, we hypothesize that the use of a simplified and computationally faster model to generate the initial conditions for a computationally more demanding model, that still needs to undergo a spin up, could be a promising strategy to reduce spin-up time in many model applications. Attempts in this direction were performed by running the same model at a coarser spatial resolution (Rodell et al., 2005; von Gunten et al., 2014). In these cases, the initial conditions obtained by the spin-up of the coarser grid model were downscaled to the original finer grid scale in the subsequent simulations. In the present study, we follow a similar approach by using also mathematically simplified, but much faster, models that can be run on local desktop computers without the need for high-performance computers. We anticipate that the simplified models could inherently introduce some inconsistencies in the simulated physical processes when relevant features are not resolved (e.g., relief, land use, feedbacks between compartments etc.). Despite these deficiencies, the simplified models may produce useful approximations of the initial conditions that can lead to reduced spin up times of the complex model.
We test this hypothesis for variable-saturated subsurface models including land-surface processes and overland flow. These models present in fact both physical and computational challenges: the dynamics and feedbacks between compartments (e.g., land surface, unsaturated and saturated zone) can lead to instabilities, and the non-linearity involved in the simulated processes require a considerable computational effort. Both aspects are treated and discussed in the present study. We consider that our chosen model application represents aspects that could be relevant also for other environmental models.
The paper is structured as follows: the complex model and the models used for pre-spin-up are described in the next sections where we focus on the main components that are relevant to the present study. Next, we introduce a case study with the experimental design and the spin-up tests. We then present results explaining the processes and the computational challenges. We finish with remarks on the use of simplified models also in other applications.
Section snippets
Complex model: Parflow-CLM
The environmental system of interest in this study is water flow in the critical zone, including land-surface processes, vadose-zone hydrology, and groundwater dynamics. As complex model we chose the coupled Parflow and CLM models as implemented in the Terrestrial System Modeling Platform - TerrSysMP (Gasper et al., 2014; Shrestha et al., 2014).
Parflow simulates the 3-D Richards equation for variably saturated subsurface flow coupled to the kinematic-wave approximation of the shallow-water
Parflow-CLM model spin-up
Fig. 4 shows the groundwater table as function of time during the spin up of Parflow-CLM at four selected observation points (green circles in Fig. 2). Please note that the origin of the x-axis is on the right-hand side of the figure, so that the corresponding negative time values relate to the time before a model reaches convergence. As a consequence, the different lines start at different points on the left marking the different spin-up times, whereas all lines meet at the right when they
Conclusions
We have shown that the time requirements for spinning up a complex coupled subsurface-landsurface model, here ParFlow-CLM, largely depends on the choice of the initial condition. In particular, we could highlight that the initial condition in the unsaturated zone should be consistent to the initial condition of the groundwater table. Overall, the following conclusions can be drawn:
- 1.
The classical approach of starting at a fixed depth to groundwater is easy to implement, but tends to take much
Authorship statement
Model simulations and code development was performed by Daniel Erdal. Daniel Erdal and Gabriele Baroni analyzed the result and structured the paper with guidance from Olaf A. Cirpka. All authors contributed to the writing and shaping of the paper.
Acknowledgment
The study was supported by Deutsche Forschungsgemeinschaft under the grants CI 26/13-2 and AT 102/9-2 in the framework of the research unit FOR 2131 “Data Assimilation for Improved Characterization of Fluxes across Compartmental Interfaces”. Additional funding has been provided by Deutsche Forschungsgemeinschaft within the Collaborative Research Center CRC 1253 “CAMPOS – Catchments as Reactors”. Computing time has been provided by the Gauss Centre for Supercomputing (http://www.gauss-centre.eu)
References (50)
- et al.
Initialisation of the soil organic matter pools of the Daisy model
Ecol. Model.
(2002) - et al.
The impacts of CENTURY model initialization scenarios on soil organic carbon dynamics simulation in French long-term experiments
Geoderma
(2018) - et al.
Probabilistic modeling of nitrogen and carbon dynamics in water-limited ecosystems
Ecol. Model., Control of Distributed Systems and Environmental Applications
(2004) - et al.
Large scale surface–subsurface hydrological model to assess climate change impacts on groundwater reserves
J. Hydrol
(2009) - et al.
A new scheme for initializing process-based ecosystem models by scaling soil carbon pools
Ecol. Model.
(2011) - et al.
Newton–Krylov-multigrid solvers for large-scale, highly heterogeneous, variably saturated flow problems
Adv. Water Resour.
(2001) - et al.
Integrated surface–groundwater flow modeling: A free-surface overland flow boundary condition in a parallel groundwater flow model
Adv. Water Resour.
(2006) - et al.
Spatial and temporal variation in respiration in a young ponderosa pine forest during a summer drought
Agric. For. Meteorol.
(2001) A terrain-following grid transform and preconditioner for parallel, large-scale, integrated hydrologic modeling
Adv. Water Resour.
(2013)- et al.
Effects of initialization on response of a fully-distributed hydrologic model
J. Hydrol
(2008)
Uncertainty in the environmental modelling process – A framework and guidance
Environ. Model. Softw
Introduction to the special issue on uncertainty quantification and risk assessment
Adv. Water Resour.
Efficient calibration of a distributed pde-based hydrological model using grid coarsening
J. Hydrol
Technical Note: Reducing the spin-up time of integrated surface water–groundwater models
Hydrol. Earth Syst. Sci.
Assessing the impact of model spin-up on surface water-groundwater interactions using an integrated hydrologic model
Water Resour. Res.
Impacts of model initialization on an integrated surface water-groundwater model
Hydrol. Process.
Crop evapotranspiration —guidelines for computing crop water requirements
Uncertainty in the determination of soil hydraulic parameters and its influence on the performance of two hydrological models of different complexity
Hydrol. Earth Syst. Sci.
Effects of uncertainty in soil properties on simulated hydrological states and fluxes at different spatio-temporal scales
Hydrol. Earth Syst. Sci.
How crucial is it to account for the antecedent moisture conditions in flood forecasting? Comparison of event-based and continuous approaches on 178 catchments
Hydrol. Earth Syst. Sci.
Towards integrated environmental models of everywhere: uncertainty, data and modelling as a learning process
Hydrol. Earth Syst. Sci.
Transition probability-based indicator geostatistics
Math. Geol.
Modeling Spatial Variability with One and Multidimensional Continuous-Lag Markov Chains
Math. Geol.
Implications of the carbon cycle steady state assumption for biogeochemical modeling performance and inverse parameter retrieval
Glob. Biogeochem. Cycles
The evolution of process-based hydrologic models: historical challenges and the collective quest for physical realism
Hydrol. Earth Syst. Sci.
Cited by (3)
Estimating Groundwater Recharge in Fully Integrated pde-Based Hydrological Models
2023, Water Resources ResearchCoupling saturated and unsaturated flow: Comparing the iterative and the non-iterative approach
2021, Hydrology and Earth System SciencesIntegration of Soft Data Into Geostatistical Simulation of Categorical Variables
2020, Frontiers in Earth Science