Elsevier

Computers & Geosciences

Volume 126, May 2019, Pages 62-72
Computers & Geosciences

Research paper
The value of simplified models for spin up of complex models with an application to subsurface hydrology

https://doi.org/10.1016/j.cageo.2019.01.014Get rights and content

Highlights

  • Aim of reducing spin-up time of large scale surface-subsurface models.

  • Accounting for the unsaturated zone is crucial when initializing a 3-D model.

  • Starting from simplified subsurface models including both saturated and unsaturated zones resulted in shortest spin up times.

Abstract

Spinning up large-scale coupled surface-subsurface numerical models can be a time and resource consuming task. If an uninformed initial condition is chosen, the spin-up can easily require 20 years of repeated simulations on high-performance computing machines. In this paper we compare the classical approach of starting from a fixed shallow depth to groundwater (here 3 m) with three more informed approaches for the definition of initial conditions in the spin up. In the first of these three approaches, we start from a known-steady state groundwater table, calculated with a 2-D groundwater model and the yearly net recharge, and combine it with an unsaturated zone that assumes hydrostatic conditions. In the second approach, we start from the same groundwater table combined with vertical profiles in the unsaturated zone with uniform vertical flow identical to the groundwater recharge. In the third approach we calculate a dynamic steady state from a simplified subsurface model combining a transient 2-D groundwater model with a limited number of 1-D transient unsaturated zone columns on top. Results for spinning-up a 3-D Parflow-CLM model using the different initial conditions show that large gains can be made by considering states in groundwater and the vadose zone that are consistent, i.e. where groundwater recharge and the vertical flux in the vadose zone agree. By this, the spin-up time was reduced from about 10 years to about 3 years of simulated time. In the light of seasonal fluctuations of net recharge, using the transient approach showed more stable results.

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)

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