Regional/basin scale parameter estimation

An LSM’s potential for humid tropical applications is due to its robust modelling of the energy and water coupling and feedbacks. Yet studies evaluating land surface models in humid tropical regions where energy and water interactions are the most intense have been limited to lowland regions. Studies have looked at large areas of wetlands in the African tropics (Dadson et al., 2010; Koster et al., 2004). At an annual scale, Blyth et al. (2011) have evaluated JULES using data from several FLUXNET stations (Baldocchi et al., 2001) measuring sensible and latent heat and carbon fluxes, and concluded that for Santarem, Brazil, in the lower Amazon, the LSM produces,

• Higher photosynthesis and lower evaporation than observed

• More pronounced annual CO2 variation than observed

• Acceptable annual streamflow variation compared to observed • Constant LAI compared to small intra-annual variation observed

Is there value in regional calibration of LSM? Beven (1989) contends that all physics-based models are essentially lumped conceptual models and therefore face the same issues with pa- rameter errors. However, there are limited studies calibrating LSMs; the model’s global extent and physics-based nature make this a challenging task and the default/a priori parameters are often left alone. The PILPS project (Liang et al., 1998; Lohmann et al., 1998; Wood et al., 1998) has looked into local calibration of LSMs on a test site (single pixel), and found that cali- bration improved the performance of models. Using the classical approach to model calibration, they employed single objective functions to manually constrain model parameters using field measurements of streamflow, soil moisture, surface temperature, or radiation. Recognizing the multi-output nature of LSMs, later research work takes advantage of multi-objective calibration techniques (e.g. in Xia et al., 2002). The technique involves searching the parameter space until no further improvements can be made to the entire set of objective functions. The optimal set of parameters is then called the Pareto set (Gupta et al., 1998). To solve for the optimal set, automated search algorithms have been used such as the multi-start weight-adaptive recur- sive parameter estimation (Pauwels, 2008), the particle swarm optimization (Scheerlinck et al., 2009) and the shuffled complex evolution algorithm (Nasonova, 2011). The maximum likelihood objective functions are derived using Bayesian statistics of the model prediction error structure. Another approach to multi-objective calibration uses the Generalized Likelihood Uncertainty Estimation (GLUE) framework developed by Beven and Binley (1992), e.g. in McCabe et al. (2005). The method is entrenched in the concept of equifinality, in which it is believed that multiple sets of the model parameters (and structures) may be behavioural in describing a system (Beven, 2006). In this way, the likelihood function of better performing parameter sets can subjectively be assigned higher weights and the non-performers can be rejected, and the

entire suite of behavioural parameter sets is retained rather than a single optimal set (Beven, 2006). The problem is therefore in defining the appropriate likelihood function and threshold for behavioural sets (Beven, 2006), requiring subjectivity by the modeller. In an extension of the GLUE method, Beven (2006) proposed fixing an upper and a lower tolerance around the observation data to allow for input uncertainty.

A third approach is the step-wise parameter estimation that has been implemented manually in Xie et al. (2007), requiring an even higher degree of subjectivity. Subjectivity is inevitable even with the more complex methods due to the high dimensionality of LSMs; a common denominator of the calibration studies mentioned is a focus on a few selected parameters that are deemed the most important for each study’s objectives.

Parameter sensitivity analysis is a useful tool to reduce parameter dimensionality prior to calibration and in identifying model deficiencies. Several methods for parameter sensitivity analysis have been described by Liang and Guo (2003):

• varying one factor at a time

• multicriteria method of Bastidas et al. (1999) • fractional factorial design (Box et al., 1978)

Liang and Guo (2003) further discuss how the last two methods consider parameter interac- tions but can result in a set of parameters that do not make physical sense, e.g, one parameter describing clay and the other describing sandy soil, but further argue that at the large scale this may still be possible due to subgrid heterogeneity. Using fractional factorial design, they analyzed the sensitivity to soil and vegetation parameters in three different climate setups and found that (1) on an annual scale, energy and water fluxes are more sensitive to soil parame- terization uncertainty than they are to vegetation parameterization uncertainty, and that (2) the same LSM in different climate setups can show different sensitivity to the same parameters. In a more recent study using a predecessor of JULES on the arid Nile catchment, Elshamy (2006), performed the method of varying one factor at a time on soil hydraulic parameters, as well as parameters describing precipitation duration, threshold temperature for convective precipitation, and fractional coverage for large and convective rain, and found that while in the subsurface runoff calculation soil hydraulic parameters are controlling, in the surface flows and canopy interception calculations, the model is more sensitive to climate parameters. Later, Bakopoulou et al. (2012) looked into parameter performance in UK chalk catchments and cor- roborated the results of Elshamy (2006) in that their soil moisture simulations are the most sensitive to soil hydraulic parameters, followed by vegetation parameters such as the root depth. A new range of data have become available to support the multi-objective calibration frame- work, for example in-situ eddy covariation measurements of surface heat and carbon fluxes at FLUXNET sites; however, the data used for calibration are also known to introduce uncertainty, and the sources of errors are detailed in Williams et al. (2009a). For areas outside the scope

of FLUXNET measurements, satellite estimates of albedo, surface temperature and subsurface water mass have also been used (e.g. in Matsui et al., 2007; Lo et al., 2010; Gutmann and Small, 2010).