Understanding complex environmental systems: a dual approach

Abstract

SUMMARYAn approach to interpreting field data exploiting the duality of data-and theory-based models, and their associated methods of system identification, is presented. This approach seeks to overcome the respective limitations of the two branches of the duality: that theory-based models are not unambiguously identifiable from the observations, while a well-identified data-based model may not be capable of a satisfactory theoretical interpretation. The purpose of the approach is thereby to gain a deeper understanding of complex, poorly defined environmental systems. Recursive methods of time-series analysis are used to identify the data-based models (as transfer functions) and companion recursive methods, specifically the recursive prediction error (RPE) algorithm, are employed for structure identification and parameter estimation of the theory-based models (in ordinary differential equation forms). The results of these identification exercises for the two classes of models can be compared in terms of the macroparameters of the studied system's time constant and steady-state gain. Two case studies are presented to illustrate the overall performance of the dual-thrust approach, on an activated sludge system and an aquaculture pond. It is found that: (1) as opposed to the exclusive use of either approach alone, more is to be gained through the joint application of the two classes of models, which historically have tended to reflect quite separate, unconnected approaches to interpreting environmental systems data; (2) to some extent, identifying the structure and estimating the parameters of one type of model can be readily improved by recourse to the corresponding results for the other; and (3) reconciliation of the results from identifying the two classes of model in the parameter space-of the time constant and steady-state gain-has significant advantages over the more familiar process of evaluating a model's performance in the terms of its (observed) state-space features.

Processing arctic eddy‐flux data using a simple carbon‐exchange model embedded in the ensemble Kalman filter

“…The first modification was to compensate for autocorrelated deviations between predictions and observations by allowing the EnKF to sequentially recalibrate unobserved components of the Kalman state vector (Lin and Beck 2007). The unobserved components of the state vector can either be variables in the embedded model or parameters augmented to the state vector.…”

“…5,6,and 8). These diel patterns are a clear indication that there is a deficiency in PLIRTLE that precludes it from capturing all of the nonrandom pattern in the NEE time series Young 1976, Lin andBeck 2007). Even if we had adjusted b so that the LAI estimates lost the diel pattern (i.e., increased b .…”

“…Because of the temporal autocorrelation in deviations of the second type, they are a clear indication of either a deficiency in the model (Lin and Beck 2007) or a comparable drift or bias in the instrumentation used to measure the input (u t ) or observation (z t ) time series (e.g., Burba et al 2008). Again, there is no way to distinguish between these two possibilities based on the time-series data alone.…”

Processing Arctic Eddy-Flux Data Using a Simple Carbon-Exchange Model Embedded in the Ensemble Kalman Filter

“…We presented two modifications to the ensemble Kalman filter (EnKF) that improve its performance for filtering time-series data. The first modification was to compensate for autocorrelated deviations between predictions and observations by allowing the EnKF to sequentially recalibrate unobserved components of the Kalman state vector (Lin and Beck 2007). The unobserved components of the state vector can either be variables in the embedded model or parameters augmented to the state vector.…”

On the identification of model structure in hydrological and environmental systems

“…It articulates the key principles of Young 's [1999] algorithms for estimating time‐varying parameters in input‐output, “externally descriptive” models into the domain of models that are internally descriptive, i.e., seek to account for the conceptual mechanisms governing the manner in which input stimuli are transcribed into output responses. Indeed, given the similarity of algorithmic approach spanning the two forms of models (“data‐based” and “theory‐based,” respectively), it contributes significantly to implementation of a recently proposed dual approach to identifying models of environmental systems [ Lin and Beck , 2006, 2007]. Above all, it realizes in specific, computational form many of the conceptual features proposed previously as desirable for the design of an algorithm for model structure identification [ Beck et al , 2002].…”