| 23 Mar 2026
Regularisation of the 4DEnVar Data Assimilation method for Calibration of Land Surface Models
Abstract. The four-dimensional ensemble variational (4DEnVar) data assimilation method is an attractive choice for land surface model calibration due to its ease of use, speed, and its circumvention of tangent linear model and adjoint calculations. However, in certain circumstances, this method may prove ineffective when implemented with a highly non-linear model, leading to out-of-range or non-physical posterior parameter values. To address this, the 4DEnVar cost function can be adapted through the introduction of a hyperparameter, which inflates the weight of the background term. In this study, we explore the anticipated challenges of applying 4DEnVar with in situ eddy-covariance flux measurements and present some explanations of the expected behaviour. We show that, when using a hyperparameter to regularise the optimisation, 4DEnVar is able to successfully calibrate two complex land surface models, JULES and ORCHIDEE, with comparable accuracy in its ability to produce model runs with an improved match to the observations. To our knowledge, this is the first study of its kind to compare parameter calibration of two different land surface models in the same experimental setting. In addition to the aforementioned benefits of using 4DEnVar, we show that the method also exhibits considerable versatility, not only with regard to the land surface model to which it is applied, but also in terms of parameter set selection and ensemble size.
Review of
Regularisation of the 4DEnVar Data Assimilation method for Calibration of Land Surface Models.
by Douglas et al.
General comments:
This methodological paper focuses on improving a land surface model calibration data assimilation scheme. The authors attempt to enhance an existing method by incorporating a tunable parameter (gamma), which can be adjusted to optimise the efficiency of model parameter retrieval. The performance of the new method is evaluated using data from a Fluxnet forest site in the context of GPP (photosynthesis) observation assimilation. The method is applied to two different models: JULES and ORCHIDEE. Photosynthesis parameter values are retrieved for both models. In the case of ORCHIDEE, the retrieval also includes phenology and hydrology parameters. This well-written paper could be accepted after minor revisions.
Particular comment:
- L. 74-76: This sounds like a result or conclusion. In the introduction, it should be rephrased as a research question to be addressed.
- L. 76-78: Results should be interpreted in the Discussion section, not the Introduction. This sentence could be replaced with a research question that needs answering.
- L. 126 (Table 1): Replace "N/A" by "-" or by "Unitless". I am surprised that a key parameter such as rooting depth has not been included in the analysis. In what way does each model describe soil moisture stress?
- L. 127 (Section 2.2): Does this method account for errors in the atmospheric variables that the models use as input?
- L. 130: "observations given the target" is unclear. Do you mean "given the value of the target"?
- L. 260: The reason why this Fluxnet site has been chosen over another should be explained. Are soil moisture deficits observed at this site?
- L. 262: 'GPP observations' are used. It should be made clear that GPP is not directly observed. I suppose the GPP values you use are derived from NEE observations and an ecosystem respiration model?
- L. 327 (Fig. 5): RMSD values should have units. Year 2010 is interesting because both calibrated models are wrong. Why is there such a large delay in peak GPP for the two models?
- L. 386 (Fig. A1): Figure A1 is not mentioned in the text. The current caption of Figure A1 includes an interpretation. This interpretation should be incorporated into the main text. The reasons why the L-curve technique cannot be used to select gamma should be clearly explained.