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This paper deals with the retrieval of agricultural crop height from space by using multipolarization Synthetic Aperture Radar (SAR) images. Coherent and incoherent crop height estimation methods are discussed for the first time with a unique TanDEM-X dataset acquired over rice cultivation areas. Indeed, with its polarimetric and interferometric capabilities, the TanDEM-X mission enables the tracking of crop height through interferometric SAR (InSAR), polarimetric interferometric SAR (PolInSAR) and the inversion of radiative transfer-based backscattering model. The paper evaluates the three aforementioned techniques simultaneously with a data set acquired in September 2014 and 2015 over rice fields in Turkey during their reproductive stage. The assessment of the absolute height accuracy and the limitations of the approaches are provided. In-situ measurements conducted in the same cultivation periods are used for validation purposes. The PolInSAR and morphological backscattering model results showed better performance with low RMSEs (12 and 13 cm) compared to the differential InSAR result having RMSE of 18 cm. The spatial baseline, i.e. the distance between satellites, is a key parameter for coherent methods such as InSAR and PolInSAR. Its effect on the absolute height accuracy is discussed using TanDEM-X pairs separated by a baseline of 101.7m and 932m. Although the InSAR based approach is demonstrated to provide sufficient crop height accuracy, the availability of a precise vegetation-free digital elevation model and a structurally dense crop are basic requirements for achieving high accuracy. The PolInSAR approach provides reliable crop height estimation if the spatial baseline is large enough for the inversion. The impact of increasing spatial baseline on the absolute accuracy of the crop height estimation is evident for both methods. However, PolInSAR is more cost-efficient, e.g. there is no need for phase unwrapping and any external vegetation free surface elevation data. Instead, the usage of radiative transfer based backscattering models provides not only crop height but also other biophysical properties of the crops with consistent accuracy. The efficient retrieval of crop height with backscattering model is achieved by metamodelling, which makes the computational cost of backscattering inversion comparable to the ones of the coherent methods. However, effectiveness depends on not only the backscattering model, but also the integration of agronomic crop growth rules. Motivated by these results, a combination of backscattering and PolInSAR inversion models would provide a successful method of future precision farming studies. This work has been supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under project 113Y446, by the Spanish Ministry of Economy and Competitiveness (MINECO) and EU FEDER under projects TEC2011-28201-C02-02 and TIN2014-55413-C2-2-P.