Irrigation is an important component of the terrestrial water cycle, but it is often poorly accounted for in models. Recent studies have attempted to integrate satellite data and land surface models via data assimilation (DA) to (1) detect and quantify irrigation, and (2) better model the related land surface variables such as soil moisture, vegetation, and evapotranspiration. In this study, different synthetic DA experiments are tested to advance satellite DA for the estimation of irrigation. We assimilate synthetic Sentinel-1 backscatter observations into the Noah-MP model coupled with an irrigation scheme. When updating soil moisture, we found that the DA sets better initial conditions to trigger irrigation in the model. However, large DA updates to wetter conditions can inhibit irrigation simulation. Building on this limitation, we propose an improved DA algorithm using a buddy check approach. The method still updates the land surface, but now the irrigation trigger is not based on the evolution of soil moisture, but on an adaptive innovation outlier detection. The new method was tested with different levels of model and observation error. For mild model and observation errors, the DA outperforms the model-only 14-day irrigation estimates by about 30% in terms of root-mean-squared differences, when frequent (daily or every other day) observations are available. The improvements can surpass 50% for high forcing errors. However, with longer observation intervals (7 days), the system strongly underestimates the irrigation amounts. The method is flexible and can be expanded to other DA systems and to a real world case.

High-resolution water budget estimates benefit from modeling of human water management and satellite data assimilation (DA) in river basins with a large human footprint. Utilizing the Noah-MP land surface model, in combination with an irrigation module, Sentinel-1 backscatter and snow depth observations, we produce a set of 0.7-km$^2$ digital water budget replicas of the Po river basin (Italy) for 2015-2023. The results demonstrate that irrigation modeling consistently improves the seasonal soil moisture variation and summer streamflow at all gauges in the valley after withdrawal of irrigation water from the streamflow (12\% error reduction relative to observed low summer streamflow), even if the basin-wide irrigation amount is underestimated. Sentinel-1 backscatter DA for soil moisture updating strongly interacts with irrigation modeling: when both are activated, the soil moisture updates are limited, and the simulated irrigation amounts are reduced. Backscatter DA systematically reduces soil moisture in the spring, which improves downstream spring streamflow. Assimilating Sentinel-1 snow depth retrievals over the surrounding Alps and Apennines further improves spring streamflow in a complementary way (2\% error reduction relative to observed high spring streamflow). Despite the seasonal improvements, irrigation modeling and Sentinel-1 backscatter DA cannot significantly improve short-term or interannual variations in soil moisture, irrigation results in a systematically prolonged high vegetation productivity, and snow depth DA only impacts the deep snowpacks. These findings help to advance the design and production of digital water budget replicas for river basins.