Since industrial agriculture is the main causative agent of eutrophication, I think that approaches to mitigate/reduce nitrate and phosphorus pollution in fresh water should be the following:
1. Reduce the application of synthetic fertilizers, or at least apply the exact dosage as suggested by soil type and crop being cultivated.
2. Increase soil organic matter (humus) as this has valuabe retention capabilities on different cations and anions (plants nutrients) as these move quickly through the soil-water (especially nitrogen
3. Ban the fertilizer anhydrous ammonia, which volatilizes in the atmosphere and later falls back through rain/snow precipitation causing acidification of soils
These nutrients are also contained in animals' manure and human feces. Therefore, a discharge of these wastes without adequate treatment (Physical, chemical, biological) into streams and rivers will cause eutrophication. Instead these wastes should be recycled on the farm to produce the organic matter that will retain these nutrients in the soil. Organic farmers know well all this. The problem is that industrial agriculture dominates the world of production and without much interest in eutrophication and other environmental issues (e.g.: soil protection from erosion, conservation of biodiversity, crop rotation and more agronomic practices that build soil organic matter) every country and community is affected.
Surprising there is not a lot of response considering it is still one of the largest issues for the aquatic ecosystem as a whole. As Bruno Borsari suggested the best method would be to directly go to the source as recognized vast input of fertilizers still come from there (albeit diffuse source). Otherwise also WWTP still release nutrients to the surface water in this regard (point source).
Nonetheless, what is often forgotten is that there are two possible pathways for eutrophication: external eutrophication (as the above) or internal eutrophication [1]. As input of nutrients from external sources reduces surface water can still have high concentration of nutrients, even though external input has been reduced. The focus on nutrient input can than be wasteful. Over decennia the nutrients N and P compounds build up within the sediment either via sedimentation of organic matter buried in there, or attached to clay particles. In sandy regions concentrations seem less high although this does not mean there are no issues. In theory reduction of fertilizers would be best option although conflicting interest are at play making this difficult.
If internal eutrophication plays a role then dredging (removal of the sediment) is the most straight forward. Yet, given we have x km of waterways or a number of large lakes it is a bit of an issue where to leave the sediment. Not to say that if we place it on land, the next heavy rainfall simply transports it back were it came from. Another way would be mowing and harvesting of aquatic plants, but could take years [2]. Moreover, assuming we were incorrect and actually the nutrient build-up within the sediment is higher than the release of nutrient to the surface water (we are still dealing with external eutrophication), it would be a lost cause.
Otherwise symptom treatment (in my opinion) is the addition of Iron salts. In some small pilot study I tried to add Fe and Ca salts to sediment and did not succeed to reduce the release of P although others seem to have success(?) [3]. There are also possibilities to reduce symptoms of eutrophication by direct addition to the surface water [4] or some also add PAC (I think they use it water preparation to flocculate floating particles [5]. I never read 4 and 5, but I worked with it on lab scale. Nevertheless, I do not think these things are a viable solution for large scale problems.
[1]
Article Internal eutrophication: How it works and what to do about i...
[2]
Article Finding the harvesting frequency to maximize nutrient remova...
[3]
Article Remediation of a Eutrophic Bay in the Baltic Sea
[4]
Data Iron addition as a shallow lake restoration measure: impacts...
[5]
Article Controlling eutrophication by combined bloom precipitation a...
Eutrophication can be mitigated also through conservation approaches both at the microscale and macroscale. For example at the micro scale (Household, farm, local community) eutrophication can be controlled through the design of constructed wetland in alternative to sewage systems for the management of human/animal waste. At the same level (micro) the construction/restoration of buffer zones adjacent to creeks and rivers will limit the loss of nutrients from cultivated fields that end in fresh water sources, on their way to the sea. Agroforestry has a vast body of literature about this topic. At the macro level instead we need to conserve, or restore wetlands along coastal zones as these will retain and metabolize nutrients contained in sediments by the plant community in place, while also increasing the water absorbing power brought to land by tropical storms and hurricanes.
I think a direct reduction of nitrate in the soil could only be done by (chemical or physicochemical) reduction into nitrogen. While there are some techniques for water, I do not know any application for soil.
Another possibility would be to cultivate nitrate using plants and harvest them. On the long-term this may reduce nitrate.
Further, I heared about some nitrate-consuming microbes. But I do not know whether they can directly applied in soil.
Eutrophication is the process in which lakes receive nutrients (phosphorus and nitrogen) and sediment from the surrounding watershed and become more fertile and shallow. Eutrophication can be slowed by reducing nutrient and sediment addition to the lake.
I think these papers could help you;
Modelling reduced coastal eutrophication with increased crop yields in Chinese agriculture, January 2017,
Soil factors influencing eutrophication. In Soilguide. A handbook for understanding and managing agricultural soils. (ed. Geoff Moore), 2001,
I think by reducing the application of chemical fertilizers in the soil. Also, the use of phytoremediation and phycoremediation techniques can prove to be helpful.
Eutrophication can reduce by decreasing the source of nutrients (e.g. by phosphate stripping at sewage treatment works, reducing fertilizer inputs, introducing buffer strips of vegetation adjacent to water bodies to trap eroding soil particles).
There are two possible approaches to reducing eutrophication: Reduce the source of nutrients (e.g. by phosphate stripping at sewage treatment works, reducing fertilizer inputs, or introducing buffer strips of vegetation adjacent to water bodies to trap eroding soil particles).