If you don't have soils expertise, look for some.  This soil has chemical imbalance, too much salt, not enough calcium.  Unless you intend to spent resources to improve this, you need to try to find native plants that grow and thrive under the conditions and provide some benefit.  Plants that help to accumulate organics are probably helpful.  Probably some info on FAO website.

I don't have specific knowledge either and from your question I presume that the ground water is saline.  If so, you need to consider either not using it or managing its use very closely. This is part of a production system that includes choice of crop.  The depth to water table should be monitored.  Depending on the source of the salt and how it is moving in the landscape, foresting some areas may help in the long run.

I had one more guess I will,call it.  When I was at University of Missouri, we irrigated a forest and bottomland forest from the 3rd stage of sewage ponds waste water at Bennett Springs State Park.  Kardos and Sopper at Penn State University in the 1970s were into major studies on the effects, etc.  They cropped reed canary grass to remove some of the nutrients they had concern over.  There goal was to treat the wastewater without damaging soil and groundwater instead of letting just evaporate or overflow.  I read someplace about adding gypsum.  I think I remember our soil scientist Dennis Law telling me that Leon soil type in Atlantic Coastal Plain has sodic properties.  That soil functions as a wetland in wet years and non-wetland in dry years.  It builds up iron concretions that apparently can restrict root growth and penetration.  The pine trees grow, but not fast.  Yet, I have seen cavities of Red-cockaded woodpeckers in some of these trees in Georgia adjacent to Okenfenokee Swamp.  RCW is a threatened species.  We have tried in SC to fertilize some of these soil with no response.  I have heard that others may rip them before replanting to help break up iron concretions.  Some plants like Spartina are adapted to tidal and brackish wetlands, and again, salt marsh habitats are coveted by an array of wildlife in coastal areas.  There is a high value sweet grasses  that the African American culture uses to hand weave baskets that grow in brackish and upland soils (two spp.), some sea oats and probably other plants.  Dr. Milham said monitor water table, yes.  And might also be useful to monitor the chemical composition of it, how rain might help dilute the concentration, etc.   We used ceramic cups on end of plastic pipes at various depths to sample groundwater in the wastewater irrigation study that I uploaded, Tennyson first author.  If you can find something native to your area that will grow there, produce goods, services, or habitats of benefit, I would look into those options first, before spending a lot of money and effort to alter and reclaim the soil into something else.

I am sorry, the Leon soils are spodic, not sodic, so disregard that section of my response.  I am on my IPad, so I don't have access to my files.

Thanks for your suggestions Dr. Pual and Hansen

In this case you dont have an opurtunuty to chemically remediate the soils. You have therefore to treat soil with plants resistant to high salinity and alkalinity along with organic matter amendments. For this reason brassica sps may be suitable because they uptake significant amounts of Na and can be cultivated winter time if it is mild.This could be one option in hand. The other is try to manage soil under dry-drainage system. This will enable to partially use your field. Or you can combine these two systems to remediate the soil.

flooding (excess sodium can be leached through this means) and phyto-remediation (calcicole)  will help to reclaim that calcareous soil.

Interesting discussion on an important topic.For managing calcareous sodic soils and for optimizing soil conditions, water is prime requirement. So on farm water harvesting is prime need.Harvested fresh water and saline ground water can alternatively be used for irrigation. If sufficient water can be  harvested, one can go for reclamation of sodic soils using gypsum as amendment. Since the soils are calcareous, one can use sulphur and pyrite also as amendments. Regular use of organic manure will have both ameliorative and nutritional benefits. Crop residue recycing will also improve soil conditions.For N supply  , acid forming source like Ammonium sulphate can be used.For P supply single super phosphate can be used  as souce which contains 50% gypsum.Selection of crops and inter  crops in cropping system are important. As Zn deficiency is well established in these soils ,regular use of Zinc sulphate is a must.

@ Dr. Subba Rao

Dear Sir,

Many thanks for your valuable suggestions. The major problem in the study area (Thimmajipet mandal, Mahabubnagar district) is water availability. The MAR is around 450-550 mm and poorly distributed. Groundwater is the only source of irrigation and water harvesting is a tough ask because of poor rainfall. Since the water availability is very low the use of amendments like gypsum is a challenge and the calcareousness aggravates the problem. Anyhow, I will try to weigh in your suggestions and explore the possibility of implementing to a maximum possible extent.

Thanks and regards. 

 Mr.Vasu,first analyze the soil properties and find out the extent of

sodicity problem in the study area.  All the soils may not need reclamation..Also analyze the ground water samples to know the extent the salinity problem of irrigation water.Some well waters may be suitable for occational irrigation .Cotton can tolerate water salinity.Farmyard and sheep and goat  manures may be avialble in the area mentioned.Apart from N ,P and Zn deficienvies may be prominent in the area.So look into the soils and resources in the area and accordingly plan the agronmic practices including manure and fertilizer use. Best wishes.

Best choise for plant is to cultivate winter crops resistant to salinity and alkalinity. I suggest barley, cabage, cauliflower etc. In the winter, relatively higher rainfall an lower evaporation reduce the water stress an enable to grow plant with higher productivity. In the summer season the continous upward movement of water an the solutes increase water stress even you crop salt resistant plants. Along with winter crops use dry dranage the field. For this you should elevate some part of the field as strips and. Make lower some parts again as strips. In this case, salts and some excessive water will move towards the lover strips by leaving relatively reduced salt in thethe effective root growth zone of the upper strips that will be more convenient for crops to grow. By this practice you can improve soil conditions, have higher water use efficiency, etc.

Rainfed calcareous and sodic soils of maharashtra recorded lower yield 2-2.5 quintals of cotton than other black cotton soil. It might be micronutrients (Fe,Zn,Mg) deficiency. If we can try to modify chemistry of calcareous soil through external inputs through only soil application like micronutrient enriched FYM,/compost/ vermicompost, mulching, green manuring.  The prevailing biophysical parameters doesn't favour us for foliar application under rainfed areas. Shallow black soils water storage is difficult and not possible for long duration cotton. Thus, we can recommend short duration cotton varieties for this soil with micronutrient application.

Dr.Manikadan, what is the problem in foliar application of micronutrients,or even NPK in rainfed crops like cotton?

Sir, Of course, foliar Spray of micronutrients will better option in irrigated cotton . But under rainfedcotton vegetative growth period and rainfall distribution period in this region same and we will not able get the benefit of foliar spray. Example if we are spraying today , it should not rain next two days or 48 hrs. If it rains all the foliar spray nutrients wasted in run off and will be fixed in nonrhizosphere. In this condition only we unable receive the full benefit of foliar spray.

Many Thanks Dr. Manikandan and Dr.Subaa Rao for your suggestions.