Total dissolved solids ( TDS) is based on chemical property. By definition TDS is sum of all chemical constituents which are in dissolved form. SAR diagram is used for the classification of water quality. For detailed study a large number of literature is already available.
If your question is "Which water quality parameters shows a good correlation with TDS ...". - I would say conductivity. All dissolved ions contribute to the conductivity of water. You can easily estimate TDS from conductivity measurement if you know the type of water you are dealing with.
To answer to this question I can add an other parameter which is the ionic strengh of the aqueous solution, which reflects in some way the magnitudes of ion-ion and ion -solvent interactions. Hence the necessity to use the activities instead of concentrations, in the case of non-dilute solutions.
When you dealing with dissolved particle or particulate (solid) the most problem as parameter water player is pH. However if you have tested into marine environment the salinity was also others important water parameter that you need to care every single time.Too mess for handling especially Cl for sodium analysis of SAR in salt realms and terrestrial region where both are affinity compared other constituent i.e Mg, Ca . But you should also take into account for another parameters of water quality too.
Total Dissolved Solids is mainly a chemical parameters, it is associated with amount of ions (mainly major and minor ions) presence in water, although it depend on the presence of Electrical Conductivity Value (EC). if you have study in coastal aquifer , comparison of Na and Cl with TDS is adopted. SAR is commonly used to determination of groundwater suitability for irrigation. the best plot for comparison of cations and anions with TDS is Gibb's plot. A large number of literature is already available detailed study of groundwater quality.
The parameter that correlates with TDS is conductivity which is a measure of mobile ions in the water. Generally high TDS may imply high mobile ions in the water.
I strongly suggest you read through the TDS section in: Study and Interpretation of the Chemical Characteristics of Natural Water, U.S. Geological Survey, Water Supply Paper 2254 By John D. Hem. It is available for free at: http://pubs.usgs.gov/wsp/wsp2254/
TDS in the lab is a measure of residue left after evaporation and raising the sample to an elevated temperature (180 DegC, if I remember correctly). You may lose some dissolved constituents due to evaporation, reactions, or volatilization. Any non-ionic solid (such as silica) will also be included in the total. This is why there is only (at best) a correlation between conductivity and lab TDS.
Field meters that report TDS actually estimate TDS based on conductivity and can be quite inaccurate in waters of unusual compositions.
Try to take measurement on water pH, electrical conductivity and temperature if the lake is unproductive. This is so because dissolved oxygen profiles is chiefly determined by temperature in freshwater lakes/rivers that are non productive due to low nutrients.
FYI more than 99% of TDS in natural waters is composed of Na+, K+, Ca++, Mg++, Cl-, CO3=, HCO3-, and SO4= ions in solution. That is why at a minimum one should analyze for these anions and use results to check charge balance for lab quality. pH will be the principal determinant defining the relative speciation of the carbonate anions.
From my previous studies on industrial wastewater, it was obtained that TDS is correlated with pH, temperature and the electrical conductivity. Specially EC and pH values can influence the wastewater TDS in a higher degree.