By parkland, do you mean green-spaces for active and passive recreation? If you do, this is a tricky matter. Most cities rely on some measure of green area per resident, or per 1,000 residents. Peter Harnik from the US non-profit - Trust for Public Land has done some work reviewing the level of green-space provision in cities in the USA. Most cities around the world have some form of enshrined standard in their planning ordinances, codes or supporting legislation. These standards typically have two forms: (i) an amount measure (ii) a proximity or accessibility measure. For example, 20 hectares of parkland per 1,000 residents and all residents will be able to access a park within 400 metres of their house. Seldom have these standards been met - usually for reasons associated with the historical provision of parkland, the function of urban land markets, histories of ethno-racial oppression and the decisions of local councils about what land, how much and where will be accepted for parks - oftentimes motivated by financial and maintenance concerns. You can access my review of the literature here: http://www98.griffith.edu.au/dspace/bitstream/handle/10072/34502/62968_1.pdf?sequence=1

You can also see my paper in Progress in Human Geography that talks about the environmental justice and political ecology perspectives of green-space provision: http://phg.sagepub.com/content/33/6/743.abstractules and a paper I wrote for practitioners in CITYgreen: https://www.academia.edu/3130290/Greenspace_planning_problems_with_standards_lessons_from_research_and_best_practices

More recently, the public health literature has led a challenge to standards, pointing to the fact that distance measures of proximity are quite arbitrary, and do not reflect barriers that are real or perceived. Moreover, people perceive distances differently to actual distances. And the distance that most people are prepared to walk to a park has declines markedly over the past 3 - 4 decades, as overweight and obesity have increased. Finally, park standards seldom recognise the need for diverse facilities in parks, the need for park programming and park activities, and rarely account for changing recreation needs as the socio-demographic composition of populations change.

While there are standard rules of thumb that can be used with the caveats that Jason highlights, sometimes local communities will set their own goals in the comprehensive plan or in a parks plan. For work we did in Houston, we built our model around the goals identified in the parks master plan and then attributed the parcel data to rapid assess whether a parcel would meet a master plan goal.

thanks Jason

your answer was very helpful

I suspect that there is another variable here. Adequacy might be defined by accessibility, as discussed above, but I would have thought that level of use would also be an important question - well equipped but empty parks within easy walking distance of everyone could not be construed as a 'success'.

Parks tend to be well used where they are NEEDED, that is, where residents to NOT have a large amount of yard space of their own. Typical Australian suburbs with housing densities of 8-12 dHa do not result in demand for parks and the result seems to be that some play equipment is put in to some barren ground (usually a storm-water detention basin, or power-line reserve) because you can't generally fit decent play equipment into a back yard.

If a park is a place for all to enjoy then it must provide what is not provided at home, and this cannot be a single activity (play equipment) solution. Denser cities NEED more parks because of what the homes lack, and ins such instances they are very well used, and exhibit a broad diversity of use.