Professor I suggest for you: Maller et al. 2006, Neighborhoods with comparatively more walk able green space and health ,2006

Thanks

Since parks are considered part of public amenities and is treated as a public good by policy makers, you may want to consider the constructs of spatial equity and accessibility, and define optimality in relation to these. Optimality would then be a relative metric rather than an absolute one.I recommend the corpus of research by Talens and Anselin as well.

m.epn.sagepub.com/content/34/7/1185.abstract

I would recommend you this paper. 

Turner, R. W.. (2002). Market Failures and the Rationale for National Parks. The Journal of Economic Education, 33(4), 347–356. Retrieved from http://www.jstor.org/stable/1183136

you may also refer to publications about hedonic price method in tourism. One of variables is proximity to the center or transportation hubs. They mostly refer to hospitality but you may apply them to your national parks. 

I do not understand the question. On the one hand, one could ask the question "how close should parks be to one another." A related question is "how large should parks be." For example, tiny parks often exist between the roadway and the sidewalk. These parks are everywhere. In contrast, there are some very large regional parks for which one in a region is plenty. This is a question that harks back to the work of Loesch or Losch.

On the other hand, one could ask the question "where should land use x locate in relation to a park." While there are benefits to parks that are capitalized into surrounding land values, there are also diseconomies associated with being very close to some parks. This suggests that property values may rise and then fall as distance to a park increases. Furthermore, this suggests that there may be an optimal location in relation to a park. This question is similar to asking about the price effects of schools or whatever has both positive and negative effects.

These two broad types of questions are not unrelated. The second type could be seen as an input to the first type.

Dear Professor Colwell, thank you very much for your comments. The relationship between park and quality of life, though clear, is complicated of course.  In my question I tried to address the issue of "how far the size matters?" I have seen publications that take in account the amount of green space in a radius 1 and 3 km from residents homes. Could you suggest the same radius? 

Then another problem is "radius from where?" Center of park or perimeter of park, neighborhood or postal code coordinates of homes?

I would appreciate it very much if you could share your opinions on these issues.

When thinking about externalities in the urban context, think about boundary effects. So distance from the boundary is what matters most.

Of course, the relationship between park and quality of life is complicated (meaning multifaceted). But the market simplifies everything. So this relationship is summarized by the property value surface around parks. So stop thinking about a radius around parks. Instead, think about the value surface in all directions. This surface is intersected by similar surfaces from other parks. For a given park type, the lines of intersections defines park market areas. Refer to Losch (August). What do you find? Are the market areas approximately hexagonal?

Dear Zedy,, as said by my colleagues, the matter is not simple and still debated. It is sure that urban green provides a large array of opportunities and benefits for human society, of social-cultural, economic, health and  environmental value (see Ecosystem Services). For this, referring to air pollution mitigation and socialization services for instance,  the better possibility would be that vegetation was located into the urban texture (see NY High Line), near inhabitants. From the practical point of view it is not always possible, because the scarcity of free and not-built spaces. For this reasons it is important to restore, connect and enhance little free areas, available into the city, as build so called "pocket parks".

Thank you Valerio. I appreciate it.

I can suggest you to read :

Miller, D., Horne, P., Morrice, J., & Donnelly, D. (2012). Physical and Visual Accessibility of Greenspace. In 12th International Conference on Design & Decision Support Systems (pp. 1–16). Eindhoven.

Many studies cite 500-m. I cannot trace the origin but the number is widely used. 

Dear all, I would suggest also to analyze how the European Environment Agency evaluates the presence of green areas in European cities for the award of the European Green Capital (http://ec.europa.eu/environment/europeangreencapital/).

Publications can be reconstructed from the many dimensions of the green areas of the city, even those concerning the results obtained through planning (http://ec.europa.eu/environment/europeangreencapital/press-communications/egca-publications/index.html).

The proximity of green areas and parks in urban areas must therefore be understood as dissemination and ease of access for all citizens.

See also for economic assessment: http://www.teebweb.org/ and in particular:http://www.teebweb.org/wp-content/uploads/2013/04/D0-Chapter-5-The-economics-of-valuing-ecosystem-services-and-biodiversity.pdf

- If we are talking about access to urban park, the criterion for distance from an individual's dwelling will depend on the population we are studying. It will be handy if you have access to the travel survey data of your study area and are able to calculate the median distance walked. This should act as a radius of the buffer you will draw around the study participant,s dwelling to evaluate access to green; can be 1 km, 3 km or any other radii.

- The second consideration is the criteria for optimised park size to make a difference in terms of walkability, physical activity and social capital.

- The third consideration will be the distribution of urban parks with respect to the matrix of population density in a city.

Dear Zydi,

I agree with what has been said, but I would also add the importance that urban parks have in terms of ecologic network. This might appear irrelevant in some parts of the world, but in highly urbanised regions (such the north of Italy), it is highly important that parks are designed and placed so to guarantee a connection between the rural, the forests, and the urbanised areas.

Speaking about urbanised areas, another approach that might be useful to consider is the amenity value of parks. This brings the quality of life back in the equation, with other aspects such as the ecologic value of parks, their accessibility by residents, of course the economic impact that parks have on the real estate market, the opportunity of their localisation in areas with high temperature peaks and high concentrations of pollutants in the air, and so on.

An interesting paper about this is Lu, S., Wang, F. 'Computer aided design system based on 3D GIS for park design', 2014 International Conference on Computer, Intelligent Computing and Education Technology, CICET 2014; Hong Kong.

And generally speaking, a basic paper is Payne, L.L., Mowen, A.J., Orsega-Smith, E. 'An examination of park preferences and behaviours among urban residents: the role of residential location, race, and age' Leis. Sci., 24 (2002), pp. 181–198.

I am not an expert in the field, but I have had the chance to work on the location of urban parks in some Italian cities -as part of projects linked to the need to the restoration and enhancement of buildings in the historic centres.

I hope my perspective can be of any help to your research.

Kindest regards,

Umberto