You could look to Natural Resource Damage Assessment (NRDA) valuation methods for examples of valuating non-use natural resource values. Non-use values aren't generally defined by the marketplace, thus public surveys are often the valuation method of choice (contingent valuation). This entails asking members of the public what they would pay to prevent the loss of those (aesthetic, etc.) uses. If you use this methodology, it can be undermined by the inclusion of more easily quantified/valuated losses (e.g., ecotourism), so be careful what services you include in that value set. I recommend reading up on NRDA valuation methods.

Here's a good paper (not mine) on non-use valuation methods: http://lawdigitalcommons.bc.edu/cgi/viewcontent.cgi?article=1123&context=ealr

Here's a breakdown of natural resource valuation methods in general (not mine):  https://webapp1.dlib.indiana.edu/virtual_disk_library/index.cgi/4928836/FID1596/html/socioecn/rvnatres.htm

I'm going to be a bit of a heretic. 

In all economic transactions, the value of a product or service is perceived by the vendor to be less than the selling price, while the value perceived by the buyer is greater than the selling price. Or rather than the price, the value of the money equal to the selling price, although that distinction is not truly relevant.

But then, it is asked, what is the value of ‘Green’? Or, what is the value of the ecological systems that surround us and provide us with ecological benefits?

As there is no vendor, there is no value to the vendor, and thus the selling price may be zero. In the concept of Environmental Economics, the ‘Government’, as the steward of The Commons, is able to set a price that reflects the price of those environmental benefits. Of course, the concept also assumes the government is effectively omniscient, omnipotent, and wise, three conditions that are not supported by the evidence.

Likewise, there really isn’t a buyer. Why would you pay for air? No one can stop air from reaching me for free. But imagine if one could, then I would pay anything I owned to get my next-to-last gasp.

So, in the case of a 'commodity' such as air, the value is less than the selling price, which is therefore nothing, and also greater than the purchase price, which could be anything. The concept of value must be uncoupled from price for at least some environmental features.

Perhaps value of the environmental feature can be estimated from a replacement cost. Thus, while I can’t estimate the value of sunlight, I can estimate the economic value of providing a similar quantity of heat and light. But that only works when there is a technological replacement for that environmental feature. So, while the case study of the New York City water supply would suggest that clean land will save about 0.5 cents/acre/ca., some environmental features cannot be replaced.

This introduces a concept that usually would have no place in a discussion of economic value. There are environmental features that cannot be replaced by current technology, are not avoidable or controllable, and are therefore not buyable or sellable.  Thus, the only value they could have is measured by the cost of their absence.  So, what is Gravity worth?  If Gravity ceased to operate tomorrow, there would be no life on the planet by the end of the day.  So arguably, the value of Gravity is infinite.  Rather than that, I would introduce the concept of ‘Sacred’ – any feature that is not replaceable, not avoidable/controllable, and/or not sellable, is Sacred, and cannot have a value that can be measured in something as vulgar as money.

For example, sunlight, by that definition, is Sacred. Even if the fraction of the Sunlight that goes to photosynthesis is considered, it is effectively Sacred, as there is no way to replace it.  If this is pared down further to the sunlight that is used to produce food, the economic value is so large (eg, all economic activity on the planet has the same value as all food production on the planet, since we all work for food) that it is effectively Sacred, even if it doesn’t precisely meet the definition (replaceable, just not at that scale).

It is clear that one could find many environmental features that meet the concept of Sacred. This illustrates that there is a need for the concept, and that there is a weakness in any financial argument, because many ‘things’ have some very high intrinsic values that cannot be reflected in financial terms. Another unit of measure is required.

Natural Services are processes that reduce the amount of time required for communities to meet their needs, without an investment of time and/or resources on the part of the community. Thus a volcano adding ash to soils, and thus increasing crop productivity, is a natural service. Weather, sunlight, tides, etc all are natural services. Natural services renew renewable resources, assimilate wastes, and in many other ways allow people to live on the world in relative comfort, because we gain disproportionately to the effort required to utilize these services.

The value of the natural service is, at an absolute minimum, the replacement time cost for the community to either do without the natural service, or to substitute the natural service with an alternative. In many cases, the natural service will not be replaceable or avoidable and is therefore Sacred. This does not invalidate this argument, rather it demonstrates that some things are not and should not be for sale.

Thus, the value of ‘Green’ is, at a minimum, the aggregate time cost of the incremental absence of the natural services associated with ‘Green’. Due to synergistic effects, this apparent value must be conservative, and possibly very much so.  And at all times, one must consider that the natural service may be priceless.

I strong recomend that you read CONSTANZA, 1997 (Nature).

Dear Rubens, Do you have the full title of the paper?

The value of the world's ecosystem services and natural capital;  Robert Costanza, Ralph d'Arge, Rudolf de Groot§, Stephen Farber∥, Monica Grasso, Bruce Hannon, Karin Limburg , Shahid Naeem, Robert V. O'Neill, Jose Paruelo, Robert G. Raskin, Paul Sutton∥∥ & Marjan van den Belt, 1997, Nature

Ephrem, these papers provide an overview of how the valuation of ecosystem services including non-use value of the forest is carried out.  l would strongly recommend that you read them.

1. Costanza R, d’Arge R, De Groot R, Farber S, Grasso M, Hannon B, et al. The value of ecosystem services: putting the issues in perspective. Ecol Econ. 1998;25(1):67–72.

2.  Pagiola S, Bishop J, Von Ritter K. Assessing the economic value of ecosystem conservation. 2004 [cited 2017 Mar 31]; Available from: http://bibliotecavirtual.minam.gob.pe/biam/handle/minam/1590

3.  Pant K., Rasul G, Chettri N, Rai K., Sharma E, ICIMOD. Value of forest ecosystem services: a quantitative estimation from the Kangchenjunga landscape in eastern Nepal. Kathmandu: International Centre for Integrated Mountain Development (ICIMOD); 2012.

Yes, 

this is called non-market valuation method. 

there are many techniques you may used such as Hedonic Price method, Travel Cost Method , or Contingent Valuation Method. 

you can find my paper were I estimated the value of clean air in Kuala Lumpur city using CVM.

Article Willingness to Pay to Improve Air Quality: A Study of Privat...

Hallo Ephrem Imanirareba, I see that some values you describe have been underline by P.R. Sarkar in His 5 Foundamental Principles of the economic theory of PROUT (PROgressive Utilisation Theory). I would like to add that a value is dependant on the OBJECTIVE you fix, according to that for example the CLEAN AIR improve the people's health and the goverment spend less in care. How much must be research... 

Or afforestation contribute to mantain a balance in rainfall, diminishing the risk of drawght and lack of drinking water. How much, must be research...

Or we know that 1 square kilometer of forest sequesters 10 tons/year of CO2, and preserve about 260 tons of water wich is slowly release in the hot season, to mantain the soil sufficienty wet...

So there are many aspects wich must be investigate according to the objectives, but I will investigate about the articles...