Theoretical method of environmental risk assessment with given environment factors

Introductuon

The article provides a theoretical approach to the environmental risk assessment taking into account the meteorological factors in a probabilistic interpretation and recommendations for the selection of the raw data. The method allows to take into account the uncertainty of the natu--‐ ral environment in the risk assessment, which is especially important for the Arctic --‐global weather cuisine.

The Dualism of the certain riscs

Virtually all authors of the publications devoted to the problem of the risk, note the ab--‐ sence of a rigorous and generally accepted definition of the concept of the risk. Defined set of spectrum--‐division is rather wide: from general methodological formulations to rigorous mathe--‐ matical concepts. Content analysis allows to distinguish two main approaches to the concept of risk:

V risk - is the expected damage (usually in terms of value), indicating the uncertainty measures to achieve it;

V risc— is the expected damage (usually in terms of value) indicating uncertainty measures to achieve it.

The fundamental difference between the approaches may be partly explained by the fact that, as the authors of [1], in English, the word "risk" has two meanings: there is an adverse event and the probability (possibility) of the event.

The relationship of these approaches is clear: having a set of uncertainties in the imple--‐ mentation of adverse events with the specified damage to an exhaustive set of different damages, we can estimate the expected average (maximum, minimum, most likely, etc.) damage and get an idea of the probability distribution of damage. In this case, under the damage can be understood and the broader concept of harm in the appropriate units of measurement.

Understanding the leading role of uncertainty in the analysis and risk assessment, including environmental risks, contributed to the development of the statistical approach, the basic meth--‐ ods which are probability (frequency) analysis and Bayesian approach [2]. In [3] provides an over--‐ view of the development of the probabilistic analysis in the risk assessment.

According to [4], the concept of the risk refers to the impact of uncertainty on the achievement of the objectives. Risk expresses the probability of an event and its "contribution" on a par with the possible impact on the achievement of a certain structure (organization). As can be seen, this definition is consistent with the definition of an international standard [5].

Modern perceptions of the risk preference probabilistic approach. For example, the law "On Environmental Protection" [6] for the definition of the environmental risk is given without fuzzy terms "environmental risk – is the probability of an event that has adverse effects on the en--‐ vironment and the negative impact caused by economic and other activities, emergencies and natural man--‐made".

In 2007, the United States Environmental Protection Agency published a report which was submitted to analysis of the environmental risk assessment and identified the development of a methodological framework [7]. The report noted that the development of assessment practices possible environmental risks by improving the methods and tools towards a more comprehensive coverage of physical, biological and socio--‐economic aspects of the issues to make more informed decisions. In particular, we are talking about the spatial and temporal detail, given the complexity of biological systems and response to environmental effects of single or multiple sources.

A probabilistic approach to the risk assessment is best able to realistic estimates, which are unattainable for deterministic methods and, in addition, allows to take into account the cumula--‐ tive effect of multiple sources of uncertainty. However, the use of a probabilistic approach re--‐ quires additional knowledge and data. With respect to the probabilistic approach to the environ--‐ mental risk assessment agency notes that the application of the theory of probability to success--‐ fully solve problems into account the uncertainties (in this case, however, it is desirable to have a sufficiently representative sample).

Option rigorous approach to the "combination" of damages and uncertainties can serve as a quote from [8]: "... theoretical probabilistic analogue of the concept of damage, obviously, is the concept of a random variable. Same set of values of the random variables and their probability in probability theory given by the distribution of the random variable. Thus, a risk I would like to un--‐ derstand the random variable. However, if risks are identified with random variables defined on different probability spaces, the problem of comparing such risks is fundamentally unsolvable and even meaningless, since the corresponding random variables as a function of elementary out--‐ comes depend on the arguments that have different meanings. Therefore, in such situations is necessary to identify the risks of distribution functions. "In that paper the object of study is the distribution of the random variable outcome or insurance fund balance of the insurance company with respect to some fixed set of insurance contracts.

Mathematical modeling study of the financial risks as a functional on the set of the distri--‐ butions with certain properties developed [9]. In this paper, the measurement of the risk is under--‐ stood as a quantitative description of the preferences on the set of probability distributions. La--‐ conic, but quite comprehensive definition of the risk is given in lectures [10], namely, the risk is any distribution of the set of all probability distributions on a measurable set of results (ie, on the set of results with the corresponding σ--‐algebra). In this paper, the author will also adhere to the probabilistic approach to risk assessment.

The problems of the hydrometeorological factors

It seems obvious that hydrometeorological (including climatic) and geographical factors are extremely important for these types of effects, since in these factors can boost / cut the effect of human impact. (See, for example, a relatively favorable outcome of the incident in the British sec--‐ tor of the North sea in the oil and gas platform company "Total", which led to the leakage of natu--‐ ral gas in 2012), and in some cases can be a source of environmental hazards (a striking example is the disaster at the Fukushima nuclear power plant as a result of the tsunami).

Hydrometeorological (including climatic) and geographical factors exceedingly, exceedingly important for a variety of the impacts on the environment, as these facts tori can cause environ--‐ mental risk and / or strengthen / weaken the effect of Antropogennogo impact, but in the known methods of the assessing environmental risks of the standartization--‐meteorological factor, as a rule, does not explicitly present.

As one of the few attempts to take into account environmental factors can result in the company's approach to calculating the RAND Corporation risk in a special study, however, associ--‐ ated with the assessment of US defense capabilities. RAND Corporation uses two values: the prob--‐ ability of a future threat and the degree of influence on the state of the US defense [11]. It is noteworthy that, although the work are only illustrative values of the characteristics of risks to such hazards as natural disasters authors, regardless of the chosen strategy give the same value. In other words, for any strategy risk from natural disaster as a probable event with fixed effects of the same.

A formal description of the method of the ecological assessment, taking into the account hydrometeorological factors

We assume that the chosen and fixed spatial and temporal conditions of the environmenta risk assessment. The method is based on the following representation:

• V    meteorological factors may affect the realization of dangerous environmental situation (or may be the cause of environmental threat, or can be the catalyst / inhibitor environmenta threats);

• V    meteorological factors relevant to the selected conditions of time and place, are formed independently of other factors;

• V    hydrometeorological phenomena may be the joint probability events;

• V    environmental threats may be due to meteorological factors (threats of natural origin) or formed independently (the threat of man--‐made), and the degree of the potential environ--‐ mental damage may depend on meteorological factors;

• V    environmental threats may be the joint probability events.

We will call the set of the hydrometeorological factors and environmental situation – is a set of the environmental threats.

Let H = {H_s} _ (s = 1) ^ S --‐ complete system of pairwise incompatible hydrometeorologica factors (ie, a complete system of hypotheses), induced by a set of adverse weather events h_j, j = 1,2,3, ..., J relating to the selected conditions of time and place.

H_s events are all kinds of work (in the probabilistic sense) yavleniyh_j and otsutstviya¯ˉh_k kind Π_ (r = 1) ^ Jh_ (l_r) Π_ (g = 1) ^ J¯ˉh_ (l_g), l_r, l_g ε {1,2, ..., J│l_r ≠ l_g}. For example, the hy--‐ drometeorological factors (hypothesis) H_s may consist in the presence of the danger of drifting ice conditions for the appearance and the appearance of bryzgovogo icing without fear of meeting an iceberg etc.

Let Q = {Q_m} _ (m = 1) ^ M --‐ complete system of pairwise incompatible adverse environ--‐ mental situations (ie, another complete system of hypotheses), induced by a set of the environ--‐ mental threats (natural or manmade) q_j, j = 1, 2,3, ..., K in the same conditions of time and place.

Events Q_m also represent all kinds of the work (in the probabilistic sense) environmenta threats q_j and their lack ¯ˉq_k kind Π_ (r = 1) ^ Kq_ (l_r) Π_ (g = 1) ^ K¯ˉq_ (l_g) , l_r, l_g ε {1,2, ..., K│l_r ≠ l_g}. For example, the ecological situation (hypothesis) Q_m may consist in the presence of dangerous conditions the oil spill and fire without collision with another vessel, etc.

Let L – is the value of the environmental damage that may occur as a result of varying envi--‐ ronmental conditions, L ∈ [0, L_max]. It is assumed that the damages have the same dimension (for example, any damage is expressed in monetary units, or a degree (share) reduction in population size, etc.). Then the (full) the likelihood of the environmental situation Q_m taking into account meteorological factors can be defined as

P(Q ! ) = I! !! P(H_S)P(Q!/H_s ) .                       (1)

Here P (H_s) --‐ unconditional probability of the s--‐th hydrometeorological factors, P (Q_m/H_s) --‐ the conditional probability of the environmental situation Q_m under the action of hydrometeorological factors H_s. Equation (1) gives the probability of the environmental situation as a value that depends on the state of the meteorological parameters, which can increase or re--‐ duce the level of the environmental threats.

At risk of the getting environmental damage L in the implementation situation Q_m we un--‐ derstand the value of

P(L) = I! !! P(Q ! )P(L/Q_m ) ,                               (2)

where L – is the environmental damage, P (Q_m) --‐ unconditional probability of the envi--‐ ronmental situation Q_m (the likelihood of the private environmental situation), P (L/Q_m) --‐ the conditional probability of occurrence of the environmental damage L for the implementation of the environmental situation Q_m.

Substituting (1) into (2), we obtain the total probability of the occurrence of the environ--‐ mental damage L with the action of the hydrometeorological factors:

P(L) = I! !! I! !! P(H ! )P(Q ! /Н) ) P(L/Q ! ) ,                       (3)

which is an expression for the environmental risk of damage L.

Definition. Distribution F = {P (L_i)} _ (i = 1) ^ I damage L as a random variable in a discrete set of realizations {L_1, L_2, ..., L_I} or the distribution function F (x) = P (L

I = SU P(L!) L!                             (4)

for the discrete case

L = J xdF(x)

for the continuous variant, where the integration is over the set of the values of damage.

In the simplest case, when I = 1, the formula (4) takes the form ¯ˉL = PL, which is widely used in numerous publications as a measure of the risk. The practical significance of the formula (3) is largely determined by the choice of systems of hypotheses H and Q. unnecessary detail will lead to a lack of data to calculate the probability (frequency), and excessive enlargement may result in skipping important for risk assessment of events.

By the coise of the conditional probabilities

Any knowledge about the state of nature that is used in the risk assessment, is forward--‐ looking. The more accurate the forecast, the more sound will risk assessment, and the more confi--‐ dence it will on the part of the consumer that, in the end, will allow to make adequate decision about choosing a course of action in the implementation of its activities. However, any forecast has unavoidable uncertainty that must be assessed and taken into account when making deci--‐ sions. For the specific predictive methods can be made practical evaluation of the marginal pre--‐ dictability of the state of nature.

From (1) it follows that for risk assessment activities need to know the probability P (H_s) s--‐ implementation of hydro--‐meteorological factors, ie the probability of occurrence of dangerous conditions of the natural environment in the area and location of the environmental threat.

If there is no data on the state of the environment forecast, as the probability of the first hydro--‐meteorological factors are taken Climate likelihood of severe weather events (combined events). then

P(H_S) = Рклим (H_s),                              (5)

where P_klim (H_s) --‐ Climate likelihood of generalized severe weather events (factors) in an area of the potential environmental threats to the period of time that the calculated risk. Cli--‐ mate is defined as the probability of the incidence of the phenomenon H_s and either given in cli--‐ mate handbooks or calculated in the standard way on the basis of available statistical data.

If there is data on the forecast state of the environment risk assessment to decide on the choice of the strategy and tactics of activity depends on the quality of prognostic information and confidence or no confidence in the forecast.

This confidence prediction value P (H_s) calculated by formula (5), in the case of the confi--‐ dence prediction.

P(Hs) = P HUЩ),                       (6)

where P (H _s/H_s) – is the element of the matrix conjugation method used prognosis [12,13] or the conditional probability of prediction [14], ie, the probability of the phenomenon H_s provided that it predicted. The value of P (H _s/H_s) provided an appropriate system of hydrometeorologi--‐ cal support.

Conclusions

Hydrometeorological factors significantly affect the state of the ecological environment, causing the gain / loss of the environmental hazards, and in some cases actually cause environ--‐ mental hazards. The proposed method of the ecological risk assessment taking into account the meteorological factors makes it possible to take into account the uncertainty in our knowledge of the natural environment in the assessment othe environmental risks, which undoubtedly true for the Arctic region.

To implement the proposed method you need representative sampling, allowing to calcu--‐ late assess the probability of hydrometeorological factors, the emergence of the environmenta situation, the implementation of the environmental situation in times of the hydrometeorologica factors and probabilities of occurrence of the environmental damage in the implementation of the environmental situation and / or adequate models for estimating these quantities.

Since the necessary data either extremely fragmentary or, more often, simply not available, it is clear that the environmental risk assessment requires systematic implementation of integrat--‐ ed environmental and hydro--‐meteorological monitoring, including in the Arctic.

The work was supported by the Russian Ministry of Education under the state contract from 03.14.2013, the № 14.515.11.0001 under the Federal Program "Research and time--‐ processing on priority directions of scientific--‐technological complex of Russia for 2007--‐2013".