Posted May 1999

## Risk definitions

Prepared by R. Gommes,
Senior Agrometeorologist, Environment and Natural Resources Service (SDRN),
FAO Research, Extension and Training Division

Introduction | Risk definitions | Risk management | Variability and losses

There is little coherence in the literature about the quantitative assessment of risk, including climatic risk, in agriculture. According to White (1994), agronomists and engineers (for instance Nash and Nash, 1995) tend to define risk as a loss, while economists tend to use the word as a synomym of "probability of occurrence of a damaging event".

This note adopts the first definition, which loosely follows the approach adopted by Reilly (1996) in a climate change impact context. It provides a convenient and consistent way of defining vulnerability and several related concepts which are often dealt with in a very "impressionistic" fashion.

We start with the simple definition below. For a given factor (or stress), we have

which we can rewrite as

where the loss can be expressed using different units (for instance loss of agricultural production in metric tons, loss of human life, loss of income, etc.). If losses can be due to several different factors, the unit acts as a common denominator, which is a convenient way of expressing a combined loss.

Most geophysical factors can be expressed on a scale of intensities, in which case the definition above applies for each intensity (discrete case) and becomes

According to the definitions adopted here, total risk and impact are roughly synonymous.

Figure 1 below illustrates a hypothetical case where the frequency displays an asymmetrical distribution as a function of intensity. This is very often the case with climatic variables, where J-shaped distributions are typical of rainfall in semi-arid areas, U-shaped curves apply to cloud cover, S-shapes to relative moisture... Positively skewed bell-shapes apply to vapor pressure, wind speed, rainfall in the more humid climates, etc. Of course, the shape of the distribution also depends on the time interval considered (see, for instance, Arléry et al, 1962, or any text of statistical climatology).

 Figure 1: Variation of vulnerability and frequency as a function of the intensity of an environmental factor

The risk, as a function of the intensity of the environmental stress is shown in Figure 2. The total risk, for the factor under consideration, is the sum of the risks associated with each intensity. Again, the asymmetrical curve is typical. Most real world examples would be considerably more skewed than shown in figure 2, resulting in the largest portion of risk (losses) being due to relatively low-intensity factors (chronic risk), while extreme factors, i.e. by definitions those with a low probability of occurrence (major risks), have a relatively minor impact in absolute terms (see note 1).

 Figure 2: Risk as a function of the intensity of an environmental factor

In many real-world situations, the response of a system as a function of an environmental factor goes through positive values and negative ones. It is only the negative ones that actually correspond to a stress. An example is given in figure 3 for food production in Niger (after Gommes, 1998). A National rainfall Index is used as a indicator of the quality of he agricultural season (Click here for more details about the national Rainfall Index). For values above 500 mm, the response is positive. Below the threshold, we enter vulnerable conditions corresponding to an average food production and consumption deficit

 Figure 3: Per capita surplus and deficit cereal production in Niger as a function of a national Rainfall Index RI. The figure assumes that consumption requirements amount to 240 Kg/year, equivalent to a production of 300 Kg with a post harvest loss of 20%. The cereal Yield/RI relation was calibrated using 1932-93 statistics

### Discussion of concepts

This section examines to what extent the concepts above are relevant in an agricultural and a climate/climate change context. To start with, the system being impacted must be relatively well defined if "risk" and "vulnerability" are to be meaningful. As in most agricultural modeling, things tend to be theoretically satisfactory at the very local scale only (plant and field). When moving to regions or countries, many concepts become rather fuzzy, for instance "soil moisture" or "crop yield response to rainfall", etc., which is one of the reasons why the classical crop models are mostly of little help in global studies.

The scale problem obviously also applies to the "intensity of environmental factor" used in Figure 1 and Figure 2. If we consider that climate behaves as a set of coherent and correlated variables, we can obviously replace the "intensity" with a indicator which will incorporate most of the variations of climate as far as they are relevant for regional agriculture. This approach was used in a study of African food security where the "intensity" was replaced by a "national rainfall index" biased towards agriculture (Gommes and Petrassi, 1994; Gommes, 1998).

The question to be answered is thus: what indicators can be used in the current context? Their desirable features include that they must be synthetic, generic and normative (refer to Bakkes et al., 1994, for a good overview of indicators).

Synthetic: the indicator must incorporate most of the factors which are known to be of relevance for agricultural production, for instance crop water consumption, a key factor in production, and dependent on water supply, radiation, CO2 concentrations... The word "synthetic" insists on the fact that the indicator reduces the dimension of the problem, i.e. the number of variables actually to be dealt with.

Generic: this feature points at the fact that the indicator should be robust enough to be applicable outside its original context. If it performs correctly in different areas and years, it may remain meaningful in the future as well.

Normative: an indicator is said to be normative if it can be compared to some reference value, which implies that the sensitivity of vulnerability to the indicator should be roughly linear or, at least, that the variation of vulnerability as a function of the indicator should not behave unpredictably. In Figure 1, vulnerability is approximately linear up to an intensity of 12, after which the response levels off; the reference value (possibly the average) does have a physical and statistical significance.
The IPCC definition of vulnerability as the extent to which climate may damage or harm a system. It depends not only on a system's sensitivity but also on its ability to adapt to new climatic conditions (IPCC, 1995) is consistent with the approach above, if we take "extent" quantitatively.

Many difficulties are, however, associated with the notion of vulnerability. They include the following:

• vulnerability can be determined empirically through impact assessments. Since extreme conditions tend to be rare, the statistical base for such assessments is bound to remain weak. In addition, the intensity of the stress factor is not always known;
• vulnerability depends on the history of the impacted system. An excellent example is provided by the Sahelian droughts in the seventies, the impact of which was far more dramatic than in 1984, when the drought actually peaked;
• vulnerability changes over time, under the influence of numerous factors, for instance population pressure and the resulting short fallow and horizontal expansion of agriculture into marginal areas. In Asia, for instance, FAO studies (FAO, 1989) indicate that some countries have reached the limit of available agricultural land, completely modifying the vulnerability profiles;
• the main difficulties are again linked with the scale, in the case of stresses that originate (spatially) outside the area covered by the impacted system (pest and disease outbreaks, for instance).
• vulnerability can be reduced through adaptation to stresses (as they occur; see note 2) or through mitigation (measures aiming at reducing future vulnerability), including structural and non-structural measures.

#### Notes

Note 1. "Structural risk", as in "structural food deficit" is equivalent to "chronic risk". The risk associated with low probabilities and high intensities would be "conjunctural risk".

Note 2. Adaptability refers to the degree to which adjustments are possible in practices, processes or structures of systems to projected or actual changes of climate. Adaptation can be spontaneous or planned, and can be carried out in response to or in anticipation of changes in conditions. (IPCC, 1995)

#### References

Arléry, R., H. Grissolet and B. Guilmet, 1973. Climatologie, méthodes et pratiques. Gauthier-Villards, Paris. 434 pp.

Bakkes, J.A., G.J. van den Born, J.C. Helder, R.J. Swart, C.W. Hope and J.D.E. Parker, 1994. An overview of environmental indicators: state of the Art and perspectives. UNEP/EATR.94-01, RIVM/402001001, RIVM, Bilthoven.

Gommes, R., and F. Petrassi. 1994. Rainfall variability and drought in sub-Saharan Africa since 1960. FAO Agrometeorology Series Working Papers N. 9 : 100 pp. Click here for a abridged version.

Gommes, R. 1998. Some Aspects of Climate variability and food security in sub-Saharan Africa. Proc. Bull. Soc. Royale Sc. Outremer, Brussels. In press.

IPCC, 1995. Contributions of working group II to the IPCC second assessment report, IPCC-XI/Doc. 4. IPCC Geneva.

Nash, J.C. and M.M. Nash, 1995

Managing Risks. Chance, 8(4):25-31.

Reilly, J., 1996. Climate Change, Global Agriculture and regional vulnerability. Pages 237-265 in: F. Bazzaz and W. Sombroek (Eds.), 1996, Global climate change and agricultural production. Direct and indirect effects of changing hydrological, pedological and plant physiological processes. FAO and John Wiley & Sons, 345 pp.

White, D.H., 1994. Climate variability, ecologically sustainable development and risk management. Agric. Systems and Information Technology, 6(2):7-8.