Response Surfaces

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A response surface is a two-dimensional representation of the sensitivity of a specific response variable (soil moisture in Fig. 9.2) to change in the two controlling climate features or processes. It is usually is presented as a plot of the response variable against the values of two driving climate variables, on the graph axes, for example, potential evapotranspiration (PET) and precipitation (P) in Fig. 9.2. The relationship between the response variable and climate determined from a pre-tested set of relationships, usually in the form of an empirical model, called a transfer function (de Freitas and Fowler 1989; Fowler and de Freitas 1990). Changes might be simply percentage adjustments to the each of the driving variables. The response variable is represented in the body of the graph as isolines. The three variables can be plotted using absolute values, or as values relative to the unamended baseline data representing no climate change (Fig. 9.2). The latter representation is a step removed

Fig. 9.2 Response surfaces showing percentage change in annual soil water surplus ('runoff' plus ground water recharge) for a range of climate change scenarios expressed as per cent change in potential evapotranspiration (PET) and precipitation (P) for a sub-temperate maritime climate (Auckland) and a semi-arid mid-latitude climate (Alexandra). The base-line reference condition, or current climate, is given by per cent change in PET = 0 and percent change in P = 0 (i.e. 0, 0 intersection marked "+"). (Fowler and de Freitas 1990)

Fig. 9.2 Response surfaces showing percentage change in annual soil water surplus ('runoff' plus ground water recharge) for a range of climate change scenarios expressed as per cent change in potential evapotranspiration (PET) and precipitation (P) for a sub-temperate maritime climate (Auckland) and a semi-arid mid-latitude climate (Alexandra). The base-line reference condition, or current climate, is given by per cent change in PET = 0 and percent change in P = 0 (i.e. 0, 0 intersection marked "+"). (Fowler and de Freitas 1990)

from the input and output but does have the advantage of providing a direct measure of sensitivity. For example, a 20% response to a 10% change in a controlling climate variable is clearly an example of impact amplification. Response surface isolines are a summary of a matrix of response points associated with various combinations of changes to the two driving climate variables (Fig. 9.2). The required data are derived from repeated runs of the transfer function with the prescribed changes to the input. The slope and closeness of the isolines are an indicator of sensitivity and discontinuities an indicator of change in response (Fig. 9.2).

De Freitas and Fowler (1989), Fowler and de Freitas (1990) and Fowler (1999) used response surfaces to illustrate the impact of climate change on various aspects of water resources in the Auckland region of New Zealand. Other water resource examples of this can be found in studies by Lynch et al. (2001) and van Minnen et al. (2000). More recently, Semadeni-Davies (2004) used response surfaces for simulated waste water inflows to the Lycksele waste water treatment plant in north-central Sweden. Information such as that shown in Fig. 9.2 gives a birds-eye view of regional sensitivity in terms of key environmental responses to a range of possible changed climate conditions. The procedure provides a means by which a variety of climate change scenarios can be used to identify regions that are more or less sensitive to certain changes. This facilitates evaluation of impact potential for policy planning purposes. A 'what if' approach to climate change predictions can then be used to assess the desirability of societal adjustments in sensitive regions designed either to amplify beneficial or dampen undesirable effects of change. An advantage of the response surface method is that it is less likely to obscure inherent sensitivities to change that can occur in scenario approach. Another is its flexibility. A wide range of new or changed scenarios can be easily handled by plotting them on the response surface. This avoids the need to rerun the transfer function, thus facilitating use by non-climate specialists such as planners and policy makers wanting to reassess impacts on water resources.

Comparison of each pair of response surface diagrams illustrates the differing sensitivity of climate types to a climate change specified in terms of P and PET in each climatic region. For example, in Fig. 9.2, the closer isolines of the change in water surplus for Alexandra indicate greater sensitivity than in the Auckland region. In both cases the steepness of the isolines shows a higher sensitivity to changes in P than to PET. It should be noted that the isolines are for relative change rather than for absolute values. Absolute changes in water surplus will be greater in Auckland than in Alexandra because of a larger baseline water surplus for Auckland. Clearly, the finer points of decision making and planning will depend on resource specific considerations, the most important of which will relate to the level of climate-based resource use. In the case of availability of water resources shown in Fig. 9.2, for example, vulnerability of society to a change in climate will depend on the demand for the resource and levels of use. If there is a high level of resource use, as there is for example in the Auckland region, the society is highly vulnerable to climatic change that leads to reduced water availability. The implications for water resource planning are clearly quite serious. In contrast to this, where there is low resource use there is a larger margin of safety, it provides a buffer against both sporadic dry periods or a trend in decreasing runoff resulting from, say, gradual climatic change leading to reduced precipitation.

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