CAPÍTULO IV DE LOS ALBACEAS
CLASIFICACIÓN DE LAS FUENTES DE LAS OBLIGACIONES
The criteria for the measurement of flexibility are systematically deduced from the definition of flexibility as '... the ability of (urban water management) systems, to use their active capacity to act and respond on relevant alterations in a performance-efficient, timely and cost-effective way.' The '... active capacity to act, ' part of the definition is presented by the metrics 'range of change', the '... performance efficient ...' part is represented by the 'system performance' and '... timely and cost-effective way' part is represented by the 'effort of change'. In the following the metrics are substantiated for urban drainage systems.
Range of Change: The metric 'range of change' indicates for which uncertain future developments an adaptation of the system is possible. A high flexibility is given, when a wide range of future states of the input factors of the system can be managed by a particular flexibility option. The metrics is describing an important characteristic mentioned in the definition of flexibility and is considered e.g. in the methods of Hocke (2004), Koste & Malhotra (1999) or Upton (1994). Smith & Wandel (2006) term this metric, which describes the changes the system, can deal with using their adaptive capacity as “coping ranges”. The metric range of change is crucial to differentiate between robustness and flexibility. 'Robust systems deliver their intended functionality under varying operating conditions without being changed' (Fricke & Schulz 2005).
On the contrary flexibility is the ability of a system to satisfy altering input factors by changing the system (Fricke & Schulz 2005).
A problem of this metric is that in theory with high change costs and long duration of change an adaptation of urban drainage systems on nearly all future developments is possible. In other words for all urban drainage systems the general capability for change (an adaptation with high costs and a long duration) is available, which can be used if the specific capability of the flexibility option is exhausted. As consequences it is certain, that an adaptation of urban drainage systems on nearly all possible future developments is possible. If required there is always the possibility for a complete redesign or new construction of the urban drainage system. This possibility is
limited by the assumption of pre-investment analysis that a retrofitting investment is only implemented when the future revenue with retrofitting is higher than without retrofitting (Schierenbeck & Woehle 2008). Hence the range of change should reflect the range provided by adaptation measures, which are cheaper than the avoided damage costs. When the damage costs are higher than the adaptation costs the system will be adapted. On the contrary when the damage costs are lower than the adaptation costs no adaptation measures will be implemented, because it is not worth to implement them. As damage costs for urban drainage systems the flooding damage costs for the remaining operational life span of the system are calculated considering the design flood frequency, the flooding area, the flooding depth and a damage value (see equation from Genovese 2006).
Equation 3.14
where:
CD(k,i,t) = damage costs for alternative solution k, scenario i and period t in EUR
pf(k,i,t) = annual flooding probability for alternative solution k, scenario i and period t
af(k,i,t) = flooded area for alternative solution k, scenario i and period t in m2
df(k,i,t) = flooding depth for alternative solution k, scenario i and period t in m
cf= damage value (e.g. average costs of m3 heated cubature) in EUR N = total number of time periods t
s = total number of scenarios i
a = total number of alternative solutions k
The range of change describes the maximal increase and decrease of input factors of the urban drainage system for different alternative solutions. The modeling process for the calculation of the input factor is presented in Figure 23 as well as in Chapter 3.3.3.4.
Equation 3.15
Equation 3.16
Equation 3.17
where:
Rng(k,i) = range of change (change of the input factors of system) for alternative solution k and
scenario i
I(k,i,t) = input of system (runoff entering drainage system) for alternative solution k, scenario i at
time t in m3
CA(k,i,t) = minimal adaptation costs to achieve UVint for alternative solution k, scenario i and
period t in EUR
CD(k,i,t) = damage costs for alternative solution k, scenario i and period t in EUR (see equation
3.14)
UV(k,i,t) = utility value for alternative solution k, scenario i and time t
UVmin = minimal required utility value (trigger criterion see Chapter 3.3.3.4)
UVint = intended utility value with UVint > UVmin (intended performance see Chapter 3.3.3.4)
UV(kf,i,t) = utility value for alternative solution k, flexibility option f, scenario I and time t
a(k,t) = urban drainage system with alternative design k at time t
a(kf,t+1) = alternative design k with flexibility option f at time t+1
f = flexibility option
N = total number of time periods t
The metric 'range of change' is assessed with the minimax regret approach, an approach for decision making under severe uncertainty (Laux 2005). The regret for a scenario is the difference between the benefit of the assessed alternative solution (expressed as range of change) and the maximal possible benefit if another alternative solution is chosen. In the assessment, for every
alternative solution only the highest possible regret for different future scenarios is considered.
The alternative with the minimal maximum regret for all future scenarios offers the best range of change for uncertain future conditions and the highest flexibility. The alternative with the least range of change in comparison with other alternatives will be dismissed. One advantage of the regret approach is that no probability of the future scenarios is required for calculation. Hence, the condition of severe uncertainty—in which the probability of the future change is unknown--is met.
The regret is described by the function of range of change. Regret is calculated via the difference between the best alternative range of change and each alternative range of change of the scenarios. The following equations were taken from Eisenfuehr & Weber (2003).
Equation 3.18
Equation 3.19
Equation 3.20
where:
RRng = minimax regret for range of change for all alternative solution k and all scenarios i RRng(k) = regret for range of change for alternative solution k for all scenarios i
RRng(k,i) = regret for range of change for alternative solution k and scenario i
Rng(k,i) = range of change for alternative solution k and scenario i
s = number of scenarios i
a = number of alternative solutions k
Performance of System: This metric represents the performance of the urban drainage system for altering future conditions and is the core of most measurement methods (e.g. Helm et al. 2009 and Sieker et al. 2008). For urban drainage systems, multiple objectives--such as the design flood frequency of the system, flooding in the receiving water body, water quality etc.--have to be
considered. The performance of the urban drainage system is described by a utility value analysis (also called multi-criteria value of benefit analysis), a tried and tested method in multi-criteria assessment. The performance of urban drainage system is categorized according to different objectives like hydraulic performance, water quality performance, ecological function and social function. It must be noted that not all performance categories--like hydraulic function, water quality control or social, economic and environmental objectives--for urban drainage systems are interchangeable. In other words, a balance of required and potential flexibility is not possible if flexibility for water quality control is required but the flexibility option only offers flexibility for hydraulic performance. Hence the performance criteria, which are not interchangeable or equal in importance, are considered independently. The detailed objectives and performance metrics for urban drainage systems are presented in Appendix A. To represent that not all objectives have the same importance or make the same contribution to the overall performance of the system, weighting factors for the different objectives and their related indicators are considered. In addition, utility functions are developed which convey the relationship between a value of the indicator and the level of achievement of objectives. The utility function suggests how effectively an objective has been achieved via different values of the indicator. Based on the objectives, the weighting factors, and the utility functions, the utility values (also called benefit values) are calculated. These values represent the performance of the system. The detailed requirements for applying a utility value analysis are presented by Fürst & Scholles (2008). The utility value analysis allows different performance objectives to be compared. It also makes it possible to add the single values up to a single combined value. The following equations were taken from Peters et al. (2001)
Equation 3.21
Equation 3.22
where: f(c) = utility function for performance criterion c
n = total number of performance criteria c N = total number of time periods t s = number of scenarios i
a = number of alternative solutions k
The future alterations of the input factors, as well as the implementation of flexibility options, can cause variable performance during the operational life span of the urban drainage system.
Flexible design should guarantee that future alterations of the input factors (such as rainfall, pervious surface, pollution load etc.) only have minor impacts on the system performance.
Variations in system performance are evaluated by assessing the performance of the systems for different future states. The performance of different alternatives solutions over time in different future scenarios is ascertained. The performance over time is described by the medium performance (described by the mean) as well as by the homogeneity of performance (described by standard deviation). The performance is considered that could be achieved at least 95% of the time. The following equations were taken from Ulshoefer & Hornschuh (1992).
Equation 3.25
Equation 3.26
where:
UV95(k,i) = utility value for 95% percentile for alternative solution k, scenario i and period t
tUV(k,I,t) = utility value for alternative solution k, scenario i and period t
(k,i) = standard deviation for alternative solution k, scenario i and period t
(k,i) = mean of the utility values for alternative solution k, scenario i and period t
N = total number of time periods t
z = z table value for 95% percentile = 1,645
tt(k,i) = total live span of the system for alternative solution k, scenario i and period t in years
d(k,i,t) = duration of the time period t for alternative solution k and scenario i in years
The system performance for the different future scenarios and alternative solutions of the urban drainage system is assessed with the minimax regret approach as already described above. The following equations were taken from Eisenfuehr & Weber (2003).
Equation 3.27
Equation 3.28
Equation 3.29
where:
RUV95 = minimax regret for the utility value for all alternative solution k and all scenarios i RUV95(k) = regret for the utility value for alternative solution k for all scenarios i
RUV95(k,i) = regret for the utility value for alternative solution k and scenario i
UV95(k,i) = utility value for alternative solution k and scenario i
s = number of scenarios i
a = number of alternative solutions k
Effort of Change: The metric 'effort of change' reflects how difficult it is to adapt a system to altering conditions of the system environment--an essential characteristic mentioned in the definition of flexibility (Hocke 2004; Upton 1994: Koste & Malhotra 1999). The metric describes the effort required to implement the flexibility options. As a result, in addition to the indicators describing the aspired performance of the system (level of flood protection, water quality etc.), indicators describing the effort required to achieve a certain performance (costs, time, resource consumption etc.) are considered. In the technical literature different metrics describing the effort of change are discussed. All approaches consider the costs of change, while some also consider the duration of change or even the resources required for change.
A metric for the effort of change are the costs. Because of the long operational life span of urban drainage systems, the costs for all changes in the whole life span of the systems, rather than the costs of a single change event, are considered. Hence the costs of change are represented as part of the whole life-cycle costs. In addition to the general construction and operation costs of the urban drainage system, the costs for the construction, maintenance and implementation of the flexibility options are also considered. Furthermore, possible economic benefits (e.g. when extraneous parts of the urban drainage systems are sold to be used in new high value land uses) are included.
The life-cycle costs are described as the net present value of the costs at different time steps (Schierenbeck & Woehle 2008) and involve discount factors for costs, which will incur at different times. In an approach described in the 'KVR Leitlinie' (LAWA 2005), a method for the calculation of the life-cycle costs tailored to the specific requirements of urban drainage systems is used. To compare alternative solutions with different operational life spans, the net present value is converted into equivalent annual costs, also called annuities. A consideration of equivalent annual costs reveals the high persistence of urban drainage systems (Gutsche 2006). Based on the urban drainage system, long-term private investments, such as investment in residential areas, are made. To preserve the value of these private investments, a continual maintenance of the drainage function is required. Thus, it is necessary to replace the urban drainage system after its operational life span with a comparable system so as to guarantee a high persistence of the system. It is assumed that the investment is repeated, which is reflected by the equivalent annual costs method (Schierenbeck & Woehle 2008).
The duration of the change process is considered as an additional metric for the effort of change (Hocke 2004). The duration of change is the time period necessary to adapt the system to altering requirements. This time period includes an observation period, decision period, implementation period, effect period and control period. Clearly, it is significant whether the flexibility option can be implemented within a few weeks or if it requires several years (even if the costs are comparable). During the period required for adaptation, the performance of the system is not meeting the intended performance standards and damage occurs.
Another metric for the effort of change could be resource consumption; resource consumption is required to change a system. Each change of the urban drainage system is reflected in a consumption of resources like the use of land, building material or energy required for management and construction measures, or water consumption. Frequent changes (implementation of flexibility options) can increase the resource consumption of a system.
However, most resource consumption is already captured by the costs of change. Hence to avoid
a double counting of input factors, resource consumption is not considered as an independent metric.
Both the cost of change and the duration of change are combined into one metric describing the overall effort of change. For this purpose the duration of change is described by the associated damage costs, incurred during the period when the system does not operate at the desired performance level. The longer the duration of change, the higher the damage costs. The duration of change is described by the damage costs and is considered in the calculation of the life-cycle costs. The following equations were taken from Schierenbeck & Woehle (2008).
EAC(ki,) = effort of change as equivalent annual costs for alternative solution k, scenario i in EUR
NPV0(k,i) = Net Present Value at period 0 (time of investment) for alternative solution k, scenario i
in EUR
RBFN(k,i) = annuity factor for interest rate i and number of periods N for alternative solution k,
scenario i and period t
CD(k,I,t0 = damage costs for alternative solution k, scenario i and period t in EUR (see equation
3.14)
CB(k,I,t) = economic benefits for solution k, scenario i and period t in EUR
CM(k,I,t0 = maintenance costs for alternative solution k, scenario i and period t in EUR
CO(k,I,t) = operation costs for alternative solution k, scenario i and period t in EUR
CA(k,I,t) = adaptation costs for alternative solution k, scenario i and period t in EUR
CI0(k,i) = initial investment costs for alternative solution k, scenario i and period 0 in EUR
i = interest rate in % t = period of time in years s = total number of scenarios i
a = total number of alternative solutions k N = total number of time periods t
To compare the life-cycle costs of different alternative solutions for various future scenarios the minimax regret approach is used like already described above (Eisenfuehr & Weber 2003).
Equation 3.33
Equation 3.34
Equation 3.35
where:
REAC = minimax regret for effort of change for all alternative solution k and all scenarios i REAC(k) = regret for effort of change for alternative solution k and all scenarios i
REAC(k,i) = regret for effort of change for alternative solution k and scenario i
EAC(k,i) = effort of change for alternative solution k and scenario i
s = number of scenarios i
a = number of alternative solutions k
The range of change metric and the effort of change metric are both based on comparable input factors: the damage and the adaptation costs. However, only the effort of change metric
considers the amount of the damage and adaptation costs (how much is the cost) where as the range of change metric focuses on the relationship between the input factors (which factor is higher). As such, there is no double counting of the same input factor.